From a5c0a0ae4c823a520ef7ed2669b835702679bc4c Mon Sep 17 00:00:00 2001 From: Quinton Miller Date: Thu, 7 Dec 2023 20:28:27 +0800 Subject: [PATCH 1/5] Implement `sprintf "%f"` in Crystal using Ryu Printf --- spec/std/float_printer/ryu_printf_spec.cr | 3184 +++++++++++++++ spec/std/sprintf_spec.cr | 52 +- src/float/printer/ryu_printf.cr | 626 +++ src/float/printer/ryu_printf_table.cr | 4412 +++++++++++++++++++++ src/string/formatter.cr | 94 +- 5 files changed, 8334 insertions(+), 34 deletions(-) create mode 100644 spec/std/float_printer/ryu_printf_spec.cr create mode 100644 src/float/printer/ryu_printf.cr create mode 100644 src/float/printer/ryu_printf_table.cr diff --git a/spec/std/float_printer/ryu_printf_spec.cr b/spec/std/float_printer/ryu_printf_spec.cr new file mode 100644 index 000000000000..f8e80d1a33dd --- /dev/null +++ b/spec/std/float_printer/ryu_printf_spec.cr @@ -0,0 +1,3184 @@ +# This file contains test cases derived from: +# +# * https://github.com/ulfjack/ryu +# +# The following is their license: +# +# Copyright 2020-2021 Junekey Jeon +# +# The contents of this file may be used under the terms of +# the Apache License v2.0 with LLVM Exceptions. +# +# (See accompanying file LICENSE-Apache or copy at +# https://llvm.org/foundation/relicensing/LICENSE.txt) +# +# Alternatively, the contents of this file may be used under the terms of +# the Boost Software License, Version 1.0. +# (See accompanying file LICENSE-Boost or copy at +# https://www.boost.org/LICENSE_1_0.txt) +# +# Unless required by applicable law or agreed to in writing, this software +# is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. + +require "spec" +require "float/printer/ryu_printf" +require "big" + +# The following two lists store: {value, fixed_precision, exp_precision} +# Iterate over them via macros only, otherwise the entire array literal will be +# materialized! +# The original specs contain also the full expected results which would have +# increased the file size by over 18x. Here we assume that `BigFloat#to_s` and +# `BigDecimal#to_s` are always correct, so that we don't have to write the long +# results in the source code. + +# These values test every power of ten that's within the range of doubles. +ALL_POWERS_OF_TEN = [ + {1e-323, 1073, 749}, + {1e-322, 1072, 749}, + {1e-321, 1073, 751}, + {1e-320, 1071, 750}, + {1e-319, 1070, 750}, + {1e-318, 1073, 754}, + {1e-317, 1074, 757}, + {1e-316, 1074, 757}, + {1e-315, 1074, 758}, + {1e-314, 1074, 759}, + {1e-313, 1074, 761}, + {1e-312, 1074, 761}, + {1e-311, 1074, 762}, + {1e-310, 1074, 763}, + {1e-309, 1074, 765}, + {1e-308, 1073, 764}, + {1e-307, 1072, 764}, + {1e-306, 1069, 763}, + {1e-305, 1066, 760}, + {1e-304, 1062, 757}, + {1e-303, 1059, 755}, + {1e-302, 1054, 751}, + {1e-301, 1052, 751}, + {1e-300, 1049, 749}, + {1e-299, 1046, 746}, + {1e-298, 1042, 743}, + {1e-297, 1039, 742}, + {1e-296, 1035, 739}, + {1e-295, 1032, 737}, + {1e-294, 1029, 735}, + {1e-293, 1022, 729}, + {1e-292, 1021, 729}, + {1e-291, 1019, 727}, + {1e-290, 1015, 725}, + {1e-289, 1012, 723}, + {1e-288, 1009, 721}, + {1e-287, 1006, 719}, + {1e-286, 1003, 717}, + {1e-285, 999, 714}, + {1e-284, 996, 712}, + {1e-283, 993, 709}, + {1e-282, 986, 704}, + {1e-281, 985, 704}, + {1e-280, 981, 700}, + {1e-279, 979, 700}, + {1e-278, 976, 697}, + {1e-277, 973, 695}, + {1e-276, 957, 681}, + {1e-275, 966, 690}, + {1e-274, 963, 688}, + {1e-273, 954, 681}, + {1e-272, 956, 683}, + {1e-271, 953, 681}, + {1e-270, 948, 678}, + {1e-269, 944, 674}, + {1e-268, 943, 674}, + {1e-267, 935, 667}, + {1e-266, 934, 667}, + {1e-265, 933, 667}, + {1e-264, 925, 661}, + {1e-263, 924, 661}, + {1e-262, 923, 661}, + {1e-261, 920, 658}, + {1e-260, 916, 655}, + {1e-259, 909, 650}, + {1e-258, 910, 651}, + {1e-257, 904, 646}, + {1e-256, 903, 646}, + {1e-255, 898, 643}, + {1e-254, 894, 639}, + {1e-253, 890, 637}, + {1e-252, 890, 637}, + {1e-251, 886, 635}, + {1e-250, 881, 631}, + {1e-249, 880, 631}, + {1e-248, 876, 627}, + {1e-247, 872, 625}, + {1e-246, 870, 623}, + {1e-245, 863, 617}, + {1e-244, 862, 617}, + {1e-243, 860, 616}, + {1e-242, 850, 607}, + {1e-241, 849, 607}, + {1e-240, 848, 607}, + {1e-239, 845, 606}, + {1e-238, 840, 601}, + {1e-237, 839, 601}, + {1e-236, 835, 599}, + {1e-235, 829, 593}, + {1e-234, 828, 593}, + {1e-233, 827, 593}, + {1e-232, 823, 591}, + {1e-231, 819, 587}, + {1e-230, 817, 587}, + {1e-229, 813, 584}, + {1e-228, 810, 582}, + {1e-227, 807, 579}, + {1e-226, 803, 576}, + {1e-225, 799, 573}, + {1e-224, 796, 572}, + {1e-223, 792, 568}, + {1e-222, 790, 568}, + {1e-221, 787, 566}, + {1e-220, 783, 562}, + {1e-219, 777, 558}, + {1e-218, 776, 558}, + {1e-217, 773, 556}, + {1e-216, 768, 552}, + {1e-215, 767, 552}, + {1e-214, 763, 548}, + {1e-213, 758, 544}, + {1e-212, 757, 544}, + {1e-211, 753, 542}, + {1e-210, 747, 537}, + {1e-209, 746, 537}, + {1e-208, 740, 532}, + {1e-207, 740, 532}, + {1e-206, 737, 531}, + {1e-205, 731, 526}, + {1e-204, 730, 526}, + {1e-203, 723, 520}, + {1e-202, 722, 520}, + {1e-201, 720, 518}, + {1e-200, 715, 514}, + {1e-199, 714, 514}, + {1e-198, 709, 510}, + {1e-197, 706, 508}, + {1e-196, 703, 507}, + {1e-195, 699, 504}, + {1e-194, 697, 503}, + {1e-193, 693, 500}, + {1e-192, 689, 497}, + {1e-191, 684, 493}, + {1e-190, 683, 493}, + {1e-189, 680, 491}, + {1e-188, 676, 487}, + {1e-187, 672, 485}, + {1e-186, 669, 482}, + {1e-185, 666, 480}, + {1e-184, 663, 479}, + {1e-183, 660, 477}, + {1e-182, 655, 473}, + {1e-181, 654, 473}, + {1e-180, 647, 467}, + {1e-179, 646, 467}, + {1e-178, 641, 462}, + {1e-177, 640, 462}, + {1e-176, 632, 455}, + {1e-175, 631, 455}, + {1e-174, 630, 455}, + {1e-173, 624, 451}, + {1e-172, 623, 451}, + {1e-171, 618, 446}, + {1e-170, 617, 446}, + {1e-169, 614, 445}, + {1e-168, 610, 442}, + {1e-167, 607, 440}, + {1e-166, 604, 438}, + {1e-165, 600, 435}, + {1e-164, 597, 432}, + {1e-163, 594, 430}, + {1e-162, 591, 428}, + {1e-161, 587, 426}, + {1e-160, 582, 421}, + {1e-159, 581, 421}, + {1e-158, 577, 419}, + {1e-157, 574, 416}, + {1e-156, 571, 415}, + {1e-155, 567, 412}, + {1e-154, 563, 408}, + {1e-153, 561, 408}, + {1e-152, 557, 405}, + {1e-151, 553, 401}, + {1e-150, 551, 401}, + {1e-149, 547, 397}, + {1e-148, 544, 395}, + {1e-147, 540, 392}, + {1e-146, 538, 392}, + {1e-145, 534, 388}, + {1e-144, 527, 382}, + {1e-143, 526, 382}, + {1e-142, 521, 379}, + {1e-141, 520, 379}, + {1e-140, 517, 376}, + {1e-139, 514, 375}, + {1e-138, 511, 373}, + {1e-137, 508, 370}, + {1e-136, 504, 368}, + {1e-135, 499, 364}, + {1e-134, 498, 364}, + {1e-133, 493, 360}, + {1e-132, 487, 354}, + {1e-131, 486, 354}, + {1e-130, 482, 352}, + {1e-129, 477, 347}, + {1e-128, 478, 350}, + {1e-127, 473, 346}, + {1e-126, 470, 343}, + {1e-125, 468, 343}, + {1e-124, 464, 339}, + {1e-123, 459, 336}, + {1e-122, 458, 336}, + {1e-121, 452, 330}, + {1e-120, 451, 330}, + {1e-119, 448, 329}, + {1e-118, 444, 325}, + {1e-117, 441, 324}, + {1e-116, 437, 320}, + {1e-115, 431, 316}, + {1e-114, 430, 316}, + {1e-113, 428, 