From 10ed707a68d2ab7ccc159316069407609084d719 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 21 Nov 2013 19:05:42 +0000 Subject: [PATCH] Initial merge of cpp_bin_float code from sandbox. [SVN r86781] --- doc/Jamfile.v2 | 3 +- doc/html/boost_multiprecision/indexes.html | 17 +- doc/html/boost_multiprecision/intro.html | 8 +- doc/html/boost_multiprecision/map.html | 2 +- doc/html/boost_multiprecision/map/ack.html | 2 +- doc/html/boost_multiprecision/map/faq.html | 2 +- doc/html/boost_multiprecision/map/hist.html | 17 +- doc/html/boost_multiprecision/map/todo.html | 2 +- doc/html/boost_multiprecision/perf.html | 4 +- .../perf/float_performance.html | 42 +- .../perf/int_real_world.html | 4 +- .../perf/integer_performance.html | 66 +- .../boost_multiprecision/perf/overhead.html | 4 +- .../perf/rational_performance.html | 42 +- .../boost_multiprecision/perf/realworld.html | 10 +- doc/html/boost_multiprecision/ref.html | 9 +- .../boost_multiprecision/ref/backendconc.html | 6 +- .../ref/cpp_bin_float_ref.html | 186 ++ .../boost_multiprecision/ref/cpp_dec_ref.html | 10 +- .../boost_multiprecision/ref/cpp_int_ref.html | 2 +- .../boost_multiprecision/ref/gmp_int_ref.html | 2 +- .../boost_multiprecision/ref/headers.html | 8 +- .../boost_multiprecision/ref/internals.html | 2 +- .../boost_multiprecision/ref/mpf_ref.html | 2 +- .../boost_multiprecision/ref/mpfr_ref.html | 8 +- doc/html/boost_multiprecision/ref/number.html | 14 +- .../boost_multiprecision/ref/tom_int_ref.html | 2 +- doc/html/boost_multiprecision/tut.html | 15 +- .../boost_multiprecision/tut/conversions.html | 48 +- doc/html/boost_multiprecision/tut/floats.html | 42 +- .../tut/floats/cpp_bin_float.html | 192 ++ .../tut/floats/cpp_dec_float.html | 14 +- .../tut/floats/float128.html | 8 +- .../tut/floats/fp_eg.html | 2 +- .../tut/floats/fp_eg/aos.html | 10 +- .../tut/floats/fp_eg/gi.html | 14 +- .../tut/floats/fp_eg/jel.html | 18 +- .../tut/floats/fp_eg/nd.html | 14 +- .../tut/floats/fp_eg/poly_eg.html | 6 +- .../tut/floats/gmp_float.html | 9 +- .../tut/floats/mpfr_float.html | 9 +- .../boost_multiprecision/tut/gen_int.html | 2 +- .../tut/input_output.html | 185 ++ .../boost_multiprecision/tut/interval.html | 2 +- .../tut/interval/mpfi.html | 17 +- doc/html/boost_multiprecision/tut/ints.html | 2 +- .../tut/ints/cpp_int.html | 8 +- .../boost_multiprecision/tut/ints/egs.html | 2 +- .../tut/ints/egs/bitops.html | 10 +- .../tut/ints/egs/factorials.html | 6 +- .../tut/ints/gmp_int.html | 8 +- .../tut/ints/tom_int.html | 8 +- doc/html/boost_multiprecision/tut/limits.html | 100 + .../tut/limits/constants.html | 705 ++++++ .../tut/limits/functions.html | 546 +++++ .../tut/limits/how_to_tell.html | 168 ++ .../tut/limits/limits32.html | 2049 +++++++++++++++++ doc/html/boost_multiprecision/tut/lits.html | 2 +- doc/html/boost_multiprecision/tut/misc.html | 2 +- .../tut/misc/debug_adaptor.html | 8 +- .../tut/misc/logged_adaptor.html | 10 +- .../tut/misc/visualizers.html | 14 +- doc/html/boost_multiprecision/tut/mixed.html | 14 +- .../boost_multiprecision/tut/primetest.html | 6 +- doc/html/boost_multiprecision/tut/random.html | 18 +- .../boost_multiprecision/tut/rational.html | 2 +- .../boost_multiprecision/tut/rational/br.html | 2 +- .../tut/rational/cpp_rational.html | 8 +- .../tut/rational/gmp_rational.html | 8 +- .../tut/rational/rational_adaptor.html | 2 +- .../tut/rational/tommath_rational.html | 8 +- .../boost_multiprecision/tut/rounding.html | 2 +- doc/html/boost_multiprecision/tut/serial.html | 63 + doc/html/index.html | 26 +- doc/multiprecision.qbk | 1395 +++++++++-- doc/numeric_limits_32_tables.qbk | 94 + doc/numeric_limits_qbk.cpp | 719 ++++++ example/cpp_bin_float_snips.cpp | 39 + example/numeric_limits_snips.cpp | 458 ++++ .../boost/multiprecision/cpp_bin_float.hpp | 1559 +++++++++++++ .../boost/multiprecision/cpp_bin_float/io.hpp | 690 ++++++ .../cpp_bin_float/transcendental.hpp | 132 ++ performance/performance_test.cpp | 20 +- performance/sf_performance.hpp | 11 +- performance/sf_performance_bessel2.cpp | 3 + performance/sf_performance_bessel6.cpp | 3 + performance/sf_performance_nct3.cpp | 3 + performance/sf_performance_nct6.cpp | 3 + performance/sf_performance_poly.cpp | 6 + test/Jamfile.v2 | 68 +- test/concepts/number_concept_check.cpp | 13 +- test/concepts/sf_concept_check_basic.cpp | 9 +- test/concepts/sf_concept_check_bessel.cpp | 10 +- test/concepts/sf_concept_check_elliptic.cpp | 10 +- test/concepts/sf_concept_check_gamma.cpp | 10 +- test/concepts/sf_concept_check_poly.cpp | 10 +- .../cpp_bin_float_include_test.cpp | 12 + test/math/instances/Jamfile.v2 | 3 +- test/math/setup.hpp | 22 +- test/sincos.ipp | 358 +++ test/test_acos.cpp | 15 +- test/test_arithmetic_cpp_bin_float_1.cpp | 28 + test/test_arithmetic_cpp_bin_float_2.cpp | 27 + test/test_arithmetic_cpp_bin_float_3.cpp | 27 + test/test_asin.cpp | 9 +- test/test_atan.cpp | 9 +- test/test_cos.cpp | 22 +- test/test_cosh.cpp | 15 +- test/test_cpp_bin_float.cpp | 219 ++ test/test_cpp_bin_float_io.cpp | 258 +++ test/test_exp.cpp | 13 +- test/test_fpclassify.cpp | 9 +- test/test_log.cpp | 16 +- test/test_numeric_limits.cpp | 24 +- test/test_pow.cpp | 9 +- test/test_round.cpp | 12 +- test/test_sin.cpp | 23 +- test/test_sinh.cpp | 9 +- test/test_sqrt.cpp | 14 +- test/test_tan.cpp | 9 +- test/test_tanh.cpp | 9 +- tools/sincos.cpp | 75 + 122 files changed, 10795 insertions(+), 606 deletions(-) create mode 100644 doc/html/boost_multiprecision/ref/cpp_bin_float_ref.html create mode 100644 doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html create mode 100644 doc/html/boost_multiprecision/tut/input_output.html create mode 100644 doc/html/boost_multiprecision/tut/limits.html create mode 100644 doc/html/boost_multiprecision/tut/limits/constants.html create mode 100644 doc/html/boost_multiprecision/tut/limits/functions.html create mode 100644 doc/html/boost_multiprecision/tut/limits/how_to_tell.html create mode 100644 doc/html/boost_multiprecision/tut/limits/limits32.html create mode 100644 doc/html/boost_multiprecision/tut/serial.html create mode 100644 doc/numeric_limits_32_tables.qbk create mode 100644 doc/numeric_limits_qbk.cpp create mode 100644 example/cpp_bin_float_snips.cpp create mode 100644 example/numeric_limits_snips.cpp create mode 100644 include/boost/multiprecision/cpp_bin_float.hpp create mode 100644 include/boost/multiprecision/cpp_bin_float/io.hpp create mode 100644 include/boost/multiprecision/cpp_bin_float/transcendental.hpp create mode 100644 test/include_test/cpp_bin_float_include_test.cpp create mode 100644 test/sincos.ipp create mode 100644 test/test_arithmetic_cpp_bin_float_1.cpp create mode 100644 test/test_arithmetic_cpp_bin_float_2.cpp create mode 100644 test/test_arithmetic_cpp_bin_float_3.cpp create mode 100644 test/test_cpp_bin_float.cpp create mode 100644 test/test_cpp_bin_float_io.cpp create mode 100644 tools/sincos.cpp diff --git a/doc/Jamfile.v2 b/doc/Jamfile.v2 index 34ed0bf5a..c9479e570 100644 --- a/doc/Jamfile.v2 +++ b/doc/Jamfile.v2 @@ -74,7 +74,8 @@ boostbook standalone pdf:index.on.type=1 ; -install pdf-install : standalone : . PDF multiprecision.pdf ; +install pdfinstall : standalone : . PDF multiprecision.pdf ; + diff --git a/doc/html/boost_multiprecision/indexes.html b/doc/html/boost_multiprecision/indexes.html index 4befa2cb5..6a5e97fa5 100644 --- a/doc/html/boost_multiprecision/indexes.html +++ b/doc/html/boost_multiprecision/indexes.html @@ -7,7 +7,6 @@ - @@ -20,22 +19,20 @@
-PrevUpHomeNext +PrevUpHome
-
-
Function Index
-
Class Index
-
Typedef Index
-
Index
-
+

+ [named_index function_name Function Index] [named_index class_name Class Index] + [named_index typedef_name Typedef Index] [index] +

-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -43,7 +40,7 @@
-PrevUpHomeNext +PrevUpHome
diff --git a/doc/html/boost_multiprecision/intro.html b/doc/html/boost_multiprecision/intro.html index 524b22032..049aa98d4 100644 --- a/doc/html/boost_multiprecision/intro.html +++ b/doc/html/boost_multiprecision/intro.html @@ -372,7 +372,7 @@
for polynomial execution:

-

Table 1.1. Evaluation of Order 6 Polynomial.

+

Table 1.1. Evaluation of Order 6 Polynomial.

@@ -486,7 +486,7 @@
(50 decimal digits):

-

Table 1.2. Evaluation of Boost.Math's Bessel function test data

+

Table 1.2. Evaluation of Boost.Math's Bessel function test data

@@ -584,7 +584,7 @@

-

Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data

+

Table 1.3. Evaluation of Boost.Math's Non-Central T distribution test data

@@ -696,7 +696,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/map.html b/doc/html/boost_multiprecision/map.html index 7117a7780..f5e451c61 100644 --- a/doc/html/boost_multiprecision/map.html +++ b/doc/html/boost_multiprecision/map.html @@ -35,7 +35,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/map/ack.html b/doc/html/boost_multiprecision/map/ack.html index 06522ee95..23a4f3224 100644 --- a/doc/html/boost_multiprecision/map/ack.html +++ b/doc/html/boost_multiprecision/map/ack.html @@ -50,7 +50,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/map/faq.html b/doc/html/boost_multiprecision/map/faq.html index 673a073be..3eb2ac352 100644 --- a/doc/html/boost_multiprecision/map/faq.html +++ b/doc/html/boost_multiprecision/map/faq.html @@ -106,7 +106,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/map/hist.html b/doc/html/boost_multiprecision/map/hist.html index 86cc3f5d2..e480d9b94 100644 --- a/doc/html/boost_multiprecision/map/hist.html +++ b/doc/html/boost_multiprecision/map/hist.html @@ -28,6 +28,13 @@
+ 1.56 +
+
  • + Added list of values for numeric_limits. +
+
+ 1.55
    @@ -65,7 +72,7 @@
- + 1.54
    @@ -120,7 +127,7 @@
- + 1.53
    @@ -136,7 +143,7 @@
- + Post review changes
@@ -190,7 +197,7 @@
- + Pre-review history
@@ -213,7 +220,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/map/todo.html b/doc/html/boost_multiprecision/map/todo.html index 883e51bea..a295d9e4d 100644 --- a/doc/html/boost_multiprecision/map/todo.html +++ b/doc/html/boost_multiprecision/map/todo.html @@ -221,7 +221,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/perf.html b/doc/html/boost_multiprecision/perf.html index a6ecb723f..f4cd63d2e 100644 --- a/doc/html/boost_multiprecision/perf.html +++ b/doc/html/boost_multiprecision/perf.html @@ -29,7 +29,7 @@
The Overhead in the Number Class Wrapper
-
Floating Point Real +
Floating-Point Real World Tests
Integer Real World Tests
@@ -43,7 +43,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/perf/float_performance.html b/doc/html/boost_multiprecision/perf/float_performance.html index 2afe30211..4c0a96375 100644 --- a/doc/html/boost_multiprecision/perf/float_performance.html +++ b/doc/html/boost_multiprecision/perf/float_performance.html @@ -37,7 +37,7 @@ for 500000 operations.

-

Table 1.10. Operator +

+

Table 1.14. Operator +

@@ -138,7 +138,7 @@

-

Table 1.11. Operator +(int)

+

Table 1.15. Operator +(int)

@@ -239,7 +239,7 @@

-

Table 1.12. Operator +(unsigned long long)

+

Table 1.16. Operator +(unsigned long long)

@@ -340,7 +340,7 @@

-

Table 1.13. Operator +=(unsigned long long)

+

Table 1.17. Operator +=(unsigned long long)

@@ -441,7 +441,7 @@

-

Table 1.14. Operator -

+

Table 1.18. Operator -

@@ -542,7 +542,7 @@

-

Table 1.15. Operator -(int)

+

Table 1.19. Operator -(int)

@@ -643,7 +643,7 @@

-

Table 1.16. Operator -(unsigned long long)

+

Table 1.20. Operator -(unsigned long long)

@@ -744,7 +744,7 @@

-

Table 1.17. Operator -=(unsigned long long)

+

Table 1.21. Operator -=(unsigned long long)

@@ -845,7 +845,7 @@

-

Table 1.18. Operator *

+

Table 1.22. Operator *

@@ -946,7 +946,7 @@

-

Table 1.19. Operator *(int)

+

Table 1.23. Operator *(int)

@@ -1047,7 +1047,7 @@

-

Table 1.20. Operator *(unsigned long long)

+

Table 1.24. Operator *(unsigned long long)

@@ -1148,7 +1148,7 @@

-

Table 1.21. Operator *=(unsigned long long)

+

Table 1.25. Operator *=(unsigned long long)

@@ -1249,7 +1249,7 @@

-

Table 1.22. Operator /

+

Table 1.26. Operator /

@@ -1350,7 +1350,7 @@

-

Table 1.23. Operator /(int)

+

Table 1.27. Operator /(int)

@@ -1451,7 +1451,7 @@

-

Table 1.24. Operator /(unsigned long long)

+

Table 1.28. Operator /(unsigned long long)

@@ -1552,7 +1552,7 @@

-

Table 1.25. Operator /=(unsigned long long)

+

Table 1.29. Operator /=(unsigned long long)

@@ -1653,7 +1653,7 @@

-

Table 1.26. Operator construct

+

Table 1.30. Operator construct

@@ -1754,7 +1754,7 @@

-

Table 1.27. Operator construct(unsigned)

+

Table 1.31. Operator construct(unsigned)

@@ -1855,7 +1855,7 @@

-

Table 1.28. Operator construct(unsigned long long)

+

Table 1.32. Operator construct(unsigned long long)

@@ -1956,7 +1956,7 @@

-

Table 1.29. Operator str

+

Table 1.33. Operator str

@@ -2064,7 +2064,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/perf/int_real_world.html b/doc/html/boost_multiprecision/perf/int_real_world.html index 7a0300375..7c8946099 100644 --- a/doc/html/boost_multiprecision/perf/int_real_world.html +++ b/doc/html/boost_multiprecision/perf/int_real_world.html @@ -6,7 +6,7 @@ - + @@ -367,7 +367,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/perf/integer_performance.html b/doc/html/boost_multiprecision/perf/integer_performance.html index a3e64acac..dbc6f2a63 100644 --- a/doc/html/boost_multiprecision/perf/integer_performance.html +++ b/doc/html/boost_multiprecision/perf/integer_performance.html @@ -37,7 +37,7 @@ for 500000 operations.

-

Table 1.30. Operator +

+

Table 1.34. Operator +

@@ -186,7 +186,7 @@

-

Table 1.31. Operator +(int)

+

Table 1.35. Operator +(int)

@@ -335,7 +335,7 @@

-

Table 1.32. Operator +(unsigned long long)

+

Table 1.36. Operator +(unsigned long long)

@@ -484,7 +484,7 @@

-

Table 1.33. Operator +=(unsigned long long)

+

Table 1.37. Operator +=(unsigned long long)

@@ -633,7 +633,7 @@

-

Table 1.34. Operator -

+

Table 1.38. Operator -

@@ -782,7 +782,7 @@

-

Table 1.35. Operator -(int)

+

Table 1.39. Operator -(int)

@@ -931,7 +931,7 @@

-

Table 1.36. Operator -(unsigned long long)

+

Table 1.40. Operator -(unsigned long long)

@@ -1080,7 +1080,7 @@

-

Table 1.37. Operator -=(unsigned long long)

+

Table 1.41. Operator -=(unsigned long long)

@@ -1229,7 +1229,7 @@

-

Table 1.38. Operator *

+

Table 1.42. Operator *

@@ -1378,7 +1378,7 @@

-

Table 1.39. Operator *(int)

+

Table 1.43. Operator *(int)

@@ -1527,7 +1527,7 @@

-

Table 1.40. Operator *(unsigned long long)

+

Table 1.44. Operator *(unsigned long long)

@@ -1676,7 +1676,7 @@

-

Table 1.41. Operator *=(unsigned long long)

+

Table 1.45. Operator *=(unsigned long long)

@@ -1825,7 +1825,7 @@

-

Table 1.42. Operator /

+

Table 1.46. Operator /

@@ -1974,7 +1974,7 @@

-

Table 1.43. Operator /(int)

+

Table 1.47. Operator /(int)

@@ -2123,7 +2123,7 @@

-

Table 1.44. Operator /(unsigned long long)

+

Table 1.48. Operator /(unsigned long long)

@@ -2272,7 +2272,7 @@

-

Table 1.45. Operator /=(unsigned long long)

+

Table 1.49. Operator /=(unsigned long long)

@@ -2421,7 +2421,7 @@

-

Table 1.46. Operator %

+

Table 1.50. Operator %

@@ -2570,7 +2570,7 @@

-

Table 1.47. Operator %(int)

+

Table 1.51. Operator %(int)

@@ -2719,7 +2719,7 @@

-

Table 1.48. Operator construct

+

Table 1.52. Operator construct

@@ -2868,7 +2868,7 @@

-

Table 1.49. Operator construct(unsigned)

+

Table 1.53. Operator construct(unsigned)

@@ -3017,7 +3017,7 @@

-

Table 1.50. Operator construct(unsigned long long)

+

Table 1.54. Operator construct(unsigned long long)

@@ -3166,7 +3166,7 @@

-

Table 1.51. Operator gcd

+

Table 1.55. Operator gcd

@@ -3315,7 +3315,7 @@

-

Table 1.52. Operator powm

+

Table 1.56. Operator powm

@@ -3464,7 +3464,7 @@

-

Table 1.53. Operator str

+

Table 1.57. Operator str

@@ -3613,7 +3613,7 @@

-

Table 1.54. Operator |

+

Table 1.58. Operator |

@@ -3762,7 +3762,7 @@

-

Table 1.55. Operator |(int)

+

Table 1.59. Operator |(int)

@@ -3911,7 +3911,7 @@

-

Table 1.56. Operator ^

+

Table 1.60. Operator ^

@@ -4060,7 +4060,7 @@

-

Table 1.57. Operator ^(int)

+

Table 1.61. Operator ^(int)

@@ -4209,7 +4209,7 @@

-

Table 1.58. Operator &

+

Table 1.62. Operator &

@@ -4358,7 +4358,7 @@

-

Table 1.59. Operator &(int)

+

Table 1.63. Operator &(int)

@@ -4507,7 +4507,7 @@

-

Table 1.60. Operator <<

+

Table 1.64. Operator <<

@@ -4656,7 +4656,7 @@

-

Table 1.61. Operator >>

+

Table 1.65. Operator >>

@@ -4816,7 +4816,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/perf/overhead.html b/doc/html/boost_multiprecision/perf/overhead.html index b03eaa14d..0bda9c57c 100644 --- a/doc/html/boost_multiprecision/perf/overhead.html +++ b/doc/html/boost_multiprecision/perf/overhead.html @@ -7,7 +7,7 @@ - + @@ -186,7 +186,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/perf/rational_performance.html b/doc/html/boost_multiprecision/perf/rational_performance.html index 196bbbfcc..00c65564c 100644 --- a/doc/html/boost_multiprecision/perf/rational_performance.html +++ b/doc/html/boost_multiprecision/perf/rational_performance.html @@ -37,7 +37,7 @@ for 500000 operations.

-

Table 1.62. Operator +

+

Table 1.66. Operator +

@@ -132,7 +132,7 @@

-

Table 1.63. Operator +(int)

+

Table 1.67. Operator +(int)

@@ -227,7 +227,7 @@

-

Table 1.64. Operator +(unsigned long long)

+

Table 1.68. Operator +(unsigned long long)

@@ -322,7 +322,7 @@

-

Table 1.65. Operator +=(unsigned long long)

+

Table 1.69. Operator +=(unsigned long long)

@@ -417,7 +417,7 @@

-

Table 1.66. Operator -

+

Table 1.70. Operator -

@@ -512,7 +512,7 @@

-

Table 1.67. Operator -(int)

+

Table 1.71. Operator -(int)

@@ -607,7 +607,7 @@

-

Table 1.68. Operator -(unsigned long long)

+

Table 1.72. Operator -(unsigned long long)

@@ -702,7 +702,7 @@

-

Table 1.69. Operator -=(unsigned long long)

+

Table 1.73. Operator -=(unsigned long long)

@@ -797,7 +797,7 @@

-

Table 1.70. Operator *

+

Table 1.74. Operator *

@@ -892,7 +892,7 @@

-

Table 1.71. Operator *(int)

+

Table 1.75. Operator *(int)

@@ -987,7 +987,7 @@

-

Table 1.72. Operator *(unsigned long long)

+

Table 1.76. Operator *(unsigned long long)

@@ -1082,7 +1082,7 @@

-

Table 1.73. Operator *=(unsigned long long)

+

Table 1.77. Operator *=(unsigned long long)

@@ -1177,7 +1177,7 @@

-

Table 1.74. Operator /

+

Table 1.78. Operator /

@@ -1272,7 +1272,7 @@

-

Table 1.75. Operator /(int)

+

Table 1.79. Operator /(int)

@@ -1367,7 +1367,7 @@

-

Table 1.76. Operator /(unsigned long long)

+

Table 1.80. Operator /(unsigned long long)

@@ -1462,7 +1462,7 @@

-

Table 1.77. Operator /=(unsigned long long)

+

Table 1.81. Operator /=(unsigned long long)

@@ -1557,7 +1557,7 @@

-

Table 1.78. Operator construct

+

Table 1.82. Operator construct

@@ -1652,7 +1652,7 @@

-

Table 1.79. Operator construct(unsigned)

+

Table 1.83. Operator construct(unsigned)

@@ -1747,7 +1747,7 @@

-

Table 1.80. Operator construct(unsigned long long)

+

Table 1.84. Operator construct(unsigned long long)

@@ -1842,7 +1842,7 @@

-

Table 1.81. Operator str

+

Table 1.85. Operator str

@@ -1944,7 +1944,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/perf/realworld.html b/doc/html/boost_multiprecision/perf/realworld.html index 5c2f7db1f..a84779229 100644 --- a/doc/html/boost_multiprecision/perf/realworld.html +++ b/doc/html/boost_multiprecision/perf/realworld.html @@ -1,7 +1,7 @@ -Floating Point Real World Tests +Floating-Point Real World Tests @@ -24,7 +24,7 @@

@@ -37,7 +37,7 @@ also shown.

-

Table 1.8. Bessel Function Performance

+

Table 1.12. Bessel Function Performance

@@ -168,7 +168,7 @@

-

Table 1.9. Non-Central T Distribution Performance

+

Table 1.13. Non-Central T Distribution Performance

@@ -270,7 +270,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/ref.html b/doc/html/boost_multiprecision/ref.html index fbec20e16..0c1bc8b17 100644 --- a/doc/html/boost_multiprecision/ref.html +++ b/doc/html/boost_multiprecision/ref.html @@ -6,7 +6,7 @@ - + @@ -20,7 +20,7 @@
-PrevUpHomeNext +PrevUpHomeNext
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -50,7 +51,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/html/boost_multiprecision/ref/backendconc.html b/doc/html/boost_multiprecision/ref/backendconc.html index 20fd41d4d..3b2b415f9 100644 --- a/doc/html/boost_multiprecision/ref/backendconc.html +++ b/doc/html/boost_multiprecision/ref/backendconc.html @@ -67,7 +67,7 @@ is a variable of type std::ios_base::fmtflags.

-

Table 1.4. Compulsory Requirements on the Backend type.

+

Table 1.8. Compulsory Requirements on the Backend type.

@@ -954,7 +954,7 @@

-

Table 1.5. Optional Requirements on the Backend Type

+

Table 1.9. Optional Requirements on the Backend Type

@@ -3897,7 +3897,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/ref/cpp_bin_float_ref.html b/doc/html/boost_multiprecision/ref/cpp_bin_float_ref.html new file mode 100644 index 000000000..bda800ccb --- /dev/null +++ b/doc/html/boost_multiprecision/ref/cpp_bin_float_ref.html @@ -0,0 +1,186 @@ + + + +cpp_bin_float + + + + + + + + + + + + + + + +
Boost C++ LibrariesHomeLibrariesPeopleFAQMore
+
+
+PrevUpHomeNext +
+
+
+
namespace boost{ namespace multiprecision{
+
+enum digit_base_type
+{
+   digit_base_2 = 2,
+   digit_base_10 = 10
+};
+
+template <unsigned Digits, digit_base_type base = digit_base_10, class Allocator = void, class Exponent = int, ExponentMin = 0, ExponentMax = 0>
+class cpp_bin_float;
+
+typedef number<cpp_bin_float<50> > cpp_bin_float_50;
+typedef number<cpp_bin_float<100> > cpp_bin_float_100;
+
+typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off>       cpp_bin_float_single;
+typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off>     cpp_bin_float_double;
+typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off>   cpp_bin_float_double_extended;
+typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off>  cpp_bin_float_quad;
+
+}} // namespaces
+
+

+ Class template cpp_bin_float + fulfils all of the requirements for a Backend + type. Its members and non-member functions are deliberately not documented: + these are considered implementation details that are subject to change. +

+

+ The class takes six template parameters: +

+
+

+
+
Digits
+

+ The number of digits precision the type should support. This is normally + expresed as base-10 digits, but that can be changed via the second + template parameter. +

+
base
+

+ An enumerated value (either digit_base_10 + or digit_base_2) that + indicates whether Digits + is base-10 or base-2 +

+
Allocator
+

+ The allocator used: defaults to type void, + meaning all storage is within the class, and no dynamic allocation + is performed, but can be set to a standard library allocator if dynamic + allocation makes more sense. +

+
Exponent
+

+ A signed integer type to use as the type of the exponent - defaults + to int. +

+
ExponentMin
+

+ The smallest (most negative) permitted exponent, defaults to zero, + meaning "define as small as possible given the limitations of + the type and our internal requirements". +

+
ExponentMax
+

+ The largest (most positive) permitted exponent, defaults to zero, meaning + "define as large as possible given the limitations of the type + and our internal requirements". +

+
+
+

+ The type of number_category<cpp_bin_float<Args...> >::type is mpl::int_<number_kind_floating_point>. +

+

+ More information on this type can be found in the tutorial. +

+
+ + Implementation + Notes +
+

+ Internally, an N-bit cpp_bin_float + is represented as an N-bit unsigned integer along with an exponent and a + sign. The integer part is normalized so that it's most significant bit is + always 1. The decimal point is assumed to be directly after the most significant + bit of the integer part. The special values zero, infinity and NaN all have + the integer part set to zero, and the exponent to one of 3 special values + above the maximum permitted exponent. +

+

+ Multiplication is trivial: multiply the two N-bit integer mantissa's to obtain + a 2N-bit number, then round and adjust the sign and exponent. +

+

+ Addition and subtraction proceed similarly - if the exponents are such that + there is overlap between the two values, then left shift the larger value + to produce a number with between N and 2N bits, then perform integer addition + or subtraction, round, and adjust the exponent. +

+

+ Division proceeds as follows: first scale the numerator by some power of + 2 so that integer division will produce either an N-bit or N+1 bit result + plus a remainder. If we get an N bit result then the size of twice the remainder + compared to the denominator gives us the rounding direction. Otherwise we + have one extra bit in the result which we can use to determine rounding (in + this case ties occur only if the remainder is zero and the extra bit is a + 1). +

+

+ Square root uses integer square root in a manner analogous to division. +

+

+ Decimal string to binary conversion proceeds as follows: first parse the + digits to produce an integer multiplied by a decimal exponent. Note that + we stop parsing digits once we have parsed as many as can possibly effect + the result - this stops the integer part growing too large when there are + a very large number of input digits provided. At this stage if the decimal + exponent is positive then the result is an integer and we can in principle + simply multiply by 10^N to get an exact integer result. In practice however, + that could produce some very large integers. We also need to be able to divide + by 10^N in the event that the exponent is negative. Therefore calculation + of the 10^N values plus the multiplication or division are performed using + limited precision integer arithmetic, plus an exponent, and a track of the + accumulated error. At the end of the calculation we will either be able to + round unambiguously, or the error will be such that we can't tell which way + to round. In the latter case we simply up the precision and try again until + we have an unambiguously rounded result. +

+

+ Binary to decimal conversion proceeds very similarly to the above, our aim + is to calculate mantissa * 2^shift * 10^E + where E is the decimal exponent + and shift is calculated so + that the result is an N bit integer assuming we want N digits printed in + the result. As before we use limitted precision arithmetic to calculate the + result and up the precision as necessary until the result is unambiguously + correctly rounded. In addition our initial calculation of the decimal exponent + may be out by 1, so we have to correct that and loop as well in the that + case. +

+
+ + + +
Copyright © 2002-2013 John Maddock and Christopher Kormanyos

+ Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

+
+
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html index b53de189f..f786543b9 100644 --- a/doc/html/boost_multiprecision/ref/cpp_dec_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_dec_ref.html @@ -6,7 +6,7 @@ - + @@ -20,7 +20,7 @@
-PrevUpHomeNext +PrevUpHomeNext

@@ -70,7 +70,7 @@

- The type of number_category<cpp_int<Args...> >::type is mpl::int_<number_kind_floating_point>. + The type of number_category<cpp_dec_float<Args...> >::type is mpl::int_<number_kind_floating_point>.

More information on this type can be found in the tutorial. @@ -78,7 +78,7 @@

-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -86,7 +86,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/html/boost_multiprecision/ref/cpp_int_ref.html b/doc/html/boost_multiprecision/ref/cpp_int_ref.html index d6ed89358..c16b92223 100644 --- a/doc/html/boost_multiprecision/ref/cpp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/cpp_int_ref.html @@ -143,7 +143,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/ref/gmp_int_ref.html b/doc/html/boost_multiprecision/ref/gmp_int_ref.html index 5488e2c7d..adb1ecea4 100644 --- a/doc/html/boost_multiprecision/ref/gmp_int_ref.html +++ b/doc/html/boost_multiprecision/ref/gmp_int_ref.html @@ -49,7 +49,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/ref/headers.html b/doc/html/boost_multiprecision/ref/headers.html index 4fd9adacb..6222fe434 100644 --- a/doc/html/boost_multiprecision/ref/headers.html +++ b/doc/html/boost_multiprecision/ref/headers.html @@ -27,7 +27,7 @@ Header File Structure
-

Table 1.6. Top level headers

+

Table 1.10. Top level headers

@@ -176,8 +176,8 @@

-

Table 1.7. Implementation Headers]

-
+

Table 1.11. Implementation Headers

+
@@ -410,7 +410,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/ref/internals.html b/doc/html/boost_multiprecision/ref/internals.html index 75238692a..02a514ead 100644 --- a/doc/html/boost_multiprecision/ref/internals.html +++ b/doc/html/boost_multiprecision/ref/internals.html @@ -100,7 +100,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/ref/mpf_ref.html b/doc/html/boost_multiprecision/ref/mpf_ref.html index 433f2c25e..cdfa14f09 100644 --- a/doc/html/boost_multiprecision/ref/mpf_ref.html +++ b/doc/html/boost_multiprecision/ref/mpf_ref.html @@ -65,7 +65,7 @@
-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

diff --git a/doc/html/boost_multiprecision/ref/mpfr_ref.html b/doc/html/boost_multiprecision/ref/mpfr_ref.html index 9ec84b6e5..72ace3a62 100644 --- a/doc/html/boost_multiprecision/ref/mpfr_ref.html +++ b/doc/html/boost_multiprecision/ref/mpfr_ref.html @@ -7,7 +7,7 @@ - + @@ -20,7 +20,7 @@
-PrevUpHomeNext +PrevUpHomeNext

@@ -65,7 +65,7 @@

-
Copyright © 2002-2012 John Maddock and Christopher Kormanyos

+

Copyright © 2002-2013 John Maddock and Christopher Kormanyos

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

@@ -73,7 +73,7 @@
-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/html/boost_multiprecision/ref/number.html b/doc/html/boost_multiprecision/ref/number.html index 43451efaa..68ae596b9 100644 --- a/doc/html/boost_multiprecision/ref/number.html +++ b/doc/html/boost_multiprecision/ref/number.html @@ -477,11 +477,11 @@
  • Zero for *this == other -
    • -
    Backend& backend();
 const Backend& backend()const;
    + +

    Returns the underlying back-end instance used by *this.

    @@ -589,7 +589,7 @@

    - Arithmetic + Arithmetic with a higher precision result 
    template <class ResultType, class Source1 class Source2>
@@ -621,7 +621,7 @@ 
    
       
    
 
    
 
-        Non-member
+        Non-member
         standard library function support
       
    
 
    unmentionable-expression-template-type    abs    (const number-or-expression-template-type&);
@@ -1255,7 +1255,7 @@ 
    
       
    
 
    
 
-        Boost.Math
+        Boost.Math
         Interoperability Support
       
    
 
    namespace boost{ namespace math{
@@ -1278,7 +1278,7 @@ 
    
       
    
 
    
 
-        std::numeric_limits
+        std::numeric_limits
         support
       
    
 
    namespace std{
@@ -1301,7 +1301,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/ref/tom_int_ref.html b/doc/html/boost_multiprecision/ref/tom_int_ref.html index d30d5c1dc..bd48e112a 100644 --- a/doc/html/boost_multiprecision/ref/tom_int_ref.html +++ b/doc/html/boost_multiprecision/ref/tom_int_ref.html @@ -49,7 +49,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut.html b/doc/html/boost_multiprecision/tut.html index 0b3fe5b2c..6c7955251 100644 --- a/doc/html/boost_multiprecision/tut.html +++ b/doc/html/boost_multiprecision/tut.html @@ -40,6 +40,7 @@
    Floating Point Numbers
    +
    cpp_bin_float
    cpp_dec_float
    gmp_float
    mpfr_float
    @@ -86,6 +87,18 @@
    Generic Integer Operations
    Boost.Serialization Support
    +
    Numeric Limits
    +
    +
    std::numeric_limits<> + constants
    +
    std::numeric_limits<> + functions
    +
    Numeric limits + for 32-bit platform
    +
    How to + Determine the Kind of a Number From std::numeric_limits
    +
    +
    Input Output

    In order to use this library you need to make two choices: @@ -104,7 +117,7 @@ -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/conversions.html b/doc/html/boost_multiprecision/tut/conversions.html index 9f2daf0e2..b69c64c97 100644 --- a/doc/html/boost_multiprecision/tut/conversions.html +++ b/doc/html/boost_multiprecision/tut/conversions.html @@ -31,51 +31,53 @@ All of the number types that are based on number have certain conversion rules in common. In particular:

    -
    • +
        +
      • Any number type can be constructed (or assigned) from any builtin arithmetic type, as long as the conversion isn't lossy (for example float to int conversion): - 
      cpp_dec_float_50 df(0.5);   // OK construction from double
 cpp_int          i(450);    // OK constructs from signed int
 cpp_int          j = 3.14;  // Error, lossy conversion.
      -
      • +
        • +
      • A number can be explicitly constructed from an arithmetic type, even when the conversion is lossy: - 
      cpp_int          i(3.14);       // OK explicit conversion
 i = static_cast<cpp_int>(3.14)  // OK explicit conversion
 i.assign(3.14);                 // OK, explicit assign and avoid a temporary from the cast above
 i = 3.14;                       // Error, no implicit assignment operator for lossy conversion.
 cpp_int          j = 3.14;      // Error, no implicit constructor for lossy conversion.
      -
      • +
        • +
      • A number can be converted to any built in type, via the convert_to member function: - 
      mpz_int z(2);
 int i = z.template convert_to<int>(); // sets i to 2
      +
      • +

    Additional conversions may be supported by particular backends.

    -
    • +
        +
      • A number can be converted to any built in type, via an explicit conversion operator: this functionality is only available on compilers supporting C++11's explicit conversion syntax. - 
      mpz_int z(2);
 int i = z;                     // Error, implicit conversion not allowed.
 int j = static_cast<int>(z);   // OK explicit conversion.
      -
      • +
        • +
      • Any number type can be explicitly constructed (or assigned) from a const char* or a std::string: - 
      // pi to 50 places from a string:
 cpp_dec_float_50 df("3.14159265358979323846264338327950288419716939937510");
 // Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:
@@ -87,10 +89,10 @@
 // assign member function, avoids having to create a temporary via a static_cast:
 i.assign("23");  // OK
      -
      • +
        • +
      • Any number type will interoperate with the builtin types in arithmetic expressions as long as the conversions are not lossy: - 
      // pi to 50 places from a string:
 cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
 // Multiply by 2 - using an integer literal here is usually more efficient
@@ -101,9 +103,9 @@
 cpp_int i = 2;
 i *= 3.14;  // Error, no *= operator will be found.
      -
      • +
        • +
      • Any number type can be streamed to and from the C++ iostreams: - 
      cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510";
 // Now print at full precision:
 std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_50>::max_digits10)
@@ -113,11 +115,11 @@
 // Now print in hex format with prefix:
 std::cout << std::hex << std::showbase << i << std::endl;
      -
      • +
        • +
      • Interconversions between number types of the same family are allowed and are implicit conversions if no loss of precision is involved, and explicit if it is: - 
      int128_t     i128 = 0;
 int266_t     i256 = i128;  // OK implicit widening conversion
 i128_t            = i256;  // Error, no assignment operator found, narrowing conversion is explicit
@@ -130,12 +132,12 @@
 f                 = f50;  // OK, conversion from fixed to variable precision, f will have 50 digits precision.
 f50               = f;    // Error, conversion from variable to fixed precision is potentially lossy, explicit cast required.
      -
      • +
        • +
      • Some interconversions between number types are completely generic, and are always available, albeit the conversions are always explicit: - 
      cpp_int cppi(2);
-// We can always convert between numbers of the same category - 
+// We can always convert between numbers of the same category -
 // int to int, rational to rational, or float to float, so this is OK
 // as long as we use an explicit conversion:
 mpz_int z(cppi);
@@ -146,14 +148,16 @@
 // However narrowing and/or implicit conversions always fail:
 cppi                =   df;    // Compiler error, conversion not allowed
      -
      • +
        • +
      • Other interconversions may be allowed as special cases, whenever the backend allows it: - 
      mpf_t     m;           // Native GMP type.
 mpf_init_set_ui(m, 0); // set to a value;
 mpf_float i(m);        // copies the value of the native type.
      +
      • +

    More information on what additional types a backend supports conversions from are given in the tutorial for each backend. The converting constructor @@ -163,7 +167,7 @@

    - + + + + + + + +
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats.html b/doc/html/boost_multiprecision/tut/floats.html index 28333a204..e99ebb1d4 100644 --- a/doc/html/boost_multiprecision/tut/floats.html +++ b/doc/html/boost_multiprecision/tut/floats.html @@ -7,7 +7,7 @@ - + @@ -20,13 +20,14 @@
    -PrevUpHomeNext +PrevUpHomeNext
    +
    cpp_bin_float
    cpp_dec_float
    gmp_float
    mpfr_float
    @@ -91,6 +92,39 @@
    +

    + cpp_bin_float<N> +

    +     		+

    + boost/multiprecision/cpp_bin_float.hpp +

    +     		+

    + 2 +

    +     		+

    + None +

    +     		+

    + Header only, all C++ implementation. Boost licence. +

    +     		+

    + Approximately 2x slower than the MPFR + or GMP libraries. +

    +

    cpp_dec_float<N> @@ -229,7 +263,7 @@ -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    @@ -237,7 +271,7 @@

    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html new file mode 100644 index 000000000..8da613225 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html @@ -0,0 +1,192 @@ + + + +cpp_bin_float + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +

    + #include <boost/multiprecision/cpp_bin_float.hpp> +

    +
    namespace boost{ namespace multiprecision{
+
+enum digit_base_type
+{
+   digit_base_2 = 2,
+   digit_base_10 = 10
+};
+
+template <unsigned Digits, digit_base_type base = digit_base_10, class Allocator = void, class Exponent = int, ExponentMin = 0, ExponentMax = 0>
+class cpp_bin_float;
+
+typedef number<cpp_bin_float<50> > cpp_bin_float_50;
+typedef number<cpp_bin_float<100> > cpp_bin_float_100;
+
+typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off>       cpp_bin_float_single;
+typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off>     cpp_bin_float_double;
+typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off>   cpp_bin_float_double_extended;
+typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off>  cpp_bin_float_quad;
+
+}} // namespaces
+
    +

    + The cpp_bin_float back-end + is used in conjunction with number: + It acts as an entirely C++ (header only and dependency free) floating-point + number type that is a drop-in replacement for the native C++ floating-point + types, but with much greater precision. +

    +

    + Type cpp_bin_float can + be used at fixed precision by specifying a non-zero Digits + template parameter. The typedefs cpp_bin_float_50 + and cpp_bin_float_100 provide + arithmetic types at 50 and 100 decimal digits precision respectively. +

    +

    + Optionally, you can specify whether the precision is specified in decimal + digits or binary bits - for example to declare a cpp_bin_float + with exactly the same precision as double + one would use number<cpp_bin_float<53, digit_base_2> >. + The typedefs cpp_bin_float_single, + cpp_bin_float_double, + cpp_bin_float_quad and + cpp_bin_float_double_extended + provide software analogues of the IEEE single, double and quad float data + types, plus the Intel-extended-double type respectively. Note that while + these types are functionally equivalent to the native IEEE types, but they + do not have the same size or bit-layout as true IEEE compatible types. +

    +

    + Normally cpp_bin_float + allocates no memory: all of the space required for its digits are allocated + directly within the class. As a result care should be taken not to use + the class with too high a digit count as stack space requirements can grow + out of control. If that represents a problem then providing an allocator + as a template parameter causes cpp_bin_float + to dynamically allocate the memory it needs: this significantly reduces + the size of cpp_bin_float + and increases the viable upper limit on the number of digits at the expense + of performance. However, please bear in mind that arithmetic operations + rapidly become very expensive as the digit count grows: + the current implementation really isn't optimized or designed for large + digit counts. Note that since the actual type of the objects allocated + is completely opaque, the suggestion would be to use an allocator with + void value_type, + for example: number<cpp_bin_float<1000, digit_base_10, std::allocator<void> > >. +

    +

    + The final template parameters determine the type and range of the exponent: + parameter Exponent can + be any signed integer type, but note that MinExponent + and MaxExponent can not + go right up to the limits of the Exponent + type as there has to be a little extra headroom for internal calculations. + You will get a compile time error if if this is the case. In addition if + MinExponent or MaxExponent are zero, then the library will choose suitable + values that are as large as possible given the constraints of the type + and need for extra headhoom for internal calculations. +

    +

    + There is full standard library and numeric_limits + support available for this type. +

    +

    + Things you should know when using this type: +

    +
      +
    • + Default constructed cpp_bin_floats + have a value of zero. +
      • +
    • + The radix of this type is 2, even when the precision is specified as + decimal digits. +
      • +
    • + The type supports both infinities and NaN's. An infinity is generated + whenever the result would overflow, and a NaN is generated for any + mathematically undefined operation. +
      • +
    • + There is a std::numeric_limits specialisation for + this type. +
      • +
    • + Any number instantiated + on this type, is convertible to any other number + instantiated on this type - for example you can convert from number<cpp_bin_float<50> > to number<cpp_bin_float<SomeOtherValue> >. + Narrowing conversions round to nearest and are explicit. +
      • +
    • + Conversion from a string results in a std::runtime_error + being thrown if the string can not be interpreted as a valid floating + point number. +
      • +
    • + All arithmetic operations are correctly rounded to nearest. String + comversions and the sqrt + function are also correctly rounded, but transcendental functions (sin, + cos, pow, exp etc) are not. +
      • +
    +
    + + cpp_bin_float + example: +
    +
    #include <boost/multiprecision/cpp_bin_float.hpp>
+
+using namespace boost::multiprecision;
+
+// Operations at fixed precision and full numeric_limits support:
+cpp_bin_float_100 b = 2;
+std::cout << std::numeric_limits<cpp_bin_float_100>::digits << std::endl;
+std::cout << std::numeric_limits<cpp_bin_float_100>::digits10 << std::endl;
+// We can use any C++ std lib function, lets print all the digits as well:
+std::cout << std::setprecision(std::numeric_limits<cpp_bin_float_100>::max_digits10)
+   << log(b) << std::endl; // print log(2)
+// We can also use any function from Boost.Math:
+std::cout << boost::math::tgamma(b) << std::endl;
+// These even work when the argument is an expression template:
+std::cout << boost::math::tgamma(b * b) << std::endl;
+// And since we have an extended exponent range we can generate some really large 
+// numbers here (4.0238726007709377354370243e+2564):
+std::cout << boost::math::tgamma(cpp_bin_float_100(1000)) << std::endl;
+
    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html index a167bb760..fe8d0e032 100644 --- a/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html +++ b/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html @@ -6,7 +6,7 @@ - + @@ -20,7 +20,7 @@
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -130,11 +130,9 @@

    - cpp_dec_float + cpp_dec_float example:
    -

    -

    #include <boost/multiprecision/cpp_dec_float.hpp>
 
 using namespace boost::multiprecision;
@@ -155,12 +153,10 @@ 
    
 // numbers here (4.0238726007709377354370243e+2564):
 std::cout << boost::math::tgamma(cpp_dec_float_100(1000)) << std::endl;
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    @@ -168,7 +164,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/html/boost_multiprecision/tut/floats/float128.html b/doc/html/boost_multiprecision/tut/floats/float128.html index 3d57b4d9f..428dbf7e5 100644 --- a/doc/html/boost_multiprecision/tut/floats/float128.html +++ b/doc/html/boost_multiprecision/tut/floats/float128.html @@ -109,11 +109,9 @@
    - float128 + float128 example:
    -

    -

    #include <boost/multiprecision/float128.hpp>
 
 using namespace boost::multiprecision;
@@ -138,8 +136,6 @@ 
    
 
 constexpr float128 pi = 3.1415926535897932384626433832795028841971693993751058Q;
    -

    -


    [3] @@ -149,7 +145,7 @@

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg.html index 33a0e676c..f3f3aa33c 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg.html @@ -41,7 +41,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html index 444f0cc2a..563ea65f0 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/aos.html @@ -39,8 +39,6 @@ The area of a circle can be computed in generic programming using Boost.Math for the constant π as shown below:

    -

    -

    #include <boost/math/constants/constants.hpp>
 
 template<typename T>
@@ -50,8 +48,6 @@
    return pi<T>() * r * r;
 }
    -

    -

    It is possible to use area_of_a_circle() with built-in floating-point types as well as floating-point types from Boost.Multiprecision. In particular, @@ -64,8 +60,6 @@ 123/100 for float, double and cpp_dec_float_50 with the program below.

