Analyze fix-point precision for unary functions
This program allows, for a given unary function, to explore the relations between the fixed point format of the argument, taken in a given range of values, and the fixed point format of the result.
Analyze the function [](I i) { return sin(i); } in the interval I(0, M_PI*2.0) with a LSB precision of -18:
auto fun = [](I i) { return sin(i); };
std::string msg = "sin(i)";
int lsb = -18;
I i(0, M_PI*2.0);
analyze(msg, fun, i, lsb, false);
The execution will produce:
TEST: lambda(i).(sin(i)); interval: [0;6.28319]; LSB: -18; truncated interval: [0;6.28319]; MSB: 3; resulting interval: [-1;1]; MSB: 1
Cases: 1647100; MSB: 1; best precision LSB: -39; very good precision LSB (0.999): -27; good precision LSB (0.99): -23
This result indicates that a LSB of -39 is required for all results to have optimal accuracy, but that with a LSB of -27, we still have 99.9% of results that have optimal accuracy.
It is also possible to ask for the histogram of the number of results per LSB precision by using analyze(msg, fun, i, lsb, true);:
LSB NUM RATIO
-39 1 1
-37 1 0.999999
-36 3 0.999999
-35 4 0.999997
-34 8 0.999995
-33 16 0.99999
-32 32 0.99998
-31 64 0.999961
-30 128 0.999922
-29 256 0.999844
-28 512 0.999689
-27 1024 0.999378
-26 2048 0.998756
-25 4096 0.997513
-24 8193 0.995026
-23 16394 0.990052
-22 32842 0.980098
-21 66147 0.960159
-20 136300 0.919999
-19 330455 0.837248
-18 524286 0.63662
-17 262145 0.318311
-16 131073 0.159155
-15 65536 0.0795774
-14 32768 0.0397887
-13 16384 0.0198944
-12 8192 0.00994718
-11 4096 0.00497359
-10 2048 0.00248679
-9 1024 0.0012434
-8 512 0.000621699
-7 256 0.000310849
-6 128 0.000155425
-5 64 7.77123e-05
-4 32 3.88562e-05
-3 16 1.94281e-05
-2 8 9.71404e-06
-1 4 4.85702e-06
0 4 2.42851e-06