314}, + {1e-112, 424, 311}, + {1e-111, 421, 310}, + {1e-110, 417, 307}, + {1e-109, 414, 304}, + {1e-108, 411, 303}, + {1e-107, 407, 300}, + {1e-106, 405, 298}, + {1e-105, 401, 295}, + {1e-104, 398, 293}, + {1e-103, 395, 291}, + {1e-102, 391, 288}, + {1e-101, 388, 287}, + {1e-100, 381, 281}, + {1e-99, 380, 281}, + {1e-98, 378, 279}, + {1e-97, 375, 278}, + {1e-96, 370, 273}, + {1e-95, 368, 272}, + {1e-94, 364, 269}, + {1e-93, 360, 266}, + {1e-92, 358, 265}, + {1e-91, 355, 264}, + {1e-90, 351, 260}, + {1e-89, 348, 259}, + {1e-88, 345, 256}, + {1e-87, 342, 255}, + {1e-86, 338, 252}, + {1e-85, 334, 248}, + {1e-84, 328, 244}, + {1e-83, 327, 244}, + {1e-82, 320, 237}, + {1e-81, 319, 237}, + {1e-80, 318, 237}, + {1e-79, 313, 233}, + {1e-78, 312, 233}, + {1e-77, 306, 228}, + {1e-76, 305, 228}, + {1e-75, 299, 223}, + {1e-74, 298, 223}, + {1e-73, 295, 221}, + {1e-72, 291, 218}, + {1e-71, 287, 215}, + {1e-70, 285, 214}, + {1e-69, 280, 210}, + {1e-68, 278, 210}, + {1e-67, 275, 207}, + {1e-66, 271, 204}, + {1e-65, 268, 202}, + {1e-64, 265, 200}, + {1e-63, 262, 199}, + {1e-62, 255, 193}, + {1e-61, 254, 193}, + {1e-60, 251, 190}, + {1e-59, 245, 186}, + {1e-58, 244, 186}, + {1e-57, 242, 184}, + {1e-56, 238, 182}, + {1e-55, 235, 179}, + {1e-54, 230, 176}, + {1e-53, 229, 176}, + {1e-52, 221, 169}, + {1e-51, 220, 169}, + {1e-50, 219, 169}, + {1e-49, 215, 165}, + {1e-48, 209, 160}, + {1e-47, 208, 160}, + {1e-46, 205, 159}, + {1e-45, 202, 156}, + {1e-44, 199, 154}, + {1e-43, 195, 152}, + {1e-42, 192, 150}, + {1e-41, 189, 148}, + {1e-40, 183, 142}, + {1e-39, 182, 142}, + {1e-38, 177, 138}, + {1e-37, 175, 138}, + {1e-36, 171, 134}, + {1e-35, 169, 134}, + {1e-34, 165, 130}, + {1e-33, 160, 127}, + {1e-32, 159, 127}, + {1e-31, 148, 117}, + {1e-30, 147, 117}, + {1e-29, 149, 119}, + {1e-28, 146, 117}, + {1e-27, 138, 111}, + {1e-26, 137, 111}, + {1e-25, 136, 111}, + {1e-24, 132, 107}, + {1e-23, 129, 105}, + {1e-22, 125, 103}, + {1e-21, 122, 100}, + {1e-20, 119, 98}, + {1e-19, 114, 94}, + {1e-18, 110, 92}, + {1e-17, 109, 92}, + {1e-16, 104, 87}, + {1e-15, 101, 86}, + {1e-14, 99, 84}, + {1e-13, 95, 82}, + {1e-12, 92, 79}, + {1e-11, 89, 77}, + {1e-10, 86, 76}, + {1e-9, 82, 73}, + {1e-8, 78, 70}, + {1e-7, 73, 65}, + {1e-6, 72, 65}, + {1e-5, 69, 64}, + {1e-4, 66, 62}, + {1e-3, 60, 57}, + {1e-2, 59, 57}, + {1e-1, 55, 54}, + {1e0, 0, 1}, # TODO: fix exp_reference + {1e1, 0, 1}, + {1e2, 0, 1}, + {1e3, 0, 1}, + {1e4, 0, 1}, + {1e5, 0, 1}, + {1e6, 0, 1}, + {1e7, 0, 1}, + {1e8, 0, 1}, + {1e9, 0, 1}, + {1e10, 0, 1}, + {1e11, 0, 1}, + {1e12, 0, 1}, + {1e13, 0, 1}, + {1e14, 0, 1}, + {1e15, 0, 1}, + {1e16, 0, 1}, + {1e17, 0, 1}, + {1e18, 0, 1}, + {1e19, 0, 1}, + {1e20, 0, 1}, + {1e21, 0, 1}, + {1e22, 0, 1}, + {1e23, 0, 22}, + {1e24, 0, 23}, + {1e25, 0, 25}, + {1e26, 0, 26}, + {1e27, 0, 27}, + {1e28, 0, 27}, + {1e29, 0, 28}, + {1e30, 0, 30}, + {1e31, 0, 30}, + {1e32, 0, 32}, + {1e33, 0, 32}, + {1e34, 0, 32}, + {1e35, 0, 34}, + {1e36, 0, 36}, + {1e37, 0, 36}, + {1e38, 0, 37}, + {1e39, 0, 38}, + {1e40, 0, 40}, + {1e41, 0, 41}, + {1e42, 0, 42}, + {1e43, 0, 43}, + {1e44, 0, 44}, + {1e45, 0, 44}, + {1e46, 0, 45}, + {1e47, 0, 47}, + {1e48, 0, 47}, + {1e49, 0, 48}, + {1e50, 0, 49}, + {1e51, 0, 50}, + {1e52, 0, 50}, + {1e53, 0, 50}, + {1e54, 0, 54}, + {1e55, 0, 55}, + {1e56, 0, 56}, + {1e57, 0, 57}, + {1e58, 0, 57}, + {1e59, 0, 58}, + {1e60, 0, 59}, + {1e61, 0, 59}, + {1e62, 0, 62}, + {1e63, 0, 63}, + {1e64, 0, 64}, + {1e65, 0, 64}, + {1e66, 0, 65}, + {1e67, 0, 66}, + {1e68, 0, 67}, + {1e69, 0, 68}, + {1e70, 0, 68}, + {1e71, 0, 71}, + {1e72, 0, 71}, + {1e73, 0, 72}, + {1e74, 0, 73}, + {1e75, 0, 74}, + {1e76, 0, 76}, + {1e77, 0, 76}, + {1e78, 0, 78}, + {1e79, 0, 78}, + {1e80, 0, 80}, + {1e81, 0, 80}, + {1e82, 0, 81}, + {1e83, 0, 83}, + {1e84, 0, 84}, + {1e85, 0, 85}, + {1e86, 0, 85}, + {1e87, 0, 86}, + {1e88, 0, 86}, + {1e89, 0, 88}, + {1e90, 0, 89}, + {1e91, 0, 90}, + {1e92, 0, 92}, + {1e93, 0, 92}, + {1e94, 0, 94}, + {1e95, 0, 94}, + {1e96, 0, 96}, + {1e97, 0, 97}, + {1e98, 0, 97}, + {1e99, 0, 98}, + {1e100, 0, 100}, + {1e101, 0, 100}, + {1e102, 0, 100}, + {1e103, 0, 103}, + {1e104, 0, 103}, + {1e105, 0, 104}, + {1e106, 0, 106}, + {1e107, 0, 106}, + {1e108, 0, 108}, + {1e109, 0, 108}, + {1e110, 0, 110}, + {1e111, 0, 110}, + {1e112, 0, 111}, + {1e113, 0, 113}, + {1e114, 0, 113}, + {1e115, 0, 113}, + {1e116, 0, 113}, + {1e117, 0, 117}, + {1e118, 0, 117}, + {1e119, 0, 118}, + {1e120, 0, 119}, + {1e121, 0, 121}, + {1e122, 0, 122}, + {1e123, 0, 122}, + {1e124, 0, 123}, + {1e125, 0, 124}, + {1e126, 0, 124}, + {1e127, 0, 126}, + {1e128, 0, 126}, + {1e129, 0, 128}, + {1e130, 0, 130}, + {1e131, 0, 130}, + {1e132, 0, 131}, + {1e133, 0, 133}, + {1e134, 0, 133}, + {1e135, 0, 134}, + {1e136, 0, 136}, + {1e137, 0, 137}, + {1e138, 0, 137}, + {1e139, 0, 137}, + {1e140, 0, 140}, + {1e141, 0, 141}, + {1e142, 0, 142}, + {1e143, 0, 143}, + {1e144, 0, 143}, + {1e145, 0, 144}, + {1e146, 0, 145}, + {1e147, 0, 146}, + {1e148, 0, 148}, + {1e149, 0, 148}, + {1e150, 0, 149}, + {1e151, 0, 151}, + {1e152, 0, 152}, + {1e153, 0, 152}, + {1e154, 0, 154}, + {1e155, 0, 155}, + {1e156, 0, 155}, + {1e157, 0, 155}, + {1e158, 0, 157}, + {1e159, 0, 158}, + {1e160, 0, 160}, + {1e161, 0, 161}, + {1e162, 0, 161}, + {1e163, 0, 161}, + {1e164, 0, 164}, + {1e165, 0, 164}, + {1e166, 0, 165}, + {1e167, 0, 167}, + {1e168, 0, 167}, + {1e169, 0, 167}, + {1e170, 0, 170}, + {1e171, 0, 170}, + {1e172, 0, 172}, + {1e173, 0, 173}, + {1e174, 0, 174}, + {1e175, 0, 174}, + {1e176, 0, 176}, + {1e177, 0, 176}, + {1e178, 0, 178}, + {1e179, 0, 178}, + {1e180, 0, 180}, + {1e181, 0, 180}, + {1e182, 0, 182}, + {1e183, 0, 182}, + {1e184, 0, 184}, + {1e185, 0, 184}, + {1e186, 0, 184}, + {1e187, 0, 186}, + {1e188, 0, 188}, + {1e189, 0, 188}, + {1e190, 0, 190}, + {1e191, 0, 190}, + {1e192, 0, 192}, + {1e193, 0, 193}, + {1e194, 0, 193}, + {1e195, 0, 194}, + {1e196, 0, 195}, + {1e197, 0, 195}, + {1e198, 0, 198}, + {1e199, 0, 199}, + {1e200, 0, 199}, + {1e201, 0, 201}, + {1e202, 0, 200}, + {1e203, 0, 202}, + {1e204, 0, 202}, + {1e205, 0, 205}, + {1e206, 0, 206}, + {1e207, 0, 206}, + {1e208, 0, 207}, + {1e209, 0, 209}, + {1e210, 0, 209}, + {1e211, 0, 210}, + {1e212, 0, 211}, + {1e213, 0, 212}, + {1e214, 0, 213}, + {1e215, 0, 214}, + {1e216, 0, 216}, + {1e217, 0, 216}, + {1e218, 0, 217}, + {1e219, 0, 218}, + {1e220, 0, 219}, + {1e221, 0, 221}, + {1e222, 0, 221}, + {1e223, 0, 221}, + {1e224, 0, 223}, + {1e225, 0, 224}, + {1e226, 0, 225}, + {1e227, 0, 225}, + {1e228, 0, 227}, + {1e229, 0, 228}, + {1e230, 0, 230}, + {1e231, 0, 231}, + {1e232, 0, 231}, + {1e233, 0, 232}, + {1e234, 0, 234}, + {1e235, 0, 235}, + {1e236, 0, 235}, + {1e237, 0, 235}, + {1e238, 0, 238}, + {1e239, 0, 238}, + {1e240, 0, 240}, + {1e241, 0, 241}, + {1e242, 0, 241}, + {1e243, 0, 243}, + {1e244, 0, 243}, + {1e245, 0, 245}, + {1e246, 0, 246}, + {1e247, 0, 246}, + {1e248, 0, 248}, + {1e249, 0, 247}, + {1e250, 0, 247}, + {1e251, 0, 251}, + {1e252, 0, 252}, + {1e253, 