    -

    -

    #include <iostream>
 #include <iomanip>
 #include <boost/multiprecision/cpp_dec_float.hpp>
@@ -102,8 +96,6 @@
       << std::endl;
 }
    -

    -

    In the next example we'll look at calling both standard library and Boost.Math functions from within generic code. We'll also show how to cope with @@ -113,7 +105,7 @@

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html index 94567aefd..73a46081d 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html @@ -31,8 +31,6 @@ Similar to the generic derivative example, we can calculate integrals in a similar manner:

    -

    -

    template<typename value_type, typename function_type>
 inline value_type integral(const value_type a,
                            const value_type b,
@@ -72,15 +70,11 @@
    return I;
 }
    -

    -

    The following sample program shows how the function can be called, we begin by defining a function object, which when integrated should yield the Bessel J function:

    -

    -

    template<typename value_type>
 class cyl_bessel_j_integral_rep
 {
@@ -99,10 +93,6 @@
    const value_type x;
 };
    -

    -

    -

    -

       /* The function can now be called as follows: */
 int main(int, char**)
 {
@@ -151,12 +141,10 @@
    std::cout << boost::math::cyl_bessel_j(2, mp_type(123) / 100) << std::endl;
 }
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html index 91dbf518f..ce943eed6 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/jel.html @@ -42,15 +42,11 @@ If we were to implement this at double precision using Boost.Math's facilities for the Gamma and Bessel function calls it would look like this:

    -

    -

    double JEL1(double v, double z)
 {
    return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / std::pow(z / 2, v);
 }
    -

    -

    Calling this function as:

    @@ -66,16 +62,12 @@ type cpp_dec_float_50 as the argument type:

    -

    -

    boost::multiprecision::cpp_dec_float_50
    JEL2(boost::multiprecision::cpp_dec_float_50 v, boost::multiprecision::cpp_dec_float_50 z)
 {
    return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / boost::multiprecision::pow(z / 2, v);
 }
    -

    -

    The implementation is almost the same as before, but with one key difference - we can no longer call std::pow, @@ -107,8 +99,6 @@ type (float, double etc), or with a multiprecision type:

    -

    -

    template <class Float>
 Float JEL3(Float v, Float z)
 {
@@ -116,8 +106,6 @@
    return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
 }
    -

    -

    Once again the code is almost the same as before, but the call to pow has changed yet again. We need the call to resolve to either std::pow @@ -165,8 +153,6 @@ from Boost.Math which calculates the return type of mixed-argument functions, here's how the new code looks now:

    -

    -

    template <class Float1, class Float2>
 typename boost::math::tools::promote_args<Float1, Float2>::type
    JEL4(Float1 v, Float2 z)
@@ -175,8 +161,6 @@
    return boost::math::tgamma(v + 1) * boost::math::cyl_bessel_j(v, z) / pow(z / 2, v);
 }
    -

    -

    As you can see the two arguments to the function are now separate template types, and the return type is computed using the promote_args @@ -217,7 +201,7 @@

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html index 6b5dd259e..373dc97e7 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/nd.html @@ -55,8 +55,6 @@ float. Let's make a generic template subroutine using this three-point central difference rule. In particular:

    -

    -

    template<typename value_type, typename function_type>
    value_type derivative(const value_type x, const value_type dx, function_type func)
 {
@@ -78,8 +76,6 @@
    return ((fifteen_m1 - six_m2) + m3) / ten_dx1;
 }
    -

    -

    The derivative() template function can be used to compute the first derivative of any @@ -94,8 +90,6 @@ The code below computes the derivative in Equation 3 for float, double and boost's multiple-precision type cpp_dec_float_50.

    -

    -

    #include <iostream>
 #include <iomanip>
 #include <boost/multiprecision/cpp_dec_float.hpp>
@@ -157,8 +151,6 @@
       << std::endl;
 }
    -

    -

    The expected value of the derivative is 0.5. This central difference rule in this example is ill-conditioned, meaning it suffers from slight @@ -174,8 +166,6 @@ result obtained from a call to gamma_p_derivative, the results agree to approximately 44 digits:

    -

    -

    cpp_dec_float_50 gd = derivative(
    cpp_dec_float_50(2),
    cpp_dec_float_50(1.0E-9),
@@ -192,12 +182,10 @@
 // 2.70670566473225383787998989944968806815253190143120e-01
 std::cout << boost::math::gamma_p_derivative(cpp_dec_float_50(2), cpp_dec_float_50(2)) << std::endl;
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html index 575b0b950..fd8b5ca30 100644 --- a/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html +++ b/doc/html/boost_multiprecision/tut/floats/fp_eg/poly_eg.html @@ -38,8 +38,6 @@ The following code evaluates sin(x) as a polynomial, accurate to at least 64 decimal places:

    -

    -

    using boost::multiprecision::cpp_dec_float;
 typedef boost::multiprecision::number<cpp_dec_float<64> > mp_type;
 
@@ -126,8 +124,6 @@
   return sum;
 }
    -

    -

    Calling the function like so:

    @@ -142,7 +138,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/gmp_float.html b/doc/html/boost_multiprecision/tut/floats/gmp_float.html index 6b829393b..8218dc9d0 100644 --- a/doc/html/boost_multiprecision/tut/floats/gmp_float.html +++ b/doc/html/boost_multiprecision/tut/floats/gmp_float.html @@ -143,11 +143,8 @@
    - - GMP example: + GMP example:
    -

    -

    #include <boost/multiprecision/gmp.hpp>
 
 using namespace boost::multiprecision;
@@ -173,12 +170,10 @@ 
    
 mpf_init(f);
 mpf_set(f, a.backend().data());
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html index ed9cf5362..f405f0af0 100644 --- a/doc/html/boost_multiprecision/tut/floats/mpfr_float.html +++ b/doc/html/boost_multiprecision/tut/floats/mpfr_float.html @@ -226,11 +226,8 @@
    - - MPFR example: + MPFR example:
    -

    -

    #include <boost/multiprecision/mpfr.hpp>
 
 using namespace boost::multiprecision;
@@ -256,8 +253,6 @@ 
    
 mpfr_init(r);
 mpfr_set(r, b.backend().data(), GMP_RNDN);
    -

    -


    [2] @@ -267,7 +262,7 @@

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/gen_int.html b/doc/html/boost_multiprecision/tut/gen_int.html index 287ddc6e2..75effaa47 100644 --- a/doc/html/boost_multiprecision/tut/gen_int.html +++ b/doc/html/boost_multiprecision/tut/gen_int.html @@ -166,7 +166,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/input_output.html b/doc/html/boost_multiprecision/tut/input_output.html new file mode 100644 index 000000000..cd442d8df --- /dev/null +++ b/doc/html/boost_multiprecision/tut/input_output.html @@ -0,0 +1,185 @@ + + + +Input Output + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +
    + + Loopback + testing +
    +

    + Loopback or round-tripping refers + to writing out a value as a decimal digit string using std::iostream, + usually to a std::stringstream, and then reading the string + back in to another value, and confirming that the two values are identical. + A trivial example using float + is: +

    +
    float write; // Value to round-trip.
+std::stringstream ss;  // Read and write std::stringstream.
+ss.precision(std::numeric_limits<T>::max_digits10);  // Ensure all potentially significant bits are output.
+ss.flags(std::ios_base::fmtflags(std::ios_base::scientific)); // Use scientific format.
+ss << write; // Output to string.
+float read;  // Expected.
+ss >> read; // Read decimal digits string from stringstream.
+BOOST_CHECK_EQUAL(write, read); // Should be the same.
+
    +

    + and this can be run in a loop for all possible values of a 32-bit float. + For other floating-point types T, + including built-in double, it + takes far too long to test all values, so a reasonable test strategy is to + use a large number of random values. +

    +
    T write;
+std::stringstream ss;
+ss.precision(std::numeric_limits<T>::max_digits10);  // Ensure all potentially significant bits are output.
+ss.flags(f); // Changed from default iostream format flags if desired.
+ss << write; // Output to stringstream.
+
+T read;
+ss >> read; // Get read using operator>> from stringstream.
+BOOST_CHECK_EQUAL(read, write);
+
+read = static_cast<T>(ss.str()); // Get read by converting from decimal digits string representation of write.
+BOOST_CHECK_EQUAL(read, write);
+
+read = static_cast<T>(write.str(0, f));  // Get read using format specified when written.
+BOOST_CHECK_EQUAL(read, write);
+
    +

    + The test at test_cpp_bin_float_io.cpp + allows any floating-point type to be round_tripped using + a wide range of fairly random values. It also includes tests compared a collection + of stringdata test cases + in a file. +

    +
    + + Comparing + with output using Built-in types +
    +

    + One can make some comparisons with the output of +

    +
    <number<cpp_bin_float<53, digit_count_2> >
+
    +

    + which has the same number of significant bits (53) as 64-bit double precision + floating-point. +

    +

    + However, although most outputs are identical, there are differences on some + platforms caused by the implementation-dependent behaviours allowed by the + C99 specification C99 + ISO/IEC 9899:TC2, incorporated by C++. +

    +

    + "For e, E, f, F, g, and G conversions, if the number of + significant decimal digits is at most DECIMAL_DIG, then the result should + be correctly rounded. If the number of significant decimal digits is more + than DECIMAL_DIG but the source value is exactly representable with DECIMAL_DIG + digits, then the result should be an exact representation with trailing + zeros. Otherwise, the source value is bounded by two adjacent decimal strings + L < U, both having DECIMAL_DIG significant digits; the value of the + resultant decimal string D should satisfy L<= D <= U, with the extra + stipulation that the error should have a correct sign for the current rounding + direction." +

    +

    + So not only is correct rounding for the full number of digits not required, + but even if the optional recomended practice + is followed, then the value of these last few digits is unspecified as long + as the value is within certain bounds. +

    +
    + + + + + +
    [Note]Note

    + Do not expect the output from different platforms to be identical, + but cpp_dec_float, cpp_bin_float (and other backends) outputs + should be correctly rounded to the number of digits requested by the set + precision and format. +

    +
    + + Macro + BOOST_MP_MIN_EXPONENT_DIGITS +
    +

    + C99 + Standard for format specifiers, 7.19.6 Formatted input/output functions + requires: +

    +

    + "The exponent always contains at least two digits, and only as many + more digits as necessary to represent the exponent." +

    +

    + So to conform to the C99 standard (incorporated by C++) +

    +
    #define BOOST_MP_MIN_EXPONENT_DIGITS 2
+
    +

    + Confusingly, Microsoft (and MinGW) do not conform to this standard and provide + at least three digits, for example 1e+001. So if you want the output to match + that from built-in floating-point types on compilers that use Microsofts + runtime then use: +

    +
    #define BOOST_MP_MIN_EXPONENT_DIGITS 3
+
    +

    + Also useful to get the minimum exponent field width is +

    +
    #define BOOST_MP_MIN_EXPONENT_DIGITS 1
+
    +

    + producing a compact output like 2e+4, + useful when conserving space is important. +

    +

    + Larger values are also supported, for example, value 4 for 2e+0004 which may be useful to ensure that + columns line up. +

    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/interval.html b/doc/html/boost_multiprecision/tut/interval.html index 318cf1560..8e38ca607 100644 --- a/doc/html/boost_multiprecision/tut/interval.html +++ b/doc/html/boost_multiprecision/tut/interval.html @@ -33,7 +33,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/interval/mpfi.html b/doc/html/boost_multiprecision/tut/interval/mpfi.html index aef8476ab..64a05e977 100644 --- a/doc/html/boost_multiprecision/tut/interval/mpfi.html +++ b/doc/html/boost_multiprecision/tut/interval/mpfi.html @@ -158,8 +158,8 @@ 

    template <unsigned Digits10, expression_template_option ExpressionTemplates>
 number<mpfi_float_backend<Digits10>, ExpressionTemplates> intersect(
-	const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a,
-	const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b);
+  const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a,
+  const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b);

    Returns the interval which is the intersection of the a @@ -168,8 +168,8 @@ 

    template <unsigned Digits10, expression_template_option ExpressionTemplates>
 number<mpfi_float_backend<Digits10>, ExpressionTemplates> hull(
-	const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a,
-	const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b);
+  const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a,
+  const number<mpfi_float_backend<Digits10>, ExpressionTemplates>&  b);

    Returns the interval which is the union of a and @@ -231,12 +231,9 @@

    - - MPFI + MPFI example:
    -

    -

    #include <boost/multiprecision/mpfi.hpp>
 
 using namespace boost::multiprecision;
@@ -265,12 +262,10 @@ 
    
 std::cout << overlap(i1, i2) << std::endl;
 std::cout << subset(i1, i2) << std::endl;
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints.html b/doc/html/boost_multiprecision/tut/ints.html index e61e42ee6..1c606ab90 100644 --- a/doc/html/boost_multiprecision/tut/ints.html +++ b/doc/html/boost_multiprecision/tut/ints.html @@ -186,7 +186,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints/cpp_int.html b/doc/html/boost_multiprecision/tut/ints/cpp_int.html index 1f03b67f8..8001bdfca 100644 --- a/doc/html/boost_multiprecision/tut/ints/cpp_int.html +++ b/doc/html/boost_multiprecision/tut/ints/cpp_int.html @@ -341,10 +341,8 @@
    - Example: + Example:
    -

    -

    #include <boost/multiprecision/cpp_int.hpp>
 
 using namespace boost::multiprecision;
@@ -364,12 +362,10 @@ 
    
 
 std::cout << u << std::endl; // prints 100!
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints/egs.html b/doc/html/boost_multiprecision/tut/ints/egs.html index 643ead62d..f53916fe4 100644 --- a/doc/html/boost_multiprecision/tut/ints/egs.html +++ b/doc/html/boost_multiprecision/tut/ints/egs.html @@ -33,7 +33,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints/egs/bitops.html b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html index 16b37024e..7b8cf2d5b 100644 --- a/doc/html/boost_multiprecision/tut/ints/egs/bitops.html +++ b/doc/html/boost_multiprecision/tut/ints/egs/bitops.html @@ -31,8 +31,6 @@ be manipulated, we'll start with an often needed calculation of 2n - 1, which we could obviously implement like this:

    -

    -

    using boost::multiprecision::cpp_int;
 
 cpp_int b1(unsigned n)
@@ -41,8 +39,6 @@
    return (r << n) - 1;
 }
    -

    -

    Calling:

    @@ -55,16 +51,12 @@

    However, we could equally just set the n'th bit in the result, like this:

    -

    -

    cpp_int b2(unsigned n)
 {
    cpp_int r(0);
    return --bit_set(r, n);
 }
    -

    -

    Note how the bit_set function sets the specified bit in its argument and then returns a reference @@ -89,7 +81,7 @@

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints/egs/factorials.html b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html index 580f47009..f97048d63 100644 --- a/doc/html/boost_multiprecision/tut/ints/egs/factorials.html +++ b/doc/html/boost_multiprecision/tut/ints/egs/factorials.html @@ -31,8 +31,6 @@ factorials which will fit into a 128-bit integer. At the end of the routine we do some fancy iostream formatting of the results:

    -

    -

    #include <boost/multiprecision/cpp_int.hpp>
 #include <iostream>
 #include <iomanip>
@@ -93,8 +91,6 @@
    }
 }
    -

    -

    The output from this routine is:

    @@ -140,7 +136,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints/gmp_int.html b/doc/html/boost_multiprecision/tut/ints/gmp_int.html index cfd4771d9..4dbceeb66 100644 --- a/doc/html/boost_multiprecision/tut/ints/gmp_int.html +++ b/doc/html/boost_multiprecision/tut/ints/gmp_int.html @@ -106,10 +106,8 @@
    - Example: + Example:
    -

    -

    #include <boost/multiprecision/gmp.hpp>
 
 using namespace boost::multiprecision;
@@ -127,12 +125,10 @@ 
    
 mpz_init(z);
 mpz_set(z, v.backend().data());
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/ints/tom_int.html b/doc/html/boost_multiprecision/tut/ints/tom_int.html index 86c411e2b..a5a5e1224 100644 --- a/doc/html/boost_multiprecision/tut/ints/tom_int.html +++ b/doc/html/boost_multiprecision/tut/ints/tom_int.html @@ -80,10 +80,8 @@
    - Example: + Example:
    -

    -

    #include <boost/multiprecision/tommath.hpp>
 
 boost::multiprecision::tom_int v = 1;
@@ -113,12 +111,10 @@ 
    
    std::cout << e.what() << std::endl;
 }
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/limits.html b/doc/html/boost_multiprecision/tut/limits.html new file mode 100644 index 000000000..5cd48aace --- /dev/null +++ b/doc/html/boost_multiprecision/tut/limits.html @@ -0,0 +1,100 @@ + + + +Numeric Limits + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +
    +
    std::numeric_limits<> + constants
    +
    std::numeric_limits<> + functions
    +
    Numeric limits + for 32-bit platform
    +
    How to + Determine the Kind of a Number From std::numeric_limits
    +
    +

    + Boost.Multiprecision tries hard to implement std::numeric_limits + for all types as far as possible and meaningful because experience with Boost.Math + has shown that this aids portability. +

    +

    + The C++ + standard library defines std::numeric_limits + in section 18.3.2. +

    +

    + This in turn refers to the C standard SC22/WG11 + N507 DRAFT INTERNATIONAL ISO/IEC STANDARD WD 10967-1 Information + technology Language independent arithmetic Part 1: Integer and Floating point + arithmetic. +

    +

    + That C Standard in turn refers to +

    +

    + IEEE754 IEEE Standard + for Binary Floating-Point Arithmetic +

    +

    + There is a useful summary at C++ + reference. +

    +

    + The chosen backend often determines how completely std::numeric_limits + is available. +

    +

    + Compiler options, processor type, and definition of macros or assembler instructions + to control denormal numbers will alter the values in the tables given below. +

    +
    + + + + + +
    [Warning]Warning

    + GMP's mpf_t does not have + a concept of overflow: operations that lead to overflow eventually run + of out of resources and terminate with stack overflow (often after several + seconds). +

    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/limits/constants.html b/doc/html/boost_multiprecision/tut/limits/constants.html new file mode 100644 index 000000000..f94fb659a --- /dev/null +++ b/doc/html/boost_multiprecision/tut/limits/constants.html @@ -0,0 +1,705 @@ + + + +std::numeric_limits<> constants + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +
    + + is_specialized +
    +

    + true for all arithmetic types + (integer, floating and fixed-point) for which std::numeric_limits<T>::numeric_limits + is specialized. +

    +

    + A typical test is +

    +
    if (std::numeric_limits<T>::is_specialized == false)
+{
+  std::cout << "type " << typeid(T).name()  << " is not specialized for std::numeric_limits!" << std::endl;
+// ...
+}
+
    +

    + Typically numeric_limits<T>::is_specialized + is true for all T where the compile-time constant members + of numeric_limits are indeed + known at compile time, and don't vary at runtime. For example floating + point types with runtime-variable precision such as mpfr_float + have no numeric_limits + specialization as it would be impossible to define all the members at compile + time. In contrast the precision of a type such as mpfr_float_50 + is known at compile time, and so it does have a numeric_limits specialization. +

    +

    + Note that not all the std::numeric_limits + member constants and functions are meaningful for all user-defined types + (UDT), such as the decimal and binary multiprecision types provided here. + More information on this is given in the sections below. +

    +
    + + infinity +
    +

    + For floating-point types, ∞ is defined wherever possible, but clearly infinity + is meaningless for __arbitrary_precision arithmetic backends, and there + is one floating point type (GMP's mpf_t, + see gmp_float) + which has no notion of infinity or NaN at all. +

    +

    + A typical test whether infinity is implemented is +

    +
    if(std::numeric_limits<T>::has_infinity)
+{
+   std::cout << std::numeric_limits<T>::infinity() << std::endl;
+}
+
    +

    + and using tests like this is strongly recommended to improve portability. +

    +

    + If the backend is switched to a type that does not support infinity then, + without checks like this, there will be trouble. +

    +
    + + is_signed +
    +

    + std::numeric_limits<T>::is_signed == + true if the type T + is signed. +

    +

    + For built-in binary types, the sign is held in a single bit, but for other + types (cpp_dec_float and cpp_bin_float) it may be a separate storage element, + usually bool. +

    +
    + + is_exact +
    +

    + std::numeric_limits<T>::is_exact == + true if type T uses exact representations. +

    +

    + This is defined as true for + all integer types and false + for floating-point types. +

    +

    + A + usable definition has been discussed. +

    +

    + ISO/IEC 10967-1, Language independent arithmetic, noted by the C++ Standard + defines +

    +
    A floating point type F shall be a finite subset of [real].
+
    +

    + The important practical distinction is that all integers (up to max()) + can be stored exactly. +

    +

    + Rational + types using two integer types are also exact. +

    +

    + Floating-point types cannot store all real values + (those in the set of ℜ) exactly. For example, + 0.5 can be stored exactly in a binary floating-point, but 0.1 cannot. What + is stored is the nearest representable real value, that is, rounded to + nearest. +

    +

    + Fixed-point types (usually decimal) are also defined as exact, in that + they only store a fixed precision, so + half cents or pennies (or less) cannot be stored. The results of computations + are rounded up or down, just like the result of integer division stored + as an integer result. +

    +

    + There are number of proposals to add + Decimal Floating Point Support to C++. +

    +

    + Decimal + TR. +

    +

    + And also C++ + Binary Fixed-Point Arithmetic. +

    +
    + + is_bounded +
    +

    + std::numeric_limits<T>::is_bounded == + true if the set of values represented + by the type T is finite. +

    +

    + This is true for all built-in + integer, fixed and floating-point types, and most multi-precision types. +

    +

    + It is only false for a few + __arbitrary_precision types like cpp_int. +

    +

    + Rational and fixed-exponent representations are exact but not integer. +

    +
    + + is_modulo +
    +

    + std::numeric_limits<T>::is_modulo is defined as true if adding two positive values of type + T can yield a result less than either value. +

    +

    + is_modulo == + true means that the type does not + overflow, but, for example, 'wraps around' to zero, when adding one to + the max() + value. +

    +

    + For most built-in integer types, std::numeric_limits<>::is_modulo + is true. +

    +

    + bool is the only exception. +

    +

    + The modulo behaviour is sometimes useful, but also can be unexpected, and + sometimes undesired, behaviour. +

    +

    + Overflow of signed integers can be especially unexpected, possibly causing + change of sign. +

    +

    + Boost.Multiprecision integer type cpp_int + is not modulo because as an __arbitrary_precision types, it expands to + hold any value that the machine resources permit. +

    +

    + However fixed precision cpp_int's + may be modulo if they are unchecked (i.e. they behave just like built in + integers), but not if they are checked (overflow causes an exception to + be raised). +

    +

    + Built-in and multi-precision floating-point types are normally not modulo. +

    +

    + Where possible, overflow is to std::numeric_limits<>::infinity(), provided std::numeric_limits<>::has_infinity + == true. +

    +
    + + radix +
    +

    + Constant std::numeric_limits<T>::radix returns either 2 (for built-in + and binary types) or 10 (for decimal types). +

    +
    + + digits +
    +

    + The number of radix digits + that be represented without change: +

    +
      +
    • + for integer types, the number of non-sign bits + in the significand. +
      • +
    • + for floating types, the number of radix digits + in the significand. +
      • +
    +

    + The values include any implicit bit, so for example, for the ubiquious + double using 64 bits (IEEE + binary64 ), digits + == 53, even though there are only 52 actual bits of the significand stored + in the representation. The value of digits + reflects the fact that there is one implicit bit which is always set to + 1. +

    +

    + The Boost.Multiprecision binary types do not use an implicit bit, so the + digits member reflects + exactly how many bits of precision were requested: +

    +
    typedef number<cpp_bin_float<53, digit_base_2> >   float64;
+typedef number<cpp_bin_float<113, digit_base_2> >  float128;
+std::numeric_limits<float64>::digits == 53.
+std::numeric_limits<float128>::digits == 113.
+
    +

    + For the most common case of radix + == 2, + std::numeric_limits<T>::digits is the number of bits in the representation, + not counting any sign bit. +

    +

    + For a decimal integer type, when radix + == 10, + it is the number of decimal digits. +

    +
    + + digits10 +
    +

    + Constant std::numeric_limits<T>::digits10 returns the number of decimal + digits that can be represented without change or loss. +

    +

    + For example, numeric_limits<unsigned char>::digits10 is 2. +

    +

    + This somewhat inscrutable definition means that an unsigned + char can hold decimal values 0..99 + without loss of precision or accuracy, usually from truncation. +

    +

    + Had the definition been 3 then that would imply it could hold 0..999, but + as we all know, an 8-bit unsigned + char can only hold 0..255, and an + attempt to store 256 or more will involve loss or change. +

    +

    + For bounded integers, it is thus one less + than number of decimal digits you need to display the biggest integer + std::numeric_limits<T>::max(). + This value can be used to predict the layout width required for +

    +
    std::cout
+  << std::setw(std::numeric_limits<short>::digits10 +1 +1) // digits10+1, and +1 for sign.
+  << std::showpos << (std::numeric_limits<short>::max)() // +32767
+  << std::endl
+  << std::setw(std::numeric_limits<short>::digits10 +1 +1)
+  << (std::numeric_limits<short>::min)() << std::endl;   // -32767
+
    +

    + For example, unsigned short + is often stored in 16 bits, so the maximum value is 0xFFFF or 65535. +

    +
    std::cout
+  << std::setw(std::numeric_limits<unsigned short>::digits10 +1 +1) // digits10+1, and +1 for sign.
+  << std::showpos << (std::numeric_limits<unsigned short>::max)() //  65535
+  << std::endl
+  << std::setw(std::numeric_limits<unsigned short>::digits10 +1 +1) // digits10+1, and +1 for sign.
+  << (std::numeric_limits<unsigned short>::min)() << std::endl;   //      0
+
    +

    + For bounded floating-point types, if we create a double + with a value with digits10 + (usually 15) decimal digits, 1e15 + or 1000000000000000 : +

    +
    std::cout.precision(std::numeric_limits<double>::max_digits10);
+double d =  1e15;
+double dp1 = d+1;
+std::cout << d << "\n" << dp1 << std::endl;
+// 1000000000000000
+// 1000000000000001
+std::cout <<  dp1 - d << std::endl; // 1
+
    +

    + and we can increment this value to 1000000000000001 + as expected and show the difference too. +

    +

    + But if we try to repeat this with more than digits10 + digits, +

    +
    std::cout.precision(std::numeric_limits<double>::max_digits10);
+double d =  1e16;
+double dp1 = d+1;
+std::cout << d << "\n" << dp1 << std::endl;
+// 10000000000000000
+// 10000000000000000
+  std::cout << dp1 - d << std::endl; // 0 !!!
+
    +

    + then we find that when we add one it has no effect, and display show that + there is loss of precision. See Loss + of significance or cancellation error. +

    +

    + So digits10 is the number + of decimal digits guaranteed to be correct. +

    +

    + For example, 'round-tripping' for double: +

    +
      +
    • + If a decimal string with at most digits10( + == 15) significant decimal digits is converted to double + and then converted back to the same number of significant decimal digits, + then the final string will match the original 15 decimal digit string. +
      • +
    • + If a double floating-point + number is converted to a decimal string with at least 17 decimal digits + and then converted back to double, + then the result will be binary indentical to the original double value. +
      • +
    +

    + For most purposes, you will much more likely want std::numeric_limits<>::max_digits10, + the number of decimal digits that ensure that a change of one least significant + bit (ULP) produces a different decimal digits string. +

    +

    + For nearly all floating-point types, max_digits10 + is digits10+2, but you should use max_digits10 + where possible. +

    +

    + If max_digits10 is not + available, you should using the Kahan + formula for floating-point type T +

    +
    max_digits10 = std::numeric_limits<T>::digits * 3010U/10000U;
+
    +

    + The factor is log10(2) = 0.3010 but must be evaluated at compile time using + only integers. +

    +

    + (See also Richard + P. Brent and Paul Zimmerman, Modern Computer Arithmetic Equation + 3.8 on page 116.). +

    +

    + The extra two (or 3) least significant digits are 'noisy' and may be junk, + but if you want to 'round-trip' - printing a value out and reading it back + in - you must use os.precision(std::numeric_limits<T>::max_digits10). + For at least one popular compiler, you must also use std::scientific + format. +

    +
    + + max_digits10 +
    +

    + std::numeric_limits<T>::max_digits10 was added for floating-point + because digits10 decimal + digits are insufficient to show a least significant bit (ULP) change giving + puzzling displays like +

    +
    0.666666666666667 != 0.666666666666667
+
    +

    + from failure to 'round-trip', for example: +

    +
    double write = 2./3; // Any arbitrary value that cannot be represented exactly.
+double read = 0;
+std::stringstream s;
+s.precision(std::numeric_limits<double>::digits10); // or `float64_t` for 64-bit IEE754 double.
+s << write;
+s >> read;
+if(read != write)
+{
+  std::cout <<  std::setprecision(std::numeric_limits<double>::digits10)
+    << read << " != " << write << std::endl;
+}
+
    +

    + If you wish to ensure that a change of one least significant bit (ULP) + produces a different decimal digits string, then max_digits10 + is the precision to use. +

    +

    + For example: +

    +
    double pi = boost::math::double_constants::pi;
+std::cout.precision(std::numeric_limits<double>::max_digits10);
+std::cout << pi << std::endl; // 3.1415926535897931
+
    +

    + will display π to the maximum possible precision using a double. +

    +

    + and similarly for a much higher precision type: +

    +
    using namespace boost::multiprecision;
+
+typedef number<cpp_dec_float<50> > cpp_dec_float_50; // 50 decimal digits.
+
+using boost::multiprecision::cpp_dec_float_50;
+
+cpp_dec_float_50 pi = boost::math::constants::pi<cpp_dec_float_50>();
+std::cout.precision(std::numeric_limits<cpp_dec_float_50>::max_digits10);
+std::cout << pi << std::endl;
+// 3.141592653589793238462643383279502884197169399375105820974944592307816406
+
    +

    + For integer types, max_digits10 + is implementation-dependant, but is usually digits10 + + 2. + This is the output field width required for the maximum value of the type + T std::numeric_limits<T>::max() + including a sign and a space. +

    +

    + So this will produce neat columns. +

    +
    std::cout << std::setw(std::numeric_limits<int>::max_digits10) ...
+
    +
    + + + + + +
    [Note]Note

    + For Microsoft Visual Studio 2010, std::numeric_limits<float>::max_digits10 + is wrongly defined as 8. It should be 9. +

    +
    + + + + + +
    [Note]Note
    +

    + For Microsoft Visual Studio, and default float format, a small range + of values approximately 0.0001 to 0.004, with exponent values of 3f2 + to 3f6, are wrongly input by one least significant bit, probably every + third value of significand. +

    +

    + A workaround is using scientific or exponential format << std::scientific. +

    +
    +
    + + + + + +
    [Note]Note

    + BOOST_NO_CXX11_NUMERIC_LIMITS is a suitable feature-test macro to determine + if std::numeric_limits<float>::max_digits10 is implemented on any + platform. If max_digits10 + is not available, you should using the Kahan + formula for floating-point type T. See above. +

    +

    + For example, to be portable, including older platforms: +

    +
      typedef float T; // Any type: `double`, cpp_dec_float_50, bin_128bit_double_type ...
+
+#if defined(BOOST_NO_CXX11_NUMERIC_LIMITS)
+   std::cout.precision(2 + std::numeric_limits<T>::digits * 3010U/10000U);
+#else
+#  if (_MSC_VER <= 1600) // Correct wrong value for float.
+     std::cout.precision(2 + std::numeric_limits<T>::digits * 3010U/10000U);
+#  else
+     std::cout.precision(std::numeric_limits<T>::max_digits10);
+#  endif
+#endif
+
+  std::cout << "std::cout.precision = " << std::cout.precision() << std::endl;
+
+  double x = 1.2345678901234567889;
+
+  std::cout << "x = " << x << std::endl; //
+
    +

    + which should output: +

    +
    std::cout.precision = 9
+x = 1.23456789
+
    +
    + + round_style +
    +

    + The rounding style determines how the result of floating-point operations + is treated when the result cannot be exactly represented + in the significand. Various rounding modes may be provided: +

    +
      +
    • + round to nearest up or down (default for floating-point types). +
      • +
    • + round up (toward positive infinity). +
      • +
    • + round down (toward negative infinity). +
      • +
    • + round toward zero (integer types). +
      • +
    • + no rounding (if decimal radix). +
      • +
    • + rounding mode is not determinable. +
      • +
    +

    + For integer types, std::numeric_limits<T>::round_style + is always towards zero, so +

    +
    std::numeric_limits<T>::round_style == std::round_to_zero;
+
    +

    + A decimal type, cpp_dec_float + rounds in no particular direction, which is to say it doesn't round at + all. And since there are several guard digits, it's not really the same + as truncation (round toward zero) either. +

    +

    + For floating-point types, it is normal to round to nearest. +

    +
    std::numeric_limits<T>::round_style == std::round_to_nearest;
+
    +

    + See function std::numeric_limits<T>::round_error for the maximum error (in + ULP) that rounding can cause. +

    +
    + + has_denorm_loss +
    +

    + true if a loss of precision + is detected as a denormalization + loss, rather than an inexact result. +

    +

    + Always false for integer types. +

    +

    + false for all types which + do not have has_denorm + == std::denorm_present. +

    +
    + + denorm_style +
    +

    + Denormalized + values are representations with a variable number of exponent bits + that can permit gradual underflow, so that, if type T is double. +

    +
    std::numeric_limits<T>::denorm_min() < std::numeric_limits<T>::min()
+
    +

    + A type may have any of the following enum + float_denorm_style values: +

    +
      +
    • + std::denorm_absent, if it does not allow + denormalized values. (Always used for all integer and exact types). +
      • +
    • + std::denorm_present, if the floating-point + type allows denormalized values. +
      • +
    • + std::denorm_indeterminate, if indeterminate + at compile time. +
      • +
    +
    + + Tinyness + before rounding +
    +

    + bool std::numeric_limits<T>::tinyness_before +

    +

    + true if a type can determine + that a value is too small to be represent as a normalized value before + rounding it. +

    +

    + Generally true for is_iec559 + floating-point built-in types, but false for integer types. +

    +

    + Standard-compliant IEEE 754 floating-point implementations may detect the + floating-point underflow at three predefined moments: +

    +
      +
    1. + After computation of a result with absolute value smaller than std::numeric_limits<T>::min(), + such implementation detects tinyness before rounding + (e.g. UltraSparc). +
      2. +
    2. + After rounding of the result to std::numeric_limits<T>::digits + bits, if the result is tiny, such implementation detects tinyness + after rounding (e.g. SuperSparc). +
      3. +
    3. + If the conversion of the rounded tiny result to subnormal form resulted + in the loss of precision, such implementation detects denorm + loss. +
      4. +
    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/limits/functions.html b/doc/html/boost_multiprecision/tut/limits/functions.html new file mode 100644 index 000000000..3ddf33bf4 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/limits/functions.html @@ -0,0 +1,546 @@ + + + +std::numeric_limits<> functions + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +
    + + max function +
    +

    + Function std::numeric_limits<T>::max() + returns the largest finite value that can be represented by the type T. + If there is no such value (and numeric_limits<T>::bounded + is false) then returns T(). +

    +

    + For built-in types there is usually a corresponding MACRO value TYPE_MAX, + where TYPE is CHAR, INT, FLOAT etc. +

    +

    + Other types, including those provided by a typedef, for example INT64_T_MAX for int64_t, + may provide a macro definition. +

    +

    + To cater for situations where no numeric_limits + specialization is available (for example because the precision of the type + varies at runtime), packaged versions of this (and other functions) are + provided using +

    +
    #include <boost/math/tools/precision.hpp>
+
+T = boost::math::tools::max_value<T>();
+
    +

    + Of course, these simply use std::numeric_limits<T>::max() if available, but otherwise 'do something + sensible'. +

    +
    + + lowest + function +
    +

    + Since C++11: std::numeric_limits<T>::lowest() + is +

    +
      +
    • + For integral types, the same as function min(). +
      • +
    • + For floating-point types, generally the negative of max() (but implementation-dependent). +
      • +
    +
    -(std::numeric_limits<double>::max)() == std::numeric_limits<double>::lowest();
+
    +
    + + min function +
    +

    + Function std::numeric_limits<T>::min() + returns the minimum finite value that can be represented by the type T. +

    +

    + For built-in types there is usually a corresponding MACRO value TYPE_MIN, + where TYPE is CHAR, INT, FLOAT etc. +

    +

    + Other types, including those provided by a typedef, for example INT64_T_MIN for int64_t, + may provide a macro definition. +

    +

    + For floating-point types, it is more fully defined as the minimum + positive normalized value. +

    +

    + See std::numeric_limits<T>::denorm_min() + for the smallest denormalized value, provided +

    +
    std::numeric_limits<T>::has_denorm == std::denorm_present
+
    +

    + To cater for situations where no numeric_limits + specialization is available (for example because the precision of the type + varies at runtime), packaged versions of this (and other functions) are + provided using +

    +
    #include <boost/math/tools/precision.hpp>
+
+T = boost::math::tools::min_value<T>();
+
    +

    + Of course, these simply use std::numeric_limits<T>::min() if available. +

    +
    + + denorm_min + function +
    +

    + Function std::numeric_limits<T>::denorm_min() + returns the smallest denormalized + value, provided +

    +
    std::numeric_limits<T>::has_denorm == std::denorm_present
+
    +
    std::cout.precision(std::numeric_limits<double>::max_digits10);
+if (std::numeric_limits<double>::has_denorm == std::denorm_present)
+{
+  double d = std::numeric_limits<double>::denorm_min();
+
+    std::cout << d << std::endl; //  4.9406564584124654e-324
+
+    int exponent;
+
+    double significand = frexp(d, &exponent);
+    std::cout << "exponent = " << std::hex << exponent << std::endl; //  fffffbcf
+    std::cout << "significand = " << std::hex << significand << std::endl; // 0.50000000000000000
+}
+else
+{
+  std::cout << "No denormalization. " << std::endl;
+}
+
    +

    + The exponent is effectively reduced from -308 to -324 (though it remains + encoded as zero and leading zeros appear in the significand, thereby losing + precision until the significand reaches zero). +

    +
    + + round_error +
    +

    + Function std::numeric_limits<T>::round_error() + returns the maximum error (in units of ULP) + that can be caused by any basic arithmetic operation. +

    +
    round_style == std::round_indeterminate;
+
    +

    + The rounding style is indeterminable at compile time. +

    +

    + For floating-point types, when rounding is to nearest, only half a bit + is lost by rounding, and round_error + == 0.5. + In contrast when rounding is towards zero, or plus/minus infinity, we can + loose up to one bit from rounding, and round_error + == 1. +

    +

    + For integer types, rounding always to zero, so at worst almost one bit + can be rounded, so round_error + == 1. +

    +

    + round_error() + can be used with std::numeric_limits<T>::epsilon() + to estimate the maximum potential error caused by rounding. For typical + floating-point types, round_error() = 1/2, so half + epsilon is the maximum potential error. +

    +
    double round_err = std::numeric_limits<double>::epsilon() // 2.2204460492503131e-016
+                 * std::numeric_limits<double>::round_error(); // 1/2
+std::cout << round_err << std::endl; // 1.1102230246251565e-016
+
    +

    + There are, of course, many occasions when much bigger loss of precision + occurs, for exampe, caused by Loss + of significance or cancellation error or very many iterations. +

    +
    + + epsilon +
    +

    + Function std::numeric_limits<T>::epsilon() + is meaningful only for non-integral types. +

    +

    + It returns the difference between 1.0 + and the next value representable by the floating-point type T. So it is + a one least-significant-bit change in this floating-point value. +

    +

    + For double (float_64t) it is 2.2204460492503131e-016 + showing all possibly significant 17 decimal digits. +

    +
    std::cout.precision(std::numeric_limits<double>::max_digits10);
+double d = 1.;
+double eps = std::numeric_limits<double>::epsilon();
+double dpeps = d+eps;
+std::cout << std::showpoint // Ensure all trailing zeros are shown.
+  << d << "\n"           // 1.0000000000000000
+  << dpeps << std::endl; // 2.2204460492503131e-016
+std::cout << dpeps - d   // 1.0000000000000002
+  << std::endl;
+
    +

    + We can explicitly increment by one bit using the function boost::math::float_next() + and the result is the same as adding epsilon. +

    +
    double one = 1.;
+double nad = boost::math::float_next(one);
+std::cout << nad << "\n"  //  1.0000000000000002
+  << nad - one // 2.2204460492503131e-016
+  << std::endl;
+
    +

    + Adding any smaller value, like half epsilon, + will have no effect on this value. +

    +
    std::cout.precision(std::numeric_limits<double>::max_digits10);
+double d = 1.;
+double eps = std::numeric_limits<double>::epsilon();
+double dpeps = d + eps/2;
+
+std::cout << std::showpoint // Ensure all trailing zeros are shown.
+  << dpeps << "\n"       // 1.0000000000000000
+  << eps/2 << std::endl; // 1.1102230246251565e-016
+std::cout << dpeps - d   // 0.00000000000000000
+  << std::endl;
+
    +

    + So this cancellation error leaves the values equal, despite adding half + epsilon. +

    +

    + To achieve greater portability over platform and floating-point type, Boost.Math + and Boost.Multiprecion provide a package of functions that 'do something + sensible' if the standard numeric_limits + is not available. To use these #include + <boost/math/tools/precision.hpp>. +

    +

    + A tolerance might be defined using this version of epsilon thus: +

    +
    RealType tolerance = boost::math::tools::epsilon<RealType>() * 2;
+
    +
    + + Tolerance + for Floating-point Comparisons +
    +

    + epsilon is very useful + to compute a tolerance when comparing floating-point values, a much more + difficult task than is commonly imagined. +

    +

    + For more information you probably want (but still need) see What + Every Computer Scientist Should Know About Floating-Point Arithmetic +

    +

    + The naive test comparing the absolute difference between two values and + a tolerance does not give useful results if the values are too large or + too small. +

    +

    + So Boost.Test uses an algorithm first devised by Knuth for reliably checking + if floating-point values are close enough. +

    +

    + See Donald. E. Knuth. The art of computer programming (vol II). Copyright + 1998 Addison-Wesley Longman, Inc., 0-201-89684-2. Addison-Wesley Professional; + 3rd edition. +

    +

    + See also: +

    +

    + Alberto + Squassia, Comparing floats +

    +

    + Alberto + Squassia, Comparing floats code +

    +

    + floating-point + comparison. +

    +

    + For example, if we want a tolerance that might suit about 9 arithmetical + operations, say sqrt(9) = 3, we could define: +

    +
    T tolerance =  3 * std::numeric_limits<T>::epsilon();
+
    +

    + This is very widely used in Boost.Math testing with Boost.Test's macro + BOOST_CHECK_CLOSE_FRACTION +

    +
    T expected = 1.0;
+T calculated = 1.0 + std::numeric_limits<T>::epsilon();
+
+using boost::test_tools::check_is_close;
+
+bool r = check_is_close(expected, calculated, tolerance);
+std::cout <<  std::boolalpha << r << std::endl;  // true
+
    +

    + If using Boost.Test, then call the macro version: +

    +
    BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance);
    +

    + used thus: +

    +
    BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance);
+
    +

    + (There is also a version using tolerance as a percentage rather than a + fraction). +

    +
    using boost::multiprecision::number;
+using boost::multiprecision::cpp_dec_float;
+using boost::multiprecision::et_off;
+
+typedef number<cpp_dec_float<50>, et_off > cpp_dec_float_50; // 50 decimal digits.
+
    +
    + + + + + +
    [Note]Note

    + that Boost.Test does not yet allow floating-point comparisons with expression + templates on, so the default expression template parameter has been replaced + by et_off. +

    +
    cpp_dec_float_50 tolerance =  3 * std::numeric_limits<cpp_dec_float_50>::epsilon();
+cpp_dec_float_50 expected = boost::math::constants::two_pi<cpp_dec_float_50>();
+cpp_dec_float_50 calculated = 2 * boost::math::constants::pi<cpp_dec_float_50>();
+using boost::test_tools::check_is_close;
+
+bool r = check_is_close(expected, calculated, tolerance);
+std::cout <<  std::boolalpha << r << std::endl;  // true
+
    +
    + + Infinity + - positive and negative +
    +

    + For floating-point types only, for which std::numeric_limits<T>::has_infinity + == true, + function std::numeric_limits<T>::infinity() + provides an implementation-defined representation for ∞. +