0, 252}, + {1e254, 0, 252}, + {1e255, 0, 254}, + {1e256, 0, 256}, + {1e257, 0, 256}, + {1e258, 0, 258}, + {1e259, 0, 258}, + {1e260, 0, 260}, + {1e261, 0, 258}, + {1e262, 0, 262}, + {1e263, 0, 262}, + {1e264, 0, 264}, + {1e265, 0, 265}, + {1e266, 0, 266}, + {1e267, 0, 266}, + {1e268, 0, 266}, + {1e269, 0, 269}, + {1e270, 0, 269}, + {1e271, 0, 270}, + {1e272, 0, 272}, + {1e273, 0, 272}, + {1e274, 0, 273}, + {1e275, 0, 274}, + {1e276, 0, 276}, + {1e277, 0, 277}, + {1e278, 0, 277}, + {1e279, 0, 279}, + {1e280, 0, 280}, + {1e281, 0, 280}, + {1e282, 0, 280}, + {1e283, 0, 282}, + {1e284, 0, 284}, + {1e285, 0, 284}, + {1e286, 0, 286}, + {1e287, 0, 287}, + {1e288, 0, 288}, + {1e289, 0, 289}, + {1e290, 0, 289}, + {1e291, 0, 290}, + {1e292, 0, 292}, + {1e293, 0, 292}, + {1e294, 0, 294}, + {1e295, 0, 294}, + {1e296, 0, 294}, + {1e297, 0, 297}, + {1e298, 0, 297}, + {1e299, 0, 299}, + {1e300, 0, 299}, + {1e301, 0, 299}, + {1e302, 0, 302}, + {1e303, 0, 303}, + {1e304, 0, 303}, + {1e305, 0, 303}, + {1e306, 0, 306}, + {1e307, 0, 306}, + {1e308, 0, 308}, +] + +# These values test every binary exponent (which would be more obvious with hexfloats). +# The mantissas were randomly generated. +ALL_BINARY_EXPONENTS = [ + {8.667315560151837e-309, 1074, 765}, + {3.402496288854889e-308, 1072, 764}, + {5.674095874064163e-308, 1068, 760}, + {1.5540526173622352e-307, 1072, 765}, + {1.990320005135143e-307, 1071, 764}, + {5.107418539046847e-307, 1070, 763}, + {9.580341507134765e-307, 1068, 761}, + {2.7686246461533843e-306, 1067, 761}, + {4.123539674247709e-306, 1066, 760}, + {1.0292523314007669e-305, 1065, 760}, + {1.869562966771459e-305, 1065, 760}, + {2.83258275754601e-305, 1063, 758}, + {6.143575467580988e-305, 1061, 756}, + {1.4317575812076783e-304, 1062, 758}, + {1.8736954404407843e-304, 1061, 757}, + {3.8678085703767116e-304, 1060, 756}, + {7.635297514304952e-304, 1058, 754}, + {1.9931833457401843e-303, 1056, 753}, + {5.7104439440441904e-303, 1057, 754}, + {5.845773229837182e-303, 1056, 753}, + {1.6446596413123796e-302, 1054, 752}, + {3.571334515579776e-302, 1054, 752}, + {5.226450761688444e-302, 1053, 751}, + {1.0747997253788843e-301, 1051, 750}, + {1.90892926200005e-301, 1051, 750}, + {6.786272682763782e-301, 1047, 746}, + {1.2172372613102281e-300, 1044, 744}, + {1.7966676643662128e-300, 1042, 742}, + {5.462819694528703e-300, 1047, 747}, + {6.961706248722051e-300, 1043, 743}, + {1.5112507155402445e-299, 1045, 746}, + {2.673980873749012e-299, 1044, 745}, + {8.503369157355244e-299, 1043, 744}, + {1.3233106901096892e-298, 1042, 744}, + {2.129178977672023e-298, 1041, 743}, + {4.178648615235546e-298, 1036, 738}, + {9.216189377840373e-298, 1038, 740}, + {2.0166542228894894e-297, 1036, 739}, + {3.5449747515908894e-297, 1034, 737}, + {8.064939085743458e-297, 1036, 739}, + {2.1182119864764602e-296, 1035, 739}, + {3.820427653349436e-296, 1034, 738}, + {9.166969936802109e-296, 1033, 737}, + {1.0587007370833377e-295, 1031, 736}, + {2.5617734189585968e-295, 1030, 735}, + {6.117667163341597e-295, 1030, 735}, + {1.2442918509206014e-294, 1028, 734}, + {3.100051235126117e-294, 1027, 733}, + {5.514599643126014e-294, 1026, 732}, + {8.019518080011996e-294, 1025, 731}, + {2.2148549407571022e-293, 1022, 729}, + {4.20911452464387e-293, 1024, 731}, + {6.673970944986261e-293, 1022, 729}, + {1.746546364023377e-292, 1021, 729}, + {2.5532945426002905e-292, 1021, 729}, + {7.167199051004838e-292, 1020, 728}, + {1.4331413352279302e-291, 1018, 727}, + {1.6537479214140957e-291, 1018, 727}, + {4.290843909020547e-291, 1017, 726}, + {9.634563122144926e-291, 1014, 723}, + {2.1086057222075156e-290, 1010, 720}, + {3.4206800637910767e-290, 1013, 723}, + {6.629016758967737e-290, 1013, 723}, + {1.352094685757577e-289, 1011, 722}, + {3.065153212531983e-289, 1011, 722}, + {5.074022975467963e-289, 1006, 717}, + {1.5066401531008766e-288, 1009, 721}, + {2.8015937941494583e-288, 1008, 720}, + {5.38303645298669e-288, 1007, 719}, + {8.441234238050258e-288, 1006, 718}, + {1.7229963037415354e-287, 1004, 717}, + {4.998022788892795e-287, 1004, 717}, + {8.728697912491584e-287, 1003, 716}, + {1.9042271010497776e-286, 1002, 716}, + {2.9003728382951163e-286, 1000, 714}, + {6.030230011480532e-286, 999, 713}, + {1.2707290656410452e-285, 997, 712}, + {3.3470583063356332e-285, 998, 713}, + {6.5966578537292035e-285, 997, 712}, + {7.427398668320939e-285, 995, 710}, + {2.5312725644714646e-284, 994, 710}, + {4.7441324100905746e-284, 994, 710}, + {7.352811059453878e-284, 992, 708}, + {1.2773195914029405e-283, 990, 707}, + {3.1336514683809336e-283, 991, 708}, + {4.624339948076099e-283, 990, 707}, + {8.894087772740341e-283, 989, 706}, + {2.3953652083727512e-282, 988, 706}, + {3.761567466326268e-282, 985, 703}, + {1.2928212167160486e-281, 985, 704}, + {2.2480352182123753e-281, 982, 701}, + {3.154850939942071e-281, 983, 702}, + {6.071363984983044e-281, 982, 701}, + {2.1910202165183368e-280, 981, 701}, + {4.3370603492214e-280, 980, 700}, + {6.968471572869319e-280, 980, 700}, + {1.473331115243779e-279, 979, 700}, + {2.66044060949483e-279, 971, 692}, + {5.683973436284207e-279, 976, 697}, + {1.4089452631685327e-278, 976, 698}, + {2.2755564362864927e-278, 973, 695}, + {3.821906858286435e-278, 973, 695}, + {8.103117627864485e-278, 973, 695}, + {1.832473425427903e-277, 970, 693}, + {2.727222054531752e-277, 970, 693}, + {7.882910515028218e-277, 964, 687}, + {1.479332526434952e-276, 966, 690}, + {2.2180410620430226e-276, 968, 692}, + {5.690649743658698e-276, 966, 690}, + {1.4121156100358157e-275, 966, 691}, + {2.6685811370633676e-275, 965, 690}, + {4.6692815012344967e-275, 963, 688}, + {9.834548098669551e-275, 958, 683}, + {1.8600057734718372e-274, 962, 688}, + {2.811775675630843e-274, 961, 687}, + {6.27142702954425e-274, 959, 685}, + {1.0250975871333601e-273, 959, 686}, + {2.5253325080332935e-273, 958, 685}, + {6.913296125147658e-273, 957, 684}, + {9.747372287629775e-273, 956, 683}, + {1.9721670909138485e-272, 953, 681}, + {4.469048372679605e-272, 953, 681}, + {1.0205638445192075e-271, 952, 681}, + {1.5594946591458144e-271, 952, 681}, + {2.3721122629194564e-271, 949, 678}, + {5.551135919284155e-271, 944, 673}, + {1.0734739674446298e-270, 947, 677}, + {2.4398554262702667e-270, 948, 678}, + {6.8642158764630495e-270, 942, 672}, + {1.2055339469240307e-269, 941, 672}, + {1.5235738192618518e-269, 945, 676}, + {4.043876497442965e-269, 944, 675}, + {8.743556251142875e-269, 941, 672}, + {1.4649312749107113e-268, 941, 673}, + {3.98040680032538e-268, 941, 673}, + {8.586286660615516e-268, 938, 670}, + {1.657418018730156e-267, 939, 672}, + {3.613106834542997e-267, 937, 670}, + {5.9183241751764955e-267, 936, 669}, + {1.1798475245572565e-266, 935, 669}, + {3.084511928870661e-266, 934, 668}, + {4.1367697432326765e-266, 930, 664}, + {1.1356367562498619e-265, 933, 668}, + {1.5494624584252724e-265, 928, 663}, + {3.028575537095104e-265, 931, 666}, + {9.42740333348115e-265, 930, 665}, + {1.729174836691517e-264, 929, 665}, + {2.1531241335994103e-264, 928, 664}, + {7.094381157920946e-264, 927, 663}, + {1.037244238361319e-263, 922, 659}, + {1.6682266784627316e-263, 925, 662}, + {5.516139500818587e-263, 924, 661}, + {1.1456020464232508e-262, 919, 657}, + {2.066981873698563e-262, 919, 657}, + {2.7219184652406806e-262, 921, 659}, + {5.081283542674735e-262, 918, 656}, + {1.6876650530578208e-261, 917, 656}, + {2.276883127404377e-261, 916, 655}, + {6.29191834725416e-261, 917, 656}, + {9.114070309202437e-261, 915, 654}, + {2.5433112499173348e-260, 909, 649}, + {4.8383034142174994e-260, 914, 654}, + {9.557162041008455e-260, 913, 653}, + {2.3218163991190385e-259, 912, 653}, + {4.4322942901196377e-259, 911, 652}, + {7.248624545665186e-259, 904, 645}, + {1.4667081257360905e-258, 909, 651}, + {3.832202635359104e-258, 908, 650}, + {6.943148025853397e-258, 905, 647}, + {9.18729939902564e-258, 906, 648}, + {3.0584908958671776e-257, 905, 648}, + {3.332730679024704e-257, 901, 644}, + {7.495951055510854e-257, 902, 645}, + {1.6420266726944826e-256, 900, 644}, + {3.9297951542678785e-256, 900, 644}, + {8.581799124622545e-256, 896, 640}, + {1.3408011506316038e-255, 899, 644}, + {3.074598537137766e-255, 898, 643}, + {8.304947313449564e-255, 893, 638}, + {1.4474411243713317e-254, 893, 639}, + {1.9586457971591685e-254, 895, 641}, + {4.686715367492042e-254, 894, 640}, + {1.3394037849881335e-253, 893, 640}, + {2.3636119615931954e-253, 892, 639}, + {2.941610445695594e-253, 891, 638}, + {5.910628843543644e-253, 890, 637}, + {1.6810396848558274e-252, 889, 637}, + {3.105977744955943e-252, 887, 635}, + {5.296557380144569e-252, 886, 634}, + {1.4534181673457758e-251, 886, 635}, + {2.3938479247234097e-251, 885, 634}, + {5.13191114201037e-251, 884, 633}, + {8.74142907505523e-251, 883, 632}, + {2.0810847152471556e-250, 881, 631}, + {3.470210840000035e-250, 879, 629}, + {7.63186683615216e-250, 879, 629}, + {1.5834019337617896e-249, 872, 623}, + {2.760497402953147e-249, 876, 627}, + {4.645119455324602e-249, 877, 628}, + {9.91990200069646e-249, 874, 625}, + {2.5293584256227207e-248, 874, 626}, + {6.890528046616735e-248, 874, 626}, + {9.9700406511611e-248, 870, 622}, + {2.0741563200652303e-247, 872, 625}, + {4.6848861238967826e-247, 869, 622}, + {7.812879056117969e-247, 870, 623}, + {1.16023447415079e-246, 868, 622}, + {2.6285314099653654e-246, 867, 621}, + {7.24619526711458e-246, 866, 620}, + {1.513557579372713e-245, 864, 619}, + {2.2022598987138438e-245, 864, 619}, + {4.1410759136055036e-245, 864, 619}, + {1.0252325908734784e-244, 863, 619}, + {2.0526028348315092e-244, 861, 617}, + {3.9232668413253934e-244, 861, 617}, + {7.579615073559597e-244, 859, 615}, + {2.042372149921196e-243, 859, 616}, + {2.9353293314833334e-243, 858, 615}, + {6.372363858570045e-243, 855, 612}, + {1.575234414235322e-242, 854, 612}, + {3.3434436478293493e-242, 855, 613}, + {5.199566493700135e-242, 853, 611}, + {1.151222665835575e-241, 853, 612}, + {1.5543636774561637e-241, 850, 609}, + {4.079493099457495e-241, 850, 609}, + {8.503783454502844e-241, 850, 609}, + {2.0072820595479573e-240, 845, 605}, + {3.536438208901198e-240, 845, 605}, + {8.722809014595794e-240, 845, 605}, + {1.3749379101340066e-239, 846, 607}, + {3.05119881849728e-239, 845, 606}, + {6.2081425746751336e-239, 844, 605}, + {1.5212878641555803e-238, 841, 603}, + {2.521616635184641e-238, 842, 604}, + {4.498289788351931e-238, 841, 603}, + {7.28128014416453e-238, 834, 596}, + {2.0208837171448896e-237, 839, 602}, + {4.2234650668214423e-237, 837, 600}, + {8.084125743595665e-237, 836, 599}, + {1.6733590187416607e-236, 835, 599}, + {2.744824473945537e-236, 835, 599}, + {6.9330212812845956e-236, 832, 596}, + {9.887608848404935e-236, 831, 595}, + {1.8140520866375598e-235, 832, 597}, + {3.4634694166405886e-235, 831, 596}, + {1.0308725436052673e-234, 830, 596}, + {1.3123008280909585e-234, 829, 595}, + {3.87322423781539e-234, 825, 591}, + {9.2010739647813e-234, 827, 593}, + {1.1992483584063614e-233, 817, 584}, + {2.3452909097606e-233, 823, 590}, + {6.55832259537843e-233, 824, 591}, + {1.01023596160976e-232, 822, 590}, + {2.5973213970621353e-232, 822, 590}, + {4.955980006523515e-232, 821, 589}, + {1.1244377262803144e-231, 820, 589}, + {2.4089050126555283e-231, 819, 588}, + {3.1957993198054626e-231, 815, 584}, + {6.380419758740376e-231, 816, 585}, + {1.6095894110621704e-230, 816, 586}, + {4.032612821947131e-230, 813, 583}, + {6.0387918131443855e-230, 811, 581}, + {8.974323011245674e-230, 813, 583}, + {1.8798157375327938e-229, 812, 583}, + {6.1019603119906395e-229, 810, 581}, + {1.1326182622927228e-228, 808, 580}, + {1.3463284210193606e-228, 808, 580}, + {4.951126320251196e-228, 806, 578}, + {8.472853590985601e-228, 806, 578}, + {1.268665118648964e-227, 802, 575}, + {2.688551806792703e-227, 805, 578}, + {4.421464033750511e-227, 803, 576}, + {1.6504299596692555e-226, 803, 577}, + {2.290009142698998e-226, 799, 573}, + {4.095081668886285e-226, 800, 574}, + {1.15703960191472e-225, 799, 574}, + {1.8221726162720878e-225, 799, 574}, + {3.7536981380660996e-225, 798, 573}, + {7.40644242989838e-225, 797, 572}, + {1.5302655517853282e-224, 796, 572}, + {3.266244852085614e-224, 794, 570}, + {6.839580807204396e-224, 794, 570}, + {1.1596240640257126e-223, 792, 569}, + {2.137739829010208e-223, 792, 569}, + {5.154905434635419e-223, 790, 567}, + {7.890896642961214e-223, 790, 567}, + {2.4268259861629554e-222, 788, 566}, + {5.1376518013281177e-222, 788, 566}, + {6.49233931232799e-222, 785, 563}, + {1.5726294053843144e-221, 784, 563}, + {2.5630401696102993e-221, 783, 562}, + {7.564140571297787e-221, 784, 563}, + {1.572950734084536e-220, 783, 563}, + {3.270170075841635e-220, 782, 562}, + {3.794310430010385e-220, 781, 561}, + {7.2152364285788e-220, 780, 560}, + {2.6272169024527132e-219, 779, 560}, + {4.969214075705504e-219, 778, 559}, + {5.88301228914231e-219, 777, 558}, + {1.4743436359705467e-218, 776, 558}, + {3.4783661139951837e-218, 774, 556}, + {5.813216384022507e-218, 774, 556}, + {1.4584641434878504e-217, 769, 552}, + {2.3948318645722384e-217, 771, 554}, + {6.217084198272334e-217, 771, 554}, + {1.2105626076543997e-216, 770, 554}, + {2.7486687055906063e-216, 768, 552}, + 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{1.9018081890692326e+250, 0, 250}, + {4.9450566101263624e+250, 0, 248}, + {1.0162079024060942e+251, 0, 251}, + {1.7447831757371136e+251, 0, 250}, + {4.270366017096213e+251, 0, 250}, + {6.868063596101005e+251, 0, 251}, + {1.822171630415365e+252, 0, 251}, + {1.9952782556234112e+252, 0, 252}, + {7.158784748789308e+252, 0, 252}, + {1.2301580219420288e+253, 0, 253}, + {2.8298450670726808e+253, 0, 253}, + {3.975680900562017e+253, 0, 252}, + {8.709330821451115e+253, 0, 253}, + {2.0174005971626055e+254, 0, 254}, + {2.394882217848989e+254, 0, 254}, + {7.067225914874603e+254, 0, 253}, + {1.8724413449264554e+255, 0, 255}, + {2.8751146201193473e+255, 0, 255}, + {6.421888796776797e+255, 0, 255}, + {7.523354749558753e+255, 0, 254}, + {2.2569755092325087e+256, 