    +

    + The 'representation' is a particular bit pattern reserved for infinity. + For IEEE754 system (for which std::numeric_limits<T>::is_iec559 + == true) + positive + and negative infinity are assigned bit patterns for all defined + floating-point types. +

    +

    + Confusingly, the string resulting from outputting this representation, + is also implementation-defined. And the string that can be input to generate + the representation is also implementation-defined. +

    +

    + For example, the output is 1.#INF + on Microsoft systems, but inf + on most *nix platforms. +

    +

    + This implementation-defined-ness has hampered use of infinity (and NaNs) + but Boost.Math and Boost.Multiprecision work hard to provide a sensible + representation for all floating-point + types, not just the built-in types, which with the use of suitable facets + to define the input and output strings, makes it possible to use these + useful features portably and including Boost.Serialization. +

    +
    + + Not-A-Number + NaN +
    +
    + + Quiet_NaN +
    +

    + For floating-point types only, for which std::numeric_limits<T>::has_quiet_NaN + == true, + function std::numeric_limits<T>::quiet_NaN() + provides an implementation-defined representation for NaN. +

    +

    + NaNs are values to + indicate that the result of an assignment or computation is meaningless. + A typical example is 0/0 but there are many others. +

    +

    + NaNs may also be used, to represent missing values: for example, these + could, by convention, be ignored in calculations of statistics like means. +

    +

    + Many of the problems with a representation for Not-A-Number + has hampered portable use, similar to those with infinity. +

    +

    + NaN can be used with binary multiprecision types like cpp_bin_float_quad: +

    +
    using boost::multiprecision::cpp_bin_float_quad;
+
+if (std::numeric_limits<cpp_bin_float_quad>::has_quiet_NaN == true)
+{
+  cpp_bin_float_quad tolerance =  3 * std::numeric_limits<cpp_bin_float_quad>::epsilon();
+
+  cpp_bin_float_quad NaN =  std::numeric_limits<cpp_bin_float_quad>::quiet_NaN();
+  std::cout << "cpp_bin_float_quad NaN is "  << NaN << std::endl; //   cpp_bin_float_quad NaN is nan
+
+  cpp_bin_float_quad expected = NaN;
+  cpp_bin_float_quad calculated = 2 * NaN;
+  using boost::test_tools::check_is_close;
+
+  bool r = check_is_close(expected, expected, tolerance);
+  std::cout <<  std::boolalpha << r << std::endl;  // false, as expected because all comparisons with NaNs are false.
+
+  r = check_is_close(expected, calculated, tolerance);
+  std::cout <<  std::boolalpha << r << std::endl;  // false, as expected because all comparisons with NaNs are false.
+}
+else
+{
+  std::cout << "Type " << typeid(cpp_bin_float_quad).name() << " does not have NaNs!" << std::endl;
+}
+
    +

    + But using Boost.Math and suitable facets can permit portable use of both + NaNs and positive and negative infinity. +

    +

    + See boost:/libs/math/example/nonfinite_facet_sstream.cpp + and we also need +

    +
    #include <boost/math/special_functions/nonfinite_num_facets.hpp>
+
    +

    + Then we can equally well use a multiprecision type cpp_bin_float_quad: +

    +
    using boost::multiprecision::cpp_bin_float_quad;
+
+typedef cpp_bin_float_quad T;
+
+using boost::math::nonfinite_num_put;
+using boost::math::nonfinite_num_get;
+{
+  std::locale old_locale;
+  std::locale tmp_locale(old_locale, new nonfinite_num_put<char>);
+  std::locale new_locale(tmp_locale, new nonfinite_num_get<char>);
+  std::stringstream ss;
+  ss.imbue(new_locale);
+  T inf = std::numeric_limits<T>::infinity();
+  ss << inf; // Write out.
+  assert(ss.str() == "inf");
+  T r;
+  ss >> r; // Read back in.
+  assert(inf == r); // Confirms that the floating-point values really are identical.
+  std::cout << "infinity output was " << ss.str() << std::endl;
+  std::cout << "infinity input was " << r << std::endl;
+}
+
    +
    infinity output was inf
+infinity input was inf
+
    +

    + Similarly we can do the same with NaN (except that we cannot use assert) +

    +
    {
+  std::locale old_locale;
+  std::locale tmp_locale(old_locale, new nonfinite_num_put<char>);
+  std::locale new_locale(tmp_locale, new nonfinite_num_get<char>);
+  std::stringstream ss;
+  ss.imbue(new_locale);
+  T n;
+  T NaN = std::numeric_limits<T>::quiet_NaN();
+  ss << NaN; // Write out.
+  assert(ss.str() == "nan");
+  std::cout << "NaN output was " << ss.str() << std::endl;
+  ss >> n; // Read back in.
+  assert(NaN == n); // Confirms that the floating-point values really are identical.
+  std::cout << "NaN input was " << n << std::endl;
+}
+
    +

    + NaN output was nan NaN input was nan +

    +
    + + Signaling + NaN +
    +

    + For floating-point types only, for which std::numeric_limits<T>::has_signaling_NaN + == true, + function std::numeric_limits<T>::signaling_NaN() + provides an implementation-defined representation for NaN that causes a + hardware trap. It should be noted however, that at least one implementation + of this function causes a hardware trap to be triggered simply by calling + std::numeric_limits<T>::signaling_NaN(), + and not only by using the value returned. +

    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/limits/how_to_tell.html b/doc/html/boost_multiprecision/tut/limits/how_to_tell.html new file mode 100644 index 000000000..cf5ff276e --- /dev/null +++ b/doc/html/boost_multiprecision/tut/limits/how_to_tell.html @@ -0,0 +1,168 @@ + + + +How to Determine the Kind of a Number From std::numeric_limits + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +

    + Based on the information above, one can see that different kinds of numbers + can be differentiated based on the information stored in std::numeric_limits. This is in addition to + the traits class number_category + provided by this library. +

    +
    + + Integer + Types +
    +

    + For an integer type T, all of the following conditions hold: +

    +
    std::numeric_limits<T>::is_specialized == true
+std::numeric_limits<T>::is_integer == true
+std::numeric_limits<T>::is_exact == true
+std::numeric_limits<T>::min_exponent == 0
+std::numeric_limits<T>::max_exponent == 0
+std::numeric_limits<T>::min_exponent10 == 0
+std::numeric_limits<T>::max_exponent10 == 0
+
    +

    + In addition the type is signed if: +

    +
    std::numeric_limits<T>::is_signed == true
+
    +

    + If the type is arbitrary precision then: +

    +
    std::numeric_limits<T>::is_bounded == false
+
    +

    + Otherwise the type is bounded, and returns a non zero value from: +

    +
    std::numeric_limits<T>::max()
+
    +

    + and has: +

    +
    std::numeric_limits<T>::is_modulo == true
+
    +

    + if the type implements modulo arithmetic on overflow. +

    +
    + + Rational + Types +
    +

    + Rational types are just like integers except that: +

    +
    std::numeric_limits<T>::is_integer == false
+
    +
    + + Fixed + Precision Types +
    +

    + There appears to be no way to tell these apart from rational types, unless + they set: +

    +
    std::numeric_limits<T>::is_exact == false
+
    +

    + This is because these types are in essense a rational type with a fixed + denominator. +

    +
    + + Floating + Point Types +
    +

    + For a floating point type T, all of the following conditions hold: +

    +
    std::numeric_limits<T>::is_specialized == true
+std::numeric_limits<T>::is_integer == false
+std::numeric_limits<T>::is_exact == false
+std::numeric_limits<T>::min_exponent != 0
+std::numeric_limits<T>::max_exponent != 0
+std::numeric_limits<T>::min_exponent10 != 0
+std::numeric_limits<T>::max_exponent10 != 0
+
    +

    + In addition the type is signed if: +

    +
    std::numeric_limits<T>::is_signed == true
+
    +

    + And the type may be decimal or binary depending on the value of: +

    +
    std::numeric_limits<T>::radix
+
    +

    + In general, there are no arbitrary precision floating point types, and + so: +

    +
    std::numeric_limits<T>::is_bounded == false
+
    +
    + + Exact + Floating Point Types +
    +

    + Exact floating point types are a field + composed of an arbitrary precision integer scaled by an exponent. Such + types have no division operator and are the same as floating point types + except: +

    +
    std::numeric_limits<T>::is_exact == true
+
    +
    + + Complex + Numbers +
    +

    + For historical reasons, complex numbers do not specialize std::numeric_limits, instead you must inspect + std::numeric_limits<T::value_type>. +

    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/limits/limits32.html b/doc/html/boost_multiprecision/tut/limits/limits32.html new file mode 100644 index 000000000..40d4570d5 --- /dev/null +++ b/doc/html/boost_multiprecision/tut/limits/limits32.html @@ -0,0 +1,2049 @@ + + + +Numeric limits for 32-bit platform + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +

    + These tables were generated using the following program and options: +

    +
    +Program:
+ numeric_limits_qbk.cpp
+Mon Nov  4 18:09:06 2013
+BuildInfo:
+  Platform Win32
+  Compiler Microsoft Visual C++ version 10.0
+  MSVC version 160040219.
+  STL Dinkumware standard library version 520
+  Boost version 1.55.0
+
    +
    +

    Table 1.4. Integer types constants (std::numeric_limits<T>::is_integer + == true + && is_exact == true)

    +
    ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + type +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + round +

    +     		+

    + radix +

    +     		+

    + digits +

    +     		+

    + digits10 +

    +
    +

    + bool +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + no +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 1 +

    +     		+

    + 0 +

    +
    +

    + char +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 7 +

    +     		+

    + 2 +

    +
    +

    + unsigned char +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 8 +

    +     		+

    + 2 +

    +
    +

    + char16_t +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 16 +

    +     		+

    + 4 +

    +
    +

    + char32_t +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 32 +

    +     		+

    + 9 +

    +
    +

    + short +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 15 +

    +     		+

    + 4 +

    +
    +

    + unsigned short +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 16 +

    +     		+

    + 4 +

    +
    +

    + int +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 31 +

    +     		+

    + 9 +

    +
    +

    + unsigned +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 32 +

    +     		+

    + 9 +

    +
    +

    + long +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 31 +

    +     		+

    + 9 +

    +
    +

    + unsigned long +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 32 +

    +     		+

    + 9 +

    +
    +

    + long long +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 63 +

    +     		+

    + 18 +

    +
    +

    + unsigned long long +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 64 +

    +     		+

    + 19 +

    +
    +

    + int32_t +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 31 +

    +     		+

    + 9 +

    +
    +

    + uint32_t +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 32 +

    +     		+

    + 9 +

    +
    +

    + int64_t +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 63 +

    +     		+

    + 18 +

    +
    +

    + uint64_t +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 64 +

    +     		+

    + 19 +

    +
    +

    + int128_t +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 128 +

    +     		+

    + 38 +

    +
    +

    + uint128_t +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 128 +

    +     		+

    + 38 +

    +
    +

    + int256_t +

    +     		+

    + signed +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 256 +

    +     		+

    + 77 +

    +
    +

    + uint256_t +

    +     		+

    + unsigned +

    +     		+

    + bound +

    +     		+

    + modulo +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 256 +

    +     		+

    + 77 +

    +
    +

    + cpp_int +

    +     		+

    + signed +

    +     		+

    + unbounded +

    +     		+

    + no +

    +     		+

    + to zero +

    +     		+

    + 2 +

    +     		+

    + 2147483647 +

    +     		+

    + 646392383 +

    +
    +
    +
    +

    Table 1.5. Integer types functions (std::numeric_limits<T>::is_integer + == true + && std::numeric_limits<T>::min() == std::numeric_limits<T>::lowest() )

    +
    +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + function +

    +     		+

    + max +

    +     		+

    + min +

    +
    +

    + bool +

    +     		+

    + 1 +

    +     		+

    + 0 +

    +
    +

    + char +

    +     		+

    + 127 +

    +     		+

    + -128 +

    +
    +

    + unsigned char +

    +     		+

    + 255 +

    +     		+

    + 0 +

    +
    +

    + char16_t +

    +     		+

    + 65535 +

    +     		+

    + 0 +

    +
    +

    + char32_t +

    +     		+

    + 4294967295 +

    +     		+

    + 0 +

    +
    +

    + short +

    +     		+

    + 32767 +

    +     		+

    + -32768 +

    +
    +

    + unsigned short +

    +     		+

    + 65535 +

    +     		+

    + 0 +

    +
    +

    + int +

    +     		+

    + 2147483647 +

    +     		+

    + -2147483648 +

    +
    +

    + unsigned int +

    +     		+

    + 4294967295 +

    +     		+

    + 0 +

    +
    +

    + long +

    +     		+

    + 2147483647 +

    +     		+

    + -2147483648 +

    +
    +

    + unsigned long +

    +     		+

    + 4294967295 +

    +     		+

    + 0 +

    +
    +

    + long long +

    +     		+

    + 9223372036854775807 +

    +     		+

    + -9223372036854775808 +

    +
    +

    + unsigned long long +

    +     		+

    + 18446744073709551615 +

    +     		+

    + 0 +

    +
    +

    + int32_t +

    +     		+

    + 2147483647 +

    +     		+

    + -2147483648 +

    +
    +

    + int64_t +

    +     		+

    + 9223372036854775807 +

    +     		+

    + -9223372036854775808 +

    +
    +

    + int128_t +

    +     		+

    + 340282366920938463463374607431768211455 +

    +     		+

    + -340282366920938463463374607431768211455 +

    +
    +
    +
    +

    Table 1.6. Floating-point types constants (std::numeric_limits<T>::is_integer==false && is_signed==true && is_modulo==false && is_exact==false && is_bound==true)

    +
    ++++++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + type +

    +     		+

    + round +

    +     		+

    + radix +

    +     		+

    + digits +

    +     		+

    + digits10 +

    +     		+

    + max_digits10 +

    +     		+

    + min_exp +

    +     		+

    + min_exp10 +

    +     		+

    + max_exp +

    +     		+

    + max_exp10 +

    +     		+

    + tiny +

    +     		+

    + trap +

    +
    +

    + float +

    +     		+

    + to nearest +

    +     		+

    + 2 +

    +     		+

    + 24 +

    +     		+

    + 6 +

    +     		+

    + 8 +

    +     		+

    + -125 +

    +     		+

    + -37 +

    +     		+

    + 128 +

    +     		+

    + 38 +

    +     		+

    + tiny +

    +     		+

    + traps +

    +
    +

    + double +

    +     		+

    + to nearest +

    +     		+

    + 2 +

    +     		+

    + 53 +

    +     		+

    + 15 +

    +     		+

    + 17 +

    +     		+

    + -1021 +

    +     		+

    + -307 +

    +     		+

    + 1024 +

    +     		+

    + 308 +

    +     		+

    + tiny +

    +     		+

    + traps +

    +
    +

    + long double +

    +     		+

    + to nearest +

    +     		+

    + 2 +

    +     		+

    + 53 +

    +     		+

    + 15 +

    +     		+

    + 17 +

    +     		+

    + -1021 +

    +     		+

    + -307 +

    +     		+

    + 1024 +

    +     		+

    + 308 +

    +     		+

    + tiny +

    +     		+

    + traps +

    +
    +

    + cpp_dec_float_50 +

    +     		+

    + indeterminate +

    +     		+

    + 10 +

    +     		+

    + 50 +

    +     		+

    + 50 +

    +     		+

    + 80 +

    +     		+

    + -222953000 +

    +     		+

    + -67108864 +

    +     		+

    + 222953000 +

    +     		+

    + 67108864 +

    +     		+

    + no +

    +     		+

    + no +

    +
    +

    + bin_128bit_double_type +

    +     		+

    + to nearest +

    +     		+

    + 2 +

    +     		+

    + 377 +

    +     		+

    + 113 +

    +     		+

    + 115 +

    +     		+

    + -2147482894 +

    +     		+

    + -646392082 +

    +     		+

    + 2147482893 +

    +     		+

    + 646392082 +

    +     		+

    + no +

    +     		+

    + traps +

    +
    +
    +
    +

    Table 1.7. Floating-point types functions (std::numeric_limits<T>::is_integer + == false)

    +
    ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    + function +

    +     		+

    + float +

    +     		+

    + double +

    +     		+

    + long double +

    +     		+

    + cpp_dec_50 +

    +     		+

    + cpp_bin_128 +

    +
    +

    + max +

    +     		+

    + 3.40282e+038 +

    +     		+

    + 1.79769e+308 +

    +     		+

    + 1.79769e+308 +

    +     		+

    + 1e+67108865 +

    +     		+

    + 1.85906e+646456766 +

    +
    +

    + min +

    +     		+

    + 1.17549e-038 +

    +     		+

    + 2.22507e-308 +

    +     		+

    + 2.22507e-308 +

    +     		+

    + 1e-67108864 +

    +     		+

    + 5.37906e-646456767 +

    +
    +

    + epsilon +

    +     		+

    + 1.19209e-007 +

    +     		+

    + 2.22045e-016 +

    +     		+

    + 2.22045e-016 +

    +     		+

    + 1e-49 +

    +     		+

    + 6.49713e-114 +

    +
    +

    + round_error +

    +     		+

    + 0.5 +

    +     		+

    + 0.5 +

    +     		+

    + 0.5 +

    +     		+

    + 0.5 +

    +     		+

    + 0.5 +

    +
    +

    + infinity +

    +     		+

    + 1.#INF +

    +     		+

    + 1.#INF +

    +     		+

    + 1.#INF +

    +     		+

    + inf +

    +     		+

    + inf +

    +
    +

    + quiet_NaN +

    +     		+

    + 1.#QNAN +

    +     		+

    + 1.#QNAN +

    +     		+

    + 1.#QNAN +

    +     		+

    + nan +

    +     		+

    + nan +

    +
    +

    + signaling_NaN +

    +     		+

    + 1.#QNAN +

    +     		+

    + 1.#QNAN +

    +     		+

    + 1.#QNAN +

    +     		+

    + 0 +

    +     		+

    + 0 +

    +
    +

    + denorm_min +

    +     		+

    + 1.4013e-045 +

    +     		+

    + 4.94066e-324 +

    +     		+

    + 4.94066e-324 +

    +     		+

    + 0 +

    +     		+

    + 0 +

    +
    +
    +
    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/boost_multiprecision/tut/lits.html b/doc/html/boost_multiprecision/tut/lits.html index a6e5ff1af..6971ffc88 100644 --- a/doc/html/boost_multiprecision/tut/lits.html +++ b/doc/html/boost_multiprecision/tut/lits.html @@ -196,7 +196,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/misc.html b/doc/html/boost_multiprecision/tut/misc.html index 8bef10d92..7438ba6ea 100644 --- a/doc/html/boost_multiprecision/tut/misc.html +++ b/doc/html/boost_multiprecision/tut/misc.html @@ -38,7 +38,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/misc/debug_adaptor.html b/doc/html/boost_multiprecision/tut/misc/debug_adaptor.html index cc6773394..5b7f0c397 100644 --- a/doc/html/boost_multiprecision/tut/misc/debug_adaptor.html +++ b/doc/html/boost_multiprecision/tut/misc/debug_adaptor.html @@ -65,14 +65,14 @@ >:

    - debugger1 +

    Otherwise you will need to expand out the view and look at the "debug_value" member:

    - debugger2 +

    It works for all the backend types equally too, here it is inspecting a @@ -80,12 +80,12 @@ >:

    - debugger3 +

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/misc/logged_adaptor.html b/doc/html/boost_multiprecision/tut/misc/logged_adaptor.html index c9b9f6e42..278e2ab06 100644 --- a/doc/html/boost_multiprecision/tut/misc/logged_adaptor.html +++ b/doc/html/boost_multiprecision/tut/misc/logged_adaptor.html @@ -89,8 +89,6 @@ The following example demonstrates this technique in a trivial algorithm that deliberately introduces cancellation error:

    -

    -

    #include <boost/multiprecision/mpfi.hpp>
 #include <boost/multiprecision/logged_adaptor.hpp>
 #include <iostream>
@@ -139,14 +137,10 @@
    return 0;
 }
    -

    -

    When we examine program output we can clearly see that the diameter of the interval increases after each subtraction:

    -

    -

    Diameter was nan after operation: Default construct
 Diameter was 0 after operation: Assignment from arithmetic type
 Diameter was 4.33681e-18 after operation: /=
@@ -204,12 +198,10 @@
 Diameter was 0.296861 after operation: -=
 Final value was: {8.51569e-15,1.14843e-14}
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/misc/visualizers.html b/doc/html/boost_multiprecision/tut/misc/visualizers.html index d80d7a1d6..8b77d657b 100644 --- a/doc/html/boost_multiprecision/tut/misc/visualizers.html +++ b/doc/html/boost_multiprecision/tut/misc/visualizers.html @@ -33,7 +33,7 @@ partial solution in the shape of "visualizers" which provide improved views of complex data structures, these visualizers need to be added to the [Visualizer] section of autoexp.dat - located in the Common7\Packages\Debugger + located in the Common7/Packages/Debugger directory of your Visual Studio installation. The actual visualizer code is in the sandbox here - just cut and paste the code into your autoexp.dat @@ -54,7 +54,7 @@ The first visualizer provides improved views of debug_adaptor:

    - debugger1 +

    The next visualizer provides improved views of cpp_int: small numbers are @@ -65,20 +65,20 @@ Here's what it looks like for small values:

    - debugger4 +

    And for larger values:

    - debugger5 +

    There is also a ~raw child member that lets you see the actual members of the class:

    - debugger6 +

    The visualizer for cpp_dec_float @@ -87,12 +87,12 @@ data members:

    - debugger7 +

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/mixed.html b/doc/html/boost_multiprecision/tut/mixed.html index 78e2edc13..343f2c2d5 100644 --- a/doc/html/boost_multiprecision/tut/mixed.html +++ b/doc/html/boost_multiprecision/tut/mixed.html @@ -43,7 +43,7 @@
    - Mixing + Mixing Operands of Differing Precision

    @@ -109,8 +109,6 @@

    For example:

    -

    -

    #include <boost/multiprecision/cpp_int.hpp>
 
 using namespace boost::multiprecision;
@@ -132,23 +130,17 @@ 
    
 ui128 = (std::numeric_limits<uint128_t>::max)();
 std::cout << std::hex << std::showbase << multiply(ui256, ui128, ui128) << std::endl;
    -

    -

    Produces the output:

    -

    -

    0xffffffffffffffff
 0x10000000000000000
 0xFFFFFFFFFFFFFFFE0000000000000001
 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE00000000000000000000000000000001
    -

    -

    - Backends + Backends With Optimized Mixed Precision Arithmetic

    @@ -166,7 +158,7 @@

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/primetest.html b/doc/html/boost_multiprecision/tut/primetest.html index 4a6d8cba0..cbbe99614 100644 --- a/doc/html/boost_multiprecision/tut/primetest.html +++ b/doc/html/boost_multiprecision/tut/primetest.html @@ -60,8 +60,6 @@ The following example searches for a prime p for which (p-1)/2 is also probably prime:

    -

    -

    #include <boost/multiprecision/cpp_int.hpp>
 #include <boost/multiprecision/miller_rabin.hpp>
 #include <iostream>
@@ -99,12 +97,10 @@
    return 1;
 }
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/random.html b/doc/html/boost_multiprecision/tut/random.html index a5196be99..98aa087eb 100644 --- a/doc/html/boost_multiprecision/tut/random.html +++ b/doc/html/boost_multiprecision/tut/random.html @@ -39,8 +39,6 @@

    Integers with N random bits are generated using independent_bits_engine:

    -

    -

    #include <boost/multiprecision/gmp.hpp>
 #include <boost/multiprecision/random.hpp>
 
@@ -60,15 +58,11 @@
 for(unsigned i = 0; i < 10; ++i)
    std::cout << gen() << std::endl;
    -

    -

    Alternatively we can generate integers in a given range using uniform_int_distribution, this will invoke the underlying engine multiple times to build up the required number of bits in the result:

    -

    -

    #include <boost/multiprecision/gmp.hpp>
 #include <boost/multiprecision/random.hpp>
 
@@ -89,8 +83,6 @@
 for(unsigned i = 0; i < 10; ++i)
    std::cout << ui(mt) << std::endl;
    -

    -

    Floating point values in [0,1) are generated using uniform_01, the trick here is to ensure that the underlying generator produces as many @@ -98,8 +90,6 @@ this purpose, note that we also have to convert decimal digits (in the floating point type) to bits (in the random number generator):

    -

    -

    #include <boost/multiprecision/gmp.hpp>
 #include <boost/multiprecision/random.hpp>
 
@@ -119,14 +109,10 @@
 for(unsigned i = 0; i < 20; ++i)
    std::cout << uf(gen) << std::endl;
    -

    -

    Finally, we can modify the above example to produce numbers distributed according to some distribution:

    -

    -

    #include <boost/multiprecision/gmp.hpp>
 #include <boost/multiprecision/random.hpp>
 
@@ -147,12 +133,10 @@
 for(unsigned i = 0; i < 20; ++i)
    std::cout << gd(gen) << std::endl;
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rational.html b/doc/html/boost_multiprecision/tut/rational.html index 3efb62a8a..f29486d99 100644 --- a/doc/html/boost_multiprecision/tut/rational.html +++ b/doc/html/boost_multiprecision/tut/rational.html @@ -247,7 +247,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rational/br.html b/doc/html/boost_multiprecision/tut/rational/br.html index d779dba41..2f331f6f9 100644 --- a/doc/html/boost_multiprecision/tut/rational/br.html +++ b/doc/html/boost_multiprecision/tut/rational/br.html @@ -37,7 +37,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html index 00dc5396a..4f1413eb8 100644 --- a/doc/html/boost_multiprecision/tut/rational/cpp_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/cpp_rational.html @@ -81,10 +81,8 @@
    - Example: + Example:
    -

    -

    #include <boost/multiprecision/cpp_int.hpp>
 
 using namespace boost::multiprecision;
@@ -103,12 +101,10 @@ 
    
 cpp_rational w(2, 3);  // component wise constructor
 std::cout << w << std::endl; // prints 2/3
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html index 91e486db6..fa6c2db2f 100644 --- a/doc/html/boost_multiprecision/tut/rational/gmp_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/gmp_rational.html @@ -107,10 +107,8 @@
    - Example: + Example:
    -

    -

    #include <boost/multiprecision/gmp.hpp>
 
 using namespace boost::multiprecision;
@@ -134,12 +132,10 @@ 
    
 mpq_init(q);
 mpq_set(q, v.backend().data());
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rational/rational_adaptor.html b/doc/html/boost_multiprecision/tut/rational/rational_adaptor.html index ae5817f63..26623160e 100644 --- a/doc/html/boost_multiprecision/tut/rational/rational_adaptor.html +++ b/doc/html/boost_multiprecision/tut/rational/rational_adaptor.html @@ -53,7 +53,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html index f339bd516..6cc3be72f 100644 --- a/doc/html/boost_multiprecision/tut/rational/tommath_rational.html +++ b/doc/html/boost_multiprecision/tut/rational/tommath_rational.html @@ -87,10 +87,8 @@
    - Example: + Example:
    -

    -

    #include <boost/multiprecision/tommath.hpp>
 
 using namespace boost::multiprecision;
@@ -109,12 +107,10 @@ 
    
 tom_rational w(2, 3); // Component wise constructor
 std::cout << w << std::endl; // prints 2/3
    -

    -

    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/rounding.html b/doc/html/boost_multiprecision/tut/rounding.html index 14938d5f5..9626a37b6 100644 --- a/doc/html/boost_multiprecision/tut/rounding.html +++ b/doc/html/boost_multiprecision/tut/rounding.html @@ -177,7 +177,7 @@
    -
    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/html/boost_multiprecision/tut/serial.html b/doc/html/boost_multiprecision/tut/serial.html new file mode 100644 index 000000000..2f05874ab --- /dev/null +++ b/doc/html/boost_multiprecision/tut/serial.html @@ -0,0 +1,63 @@ + + + +Boost.Serialization Support + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    +
    +

    + Support for serialization comes in two forms: +

    +
    +
    + + + +
    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +

    +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/html/index.html b/doc/html/index.html index 5bea9f7d9..3e407c443 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -28,7 +28,7 @@

    Christopher Kormanyos

    -

    Copyright © 2002-2012 John Maddock and Christopher Kormanyos

    +

    Copyright © 2002-2013 John Maddock and Christopher Kormanyos

    Distributed under the Boost Software License, Version 1.0. (See accompanying @@ -55,6 +55,7 @@

    Floating Point Numbers
    +
    cpp_bin_float
    cpp_dec_float
    gmp_float
    mpfr_float
    @@ -101,6 +102,18 @@
    Generic Integer Operations
    Boost.Serialization Support
    +
    Numeric Limits
    +
    +
    std::numeric_limits<> + constants
    +
    std::numeric_limits<> + functions
    +
    Numeric limits + for 32-bit platform
    +
    How to + Determine the Kind of a Number From std::numeric_limits
    +
    +
    Input Output
    Reference
    @@ -110,6 +123,7 @@
    tom_int
    gmp_float
    mpfr_float_backend
    +
    cpp_bin_float
    cpp_dec_float
    Internal Support Code
    @@ -120,7 +134,7 @@
    The Overhead in the Number Class Wrapper
    -
    Floating Point Real +
    Floating-Point Real World Tests
    Integer Real World Tests
    @@ -139,17 +153,11 @@
    Acknowledgements
    Indexes
    -
    -
    Function Index
    -
    Class Index
    -
    Typedef Index
    -
    Index
    -
    - +