0, 254}, + {5.3636854859010334e+256, 0, 256}, + {7.261725338002667e+256, 0, 256}, + {1.8966691176866934e+257, 0, 257}, + {4.4518263636702484e+257, 0, 256}, + {9.255196758728659e+257, 0, 257}, + {1.8593264122501495e+258, 0, 258}, + {3.6316167357983088e+258, 0, 258}, + {6.877505680971994e+258, 0, 258}, + {8.77084305549325e+258, 0, 258}, + {1.722353804283124e+259, 0, 259}, + {3.422411361841639e+259, 0, 259}, + {7.034346313302069e+259, 0, 259}, + {2.1022143522712643e+260, 0, 258}, + {3.9689033579839334e+260, 0, 260}, + {5.348655415676104e+260, 0, 260}, + {1.6669857056073904e+261, 0, 261}, + {2.5268130061515184e+261, 0, 261}, + {7.013556395550645e+261, 0, 261}, + {1.115205775476797e+262, 0, 261}, + {1.8218885128879403e+262, 0, 262}, + {4.882195462759247e+262, 0, 262}, + {1.1647232869439797e+263, 0, 263}, + {2.4733296974221884e+263, 0, 263}, + {3.825561477223162e+263, 0, 263}, + {5.295052253043566e+263, 0, 263}, + {1.7290409059596491e+264, 0, 264}, + {2.8917911522817363e+264, 0, 264}, + {5.3515050581631755e+264, 0, 263}, + {1.0862117360156829e+265, 0, 265}, + {2.312878548854693e+265, 0, 265}, + {5.710434640774437e+265, 0, 265}, + {1.1391963969865948e+266, 0, 266}, + {1.93471671572856e+266, 0, 265}, + {4.71279659258191e+266, 0, 266}, + {9.710448034768053e+266, 0, 266}, + {1.7049690600947821e+267, 0, 267}, + {2.1264667446960467e+267, 0, 267}, + {7.398129672423321e+267, 0, 267}, + {9.763305417386079e+267, 0, 267}, + {2.0663273080075778e+268, 0, 268}, + {5.79917895558858e+268, 0, 268}, + {7.426275326973986e+268, 0, 268}, + {2.1266018116022865e+269, 0, 268}, + {4.31743642311704e+269, 0, 269}, + {8.537997866147938e+269, 0, 269}, + {1.498071428134464e+270, 0, 268}, + {2.2911327982233443e+270, 0, 269}, + {8.038363677318397e+270, 0, 270}, + {1.6367042236629719e+271, 0, 271}, + {1.7563972945923824e+271, 0, 271}, + {4.380651719659702e+271, 0, 271}, + {1.0481984706425231e+272, 0, 272}, + {2.1003524500133663e+272, 0, 272}, + {5.0546833046720617e+272, 0, 272}, + {5.467994685893837e+272, 0, 272}, + {1.2485068025844776e+273, 0, 272}, + {2.8248640371828673e+273, 0, 272}, + {8.391364185949281e+273, 0, 273}, + {1.4139675630970964e+274, 0, 273}, + {2.907211624912509e+274, 0, 274}, + {4.372977278689428e+274, 0, 274}, + {1.2067462091729205e+275, 0, 275}, + {2.224391242910452e+275, 0, 275}, + {4.317611102271228e+275, 0, 275}, + {5.865999613363234e+275, 0, 275}, + {1.8057130538588834e+276, 0, 276}, + {2.684819410822478e+276, 0, 276}, + {6.918394090981146e+276, 0, 276}, + {9.614934849906353e+276, 0, 276}, + {3.489094951176538e+277, 0, 277}, + {6.096297720785519e+277, 0, 276}, + {7.672262077744885e+277, 0, 277}, + {1.7454649363112346e+278, 0, 278}, + {4.3709703490882645e+278, 0, 278}, + {1.0726114671866103e+279, 0, 279}, + {1.3228423831361687e+279, 0, 279}, + {3.696652073770945e+279, 0, 279}, + {5.506752176655332e+279, 0, 278}, + {1.4487895211141177e+280, 0, 280}, + {2.9868446101560017e+280, 0, 279}, + {5.1539637484359395e+280, 0, 280}, + {1.3665660611345062e+281, 0, 281}, + {2.7298170376572543e+281, 0, 280}, + {4.090888763436566e+281, 0, 280}, + {7.150463385743894e+281, 0, 281}, + {1.5175210833272951e+282, 0, 282}, + {4.186412589165422e+282, 0, 282}, + {6.374560719497041e+282, 0, 282}, + {1.5603097675062575e+283, 0, 283}, + {2.303138994294191e+283, 0, 283}, + {6.845537430162203e+283, 0, 283}, + {8.140470197133932e+283, 0, 283}, + {2.8387070865957636e+284, 0, 284}, + {4.7222972051563225e+284, 0, 283}, + {7.735866498835463e+284, 0, 284}, + {1.456494620618158e+285, 0, 285}, + {3.765187536411294e+285, 0, 285}, + {5.407406833340397e+285, 0, 284}, + {1.6691777225183443e+286, 0, 286}, + {2.842291093748383e+286, 0, 285}, + {3.9527246153864666e+286, 0, 286}, + {9.117687890595329e+286, 0, 286}, + {2.6403715176860095e+287, 0, 287}, + {4.672760871330719e+287, 0, 287}, + {9.585177496788628e+287, 0, 285}, + {1.823719730845468e+288, 0, 287}, + {3.3099160671433535e+288, 0, 288}, + {8.394239974695799e+288, 0, 287}, + {1.3765053672754183e+289, 0, 289}, + {3.643679829326757e+289, 0, 289}, + {6.662084711556889e+289, 0, 289}, + {1.4882800748283324e+290, 0, 290}, + {1.8128485634074353e+290, 0, 290}, + {3.59863757645859e+290, 0, 289}, + {1.1306303530723758e+291, 0, 291}, + {1.9883184243838977e+291, 0, 291}, + {3.152458971727972e+291, 0, 291}, + {5.55344865848389e+291, 0, 289}, + {1.9381607498203374e+292, 0, 291}, + {3.364847896300297e+292, 0, 292}, + {6.842765724941906e+292, 0, 291}, + {1.249825938708993e+293, 0, 293}, + {2.392791615385826e+293, 0, 293}, + {4.152722646899415e+293, 0, 293}, + {6.790906283978802e+293, 0, 293}, + {1.3561785760749324e+294, 0, 294}, + {3.341059095259842e+294, 0, 293}, + {9.977930881477503e+294, 0, 294}, + {1.515106038250912e+295, 0, 294}, + {3.002184910089352e+295, 0, 295}, + {5.876579596327993e+295, 0, 295}, + {1.4003917488295084e+296, 0, 296}, + {3.1684232621942047e+296, 0, 296}, + {3.4747005896842154e+296, 0, 296}, + {7.669723855021269e+296, 0, 296}, + {1.3614131925096533e+297, 0, 297}, + {3.191738550947262e+297, 0, 297}, + {8.888378843987562e+297, 0, 297}, + {1.5112090835975456e+298, 0, 298}, + {2.3682327923940456e+298, 0, 298}, + {5.099780421145732e+298, 0, 298}, + {1.0673033377644726e+299, 0, 298}, + {2.378013021177001e+299, 0, 299}, + {6.554057728282088e+299, 0, 299}, + {8.318933161474208e+299, 0, 299}, + {1.3614082701057758e+300, 0, 300}, + {5.35086581101499e+300, 0, 300}, + {8.494089296675853e+300, 0, 299}, + {1.0890134027784214e+301, 0, 301}, + {2.358927877102592e+301, 0, 301}, + {8.117690363105265e+301, 0, 301}, + {9.341511426794588e+301, 0, 301}, + {2.64210043201936e+302, 0, 302}, + {6.847933389378864e+302, 0, 302}, + {1.1002556200184007e+303, 0, 303}, + {2.5611530892094995e+303, 0, 303}, + {5.076344585537476e+303, 0, 303}, + {8.304487832500949e+303, 0, 303}, + {1.1230804446665463e+304, 0, 304}, + {4.2777559220816043e+304, 0, 304}, + {6.283260967439312e+304, 0, 304}, + {1.3747215164191865e+305, 0, 305}, + {3.3096929273918684e+305, 0, 305}, + {6.171133478197849e+305, 0, 305}, + {1.2292521010494213e+306, 0, 306}, + {2.2862202954633178e+306, 0, 305}, + {3.5065941308845355e+306, 0, 306}, + {1.0940422247589228e+307, 0, 307}, + {2.0068458193014486e+307, 0, 306}, + {2.7914963723745636e+307, 0, 307}, + {6.123699292104195e+307, 0, 307}, + {1.7026387749989901e+308, 0, 308}, +] + +struct BigFloat + def to_s(*, point_range : Range = -3..15) + String.build do |io| + to_s(io, point_range: point_range) + end + end + + def to_s(io : IO, *, point_range : Range = -3..15) : Nil + cstr = LibGMP.mpf_get_str(nil, out decimal_exponent, 10, 0, self) + length = LibC.strlen(cstr) + buffer = Slice.new(cstr, length) + + # add negative sign + if buffer[0]? == 45 # '-' + io << '-' + buffer = buffer[1..] + length -= 1 + end + + point = decimal_exponent + exp = point + exp_mode = !point_range.includes?(point) + point = 1 if exp_mode + + # add leading zero + io << '0' if point < 1 + + # add integer part digits + if decimal_exponent > 0 && !exp_mode + # whole number but not big enough to be exp form + io.write_string buffer[0, {decimal_exponent, length}.min] + buffer = buffer[{decimal_exponent, length}.min...] + (point - length).times { io << '0' } + elsif point > 0 + io.write_string buffer[0, point] + buffer = buffer[point...] + end + + # TODO: allow this to be not written at all + io << '.' + + # add leading zeros after point + if point < 0 + (-point).times { io << '0' } + end + + # add fractional part digits + io.write_string buffer + + # print trailing 0 if whole number or exp notation of power of ten + if (decimal_exponent >= length && !exp_mode) || ((exp != point || exp_mode) && length == 1) + io << '0' + end + + # exp notation + if exp_mode + io << 'e' + io << '+' if exp > 0 + (exp - 1).to_s(io) + end + end +end + +private def fixed_reference(value, precision) + if precision == 0 + value.to_big_i.to_s + else + BigFloat.new(value, 4096).to_s(point_range: ..) + end +end + +private def exp_reference(value, precision) + BigFloat.new(value, 4096).to_s(point_range: 0...0) +end + +private def ieee_parts_to_f64(sign, exponent, mantissa) + ((sign ? 1_u64 << 63 : 0_u64) | (exponent.to_u64 << 52) | mantissa.to_u64).unsafe_as(Float64) +end + +private macro expect_fixed(float, precision, string) + Float::Printer::RyuPrintf.d2fixed({{ float }}, {{ precision }}).should eq({{ string }}) +end + +private macro expect_exp(float, precision, string) + Float::Printer::RyuPrintf.d2exp({{ float }}, {{ precision }}).should eq({{ string }}) +end + +describe Float::Printer::RyuPrintf do + describe ".d2fixed" do + it "Basic" do + expect_fixed( + ieee_parts_to_f64(false, 1234, 99999), 0, + "3291009114715486435425664845573426149758869524108446525879746560") + end + + it "Zero" do + expect_fixed(0.0, 4, "0.0000") + expect_fixed(0.0, 3, "0.000") + expect_fixed(0.0, 2, "0.00") + expect_fixed(0.0, 1, "0.0") + expect_fixed(0.0, 0, "0") + end + + it "MinMax" do + expect_fixed(ieee_parts_to_f64(false, 0, 1), 1074, + "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004940656458412465441765687928682213723650598026143247644255856825006755072702087518652998363616359923797965646954457177309266567103559397963987747960107818781263007131903114045278458171678489821036887186360569987307230500063874091535649843873124733972731696151400317153853980741262385655911710266585566867681870395603106249319452715914924553293054565444011274801297099995419319894090804165633245247571478690147267801593552386115501348035264934720193790268107107491703332226844753335720832431936092382893458368060106011506169809753078342277318329247904982524730776375927247874656084778203734469699533647017972677717585125660551199131504891101451037862738167250955837389733598993664809941164205702637090279242767544565229087538682506419718265533447265625") + + expect_fixed(ieee_parts_to_f64(false, 2046, 0xFFFFFFFFFFFFFu64), 0, + "179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368") + end + + it "AllPowersOfTen" do + {% for tc in ALL_POWERS_OF_TEN %} + expect_fixed({{ tc[0] }}, {{ tc[1] }}, fixed_reference({{ tc[0] }}, {{ tc[1] }})) + {% end %} + end + + it "RoundToEven" do + expect_fixed(0.125, 3, "0.125") + expect_fixed(0.125, 2, "0.12") + expect_fixed(0.375, 3, "0.375") + expect_fixed(0.375, 2, "0.38") + end + + it "RoundToEvenInteger" do + expect_fixed(2.5, 1, "2.5") + expect_fixed(2.5, 0, "2") + expect_fixed(3.5, 1, "3.5") + expect_fixed(3.5, 0, "4") + end + + it "NonRoundToEvenScenarios" do + expect_fixed(0.748046875, 3, "0.748") + expect_fixed(0.748046875, 2, "0.75") + expect_fixed(0.748046875, 1, "0.7") # 0.75 would round to "0.8", but this is smaller + + expect_fixed(0.2509765625, 3, "0.251") + expect_fixed(0.2509765625, 2, "0.25") + expect_fixed(0.2509765625, 1, "0.3") # 0.25 would round to "0.2", but this is larger + + expect_fixed(ieee_parts_to_f64(false, 1021, 1), 54, "0.250000000000000055511151231257827021181583404541015625") + expect_fixed(ieee_parts_to_f64(false, 1021, 1), 3, "0.250") + expect_fixed(ieee_parts_to_f64(false, 1021, 1), 2, "0.25") + expect_fixed(ieee_parts_to_f64(false, 1021, 1), 1, "0.3") # 0.25 would round to "0.2", but this is larger (again) + end + + it "VaryingPrecision" do + expect_fixed(1729.142857142857, 47, "1729.14285714285711037518922239542007446289062500000") + expect_fixed(1729.142857142857, 46, "1729.1428571428571103751892223954200744628906250000") + expect_fixed(1729.142857142857, 45, "1729.142857142857110375189222395420074462890625000") + expect_fixed(1729.142857142857, 44, "1729.14285714285711037518922239542007446289062500") + expect_fixed(1729.142857142857, 43, "1729.1428571428571103751892223954200744628906250") + expect_fixed(1729.142857142857, 42, "1729.142857142857110375189222395420074462890625") + expect_fixed(1729.142857142857, 41, "1729.14285714285711037518922239542007446289062") + expect_fixed(1729.142857142857, 40, "1729.1428571428571103751892223954200744628906") + expect_fixed(1729.142857142857, 39, "1729.142857142857110375189222395420074462891") + expect_fixed(1729.142857142857, 38, "1729.14285714285711037518922239542007446289") + expect_fixed(1729.142857142857, 37, "1729.1428571428571103751892223954200744629") + expect_fixed(1729.142857142857, 36, "1729.142857142857110375189222395420074463") + expect_fixed(1729.142857142857, 35, "1729.14285714285711037518922239542007446") + expect_fixed(1729.142857142857, 34, "1729.1428571428571103751892223954200745") + expect_fixed(1729.142857142857, 33, "1729.142857142857110375189222395420074") + expect_fixed(1729.142857142857, 32, "1729.14285714285711037518922239542007") + expect_fixed(1729.142857142857, 31, "1729.1428571428571103751892223954201") + expect_fixed(1729.142857142857, 30, "1729.142857142857110375189222395420") + expect_fixed(1729.142857142857, 29, "1729.14285714285711037518922239542") + expect_fixed(1729.142857142857, 28, "1729.1428571428571103751892223954") + expect_fixed(1729.142857142857, 27, "1729.142857142857110375189222395") + expect_fixed(1729.142857142857, 26, "1729.14285714285711037518922240") + expect_fixed(1729.142857142857, 25, "1729.1428571428571103751892224") + expect_fixed(1729.142857142857, 24, "1729.142857142857110375189222") + expect_fixed(1729.142857142857, 23, "1729.14285714285711037518922") + expect_fixed(1729.142857142857, 22, "1729.1428571428571103751892") + expect_fixed(1729.142857142857, 21, "1729.142857142857110375189") + expect_fixed(1729.142857142857, 20, "1729.14285714285711037519") + expect_fixed(1729.142857142857, 19, "1729.1428571428571103752") + expect_fixed(1729.142857142857, 18, "1729.142857142857110375") + expect_fixed(1729.142857142857, 17, "1729.14285714285711038") + expect_fixed(1729.142857142857, 16, "1729.1428571428571104") + expect_fixed(1729.142857142857, 15, "1729.142857142857110") + expect_fixed(1729.142857142857, 14, "1729.14285714285711") + expect_fixed(1729.142857142857, 13, "1729.1428571428571") + expect_fixed(1729.142857142857, 