    Last revised: September 30, 2013 at 17:51:19 GMT

    Last revised: November 21, 2013 at 18:50:39 GMT
    diff --git a/doc/multiprecision.qbk b/doc/multiprecision.qbk index f098b3296..1db21309a 100644 --- a/doc/multiprecision.qbk +++ b/doc/multiprecision.qbk @@ -1,13 +1,16 @@ -[/ - Copyright 2011 John Maddock. +[/ + Copyright 2011, 2013 John Maddock. + Copyright 2013 Paul A. Bristow. + Copyright 2013 Christopher Kormanyos. + Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt). ] [library Boost.Multiprecision - [quickbook 1.5] - [copyright 2002-2012 John Maddock and Christopher Kormanyos] + [quickbook 1.7] + [copyright 2002-2013 John Maddock and Christopher Kormanyos] [purpose Multiprecision Number library] [license Distributed under the Boost Software License, Version 1.0. @@ -18,18 +21,21 @@ [/last-revision $Date: 2011-07-08 18:51:46 +0100 (Fri, 08 Jul 2011) $] ] -[include html4_symbols.qbk] +[import html4_symbols.qbk] + [import ../example/gmp_snips.cpp] [import ../example/mpfr_snips.cpp] [import ../example/mpfi_snips.cpp] [import ../example/float128_snips.cpp] [import ../example/cpp_dec_float_snips.cpp] +[import ../example/cpp_bin_float_snips.cpp] [import ../example/tommath_snips.cpp] [import ../example/cpp_int_snips.cpp] [import ../example/random_snips.cpp] [import ../example/safe_prime.cpp] [import ../example/mixed_integer_arithmetic.cpp] [import ../example/logged_adaptor.cpp] +[import ../example/numeric_limits_snips.cpp] [template mpfr[] [@http://www.mpfr.org MPFR]] [template mpfi[] [@http://perso.ens-lyon.fr/nathalie.revol/software.html MPFI]] @@ -59,6 +65,7 @@ [def __gmp_float [link boost_multiprecision.tut.floats.gmp_float gmp_float]] [def __mpf_float [link boost_multiprecision.tut.floats.gmp_float gmp_float]] [def __mpfr_float_backend [link boost_multiprecision.tut.floats.mpfr_float mpfr_float]] +[def __cpp_bin_float [link boost_multiprecision.tut.floats.cpp_bin_float cpp_bin_float]] [def __cpp_dec_float [link boost_multiprecision.tut.floats.cpp_dec_float cpp_dec_float]] [def __gmp_rational [link boost_multiprecision.tut.rational.gmp_rational gmp_rational]] [def __cpp_rational [link boost_multiprecision.tut.rational.cpp_rational cpp_rational]] @@ -94,7 +101,7 @@ interfaces to GMP, MPFR, MPIR, TomMath as well as its own collection of Boost-licensed, header-only back ends for integers, rationals and floats. In addition, user-defined back ends can be created and used with the interface of Multiprecision, -provided the class implementation adheres to the necessary +provided the class implementation adheres to the necessary [link boost_multiprecision.ref.backendconc concepts]. Depending upon the number type, precision may be arbitrarily large @@ -119,7 +126,8 @@ Should you just wish to cut to the chase and use a fully Boost-licensed number t __cpp_int for multiprecision integers, __cpp_dec_float for multiprecision floating point types and __cpp_rational for rational types. -The library is often used via one of the predefined typedefs: for example if you wanted an [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] +The library is often used via one of the predefined typedefs: for example if you wanted an +[@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] integer type using [gmp] as the underlying implementation then you could use: #include // Defines the wrappers around the GMP library's types @@ -184,7 +192,7 @@ Mixed arithmetic will fail if the conversion is either ambiguous or explicit: On compilers that support rvalue-references, class `number` is move-enabled if the underlying backend is. -In addition the non-expression template operator overloads (see below) are move aware and have overloads +In addition the non-expression template operator overloads (see below) are move aware and have overloads that look something like: template @@ -201,7 +209,7 @@ However, there are still many simple expressions such as: Which don't noticeably benefit from move support. Therefore, optimal performance comes from having both move-support, and expression templates enabled. -Note that while "moved-from" objects are left in a sane state, they have an unspecified value, and the only permitted +Note that while "moved-from" objects are left in a sane state, they have an unspecified value, and the only permitted operations on them are destruction or the assignment of a new value. Any other operation should be considered a programming error and all of our backends will trigger an assertion if any other operation is attempted. This behavior allows for optimal performance on move-construction (i.e. no allocation required, we just take ownership of the existing @@ -231,8 +239,8 @@ of references to the arguments of the function, plus some compile-time informati is. The great advantage of this method is the ['elimination of temporaries]: for example the "naive" implementation -of `operator*` above, requires one temporary for computing the result, and at least another one to return it. It's true -that sometimes this overhead can be reduced by using move-semantics, but it can't be eliminated completely. For example, +of `operator*` above, requires one temporary for computing the result, and at least another one to return it. It's true +that sometimes this overhead can be reduced by using move-semantics, but it can't be eliminated completely. For example, lets suppose we're evaluating a polynomial via Horner's method, something like this: T a[7] = { /* some values */ }; @@ -243,8 +251,8 @@ If type `T` is a `number`, then this expression is evaluated ['without creating if we were using the [mpfr_class] C++ wrapper for [mpfr] - then this expression would result in no less than 11 temporaries (this is true even though [mpfr_class] does use expression templates to reduce the number of temporaries somewhat). Had we used an even simpler wrapper around [mpfr] like [mpreal] things would have been even worse and no less that 24 temporaries -are created for this simple expression (note - we actually measure the number of memory allocations performed rather than -the number of temporaries directly, note also that the [mpf_class] wrapper that will be supplied with GMP-5.1 reduces the number of +are created for this simple expression (note - we actually measure the number of memory allocations performed rather than +the number of temporaries directly, note also that the [mpf_class] wrapper that will be supplied with GMP-5.1 reduces the number of temporaries to pretty much zero). Note that if we compile with expression templates disabled and rvalue-reference support on, then actually still have no wasted memory allocations as even though temporaries are created, their contents are moved rather than copied. @@ -318,7 +326,7 @@ One other potential pitfall that's only possible in C++11: you should never stor unless you're absolutely sure that the lifetimes of `a`, `b` and `c` will outlive that of `my_expression`. And finally... the performance improvements from an expression template library like this are often not as -dramatic as the reduction in number of temporaries would suggest. For example if we compare this library with +dramatic as the reduction in number of temporaries would suggest. For example if we compare this library with [mpfr_class] and [mpreal], with all three using the underlying [mpfr] library at 50 decimal digits precision then we see the following typical results for polynomial execution: @@ -329,7 +337,7 @@ we see the following typical results for polynomial execution: [[[mpreal]] [1.6 (0.0151s)] [9.3 (27947 total)]] ] -As you can see, the execution time increases a lot more slowly than the number of memory allocations. There are +As you can see, the execution time increases a lot more slowly than the number of memory allocations. There are a number of reasons for this: * The cost of extended-precision multiplication and division is so great, that the times taken for these tend to @@ -351,7 +359,7 @@ again, all are using [mpfr] to carry out the underlying arithmetic, and all are [table Evaluation of Boost.Math's Bessel function test data [[Library] [Relative Time] [Relative Number of Memory Allocations]] [[mpfr_float_50] [1.0 (5.78s)] [1.0 (1611963)]] -[[number, et_off>[br](but with rvalue reference support)] +[[number, et_off>[br](but with rvalue reference support)] [1.1 (6.29s)] [2.64 (4260868)]] [[[mpfr_class]] [1.1 (6.28s)] [2.45 (3948316)]] [[[mpreal]] [1.65 (9.54s)] [8.21 (13226029)]] @@ -360,7 +368,7 @@ again, all are using [mpfr] to carry out the underlying arithmetic, and all are [table Evaluation of Boost.Math's Non-Central T distribution test data [[Library][Relative Time][Relative Number of Memory Allocations]] [[number] [1.0 (263s)][1.0 (127710873)]] -[[number, et_off>[br](but with rvalue reference support)] +[[number, et_off>[br](but with rvalue reference support)] [1.0 (260s)][1.2 (156797871)]] [[[mpfr_class]] [1.1 (287s)][2.1 (268336640)]] [[[mpreal]] [1.5 (389s)][3.6 (466960653)]] @@ -373,9 +381,9 @@ with MPFR 3.0 and MPIR 2.3.0. [section:tut Tutorial] -In order to use this library you need to make two choices: +In order to use this library you need to make two choices: -* What kind of number do I want ([link boost_multiprecision.tut.ints integer], +* What kind of number do I want ([link boost_multiprecision.tut.ints integer], [link boost_multiprecision.tut.floats floating point] or [link boost_multiprecision.tut.rational rational]). * Which back-end do I want to perform the actual arithmetic (Boost-supplied, GMP, MPFR, Tommath etc)? @@ -402,10 +410,10 @@ The following back-ends provide integer arithmetic: enum cpp_integer_type { signed_magnitude, unsigned_magnitude }; enum cpp_int_check_type { checked, unchecked }; - template > class cpp_int_backend; // @@ -450,9 +458,9 @@ The following back-ends provide integer arithmetic: }} // namespaces -The `cpp_int_backend` type is normally used via one of the convenience typedefs given above. +The `cpp_int_backend` type is normally used via one of the convenience typedefs given above. -This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and +This back-end is the "Swiss Army Knife" of integer types as it can represent both fixed and [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] integer types, and both signed and unsigned types. There are five template arguments: @@ -467,7 +475,7 @@ integer types, and both signed and unsigned types. There are five template argu type `void`. Note that this parameter should not be used simply to prevent large memory allocations, not only is that role better performed by the allocator, but fixed precision integers have a tendency to allocate all of MaxBits of storage more often than one would expect.]] -[[SignType][Determines whether the resulting type is signed or not. Note that for +[[SignType][Determines whether the resulting type is signed or not. Note that for [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types this parameter must be `signed_magnitude`. For fixed precision types then this type may be either `signed_magnitude` or `unsigned_magnitude`.]] @@ -475,7 +483,7 @@ integer types, and both signed and unsigned types. There are five template argu [[Allocator][The allocator to use for dynamic memory allocation, or type `void` if MaxBits == MinBits.]] ] -When the template parameter Checked is set to `checked` then the result is a ['checked-integer], checked +When the template parameter Checked is set to `checked` then the result is a ['checked-integer], checked and unchecked integers have the following properties: [table @@ -495,7 +503,7 @@ Things you should know when using this type: * Default constructed `cpp_int_backend`s have the value zero. * Division by zero results in a `std::overflow_error` being thrown. * Construction from a string that contains invalid non-numeric characters results in a `std::runtime_error` being thrown. -* Since the precision of `cpp_int_backend` is necessarily limited when the allocator parameter is void, +* Since the precision of `cpp_int_backend` is necessarily limited when the allocator parameter is void, care should be taken to avoid numeric overflow when using this type unless you actually want modulo-arithmetic behavior. * The type uses a sign-magnitude representation internally, so type `int128_t` has 128-bits of precision plus an extra sign bit. @@ -506,10 +514,10 @@ That said it should be noted that there's no requirement for built-in types to b is the most common format by far. * Attempting to print negative values as either an Octal or Hexadecimal string results in a `std::runtime_error` being thrown, this is a direct consequence of the sign-magnitude representation. -* The fixed precision types `[checked_][u]intXXX_t` have expression template support turned off - it seems to make little +* The fixed precision types `[checked_][u]intXXX_t` have expression template support turned off - it seems to make little difference to the performance of these types either way - so we may as well have the faster compile times by turning the feature off. -* Unsigned types support subtraction - the result is "as if" a 2's complement operation had been performed as long as they are not +* Unsigned types support subtraction - the result is "as if" a 2's complement operation had been performed as long as they are not ['checked-integers] (see above). In other words they behave pretty much as a built in integer type would in this situation. So for example if we were using `uint128_t` then `uint128_t(1)-4` would result in the value `0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD` @@ -517,8 +525,8 @@ the feature off. been thrown. * Unary negation of unsigned types results in a compiler error (static assertion). * This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. -* When used at fixed precision, the size of this type is always one machine word larger than you would expect for an N-bit integer: -the extra word stores both the sign, and how many machine words in the integer are actually in use. +* When used at fixed precision, the size of this type is always one machine word larger than you would expect for an N-bit integer: +the extra word stores both the sign, and how many machine words in the integer are actually in use. The latter is an optimisation for larger fixed precision integers, so that a 1024-bit integer has almost the same performance characteristics as a 128-bit integer, rather than being 4 times slower for addition and 16 times slower for multiplication (assuming the values involved would always fit in 128 bits). @@ -527,7 +535,7 @@ an integer type wide enough for the "worst case scenario" with only minor perfor the arithmetic could in fact be done with a narrower type. * When used at fixed precision and MaxBits is smaller than the number of bits in the largest native integer type, then internally `cpp_int_backend` switches to a "trivial" implementation where it is just a thin wrapper around a single -integer. Note that it will still be slightly slower than a bare native integer, as it emulates a +integer. Note that it will still be slightly slower than a bare native integer, as it emulates a signed-magnitude representation rather than simply using the platforms native sign representation: this ensures there is no step change in behavior as a cpp_int grows in size. * Fixed precision `cpp_int`'s have some support for `constexpr` values and user-defined literals, see @@ -568,10 +576,10 @@ Things you should know when using this type: * No changes are made to the GMP library's global settings - so you can safely mix this type with existing code that uses [gmp]. * Default constructed `gmp_int`s have the value zero (this is GMP's default behavior). -* Formatted IO for this type does not support octal or hexadecimal notation for negative values, +* Formatted IO for this type does not support octal or hexadecimal notation for negative values, as a result performing formatted output on this type when the argument is negative and either of the flags `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. -* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid integer. * Division by zero results in a `std::overflow_error` being thrown. * Although this type is a wrapper around [gmp] it will work equally well with [mpir]. Indeed use of [mpir] @@ -606,10 +614,10 @@ Things you should know when using this type: rather strange beast as it's a signed type that is not a 2's complement type. As a result the bitwise operations `| & ^` will throw a `std::runtime_error` exception if either of the arguments is negative. Similarly the complement operator`~` is deliberately not implemented for this type. -* Formatted IO for this type does not support octal or hexadecimal notation for negative values, +* Formatted IO for this type does not support octal or hexadecimal notation for negative values, as a result performing formatted output on this type when the argument is negative and either of the flags `std::ios_base::oct` or `std::ios_base::hex` are set, will result in a `std::runtime_error` will be thrown. -* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid integer. * Division by zero results in a `std::overflow_error` being thrown. @@ -641,12 +649,95 @@ The following back-ends provide floating point arithmetic: [table [[Backend Type][Header][Radix][Dependencies][Pros][Cons]] +[[`cpp_bin_float`][boost/multiprecision/cpp_bin_float.hpp][2][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] [[`cpp_dec_float`][boost/multiprecision/cpp_dec_float.hpp][10][None][Header only, all C++ implementation. Boost licence.][Approximately 2x slower than the [mpfr] or [gmp] libraries.]] [[`mpf_float`][boost/multiprecision/gmp.hpp][2][[gmp]][Very fast and efficient back-end.][Dependency on GNU licensed [gmp] library.]] [[`mpfr_float`][boost/multiprecision/mpfr.hpp][2][[gmp] and [mpfr]][Very fast and efficient back-end, with its own standard library implementation.][Dependency on GNU licensed [gmp] and [mpfr] libraries.]] [[`float128`][boost/multiprecision/float128.hpp][2][Either [quadmath] or the Intel C++ Math library.][Very fast and efficient back-end for 128-bit floating point values (113-bit mantissa, equivalent to FORTRAN's QUAD real)][Depends on the compiler being either recent GCC or Intel C++ versions.]] ] +[section:cpp_bin_float cpp_bin_float] + +`#include ` + + namespace boost{ namespace multiprecision{ + + enum digit_base_type + { + digit_base_2 = 2, + digit_base_10 = 10 + }; + + template + class cpp_bin_float; + + typedef number > cpp_bin_float_50; + typedef number > cpp_bin_float_100; + + typedef number, et_off> cpp_bin_float_single; + typedef number, et_off> cpp_bin_float_double; + typedef number, et_off> cpp_bin_float_double_extended; + typedef number, et_off> cpp_bin_float_quad; + + }} // namespaces + +The `cpp_bin_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free) +floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with +much greater precision. + +Type `cpp_bin_float` can be used at fixed precision by specifying a non-zero `Digits` template parameter. +The typedefs `cpp_bin_float_50` and `cpp_bin_float_100` provide arithmetic types at 50 and 100 decimal digits precision +respectively. + +Optionally, you can specify whether the precision is specified in decimal digits or binary bits - for example +to declare a `cpp_bin_float` with exactly the same precision as `double` one would use +`number >`. The typedefs `cpp_bin_float_single`, `cpp_bin_float_double`, +`cpp_bin_float_quad` and `cpp_bin_float_double_extended` provide +software analogues of the IEEE single, double and quad float data types, plus the Intel-extended-double type respectively. +Note that while these types are functionally equivalent to the native IEEE types, but they do not have the same size +or bit-layout as true IEEE compatible types. + +Normally `cpp_bin_float` allocates no memory: all of the space required for its digits are allocated +directly within the class. As a result care should be taken not to use the class with too high a digit count +as stack space requirements can grow out of control. If that represents a problem then providing an allocator +as a template parameter causes `cpp_bin_float` to dynamically allocate the memory it needs: this +significantly reduces the size of `cpp_bin_float` and increases the viable upper limit on the number of digits +at the expense of performance. However, please bear in mind that arithmetic operations rapidly become ['very] expensive +as the digit count grows: the current implementation really isn't optimized or designed for large digit counts. +Note that since the actual type of the objects allocated +is completely opaque, the suggestion would be to use an allocator with `void` `value_type`, for example: +`number > >`. + +The final template parameters determine the type and range of the exponent: parameter `Exponent` can be +any signed integer type, but note that `MinExponent` and `MaxExponent` can not go right up to the limits +of the `Exponent` type as there has to be a little extra headroom for internal calculations. You will +get a compile time error if if this is the case. In addition if MinExponent or MaxExponent are zero, then +the library will choose suitable values that are as large as possible given the constraints of the type +and need for extra headhoom for internal calculations. + +There is full standard library and `numeric_limits` support available for this type. + +Things you should know when using this type: + +* Default constructed `cpp_bin_float`s have a value of zero. +* The radix of this type is 2, even when the precision is specified as decimal digits. +* The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, +and a NaN is generated for any mathematically undefined operation. +* There is a `std::numeric_limits` specialisation for this type. +* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - +for example you can convert from `number >` to `number >`. +Narrowing conversions round to nearest and are `explicit`. +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +as a valid floating point number. +* All arithmetic operations are correctly rounded to nearest. String comversions and the `sqrt` function +are also correctly rounded, but transcendental functions (sin, cos, pow, exp etc) are not. + +[h5 cpp_bin_float example:] + +[cpp_bin_float_eg] + +[endsect] + [section:cpp_dec_float cpp_dec_float] `#include ` @@ -662,14 +753,14 @@ The following back-ends provide floating point arithmetic: }} // namespaces The `cpp_dec_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free) -floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with +floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. -Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. +Type `cpp_dec_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter. The typedefs `cpp_dec_float_50` and `cpp_dec_float_100` provide arithmetic types at 50 and 100 decimal digits precision respectively. Optionally, you can specify an integer type to use for the exponent, this defaults to a 32-bit integer type which is more than large enough for the vast majority of use cases, but larger types such as `long long` can also be specified -if you need a truly huge exponent range. In any case the ExponentType must be a built in signed integer type at least 2 bytes +if you need a truly huge exponent range. In any case the ExponentType must be a built in signed integer type at least 2 bytes and 16-bits wide. Normally `cpp_dec_float` allocates no memory: all of the space required for its digits are allocated @@ -691,15 +782,15 @@ Normally these should not be visible to the user. * The type supports both infinities and NaN's. An infinity is generated whenever the result would overflow, and a NaN is generated for any mathematically undefined operation. * There is a `std::numeric_limits` specialisation for this type. -* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - +* Any `number` instantiated on this type, is convertible to any other `number` instantiated on this type - for example you can convert from `number >` to `number >`. Narrowing conversions are truncating and `explicit`. * Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid floating point number. * The actual precision of a `cpp_dec_float` is always slightly higher than the number of digits specified in -the template parameter, actually how much higher is an implementation detail but is always at least 8 decimal +the template parameter, actually how much higher is an implementation detail but is always at least 8 decimal digits. -* Operations involving `cpp_dec_float` are always truncating. However, note that since their are guard digits +* Operations involving `cpp_dec_float` are always truncating. However, note that since their are guard digits in effect, in practice this has no real impact on accuracy for most use cases. [h5 cpp_dec_float example:] @@ -726,7 +817,7 @@ in effect, in practice this has no real impact on accuracy for most use cases. }} // namespaces The `gmp_float` back-end is used in conjunction with `number` : it acts as a thin wrapper around the [gmp] `mpf_t` -to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. Type `gmp_float` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or @@ -754,13 +845,13 @@ existing [gmp] code. * It is not possible to round-trip objects of this type to and from a string and get back exactly the same value. This appears to be a limitation of [gmp]. * Since the underlying [gmp] types have no notion of infinities or NaN's, care should be taken -to avoid numeric overflow or division by zero. That latter will result in a std::overflow_error being thrown, +to avoid numeric overflow or division by zero. That latter will result in a std::overflow_error being thrown, while generating excessively large exponents may result in instability of the underlying [gmp] -library (in testing, converting a number with an excessively large or small exponent +library (in testing, converting a number with an excessively large or small exponent to a string caused [gmp] to segfault). * This type can equally be used with [mpir] as the underlying implementation - indeed that is the recommended option on Win32. -* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid floating point number. * Division by zero results in a `std::overflow_error` being thrown. @@ -797,7 +888,7 @@ as a valid floating point number. }} // namespaces The `mpfr_float_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpfr] `mpfr_t` -to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision. Type `mpfr_float_backend` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or @@ -813,7 +904,7 @@ within `mpfr_float_backend`). The latter option can result in significantly fas expense of growing the size of `mpfr_float_backend`. It can only be used at fixed precision, and should only be used for lower digit counts. Note that we can not guarantee that using `allocate_stack` won't cause any calls to mpfr's allocation routines, as mpfr may call these inside it's own code. -The following table gives an idea of the performance tradeoff's at 50 decimal digits +The following table gives an idea of the performance tradeoff's at 50 decimal digits precision[footnote Compiled with VC++10 and /Ox, with MPFR-3.0.0 and MPIR-2.3.0]: [table @@ -843,7 +934,7 @@ Things you should know when using this type: [mpfr] or [gmp] code. * The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. * This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. -* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid floating point number. * Division by zero results in an infinity. @@ -866,17 +957,17 @@ as a valid floating point number. }} // namespaces The `float128` number type is a very thin wrapper around GCC's `__float128` or Intel's `_Quad` data types -and provides an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +and provides an real-number type that is a drop-in replacement for the native C++ floating-point types, but with a 113 bit mantissa, and compatible with FORTRAN's 128-bit QUAD real. All the usual standard library and `numeric_limits` support are available, performance should be equivalent -to the underlying native types: for example the LINPACK benchmarks for GCC's `__float128` and +to the underlying native types: for example the LINPACK benchmarks for GCC's `__float128` and `boost::multiprecision::float128` both achieved 5.6 MFLOPS[footnote On 64-bit Ubuntu 11.10, GCC-4.8.0, Intel Core 2 Duo T5800.]. As well as the usual conversions from arithmetic and string types, instances of `float128` are copy constructible and assignable from GCC's `__float128` and Intel's `_Quad` data types. -It's also possible to access the underlying `__float128` or `_Quad` type via the `data()` member +It's also possible to access the underlying `__float128` or `_Quad` type via the `data()` member function of `float128_backend`. Things you should know when using this type: @@ -965,7 +1056,7 @@ There is one currently only one interval number type supported - [mpfi]. }} // namespaces The `mpfi_float_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpfi] `mpfi_t` -to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with +to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with much greater precision and implementing interval arithmetic. Type `mpfi_float_backend` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or @@ -992,83 +1083,83 @@ Things you should know when using this type: [mpfr] or [gmp] code. * The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32. * This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware. -* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted +* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted as a valid floating point number. * Division by zero results in an infinity. There are some additional non member functions for working on intervals: - template - number, ExpressionTemplates> lower(const number, ExpressionTemplates>& val); + template + number, ExpressionTemplates> lower(const number, ExpressionTemplates>& val); Returns the lower end of the interval. - template - number, ExpressionTemplates> upper(const number, ExpressionTemplates>& val); + template + number, ExpressionTemplates> upper(const number, ExpressionTemplates>& val); Returns the upper end of the interval. - template - number, ExpressionTemplates> median(const number, ExpressionTemplates>& val); + template + number, ExpressionTemplates> median(const number, ExpressionTemplates>& val); Returns the mid point of the interval. - template - number, ExpressionTemplates> width(const number, ExpressionTemplates>& val); + template + number, ExpressionTemplates> width(const number, ExpressionTemplates>& val); Returns the absolute width of the interval. - template - number, ExpressionTemplates> intersect( - const number, ExpressionTemplates>& a, - const number, ExpressionTemplates>& b); + template + number, ExpressionTemplates> intersect( + const number, ExpressionTemplates>& a, + const number, ExpressionTemplates>& b); -Returns the interval which is the intersection of the ['a] and ['b]. Returns an +Returns the interval which is the intersection of the ['a] and ['b]. Returns an unspecified empty interval if there is no such intersection. - template - number, ExpressionTemplates> hull( - const number, ExpressionTemplates>& a, - const number, ExpressionTemplates>& b); + template + number, ExpressionTemplates> hull( + const number, ExpressionTemplates>& a, + const number, ExpressionTemplates>& b); Returns the interval which is the union of ['a] and ['b]. - template - bool overlap(const number, ExpressionTemplates>& a, - const number, ExpressionTemplates>& b); + template + bool overlap(const number, ExpressionTemplates>& a, + const number, ExpressionTemplates>& b); Returns `true` only if the intervals ['a] and ['b] overlap. - template - bool in(const number, ExpressionTemplates1>& a, - const number, ExpressionTemplates2>& b); + template + bool in(const number, ExpressionTemplates1>& a, + const number, ExpressionTemplates2>& b); Returns `true` only if point ['a] is contained within the interval ['b]. - template - bool zero_in(const number, ExpressionTemplates>& a); + template + bool zero_in(const number, ExpressionTemplates>& a); Returns `true` only if the interval ['a] contains the value zero. - template - bool subset(const number, ExpressionTemplates>& a, - const number, ExpressionTemplates>& b); + template + bool subset(const number, ExpressionTemplates>& a, + const number, ExpressionTemplates>& b); Returns `true` only if ['a] is a subset of ['b]. - template - bool proper_subset(const number, ExpressionTemplates>& a, - const number, ExpressionTemplates>& b); + template + bool proper_subset(const number, ExpressionTemplates>& a, + const number, ExpressionTemplates>& b); Returns `true` only if ['a] is a proper subset of ['b]. - template - bool empty(const number, ExpressionTemplates>& a); + template + bool empty(const number, ExpressionTemplates>& a); Returns `true` only if ['a] is an empty interval, equivalent to `upper(a) < lower(a)`. - template - bool singleton(const number, ExpressionTemplates>& a); + template + bool singleton(const number, ExpressionTemplates>& a); Returns `true` if `lower(a) == upper(a)`. @@ -1192,7 +1283,7 @@ interpreted as a valid rational number. }} // namespaces -The `tommath_rational` back-end is used via the typedef `boost::multiprecision::tom_rational`. It acts as a thin wrapper around +The `tommath_rational` back-end is used via the typedef `boost::multiprecision::tom_rational`. It acts as a thin wrapper around `boost::rational` to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision. @@ -1234,7 +1325,7 @@ Note that using the library in this way largely negates the effect of the expres namespace boost{ namespace multiprecision{ - template + template class rational_adpater; }} @@ -1285,7 +1376,7 @@ Backend types listed in this section are predominantly designed to aid debugging }} // namespaces -The `logged_adaptor` type is used in conjunction with `number` and some other backend type: it acts as a thin wrapper around +The `logged_adaptor` type is used in conjunction with `number` and some other backend type: it acts as a thin wrapper around some other backend to class `number` and logs all the events that take place on that object. Before any number operation takes place, it calls `log_prefix_event` with the arguments to the operation (up to 4), plus a string describing the operation. Then after the operation it calls `log_postfix_event` with the result of the operation, plus a string describing the operation. @@ -1323,7 +1414,7 @@ When we examine program output we can clearly see that the diameter of the inter }} // namespaces -The `debug_adaptor` type is used in conjunction with `number` and some other backend type: it acts as a thin wrapper around +The `debug_adaptor` type is used in conjunction with `number` and some other backend type: it acts as a thin wrapper around some other backend to class `number` and intercepts all operations on that object storing the result as a string within itself. This type provides `numeric_limits` support whenever the template argument Backend does so. @@ -1354,8 +1445,8 @@ It works for all the backend types equally too, here it is inspecting a `number< Let's face it debugger multiprecision numbers is hard - simply because we can't easily inspect the value of the numbers. Visual C++ provides a partial solution in the shape of "visualizers" which provide improved views of complex data structures, -these visualizers need to be added to the `[Visualizer]` section of `autoexp.dat` located in the `Common7\Packages\Debugger` -directory of your Visual Studio installation. The actual visualizer code is in the sandbox +these visualizers need to be added to the `[Visualizer]` section of `autoexp.dat` located in the `Common7/Packages/Debugger` +directory of your Visual Studio installation. The actual visualizer code is in the sandbox [@https://svn.boost.org/svn/boost/sandbox/boost_docs/subprojects/DebuggerVisualizers/multiprecision.vis.txt here] - just cut and paste the code into your `autoexp.dat` file. @@ -1367,7 +1458,7 @@ The first visualizer provides improved views of `debug_adaptor`: [$../debugger1.png] The next visualizer provides improved views of cpp_int: small numbers are displayed as actual values, while larger numbers are -displayed as an array of hexadecimal parts, with the most significant part first. +displayed as an array of hexadecimal parts, with the most significant part first. Here's what it looks like for small values: @@ -1418,7 +1509,7 @@ In particular: Additional conversions may be supported by particular backends. -* A `number` can be converted to any built in type, via an explicit conversion operator: +* A `number` can be converted to any built in type, via an explicit conversion operator: this functionality is only available on compilers supporting C++11's explicit conversion syntax. mpz_int z(2); @@ -1452,7 +1543,7 @@ are not lossy: i *= 3.14; // Error, no *= operator will be found. * Any number type can be streamed to and from the C++ iostreams: - + cpp_dec_float_50 df = "3.14159265358979323846264338327950288419716939937510"; // Now print at full precision: @@ -1473,7 +1564,7 @@ loss of precision is involved, and explicit if it is: mpz_int z = 0; mpf_float f = z; // OK, GMP handles this conversion natively, and it's not lossy and therefore implicit - + mpf_float_50 f50 = 2; f = f50; // OK, conversion from fixed to variable precision, f will have 50 digits precision. f50 = f; // Error, conversion from variable to fixed precision is potentially lossy, explicit cast required. @@ -1481,7 +1572,7 @@ loss of precision is involved, and explicit if it is: * Some interconversions between number types are completely generic, and are always available, albeit the conversions are always ['explicit]: cpp_int cppi(2); - // We can always convert between numbers of the same category - + // We can always convert between numbers of the same category - // int to int, rational to rational, or float to float, so this is OK // as long as we use an explicit conversion: mpz_int z(cppi); @@ -1554,8 +1645,8 @@ uses the Miller-Rabin algorithm straight out of Knuth Vol 2, which recommends 25 trials for a pretty strong likelihood that /n/ is prime. The third optional argument is for a Uniform Random Number Generator from Boost.Random. When not provided the `mt19937` -generator is used. Note that when producing random primes then you should probably use a different random number generator -to produce candidate prime numbers for testing, than is used internally by `miller_rabin_test` for determining +generator is used. Note that when producing random primes then you should probably use a different random number generator +to produce candidate prime numbers for testing, than is used internally by `miller_rabin_test` for determining whether the value is prime. It also helps of course to seed the generators with some source of randomness. The following example searches for a prime `p` for which `(p-1)/2` is also probably prime: @@ -1566,19 +1657,19 @@ The following example searches for a prime `p` for which `(p-1)/2` is also proba [section:lits Literal Types and `constexpr` Support] -[note The features described in this section make heavy use of C++11 language features, currently +[note The features described in this section make heavy use of C++11 language features, currently (as of May 2013) only GCC-4.7 and later, and Clang 3.3 and later have the support required to make these features work.] -There is limited support for `constexpr` and user-defined literals in the library, currently the +There is limited support for `constexpr` and user-defined literals in the library, currently the `number` front end supports `constexpr` -on default construction and all forwarding constructors, but not on any of the non-member operators. So if -some type `B` is a literal type, then `number` is also a literal type, and you will be able to +on default construction and all forwarding constructors, but not on any of the non-member operators. So if +some type `B` is a literal type, then `number` is also a literal type, and you will be able to compile-time-construct such a type from any literal that `B` is compile-time-constructible from. However, you will not be able to perform compile-time arithmetic on such types. Currently the only backend type provided by the library that is also a literal type are instantiations -of `cpp_int_backend` where the Allocator parameter is type `void`, and the Checked parameter is +of `cpp_int_backend` where the Allocator parameter is type `void`, and the Checked parameter is `boost::multiprecision::unchecked`. For example: @@ -1681,7 +1772,7 @@ The following table summarises the situation for conversions from native types: [section:mixed Mixed Precision Arithmetic] -Mixed precision arithmetic is fully supported by the library. +Mixed precision arithmetic is fully supported by the library. There are two different forms: @@ -1710,7 +1801,7 @@ For example: [h4 Operands of the Same Precision] -Sometimes you want to apply an operator to two arguments of the same precision in +Sometimes you want to apply an operator to two arguments of the same precision in such a way as to obtain a result of higher precision. The most common situation occurs with fixed precision integers, where you want to multiply two N-bit numbers to obtain a 2N-bit result. This is supported in this library by the following @@ -1726,7 +1817,7 @@ free functions: ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); These functions apply the named operator to the arguments ['a] and ['b] and store the -result in ['result], returning ['result]. In all cases they behave "as if" +result in ['result], returning ['result]. In all cases they behave "as if" arguments ['a] and ['b] were first promoted to type `ResultType` before applying the operator, though particular backends may well avoid that step by way of an optimization. @@ -1744,9 +1835,9 @@ Produces the output: [h4 Backends With Optimized Mixed Precision Arithmetic] -The following backends have at least some direct support for mixed precision arithmetic, +The following backends have at least some direct support for mixed precision arithmetic, and therefore avoid creating unnecessary temporaries when using the interfaces above. -Therefore when using these types it's more efficient to use mixed precision arithmetic, +Therefore when using these types it's more efficient to use mixed precision arithmetic, than it is to explicitly cast the operands to the result type: __mpfr_float_backend, __mpf_float, __cpp_int. @@ -1755,7 +1846,7 @@ __mpfr_float_backend, __mpf_float, __cpp_int. [section:gen_int Generic Integer Operations] -All of the [link boost_multiprecision.ref.number.integer_functions non-member integer operations] are overloaded for the +All of the [link boost_multiprecision.ref.number.integer_functions non-member integer operations] are overloaded for the built in integer types in ``. Where these operations require a temporary increase in precision (such as for powm), then @@ -1862,6 +1953,861 @@ support which requires the underlying backend to be serializable. [endsect] +[section:limits Numeric Limits] + +Boost.Multiprecision tries hard to implement `std::numeric_limits` for all types +as far as possible and meaningful because experience with Boost.Math +has shown that this aids portability. + +The [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3690.pdf C++ standard library] +defines `std::numeric_limits` in section 18.3.2. + +This in turn refers to the C standard +[@http://www.open-std.org/jtc1/sc22/wg11/docs/n507.pdf SC22/WG11 N507 DRAFT INTERNATIONAL ISO/IEC STANDARD + WD 10967-1] +Information technology Language independent arithmetic Part 1: Integer and Floating point arithmetic. + +That C Standard in turn refers to + +[@http://754r.ucbtest.org/standards/754.pdf IEEE754 IEEE Standard for Binary +Floating-Point Arithmetic] + +There is a useful summary at +[@http://www.cplusplus.com/reference/limits/numeric_limits/ C++ reference]. + +The chosen backend often determines how completely `std::numeric_limits` is available. + +Compiler options, processor type, and definition of macros or assembler instructions to control denormal numbers will alter +the values in the tables given below. + +[warning GMP's `mpf_t` does not have a concept of overflow: +operations that lead to overflow eventually run of out of resources +and terminate with stack overflow (often after several seconds).] + +[section:constants std::numeric_limits<> constants] + + +[h4 is_specialized] + +`true` for all arithmetic types (integer, floating and fixed-point) +for which `std::numeric_limits::numeric_limits` is specialized. + +A typical test is + + if (std::numeric_limits::is_specialized == false) + { + std::cout << "type " << typeid(T).name() << " is not specialized for std::numeric_limits!" << std::endl; + // ... + } + +Typically `numeric_limits::is_specialized` is `true` for all `T` where the compile-time constant +members of `numeric_limits` are indeed known at compile time, and don't vary at runtime. For example +floating point types with runtime-variable precision such as `mpfr_float` have no `numeric_limits` +specialization as it would be impossible to define all the members at compile time. In contrast +the precision of a type such as `mpfr_float_50` is known at compile time, and so it ['does] have a +`numeric_limits` specialization. + +Note that not all the `std::numeric_limits` member constants and functions are meaningful for all user-defined types (UDT), +such as the decimal and binary multiprecision types provided here. More information on this is given in the sections below. + +[h4 infinity] + +For floating-point types, [infin] is defined wherever possible, +but clearly infinity is meaningless for __arbitrary_precision arithmetic backends, +and there is one floating point type (GMP's `mpf_t`, see __mpf_float) which has no notion +of infinity or NaN at all. + +A typical test whether infinity is implemented is + + if(std::numeric_limits::has_infinity) + { + std::cout << std::numeric_limits::infinity() << std::endl; + } + +and using tests like this is strongly recommended to improve portability. + +If the backend is switched to a type that does not support infinity then, +without checks like this, there will be trouble. + +[h4 is_signed] + +`std::numeric_limits::is_signed == true` if the type `T` is signed. + +For built-in binary types, the sign is held in a single bit, +but for other types (cpp_dec_float and cpp_bin_float) +it may be a separate storage element, usually `bool`. + +[h4 is_exact] + +`std::numeric_limits::is_exact == true` if type T uses exact representations. + +This is defined as `true` for all integer types and `false` for floating-point types. + +[@http://stackoverflow.com/questions/14203654/stdnumeric-limitsis-exact-what-is-a-usable-definition A usable definition] +has been discussed. + +ISO/IEC 10967-1, Language independent arithmetic, noted by the C++ Standard defines + + A floating point type F shall be a finite subset of [real]. + +The important practical distinction is that all integers (up to `max()`) can be stored exactly. + +[@http://en.wikipedia.org/wiki/Rational_number Rational] +types using two integer types are also exact. + +Floating-point types [*cannot store all real values] +(those in the set of [real]) [*exactly]. +For example, 0.5 can be stored exactly in a binary floating-point, but 0.1 cannot. +What is stored is the nearest representable real value, that is, rounded to nearest. + +Fixed-point types (usually decimal) are also defined as exact, in that they only +store a [*fixed precision], so half cents or pennies (or less) cannot be stored. +The results of computations are rounded up or down, +just like the result of integer division stored as an integer result. + +There are number of proposals to +[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html +add Decimal Floating Point Support to C++]. + +[@http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2009/n2849.pdf Decimal TR]. + +And also +[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3352.html +C++ Binary Fixed-Point Arithmetic]. + +[h4 is_bounded] + +`std::numeric_limits::is_bounded == true` if the set of values represented by the type `T` is finite. + +This is `true` for all built-in integer, fixed and floating-point types, +and most multi-precision types. + +It is only `false` for a few __arbitrary_precision types like `cpp_int`. + +Rational and fixed-exponent representations are exact but not integer. + +[h4 is_modulo] + +`std::numeric_limits::is_modulo` is defined as `true` if adding two positive values of type T +can yield a result less than either value. + +`is_modulo == true` means that the type does not overflow, but, for example, +'wraps around' to zero, when adding one to the `max()` value. + +For most built-in integer types, `std::numeric_limits<>::is_modulo` is `true`. + +`bool` is the only exception. + +The modulo behaviour is sometimes useful, +but also can be unexpected, and sometimes undesired, behaviour. + +Overflow of signed integers can be especially unexpected, +possibly causing change of sign. + +Boost.Multiprecision integer type `cpp_int` is not modulo +because as an __arbitrary_precision types, +it expands to hold any value that the machine resources permit. + +However fixed precision __cpp_int's may be modulo if they are unchecked +(i.e. they behave just like built in integers), but not if they are checked +(overflow causes an exception to be raised). + +Built-in and multi-precision floating-point types are normally not modulo. + +Where possible, overflow is to `std::numeric_limits<>::infinity()`, +provided `std::numeric_limits<>::has_infinity == true`. + +[h4 radix] + +Constant `std::numeric_limits::radix` returns either 2 (for built-in and binary types) +or 10 (for decimal types). + +[h4 digits] + +The number of `radix` digits that be represented without change: + +* for integer types, the number of [*non-sign bits] in the significand. +* for floating types, the number of [*radix digits] in the significand. + +The values include any implicit bit, so for example, for the ubiquious +`double` using 64 bits +([@http://en.wikipedia.org/wiki/Double_precision_floating-point_format IEEE binary64 ]), +`digits` == 53, even though there are only 52 actual bits of the significand stored in the representation. +The value of `digits` reflects the fact that there is one implicit bit which is always set to 1. + +The Boost.Multiprecision binary types do not use an implicit bit, so the +`digits` member reflects exactly how many bits of precision were requested: + + typedef number > float64; + typedef number > float128; + std::numeric_limits::digits == 53. + std::numeric_limits::digits == 113. + +For the most common case of `radix == 2`, +`std::numeric_limits::digits` is the number of bits in the representation, +not counting any sign bit. + +For a decimal integer type, when `radix == 10`, it is the number of decimal digits. + +[h4 digits10] + +Constant `std::numeric_limits::digits10` returns the number of +decimal digits that can be represented without change or loss. + +For example, `numeric_limits::digits10` is 2. + +This somewhat inscrutable definition means that an `unsigned char` +can hold decimal values `0..99` +without loss of precision or accuracy, usually from truncation. + +Had the definition been 3 then that would imply it could hold 0..999, +but as we all know, an 8-bit `unsigned char` can only hold 0..255, +and an attempt to store 256 or more will involve loss or change. + +For bounded integers, it is thus [*one less] than number of decimal digits +you need to display the biggest integer `std::numeric_limits::max()`. +This value can be used to predict the layout width required for + +[digits10_1] + +For example, `unsigned short` is often stored in 16 bits, +so the maximum value is 0xFFFF or 65535. + +[digits10_2] + + +For bounded floating-point types, +if we create a `double` with a value with `digits10` (usually 15) decimal digits, +`1e15` or `1000000000000000` : + +[digits10_3] + +and we can increment this value to `1000000000000001` +as expected and show the difference too. + +But if we try to repeat this with more than `digits10` digits, + +[digits10_4] + +then we find that when we add one it has no effect, +and display show that there is loss of precision. See +[@http://en.wikipedia.org/wiki/Loss_of_significance Loss of significance or cancellation error]. + +So `digits10` is the number of decimal digits [*guaranteed] to be correct. + +For example, 'round-tripping' for `double`: + +* If a decimal string with at most `digits10`( == 15) significant decimal digits +is converted to `double` and then converted back to the +same number of significant decimal digits, +then the final string will match the original 15 decimal digit string. +* If a `double` floating-point number is converted to a decimal string +with at least 17 decimal digits +and then converted back to `double`, +then the result will be binary indentical to the original `double` value. + +For most purposes, you will much more likely want +`std::numeric_limits<>::max_digits10`, +the number of decimal digits that ensure that a change of one least significant bit (ULP) +produces a different decimal digits string. + +For nearly all floating-point types, `max_digits10` is `digits10+2`, +but you should use `max_digits10` where possible. + +If `max_digits10` is not available, you should using the +[@http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF Kahan formula for floating-point type T] + + max_digits10 = std::numeric_limits::digits * 3010U/10000U; + +The factor is log[sub 10](2) = 0.3010 +but must be evaluated at compile time using only integers. + +(See also +[@http://www.loria.fr/~zimmerma/mca/mca-cup-0.5.9.pdf Richard P. Brent and Paul Zimmerman, Modern Computer Arithmetic] +Equation 3.8 on page 116.). + +The extra two (or 3) least significant digits are 'noisy' and may be junk, +but if you want to 'round-trip' - printing a value out and reading it back in - +you must use `os.precision(std::numeric_limits::max_digits10)`. +For at least one popular compiler, you must also use `std::scientific` format. + +[h4 max_digits10] + +`std::numeric_limits::max_digits10` was added for floating-point +because `digits10` decimal digits are insufficient to show +a least significant bit (ULP) change giving puzzling displays like + + 0.666666666666667 != 0.666666666666667 + +from failure to 'round-trip', for example: + +[max_digits10_2] + +If you wish to ensure that a change of one least significant bit (ULP) +produces a different decimal digits string, +then `max_digits10` is the precision to use. + +For example: + +[max_digits10_3] + +will display [pi] to the maximum possible precision using a `double`. + +[max_digits10_4] + +For integer types, `max_digits10` is implementation-dependant, +but is usually `digits10 + 2`. +This is the output field width required for the maximum value of the type T +`std::numeric_limits::max()` including a sign and a space. + +So this will produce neat columns. + + std::cout << std::setw(std::numeric_limits::max_digits10) ... + +[note For Microsoft Visual Studio 2010, +`std::numeric_limits::max_digits10` is wrongly defined as 8. It should be 9.] + +[note For Microsoft Visual Studio, and default float format, a small range of values +approximately 0.0001 to 0.004, with exponent values of 3f2 to 3f6, +are wrongly input by one least significant bit, +probably every third value of significand. + +A workaround is using scientific or exponential format `<< std::scientific`.] + +[note BOOST_NO_CXX11_NUMERIC_LIMITS is a suitable feature-test macro to determine if +`std::numeric_limits::max_digits10` is implemented on any platform. +If `max_digits10` is not available, you should using the +[@http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF Kahan formula for floating-point type T]. +See above.] + +[max_digits10_1] [/ example for using max_digits10] + +[h4 round_style] + +The rounding style determines how the result of floating-point operations +is treated when the result cannot be [*exactly represented] in the significand. +Various rounding modes may be provided: + +* round to nearest up or down (default for floating-point types). +* round up (toward positive infinity). +* round down (toward negative infinity). +* round toward zero (integer types). +* no rounding (if decimal radix). +* rounding mode is not determinable. + +For integer types, `std::numeric_limits::round_style` is always towards zero, so + + std::numeric_limits::round_style == std::round_to_zero; + +A decimal type, `cpp_dec_float` rounds in no particular direction, +which is to say it doesn't round at all. +And since there are several guard digits, +it's not really the same as truncation (round toward zero) either. + +For floating-point types, it is normal to round to nearest. + + std::numeric_limits::round_style == std::round_to_nearest; + +See function `std::numeric_limits::round_error` for the maximum error (in ULP) +that rounding can cause. + +[h4 has_denorm_loss] + +`true` if a loss of precision is detected as a +[@http://en.wikipedia.org/wiki/Denormalization denormalization] loss, +rather than an inexact result. + +Always `false` for integer types. + +`false` for all types which do not have `has_denorm` == `std::denorm_present`. + +[h4 denorm_style] + +[@http://en.wikipedia.org/wiki/Denormal_number Denormalized values] are +representations with a variable number of exponent bits that can permit +gradual underflow, so that, if type T is `double`. + + std::numeric_limits::denorm_min() < std::numeric_limits::min() + +A type may have any of the following `enum float_denorm_style` values: + +* `std::denorm_absent`, if it does not allow denormalized values. +(Always used for all integer and exact types). +* `std::denorm_present`, if the floating-point type allows denormalized values. +*`std::denorm_indeterminate`, if indeterminate at compile time. + +[h4 Tinyness before rounding] + +`bool std::numeric_limits::tinyness_before` + +`true` if a type can determine that a value is too small +to be represent as a normalized value before rounding it. + +Generally true for `is_iec559` floating-point built-in types, +but false for integer types. + +Standard-compliant IEEE 754 floating-point implementations may detect the floating-point underflow at three predefined moments: + +# After computation of a result with absolute value smaller than +`std::numeric_limits::min()`, +such implementation detects ['tinyness before rounding] (e.g. UltraSparc). + +# After rounding of the result to `std::numeric_limits::digits` bits, +if the result is tiny, such implementation detects ['tinyness after rounding] +(e.g. SuperSparc). + +# If the conversion of the rounded tiny result to subnormal form +resulted in the loss of precision, such implementation detects ['denorm loss]. + +[endsect] [/section:constants std::numeric_limits<> Constants] + +[section:functions std::numeric_limits<> functions] + +[h4 max function] + +Function `std::numeric_limits::max()` returns the largest finite value +that can be represented by the type T. If there is no such value (and +`numeric_limits::bounded` is `false`) then returns `T()`. + +For built-in types there is usually a corresponding MACRO value TYPE_MAX, +where TYPE is CHAR, INT, FLOAT etc. + +Other types, including those provided by a typedef, +for example `INT64_T_MAX` for `int64_t`, may provide a macro definition. + +To cater for situations where no `numeric_limits` specialization is available +(for example because the precision of the type varies at runtime), +packaged versions of this (and other functions) are provided using + + #include + + T = boost::math::tools::max_value(); + +Of course, these simply use `std::numeric_limits::max()` if available, +but otherwise 'do something sensible'. + +[h4 lowest function] + +Since C++11: `std::numeric_limits::lowest()` is + +* For integral types, the same as function `min()`. +* For floating-point types, generally the negative of `max()` +(but implementation-dependent). + +[digits10_5] + +[h4 min function] + +Function `std::numeric_limits::min()` returns the minimum finite value +that can be represented by the type T. + +For built-in types there is usually a corresponding MACRO value TYPE_MIN, +where TYPE is CHAR, INT, FLOAT etc. + +Other types, including those provided by a typedef, +for example `INT64_T_MIN` for `int64_t`, may provide a macro definition. + +For floating-point types, +it is more fully defined as the ['minimum positive normalized value]. + +See `std::numeric_limits::denorm_min()` for the smallest denormalized value, provided + + std::numeric_limits::has_denorm == std::denorm_present + + +To cater for situations where no `numeric_limits` specialization is available +(for example because the precision of the type varies at runtime), +packaged versions of this (and other functions) are provided using + + #include + + T = boost::math::tools::min_value(); + +Of course, these simply use `std::numeric_limits::min()` if available. + +[h4 denorm_min function] + +Function `std::numeric_limits::denorm_min()` +returns the smallest +[@http://en.wikipedia.org/wiki/Denormal_number denormalized value], +provided + + std::numeric_limits::has_denorm == std::denorm_present + +[denorm_min_1] + +The exponent is effectively reduced from -308 to -324 +(though it remains encoded as zero and leading zeros appear in the significand, +thereby losing precision until the significand reaches zero). + +[h4 round_error] + +Function `std::numeric_limits::round_error()` returns the maximum error +(in units of [@http://en.wikipedia.org/wiki/Unit_in_the_last_place ULP]) +that can be caused by any basic arithmetic operation. + + round_style == std::round_indeterminate; + +The rounding style is indeterminable at compile time. + +For floating-point types, when rounding is to nearest, +only half a bit is lost by rounding, and `round_error == 0.5`. +In contrast when rounding is towards zero, or plus/minus infinity, +we can loose up to one bit from rounding, and `round_error == 1`. + +For integer types, rounding always to zero, so at worst almost one bit can be rounded, +so `round_error == 1`. + +`round_error()` can be used with `std::numeric_limits::epsilon()` to estimate +the maximum potential error caused by rounding. For typical floating-point types, +`round_error() = 1/2`, so half epsilon is the maximum potential error. + +[round_error_1] + +There are, of course, many occasions when much bigger loss of precision occurs, +for exampe, caused by +[@http://en.wikipedia.org/wiki/Loss_of_significance Loss of significance or cancellation error] +or very many iterations. + +[h4 epsilon] + +Function `std::numeric_limits::epsilon()` is meaningful only for non-integral types. + +It returns the difference between `1.0` and the next value representable +by the floating-point type T. +So it is a one least-significant-bit change in this floating-point value. + +For `double` (`float_64t`) it is `2.2204460492503131e-016` +showing all possibly significant 17 decimal digits. + +[epsilon_1] + +We can explicitly increment by one bit using the function `boost::math::float_next()` +and the result is the same as adding `epsilon`. + +[epsilon_2] + +Adding any smaller value, like half `epsilon`, will have no effect on this value. + +[epsilon_3] + +So this cancellation error leaves the values equal, despite adding half `epsilon`. + +To achieve greater portability over platform and floating-point type, +Boost.Math and Boost.Multiprecion provide a package of functions that +'do something sensible' if the standard `numeric_limits` is not available. +To use these `#include `. + +[epsilon_4] + +[h5 Tolerance for Floating-point Comparisons] + +`epsilon` is very useful to compute a tolerance when comparing floating-point values, +a much more difficult task than is commonly imagined. + +For more information you probably want (but still need) see +[@http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html What Every Computer Scientist Should Know About Floating-Point Arithmetic] + +The naive test comparing the absolute difference between two values and a tolerance +does not give useful results if the values are too large or too small. + +So Boost.Test uses an algorithm first devised by Knuth +for reliably checking if floating-point values are close enough. + +See Donald. E. Knuth. The art of computer programming (vol II). +Copyright 1998 Addison-Wesley Longman, Inc., 0-201-89684-2. +Addison-Wesley Professional; 3rd edition. + +See also: + +[@http://adtmag.com/articles/2000/03/15/comparing-floats-how-to-determine-if-floating-quantities-are-close-enough-once-a-tolerance-has-been.aspx Alberto Squassia, Comparing floats] + +[@http://adtmag.com/articles/2000/03/16/comparing-floats-how-to-determine-if-floating-quantities-are-close-enough-once-a-tolerance-has-been.aspx Alberto Squassia, Comparing floats code] + +[@boost:/libs/test/doc/html/utf/testing-tools/floating_point_comparison.html floating-point comparison]. + +[tolerance_1] + +used thus: + + BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance); + +(There is also a version using tolerance as a percentage rather than a fraction). + +[tolerance_2] + +[h4 Infinity - positive and negative] + +For floating-point types only, for which +`std::numeric_limits::has_infinity == true`, +function `std::numeric_limits::infinity()` +provides an implementation-defined representation for [infin]. + +The 'representation' is a particular bit pattern reserved for infinity. +For IEEE754 system (for which `std::numeric_limits::is_iec559 == true`) +[@http://en.wikipedia.org/wiki/IEEE_754-1985#Positive_and_negative_infinity positive and negative infinity] +are assigned bit patterns for all defined floating-point types. + +Confusingly, the string resulting from outputting this representation, is also +implementation-defined. And the string that can be input to generate the representation is also implementation-defined. + +For example, the output is `1.#INF` on Microsoft systems, but `inf` on most *nix platforms. + +This implementation-defined-ness has hampered use of infinity (and NaNs) +but Boost.Math and Boost.Multiprecision work hard to provide a sensible representation +for [*all] floating-point types, not just the built-in types, +which with the use of suitable facets to define the input and output strings, makes it possible +to use these useful features portably and including Boost.Serialization. + +[h4 Not-A-Number NaN] + +[h5 Quiet_NaN] + +For floating-point types only, for which +`std::numeric_limits::has_quiet_NaN == true`, +function `std::numeric_limits::quiet_NaN()` +provides an implementation-defined representation for NaN. + +[@http://en.wikipedia.org/wiki/NaN NaNs] are values to indicate that the +result of an assignment or computation is meaningless. +A typical example is `0/0` but there are many others. + +NaNs may also be used, to represent missing values: for example, +these could, by convention, be ignored in calculations of statistics like means. + +Many of the problems with a representation for +[@http://en.wikipedia.org/wiki/NaN Not-A-Number] has hampered portable use, +similar to those with infinity. + +[nan_1] + +But using Boost.Math and suitable facets can permit portable use +of both NaNs and positive and negative infinity. + +[facet_1] + +[h5 Signaling NaN] + +For floating-point types only, for which +`std::numeric_limits::has_signaling_NaN == true`, +function `std::numeric_limits::signaling_NaN()` +provides an implementation-defined representation for NaN that causes a hardware trap. +It should be noted however, that at least one implementation of this function causes a hardware +trap to be triggered simply by calling `std::numeric_limits::signaling_NaN()`, and not only +by using the value returned. + +[endsect] [/section:functions std::numeric_limits<> functions] + +[/ Tables of values for numeric_limits for various built-in and cpp_bin_float types] +[include numeric_limits_32_tables.qbk] +[/include numeric_limits_64_tables.qbk] + +[section:how_to_tell How to Determine the Kind of a Number From `std::numeric_limits`] + +Based on the information above, one can see that different kinds of numbers can be +differentiated based on the information stored in `std::numeric_limits`. This is +in addition to the traits class [link boost_multiprecision.ref.number.traits_class_support +number_category] provided by this library. + +[h4 Integer Types] + +For an integer type T, all of the following conditions hold: + + std::numeric_limits::is_specialized == true + std::numeric_limits::is_integer == true + std::numeric_limits::is_exact == true + std::numeric_limits::min_exponent == 0 + std::numeric_limits::max_exponent == 0 + std::numeric_limits::min_exponent10 == 0 + std::numeric_limits::max_exponent10 == 0 + +In addition the type is /signed/ if: + + std::numeric_limits::is_signed == true + +If the type is arbitrary precision then: + + std::numeric_limits::is_bounded == false + +Otherwise the type is bounded, and returns a non zero value +from: + + std::numeric_limits::max() + +and has: + + std::numeric_limits::is_modulo == true + +if the type implements modulo arithmetic on overflow. + +[h4 Rational Types] + +Rational types are just like integers except that: + + std::numeric_limits::is_integer == false + +[h4 Fixed Precision Types] + +There appears to be no way to tell these apart from rational types, unless they set: + + std::numeric_limits::is_exact == false + +This is because these types are in essense a rational type with a fixed denominator. + +[h4 Floating Point Types] + +For a floating point type T, all of the following conditions hold: + + std::numeric_limits::is_specialized == true + std::numeric_limits::is_integer == false + std::numeric_limits::is_exact == false + std::numeric_limits::min_exponent != 0 + std::numeric_limits::max_exponent != 0 + std::numeric_limits::min_exponent10 != 0 + std::numeric_limits::max_exponent10 != 0 + +In addition the type is /signed/ if: + + std::numeric_limits::is_signed == true + +And the type may be decimal or binary depending on the value of: + + std::numeric_limits::radix + +In general, there are no arbitrary precision floating point types, and so: + + std::numeric_limits::is_bounded == false + +[h4 Exact Floating Point Types] + +Exact floating point types are a [@http://en.wikipedia.org/wiki/Field_%28mathematics%29 field] +composed of an arbitrary precision integer scaled by an exponent. Such types +have no division operator and are the same as floating point types except: + + std::numeric_limits::is_exact == true + +[h4 Complex Numbers] + +For historical reasons, complex numbers do not specialize `std::numeric_limits`, instead you must +inspect `std::numeric_limits`. + +[endsect] + +[endsect] [/section:limits Numeric Limits] + + +[section:input_output Input Output] + + +[h4 Loopback testing] + +['Loopback] or ['round-tripping] refers to writing out a value as a decimal digit string using `std::iostream`, +usually to a `std::stringstream`, and then reading the string back in to another value, +and confirming that the two values are identical. A trivial example using `float` is: + + float write; // Value to round-trip. + std::stringstream ss; // Read and write std::stringstream. + ss.precision(std::numeric_limits::max_digits10); // Ensure all potentially significant bits are output. + ss.flags(std::ios_base::fmtflags(std::ios_base::scientific)); // Use scientific format. + ss << write; // Output to string. + float read; // Expected. + ss >> read; // Read decimal digits string from stringstream. + BOOST_CHECK_EQUAL(write, read); // Should be the same. + +and this can be run in a loop for all possible values of a 32-bit float. +For other floating-point types `T`, including built-in `double`, +it takes far too long to test all values, +so a reasonable test strategy is to use a large number of random values. + + T write; + std::stringstream ss; + ss.precision(std::numeric_limits::max_digits10); // Ensure all potentially significant bits are output. + ss.flags(f); // Changed from default iostream format flags if desired. + ss << write; // Output to stringstream. + + T read; + ss >> read; // Get read using operator>> from stringstream. + BOOST_CHECK_EQUAL(read, write); + + read = static_cast(ss.str()); // Get read by converting from decimal digits string representation of write. + BOOST_CHECK_EQUAL(read, write); + + read = static_cast(write.str(0, f)); // Get read using format specified when written. + BOOST_CHECK_EQUAL(read, write); + + +The test at +[@../../test/test_cpp_bin_float_io.cpp test_cpp_bin_float_io.cpp] +allows any floating-point type to be ['round_tripped] using a wide range of fairly random values. +It also includes tests compared a collection of +[@../../test/string_data.ipp stringdata] test cases in a file. + +[h4 Comparing with output using Built-in types] + +One can make some comparisons with the output of + + > + +which has the same number of significant bits (53) as 64-bit double precision floating-point. + +However, although most outputs are identical, there are differences on some platforms +caused by the implementation-dependent behaviours allowed by the C99 specification +[@http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf C99 ISO/IEC 9899:TC2], +incorporated by C++. + +[:['"For e, E, f, F, g, and G conversions, if the number of significant decimal digits +is at most DECIMAL_DIG, then the result should be correctly rounded. +If the number of significant decimal digits is more than DECIMAL_DIG +but the source value is exactly representable with DECIMAL_DIG digits, +then the result should be an exact representation with trailing zeros. +Otherwise, the source value is bounded by two adjacent decimal strings L < U, +both having DECIMAL_DIG significant digits; +the value of the resultant decimal string D should satisfy L<= D <= U, +with the extra stipulation that the error should have a correct sign +for the current rounding direction."]] + +So not only is correct rounding for the full number of digits not required, +but even if the *optional* recomended practice is followed, +then the value of these last few digits is unspecified +as long as the value is within certain bounds. + +[note Do not expect the output from different platforms +to be [*identical], but `cpp_dec_float`, `cpp_bin_float` (and other backends) outputs should be +correctly rounded to the number of digits requested by the set precision and format.] + + +[h4 Macro BOOST_MP_MIN_EXPONENT_DIGITS] + +[@http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf C99 Standard] +for [/e and E] format specifiers, 7.19.6 Formatted input/output functions requires: + +\"The exponent always contains at least two digits, +and only as many more digits as necessary to represent the exponent.\" + +So to conform to the C99 standard (incorporated by C++) + + #define BOOST_MP_MIN_EXPONENT_DIGITS 2 + +Confusingly, Microsoft (and MinGW) do not conform to this standard and provide +[*at least three digits], for example `1e+001`. +So if you want the output to match that from +built-in floating-point types on compilers that use Microsofts runtime then use: + + #define BOOST_MP_MIN_EXPONENT_DIGITS 3 + +Also useful to get the minimum exponent field width is + + #define BOOST_MP_MIN_EXPONENT_DIGITS 1 + +producing a compact output like `2e+4`, +useful when conserving space is important. + +Larger values are also supported, for example, value 4 for `2e+0004` +which may be useful to ensure that columns line up. + +[endsect] [/section:input_output Input Output] + + [endsect] [section:ref Reference] @@ -1874,7 +2820,7 @@ support which requires the underlying backend to be serializable. enum expression_template_option { et_on = 1, et_off = 0 }; - template struct expression_template_default + template struct expression_template_default { static const expression_template_option value = et_on; }; template ::value> @@ -1924,7 +2870,7 @@ support which requires the underlying backend to be serializable. // Comparison: int compare(const number& o)const; template - typename enable_if >, int>::type + typename enable_if >, int>::type compare(const V& o)const; // Access to the underlying implementation: Backend& backend(); @@ -2076,7 +3022,7 @@ support which requires the underlying backend to be serializable. This enumerated type is used to specify whether expression templates are turned on (et_on) or turned off (et_off). - template struct expression_template_default + template struct expression_template_default { static const expression_template_option value = et_on; }; This traits class specifies the default expression template option to be used with a particular Backend type. @@ -2211,7 +3157,7 @@ the default precision and the precision of `*this` respectively. int compare(const number& o)const; template - typename enable_if >, int>::type + typename enable_if >, int>::type compare(const V& other)const; Returns: @@ -2263,7 +3209,7 @@ The return type of these operators is either: * Type `number` when `ExpressionTemplates` is `false`. * Type `bool` if the operator is a comparison operator. -Finally note that the second argument to the left and right shift operations must be a builtin integer type, +Finally note that the second argument to the left and right shift operations must be a builtin integer type, and that the argument must be positive (negative arguments result in a `std::runtime_error` being thrown). [h4 swap] @@ -2299,7 +3245,7 @@ this library support all of the iostream formatting flags, field width and preci ResultType& multiply(ResultType& result, const Source1& a, const Source2& b); These functions apply the named operator to the arguments ['a] and ['b] and store the -result in ['result], returning ['result]. In all cases they behave "as if" +result in ['result], returning ['result]. In all cases they behave "as if" arguments ['a] and ['b] were first promoted to type `ResultType` before applying the operator, though particular backends may well avoid that step by way of an optimization. @@ -2347,7 +3293,7 @@ otherwise the return type is an expression template. These functions are normally implemented by the Backend type. However, default versions are provided for Backend types that don't have native support for these functions. Please note however, that this default support requires the precision of the type -to be a compile time constant - this means for example that the [gmp] MPF Backend will not work with these functions when that type is +to be a compile time constant - this means for example that the [gmp] MPF Backend will not work with these functions when that type is used at variable precision. Also note that with the exception of `abs` that these functions can only be used with floating-point Backend types (if any other types @@ -2414,7 +3360,7 @@ A traits class that inherits from `mpl::true_` if T is an expression template ty In addition to functioning with types from this library, these functions are also overloaded for built in integer types if you include ``. Further, when used with fixed precision types (whether built in integers or multiprecision ones), the functions will promote to a wider type internally when the algorithm -requires it. Versions overloaded for built in integer types return that integer type rather than an expression +requires it. Versions overloaded for built in integer types return that integer type rather than an expression template. ``['unmentionable-expression-template-type]`` gcd(const ``['number-or-expression-template-type]``& a, const ``['number-or-expression-template-type]``& b); @@ -2427,7 +3373,7 @@ Returns the smallest integer `x` that is divisible by both `a` and `b`. ``['unmentionable-expression-template-type]`` pow(const ``['number-or-expression-template-type]``& b, unsigned p); -Returns ['b[super p]] as an expression template. Note that this function should be used with extreme care as the result can grow so +Returns ['b[super p]] as an expression template. Note that this function should be used with extreme care as the result can grow so large as to take "effectively forever" to compute, or else simply run the host machine out of memory. This is the one function in this category that is not overloaded for built in integer types, further, it's probably not a good idea to use it with fixed precision `cpp_int`'s either. @@ -2549,10 +3495,10 @@ whose precision can vary at compile time (such as `mpf_float`). enum cpp_integer_type { signed_magnitude, unsigned_magnitude }; enum cpp_int_check_type { checked, unchecked }; - template > class cpp_int_backend; // @@ -2597,8 +3543,8 @@ whose precision can vary at compile time (such as `mpf_float`). }} // namespaces -Class template `cpp_int_backend` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Class template `cpp_int_backend` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The template arguments are: @@ -2614,7 +3560,7 @@ The template arguments are: type `void`. Note that this parameter should not be used simply to prevent large memory allocations, not only is that role better performed by the allocator, but fixed precision integers have a tendency to allocate all of MaxBits of storage more often than one would expect.]] -[[SignType][Determines whether the resulting type is signed or not. Note that for +[[SignType][Determines whether the resulting type is signed or not. Note that for [@http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic arbitrary precision] types this parameter must be `signed_magnitude`. For fixed precision types then this type may be either `signed_magnitude` or `unsigned_magnitude`.]] @@ -2638,8 +3584,8 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces -Class template `gmp_int` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Class template `gmp_int` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The type of `number_category >::type` is `mpl::int_`. @@ -2658,8 +3604,8 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces -Class template `tommath_int` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Class template `tommath_int` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The type of `number_category >::type` is `mpl::int_`. @@ -2683,8 +3629,8 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces -Class template `gmp_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Class template `gmp_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type @@ -2714,8 +3660,8 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces -Class template `mpfr_float_backend` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Class template `mpfr_float_backend` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The class takes a single template parameter - `Digits10` - which is the number of decimal digits precision the type @@ -2730,6 +3676,98 @@ More information on this type can be found in the [link boost_multiprecision.tut [endsect] +[section:cpp_bin_float_ref cpp_bin_float] + + namespace boost{ namespace multiprecision{ + + enum digit_base_type + { + digit_base_2 = 2, + digit_base_10 = 10 + }; + + template + class cpp_bin_float; + + typedef number > cpp_bin_float_50; + typedef number > cpp_bin_float_100; + + typedef number, et_off> cpp_bin_float_single; + typedef number, et_off> cpp_bin_float_double; + typedef number, et_off> cpp_bin_float_double_extended; + typedef number, et_off> cpp_bin_float_quad; + + }} // namespaces + +Class template `cpp_bin_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +to change. + +The class takes six template parameters: + +[variablelist +[[Digits][The number of digits precision the type +should support. This is normally expresed as base-10 digits, but that can be changed via the second template parameter.]] +[[base][An enumerated value (either `digit_base_10` or `digit_base_2`) that indicates whether `Digits` is base-10 or base-2]] +[[Allocator][The allocator used: defaults to type `void`, meaning all storage is within the class, and no dynamic +allocation is performed, but can be set to a standard library allocator if dynamic allocation makes more sense.]] +[[Exponent][A signed integer type to use as the type of the exponent - defaults to `int`.]] +[[ExponentMin][The smallest (most negative) permitted exponent, defaults to zero, meaning "define as small as possible +given the limitations of the type and our internal requirements".]] +[[ExponentMax][The largest (most positive) permitted exponent, defaults to zero, meaning "define as large as possible +given the limitations of the type and our internal requirements".]] +] + +The type of `number_category >::type` is `mpl::int_`. + +More information on this type can be found in the [link boost_multiprecision.tut.floats.cpp_bin_float tutorial]. + +[h4 Implementation Notes] + +Internally, an N-bit `cpp_bin_float` is represented as an N-bit unsigned integer along with an exponent and a sign. +The integer part is normalized so that it's most significant bit is always 1. The decimal point is assumed to be +directly after the most significant bit of the integer part. The special values zero, infinity and NaN all have +the integer part set to zero, and the exponent to one of 3 special values above the maximum permitted exponent. + +Multiplication is trivial: multiply the two N-bit integer mantissa's to obtain a 2N-bit number, then round and +adjust the sign and exponent. + +Addition and subtraction proceed similarly - if the exponents are such that there is overlap between the two +values, then left shift the larger value to produce a number with between N and 2N bits, then perform integer +addition or subtraction, round, and adjust the exponent. + +Division proceeds as follows: first scale the numerator by some power of 2 so that integer division will +produce either an N-bit or N+1 bit result plus a remainder. If we get an N bit result then the size of +twice the remainder compared to the denominator gives us the rounding direction. Otherwise we have one extra bit +in the result which we can use to determine rounding (in this case ties occur only if the remainder is zero and +the extra bit is a 1). + +Square root uses integer square root in a manner analogous to division. + +Decimal string to binary conversion proceeds as follows: first parse the digits to +produce an integer multiplied by a decimal exponent. Note that we stop parsing digits +once we have parsed as many as can possibly effect the result - this stops the integer +part growing too large when there are a very large number of input digits provided. +At this stage if the decimal exponent is positive then the result is an integer and we +can in principle simply multiply by 10^N to get an exact integer result. In practice +however, that could produce some very large integers. We also need to be able to divide +by 10^N in the event that the exponent is negative. Therefore calculation of the 10^N +values plus the multiplication or division are performed using limited precision +integer arithmetic, plus an exponent, and a track of the accumulated error. At the end of +the calculation we will either be able to round unambiguously, or the error will be such +that we can't tell which way to round. In the latter case we simply up the precision and try +again until we have an unambiguously rounded result. + +Binary to decimal conversion proceeds very similarly to the above, our aim is to calculate +`mantissa * 2^shift * 10^E` where `E` is the decimal exponent and `shift` is calculated +so that the result is an N bit integer assuming we want N digits printed in the result. +As before we use limitted precision arithmetic to calculate the result and up the +precision as necessary until the result is unambiguously correctly rounded. In addition +our initial calculation of the decimal exponent may be out by 1, so we have to correct +that and loop as well in the that case. + +[endsect] + [section:cpp_dec_ref cpp_dec_float] namespace boost{ namespace multiprecision{ @@ -2742,8 +3780,8 @@ More information on this type can be found in the [link boost_multiprecision.tut }} // namespaces -Class template `cpp_dec_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. -Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject +Class template `cpp_dec_float` fulfils all of the requirements for a [link boost_multiprecision.ref.backendconc Backend] type. +Its members and non-member functions are deliberately not documented: these are considered implementation details that are subject to change. The class takes three template parameters: @@ -2757,7 +3795,7 @@ template argument should not be set too high or the class's size will grow unrea allocation is performed, but can be set to a standard library allocator if dynamic allocation makes more sense.]] ] -The type of `number_category >::type` is `mpl::int_`. +The type of `number_category >::type` is `mpl::int_`. More information on this type can be found in the [link boost_multiprecision.tut.floats.cpp_dec_float tutorial]. @@ -2827,10 +3865,10 @@ it's own. Typically the backend will implement these to improve performance. In the following tables, type B is the `Backend` template argument to `number`, `b` and `b2` are a variables of type B, `cb`, `cb2` and `cb3` are constant variables of type `const B`, -`rb` is a variable of type `B&&`, `a` and `a2` are variables of Arithmetic type, +`rb` is a variable of type `B&&`, `a` and `a2` are variables of Arithmetic type, `s` is a variable of type `const char*`, `ui` is a variable of type `unsigned`, `bb` is a variable of type `bool`, `pa` is a variable of type pointer-to-arithmetic-type, `exp` is a variable of type `B::exp_type`, -`pexp` is a variable of type `B::exp_type*`, `i` is a variable of type `int`, `pi` pointer to a variable of type `int`, +`pexp` is a variable of type `B::exp_type*`, `i` is a variable of type `int`, `pi` pointer to a variable of type `int`, B2 is another type that meets these requirements, b2 is a variable of type B2, `ss` is variable of type `std::streamsize` and `ff` is a variable of type `std::ios_base::fmtflags`. @@ -2901,10 +3939,10 @@ and `ff` is a variable of type `std::ios_base::fmtflags`. [[`B(b2)`][`B`][Copy constructor from a different back-end type. When not provided, a generic interconversion routine is used. This constructor may be `explicit` if the corresponding frontend constructor should also be `explicit`.][[space]]] [[`b = b2`][`b&`][Assignment operator from a different back-end type. When not provided, a generic interconversion routine is used.][[space]]] -[[`assign_components(b, a, a)`][`void`][Assigns to `b` the two components in the following arguments. +[[`assign_components(b, a, a)`][`void`][Assigns to `b` the two components in the following arguments. Only applies to rational and complex number types. When not provided, arithmetic operations are used to synthesise the result from the two values.][[space]]] -[[`assign_components(b, b2, b2)`][`void`][Assigns to `b` the two components in the following arguments. +[[`assign_components(b, b2, b2)`][`void`][Assigns to `b` the two components in the following arguments. Only applies to rational and complex number types. When not provided, arithmetic operations are used to synthesise the result from the two values.][[space]]] @@ -2939,12 +3977,12 @@ and `ff` is a variable of type `std::ios_base::fmtflags`. The type of `a` shall be listed in one of the type lists `B::signed_types`, `B::unsigned_types` or `B::float_types`. When not provided, the default implementation returns `eval_lt(cb, a)`.][[space]]] -[[`eval_is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`. The default version of this function - returns `cb.compare(ui_type(0)) == 0`, where `ui_type` is `ui_type` is +[[`eval_is_zero(cb)`][`bool`][Returns `true` if `cb` is zero, otherwise `false`. The default version of this function + returns `cb.compare(ui_type(0)) == 0`, where `ui_type` is `ui_type` is `typename mpl::front::type`.][[space]]] [[`eval_get_sign(cb)`][`int`][Returns a value < zero if `cb` is negative, a value > zero if `cb` is positive, and zero if `cb` is zero. - The default version of this function - returns `cb.compare(ui_type(0))`, where `ui_type` is `ui_type` is + The default version of this function + returns `cb.compare(ui_type(0))`, where `ui_type` is `ui_type` is `typename mpl::front::type`.][[space]]] [[['Basic arithmetic:]]] @@ -3201,7 +4239,7 @@ inherit from the type `std::runtime_error`. For example, a floating point type whenever the result of an operation would be infinite, and `std::underflow_error` whenever it would round to zero. [note -The non-member functions are all named with an "eval_" prefix to avoid conflicts with template classes of the same name - +The non-member functions are all named with an "eval_" prefix to avoid conflicts with template classes of the same name - in point of fact this naming convention shouldn't be necessary, but rather works around some compiler bugs.] [endsect] @@ -3222,7 +4260,7 @@ in point of fact this naming convention shouldn't be necessary, but rather works [[concepts/number_archetypes.hpp][Defines a backend concept archetypes for testing use.]] ] -[table Implementation Headers] +[table Implementation Headers [[Header][Contains]] [[cpp_int/add.hpp][Add and subtract operators for `cpp_int_backend`.]] [[cpp_int/bitwise.hpp][Bitwise operators for `cpp_int_backend`.]] @@ -3266,7 +4304,7 @@ inside class `number`: As you can see whether or not there is an overhead, and how large it is depends on the actual situation, but the overhead is in any cases small. Expression templates generally add a greater overhead the more complex the expression becomes due to the logic of figuring out how to best unpack and evaluate -the expression, but of course this is also the situation where you save more temporaries. For a +the expression, but of course this is also the situation where you save more temporaries. For a "trivial" backend like this, saving temporaries has no benefit, but for larger types it becomes a bigger win. @@ -3288,7 +4326,7 @@ Windows Vista machine. [endsect] -[section:realworld Floating Point Real World Tests] +[section:realworld Floating-Point Real World Tests] These tests test the total time taken to execute all of Boost.Math's test cases for these functions. In each case the best performing library gets a relative score of 1, with the total execution time @@ -3346,7 +4384,7 @@ type which was custom written for this specific task: Note how for this use case, any dynamic allocation is a performance killer. -The next [@../../performance/miller_rabin_performance.cpp tests] measure the time taken to generate 1000 128-bit +The next [@../../performance/miller_rabin_performance.cpp tests] measure the time taken to generate 1000 128-bit random numbers and test for primality using the Miller Rabin test. This is primarily a test of modular-exponentiation since that is the rate limiting step: @@ -3879,6 +4917,10 @@ Windows Vista machine. [section:hist History] +[h4 1.56] + +* Added list of values for numeric_limits. + [h4 1.55] * Added support for Boost.Serialization. @@ -3939,9 +4981,9 @@ than either of the arguments. *2011-2012, John Maddock adds an expression template enabled front end to Christopher's code, and adds support for other backends. * 2011, Christopher Kormanyos publishes the decimal floating point code under the Boost -Software Licence. The code is published as: [@http://doi.acm.org/10.1145/1916461.1916469 -"Algorithm 910: A Portable C++ Multiple-Precision -System for Special-Function Calculations"], in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, +Software Licence. The code is published as: [@http://doi.acm.org/10.1145/1916461.1916469 +"Algorithm 910: A Portable C++ Multiple-Precision +System for Special-Function Calculations"], in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. * 2002-2011, Christopher Kormanyos develops the all C++ decimal arithmetic floating point code. @@ -3960,7 +5002,7 @@ More a list of what ['could] be done, rather than what ['should] be done (which * Add better multiplication routines (Karatsuba, FFT etc) to cpp_int_backend. * Add assembly level routines to cpp_int_backend. * Add an all C++ Boost licensed binary floating point type. -* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it, +* Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it, the hard part is IO and binary-decimal conversion. * Should there be a choice of rounding mode (probably MPFR specific)? * We can reuse temporaries in multiple subtrees (temporary caching). @@ -3969,8 +5011,8 @@ the hard part is IO and binary-decimal conversion. Things requested in review: -* The performances of mp_number, false>respect to -float and mp_number, false> and int should be +* The performances of mp_number, false>respect to +float and mp_number, false> and int should be given to show the cost of using the generic interface (Mostly done, just need to update docs to the latest results). * Should we provide min/max overloads for expression templates? (Not done - we can't overload functions declared in the std namespace :-( ). * The rounding applied when converting must be documented (Done). @@ -3979,7 +5021,7 @@ given to show the cost of using the generic interface (Mostly done, just need to * We can reuse temporaries in multiple subtrees (temporary caching) Moved to TODO list. * Emphasise in the docs that ET's may reorder operations (done 2012/10/31). * Document what happens to small fixed precision cpp_int's (done 2012/10/31). -* The use of bool in template parameters could be improved by the use of +* The use of bool in template parameters could be improved by the use of an enum class which will be more explicit. E.g `enum class expression_template {disabled, enabled}; enum class sign {unsigned, signed};` (Partly done 2012/09/15, done 2012/10/31). * Each back-end should document the requirements it satisfies (not currently scheduled for inclusion: it's @@ -3987,23 +5029,23 @@ deliberately an implementation detail, and "optional" requirements are optimisat by the user). Not done: this is an implementation detail, the exact list of requirements satisfied is purely an optimization, not something the user can detect. * A backend for an overflow aware integers (done 2012/10/31). -* IIUC convert_to is used to emulate in c++98 compilers C++11 explicit -conversions. Could the explicit conversion operator be added on +* IIUC convert_to is used to emulate in c++98 compilers C++11 explicit +conversions. Could the explicit conversion operator be added on compilers supporting it? (Done 2012/09/15). -* The front-end should make the differences between implicit and explicit +* The front-end should make the differences between implicit and explicit construction (Done 2012/09/15). -* The tutorial should add more examples concerning implicit or explicit +* The tutorial should add more examples concerning implicit or explicit conversions. (Done 2012/09/15). -* The documentation must explain how move semantics helps in this domain +* The documentation must explain how move semantics helps in this domain and what the backend needs to do to profit from this optimization. (Done 2012/09/15). -* The documentation should contain Throws specification on the mp_number +* The documentation should contain Throws specification on the mp_number and backend requirements operations. (Done 2012/09/15). -* The library interface should use the noexcept (BOOST_NOEXCEPT, ...) +* The library interface should use the noexcept (BOOST_NOEXCEPT, ...) facilities (Done 2012/09/15). -* It is unfortunate that the generic mp_number front end can not make use +* It is unfortunate that the generic mp_number front end can not make use constexpr as not all the backends can ensure this (done - we can go quite a way). -* literals: The library doesn't provide some kind of literals. I think that the -mp_number class should provide a way to create literals if the backend +* literals: The library doesn't provide some kind of literals. I think that the +mp_number class should provide a way to create literals if the backend is able to. (Done 2012/09/15). * The ExpresionTemplate parameter could be defaulted to a traits class for more sensible defaults (done 2012/09/20). * In a = exp1 op exp2 where a occurs inside one of exp1 or exp2 then we can optimise and eliminate one more temporary (done 2012/09/20). @@ -4012,7 +5054,7 @@ is able to. (Done 2012/09/15). [h4 Pre-Review Comments] -* Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits +* Make fixed precision orthogonal to Allocator type in cpp_int. Possible solution - add an additional MaxBits template argument that defaults to 0 (meaning keep going till no more space/memory). Done. * Can ring types (exact floating point types) be supported? The answer should be yes, but someone needs to write it (Moved to TODO list). * Should there be a choice of rounding mode (probably MPFR specific)? Moved to TODO list. @@ -4056,7 +5098,7 @@ Open question - what should be the default - int32_t or int64_t? (done 2012/09/ [Bitwise operations on negative values (or indeed any signed integer type) are unspecified by the standard. As a result any attempt to carry out a bitwise operation on a negative checked-integer will result in a `std::range_error` being thrown.]] [[Why do I get compiler errors when trying to use the complement operator?] - [Use of the complement operator on signed types is problematic as the result is unspecified by the standard, and is further + [Use of the complement operator on signed types is problematic as the result is unspecified by the standard, and is further complicated by the fact that most extended precision integer types use a sign-magnitude representation rather than the 2's complement one favored by most native integer types. As a result the complement operator is deliberately disabled for checked `cpp_int`'s. Unchecked `cpp_int`'s give the same valued result as a 2's complement type would, but not the same bit-pattern.]] @@ -4081,8 +5123,8 @@ This library would not have happened without: * Christopher Kormanyos' C++ decimal number code. * Paul Bristow for patiently testing, and commenting on the library. * All the folks at GMP, MPFR and libtommath, for providing the "guts" that makes this library work. -* [@http://www-cs-faculty.stanford.edu/~uno/taocp.html "The Art Of Computer Programming"], -Donald E. Knuth, Volume 2: Seminumerical Algorithms, Third Edition +* [@http://www-cs-faculty.stanford.edu/~uno/taocp.html "The Art Of Computer Programming"], +Donald E. Knuth, Volume 2: Seminumerical Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xiv+762pp. ISBN 0-201-89684-2 [endsect] @@ -4091,6 +5133,7 @@ Donald E. Knuth, Volume 2: Seminumerical Algorithms, Third Edition [section:indexes Indexes] +[/temp for sandbox version] [include ../../../tools/auto_index/include/auto_index_helpers.qbk] [named_index function_name Function Index] [named_index class_name Class Index] @@ -4100,3 +5143,5 @@ Donald E. Knuth, Volume 2: Seminumerical Algorithms, Third Edition [endsect] + + diff --git a/doc/numeric_limits_32_tables.qbk b/doc/numeric_limits_32_tables.qbk new file mode 100644 index 000000000..06d054907 --- /dev/null +++ b/doc/numeric_limits_32_tables.qbk @@ -0,0 +1,94 @@ +[/ +Copyright 2013 Paul A. Bristow. +Copyright 2013 John Maddock. +Distributed under the Boost Software License, Version 1.0. +(See accompanying file LICENSE_1_0.txt or copy at +http://www.boost.org/LICENSE_1_0.txt). +] + +[section:limits32 Numeric limits for 32-bit platform] +These tables were generated using the following program and options: + +[pre + +Program: + numeric_limits_qbk.cpp +Mon Nov 4 18:09:06 2013 +BuildInfo: + Platform Win32 + Compiler Microsoft Visual C++ version 10.0 + MSVC version 160040219. + STL Dinkumware standard library version 520 + Boost version 1.55.0 +] + +[table:integral_constants Integer types constants (`std::numeric_limits::is_integer == true` && is_exact == true) +[[type][signed][bound][modulo][round][radix][digits][digits10]] +[[bool][unsigned][bound][no][to zero][2][1][0]] +[[char][signed][bound][modulo][to zero][2][7][2]] +[[unsigned char][unsigned][bound][modulo][to zero][2][8][2]] +[[char16_t][unsigned][bound][modulo][to zero][2][16][4]] +[[char32_t][unsigned][bound][modulo][to zero][2][32][9]] +[[short][signed][bound][modulo][to zero][2][15][4]] +[[unsigned short][unsigned][bound][modulo][to zero][2][16][4]] +[[int][signed][bound][modulo][to zero][2][31][9]] +[[unsigned][unsigned][bound][modulo][to zero][2][32][9]] +[[long][signed][bound][modulo][to zero][2][31][9]] +[[unsigned long][unsigned][bound][modulo][to zero][2][32][9]] +[[long long][signed][bound][modulo][to zero][2][63][18]] +[[unsigned long long][unsigned][bound][modulo][to zero][2][64][19]] +[[int32_t][signed][bound][modulo][to zero][2][31][9]] +[[uint32_t][unsigned][bound][modulo][to zero][2][32][9]] +[[int64_t][signed][bound][modulo][to zero][2][63][18]] +[[uint64_t][unsigned][bound][modulo][to zero][2][64][19]] +[[int128_t][signed][bound][modulo][to zero][2][128][38]] +[[uint128_t][unsigned][bound][modulo][to zero][2][128][38]] +[[int256_t][signed][bound][modulo][to zero][2][256][77]] +[[uint256_t][unsigned][bound][modulo][to zero][2][256][77]] +[[cpp_int][signed][unbounded][no][to zero][2][2147483647][646392383]] +] + +[table:integral_functions Integer types functions (`std::numeric_limits::is_integer == true && std::numeric_limits::min() == std::numeric_limits::lowest()` ) +[[function][max][min]] +[[bool][1][0]] +[[char][127][-128]] +[[unsigned char][255][0]] +[[char16_t][65535][0]] +[[char32_t][4294967295][0]] +[[short][32767][-32768]] +[[unsigned short][65535][0]] +[[int][2147483647][-2147483648]] +[[unsigned int][4294967295][0]] +[[long][2147483647][-2147483648]] +[[unsigned long][4294967295][0]] +[[long long][9223372036854775807][-9223372036854775808]] +[[unsigned long long][18446744073709551615][0]] +[[int32_t][2147483647][-2147483648]] +[[int64_t][9223372036854775807][-9223372036854775808]] +[[int128_t][340282366920938463463374607431768211455][-340282366920938463463374607431768211455]]] +[table:float_functions Floating-point types constants (`std::numeric_limits::is_integer==false && is_signed==true && is_modulo==false && is_exact==false && is_bound==true`) +[[type][round][radix][digits][digits10][max_digits10][min_exp][min_exp10][max_exp][max_exp10][tiny][trap]] +[[float][to nearest][2][24][6][8][-125][-37][128][38][tiny][traps]] + +[[double][to nearest][2][53][15][17][-1021][-307][1024][308][tiny][traps]] + +[[long double][to nearest][2][53][15][17][-1021][-307][1024][308][tiny][traps]] + +[[cpp_dec_float_50][indeterminate][10][50][50][80][-222953000][-67108864][222953000][67108864][no][no]] + +[[bin_128bit_double_type][to nearest][2][377][113][115][-2147482894][-646392082][2147482893][646392082][no][traps]] +] +[table:float_functions Floating-point types functions (`std::numeric_limits::is_integer == false`) +[[function][float][double][long double][cpp_dec_50][cpp_bin_128]][[max][3.40282e+038][1.79769e+308][1.79769e+308][1e+67108865][1.85906e+646456766]] +[[min][1.17549e-038][2.22507e-308][2.22507e-308][1e-67108864][5.37906e-646456767]] +[[epsilon][1.19209e-007][2.22045e-016][2.22045e-016][1e-49][6.49713e-114]] +[[round_error][0.5][0.5][0.5][0.5][0.5]] +[[infinity][1.