12, "1729.142857142857") + expect_fixed(1729.142857142857, 11, "1729.14285714286") + expect_fixed(1729.142857142857, 10, "1729.1428571429") + expect_fixed(1729.142857142857, 9, "1729.142857143") + expect_fixed(1729.142857142857, 8, "1729.14285714") + expect_fixed(1729.142857142857, 7, "1729.1428571") + expect_fixed(1729.142857142857, 6, "1729.142857") + expect_fixed(1729.142857142857, 5, "1729.14286") + expect_fixed(1729.142857142857, 4, "1729.1429") + expect_fixed(1729.142857142857, 3, "1729.143") + expect_fixed(1729.142857142857, 2, "1729.14") + expect_fixed(1729.142857142857, 1, "1729.1") + expect_fixed(1729.142857142857, 0, "1729") + end + + it "Carrying" do + expect_fixed(0.0009, 4, "0.0009") + expect_fixed(0.0009, 3, "0.001") + expect_fixed(0.0029, 4, "0.0029") + expect_fixed(0.0029, 3, "0.003") + expect_fixed(0.0099, 4, "0.0099") + expect_fixed(0.0099, 3, "0.010") + expect_fixed(0.0299, 4, "0.0299") + expect_fixed(0.0299, 3, "0.030") + expect_fixed(0.0999, 4, "0.0999") + expect_fixed(0.0999, 3, "0.100") + expect_fixed(0.2999, 4, "0.2999") + expect_fixed(0.2999, 3, "0.300") + expect_fixed(0.9999, 4, "0.9999") + expect_fixed(0.9999, 3, "1.000") + expect_fixed(2.9999, 4, "2.9999") + expect_fixed(2.9999, 3, "3.000") + expect_fixed(9.9999, 4, "9.9999") + expect_fixed(9.9999, 3, "10.000") + expect_fixed(29.9999, 4, "29.9999") + expect_fixed(29.9999, 3, "30.000") + expect_fixed(99.9999, 4, "99.9999") + expect_fixed(99.9999, 3, "100.000") + expect_fixed(299.9999, 4, "299.9999") + expect_fixed(299.9999, 3, "300.000") + + expect_fixed(0.09, 2, "0.09") + expect_fixed(0.09, 1, "0.1") + expect_fixed(0.29, 2, "0.29") + expect_fixed(0.29, 1, "0.3") + expect_fixed(0.99, 2, "0.99") + expect_fixed(0.99, 1, "1.0") + expect_fixed(2.99, 2, "2.99") + expect_fixed(2.99, 1, "3.0") + expect_fixed(9.99, 2, "9.99") + expect_fixed(9.99, 1, "10.0") + expect_fixed(29.99, 2, "29.99") + expect_fixed(29.99, 1, "30.0") + expect_fixed(99.99, 2, "99.99") + expect_fixed(99.99, 1, "100.0") + expect_fixed(299.99, 2, "299.99") + expect_fixed(299.99, 1, "300.0") + + expect_fixed(0.9, 1, "0.9") + expect_fixed(0.9, 0, "1") + expect_fixed(2.9, 1, "2.9") + expect_fixed(2.9, 0, "3") + expect_fixed(9.9, 1, "9.9") + expect_fixed(9.9, 0, "10") + expect_fixed(29.9, 1, "29.9") + expect_fixed(29.9, 0, "30") + expect_fixed(99.9, 1, "99.9") + expect_fixed(99.9, 0, "100") + expect_fixed(299.9, 1, "299.9") + expect_fixed(299.9, 0, "300") + end + + it "RoundingResultZero" do + expect_fixed(0.004, 3, "0.004") + expect_fixed(0.004, 2, "0.00") + expect_fixed(0.4, 1, "0.4") + expect_fixed(0.4, 0, "0") + expect_fixed(0.5, 1, "0.5") + expect_fixed(0.5, 0, "0") + end + + it "AllBinaryExponents" do + {% for tc in ALL_BINARY_EXPONENTS %} + expect_fixed({{ tc[0] }}, {{ tc[1] }}, fixed_reference({{ tc[0] }}, {{ tc[1] }})) + {% end %} + end + + it "Regression" do + expect_fixed(7.018232e-82, 6, "0.000000") + end + end + + describe ".d2exp" do + it "Basic" do + expect_exp(ieee_parts_to_f64(false, 1234, 99999), 62, + "3.29100911471548643542566484557342614975886952410844652587974656e+63") + end + + it "Zero" do + expect_exp(0.0, 4, "0.0000e+0") + expect_exp(0.0, 3, "0.000e+0") + expect_exp(0.0, 2, "0.00e+0") + expect_exp(0.0, 1, "0.0e+0") + expect_exp(0.0, 0, "0e+0") + end + + it "MinMax" do + expect_exp(ieee_parts_to_f64(false, 0, 1), 750, + "4.940656458412465441765687928682213723650598026143247644255856825006755072702087518652998363616359923797965646954457177309266567103559397963987747960107818781263007131903114045278458171678489821036887186360569987307230500063874091535649843873124733972731696151400317153853980741262385655911710266585566867681870395603106249319452715914924553293054565444011274801297099995419319894090804165633245247571478690147267801593552386115501348035264934720193790268107107491703332226844753335720832431936092382893458368060106011506169809753078342277318329247904982524730776375927247874656084778203734469699533647017972677717585125660551199131504891101451037862738167250955837389733598993664809941164205702637090279242767544565229087538682506419718265533447265625e-324") + + expect_exp(ieee_parts_to_f64(false, 2046, 0xFFFFFFFFFFFFFu64), 308, + "1.79769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368e+308") + end + + it "AllPowersOfTen" do + {% for tc in ALL_POWERS_OF_TEN %} + expect_exp({{ tc[0] }}, {{ tc[2] }}, exp_reference({{ tc[0] }}, {{ tc[2] }})) + {% end %} + end + + it "RoundToEven" do + expect_exp(0.125, 2, "1.25e-1") + expect_exp(0.125, 1, "1.2e-1") + expect_exp(0.375, 2, "3.75e-1") + expect_exp(0.375, 1, "3.8e-1") + end + + it "RoundToEvenInteger" do + expect_exp(2.5, 1, "2.5e+0") + expect_exp(2.5, 0, "2e+0") + expect_exp(3.5, 1, "3.5e+0") + expect_exp(3.5, 0, "4e+0") + end + + it "NonRoundToEvenScenarios" do + expect_exp(0.748046875, 2, "7.48e-1") + expect_exp(0.748046875, 1, "7.5e-1") + expect_exp(0.748046875, 0, "7e-1") # 0.75 would round to "8e-1", but this is smaller + + expect_exp(0.2509765625, 2, "2.51e-1") + expect_exp(0.2509765625, 1, "2.5e-1") + expect_exp(0.2509765625, 0, "3e-1") # 0.25 would round to "2e-1", but this is larger + + expect_exp(ieee_parts_to_f64(false, 1021, 1), 53, "2.50000000000000055511151231257827021181583404541015625e-1") + expect_exp(ieee_parts_to_f64(false, 1021, 1), 2, "2.50e-1") + expect_exp(ieee_parts_to_f64(false, 1021, 1), 1, "2.5e-1") + expect_exp(ieee_parts_to_f64(false, 1021, 1), 0, "3e-1") # 0.25 would round to "2e-1", but this is larger (again) + end + + it "VaryingPrecision" do + expect_exp(1729.142857142857, 50, "1.72914285714285711037518922239542007446289062500000e+3") + expect_exp(1729.142857142857, 49, "1.7291428571428571103751892223954200744628906250000e+3") + expect_exp(1729.142857142857, 48, "1.729142857142857110375189222395420074462890625000e+3") + expect_exp(1729.142857142857, 47, "1.72914285714285711037518922239542007446289062500e+3") + expect_exp(1729.142857142857, 46, "1.7291428571428571103751892223954200744628906250e+3") + expect_exp(1729.142857142857, 45, "1.729142857142857110375189222395420074462890625e+3") + expect_exp(1729.142857142857, 44, "1.72914285714285711037518922239542007446289062e+3") + expect_exp(1729.142857142857, 43, "1.7291428571428571103751892223954200744628906e+3") + expect_exp(1729.142857142857, 42, "1.729142857142857110375189222395420074462891e+3") + expect_exp(1729.142857142857, 41, "1.72914285714285711037518922239542007446289e+3") + expect_exp(1729.142857142857, 40, "1.7291428571428571103751892223954200744629e+3") + expect_exp(1729.142857142857, 39, "1.729142857142857110375189222395420074463e+3") + expect_exp(1729.142857142857, 38, "1.72914285714285711037518922239542007446e+3") + expect_exp(1729.142857142857, 37, "1.7291428571428571103751892223954200745e+3") + expect_exp(1729.142857142857, 36, "1.729142857142857110375189222395420074e+3") + expect_exp(1729.142857142857, 35, "1.72914285714285711037518922239542007e+3") + expect_exp(1729.142857142857, 