#INF][1.#INF][1.#INF][inf][inf]] +[[quiet_NaN][1.#QNAN][1.#QNAN][1.#QNAN][nan][nan]] +[[signaling_NaN][1.#QNAN][1.#QNAN][1.#QNAN][0][0]] +[[denorm_min][1.4013e-045][4.94066e-324][4.94066e-324][0][0]] +] + + +[endsect] [/section:limits32 Numeric limits for 32-bit platform] + diff --git a/doc/numeric_limits_qbk.cpp b/doc/numeric_limits_qbk.cpp new file mode 100644 index 000000000..5f4f6b194 --- /dev/null +++ b/doc/numeric_limits_qbk.cpp @@ -0,0 +1,719 @@ +// Copyright Paul A. Bristow 2013 + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +// Program to list all numeric_limits items for any type to a file in Quickbook format. + +// C standard http://www.open-std.org/jtc1/sc22/wg11/docs/n507.pdf +// SC22/WG11 N507 DRAFT INTERNATIONAL ISO/IEC STANDARD WD 10967-1 +// Information technology Language independent arithmetic Part 1: Integer and Floating point arithmetic + +/* E.3 C++ +The programming language C++ is defined by ISO/IEC 14882:1998, Programming languages C++ [18]. +An implementation should follow all the requirements of LIA-1 unless otherwise specified by +this language binding. +*/ + +// http://754r.ucbtest.org/standards/754.pdf + +// http://www.cesura17.net/~will/Professional/Research/Papers/retrospective.pdf + +// http://www.exploringbinary.com/using-integers-to-check-a-floating-point-approximation/ + +// http://stackoverflow.com/questions/12466745/how-to-convert-float-to-doubleboth-stored-in-ieee-754-representation-without-loss + + +#ifdef _MSC_VER +# pragma warning (disable : 4127) // conditional expression is constant. +# pragma warning (disable : 4100) // unreferenced formal parameter. +#endif + + +#include +#include +#include +#include +#include +#include // numeric_limits + +#include + +#include +#include + +// May need extra includes for other types, for example: +#include // is decimal. +#include // is binary. + + +// Assume that this will be run on MSVC to get the 32 or 64 bit info. +#ifdef _WIN32 + std::string bits32_64 = "32"; +std::string filename = "numeric_limits_32_tables.qbk"; +#else + std::string bits32_64 = "64"; +std::string filename = "numeric_limits_64_tables.qbk"; +#endif + +#ifdef INT32_T_MAX + int i = INT256_T_MAX; +#endif + +std::array integer_type_names = +{ +"bool", +"char", +"unsigned char", +"char16_t", +"char32_t", +"short", +"unsigned short", +"int", +"unsigned int", +"long", +"unsigned long", +"long long", +"unsigned long long", +"int32_t", +//"uint32_t", +"int64_t", +//"uint64_t", +"int128_t", +//"uint128_t" // Too big? +//"int256_t", +//"uint256_t" +//"int512_t" +}; + +std::array float_type_names = +{ + "function", "float", "double", "long double", "cpp_dec_50", "cpp_bin_128" +}; + +// Table headings for integer constants. +std::array integer_constant_heads = +{ + "type", "signed", "bound", "modulo", "round", "radix", "digits", "digits10", // "max_digits10" +}; + +// Table headings for integer functions. +std::array integer_function_heads = +{ + "max", // "lowest", assumes is same for all integer types, so not worth listing. + "min" +}; + +// Table headings for float constants. +std::array float_constant_heads = +{ + "type", // "signed", "exact", "bound", // "modulo", + "round", "radix", "digits", "digits10", "max_digits10", "min_exp", "min_exp10", "max_exp", "max_exp10", "tiny", "trap" +}; + +// Table headings for float functions. +std::array float_function_heads = +{ + "function", "max", "lowest", "min", "eps", "round", "infinity", "NaN", "sig_NaN", "denorm_min" +}; + +std::string versions() +{ // Build a string of info about Boost, platform, STL, etc. + std::stringstream mess; + //mess << "\n" << "Program:\n\" " __FILE__ << "\"\n"; // \n is mis-interpreted! + mess << "\n" << "Program:\n numeric_limits_qbk.cpp \n"; +#ifdef __TIMESTAMP__ + mess << __TIMESTAMP__; +#endif + mess << "\nBuildInfo:\n" " Platform " << BOOST_PLATFORM; + mess << "\n Compiler " BOOST_COMPILER; +#ifdef _MSC_FULL_VER + mess << "\n MSVC version "<< BOOST_STRINGIZE(_MSC_FULL_VER) << "."; +#endif + mess << "\n STL " BOOST_STDLIB; + mess << "\n Boost version " << BOOST_VERSION/100000 << "." << BOOST_VERSION/100 % 1000 << "." << BOOST_VERSION % 100 << std::endl; + return mess.str(); +} // std::string versions() + +template +void out_round_style(std::ostream& os) +{ //! Send short string describing STD::round_style to stream os. + // os << "Round style is "; + if (std::numeric_limits::round_style == std::round_indeterminate) + { + os << "indeterminate" ; + } + else if (std::numeric_limits::round_style == std::round_toward_zero) + { + os << "to zero" ; + } + else if (std::numeric_limits::round_style == std::round_to_nearest) + { + os << "to nearest" ; + } + else if (std::numeric_limits::round_style == std::round_toward_infinity) + { + os << "to infin[]"; // Or << "to \u221E" << "to infinity" ; + } + else if (std::numeric_limits::round_style == std::round_toward_neg_infinity) + { + os << "to -infin[]" ; + } + else + { + os << "undefined!"; + std::cout << "std::numeric_limits::round_style is undefined value!" << std::endl; + } + return; +} // out_round_style(std::ostream& os); + +template +void integer_constants(std::string type_name, std::ostream& os) +{ //! Output a line of table integer constant values to ostream os. + os << "\n[" + "[" << type_name << "]" ; + os << "[" << (std::numeric_limits::is_signed ? "signed" : "unsigned") << "]" ; + // Is always exact for integer types, so removed: + // os << "[" << (std::numeric_limits::is_exact ? "exact" : "inexact") << "]" ; + os << "[" << (std::numeric_limits::is_bounded ? "bound" : "unbounded") << "]" ; + os << "[" << (std::numeric_limits::is_modulo ? "modulo" : "no") << "]" ; + os << "[" ; out_round_style(os); os << "]" ; + os << "[" << std::numeric_limits::radix << "]" ; + os << "[" << std::numeric_limits::digits << "]" ; + os << "[" << std::numeric_limits::digits10 << "]" ; + // Undefined for integers, so removed: + // os << "[" << std::numeric_limits::max_digits10 << "]" + os << "]"; +} // void integer_constants + + +template +void float_constants(std::string type_name, std::ostream& os) +{ //! Output a row of table values to `ostream` os. + os << "\n[" + "[" << type_name << "]" ; + //os << "[" << (std::numeric_limits::is_signed ? "signed" : "unsigned") << "]" ; + //os << "[" << (std::numeric_limits::is_exact ? "exact" : "inexact") << "]" ; + //os << "[" << (std::numeric_limits::is_bounded ? "bound" : "no") << "]" ; + // os << "[" << (std::numeric_limits::is_modulo ? "modulo" : "no") << "]" ; + os << "[" ; out_round_style(os); os << "]" ; + os << "[" << std::numeric_limits::radix << "]" ; + os << "[" << std::numeric_limits::digits << "]" ; + os << "[" << std::numeric_limits::digits10 << "]" ; + os << "[" << std::numeric_limits::max_digits10 << "]"; + os << "[" << std::numeric_limits::min_exponent << "]" ; + os << "[" << std::numeric_limits::min_exponent10 << "]" ; + os << "[" << std::numeric_limits::max_exponent << "]" ; + os << "[" << std::numeric_limits::max_exponent10 << "]" ; + os << "[" << (std::numeric_limits::tinyness_before ? "tiny" : "no") << "]" ; + os << "[" << (std::numeric_limits::traps ? "traps" : "no") << "]" ; + os << "]" "\n"; // end of row. +} // void float_constants + +/* Types across and two functions down. + +template +void integer_functions(std::string type_name, std::ostream& os) +{ //! Output a line of table integer function values to `ostream` os. + os << "\n[" + "[" << type_name << "]" ; + os << "[" << std::numeric_limits::max() << "]" ; + //os << "[" << std::numeric_limits::lowest() << "]" ; always == min for integer types, + // so removed to save space. + os << "[" << std::numeric_limits::min() << "]" + "]"; +} // void integer_functions + +*/ + +// Types down and two (or three) functions across. +template +void integer_functions(std::string type_name, std::ostream& os) +{ //! Output a line of table integer function values to `ostream` os. + os << "\n[" // start of row. + "[" << type_name << "]" ; + os << "[" << std::numeric_limits::max() << "]" ; + // os << "[" << std::numeric_limits::lowest() << "]" ; + os << "[" << std::numeric_limits::min() << "]" ; + os << "]"; // end of row. +} // void integer_functions + + +template +void float_functions(std::string type_name, std::ostream& os) +{ //! Output a line of table float-point function values to `ostream` os. + os << "\n[" // start of row. + "[" << type_name << "]" ; + os << "[" << std::numeric_limits::max() << "]" ; + os << "[" << std::numeric_limits::lowest() << "]" ; + os << "[" << std::numeric_limits::min() << "]" + os << "[" << std::numeric_limits::epsilon() << "]" + os << "[" << std::numeric_limits::round_error() << "]" + os << "[" << std::numeric_limits::infinity() << "]" + os << "[" << std::numeric_limits::quiet_NaN() << "]" + os << "[" << std::numeric_limits::signaling_NaN() << "]" + os << "[" << std::numeric_limits::denorm_min() << "]" + "]"; // end of row. +} // void float_functions + +template +int numeric_limits_list(std::string description) +{//! Output numeric_limits for numeric_limits, for example `numeric_limits_list()`. + // This is not used for Quickbook format. + // std::cout << versions() << std::endl; + + std::cout << "\n" << description << "\n" << std::endl; // int, int64_t rather than full long typeid(T).name(). + + std::cout << "Type " << typeid(T).name() << " std::numeric_limits::<" << typeid(T).name() << ">\n" << std::endl; + // ull long typeid(T).name() + + if (std::numeric_limits::is_specialized == false) + { + std::cout << "type " << typeid(T).name() << " is not specialized for std::numeric_limits!" << std::endl; + //return -1; + } + + // Member constants. + + std::cout << (std::numeric_limits::is_signed ? "is signed." : "unsigned.") << std::endl; + std::cout << (std::numeric_limits::is_integer ? "is integer." : "not integer (fixed or float-point).") << std::endl; + std::cout << (std::numeric_limits::is_exact ? "is exact." : "not exact.") << std::endl; + std::cout << (std::numeric_limits::has_infinity ? "has infinity." : "no infinity.") << std::endl; + std::cout << (std::numeric_limits::has_quiet_NaN ? "has quiet NaN." : "no quiet NaN.") << std::endl; + std::cout << (std::numeric_limits::has_signaling_NaN ? "has signaling NaN." : "no signaling NaN.") << std::endl; + if (!std::numeric_limits::is_integer) + { // is floating_point + std::cout << "Denorm style is " ; + if (std::numeric_limits::has_denorm == std::denorm_absent) + { + std::cout << "denorm_absent." << std::endl; + } + else if (std::numeric_limits::has_denorm == std::denorm_present) + { + std::cout << "denorm_present." << std::endl; + } + else if (std::numeric_limits::has_denorm == std::denorm_indeterminate) + { + std::cout << "denorm_indeterminate." << std::endl; + } + else + { + std::cout << "std::numeric_limits::has_denorm unexpected value!" << std::endl; + } + + std::cout << (std::numeric_limits::has_denorm_loss ? "has denorm loss." : "no denorm loss.") << std::endl; + // true if a loss of accuracy is detected as a denormalization loss, rather than an inexact result. + + std::cout << "Round style is "; + if (std::numeric_limits::round_style == std::round_indeterminate) + { + std::cout << "round_indeterminate!" << std::endl; + } + else if (std::numeric_limits::round_style == std::round_toward_zero) + { + std::cout << "round_toward_zero." << std::endl; + } + else if (std::numeric_limits::round_style == std::round_to_nearest) + { + std::cout << "round_to_nearest." << std::endl; + } + else if (std::numeric_limits::round_style == std::round_toward_infinity) + { + std::cout << "round_toward_infinity." << std::endl; + } + else if (std::numeric_limits::round_style == std::round_toward_neg_infinity) + { + std::cout << "round_toward_neg_infinity." << std::endl; + } + else + { + std::cout << "undefined value!" << std::endl; + } + + } // is floating_point + + std::cout << (std::numeric_limits::is_iec559 ? "is IEC599." : "not IEC599.") << std::endl; + std::cout << (std::numeric_limits::is_bounded ? "is bound." : "unbounded.") << std::endl; + std::cout << (std::numeric_limits::is_modulo ? "is modulo." : "no modulo.") << std::endl; + std::cout << std::dec << "radix " << std::numeric_limits::radix << std::endl; + std::cout << "digits " << std::numeric_limits::digits << std::endl; + std::cout << "digits10 " << std::numeric_limits::digits10 << std::endl; + + std::cout.precision(std::numeric_limits::max_digits10); // Full precision for floating-point values like max, min ... + + std::cout << "max_digits10 " << std::numeric_limits::max_digits10 << std::endl; + std::cout << "min_exponent " << std::numeric_limits::min_exponent << std::endl; + std::cout << "min_exponent10 " << std::numeric_limits::min_exponent10 << std::endl; + std::cout << "max_exponent " << std::numeric_limits::max_exponent << std::endl; + std::cout << "max_exponent10 " << std::numeric_limits::max_exponent10 << std::endl; + + std::cout << (std::numeric_limits::tinyness_before ? "Can tiny values before rounding." : "no tinyness_before.") << std::endl; + // true if the type can detect tiny values before rounding; false if it cannot. + std::cout << (std::numeric_limits::traps ? "traps" : "no trapping.") << std::endl; + // Whether trapping that reports on arithmetic exceptions is implemented for a type. + + std::cout << "Member functions." << std::endl; + // (assumes operator<< for type T is available). + // If floating-point then hex format may not be available. + + std::cout << "max = " << std::numeric_limits::max() << std::endl; + //if (std::numeric_limits::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits::max() << std::endl; + //} + + std::cout << "lowest = " << std::dec << std::numeric_limits::lowest() << std::endl; + //if (std::numeric_limits::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits::lowest() << std::endl; + //} + + std::cout << "min = " << std::dec << std::numeric_limits::min() << std::endl; + //if (std::numeric_limits::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits::min() << std::endl; + //} + + std::cout << "epsilon = " << std::dec << std::numeric_limits::epsilon() << std::endl; + //if (std::numeric_limits::is_integer) + //{ + // std::cout << " = " << std::hex << std::numeric_limits::epsilon() << std::endl; + //} + // round_error is always zero for integer types. + // round_error is usually 1/2 = (T)0.5 for floating-point types. + // round_error is ? for fixed-point. + std::cout << "round_error = " << std::numeric_limits::round_error() << " ULP." << std::endl; + + std::cout << "infinity = " << std::dec << std::numeric_limits::infinity() << std::endl; + std::cout << " = " << std::hex << std::numeric_limits::infinity() << std::endl; + + std::cout << "quiet_NaN = " << std::dec << std::numeric_limits::quiet_NaN() << std::endl; + std::cout << " = " << std::hex << std::numeric_limits::quiet_NaN() << std::endl; + + std::cout << "signaling_NaN = " << std::dec << std::numeric_limits::signaling_NaN() << std::endl; + std::cout << " = " << std::hex << std::numeric_limits::signaling_NaN() << std::endl; + + // Only meaningful if (std::numeric_limits::has_denorm == std::denorm_present) + // so might not bother to show if absent? + std::cout << "denorm_min = " << std::numeric_limits::denorm_min() << std::endl; + std::cout << " = " << std::numeric_limits::denorm_min() << std::endl; + return 0; +} + +int main() +{ + + + + try + { + using namespace boost::multiprecision; + + std::cout << versions() << std::endl; + + std::ofstream fout(filename, std::ios_base::out); + if (!fout.is_open()) + { + std::cout << "Unable to open file " << filename << " for output.\n" << std::endl; + return -1; // boost::EXIT_FAILURE; + } + fout << + "[/""\n" + "Copyright 2013 Paul A. Bristow.""\n" + "Copyright 2013 John Maddock.""\n" + "Distributed under the Boost Software License, Version 1.0.""\n" + "(See accompanying file LICENSE_1_0.txt or copy at""\n" + "http://www.boost.org/LICENSE_1_0.txt).""\n" + "]""\n" + << std::endl; + + fout << "[section:limits"<< bits32_64 << " Numeric limits for " << bits32_64 << "-bit platform]" << std::endl; + + // Output platform version info (32 or 64). + fout << "These tables were generated using the following program and options:\n\n" + "[pre""\n" + << versions() + << "]""\n" + << std::endl; + + fout << "[table:integral_constants Integer types constants (`std::numeric_limits::is_integer == true` && is_exact == true)" "\n" + "["; + + for (size_t i = 0; i < integer_constant_heads.size(); i++) + { // signed, bound, modulo ... + fout << "[" << integer_constant_heads[i] << "]" ; + } + fout << "]"; + + integer_constants("bool", fout); + integer_constants("char", fout); + integer_constants("unsigned char", fout); + integer_constants("char16_t", fout); + integer_constants("char32_t", fout); + integer_constants("short", fout); + integer_constants("unsigned short", fout); + integer_constants("int", fout); + integer_constants("unsigned", fout); + integer_constants("long", fout); + integer_constants("unsigned long", fout); + integer_constants("long long", fout); + integer_constants("unsigned long long", fout); + integer_constants("int32_t", fout); + integer_constants("uint32_t", fout); + integer_constants("int64_t", fout); + integer_constants("uint64_t", fout); + integer_constants("int128_t", fout); + integer_constants("uint128_t", fout); + integer_constants("int256_t", fout); + integer_constants("uint256_t", fout); + // integer_constants("int512_t", fout); + //integer_constants("uint512_t", fout); // Too big? + integer_constants("cpp_int", fout); + + fout << "\n]\n\n"; + + + fout << "[table:integral_functions Integer types functions (`std::numeric_limits::is_integer == true && std::numeric_limits::min() == std::numeric_limits::lowest()` )" "\n" + "["; + // Display types across the page, and 2 (or 3) functions as rows. + + fout << "[function]"; + for (size_t i = 0; i < integer_function_heads.size(); i++) + { + fout << "[" << integer_function_heads[i] << "]" ; + } + fout << "]"; // end of headings. + integer_functions("bool", fout); + //integer_functions("char", fout); // Need int value not char. + fout << "\n[" // start of row. + "[" << "char"<< "]" ; + fout << "[" << static_cast((std::numeric_limits::max)()) << "]" ; + // fout << "[" << (std::numeric_limits::lowest)() << "]" ; + fout << "[" << static_cast((std::numeric_limits::min)()) << "]" ; + fout << "]"; // end of row. + //integer_functions("unsigned char", fout); // Need int value not char. + fout << "\n[" // start of row. + "[" << "unsigned char"<< "]" ; + fout << "[" << static_cast((std::numeric_limits::max)()) << "]" ; + // fout << "[" << std::numeric_limits::lowest() << "]" ; + fout << "[" << static_cast(std::numeric_limits::min()) << "]" ; + fout << "]"; // end of row. + + integer_functions("char16_t", fout); + integer_functions("char32_t", fout); + integer_functions("short", fout); + integer_functions("unsigned short", fout); + integer_functions("int", fout); + integer_functions("unsigned int", fout); + integer_functions("long", fout); + integer_functions("unsigned long", fout); + integer_functions("long long", fout); + integer_functions("unsigned long long", fout); + integer_functions("int32_t", fout); + integer_functions("int64_t", fout); + integer_functions("int128_t", fout); + fout << "]" "\n"; // end of table; + + + //fout << "[[max]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << static_cast(std::numeric_limits::max()) << "]" + // << "[" << static_cast(std::numeric_limits::max()) << "]" + // << "[" << static_cast(std::numeric_limits::max()) << "]" + // << "[" << static_cast(std::numeric_limits::max()) << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // << "[" << std::numeric_limits::max() << "]" + // //<< "[" << std::numeric_limits::max() << "]" // too big? + // //<< "[" << std::numeric_limits::max() << "]" // too big? + // << "]" "\n"; + ///* Assume lowest() is not useful as == min for all integer types. + // */ + + //fout << "[[min]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << static_cast(std::numeric_limits::min()) << "]" + // << "[" << static_cast(std::numeric_limits::min()) << "]" + // << "[" << static_cast(std::numeric_limits::min()) << "]" + // << "[" << static_cast(std::numeric_limits::min()) << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // << "[" << std::numeric_limits::min() << "]" + // // << "[" << std::numeric_limits::min() << "]" // too big? + // // << "[" << std::numeric_limits::min() << "]" // too big? + // << "]""\n"; + + + + // Floating-point + + typedef number > cpp_dec_float_50; // 50 decimal digits. + typedef number > bin_128bit_double_type; // == Binary rare long double. + + fout << + //"[table:float_functions Floating-point types constants (`std::numeric_limits::is_integer == false && std::numeric_limits::is_modulo == false` )" "\n" + "[table:float_functions Floating-point types constants (`std::numeric_limits::is_integer==false && is_signed==true && is_modulo==false && is_exact==false && is_bound==true`)" "\n" + "["; + for (size_t i = 0; i < float_constant_heads.size(); i++) + { + fout << "[" << float_constant_heads[i] << "]" ; + } + fout << "]"; // end of headings. + + float_constants("float", fout); + float_constants("double", fout); + float_constants("long double", fout); + float_constants("cpp_dec_float_50", fout); + float_constants("bin_128bit_double_type", fout); + fout << "]" "\n"; // end of table; + + fout << + "[table:float_functions Floating-point types functions (`std::numeric_limits::is_integer == false`)" "\n" + "["; + + for (size_t i = 0; i < float_type_names.size(); i++) + { + fout << "[" << float_type_names[i] << "]" ; + } + fout << "]"; // end of headings. + + fout << "[[max]" + << "[" << std::numeric_limits::max() << "]" + << "[" << std::numeric_limits::max() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Perhaps to test Long double is not just a duplication of double (but need change is headings too). + << "[" << std::numeric_limits::max() << "]" +//#endif + << "[" << std::numeric_limits::max() << "]" + << "[" << std::numeric_limits::max() << "]" + << "]" "\n"; // end of row. + + fout << "[[min]" + << "[" << std::numeric_limits::min() << "]" + << "[" << std::numeric_limits::min() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits::min() << "]" +//#endif + << "[" << std::numeric_limits::min() << "]" + << "[" << std::numeric_limits::min() << "]" + << "]" "\n"; // end of row. + + fout << "[[epsilon]" + << "[" << std::numeric_limits::epsilon() << "]" + << "[" << std::numeric_limits::epsilon() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits::epsilon() << "]" +//#endif + << "[" << std::numeric_limits::epsilon() << "]" + << "[" << std::numeric_limits::epsilon() << "]" + << "]" "\n"; // end of row. + + fout << "[[round_error]" + << "[" << std::numeric_limits::round_error() << "]" + << "[" << std::numeric_limits::round_error() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits::round_error() << "]" +//#endif + << "[" << std::numeric_limits::round_error() << "]" + << "[" << std::numeric_limits::round_error() << "]" + << "]" "\n"; // end of row. + + fout << "[[infinity]" + << "[" << std::numeric_limits::infinity() << "]" + << "[" << std::numeric_limits::infinity() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits::infinity() << "]" +//#endif + << "[" << std::numeric_limits::infinity() << "]" + << "[" << std::numeric_limits::infinity() << "]" + << "]" "\n"; // end of row. + + fout << "[[quiet_NaN]" + << "[" << std::numeric_limits::quiet_NaN() << "]" + << "[" << std::numeric_limits::quiet_NaN() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits::quiet_NaN() << "]" +//#endif + << "[" << std::numeric_limits::quiet_NaN() << "]" + << "[" << std::numeric_limits::quiet_NaN() << "]" + << "]" "\n"; // end of row. + + fout << "[[signaling_NaN]" + << "[" << std::numeric_limits::signaling_NaN() << "]" + << "[" << std::numeric_limits::signaling_NaN() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits::signaling_NaN() << "]" +//#endif + << "[" << std::numeric_limits::signaling_NaN() << "]" + << "[" << std::numeric_limits::signaling_NaN() << "]" + << "]" "\n"; // end of row. + + fout << "[[denorm_min]" + << "[" << std::numeric_limits::denorm_min() << "]" + << "[" << std::numeric_limits::denorm_min() << "]" +//#if LDBL_MANT_DIG > DBL_MANT_DIG + // Long double is not just a duplication of double. + << "[" << std::numeric_limits::denorm_min() << "]" +//#endif + << "[" << std::numeric_limits::denorm_min() << "]" + << "[" << std::numeric_limits::denorm_min() << "]" + << "]" "\n"; // end of row. + + + + fout << "]" "\n"; // end of table; + + + fout << "\n\n" + "[endsect] [/section:limits32 Numeric limits for 32-bit platform]" "\n" << std::endl; + + + + fout.close(); + } + catch(std::exception ex) + { + std::cout << "exception thrown: " << ex.what() << std::endl; + } + + +} // int main() + +/* + Description: Autorun "J:\Cpp\Misc\Debug\numeric_limits_qbk.exe" + + Program: I:\boost-sandbox\multiprecision.cpp_bin_float\libs\multiprecision\doc\numeric_limits_qbk.cpp + Wed Aug 28 14:17:21 2013 + BuildInfo: + Platform Win32 + Compiler Microsoft Visual C++ version 10.0 + MSVC version 160040219. + STL Dinkumware standard library version 520 + Boost version 1.55.0 + + */ + diff --git a/example/cpp_bin_float_snips.cpp b/example/cpp_bin_float_snips.cpp new file mode 100644 index 000000000..ed0043640 --- /dev/null +++ b/example/cpp_bin_float_snips.cpp @@ -0,0 +1,39 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include +#include +#include + +void t1() +{ + //[cpp_bin_float_eg + //=#include + + using namespace boost::multiprecision; + + // Operations at fixed precision and full numeric_limits support: + cpp_bin_float_100 b = 2; + std::cout << std::numeric_limits::digits << std::endl; + std::cout << std::numeric_limits::digits10 << std::endl; + // We can use any C++ std lib function, lets print all the digits as well: + std::cout << std::setprecision(std::numeric_limits::max_digits10) + << log(b) << std::endl; // print log(2) + // We can also use any function from Boost.Math: + std::cout << boost::math::tgamma(b) << std::endl; + // These even work when the argument is an expression template: + std::cout << boost::math::tgamma(b * b) << std::endl; + // And since we have an extended exponent range we can generate some really large + // numbers here (4.0238726007709377354370243e+2564): + std::cout << boost::math::tgamma(cpp_bin_float_100(1000)) << std::endl; + //] +} + +int main() +{ + t1(); + return 0; +} + diff --git a/example/numeric_limits_snips.cpp b/example/numeric_limits_snips.cpp new file mode 100644 index 000000000..02bd6da20 --- /dev/null +++ b/example/numeric_limits_snips.cpp @@ -0,0 +1,458 @@ +// Copyright Paul A. Bristow 2013 +// Copyright John Maddock 2013 +// Copyright Christopher Kormanyos + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +// Examples of numeric_limits usage as snippets for multiprecision documentation. + +// Includes text as Quickbook comments. + +#include +#include +#include +#include +#include // numeric_limits +#include +#include +#include + +#include +#include + + + +#include +#include +#include +#include // is decimal. +#include // is binary. + +#include // Boost.Test +#include + + + +template +bool nearly_equal(RealType a, RealType b) +{ + const RealType tolerance = 3 * std::numeric_limits::epsilon(); + return (a - tolerance * std::abs(a) <= b + tolerance * std::abs(b)) // + && (a + tolerance * std::abs(a) >= b - tolerance * std::abs(b)); +} + +int main() +{ + try + { + +// Example of portable way to get std::numeric_limits::max_digits10. + +//[max_digits10_1 +/*`For example, to be portable, including older platforms: +*/ + + typedef float T; // Any type: `double`, cpp_dec_float_50, bin_128bit_double_type ... + +#if defined(BOOST_NO_CXX11_NUMERIC_LIMITS) + std::cout.precision(2 + std::numeric_limits::digits * 3010U/10000U); +#else +# if (_MSC_VER <= 1600) // Correct wrong value for float. + std::cout.precision(2 + std::numeric_limits::digits * 3010U/10000U); +# else + std::cout.precision(std::numeric_limits::max_digits10); +# endif +#endif + + std::cout << "std::cout.precision = " << std::cout.precision() << std::endl; + + double x = 1.2345678901234567889; + + std::cout << "x = " << x << std::endl; // + +/*`which should output: + + std::cout.precision = 9 + x = 1.23456789 +*/ + +//] [/max_digits10_1] + + { +//[max_digits10_2 + + double write = 2./3; // Any arbitrary value that cannot be represented exactly. + double read = 0; + std::stringstream s; + s.precision(std::numeric_limits::digits10); // or `float64_t` for 64-bit IEE754 double. + s << write; + s >> read; + if(read != write) + { + std::cout << std::setprecision(std::numeric_limits::digits10) + << read << " != " << write << std::endl; + } + +//] [/max_digits10_2] + // 0.666666666666667 != 0.666666666666667 + } + + { +//[max_digits10_3 + + double pi = boost::math::double_constants::pi; + std::cout.precision(std::numeric_limits::max_digits10); + std::cout << pi << std::endl; // 3.1415926535897931 + +//] [/max_digits10_3] + } + { +//[max_digits10_4 +/*`and similarly for a much higher precision type: +*/ + + using namespace boost::multiprecision; + + typedef number > cpp_dec_float_50; // 50 decimal digits. + + using boost::multiprecision::cpp_dec_float_50; + + cpp_dec_float_50 pi = boost::math::constants::pi(); + std::cout.precision(std::numeric_limits::max_digits10); + std::cout << pi << std::endl; + // 3.141592653589793238462643383279502884197169399375105820974944592307816406 +//] [/max_digits10_4] + } + + { +//[max_digits10_5 + + for (int i = 2; i < 15; i++) + { + std::cout << std::setw(std::numeric_limits::max_digits10) + << boost::math::factorial(i) << std::endl; + } + +//] [/max_digits10_5] + } + + } + catch(std::exception ex) + { + std::cout << "Caught Exception " << ex.what() << std::endl; + } + + { +//[max_digits10_6 + + typedef double T; + + bool denorm = std::numeric_limits::denorm_min() < std::numeric_limits::min(); + BOOST_ASSERT(denorm); + +//] [/max_digits10_6] + } + + { + unsigned char c = 256; + std::cout << "char c = " << (int)c << std::endl; + } + + { +//[digits10_1 + std::cout + << std::setw(std::numeric_limits::digits10 +1 +1) // digits10+1, and +1 for sign. + << std::showpos << (std::numeric_limits::max)() // +32767 + << std::endl + << std::setw(std::numeric_limits::digits10 +1 +1) + << (std::numeric_limits::min)() << std::endl; // -32767 +//] [/digits10_1] + } + + { +//[digits10_2 + std::cout + << std::setw(std::numeric_limits::digits10 +1 +1) // digits10+1, and +1 for sign. + << std::showpos << (std::numeric_limits::max)() // 65535 + << std::endl + << std::setw(std::numeric_limits::digits10 +1 +1) // digits10+1, and +1 for sign. + << (std::numeric_limits::min)() << std::endl; // 0 +//] [/digits10_2] + } + + std::cout <::max_digits10); + double d = 1e15; + double dp1 = d+1; + std::cout << d << "\n" << dp1 << std::endl; + // 1000000000000000 + // 1000000000000001 + std::cout << dp1 - d << std::endl; // 1 +//] [/digits10_3] + } + + { +//[digits10_4 + std::cout.precision(std::numeric_limits::max_digits10); + double d = 1e16; + double dp1 = d+1; + std::cout << d << "\n" << dp1 << std::endl; + // 10000000000000000 + // 10000000000000000 + std::cout << dp1 - d << std::endl; // 0 !!! +//] [/digits10_4] + } + + { +//[epsilon_1 + std::cout.precision(std::numeric_limits::max_digits10); + double d = 1.; + double eps = std::numeric_limits::epsilon(); + double dpeps = d+eps; + std::cout << std::showpoint // Ensure all trailing zeros are shown. + << d << "\n" // 1.0000000000000000 + << dpeps << std::endl; // 2.2204460492503131e-016 + std::cout << dpeps - d // 1.0000000000000002 + << std::endl; +//] [epsilon_1] + } + + { +//[epsilon_2 + double one = 1.; + double nad = boost::math::float_next(one); + std::cout << nad << "\n" // 1.0000000000000002 + << nad - one // 2.2204460492503131e-016 + << std::endl; +//] [epsilon_2] + } + { +//[epsilon_3 + std::cout.precision(std::numeric_limits::max_digits10); + double d = 1.; + double eps = std::numeric_limits::epsilon(); + double dpeps = d + eps/2; + + std::cout << std::showpoint // Ensure all trailing zeros are shown. + << dpeps << "\n" // 1.0000000000000000 + << eps/2 << std::endl; // 1.1102230246251565e-016 + std::cout << dpeps - d // 0.00000000000000000 + << std::endl; +//] [epsilon_3] + } + + { + typedef double RealType; +//[epsilon_4 +/*`A tolerance might be defined using this version of epsilon thus: +*/ + RealType tolerance = boost::math::tools::epsilon() * 2; +//] [epsilon_4] + } + + { +//[digits10_5 + -(std::numeric_limits::max)() == std::numeric_limits::lowest(); +//] [/digits10_5] + } + + { +//[denorm_min_1 + std::cout.precision(std::numeric_limits::max_digits10); + if (std::numeric_limits::has_denorm == std::denorm_present) + { + double d = std::numeric_limits::denorm_min(); + + std::cout << d << std::endl; // 4.9406564584124654e-324 + + int exponent; + + double significand = frexp(d, &exponent); + std::cout << "exponent = " << std::hex << exponent << std::endl; // fffffbcf + std::cout << "significand = " << std::hex << significand << std::endl; // 0.50000000000000000 + } + else + { + std::cout << "No denormalization. " << std::endl; + } +//] [denorm_min_1] + } + + { +//[round_error_1 + double round_err = std::numeric_limits::epsilon() // 2.2204460492503131e-016 + * std::numeric_limits::round_error(); // 1/2 + std::cout << round_err << std::endl; // 1.1102230246251565e-016 +//] [/round_error_1] + } + + { + typedef double T; +//[tolerance_1 +/*`For example, if we want a tolerance that might suit about 9 arithmetical operations, +say sqrt(9) = 3, we could define: +*/ + + T tolerance = 3 * std::numeric_limits::epsilon(); + +/*`This is very widely used in Boost.Math testing +with Boost.Test's macro `BOOST_CHECK_CLOSE_FRACTION` +*/ + + T expected = 1.0; + T calculated = 1.0 + std::numeric_limits::epsilon(); + + using boost::test_tools::check_is_close; + + bool r = check_is_close(expected, calculated, tolerance); + std::cout << std::boolalpha << r << std::endl; // true + +/*`If using Boost.Test, then call the macro version: +``BOOST_CHECK_CLOSE_FRACTION(expected, calculated, tolerance);`` +*/ + + +//] [/tolerance_1] + } + + { +//[tolerance_2 + + using boost::multiprecision::number; + using boost::multiprecision::cpp_dec_float; + using boost::multiprecision::et_off; + + typedef number, et_off > cpp_dec_float_50; // 50 decimal digits. +/*`[note that Boost.Test does not yet allow floating-point comparisons with expression templates on, +so the default expression template parameter has been replaced by `et_off`.] +*/ + + cpp_dec_float_50 tolerance = 3 * std::numeric_limits::epsilon(); + cpp_dec_float_50 expected = boost::math::constants::two_pi(); + cpp_dec_float_50 calculated = 2 * boost::math::constants::pi(); + using boost::test_tools::check_is_close; + + bool r = check_is_close(expected, calculated, tolerance); + std::cout << std::boolalpha << r << std::endl; // true + +//] [/tolerance_2] + } + + { +//[tolerance_3 + + using boost::multiprecision::cpp_bin_float_quad; + + cpp_bin_float_quad tolerance = 3 * std::numeric_limits::epsilon(); + cpp_bin_float_quad expected = boost::math::constants::two_pi(); + cpp_bin_float_quad calculated = 2 * boost::math::constants::pi(); + using boost::test_tools::check_is_close; + + bool r = check_is_close(expected, calculated, tolerance); + std::cout << std::boolalpha << r << std::endl; // true + +//] [/tolerance_3] + } + + { +//[nan_1] + +/*`NaN can be used with binary multiprecision types like `cpp_bin_float_quad`: +*/ + using boost::multiprecision::cpp_bin_float_quad; + + if (std::numeric_limits::has_quiet_NaN == true) + { + cpp_bin_float_quad tolerance = 3 * std::numeric_limits::epsilon(); + + cpp_bin_float_quad NaN = std::numeric_limits::quiet_NaN(); + std::cout << "cpp_bin_float_quad NaN is " << NaN << std::endl; // cpp_bin_float_quad NaN is nan + + cpp_bin_float_quad expected = NaN; + cpp_bin_float_quad calculated = 2 * NaN; + using boost::test_tools::check_is_close; + + bool r = check_is_close(expected, expected, tolerance); + std::cout << std::boolalpha << r << std::endl; // false, as expected because all comparisons with NaNs are false. + + r = check_is_close(expected, calculated, tolerance); + std::cout << std::boolalpha << r << std::endl; // false, as expected because all comparisons with NaNs are false. + } + else + { + std::cout << "Type " << typeid(cpp_bin_float_quad).name() << " does not have NaNs!" << std::endl; + } + +//] [/nan_1] + } + + { +//[facet_1] + +/*` +See [@boost:/libs/math/example/nonfinite_facet_sstream.cpp] +and we also need + + #include + +Then we can equally well use a multiprecision type cpp_bin_float_quad: + +*/ + using boost::multiprecision::cpp_bin_float_quad; + + typedef cpp_bin_float_quad T; + + using boost::math::nonfinite_num_put; + using boost::math::nonfinite_num_get; + { + std::locale old_locale; + std::locale tmp_locale(old_locale, new nonfinite_num_put); + std::locale new_locale(tmp_locale, new nonfinite_num_get); + std::stringstream ss; + ss.imbue(new_locale); + T inf = std::numeric_limits::infinity(); + ss << inf; // Write out. + assert(ss.str() == "inf"); + T r; + ss >> r; // Read back in. + assert(inf == r); // Confirms that the floating-point values really are identical. + std::cout << "infinity output was " << ss.str() << std::endl; + std::cout << "infinity input was " << r << std::endl; + } + +/*` + infinity output was inf + infinity input was inf + +Similarly we can do the same with NaN (except that we cannot use `assert`) +*/ + { + std::locale old_locale; + std::locale tmp_locale(old_locale, new nonfinite_num_put); + std::locale new_locale(tmp_locale, new nonfinite_num_get); + std::stringstream ss; + ss.imbue(new_locale); + T n; + T NaN = std::numeric_limits::quiet_NaN(); + ss << NaN; // Write out. + assert(ss.str() == "nan"); + std::cout << "NaN output was " << ss.str() << std::endl; + ss >> n; // Read back in. + assert(NaN == n); // Confirms that the floating-point values really are identical. + std::cout << "NaN input was " << n << std::endl; + } +/*` + NaN output was nan + NaN input was nan + +*/ +//] [/facet_1] + } + +} // int main() diff --git a/include/boost/multiprecision/cpp_bin_float.hpp b/include/boost/multiprecision/cpp_bin_float.hpp new file mode 100644 index 000000000..a93a3c8c2 --- /dev/null +++ b/include/boost/multiprecision/cpp_bin_float.hpp @@ -0,0 +1,1559 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MATH_CPP_BIN_FLOAT_HPP +#define BOOST_MATH_CPP_BIN_FLOAT_HPP + +#include +#include +#include +#include + +namespace boost{ namespace multiprecision{ namespace backends{ + +enum digit_base_type +{ + digit_base_2 = 2, + digit_base_10 = 10 +}; + +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4522) // multiple assignment operators specified +#endif + +template +class cpp_bin_float +{ +public: + static const unsigned bit_count = DigitBase == digit_base_2 ? Digits : (Digits * 1000uL) / 301uL + ((Digits * 1000uL) % 301 ? 2u : 1u); + typedef cpp_int_backend::value ? bit_count : 0, bit_count, is_void::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator> rep_type; + typedef cpp_int_backend::value ? 2 * bit_count : 0, 2 * bit_count, is_void::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator> double_rep_type; + + typedef typename rep_type::signed_types signed_types; + typedef typename rep_type::unsigned_types unsigned_types; + typedef boost::mpl::list float_types; + typedef Exponent exponent_type; + + static const exponent_type max_exponent_limit = boost::integer_traits::const_max - 2 * static_cast(bit_count); + static const exponent_type min_exponent_limit = boost::integer_traits::const_min + 2 * static_cast(bit_count); + + BOOST_STATIC_ASSERT_MSG(MinExponent >= min_exponent_limit, "Template parameter MinExponent is too negative for our internal logic to function correctly, sorry!"); + BOOST_STATIC_ASSERT_MSG(MaxExponent <= max_exponent_limit, "Template parameter MaxExponent is too large for our internal logic to function correctly, sorry!"); + BOOST_STATIC_ASSERT_MSG(MinExponent <= 0, "Template parameter MinExponent can not be positive!"); + BOOST_STATIC_ASSERT_MSG(MaxExponent >= 0, "Template parameter MaxExponent can not be negative!"); + + static const exponent_type max_exponent = MaxExponent == 0 ? max_exponent_limit : MaxExponent; + static const exponent_type min_exponent = MinExponent == 0 ? min_exponent_limit : MinExponent; + + static const exponent_type exponent_zero = max_exponent + 1; + static const exponent_type exponent_infinity = max_exponent + 2; + static const exponent_type exponent_nan = max_exponent + 3; + +private: + + rep_type m_data; + exponent_type m_exponent; + bool m_sign; +public: + cpp_bin_float() : m_data(), m_exponent(exponent_nan), m_sign(false) {} + + cpp_bin_float(const cpp_bin_float &o) + : m_data(o.m_data), m_exponent(o.m_exponent), m_sign(o.m_sign) {} + + template + cpp_bin_float(const cpp_bin_float &o, typename boost::enable_if_c<(bit_count >= cpp_bin_float::bit_count)>::type const* = 0) + : m_exponent(o.exponent()), m_sign(o.sign()) + { + typename cpp_bin_float::rep_type b(o.bits()); + copy_and_round(*this, b); + } + + template + explicit cpp_bin_float(const cpp_bin_float &o, typename boost::disable_if_c<(bit_count >= cpp_bin_float::bit_count)>::type const* = 0) + : m_exponent(o.exponent()), m_sign(o.sign()) + { + typename cpp_bin_float::rep_type b(o.bits()); + copy_and_round(*this, b); + } + + template + cpp_bin_float(const Float& f, + typename boost::enable_if_c< + (number_category::value == number_kind_floating_point) + && (std::numeric_limits::digits <= bit_count) + && (std::numeric_limits::radix == 2) + >::type const* = 0) + : m_data(), m_exponent(0), m_sign(false) + { + this->assign_float(f); + } + + cpp_bin_float& operator=(const cpp_bin_float &o) + { + m_data = o.m_data; + m_exponent = o.m_exponent; + m_sign = o.m_sign; + return *this; + } + + template + typename boost::enable_if_c= cpp_bin_float::bit_count, cpp_bin_float&>::type operator=(const cpp_bin_float &o) + { + typename cpp_bin_float::rep_type b(o.bits()); + copy_and_round(*this, b); + } + + template + typename boost::enable_if_c< + (number_category::value == number_kind_floating_point) + && (std::numeric_limits::digits <= bit_count) + && (std::numeric_limits::radix == 2), cpp_bin_float&>::type operator=(const Float& f) + { + return assign_float(f); + } + + template + typename boost::enable_if_c::value, cpp_bin_float&>::type assign_float(Float f) + { + BOOST_MATH_STD_USING + using default_ops::eval_add; + + switch((boost::math::fpclassify)(f)) + { + case FP_ZERO: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_zero; + return *this; + case FP_NAN: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_nan; + return *this; + case FP_INFINITE: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_infinity; + return *this; + } + if(f < 0) + { + *this = -f; + this->negate(); + return *this; + } + + typedef typename mpl::front::type ui_type; + m_data = static_cast(0u); + m_sign = false; + m_exponent = 0; + + static const int bits = sizeof(int) * CHAR_BIT - 1; + int e; + f = frexp(f, &e); + while(f) + { + f = ldexp(f, bits); + e -= bits; + int ipart = itrunc(f); + f -= ipart; + m_exponent += bits; + eval_add(*this, ipart); + } + m_exponent += static_cast(e); + return *this; + } + + template + typename boost::enable_if_c< + (number_category::value == number_kind_floating_point) + && !is_floating_point::value + /*&& (std::numeric_limits >::radix == 2)*/, + cpp_bin_float&>::type assign_float(Float f) + { + BOOST_MATH_STD_USING + using default_ops::eval_add; + using default_ops::eval_get_sign; + using default_ops::eval_convert_to; + using default_ops::eval_subtract; + + typedef typename boost::multiprecision::detail::canonical::type f_int_type; + typedef typename boost::multiprecision::detail::canonical::type bf_int_type; + + switch(eval_fpclassify(f)) + { + case FP_ZERO: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_zero; + return *this; + case FP_NAN: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_nan; + return *this; + case FP_INFINITE: + m_data = limb_type(0); + m_sign = false; + m_exponent = exponent_infinity; + return *this; + } + if(eval_get_sign(f) < 0) + { + f.negate(); + *this = f; + this->negate(); + return *this; + } + + typedef typename mpl::front::type ui_type; + m_data = static_cast(0u); + m_sign = false; + m_exponent = 0; + + static const int bits = sizeof(int) * CHAR_BIT - 1; + int e; + eval_frexp(f, f, &e); + while(eval_get_sign(f) != 0) + { + eval_ldexp(f, f, bits); + e -= bits; + int ipart; + eval_convert_to(&ipart, f); + eval_subtract(f, static_cast(ipart)); + m_exponent += bits; + eval_add(*this, static_cast(ipart)); + } + m_exponent += e; + if(m_exponent > max_exponent) + m_exponent = exponent_infinity; + if(m_exponent < min_exponent) + { + m_data = limb_type(0u); + m_exponent = exponent_zero; + m_sign = false; + } + else if(eval_get_sign(m_data) == 0) + { + m_exponent = exponent_zero; + m_sign = false; + } + return *this; + } + + template + typename boost::enable_if, cpp_bin_float&>::type operator=(const I& i) + { + using default_ops::eval_bit_test; + if(!i) + { + m_data = static_cast(0); + m_exponent = exponent_zero; + m_sign = false; + } + else + { + typedef typename make_unsigned::type ui_type; + ui_type fi = static_cast(boost::multiprecision::detail::abs(i)); + typedef typename boost::multiprecision::detail::canonical::type ar_type; + m_data = static_cast(fi); + unsigned shift = msb(fi); + if(shift >= bit_count) + { + m_exponent = static_cast(shift); + m_data = static_cast(fi >> (shift + 1 - bit_count)); + } + else + { + m_exponent = static_cast(shift); + eval_left_shift(m_data, bit_count - shift - 1); + } + BOOST_ASSERT(eval_bit_test(m_data, bit_count-1)); + m_sign = i < 0; + } + return *this; + } + + cpp_bin_float& operator=(const char *s); + + void swap(cpp_bin_float &o) BOOST_NOEXCEPT + { + m_data.swap(o.m_data); + std::swap(m_exponent, o.m_exponent); + std::swap(m_sign, o.m_sign); + } + + std::string str(std::streamsize dig, std::ios_base::fmtflags f) const; + + void negate() + { + if((m_exponent != exponent_zero) && (m_exponent != exponent_nan)) + m_sign = !m_sign; + } + + int compare(const cpp_bin_float &o) const BOOST_NOEXCEPT + { + if(m_sign != o.m_sign) + return m_sign ? -1 : 1; + int result; + if(m_exponent != o.m_exponent) + { + if(m_exponent == exponent_zero) + result = -1; + else if(o.m_exponent == exponent_zero) + result = 1; + else + result = m_exponent > o.m_exponent ? 1 : -1; + } + else + result = m_data.compare(o.m_data); + if(m_sign) + result = -result; + return result; + } + template + int compare(const A& o) const BOOST_NOEXCEPT + { + cpp_bin_float b; + b = o; + return compare(b); + } + + rep_type& bits() { return m_data; } + const rep_type& bits()const { return m_data; } + exponent_type& exponent() { return m_exponent; } + const exponent_type& exponent()const { return m_exponent; } + bool& sign() { return m_sign; } + const bool& sign()const { return m_sign; } + void check_invariants() + { + using default_ops::eval_bit_test; + using default_ops::eval_is_zero; + if((m_exponent <= max_exponent) && (m_exponent >= min_exponent)) + { + BOOST_ASSERT(eval_bit_test(m_data, bit_count - 1)); + } + else + { + BOOST_ASSERT(m_exponent > max_exponent); + BOOST_ASSERT(m_exponent <= exponent_nan); + BOOST_ASSERT(eval_is_zero(m_data)); + } + } +}; + +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + +template +inline void copy_and_round(cpp_bin_float &res, Int &arg) +{ + // Precondition: exponent of res must have been set before this function is called + // as we may need to adjust it based on how many cpp_bin_float::bit_count in arg are set. + using default_ops::eval_msb; + using default_ops::eval_lsb; + using default_ops::eval_left_shift; + using default_ops::eval_bit_test; + using default_ops::eval_right_shift; + using default_ops::eval_increment; + using default_ops::eval_get_sign; + + // cancellation may have resulted in arg being all zeros: + if(eval_get_sign(arg) == 0) + { + res.exponent() = cpp_bin_float::exponent_zero; + res.sign() = false; + res.bits() = static_cast(0u); + return; + } + int msb = eval_msb(arg); + if(cpp_bin_float::bit_count > msb + 1) + { + // Must have had cancellation in subtraction, shift left and copy: + eval_left_shift(arg, cpp_bin_float::bit_count - msb - 1); + res.exponent() -= static_cast(cpp_bin_float::bit_count - msb - 1); + } + else if(cpp_bin_float::bit_count < msb + 1) + { + // We have more cpp_bin_float::bit_count than we need, so round as required, + // first get the rounding bit: + bool roundup = eval_bit_test(arg, msb - cpp_bin_float::bit_count); + // Then check for a tie: + if(roundup && (msb - cpp_bin_float::bit_count == eval_lsb(arg))) + { + // Ties round towards even: + if(!eval_bit_test(arg, msb - cpp_bin_float::bit_count + 1)) + roundup = false; + } + // Shift off the cpp_bin_float::bit_count we don't need: + eval_right_shift(arg, msb - cpp_bin_float::bit_count + 1); + res.exponent() += static_cast(msb - (int)cpp_bin_float::bit_count + 1); + if(roundup) + { + eval_increment(arg); + if(eval_bit_test(arg, cpp_bin_float::bit_count)) + { + // This happens very very rairly: + eval_right_shift(arg, 1u); + ++res.exponent(); + } + } + } + BOOST_ASSERT((eval_msb(arg) == cpp_bin_float::bit_count - 1)); + res.bits() = arg; + + if(res.exponent() > cpp_bin_float::max_exponent) + { + // Overflow: + res.exponent() = cpp_bin_float::exponent_infinity; + res.bits() = static_cast(0u); + } + else if(res.exponent() < cpp_bin_float::min_exponent) + { + // Underflow: + res.exponent() = cpp_bin_float::exponent_zero; + res.bits() = static_cast(0u); + res.sign() = false; + } +} + +template +inline void do_eval_add(cpp_bin_float &res, const cpp_bin_float &a, const cpp_bin_float &b) +{ + using default_ops::eval_add; + using default_ops::eval_bit_test; + + typename cpp_bin_float::double_rep_type dt; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float::exponent_zero: + res = b; + if(res.sign()) + res.negate(); + return; + case cpp_bin_float::exponent_infinity: + if(b.exponent() == cpp_bin_float::exponent_nan) + res = b; + else + res = a; + return; // ault is still infinite. + case cpp_bin_float::exponent_nan: + res = a; + return; // ault is still a NaN. + } + switch(b.exponent()) + { + case cpp_bin_float::exponent_zero: + res = a; + return; + case cpp_bin_float::exponent_infinity: + res = b; + if(res.sign()) + res.negate(); + return; // ault is infinite. + case cpp_bin_float::exponent_nan: + res = b; + return; // ault is a NaN. + } + + typename cpp_bin_float::exponent_type e_diff = a.exponent() - b.exponent(); + bool s = a.sign(); + if(e_diff >= 0) + { + dt = a.bits(); + if(e_diff < cpp_bin_float::bit_count) + { + eval_left_shift(dt, e_diff); + res.exponent() = a.exponent() - e_diff; + eval_add(dt, b.bits()); + } + else + res.exponent() = a.exponent(); + } + else + { + dt= b.bits(); + if(-e_diff < cpp_bin_float::bit_count) + { + eval_left_shift(dt, -e_diff); + res.exponent() = b.exponent() + e_diff; + eval_add(dt, a.bits()); + } + else + res.exponent() = b.exponent(); + } + + copy_and_round(res, dt); + res.check_invariants(); + if(res.sign() != s) + res.negate(); +} + +template +inline void do_eval_subtract(cpp_bin_float &res, const cpp_bin_float &a, const cpp_bin_float &b) +{ + using default_ops::eval_subtract; + using default_ops::eval_bit_test; + + typename cpp_bin_float::double_rep_type dt; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float::exponent_zero: + if(b.exponent() == cpp_bin_float::exponent_nan) + res = std::numeric_limits > >::quiet_NaN().backend(); + else + { + res = b; + if(!res.sign()) + res.negate(); + } + return; + case cpp_bin_float::exponent_infinity: + if((b.exponent() == cpp_bin_float::exponent_nan) || (b.exponent() == cpp_bin_float::exponent_infinity)) + res = std::numeric_limits > >::quiet_NaN().backend(); + else + res = a; + return; + case cpp_bin_float::exponent_nan: + res = a; + return; // result is still a NaN. + } + switch(b.exponent()) + { + case cpp_bin_float::exponent_zero: + res = a; + return; + case cpp_bin_float::exponent_infinity: + res.exponent() = cpp_bin_float::exponent_nan; + res.sign() = false; + res.bits() = static_cast(0u); + return; // result is a NaN. + case cpp_bin_float::exponent_nan: + res = b; + return; // result is still a NaN. + } + + typename cpp_bin_float::exponent_type e_diff = a.exponent() - b.exponent(); + bool s = a.sign(); + if((e_diff > 0) || ((e_diff == 0) && a.bits().compare(b.bits()) >= 0)) + { + dt = a.bits(); + if(e_diff < cpp_bin_float::bit_count) + { + eval_left_shift(dt, e_diff); + res.exponent() = a.exponent() - e_diff; + eval_subtract(dt, b.bits()); + } + else + res.exponent() = a.exponent(); + } + else + { + dt = b.bits(); + if(-e_diff < cpp_bin_float::bit_count) + { + eval_left_shift(dt, -e_diff); + res.exponent() = b.exponent() + e_diff; + eval_subtract(dt, a.bits()); + } + else + res.exponent() = b.exponent(); + s = !s; + } + + copy_and_round(res, dt); + if(res.sign() != s) + res.negate(); + res.check_invariants(); +} + +template +inline void eval_add(cpp_bin_float &res, const cpp_bin_float &a, const cpp_bin_float &b) +{ + if(a.sign() == b.sign()) + do_eval_add(res, a, b); + else + do_eval_subtract(res, a, b); +} + +template +inline void eval_add(cpp_bin_float &res, const cpp_bin_float &a) +{ + return eval_add(res, res, a); +} + +template +inline void eval_subtract(cpp_bin_float &res, const cpp_bin_float &a, const cpp_bin_float &b) +{ + if(a.sign() != b.sign()) + do_eval_add(res, a, b); + else + do_eval_subtract(res, a, b); +} + +template +inline void eval_subtract(cpp_bin_float &res, const cpp_bin_float &a) +{ + return eval_subtract(res, res, a); +} + +template +inline void eval_multiply(cpp_bin_float &res, const cpp_bin_float &a, const cpp_bin_float &b) +{ + using default_ops::eval_bit_test; + using default_ops::eval_multiply; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float::exponent_zero: + if(b.exponent() == cpp_bin_float::exponent_nan) + res = b; + else + res = a; + return; + case cpp_bin_float::exponent_infinity: + switch(b.exponent()) + { + case cpp_bin_float::exponent_zero: + res = std::numeric_limits > >::quiet_NaN().backend(); + break; + case cpp_bin_float::exponent_nan: + res = b; + break; + default: + res = a; + break; + } + return; + case cpp_bin_float::exponent_nan: + res = a; + return; + } + if(b.exponent() > cpp_bin_float::max_exponent) + { + res = b; + return; + } + if((a.exponent() > 0) && (b.exponent() > 0)) + { + if(cpp_bin_float::max_exponent + 2 - a.exponent() < b.exponent()) + { + // We will certainly overflow: + res.exponent() = cpp_bin_float::exponent_infinity; + res.sign() = a.sign() != b.sign(); + res.bits() = static_cast(0u); + return; + } + } + if((a.exponent() < 0) && (b.exponent() < 0)) + { + if(cpp_bin_float::min_exponent - 2 - a.exponent() > b.exponent()) + { + // We will certainly underflow: + res.exponent() = cpp_bin_float::exponent_zero; + res.sign() = false; + res.bits() = static_cast(0u); + return; + } + } + + typename cpp_bin_float::double_rep_type dt; + eval_multiply(dt, a.bits(), b.bits()); + res.exponent() = a.exponent() + b.exponent() - cpp_bin_float::bit_count + 1; + copy_and_round(res, dt); + res.check_invariants(); + res.sign() = a.sign() != b.sign(); +} + +template +inline void eval_multiply(cpp_bin_float &res, const cpp_bin_float &a) +{ + eval_multiply(res, res, a); +} + +template +inline typename enable_if_c::value>::type eval_multiply(cpp_bin_float &res, const cpp_bin_float &a, const U &b) +{ + using default_ops::eval_bit_test; + using default_ops::eval_multiply; + + // Special cases first: + switch(a.exponent()) + { + case cpp_bin_float::exponent_zero: + res = a; + return; + case cpp_bin_float::exponent_infinity: + if(b == 0) + res = std::numeric_limits > >::quiet_NaN().backend(); + else + res = a; + return; + case cpp_bin_float::exponent_nan: + res = a; + return; + } + + typename cpp_bin_float::double_rep_type dt; + typedef typename boost::multiprecision::detail::canonical::double_rep_type>::type canon_ui_type; + eval_multiply(dt, a.bits(), static_cast(b)); + res.exponent() = a.exponent(); + copy_and_round(res, dt); + res.check_invariants(); + res.sign() = a.sign(); +} + +template +inline typename enable_if_c::value>::type eval_multiply(cpp_bin_float &res, const U &b) +{ + eval_multiply(res, res, b); +} + +template +inline typename enable_if_c::value>::type eval_multiply(cpp_bin_float &res, const cpp_bin_float &a, const S &b) +{ + typedef typename make_unsigned::type ui_type; + eval_multiply(res, a, static_cast(boost::multiprecision::detail::abs(b))); + if(b < 0) + res.negate(); +} + +template +inline typename enable_if_c::value>::type eval_multiply(cpp_bin_float &res, const S &b) +{ + eval_multiply(res, res, b); +} + +template +inline void eval_divide(cpp_bin_float &res, const cpp_bin_float &u, const cpp_bin_float &v) +{ + using default_ops::eval_subtract; + using default_ops::eval_qr; + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_increment; + + // + // Special cases first: + // + switch(u.exponent()) + { + case cpp_bin_float::exponent_zero: + switch(v.exponent()) + { + case cpp_bin_float::exponent_zero: + case cpp_bin_float::exponent_nan: + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + res = u; + return; + case cpp_bin_float::exponent_infinity: + switch(v.exponent()) + { + case cpp_bin_float::exponent_infinity: + case cpp_bin_float::exponent_nan: + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + res = u; + return; + case cpp_bin_float::exponent_nan: + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + switch(v.exponent()) + { + case cpp_bin_float::exponent_zero: + { + bool s = u.sign() != v.sign(); + res = std::numeric_limits > >::infinity().backend(); + res.sign() = s; + return; + } + case cpp_bin_float::exponent_infinity: + res.exponent() = cpp_bin_float::exponent_zero; + res.bits() = limb_type(0); + res.sign() = false; + return; + case cpp_bin_float::exponent_nan: + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + + // We can scale u and v so that both are integers, then perform integer + // division to obtain quotient q and remainder r, such that: + // + // q * v + r = u + // + // and hense: + // + // q + r/v = u/v + // + // From this, assuming q has "cpp_bin_float::bit_count" cpp_bin_float::bit_count, we only need to determine whether + // r/v is less than, equal to, or greater than 0.5 to determine rounding - + // this we can do with a shift and comparison. + // + // We can set the exponent and sign of the result up front: + // + res.exponent() = u.exponent() - v.exponent() - 1; + res.sign() = u.sign() != v.sign(); + // + // Now get the quotient and remainder: + // + typename cpp_bin_float::double_rep_type t(u.bits()), t2(v.bits()), q, r; + eval_left_shift(t, cpp_bin_float::bit_count); + eval_qr(t, t2, q, r); + // + // We now have either "cpp_bin_float::bit_count" or "cpp_bin_float::bit_count+1" significant cpp_bin_float::bit_count in q. + // + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + if(eval_bit_test(q, cpp_bin_float::bit_count)) + { + // + // OK we have cpp_bin_float::bit_count+1 cpp_bin_float::bit_count, so we already have rounding info, + // we just need to changes things if the last bit is 1 and the + // remainder is non-zero (ie we do not have a tie). + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float::bit_count)); + if((q.limbs()[0] & 1u) && eval_get_sign(r)) + { + eval_increment(q); + } + } + else + { + // + // We have exactly "cpp_bin_float::bit_count" cpp_bin_float::bit_count in q. + // Get rounding info, which we can get by comparing 2r with v. + // We want to call copy_and_round to handle rounding and general cleanup, + // so we'll left shift q and add some fake digits on the end to represent + // how we'll be rounding. + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float::bit_count - 1)); + static const unsigned lshift = cpp_bin_float::bit_count < limb_bits ? 2 : limb_bits; + eval_left_shift(q, lshift); + res.exponent() -= lshift; + eval_left_shift(r, 1u); + int c = r.compare(v.bits()); + if(c == 0) + q.limbs()[0] |= static_cast(1u) << (lshift - 1); + else if(c > 0) + q.limbs()[0] |= (static_cast(1u) << (lshift - 1)) + static_cast(1u); + } + copy_and_round(res, q); +} + +template +inline void eval_divide(cpp_bin_float &res, const cpp_bin_float &arg) +{ + eval_divide(res, res, arg); +} + +template +inline typename enable_if_c::value>::type eval_divide(cpp_bin_float &res, const cpp_bin_float &u, const U &v) +{ + using default_ops::eval_subtract; + using default_ops::eval_qr; + using default_ops::eval_bit_test; + using default_ops::eval_get_sign; + using default_ops::eval_increment; + + // + // Special cases first: + // + switch(u.exponent()) + { + case cpp_bin_float::exponent_zero: + if(v == 0) + { + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + res = u; + return; + case cpp_bin_float::exponent_infinity: + res = u; + return; + case cpp_bin_float::exponent_nan: + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + if(v == 0) + { + bool s = u.sign(); + res = std::numeric_limits > >::infinity().backend(); + res.sign() = s; + return; + } + + // We can scale u and v so that both are integers, then perform integer + // division to obtain quotient q and remainder r, such that: + // + // q * v + r = u + // + // and hense: + // + // q + r/v = u/v + // + // From this, assuming q has "cpp_bin_float::bit_count" cpp_bin_float::bit_count, we only need to determine whether + // r/v is less than, equal to, or greater than 0.5 to determine rounding - + // this we can do with a shift and comparison. + // + // We can set the exponent and sign of the result up front: + // + int gb = msb(v); + res.exponent() = u.exponent() - static_cast(gb) - static_cast(1); + res.sign() = u.sign(); + // + // Now get the quotient and remainder: + // + typename cpp_bin_float::double_rep_type t(u.bits()), q, r; + eval_left_shift(t, gb + 1); + eval_qr(t, number::double_rep_type>::canonical_value(v), q, r); + // + // We now have either "cpp_bin_float::bit_count" or "cpp_bin_float::bit_count+1" significant cpp_bin_float::bit_count in q. + // + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + if(eval_bit_test(q, cpp_bin_float::bit_count)) + { + // + // OK we have cpp_bin_float::bit_count+1 cpp_bin_float::bit_count, so we already have rounding info, + // we just need to changes things if the last bit is 1 and the + // remainder is non-zero (ie we do not have a tie). + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float::bit_count)); + if((q.limbs()[0] & 1u) && eval_get_sign(r)) + { + eval_increment(q); + } + } + else + { + // + // We have exactly "cpp_bin_float::bit_count" cpp_bin_float::bit_count in q. + // Get rounding info, which we can get by comparing 2r with v. + // We want to call copy_and_round to handle rounding and general cleanup, + // so we'll left shift q and add some fake cpp_bin_float::bit_count on the end to represent + // how we'll be rounding. + // + BOOST_ASSERT((eval_msb(q) == cpp_bin_float::bit_count - 1)); + static const unsigned lshift = cpp_bin_float::bit_count < limb_bits ? 2 : limb_bits; + eval_left_shift(q, lshift); + res.exponent() -= lshift; + eval_left_shift(r, 1u); + int c = r.compare(number::double_rep_type>::canonical_value(v)); + if(c == 0) + q.limbs()[0] |= static_cast(1u) << (lshift - 1); + else if(c > 0) + q.limbs()[0] |= (static_cast(1u) << (lshift - 1)) + static_cast(1u); + } + copy_and_round(res, q); +} + +template +inline typename enable_if_c::value>::type eval_divide(cpp_bin_float &res, const U &v) +{ + eval_divide(res, res, v); +} + +template +inline typename enable_if_c::value>::type eval_divide(cpp_bin_float &res, const cpp_bin_float &u, const S &v) +{ + typedef typename make_unsigned::type ui_type; + eval_divide(res, u, static_cast(boost::multiprecision::detail::abs(v))); + if(v < 0) + res.negate(); +} + +template +inline typename enable_if_c::value>::type eval_divide(cpp_bin_float &res, const S &v) +{ + eval_divide(res, res, v); +} + +template +inline int eval_get_sign(const cpp_bin_float &arg) +{ + return arg.exponent() == cpp_bin_float::exponent_zero ? 0 : arg.sign() ? -1 : 1; +} + +template +inline bool eval_is_zero(const cpp_bin_float &arg) +{ + return arg.exponent() == cpp_bin_float::exponent_zero; +} + +template +inline bool eval_eq(const cpp_bin_float &a, cpp_bin_float &b) +{ + return (a.exponent() == b.exponent()) + && (a.sign() == b.sign()) + && (a.bits().compare(b.bits()) == 0) + && (a.exponent() != cpp_bin_float::exponent_nan); +} + +template +inline void eval_convert_to(long long *res, const cpp_bin_float &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + *res = 0; + return; + case cpp_bin_float::exponent_nan: + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + case cpp_bin_float::exponent_infinity: + *res = (std::numeric_limits::max)(); + if(arg.sign()) + *res = -*res; + return; + } + typename cpp_bin_float::rep_type man(arg.bits()); + typename mpl::if_c::exponent_type) < sizeof(int), int, typename cpp_bin_float::exponent_type>::type shift + = (int)cpp_bin_float::bit_count - 1 - arg.exponent(); + if(shift > (int)cpp_bin_float::bit_count - 1) + { + *res = 0; + return; + } + else if(shift < 0) + { + // TODO: what if we have fewer cpp_bin_float::bit_count than a long long? + *res = (std::numeric_limits::max)(); + if(arg.sign()) + *res = -*res; + return; + } + eval_right_shift(man, shift); + eval_convert_to(res, man); + if(arg.sign()) + *res = -*res; +} + +template +inline void eval_convert_to(unsigned long long *res, const cpp_bin_float &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + *res = 0; + return; + case cpp_bin_float::exponent_nan: + BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer.")); + case cpp_bin_float::exponent_infinity: + *res = (std::numeric_limits::max)(); + return; + } + typename cpp_bin_float::rep_type man(arg.bits()); + typename mpl::if_c::exponent_type) < sizeof(int), int, typename cpp_bin_float::exponent_type>::type shift + = (int)cpp_bin_float::bit_count - 1 - arg.exponent(); + if(shift > (int)cpp_bin_float::bit_count - 1) + { + *res = 0; + return; + } + else if(shift < 0) + { + // TODO: what if we have fewer cpp_bin_float::bit_count than a long long? + *res = (std::numeric_limits::max)(); + return; + } + eval_right_shift(man, shift); + eval_convert_to(res, man); +} + +template +inline void eval_convert_to(long double *res, const cpp_bin_float &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + *res = 0; + return; + case cpp_bin_float::exponent_nan: + *res = std::numeric_limits::quiet_NaN(); + return; + case cpp_bin_float::exponent_infinity: + *res = (std::numeric_limits::infinity)(); + if(arg.sign()) + *res = -*res; + return; + } + typename cpp_bin_float::exponent_type e = arg.exponent(); + e -= cpp_bin_float::bit_count - 1; + *res = std::ldexp(static_cast(*arg.bits().limbs()), e); + for(unsigned i = 1; i < arg.bits().size(); ++i) + { + e += sizeof(*arg.bits().limbs()) * CHAR_BIT; + *res += std::ldexp(static_cast(arg.bits().limbs()[i]), e); + } + if(arg.sign()) + *res = -*res; +} + +template +inline void eval_frexp(cpp_bin_float &res, const cpp_bin_float &arg, Exponent *e) +{ + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + case cpp_bin_float::exponent_nan: + case cpp_bin_float::exponent_infinity: + *e = 0; + res = arg; + return; + } + res = arg; + *e = arg.exponent() + 1; + res.exponent() = -1; +} + +template +inline void eval_frexp(cpp_bin_float &res, const cpp_bin_float &arg, I *pe) +{ + Exponent e; + eval_frexp(res, arg, &e); + if((e > (std::numeric_limits::max)()) || (e < (std::numeric_limits::min)())) + { + BOOST_THROW_EXCEPTION(std::runtime_error("Exponent was outside of the range of the argument type to frexp.")); + } + *pe = static_cast(e); +} + +template +inline void eval_ldexp(cpp_bin_float &res, const cpp_bin_float &arg, Exponent e) +{ + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + case cpp_bin_float::exponent_nan: + case cpp_bin_float::exponent_infinity: + res = arg; + return; + } + if((e > 0) && (cpp_bin_float::max_exponent - e < arg.exponent())) + { + // Overflow: + res = std::numeric_limits > >::infinity().backend(); + res.sign() = arg.sign(); + } + else if((e < 0) && (cpp_bin_float::min_exponent - e > arg.exponent())) + { + // Underflow: + res = limb_type(0); + } + else + { + res = arg; + res.exponent() += e; + } +} + +template +inline typename enable_if_c::value>::type eval_ldexp(cpp_bin_float &res, const cpp_bin_float &arg, I e) +{ + typedef typename make_signed::type si_type; + if(e > static_cast((std::numeric_limits::max)())) + res = std::numeric_limits > >::infinity().backend(); + else + eval_ldexp(res, arg, static_cast(e)); +} + +template +inline typename enable_if_c::value>::type eval_ldexp(cpp_bin_float &res, const cpp_bin_float &arg, I e) +{ + if((e > (std::numeric_limits::max)()) || (e < (std::numeric_limits::min)())) + { + res = std::numeric_limits > >::infinity().backend(); + if(e < 0) + res.negate(); + } + else + eval_ldexp(res, arg, static_cast(e)); +} + +/* +* Sign manipulation +*/ + +template +inline void eval_abs(cpp_bin_float &res, const cpp_bin_float &arg) +{ + res = arg; + res.sign() = false; +} + +template +inline void eval_fabs(cpp_bin_float &res, const cpp_bin_float &arg) +{ + res = arg; + res.sign() = false; +} + +template +inline int eval_fpclassify(const cpp_bin_float &arg) +{ + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + return FP_ZERO; + case cpp_bin_float::exponent_infinity: + return FP_INFINITE; + case cpp_bin_float::exponent_nan: + return FP_NAN; + } + return FP_NORMAL; +} + +template +inline void eval_sqrt(cpp_bin_float &res, const cpp_bin_float &arg) +{ + using default_ops::eval_integer_sqrt; + using default_ops::eval_bit_test; + using default_ops::eval_increment; + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + case cpp_bin_float::exponent_nan: + res = arg; + return; + case cpp_bin_float::exponent_infinity: + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + if(arg.sign()) + { + res = std::numeric_limits > >::quiet_NaN().backend(); + return; + } + + typename cpp_bin_float::double_rep_type t(arg.bits()), r, s; + eval_left_shift(t, arg.exponent() & 1 ? cpp_bin_float::bit_count : cpp_bin_float::bit_count - 1); + eval_integer_sqrt(s, r, t); + + if(!eval_bit_test(s, cpp_bin_float::bit_count)) + { + // We have exactly the right number of cpp_bin_float::bit_count in the result, round as required: + if(s.compare(r) < 0) + { + eval_increment(s); + } + } + typename cpp_bin_float::exponent_type ae = arg.exponent(); + res.exponent() = ae / 2; + if((ae & 1) && (ae < 0)) + --res.exponent(); + copy_and_round(res, s); +} + +template +inline void eval_floor(cpp_bin_float &res, const cpp_bin_float &arg) +{ + using default_ops::eval_increment; + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + case cpp_bin_float::exponent_nan: + case cpp_bin_float::exponent_infinity: + res = arg; + return; + } + typename mpl::if_c::exponent_type) < sizeof(int), int, typename cpp_bin_float::exponent_type>::type shift = + (int)cpp_bin_float::bit_count - arg.exponent() - 1; + if((arg.exponent() > (int)cpp_bin_float::max_exponent) || (shift <= 0)) + { + // Either arg is already an integer, or a special value: + res = arg; + return; + } + if(shift >= (int)cpp_bin_float::bit_count) + { + res = static_cast(arg.sign() ? -1 : 0); + return; + } + bool fractional = (int)eval_lsb(arg.bits()) < shift; + res = arg; + eval_right_shift(res.bits(), shift); + if(fractional && res.sign()) + { + eval_increment(res.bits()); + if(eval_msb(res.bits()) != cpp_bin_float::bit_count - 1 - shift) + { + // Must have extended result by one bit in the increment: + --shift; + ++res.exponent(); + } + } + eval_left_shift(res.bits(), shift); +} + +template +inline void eval_ceil(cpp_bin_float &res, const cpp_bin_float &arg) +{ + using default_ops::eval_increment; + switch(arg.exponent()) + { + case cpp_bin_float::exponent_zero: + case cpp_bin_float::exponent_nan: + case cpp_bin_float::exponent_infinity: + res = arg; + return; + } + typename mpl::if_c::exponent_type) < sizeof(int), int, typename cpp_bin_float::exponent_type>::type shift = (int)cpp_bin_float::bit_count - arg.exponent() - 1; + if((arg.exponent() > (int)cpp_bin_float::max_exponent) || (shift <= 0)) + { + // Either arg is already an integer, or a special value: + res = arg; + return; + } + if(shift >= cpp_bin_float::bit_count) + { + res = static_cast(arg.sign() ? 0 : 1); + return; + } + bool fractional = (int)eval_lsb(arg.bits()) < shift; + res = arg; + eval_right_shift(res.bits(), shift); + if(fractional && !res.sign()) + { + eval_increment(res.bits()); + if(eval_msb(res.bits()) != cpp_bin_float::bit_count - 1 - shift) + { + // Must have extended result by one bit in the increment: + --shift; + ++res.exponent(); + } + } + eval_left_shift(res.bits(), shift); +} + +} // namespace backends + +#ifdef BOOST_NO_SFINAE_EXPR + +namespace detail{ + +template +struct is_explicitly_convertible, backends::cpp_bin_float > : public mpl::true_ {}; + +} +#endif + + +using backends::cpp_bin_float; +using backends::digit_base_2; +using backends::digit_base_10; + +template +struct number_category > : public boost::mpl::int_{}; + +template +struct expression_template_default > +{ + static const expression_template_option value = is_void::value ? et_off : et_on; +}; + +typedef number > cpp_bin_float_50; +typedef number > cpp_bin_float_100; + +typedef number, et_off> cpp_bin_float_single; +typedef number, et_off> cpp_bin_float_double; +typedef number, et_off> cpp_bin_float_double_extended; +typedef number, et_off> cpp_bin_float_quad; + +}} // namespaces + +#include +#include + +namespace std{ + +// +// numeric_limits [partial] specializations for the types declared in this header: +// +template +class numeric_limits, ExpressionTemplates> > +{ + typedef boost::multiprecision::number, ExpressionTemplates> number_type; +public: + BOOST_STATIC_CONSTEXPR bool is_specialized = true; + static number_type (min)() + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1u; + value.second.backend().exponent() = boost::multiprecision::cpp_bin_float::min_exponent; + } + return value.second; + } + static number_type (max)() + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + eval_complement(value.second.backend().bits(), value.second.backend().bits()); + value.second.backend().exponent() = boost::multiprecision::cpp_bin_float::max_exponent; + } + return value.second; + } + BOOST_STATIC_CONSTEXPR number_type lowest() + { + return -(max)(); + } + BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_bin_float::bit_count; + BOOST_STATIC_CONSTEXPR int digits10 = digits * 301 / 1000; + // Is this really correct??? + BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 2; + BOOST_STATIC_CONSTEXPR bool is_signed = true; + BOOST_STATIC_CONSTEXPR bool is_integer = false; + BOOST_STATIC_CONSTEXPR bool is_exact = false; + BOOST_STATIC_CONSTEXPR int radix = 2; + static number_type epsilon() + { + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + value.second = ldexp(value.second, 1 - (int)digits); + } + return value.second; + } + // What value should this be???? + static number_type round_error() + { + // returns 0.5 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second = 1; + value.second = ldexp(value.second, -1); + } + return value.second; + } + BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float::exponent_type min_exponent = boost::multiprecision::cpp_bin_float::min_exponent; + BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float::exponent_type min_exponent10 = (min_exponent / 1000) * 301L; + BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float::exponent_type max_exponent = boost::multiprecision::cpp_bin_float::max_exponent; + BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float::exponent_type max_exponent10 = (max_exponent / 1000) * 301L; + BOOST_STATIC_CONSTEXPR bool has_infinity = true; + BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; + BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; + BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent; + BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; + static number_type infinity() + { + // returns epsilon/2 + initializer.do_nothing(); + static std::pair value; + if(!value.first) + { + value.first = true; + value.second.backend().exponent() = boost::multiprecision::cpp_bin_float::exponent_infinity; + } + return value.second; + } + static number_type quiet_NaN() + { + return number_type(); + } + BOOST_STATIC_CONSTEXPR number_type signaling_NaN() + { + return number_type(0); + } + BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(0); } + BOOST_STATIC_CONSTEXPR bool is_iec559 = false; + BOOST_STATIC_CONSTEXPR bool is_bounded = true; + BOOST_STATIC_CONSTEXPR bool is_modulo = false; + BOOST_STATIC_CONSTEXPR bool traps = true; + BOOST_STATIC_CONSTEXPR bool tinyness_before = false; + BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest; +private: + struct data_initializer + { + data_initializer() + { + std::numeric_limits > >::epsilon(); + std::numeric_limits > >::round_error(); + (std::numeric_limits > >::min)(); + (std::numeric_limits > >::max)(); + std::numeric_limits > >::infinity(); + std::numeric_limits > >::quiet_NaN(); + } + void do_nothing()const{} + }; + static const data_initializer initializer; +}; + +template +const typename numeric_limits, ExpressionTemplates> >::data_initializer numeric_limits, ExpressionTemplates> >::initializer; + +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION + +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::digits10; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::max_digits10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_signed; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_integer; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_exact; +template +BOOST_CONSTEXPR_OR_CONST int numeric_limits, ExpressionTemplates> >::radix; +template +BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float::exponent_type numeric_limits, ExpressionTemplates> >::min_exponent; +template +BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float::exponent_type numeric_limits, ExpressionTemplates> >::min_exponent10; +template +BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float::exponent_type numeric_limits, ExpressionTemplates> >::max_exponent; +template +BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float::exponent_type numeric_limits, ExpressionTemplates> >::max_exponent10; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_infinity; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_quiet_NaN; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_signaling_NaN; +template +BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits, ExpressionTemplates> >::has_denorm; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::has_denorm_loss; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_iec559; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_bounded; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::is_modulo; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::traps; +template +BOOST_CONSTEXPR_OR_CONST bool numeric_limits, ExpressionTemplates> >::tinyness_before; +template +BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits, ExpressionTemplates> >::round_style; + +#endif + +} // namespace std + +#endif diff --git a/include/boost/multiprecision/cpp_bin_float/io.hpp b/include/boost/multiprecision/cpp_bin_float/io.hpp new file mode 100644 index 000000000..a744b4460 --- /dev/null +++ b/include/boost/multiprecision/cpp_bin_float/io.hpp @@ -0,0 +1,690 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MP_CPP_BIN_FLOAT_IO_HPP +#define BOOST_MP_CPP_BIN_FLOAT_IO_HPP + +namespace boost{ namespace multiprecision{ namespace cpp_bf_io_detail{ + +// +// Multiplies a by b and shifts the result so it fits inside max_bits bits, +// returns by how much the result was shifted. +// +template +inline I restricted_multiply(cpp_int& result, const cpp_int& a, const cpp_int& b, I max_bits, boost::int64_t& error) +{ + result = a * b; + I gb = msb(result); + I rshift = 0; + if(gb > max_bits) + { + rshift = gb - max_bits; + I lb = lsb(result); + int roundup = 0; + // The error rate increases by the error of both a and b, + // this may be overly pessimistic in many case as we're assuming + // that a and b have the same level of uncertainty... + if(lb < rshift) + error = error ? error * 2 : 1; + if(rshift) + { + BOOST_ASSERT(rshift < INT_MAX); + if(bit_test(result, static_cast(rshift - 1))) + { + if(lb == rshift - 1) + roundup = 1; + else + roundup = 2; + } + result >>= rshift; + } + if((roundup == 2) || ((roundup == 1) && (result.backend().limbs()[0] & 1))) + ++result; + } + return rshift; +} +// +// Computes a^e shifted to the right so it fits in max_bits, returns how far +// to the right we are shifted. +// +template +inline I restricted_pow(cpp_int& result, const cpp_int& a, I e, I max_bits, boost::int64_t& error) +{ + BOOST_ASSERT(&result != &a); + I exp = 0; + if(e == 1) + { + result = a; + return exp; + } + else if(e == 2) + { + return restricted_multiply(result, a, a, max_bits, error); + } + else if(e == 3) + { + exp = restricted_multiply(result, a, a, max_bits, error); + exp += restricted_multiply(result, result, a, max_bits, error); + return exp; + } + I p = e / 2; + exp = restricted_pow(result, a, p, max_bits, error); + exp *= 2; + exp += restricted_multiply(result, result, result, max_bits, error); + if(e & 1) + exp += restricted_multiply(result, result, a, max_bits, error); + return exp; +} + +inline int get_round_mode(const cpp_int& what, boost::int64_t location, boost::int64_t error) +{ + // + // Can we round what at /location/, if the error in what is /error/ in + // units of 0.5ulp. Return: + // + // -1: Can't round. + // 0: leave as is. + // 1: tie. + // 2: round up. + // + BOOST_ASSERT(location >= 0); + BOOST_ASSERT(location < INT_MAX); + boost::int64_t error_radius = error & 1 ? (1 + error) / 2 : error / 2; + if(error_radius && ((int)msb(error_radius) >= location)) + return -1; + if(bit_test(what, static_cast(location))) + { + if((int)lsb(what) == location) + return error ? -1 : 1; // Either a tie or can't round depending on whether we have any error + if(!error) + return 2; // no error, round up. + cpp_int t = what - error_radius; + if((int)lsb(t) >= location) + return -1; + return 2; + } + else if(error) + { + cpp_int t = what + error_radius; + return bit_test(t, static_cast(location)) ? -1 : 0; + } + return 0; +} + +inline int get_round_mode(cpp_int& r, cpp_int& d, boost::int64_t error, const cpp_int& q) +{ + // + // Lets suppose we have an inexact division by d+delta, where the true + // value for the divisor is d, and with |delta| <= error/2, then + // we have calculated q and r such that: + // + // n r + // --- = q + ----------- + // d + error d + error + // + // Rearranging for n / d we get: + // + // n delta*q + r + // --- = q + ------------- + // d d + // + // So rounding depends on whether 2r + error * q > d. + // + // We return: + // 0 = down down. + // 1 = tie. + // 2 = round up. + // -1 = couldn't decide. + // + r <<= 1; + int c = r.compare(d); + if(c == 0) + return error ? -1 : 1; + if(c > 0) + { + if(error) + { + r -= error * q; + return r.compare(d) > 0 ? 2 : -1; + } + return 2; + } + if(error) + { + r += error * q; + return r.compare(d) < 0 ? 0 : -1; + } + return 0; +} + +} // namespace + +namespace backends{ + +template +cpp_bin_float& cpp_bin_float::operator=(const char *s) +{ + cpp_int n; + boost::intmax_t decimal_exp = 0; + boost::intmax_t digits_seen = 0; + static const boost::intmax_t max_digits_seen = 4 + (cpp_bin_float::bit_count * 301L) / 1000; + bool ss = false; + // + // Extract the sign: + // + if(*s == '-') + { + ss = true; + ++s; + } + else if(*s == '+') + ++s; + // + // Special cases first: + // + if((std::strcmp(s, "nan") == 0) || (std::strcmp(s, "NaN") == 0) || (std::strcmp(s, "NAN") == 0)) + { + return *this = std::numeric_limits > >::quiet_NaN().backend(); + } + if((std::strcmp(s, "inf") == 0) || (std::strcmp(s, "Inf") == 0) || (std::strcmp(s, "INF") == 0) || (std::strcmp(s, "infinity") == 0) || (std::strcmp(s, "Infinity") == 0) || (std::strcmp(s, "INFINITY") == 0)) + { + *this = std::numeric_limits > >::infinity().backend(); + if(ss) + negate(); + return *this; + } + // + // Digits before the point: + // + while(*s && (*s >= '0') && (*s <= '9')) + { + n *= 10u; + n += *s - '0'; + if(digits_seen || (*s != '0')) + ++digits_seen; + ++s; + } + // The decimal point (we really should localise this!!) + if(*s && (*s == '.')) + ++s; + // + // Digits after the point: + // + while(*s && (*s >= '0') && (*s <= '9')) + { + n *= 10u; + n += *s - '0'; + --decimal_exp; + if(digits_seen || (*s != '0')) + ++digits_seen; + ++s; + if(digits_seen > max_digits_seen) + break; + } + // + // Digits we're skipping: + // + while(*s && (*s >= '0') && (*s <= '9')) + ++s; + // + // See if there's an exponent: + // + if(*s && ((*s == 'e') || (*s == 'E'))) + { + ++s; + boost::intmax_t e = 0; + bool es = false; + if(*s && (*s == '-')) + { + es = true; + ++s; + } + else if(*s && (*s == '+')) + ++s; + while(*s && (*s >= '0') && (*s <= '9')) + { + e *= 10u; + e += *s - '0'; + ++s; + } + if(es) + e = -e; + decimal_exp += e; + } + if(*s) + { + // + // Oops unexpected input at the end of the number: + // + BOOST_THROW_EXCEPTION(std::runtime_error("Unable to parse string as a valid floating point number.")); + } + if(n == 0) + { + // Result is necessarily zero: + *this = static_cast(0u); + return *this; + } + + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + // + // Set our working precision - this is heuristic based, we want + // a value as small as possible > cpp_bin_float::bit_count to avoid large computations + // and excessive memory usage, but we also want to avoid having to + // up the computation and start again at a higher precision. + // So we round cpp_bin_float::bit_count up to the nearest whole number of limbs, and add + // one limb for good measure. This works very well for small exponents, + // but for larger exponents we may may need to restart, we could add some + // extra precision right from the start for larger exponents, but this + // seems to be slightly slower in the *average* case: + // +#ifdef BOOST_MP_STRESS_IO + boost::intmax_t max_bits = cpp_bin_float::bit_count + 32; +#else + boost::intmax_t max_bits = cpp_bin_float::bit_count + (cpp_bin_float::bit_count % limb_bits ? limb_bits - cpp_bin_float::bit_count % limb_bits : 0) + limb_bits; +#endif + boost::int64_t error = 0; + boost::intmax_t calc_exp = 0; + boost::intmax_t final_exponent = 0; + + if(decimal_exp >= 0) + { + // Nice and simple, the result is an integer... + do + { + cpp_int t; + if(decimal_exp) + { + calc_exp = boost::multiprecision::cpp_bf_io_detail::restricted_pow(t, cpp_int(5), decimal_exp, max_bits, error); + calc_exp += boost::multiprecision::cpp_bf_io_detail::restricted_multiply(t, t, n, max_bits, error); + } + else + t = n; + final_exponent = (boost::int64_t)cpp_bin_float::bit_count - 1 + decimal_exp + calc_exp; + int rshift = msb(t) - cpp_bin_float::bit_count + 1; + if(rshift > 0) + { + final_exponent += rshift; + int roundup = boost::multiprecision::cpp_bf_io_detail::get_round_mode(t, rshift - 1, error); + t >>= rshift; + if((roundup == 2) || ((roundup == 1) && t.backend().limbs()[0] & 1)) + ++t; + else if(roundup < 0) + { +#ifdef BOOST_MP_STRESS_IO + max_bits += 32; +#else + max_bits *= 2; +#endif + error = 0; + continue; + } + } + else + { + BOOST_ASSERT(!error); + } + if(final_exponent > cpp_bin_float::max_exponent) + { + exponent() = cpp_bin_float::max_exponent; + final_exponent -= cpp_bin_float::max_exponent; + } + else if(final_exponent < cpp_bin_float::min_exponent) + { + // Underflow: + exponent() = cpp_bin_float::min_exponent; + final_exponent -= cpp_bin_float::min_exponent; + } + else + { + exponent() = static_cast(final_exponent); + final_exponent = 0; + } + copy_and_round(*this, t.backend()); + break; + } + while(true); + + if(ss != sign()) + negate(); + } + else + { + // Result is the ratio of two integers: we need to organise the + // division so as to produce at least an N-bit result which we can + // round according to the remainder. + //cpp_int d = pow(cpp_int(5), -decimal_exp); + do + { + cpp_int d; + calc_exp = boost::multiprecision::cpp_bf_io_detail::restricted_pow(d, cpp_int(5), -decimal_exp, max_bits, error); + int shift = (int)cpp_bin_float::bit_count - msb(n) + msb(d); + final_exponent = cpp_bin_float::bit_count - 1 + decimal_exp - calc_exp; + if(shift > 0) + { + n <<= shift; + final_exponent -= static_cast(shift); + } + cpp_int q, r; + divide_qr(n, d, q, r); + int gb = msb(q); + BOOST_ASSERT((gb >= cpp_bin_float::bit_count - 1)); + // + // Check for rounding conditions we have to + // handle ourselves: + // + int roundup = 0; + if(gb == cpp_bin_float::bit_count - 1) + { + // Exactly the right number of bits, use the remainder to round: + roundup = boost::multiprecision::cpp_bf_io_detail::get_round_mode(r, d, error, q); + } + else if(bit_test(q, gb - (int)cpp_bin_float::bit_count) && ((int)lsb(q) == (gb - (int)cpp_bin_float::bit_count))) + { + // Too many bits in q and the bits in q indicate a tie, but we can break that using r, + // note that the radius of error in r is error/2 * q: + int shift = gb - (int)cpp_bin_float::bit_count + 1; + q >>= shift; + final_exponent += static_cast(shift); + BOOST_ASSERT((msb(q) >= cpp_bin_float::bit_count - 1)); + if(error && (r < (error / 2) * q)) + roundup = -1; + else if(error && (r + (error / 2) * q >= d)) + roundup = -1; + else + roundup = r ? 2 : 1; + } + else if(error && (((error / 2) * q + r >= d) || (r < (error / 2) * q))) + { + // We might have been rounding up, or got the wrong quotient: can't tell! + roundup = -1; + } + if(roundup < 0) + { +#ifdef BOOST_MP_STRESS_IO + max_bits += 32; +#else + max_bits *= 2; +#endif + error = 0; + if(shift > 0) + { + n >>= shift; + final_exponent += static_cast(shift); + } + continue; + } + else if((roundup == 2) || ((roundup == 1) && q.backend().limbs()[0] & 1)) + ++q; + if(final_exponent > cpp_bin_float::max_exponent) + { + // Overflow: + exponent() = cpp_bin_float::max_exponent; + final_exponent -= cpp_bin_float::max_exponent; + } + else if(final_exponent < cpp_bin_float::min_exponent) + { + // Underflow: + exponent() = cpp_bin_float::min_exponent; + final_exponent -= cpp_bin_float::min_exponent; + } + else + { + exponent() = static_cast(final_exponent); + final_exponent = 0; + } + copy_and_round(*this, q.backend()); + if(ss != sign()) + negate(); + break; + } + while(true); + } + // + // Check for scaling and/or over/under-flow: + // + final_exponent += exponent(); + if(final_exponent > cpp_bin_float::max_exponent) + { + // Overflow: + exponent() = cpp_bin_float::exponent_infinity; + bits() = limb_type(0); + } + else if(final_exponent < cpp_bin_float::min_exponent) + { + // Underflow: + exponent() = cpp_bin_float::exponent_zero; + bits() = limb_type(0); + sign() = 0; + } + else + { + exponent() = static_cast(final_exponent); + } + return *this; +} + +template +std::string cpp_bin_float::str(std::streamsize dig, std::ios_base::fmtflags f) const +{ + if(dig == 0) + dig = std::numeric_limits > >::max_digits10; + + bool scientific = (f & std::ios_base::scientific) == std::ios_base::scientific; + bool fixed = !scientific && (f & std::ios_base::fixed); + + std::string s; + + if(exponent() <= cpp_bin_float::max_exponent) + { + // How far to left-shift in order to demormalise the mantissa: + boost::intmax_t shift = (int)cpp_bin_float::bit_count - exponent() - 1; + boost::intmax_t digits_wanted = static_cast(dig); + boost::intmax_t base10_exp = exponent() >= 0 ? static_cast(std::floor(0.30103 * exponent())) : static_cast(std::ceil(0.30103 * exponent())); + // + // For fixed formatting we want /dig/ digits after the decimal point, + // so if the exponent is zero, allowing for the one digit before the + // decimal point, we want 1 + dig digits etc. + // + if(fixed) + digits_wanted += 1 + base10_exp; + if(scientific) + digits_wanted += 1; + if(digits_wanted < -1) + { + // Fixed precision, no significant digits, and nothing to round! + s = "0"; + if(sign()) + s.insert(0, 1, '-'); + boost::multiprecision::detail::format_float_string(s, base10_exp, dig, f, true); + return s; + } + // + // power10 is the base10 exponent we need to multiply/divide by in order + // to convert our denormalised number to an integer with the right number of digits: + // + boost::intmax_t power10 = digits_wanted - base10_exp - 1; + // + // If we calculate 5^power10 rather than 10^power10 we need to move + // 2^power10 into /shift/ + // + shift -= power10; + cpp_int i; + int roundup = 0; // 0=no rounding, 1=tie, 2=up + static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT; + // + // Set our working precision - this is heuristic based, we want + // a value as small as possible > cpp_bin_float::bit_count to avoid large computations + // and excessive memory usage, but we also want to avoid having to + // up the computation and start again at a higher precision. + // So we round cpp_bin_float::bit_count up to the nearest whole number of limbs, and add + // one limb for good measure. This works very well for small exponents, + // but for larger exponents we add a few extra limbs to max_bits: + // +#ifdef BOOST_MP_STRESS_IO + boost::intmax_t max_bits = cpp_bin_float::bit_count + 32; +#else + boost::intmax_t max_bits = cpp_bin_float::bit_count + (cpp_bin_float::bit_count % limb_bits ? limb_bits - cpp_bin_float::bit_count % limb_bits : 0) + limb_bits; + if(power10) + max_bits += (msb(std::abs(power10)) / 8) * limb_bits; +#endif + do + { + boost::int64_t error = 0; + boost::intmax_t calc_exp = 0; + // + // Our integer result is: bits() * 2^-shift * 5^power10 + // + i = bits(); + if(shift < 0) + { + if(power10 >= 0) + { + // We go straight to the answer with all integer arithmetic, + // the result is always exact and never needs rounding: + BOOST_ASSERT(power10 <= (boost::intmax_t)INT_MAX); + i <<= -shift; + if(power10) + i *= pow(cpp_int(5), static_cast(power10)); + } + else if(power10 < 0) + { + cpp_int d; + calc_exp = boost::multiprecision::cpp_bf_io_detail::restricted_pow(d, cpp_int(5), -power10, max_bits, error); + shift += calc_exp; + BOOST_ASSERT(shift < 0); // Must still be true! + i <<= -shift; + cpp_int r; + divide_qr(i, d, i, r); + roundup = boost::multiprecision::cpp_bf_io_detail::get_round_mode(r, d, error, i); + if(roundup < 0) + { +#ifdef BOOST_MP_STRESS_IO + max_bits += 32; +#else + max_bits *= 2; +#endif + shift = (int)cpp_bin_float::bit_count - exponent() - 1 - power10; + continue; + } + } + } + else + { + // + // Our integer is bits() * 2^-shift * 10^power10 + // + if(power10 > 0) + { + if(power10) + { + cpp_int t; + calc_exp = boost::multiprecision::cpp_bf_io_detail::restricted_pow(t, cpp_int(5), power10, max_bits, error); + calc_exp += boost::multiprecision::cpp_bf_io_detail::restricted_multiply(i, i, t, max_bits, error); + shift -= calc_exp; + } + if((shift < 0) || ((shift == 0) && error)) + { + // We only get here if we were asked for a crazy number of decimal digits - + // more than are present in a 2^max_bits number. +#ifdef BOOST_MP_STRESS_IO + max_bits += 32; +#else + max_bits *= 2; +#endif + shift = (int)cpp_bin_float::bit_count - exponent() - 1 - power10; + continue; + } + if(shift) + { + roundup = boost::multiprecision::cpp_bf_io_detail::get_round_mode(i, shift - 1, error); + if(roundup < 0) + { +#ifdef BOOST_MP_STRESS_IO + max_bits += 32; +#else + max_bits *= 2; +#endif + shift = (int)cpp_bin_float::bit_count - exponent() - 1 - power10; + continue; + } + i >>= shift; + } + } + else + { + // We're right shifting, *and* dividing by 5^-power10, + // so 5^-power10 can never be that large or we'd simply + // get zero as a result, and that case is already handled above: + cpp_int r; + BOOST_ASSERT(-power10 < INT_MAX); + cpp_int d = pow(cpp_int(5), static_cast(-power10)); + d <<= shift; + divide_qr(i, d, i, r); + r <<= 1; + int c = r.compare(d); + roundup = c < 0 ? 0 : c == 0 ? 1 : 2; + } + } + s = i.str(0, std::ios_base::fmtflags(0)); + // + // Check if we got the right number of digits, this + // is really a test of whether we calculated the + // decimal exponent correctly: + // + boost::intmax_t digits_got = i ? static_cast(s.size()) : 0; + if(digits_got != digits_wanted) + { + base10_exp += digits_got - digits_wanted; + if(fixed) + digits_wanted = digits_got; // strange but true. + power10 = digits_wanted - base10_exp - 1; + shift = (int)cpp_bin_float::bit_count - exponent() - 1 - power10; + if(fixed) + break; + roundup = 0; + } + else + break; + } + while(true); + // + // Check whether we need to round up: note that we could equally round up + // the integer /i/ above, but since we need to perform the rounding *after* + // the conversion to a string and the digit count check, we might as well + // do it here: + // + if((roundup == 2) || ((roundup == 1) && ((s[s.size() - 1] - '0') & 1))) + { + boost::multiprecision::detail::round_string_up_at(s, static_cast(s.size() - 1), base10_exp); + } + + if(sign()) + s.insert(0, 1, '-'); + + boost::multiprecision::detail::format_float_string(s, base10_exp, dig, f, false); + } + else + { + switch(exponent()) + { + case exponent_zero: + s = "0"; + boost::multiprecision::detail::format_float_string(s, 0, dig, f, true); + break; + case exponent_nan: + s = "nan"; + break; + case exponent_infinity: + s = sign() ? "-inf" : f & std::ios_base::showpos ? "+inf" : "inf"; + break; + } + } + return s; +} + +}}} // namespaces + +#endif + diff --git a/include/boost/multiprecision/cpp_bin_float/transcendental.hpp b/include/boost/multiprecision/cpp_bin_float/transcendental.hpp new file mode 100644 index 000000000..63fd5a696 --- /dev/null +++ b/include/boost/multiprecision/cpp_bin_float/transcendental.hpp @@ -0,0 +1,132 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2013 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifndef BOOST_MULTIPRECISION_CPP_BIN_FLOAT_TRANSCENDENTAL_HPP +#define BOOST_MULTIPRECISION_CPP_BIN_FLOAT_TRANSCENDENTAL_HPP + +namespace boost{ namespace multiprecision{ namespace backends{ + +template +void eval_exp_taylor(cpp_bin_float &res, const cpp_bin_float &arg) +{ + static const int bits = cpp_bin_float::bit_count; + // + // Taylor series for small argument, note returns exp(x) - 1: + // + res = limb_type(0); + cpp_bin_float num(arg), denom, t; + denom = limb_type(1); + eval_add(res, num); + + for(unsigned k = 2; ; ++k) + { + eval_multiply(denom, k); + eval_multiply(num, arg); + eval_divide(t, num, denom); + eval_add(res, t); + if(eval_is_zero(t) || (res.exponent() - bits > t.exponent())) + break; + } +} + +template +void eval_exp(cpp_bin_float &res, const cpp_bin_float &arg) +{ + // + // This is based on MPFR's method, let: + // + // n = floor(x / ln(2)) + // + // Then: + // + // r = x - n ln(2) : 0 <= r < ln(2) + // + // We can reduce r further by dividing by 2^k, with k ~ sqrt(n), + // so if: + // + // e0 = exp(r / 2^k) - 1 + // + // With e0 evaluated by taylor series for small arguments, then: + // + // exp(x) = 2^n (1 + e0)^2^k + // + // Note that to preserve precision we actually square (1 + e0) k times, calculating + // the result less one each time, i.e. + // + // (1 + e0)^2 - 1 = e0^2 + 2e0 + // + // Then add the final 1 at the end, given that e0 is small, this effectively wipes + // out the error in the last step. + // + using default_ops::eval_multiply; + using default_ops::eval_subtract; + using default_ops::eval_add; + using default_ops::eval_convert_to; + + int type = eval_fpclassify(arg); + bool isneg = eval_get_sign(arg) < 0; + if(type == FP_NAN) + { + res = arg; + return; + } + else if(type == FP_INFINITE) + { + res = arg; + if(isneg) + res = limb_type(0u); + else + res = arg; + return; + } + else if(type == FP_ZERO) + { + res = limb_type(1); + return; + } + cpp_bin_float t, n; + if(isneg) + { + t = arg; + t.negate(); + eval_exp(res, t); + t.swap(res); + res = limb_type(1); + eval_divide(res, t); + return; + } + + eval_divide(n, arg, default_ops::get_constant_ln2 >()); + eval_floor(n, n); + eval_multiply(t, n, default_ops::get_constant_ln2 >()); + eval_subtract(t, arg); + t.negate(); + BOOST_ASSERT(t.compare(limb_type(0)) >= 0); + BOOST_ASSERT(t.compare(default_ops::get_constant_ln2 >()) < 0); + + Exponent k, nn; + eval_convert_to(&nn, n); + k = nn ? Exponent(1) << (msb(nn) / 2) : 0; + eval_ldexp(t, t, -k); + + eval_exp_taylor(res, t); + // + // Square 1 + res k times: + // + for(int s = 0; s < k; ++s) + { + t.swap(res); + eval_multiply(res, t, t); + eval_ldexp(t, t, 1); + eval_add(res, t); + } + eval_add(res, limb_type(1)); + eval_ldexp(res, res, nn); +} + +}}} // namespaces + +#endif + diff --git a/performance/performance_test.cpp b/performance/performance_test.cpp index ff44b84a4..61bba9451 100644 --- a/performance/performance_test.cpp +++ b/performance/performance_test.cpp @@ -12,7 +12,7 @@ #if !defined(TEST_MPF) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPQ) \ && !defined(TEST_TOMMATH) && !defined(TEST_TOMMATH_BOOST_RATIONAL) && !defined(TEST_MPZ_BOOST_RATIONAL)\ - && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_RATIONAL) + && !defined(TEST_CPP_INT) && !defined(TEST_CPP_INT_RATIONAL) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF # define TEST_MPZ # define TEST_MPQ @@ -22,6 +22,7 @@ # define TEST_TOMMATH # define TEST_CPP_INT # define TEST_CPP_INT_RATIONAL +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -39,6 +40,9 @@ #ifdef TEST_CPP_DEC_FLOAT #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif #if defined(TEST_MPFR) #include #endif @@ -84,15 +88,6 @@ struct stopwatch unsigned bits_wanted; // for integer types -namespace boost{ namespace multiprecision{ - -template<> -class number_category : public mpl::int_{}; -template<> -class number_category : public mpl::int_{}; - -}} - template struct tester { @@ -841,6 +836,11 @@ int main() test("cpp_dec_float", 100); test > >("cpp_dec_float", 500); #endif +#ifdef TEST_CPP_BIN_FLOAT + test("cpp_bin_float", 50); + test("cpp_bin_float", 100); + test >::digits> > >("cpp_bin_float", 500); +#endif #ifdef TEST_MPFR test("mpfr_float", 50); test("mpfr_float", 100); diff --git a/performance/sf_performance.hpp b/performance/sf_performance.hpp index c525c6750..4b056e1e2 100644 --- a/performance/sf_performance.hpp +++ b/performance/sf_performance.hpp @@ -7,12 +7,13 @@ #define BOOST_MATH_PROMOTE_DOUBLE_POLICY false #if !defined(TEST_MPFR) && !defined(TEST_MPREAL) && !defined(TEST_MPF) && !defined(TEST_MPREAL) \ - && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) && !defined(TEST_FLOAT) + && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_CLASS) && !defined(TEST_FLOAT) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPFR # define TEST_MPF # define TEST_CPP_DEC_FLOAT -# define TEST_MPFR_CLASS -# define TEST_MPREAL +# define TEST_CPP_BIN_FLOAT +//# define TEST_MPFR_CLASS +//# define TEST_MPREAL # define TEST_FLOAT #endif @@ -34,6 +35,10 @@ #ifdef TEST_CPP_DEC_FLOAT #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#include +#endif #include #include #include diff --git a/performance/sf_performance_bessel2.cpp b/performance/sf_performance_bessel2.cpp index 3eecda8e4..13b0f597d 100644 --- a/performance/sf_performance_bessel2.cpp +++ b/performance/sf_performance_bessel2.cpp @@ -14,4 +14,7 @@ void bessel_tests_2() #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_bessel, 3); #endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_50", test_bessel, 3); +#endif } diff --git a/performance/sf_performance_bessel6.cpp b/performance/sf_performance_bessel6.cpp index f9c61cd2d..342c10930 100644 --- a/performance/sf_performance_bessel6.cpp +++ b/performance/sf_performance_bessel6.cpp @@ -10,6 +10,9 @@ void bessel_tests_6() #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_bessel); #endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_100", test_bessel); +#endif #ifdef TEST_MPFR_CLASS time_proc("mpfr_class", test_bessel); #endif diff --git a/performance/sf_performance_nct3.cpp b/performance/sf_performance_nct3.cpp index 714831b83..a229669ae 100644 --- a/performance/sf_performance_nct3.cpp +++ b/performance/sf_performance_nct3.cpp @@ -13,6 +13,9 @@ void nct_tests_3() #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_nct); #endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_50", test_nct, 3); +#endif #ifdef TEST_MPFR_CLASS time_proc("mpfr_class", test_nct); #endif diff --git a/performance/sf_performance_nct6.cpp b/performance/sf_performance_nct6.cpp index 76e0a7e1b..571ff56ef 100644 --- a/performance/sf_performance_nct6.cpp +++ b/performance/sf_performance_nct6.cpp @@ -13,6 +13,9 @@ void nct_tests_6() #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_nct); #endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_100", test_nct); +#endif #ifdef TEST_MPFR_CLASS time_proc("mpfr_class", test_nct); #endif diff --git a/performance/sf_performance_poly.cpp b/performance/sf_performance_poly.cpp index 138a39bdc..563ac6684 100644 --- a/performance/sf_performance_poly.cpp +++ b/performance/sf_performance_poly.cpp @@ -29,6 +29,9 @@ void poly_tests() #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_50", test_polynomial); #endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_50", test_polynomial); +#endif #ifdef TEST_MPFR_CLASS time_proc("mpfr_class", test_polynomial); #endif @@ -57,6 +60,9 @@ void poly_tests() #ifdef TEST_CPP_DEC_FLOAT time_proc("cpp_dec_float_100", test_polynomial); #endif +#ifdef TEST_CPP_BIN_FLOAT + time_proc("cpp_bin_float_100", test_polynomial); +#endif #ifdef TEST_MPFR_CLASS time_proc("mpfr_class", test_polynomial); #endif diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 9263b2247..c4ebb4bf5 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -60,6 +60,10 @@ run test_arithmetic_cpp_dec_float_1.cpp ; run test_arithmetic_cpp_dec_float_2.cpp ; run test_arithmetic_cpp_dec_float_3.cpp ; +run test_arithmetic_cpp_bin_float_1.cpp ; +run test_arithmetic_cpp_bin_float_2.cpp ; +run test_arithmetic_cpp_bin_float_3.cpp ; + run test_arithmetic_mpf_50.cpp gmp : : : [ check-target-builds ../config//has_gmp : : no ] ; run test_arithmetic_mpf.cpp gmp : : : [ check-target-builds ../config//has_gmp : : no ] ; run test_arithmetic_mpz.cpp gmp : : : [ check-target-builds ../config//has_gmp : : no ] ; @@ -172,6 +176,13 @@ run test_numeric_limits.cpp TEST_CPP_DEC_FLOAT : test_numeric_limits_cpp_dec_float ; +run test_numeric_limits.cpp + : # command line + : # input files + : # requirements + TEST_CPP_BIN_FLOAT + : test_numeric_limits_cpp_bin_float ; + run test_numeric_limits.cpp $(TOMMATH) : # command line : # input files @@ -240,6 +251,12 @@ for local source in test_exp.cpp test_log.cpp test_pow.cpp test_sinh.cpp test_sq : # requirements TEST_CPP_DEC_FLOAT : $(source:B)_cpp_dec_float ; + run $(source) + : # command line + : # input files + : # requirements + TEST_CPP_BIN_FLOAT + : $(source:B)_cpp_bin_float ; run $(source) quadmath : # command line : # input files @@ -327,12 +344,41 @@ run test_test.cpp ; run test_cpp_int_lit.cpp ; compile test_constexpr.cpp : [ check-target-builds ../config//has_float128 : HAVE_FLOAT128 : ] [ check-target-builds ../config//has_intel_quad : HAVE_FLOAT128 : ] ; +run test_cpp_bin_float_io.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + TEST_CPP_BIN_FLOAT + TEST1 + release # Otherwise runtime is slow + : test_cpp_bin_float_io_1 + ; + +run test_cpp_bin_float_io.cpp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + TEST_CPP_BIN_FLOAT + TEST2 + release # Otherwise runtime is slow + : test_cpp_bin_float_io_2 + ; + +run test_cpp_bin_float.cpp mpfr gmp /boost/system//boost_system /boost/chrono//boost_chrono + : # command line + : # input files + : # requirements + TEST_MPFR + [ check-target-builds ../config//has_mpfr : : no ] + release # Otherwise runtime is slow + ; + run test_float_io.cpp : # command line : # input files : # requirements TEST_CPP_DEC_FLOAT - #release # Otherwise runtime is slow + release # Otherwise runtime is slow : test_float_io_cpp_dec_float ; run test_float_io.cpp gmp @@ -521,6 +567,7 @@ run ../example/logged_adaptor.cpp mpfi mpfr gmp run ../example/cpp_dec_float_snips.cpp ; run ../example/cpp_int_snips.cpp ; +run ../example/cpp_bin_float_snips.cpp ; run ../example/tommath_snips.cpp $(TOMMATH) : # command line @@ -551,6 +598,7 @@ compile include_test/tommath_include_test.cpp [ check-target-builds ../config//has_tommath : : no ] ; compile include_test/cpp_int_include_test.cpp ; compile include_test/cpp_dec_float_include_test.cpp ; +compile include_test/cpp_bin_float_include_test.cpp ; run ublas_interop/test1.cpp ublas_interop/test11.cpp ublas_interop/test12.cpp ublas_interop/test13.cpp ; run ublas_interop/test2.cpp ublas_interop/test21.cpp ublas_interop/test22.cpp ublas_interop/test23.cpp ; @@ -629,6 +677,18 @@ if $(enable-specfun) msvc:-bigobj release : $(source:B)_cpp_dec_float ; + run $(source) /boost/test//boost_unit_test_framework/static + /boost/regex//boost_regex/static + math/instances//test_instances_cpp_bin_float/static + : # command line + : # input files + : # requirements + TEST_CPP_BIN_FLOAT + BOOST_ALL_NO_LIB + speed + msvc:-bigobj + release + : $(source:B)_cpp_bin_float ; run $(source) quadmath /boost/test//boost_unit_test_framework/static /boost/regex//boost_regex/static @@ -723,6 +783,12 @@ if ! $(disable-concepts) off : $(source:B)_cpp_dec_float ; + compile $(source) + : # requirements + TEST_CPP_BIN_FLOAT + off + : $(source:B)_cpp_bin_float ; + compile $(source) : # requirements TEST_CPP_DEC_FLOAT_NO_ET diff --git a/test/concepts/number_concept_check.cpp b/test/concepts/number_concept_check.cpp index ea4730c47..12c86a993 100644 --- a/test/concepts/number_concept_check.cpp +++ b/test/concepts/number_concept_check.cpp @@ -21,7 +21,8 @@ #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ - && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_BACKEND # define TEST_MPZ @@ -33,6 +34,7 @@ # define TEST_CPP_DEC_FLOAT # define TEST_CPP_DEC_FLOAT_NO_ET # define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -52,6 +54,9 @@ #if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) #include #endif +#if defined(TEST_CPP_BIN_FLOAT) +#include +#endif #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include #endif @@ -192,6 +197,9 @@ void foo() #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif @@ -226,6 +234,9 @@ int main() #ifdef TEST_CPP_DEC_FLOAT BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); #endif +#ifdef TEST_CPP_BIN_FLOAT + BOOST_CONCEPT_ASSERT((boost::math::concepts::RealTypeConcept)); +#endif #ifdef TEST_LOGGED_ADAPTER typedef boost::multiprecision::number > > num_t; test_extra(num_t()); diff --git a/test/concepts/sf_concept_check_basic.cpp b/test/concepts/sf_concept_check_basic.cpp index acff38796..2d79d0725 100644 --- a/test/concepts/sf_concept_check_basic.cpp +++ b/test/concepts/sf_concept_check_basic.cpp @@ -21,7 +21,7 @@ #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) && !defined(TEST_MPFR_30) \ - && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) + && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_BACKEND # define TEST_MPZ @@ -33,6 +33,7 @@ # define TEST_CPP_DEC_FLOAT # define TEST_CPP_DEC_FLOAT_NO_ET # define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -52,6 +53,9 @@ #if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) #include #endif +#if defined(TEST_CPP_BIN_FLOAT) +#include +#endif #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include #endif @@ -145,6 +149,9 @@ void foo() #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif diff --git a/test/concepts/sf_concept_check_bessel.cpp b/test/concepts/sf_concept_check_bessel.cpp index 9b47541b3..8743419f0 100644 --- a/test/concepts/sf_concept_check_bessel.cpp +++ b/test/concepts/sf_concept_check_bessel.cpp @@ -21,7 +21,8 @@ #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ - && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_BACKEND # define TEST_MPZ @@ -33,6 +34,7 @@ # define TEST_CPP_DEC_FLOAT # define TEST_CPP_DEC_FLOAT_NO_ET # define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -52,6 +54,9 @@ #if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) #include #endif +#if defined(TEST_CPP_BIN_FLOAT) +#include +#endif #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include #endif @@ -112,6 +117,9 @@ void foo() #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif diff --git a/test/concepts/sf_concept_check_elliptic.cpp b/test/concepts/sf_concept_check_elliptic.cpp index 66988c029..0bd6d6f76 100644 --- a/test/concepts/sf_concept_check_elliptic.cpp +++ b/test/concepts/sf_concept_check_elliptic.cpp @@ -21,7 +21,8 @@ #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ - && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_BACKEND # define TEST_MPZ @@ -33,6 +34,7 @@ # define TEST_CPP_DEC_FLOAT # define TEST_CPP_DEC_FLOAT_NO_ET # define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -52,6 +54,9 @@ #if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) #include #endif +#if defined(TEST_CPP_BIN_FLOAT) +#include +#endif #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include #endif @@ -116,6 +121,9 @@ void foo() #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif diff --git a/test/concepts/sf_concept_check_gamma.cpp b/test/concepts/sf_concept_check_gamma.cpp index d62209e76..fd07db1c4 100644 --- a/test/concepts/sf_concept_check_gamma.cpp +++ b/test/concepts/sf_concept_check_gamma.cpp @@ -21,7 +21,8 @@ #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ - && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_BACKEND # define TEST_MPZ @@ -33,6 +34,7 @@ # define TEST_CPP_DEC_FLOAT # define TEST_CPP_DEC_FLOAT_NO_ET # define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -55,6 +57,9 @@ #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include #endif +#if defined(TEST_CPP_BIN_FLOAT) +#include +#endif #ifdef TEST_LOGGED_ADAPTER #include #endif @@ -134,6 +139,9 @@ void foo() #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif diff --git a/test/concepts/sf_concept_check_poly.cpp b/test/concepts/sf_concept_check_poly.cpp index cde5c6793..44414b9a2 100644 --- a/test/concepts/sf_concept_check_poly.cpp +++ b/test/concepts/sf_concept_check_poly.cpp @@ -21,7 +21,8 @@ #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR_50)\ && !defined(TEST_MPFR_6) && !defined(TEST_MPFR_15) && !defined(TEST_MPFR_17) \ - && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER) + && !defined(TEST_MPFR_30) && !defined(TEST_CPP_DEC_FLOAT_NO_ET) && !defined(TEST_LOGGED_ADAPTER)\ + && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_BACKEND # define TEST_MPZ @@ -33,6 +34,7 @@ # define TEST_CPP_DEC_FLOAT # define TEST_CPP_DEC_FLOAT_NO_ET # define TEST_LOGGED_ADAPTER +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -52,6 +54,9 @@ #if defined(TEST_CPP_DEC_FLOAT) || defined(TEST_CPP_DEC_FLOAT_NO_ET) || defined(TEST_LOGGED_ADAPTER) #include #endif +#if defined(TEST_CPP_BIN_FLOAT) +#include +#endif #if defined(TEST_MPFR_50) || defined(TEST_MPFR_6) || defined(TEST_MPFR_15) || defined(TEST_MPFR_17) || defined(TEST_MPFR_30) #include #endif @@ -107,6 +112,9 @@ void foo() #ifdef TEST_CPP_DEC_FLOAT test_extra(boost::multiprecision::cpp_dec_float_50()); #endif +#ifdef TEST_CPP_BIN_FLOAT + test_extra(boost::multiprecision::cpp_bin_float_50()); +#endif #ifdef TEST_CPP_DEC_FLOAT_NO_ET test_extra(boost::multiprecision::number, boost::multiprecision::et_off>()); #endif diff --git a/test/include_test/cpp_bin_float_include_test.cpp b/test/include_test/cpp_bin_float_include_test.cpp new file mode 100644 index 000000000..b36c89e1b --- /dev/null +++ b/test/include_test/cpp_bin_float_include_test.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#include + +using namespace boost::multiprecision; + +cpp_bin_float<50> a; + + diff --git a/test/math/instances/Jamfile.v2 b/test/math/instances/Jamfile.v2 index 49136320e..9e6aa4729 100644 --- a/test/math/instances/Jamfile.v2 +++ b/test/math/instances/Jamfile.v2 @@ -68,13 +68,14 @@ rule generate_objs ( suffix : variant_count : build_opts * ) lib test_instances_mpf : [ generate_objs "_mpf" : 4 : TEST_MPF_50 ] : [ check-target-builds ../../../config//has_gmp : : no ] ; lib test_instances_mpfr : [ generate_objs "_mpfr" : 3 : TEST_MPFR_50 ] : [ check-target-builds ../../../config//has_mpfr : : no ] ; lib test_instances_cpp_dec_float : [ generate_objs "_cpp_dec_float" : 3 : TEST_CPP_DEC_FLOAT ] : ; +lib test_instances_cpp_bin_float : [ generate_objs "_cpp_bin_float" : 1 : TEST_CPP_BIN_FLOAT ] : ; lib test_instances_float128 : [ generate_objs "_float128" : 1 : TEST_FLOAT128 ] : [ check-target-builds ../../../config//has_float128 : : no ] ; lib test_instances_intel_quad : [ generate_objs "_intel_quad" : 1 : TEST_FLOAT128 -Qoption,cpp,--extended_float_type ] : [ check-target-builds ../../../config//has_intel_quad : -Qoption,cpp,--extended_float_type : no ] ; explicit test_instances_mpf ; explicit test_instances_mpfr ; explicit test_instances_cpp_dec_float ; +explicit test_instances_cpp_bin_float ; explicit test_instances_float128 ; explicit test_instances_intel_quad ; - diff --git a/test/math/setup.hpp b/test/math/setup.hpp index 02f03206b..ea019f312 100644 --- a/test/math/setup.hpp +++ b/test/math/setup.hpp @@ -13,11 +13,12 @@ #define BOOST_MATH_SMALL_CONSTANT(x) x #if !defined(TEST_MPF_50) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) \ - && !defined(TEST_MPFR_50) && !defined(TEST_FLOAT128) + && !defined(TEST_MPFR_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_CPP_DEC_FLOAT # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -91,6 +92,19 @@ typedef boost::multiprecision::number + +#define CPP_BIN_FLOAT_TESTS test(cpp_bin_float_quad(), "cpp_bin_float_quad"); + +typedef boost::multiprecision::cpp_bin_float_quad test_type_1; + +#else + +#define CPP_BIN_FLOAT_TESTS + +#endif + #ifdef TEST_FLOAT128 #include @@ -115,13 +129,15 @@ typedef boost::multiprecision::float128 test_type_1; MPF_TESTS\ MPFR_TESTS\ CPP_DEC_FLOAT_TESTS\ - FLOAT128_TESTS + FLOAT128_TESTS\ + CPP_BIN_FLOAT_TESTS #define ALL_SMALL_TESTS\ MPF_SMALL_TESTS\ MPFR_TESTS\ CPP_DEC_FLOAT_TESTS\ - FLOAT128_TESTS + FLOAT128_TESTS\ + CPP_BIN_FLOAT_TESTS #endif diff --git a/test/sincos.ipp b/test/sincos.ipp new file mode 100644 index 000000000..2273549d1 --- /dev/null +++ b/test/sincos.ipp @@ -0,0 +1,358 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_STRINGIZE(x)) +#endif + static const boost::array, 351> sincos = {{ + { SC_(0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), 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SC_(9.97105451691637836980566977886191495470310625478984302514468734081978317004712365179572388160094873766545892259684126612171730371334431713402903857531243843855031719141960805464286066705907297221591074259625271788178601626673326754719816154765918422856170761025895221537060495081964634143881365727528637573199554544101393148199185537988251924073321046398397270592899501388280072694753480150196648362062195285790390273399747995245778399713979670854796624214784952767383795902013605892666997263955330095e-01), SC_(7.60310344978606994311454252807960986535803469428379193529425796476644344334413001865738243975566508261589698713562091901145249736705485695273728137391377751615494502695150924195446763383201607951069471691560757133118887684442353070862022248337360915742210326532477359739395822627983312298986859616214217003217070111399151039551118513567199164797534425187953687276545896053419230138261452230491054544837629498576689887971671483487696900902095055042924520918068327882892863731988941436799798706418513466e-02) } + }}; +//#undef SC_ + diff --git a/test/test_acos.cpp b/test/test_acos.cpp index 90e57e810..288112126 100644 --- a/test/test_acos.cpp +++ b/test/test_acos.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFI_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -90,7 +94,11 @@ void test() } } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 20); +#ifdef TEST_CPP_BIN_FLOAT + BOOST_TEST(max_err < 120); +#else + BOOST_TEST(max_err < 60); +#endif BOOST_TEST(asin(T(0)) == 0); } @@ -129,6 +137,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_arithmetic_cpp_bin_float_1.cpp b/test/test_arithmetic_cpp_bin_float_1.cpp new file mode 100644 index 000000000..fb3a3377e --- /dev/null +++ b/test/test_arithmetic_cpp_bin_float_1.cpp @@ -0,0 +1,28 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include + +#include "libs/multiprecision/test/test_arithmetic.hpp" + +template +struct related_type > > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<(D / 2 > std::numeric_limits::digits10 ? D / 2 : D)> > type; +}; + +int main() +{ + test(); + //test > >(); + //test > > >(); + //test(); + return boost::report_errors(); +} + diff --git a/test/test_arithmetic_cpp_bin_float_2.cpp b/test/test_arithmetic_cpp_bin_float_2.cpp new file mode 100644 index 000000000..391aa160e --- /dev/null +++ b/test/test_arithmetic_cpp_bin_float_2.cpp @@ -0,0 +1,27 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include + +#include "libs/multiprecision/test/test_arithmetic.hpp" + +template +struct related_type > > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<(D / 2 > std::numeric_limits::digits10 ? D / 2 : D)> > type; +}; + +int main() +{ + //test(); + test > > >(); + //test(); + return boost::report_errors(); +} + diff --git a/test/test_arithmetic_cpp_bin_float_3.cpp b/test/test_arithmetic_cpp_bin_float_3.cpp new file mode 100644 index 000000000..ac86da6d3 --- /dev/null +++ b/test/test_arithmetic_cpp_bin_float_3.cpp @@ -0,0 +1,27 @@ +/////////////////////////////////////////////////////////////// +// Copyright 2012 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_ + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include + +#include "libs/multiprecision/test/test_arithmetic.hpp" + +template +struct related_type > > +{ + typedef boost::multiprecision::number< boost::multiprecision::cpp_bin_float<(D / 2 > std::numeric_limits::digits10 ? D / 2 : D)> > type; +}; + +int main() +{ + //test(); + //test > > >(); + test(); + return boost::report_errors(); +} + diff --git a/test/test_asin.cpp b/test/test_asin.cpp index d54d98892..589106842 100644 --- a/test/test_asin.cpp +++ b/test/test_asin.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFI_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -128,6 +132,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_atan.cpp b/test/test_atan.cpp index a7e97a611..49ab34dce 100644 --- a/test/test_atan.cpp +++ b/test/test_atan.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFI_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif #ifdef BOOST_MSVC #pragma warning(disable:4127) @@ -282,6 +286,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_cos.cpp b/test/test_cos.cpp index be1efbc72..ee48a85cb 100644 --- a/test/test_cos.cpp +++ b/test/test_cos.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFI_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -296,6 +300,19 @@ void test() #else BOOST_TEST(fabs(cos(half_pi)) < std::numeric_limits::epsilon()); #endif + +#include "sincos.ipp" + max_err = 0; + for(unsigned k = 0; k < sincos.size(); k++) + { + T val = cos(sincos[k][0]); + T e = relative_error(val, sincos[k][2]); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); } @@ -333,6 +350,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_cosh.cpp b/test/test_cosh.cpp index 50ea52af9..97bb068a8 100644 --- a/test/test_cosh.cpp +++ b/test/test_cosh.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFI_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -121,12 +125,18 @@ void test() T e = relative_error(val, T(data[k])); unsigned err = e.template convert_to(); if(err > max_err) + { + std::cout << x * x << std::endl; max_err = err; + } val = boost::multiprecision::cosh(-x * x); e = relative_error(val, T(data[k])); err = e.template convert_to(); if(err > max_err) + { + std::cout << x * x << std::endl; max_err = err; + } } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 2000); @@ -167,6 +177,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_cpp_bin_float.cpp b/test/test_cpp_bin_float.cpp new file mode 100644 index 000000000..95da6e88e --- /dev/null +++ b/test/test_cpp_bin_float.cpp @@ -0,0 +1,219 @@ +// Copyright John Maddock 2013. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include +#ifdef TEST_MPFR +#include +#endif +#include +#include +#include "libs/multiprecision/test/test.hpp" +#include +#include + +template +T generate_random() +{ + typedef int e_type; + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + e_type e; + val = frexp(val, &e); + + static boost::random::uniform_int_distribution ui(-20, 20); + return ldexp(val, ui(gen)); +} + + +using namespace boost::multiprecision; +#ifdef TEST_MPFR +typedef number > good_type; +#else +typedef double good_type; +#endif +typedef number::digits, digit_base_2>, et_off> test_type; + +void test_special_cases() +{ + test_type max_val = (std::numeric_limits::max)(); + test_type min_val = (std::numeric_limits::min)(); + test_type eps = std::numeric_limits::epsilon(); + test_type inf_val = (std::numeric_limits::infinity)(); + test_type nan_val = (std::numeric_limits::quiet_NaN)(); + + BOOST_CHECK((boost::math::isnormal)(max_val)); + BOOST_CHECK((boost::math::isnormal)(-max_val)); + BOOST_CHECK((boost::math::isnormal)(min_val)); + BOOST_CHECK((boost::math::isnormal)(-min_val)); + BOOST_CHECK((boost::math::isinf)(inf_val)); + BOOST_CHECK((boost::math::isinf)(-inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val)); + BOOST_CHECK((boost::math::isnan)(-nan_val)); + + if(std::numeric_limits::has_denorm) + min_val = std::numeric_limits::denorm_min(); + + BOOST_CHECK(test_type(1) + eps != test_type(1)); + BOOST_CHECK(test_type(1) + eps / 2 == test_type(1)); + + // Overflow: + BOOST_CHECK_EQUAL(max_val + max_val * eps, inf_val); + BOOST_CHECK_EQUAL(-max_val - max_val * eps, -inf_val); + BOOST_CHECK_EQUAL(max_val * 2, inf_val); + BOOST_CHECK_EQUAL(max_val * -2, -inf_val); + BOOST_CHECK_EQUAL(max_val / 0.5, inf_val); + BOOST_CHECK_EQUAL(max_val / -0.5, -inf_val); + // Underflow: + BOOST_CHECK_EQUAL(min_val * 2 - 1.5 * min_val, 0); + BOOST_CHECK_EQUAL(-min_val * 2 + 1.5 * min_val, 0); + BOOST_CHECK_EQUAL(min_val / 2, 0); + BOOST_CHECK_EQUAL(min_val * 0.5, 0); + BOOST_CHECK_EQUAL(min_val - min_val, 0); + BOOST_CHECK_EQUAL(max_val - max_val, 0); + BOOST_CHECK_EQUAL(-min_val + min_val, 0); + BOOST_CHECK_EQUAL(-max_val + max_val, 0); + // Things involving zero: + BOOST_CHECK_EQUAL(max_val + 0, max_val); + BOOST_CHECK_EQUAL(max_val - 0, max_val); + BOOST_CHECK_EQUAL(0 + max_val, max_val); + BOOST_CHECK_EQUAL(0 - max_val, -max_val); + BOOST_CHECK_EQUAL(max_val * 0, 0); + BOOST_CHECK_EQUAL(0 * max_val, 0); + BOOST_CHECK_EQUAL(max_val / 0, inf_val); + BOOST_CHECK_EQUAL(0 / max_val, 0); + BOOST_CHECK_EQUAL(-max_val / 0, -inf_val); + BOOST_CHECK_EQUAL(0 / -max_val, 0); + // Things involving infinity: + BOOST_CHECK_EQUAL(inf_val + 2, inf_val); + BOOST_CHECK_EQUAL(inf_val + inf_val, inf_val); + BOOST_CHECK_EQUAL(-inf_val - 2, -inf_val); + BOOST_CHECK_EQUAL(inf_val - 2, inf_val); + BOOST_CHECK_EQUAL(-inf_val + 2, -inf_val); + BOOST_CHECK((boost::math::isnan)(inf_val - inf_val)); + BOOST_CHECK_EQUAL(inf_val * 2, inf_val); + BOOST_CHECK_EQUAL(-inf_val * 2, -inf_val); + BOOST_CHECK((boost::math::isnan)(inf_val * 0)); + BOOST_CHECK((boost::math::isnan)(-inf_val * 0)); + BOOST_CHECK_EQUAL(inf_val / 2, inf_val); + BOOST_CHECK_EQUAL(-inf_val / 2, -inf_val); + BOOST_CHECK_EQUAL(inf_val / 0, inf_val); + BOOST_CHECK_EQUAL(-inf_val / 0, -inf_val); + BOOST_CHECK((boost::math::isnan)(inf_val / inf_val)); + BOOST_CHECK((boost::math::isnan)(-inf_val / inf_val)); + // Things involving nan: + BOOST_CHECK((boost::math::isnan)(nan_val + 2)); + BOOST_CHECK((boost::math::isnan)(nan_val - 2)); + BOOST_CHECK((boost::math::isnan)(nan_val + 0)); + BOOST_CHECK((boost::math::isnan)(nan_val - 0)); + BOOST_CHECK((boost::math::isnan)(nan_val + inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val - inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val + nan_val)); + BOOST_CHECK((boost::math::isnan)(nan_val - nan_val)); + BOOST_CHECK((boost::math::isnan)(2 + nan_val)); + BOOST_CHECK((boost::math::isnan)(2 - nan_val)); + BOOST_CHECK((boost::math::isnan)(0 - nan_val)); + BOOST_CHECK((boost::math::isnan)(0 - nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val + nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val - nan_val)); + BOOST_CHECK((boost::math::isnan)(nan_val * 2)); + BOOST_CHECK((boost::math::isnan)(nan_val / 2)); + BOOST_CHECK((boost::math::isnan)(nan_val * 0)); + BOOST_CHECK((boost::math::isnan)(nan_val / 0)); + BOOST_CHECK((boost::math::isnan)(nan_val * inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val / inf_val)); + BOOST_CHECK((boost::math::isnan)(nan_val * nan_val)); + BOOST_CHECK((boost::math::isnan)(nan_val / nan_val)); + BOOST_CHECK((boost::math::isnan)(2 * nan_val)); + BOOST_CHECK((boost::math::isnan)(2 / nan_val)); + BOOST_CHECK((boost::math::isnan)(0 / nan_val)); + BOOST_CHECK((boost::math::isnan)(0 / nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val * nan_val)); + BOOST_CHECK((boost::math::isnan)(inf_val / nan_val)); +} + +int main() +{ + test_special_cases(); + unsigned error_count = 0; + for(unsigned i = 0; i < 100000; ++i) + { + good_type a = generate_random(); + good_type b = generate_random(); + test_type ta(a); + test_type tb(b); + + BOOST_CHECK_EQUAL(test_type(a * b), ta * tb); + BOOST_CHECK_EQUAL(test_type(-a * b), -ta * tb); + BOOST_CHECK_EQUAL(test_type(a * -b), ta * -tb); + BOOST_CHECK_EQUAL(test_type(-a * -b), -ta * -tb); + + BOOST_CHECK_EQUAL(test_type(a + b), ta + tb); + BOOST_CHECK_EQUAL(test_type(-a + b), -ta + tb); + BOOST_CHECK_EQUAL(test_type(a + -b), ta + -tb); + BOOST_CHECK_EQUAL(test_type(-a + -b), -ta + -tb); + + BOOST_CHECK_EQUAL(test_type(a - b), ta - tb); + BOOST_CHECK_EQUAL(test_type(-a - b), -ta - tb); + BOOST_CHECK_EQUAL(test_type(a - -b), ta - -tb); + BOOST_CHECK_EQUAL(test_type(-a - -b), -ta - -tb); + + BOOST_CHECK_EQUAL(test_type(a / b), ta / tb); + BOOST_CHECK_EQUAL(test_type(-a / b), -ta / tb); + BOOST_CHECK_EQUAL(test_type(a / -b), ta / -tb); + BOOST_CHECK_EQUAL(test_type(-a / -b), -ta / -tb); + + BOOST_CHECK_EQUAL(test_type(sqrt(a)), sqrt(ta)); + BOOST_CHECK_EQUAL(test_type(floor(a)), floor(ta)); + BOOST_CHECK_EQUAL(test_type(floor(-a)), floor(-ta)); + BOOST_CHECK_EQUAL(test_type(ceil(a)), ceil(ta)); + BOOST_CHECK_EQUAL(test_type(ceil(-a)), ceil(-ta)); + + static boost::random::mt19937 i_gen; + + int si = i_gen(); + BOOST_CHECK_EQUAL(test_type(a * si), ta * si); + BOOST_CHECK_EQUAL(test_type(-a * si), -ta * si); + BOOST_CHECK_EQUAL(test_type(-a * -si), -ta * -si); + BOOST_CHECK_EQUAL(test_type(a * -si), ta * -si); + unsigned ui = std::abs(si); + BOOST_CHECK_EQUAL(test_type(a * ui), ta * ui); + BOOST_CHECK_EQUAL(test_type(-a * ui), -ta * ui); + + // Divide: + BOOST_CHECK_EQUAL(test_type(a / si), ta / si); + BOOST_CHECK_EQUAL(test_type(-a / si), -ta / si); + BOOST_CHECK_EQUAL(test_type(-a / -si), -ta / -si); + BOOST_CHECK_EQUAL(test_type(a / -si), ta / -si); + BOOST_CHECK_EQUAL(test_type(a / ui), ta / ui); + BOOST_CHECK_EQUAL(test_type(-a / ui), -ta / ui); + // Error reporting: + if(boost::detail::test_errors() != error_count) + { + error_count = boost::detail::test_errors(); + std::cout << std::setprecision(std::numeric_limits::max_digits10) << std::scientific; + std::cout << "a (mpfr) = " << a << std::endl; + std::cout << "a (test) = " << ta << std::endl; + std::cout << "b (mpfr) = " << b << std::endl; + std::cout << "b (test) = " << tb << std::endl; + std::cout << "si = " << si << std::endl; + std::cout << "ui = " << ui << std::endl; + } + } + return boost::report_errors(); +} + diff --git a/test/test_cpp_bin_float_io.cpp b/test/test_cpp_bin_float_io.cpp new file mode 100644 index 000000000..bc76f29cf --- /dev/null +++ b/test/test_cpp_bin_float_io.cpp @@ -0,0 +1,258 @@ +// Copyright John Maddock 2013. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# define _SCL_SECURE_NO_WARNINGS +#endif + +#include + +#include +#include +#include +#include "test.hpp" +#include +#include +#include + +#ifdef BOOST_MSVC +#pragma warning(disable:4127) +#endif + +template +struct stopwatch +{ + typedef typename Clock::duration duration; + stopwatch() + { + m_start = Clock::now(); + } + duration elapsed() + { + return Clock::now() - m_start; + } + void reset() + { + m_start = Clock::now(); + } + +private: + typename Clock::time_point m_start; +}; + + +void print_flags(std::ios_base::fmtflags f) +{ + std::cout << "Formatting flags were: "; + if(f & std::ios_base::scientific) + std::cout << "scientific "; + if(f & std::ios_base::fixed) + std::cout << "fixed "; + if(f & std::ios_base::showpoint) + std::cout << "showpoint "; + if(f & std::ios_base::showpos) + std::cout << "showpos "; + std::cout << std::endl; +} + + +template +void test() +{ + typedef T mp_t; + boost::array f = + {{ + std::ios_base::fmtflags(0), std::ios_base::showpoint, std::ios_base::showpos, std::ios_base::scientific, std::ios_base::scientific|std::ios_base::showpos, + std::ios_base::scientific|std::ios_base::showpoint, std::ios_base::fixed, std::ios_base::fixed|std::ios_base::showpoint, + std::ios_base::fixed|std::ios_base::showpos + }}; + + boost::array, 40> string_data = {{ +#include "libs/multiprecision/test/string_data.ipp" + }}; + + double num = 123456789.0; + double denom = 1; + double val = num; + for(unsigned j = 0; j < 40; ++j) + { + unsigned col = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = string_data[j][col]; + if(ss.str() != expect) + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } + num = -num; + if(j & 1) + denom *= 8; + val = num / denom; + } + + boost::array zeros = + {{ "0", "0.", "+0", "0.0e+00", "+0.0e+00", "0.0e+00", "0.0", "0.0", "+0.0", "0", "0.0", "+0", "0.00e+00", "+0.00e+00", "0.00e+00", "0.00", "0.00", "+0.00", "0", "0.00", "+0", "0.000e+00", "+0.000e+00", "0.000e+00", "0.000", "0.000", "+0.000", "0", "0.000", "+0", "0.0000e+00", "+0.0000e+00", "0.0000e+00", "0.0000", "0.0000", "+0.0000", "0", "0.0000", "+0", "0.00000e+00", "+0.00000e+00", "0.00000e+00", "0.00000", "0.00000", "+0.00000", "0", "0.00000", "+0", "0.000000e+00", "+0.000000e+00", "0.000000e+00", "0.000000", "0.000000", "+0.000000", "0", "0.000000", "+0", "0.0000000e+00", "+0.0000000e+00", "0.0000000e+00", "0.0000000", "0.0000000", "+0.0000000", "0", "0.0000000", "+0", "0.00000000e+00", "+0.00000000e+00", "0.00000000e+00", "0.00000000", "0.00000000", "+0.00000000", "0", "0.00000000", "+0", "0.000000000e+00", "+0.000000000e+00", "0.000000000e+00", "0.000000000", "0.000000000", "+0.000000000", "0", "0.000000000", "+0", "0.0000000000e+00", "+0.0000000000e+00", "0.0000000000e+00", "0.0000000000", "0.0000000000", "+0.0000000000", "0", "0.0000000000", "+0", "0.00000000000e+00", "+0.00000000000e+00", "0.00000000000e+00", "0.00000000000", "0.00000000000", "+0.00000000000", "0", "0.00000000000", "+0", "0.000000000000e+00", "+0.000000000000e+00", "0.000000000000e+00", "0.000000000000", "0.000000000000", "+0.000000000000", "0", "0.000000000000", "+0", "0.0000000000000e+00", "+0.0000000000000e+00", "0.0000000000000e+00", "0.0000000000000", "0.0000000000000", "+0.0000000000000" }}; + + unsigned col = 0; + val = 0; + for(unsigned prec = 1; prec < 14; ++prec) + { + for(unsigned i = 0; i < f.size(); ++i, ++col) + { + std::stringstream ss; + ss.precision(prec); + ss.flags(f[i]); + ss << mp_t(val); + const char* expect = zeros[col]; + if(ss.str() != expect) + { + std::cout << std::setprecision(20) << "Testing value " << val << std::endl; + print_flags(f[i]); + std::cout << "Precision is: " << prec << std::endl; + std::cout << "Got: " << ss.str() << std::endl; + std::cout << "Expected: " << expect << std::endl; + ++boost::detail::test_errors(); + mp_t(val).str(prec, f[i]); // for debugging + } + } + } + + if(std::numeric_limits::has_infinity) + { + T val = std::numeric_limits::infinity(); + BOOST_CHECK_EQUAL(val.str(), "inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "+inf"); + val = -val; + BOOST_CHECK_EQUAL(val.str(), "-inf"); + BOOST_CHECK_EQUAL(val.str(0, std::ios_base::showpos), "-inf"); + + val = static_cast("inf"); + BOOST_CHECK_EQUAL(val, std::numeric_limits::infinity()); + val = static_cast("+inf"); + BOOST_CHECK_EQUAL(val, std::numeric_limits::infinity()); + val = static_cast("-inf"); + BOOST_CHECK_EQUAL(val, -std::numeric_limits::infinity()); + } + if(std::numeric_limits::has_quiet_NaN) + { + T val = std::numeric_limits::quiet_NaN(); + BOOST_CHECK_EQUAL(val.str(), "nan"); + val = static_cast("nan"); + BOOST_CHECK((boost::math::isnan)(val)); + } + // + // Min and max values: + // + T t((std::numeric_limits::max)().str(std::numeric_limits::max_digits10, std::ios_base::scientific)); + BOOST_CHECK_EQUAL(t, (std::numeric_limits::max)()); + t = T((std::numeric_limits::min)().str(std::numeric_limits::max_digits10, std::ios_base::scientific)); + BOOST_CHECK_EQUAL(t, (std::numeric_limits::min)()); + t = T((std::numeric_limits::lowest)().str(std::numeric_limits::max_digits10, std::ios_base::scientific)); + BOOST_CHECK_EQUAL(t, (std::numeric_limits::lowest)()); +} + +template +T generate_random() +{ + typedef typename T::backend_type::exponent_type e_type; + static boost::random::mt19937 gen; + T val = gen(); + T prev_val = -1; + while(val != prev_val) + { + val *= (gen.max)(); + prev_val = val; + val += gen(); + } + e_type e; + val = frexp(val, &e); + + static boost::random::uniform_int_distribution ui(0, std::numeric_limits::max_exponent); + return ldexp(val, ui(gen)); +} + +template +void do_round_trip(const T& val, std::ios_base::fmtflags f) +{ + std::stringstream ss; +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS + ss << std::setprecision(std::numeric_limits::max_digits10); +#else + ss << std::setprecision(max_digits10_proxy::value); +#endif + ss.flags(f); + ss << val; + T new_val = static_cast(ss.str()); + BOOST_CHECK_EQUAL(new_val, val); + new_val = static_cast(val.str(0, f)); + BOOST_CHECK_EQUAL(new_val, val); +} + +template +void do_round_trip(const T& val) +{ + do_round_trip(val, std::ios_base::fmtflags(0)); + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::scientific)); + if((fabs(val) > 1) && (fabs(val) < 1e100)) + do_round_trip(val, std::ios_base::fmtflags(std::ios_base::fixed)); +} + +template +void test_round_trip() +{ + std::cout << "Testing type " << typeid(T).name() << std::endl; + std::cout << "digits = " << std::numeric_limits::digits << std::endl; + std::cout << "digits10 = " << std::numeric_limits::digits10 << std::endl; + std::cout << "max_digits10 = " << std::numeric_limits::max_digits10 << std::endl; + + stopwatch w; + + while(boost::chrono::duration_cast >(w.elapsed()).count() < 200) + { + T val = generate_random(); + do_round_trip(val); + do_round_trip(T(-val)); + do_round_trip(T(1/val)); + do_round_trip(T(-1/val)); + } + + std::cout << "Execution time = " << boost::chrono::duration_cast >(w.elapsed()).count() << "s" << std::endl; +} + +#if !defined(TEST1) && !defined(TEST2) +# define TEST1 +# define TEST2 +#endif + +int main() +{ + using namespace boost::multiprecision; +#ifdef TEST1 + test > >(); + test_round_trip > >(); +#endif +#ifdef TEST2 + test > >(); + test_round_trip > >(); +#endif + return boost::report_errors(); +} + diff --git a/test/test_exp.cpp b/test/test_exp.cpp index 77336684d..f3eae923f 100644 --- a/test/test_exp.cpp +++ b/test/test_exp.cpp @@ -18,13 +18,14 @@ #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) \ && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) \ - && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) + && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFI_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -53,6 +54,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -136,6 +140,8 @@ void test() std::cout << "Max error was: " << max_err << std::endl; #if defined(BOOST_INTEL) && defined(TEST_FLOAT128) BOOST_TEST(max_err < 40000); +#elif defined(TEST_CPP_BIN_FLOAT) + BOOST_TEST(max_err < 6000); #else BOOST_TEST(max_err < 5000); #endif @@ -173,7 +179,7 @@ void test() } } std::cout << "Max error was: " << max_err << std::endl; - BOOST_TEST(max_err < 10); + BOOST_TEST(max_err < 20); BOOST_TEST(exp(T(0)) == 1); } @@ -216,6 +222,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_fpclassify.cpp b/test/test_fpclassify.cpp index 1de6e72f6..dd5221cfc 100644 --- a/test/test_fpclassify.cpp +++ b/test/test_fpclassify.cpp @@ -14,13 +14,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_MPFI_50 # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -49,6 +50,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif #ifdef _MSC_VER #pragma warning(disable: 4127) // conditional expression is constant @@ -329,6 +333,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_log.cpp b/test/test_log.cpp index 6ee7b57eb..669deb1e8 100644 --- a/test/test_log.cpp +++ b/test/test_log.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFR_50 # define TEST_MPFI_50 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -202,6 +206,13 @@ void test() BOOST_TEST(max_err < 10); #endif BOOST_TEST(log(T(1)) == 0); + // + // Some tricky special cases: + // + BOOST_CHECK((boost::math::isfinite)(log((std::numeric_limits::max)()))); + BOOST_CHECK((boost::math::isfinite)(log((std::numeric_limits::min)()))); + BOOST_CHECK((boost::math::isfinite)(log10((std::numeric_limits::max)()))); + BOOST_CHECK((boost::math::isfinite)(log10((std::numeric_limits::min)()))); } @@ -242,6 +253,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_numeric_limits.cpp b/test/test_numeric_limits.cpp index 37a8527ac..cb7f51cee 100644 --- a/test/test_numeric_limits.cpp +++ b/test/test_numeric_limits.cpp @@ -11,7 +11,7 @@ #if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_MPZ) && \ !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPQ) && \ - !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) && !defined(TEST_MPFI_50) &&!defined(TEST_FLOAT128) + !defined(TEST_TOMMATH) && !defined(TEST_CPP_INT) && !defined(TEST_MPFI_50) &&!defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPF # define TEST_BACKEND @@ -24,6 +24,7 @@ # define TEST_CPP_INT # define TEST_MPFI_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -58,6 +59,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif #ifdef BOOST_MSVC #pragma warning(disable:4127) @@ -126,6 +130,21 @@ void test_specific(const boost::mpl::int_::round_style == std::round_to_nearest) + { + BOOST_CHECK_EQUAL(std::numeric_limits::round_error(), 0.5); + } + else if(std::numeric_limits::round_style != std::round_indeterminate) + { + // Round error is 1.0: + BOOST_CHECK_EQUAL(std::numeric_limits::round_error(), 1); + } + else + { + // Round error is presumably somewhere between 0.5 and 1: + BOOST_CHECK((std::numeric_limits::round_error() <= 1) && (std::numeric_limits::round_error() >= 0.5)); + } } template @@ -260,6 +279,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_pow.cpp b/test/test_pow.cpp index 3e904e733..6f2afea13 100644 --- a/test/test_pow.cpp +++ b/test/test_pow.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 //# define TEST_MPF # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFR_50 # define TEST_MPFI_50 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -833,6 +837,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_round.cpp b/test/test_round.cpp index a2b091551..5edd7cd89 100644 --- a/test/test_round.cpp +++ b/test/test_round.cpp @@ -15,13 +15,16 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT)\ + && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128)\ + && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_MPFI_50 # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -47,6 +50,9 @@ #ifdef TEST_CPP_DEC_FLOAT #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif #ifdef TEST_FLOAT128 #include #endif @@ -434,6 +440,10 @@ int main() test > > >(); #endif #endif +#ifdef TEST_CPP_BIN_FLOAT + test(); + test(); +#endif #ifdef TEST_BACKEND test >(); #endif diff --git a/test/test_sin.cpp b/test/test_sin.cpp index ed356a7eb..bfdb9ff34 100644 --- a/test/test_sin.cpp +++ b/test/test_sin.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_MPFI_50 # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -282,6 +286,20 @@ void test() } std::cout << "Max error was: " << max_err << std::endl; BOOST_TEST(max_err < 20); + +#include "sincos.ipp" + max_err = 0; + for(unsigned k = 0; k < sincos.size(); k++) + { + T val = sin(sincos[k][0]); + T e = relative_error(val, sincos[k][1]); + unsigned err = e.template convert_to(); + if(err > max_err) + max_err = err; + } + std::cout << "Max error was: " << max_err << std::endl; + BOOST_TEST(max_err < 20); + } @@ -322,6 +340,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_sinh.cpp b/test/test_sinh.cpp index ff69da1eb..3fe4ec327 100644 --- a/test/test_sinh.cpp +++ b/test/test_sinh.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_MPFI_50 # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -246,6 +250,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_sqrt.cpp b/test/test_sqrt.cpp index 54b7b22db..f845492e0 100644 --- a/test/test_sqrt.cpp +++ b/test/test_sqrt.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_MPFI_50 # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -179,6 +183,11 @@ void test() #else BOOST_TEST(max_err < 20); #endif + // + // Some tricky special cases: + // + BOOST_CHECK((boost::math::isfinite)(sqrt((std::numeric_limits::max)()))); + BOOST_CHECK((boost::math::isfinite)(sqrt((std::numeric_limits::min)()))); } @@ -222,6 +231,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_tan.cpp b/test/test_tan.cpp index a72622e50..8dc9dcbdc 100644 --- a/test/test_tan.cpp +++ b/test/test_tan.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFI_50 # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_MPFR_50 # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -619,6 +623,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/test/test_tanh.cpp b/test/test_tanh.cpp index 647c377de..e45c6bce6 100644 --- a/test/test_tanh.cpp +++ b/test/test_tanh.cpp @@ -16,13 +16,14 @@ #include #include "test.hpp" -#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) +#if !defined(TEST_MPF_50) && !defined(TEST_MPF) && !defined(TEST_BACKEND) && !defined(TEST_CPP_DEC_FLOAT) && !defined(TEST_MPFR) && !defined(TEST_MPFR_50) && !defined(TEST_MPFI_50) && !defined(TEST_FLOAT128) && !defined(TEST_CPP_BIN_FLOAT) # define TEST_MPF_50 # define TEST_MPFR_50 # define TEST_MPFI_50 # define TEST_BACKEND # define TEST_CPP_DEC_FLOAT # define TEST_FLOAT128 +# define TEST_CPP_BIN_FLOAT #ifdef _MSC_VER #pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!") @@ -51,6 +52,9 @@ #ifdef TEST_FLOAT128 #include #endif +#ifdef TEST_CPP_BIN_FLOAT +#include +#endif template void test() @@ -162,6 +166,9 @@ int main() #endif #ifdef TEST_FLOAT128 test(); +#endif +#ifdef TEST_CPP_BIN_FLOAT + test(); #endif return boost::report_errors(); } diff --git a/tools/sincos.cpp b/tools/sincos.cpp new file mode 100644 index 000000000..88dde7428 --- /dev/null +++ b/tools/sincos.cpp @@ -0,0 +1,75 @@ +// Copyright John Maddock 2013. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +//[special_data_example + +#include +#include +#include +#include +#include + +using namespace boost::math::tools; +using namespace boost::math; +using namespace std; +using namespace boost::multiprecision; + +typedef number > mp_type; + + +boost::math::tuple generate(mp_type a) +{ + mp_type ts, tc; + ts = sin(a); + tc = cos(a); + return boost::math::make_tuple(a, ts, tc); +} + +int cpp_main(int argc, char*argv []) +{ + parameter_info arg1, arg2; + test_data data; + + bool cont; + std::string line; + + if(argc < 1) + return 1; + + do{ + // + // User interface which prompts for + // range of input parameters: + // + if(0 == get_user_parameter_info(arg1, "a")) + return 1; + arg1.type |= dummy_param; + + data.insert(&generate, arg1); + + std::cout << "Any more data [y/n]?"; + std::getline(std::cin, line); + boost::algorithm::trim(line); + cont = (line == "y"); + }while(cont); + // + // Just need to write the results to a file: + // + std::cout << "Enter name of test data file [default=sincos.ipp]"; + std::getline(std::cin, line); + boost::algorithm::trim(line); + if(line == "") + line = "sincos.ipp"; + std::ofstream ofs(line.c_str()); + line.erase(line.find('.')); + ofs << std::scientific << std::setprecision(500); + write_code(ofs, data, line.c_str()); + + return 0; +} + +//] +