34, "1.7291428571428571103751892223954201e+3") + expect_exp(1729.142857142857, 33, "1.729142857142857110375189222395420e+3") + expect_exp(1729.142857142857, 32, "1.72914285714285711037518922239542e+3") + expect_exp(1729.142857142857, 31, "1.7291428571428571103751892223954e+3") + expect_exp(1729.142857142857, 30, "1.729142857142857110375189222395e+3") + expect_exp(1729.142857142857, 29, "1.72914285714285711037518922240e+3") + expect_exp(1729.142857142857, 28, "1.7291428571428571103751892224e+3") + expect_exp(1729.142857142857, 27, "1.729142857142857110375189222e+3") + expect_exp(1729.142857142857, 26, "1.72914285714285711037518922e+3") + expect_exp(1729.142857142857, 25, "1.7291428571428571103751892e+3") + expect_exp(1729.142857142857, 24, "1.729142857142857110375189e+3") + expect_exp(1729.142857142857, 23, "1.72914285714285711037519e+3") + expect_exp(1729.142857142857, 22, "1.7291428571428571103752e+3") + expect_exp(1729.142857142857, 21, "1.729142857142857110375e+3") + expect_exp(1729.142857142857, 20, "1.72914285714285711038e+3") + expect_exp(1729.142857142857, 19, "1.7291428571428571104e+3") + expect_exp(1729.142857142857, 18, "1.729142857142857110e+3") + expect_exp(1729.142857142857, 17, "1.72914285714285711e+3") + expect_exp(1729.142857142857, 16, "1.7291428571428571e+3") + expect_exp(1729.142857142857, 15, "1.729142857142857e+3") + expect_exp(1729.142857142857, 14, "1.72914285714286e+3") + expect_exp(1729.142857142857, 13, "1.7291428571429e+3") + expect_exp(1729.142857142857, 12, "1.729142857143e+3") + expect_exp(1729.142857142857, 11, "1.72914285714e+3") + expect_exp(1729.142857142857, 10, "1.7291428571e+3") + expect_exp(1729.142857142857, 9, "1.729142857e+3") + expect_exp(1729.142857142857, 8, "1.72914286e+3") + expect_exp(1729.142857142857, 7, "1.7291429e+3") + expect_exp(1729.142857142857, 6, "1.729143e+3") + expect_exp(1729.142857142857, 5, "1.72914e+3") + expect_exp(1729.142857142857, 4, "1.7291e+3") + expect_exp(1729.142857142857, 3, "1.729e+3") + expect_exp(1729.142857142857, 2, "1.73e+3") + expect_exp(1729.142857142857, 1, "1.7e+3") + expect_exp(1729.142857142857, 0, "2e+3") + end + + it "Carrying" do + expect_exp(2.0009, 4, "2.0009e+0") + expect_exp(2.0009, 3, "2.001e+0") + expect_exp(2.0029, 4, "2.0029e+0") + expect_exp(2.0029, 3, "2.003e+0") + expect_exp(2.0099, 4, "2.0099e+0") + expect_exp(2.0099, 3, "2.010e+0") + expect_exp(2.0299, 4, "2.0299e+0") + expect_exp(2.0299, 3, "2.030e+0") + expect_exp(2.0999, 4, "2.0999e+0") + expect_exp(2.0999, 3, "2.100e+0") + expect_exp(2.2999, 4, "2.2999e+0") + expect_exp(2.2999, 3, "2.300e+0") + expect_exp(2.9999, 4, "2.9999e+0") + expect_exp(2.9999, 3, "3.000e+0") + expect_exp(9.9999, 4, "9.9999e+0") + expect_exp(9.9999, 3, "1.000e+1") + + expect_exp(2.09, 2, "2.09e+0") + expect_exp(2.09, 1, "2.1e+0") + expect_exp(2.29, 2, "2.29e+0") + expect_exp(2.29, 1, "2.3e+0") + expect_exp(2.99, 2, "2.99e+0") + expect_exp(2.99, 1, "3.0e+0") + expect_exp(9.99, 2, "9.99e+0") + expect_exp(9.99, 1, "1.0e+1") + + expect_exp(2.9, 1, "2.9e+0") + expect_exp(2.9, 0, "3e+0") + expect_exp(9.9, 1, "9.9e+0") + expect_exp(9.9, 0, "1e+1") + end + + it "Exponents" do + expect_exp(9.99e-100, 2, "9.99e-100") + expect_exp(9.99e-99, 2, "9.99e-99") + expect_exp(9.99e-10, 2, "9.99e-10") + expect_exp(9.99e-9, 2, "9.99e-9") + expect_exp(9.99e-1, 2, "9.99e-1") + expect_exp(9.99e+0, 2, "9.99e+0") + expect_exp(9.99e+1, 2, "9.99e+1") + expect_exp(9.99e+9, 2, "9.99e+9") + expect_exp(9.99e+10, 2, "9.99e+10") + expect_exp(9.99e+99, 2, "9.99e+99") + expect_exp(9.99e+100, 2, "9.99e+100") + + expect_exp(9.99e-100, 1, "1.0e-99") + expect_exp(9.99e-99, 1, "1.0e-98") + expect_exp(9.99e-10, 1, "1.0e-9") + expect_exp(9.99e-9, 1, "1.0e-8") + expect_exp(9.99e-1, 1, "1.0e+0") + expect_exp(9.99e+0, 1, "1.0e+1") + expect_exp(9.99e+1, 1, "1.0e+2") + expect_exp(9.99e+9, 1, "1.0e+10") + expect_exp(9.99e+10, 1, "1.0e+11") + expect_exp(9.99e+99, 1, "1.0e+100") + expect_exp(9.99e+100, 1, "1.0e+101") + end + + it "AllBinaryExponents" do + {% for tc in ALL_BINARY_EXPONENTS %} + expect_exp({{ tc[0] }}, {{ tc[2] }}, exp_reference({{ tc[0] }}, {{ tc[2] }})) + {% end %} + end + + it "PrintDecimalPoint" do + # These values exercise each codepath. + expect_exp(1e+54, 0, "1e+54") + expect_exp(1e+54, 1, "1.0e+54") + expect_exp(1e-63, 0, "1e-63") + expect_exp(1e-63, 1, "1.0e-63") + expect_exp(1e+83, 0, "1e+83") + expect_exp(1e+83, 1, "1.0e+83") + end + end +end diff --git a/spec/std/sprintf_spec.cr b/spec/std/sprintf_spec.cr index ad6ceda4809d..82a4af02c523 100644 --- a/spec/std/sprintf_spec.cr +++ b/spec/std/sprintf_spec.cr @@ -378,20 +378,37 @@ describe "::sprintf" do end describe "floats" do - pending_win32 "works" do - assert_sprintf "%f", 123, "123.000000" + context "fixed format" do + it "works" do + assert_sprintf "%f", 123, "123.000000" + + assert_sprintf "%12f", 123.45, " 123.450000" + assert_sprintf "%-12f", 123.45, "123.450000 " + assert_sprintf "% f", 123.45, " 123.450000" + assert_sprintf "%+f", 123, "+123.000000" + assert_sprintf "%012f", 123, "00123.000000" + assert_sprintf "%.f", 1234.56, "1235" + assert_sprintf "%.2f", 1234.5678, "1234.57" + assert_sprintf "%10.2f", 1234.5678, " 1234.57" + assert_sprintf "%*.2f", [10, 1234.5678], " 1234.57" + assert_sprintf "%*.*f", [10, 2, 1234.5678], " 1234.57" + assert_sprintf "%.2f", 2.536_f32, "2.54" + assert_sprintf "%+0*.*f", [10, 2, 2.536_f32], "+000002.54" + assert_sprintf "%#.0f", 1234.56, "1235." + assert_sprintf "%#.1f", 1234.56, "1234.6" + + expect_raises(ArgumentError, "Expected dynamic value '*' to be an Int - \"not a number\" (String)") do + sprintf("%*f", ["not a number", 2.536_f32]) + end + + assert_sprintf "%12.2f %12.2f %6.2f %.2f", [2.0, 3.0, 4.0, 5.0], " 2.00 3.00 4.00 5.00" + + assert_sprintf "%f", 1e15, "1000000000000000.000000" + end + end + pending_win32 "works for other formats" do assert_sprintf "%g", 123, "123" - assert_sprintf "%12f", 123.45, " 123.450000" - assert_sprintf "%-12f", 123.45, "123.450000 " - assert_sprintf "% f", 123.45, " 123.450000" - assert_sprintf "%+f", 123, "+123.000000" - assert_sprintf "%012f", 123, "00123.000000" - assert_sprintf "%.f", 1234.56, "1235" - assert_sprintf "%.2f", 1234.5678, "1234.57" - assert_sprintf "%10.2f", 1234.5678, " 1234.57" - assert_sprintf "%*.2f", [10, 1234.5678], " 1234.57" - assert_sprintf "%0*.2f", [10, 1234.5678], "0001234.57" assert_sprintf "%e", 123.45, "1.234500e+02" assert_sprintf "%E", 123.45, "1.234500E+02" assert_sprintf "%G", 12345678.45, "1.23457E+07" @@ -399,17 +416,6 @@ describe "::sprintf" do assert_sprintf "%A", 12345678.45, "0X1.78C29CE666666P+23" assert_sprintf "%100.50g", 123.45, " 123.4500000000000028421709430404007434844970703125" assert_sprintf "%#.12g", 12345.0, "12345.0000000" - - assert_sprintf "%.2f", 2.536_f32, "2.54" - assert_sprintf "%0*.*f", [10, 2, 2.536_f32], "0000002.54" - - expect_raises(ArgumentError, "Expected dynamic value '*' to be an Int - \"not a number\" (String)") do - sprintf("%*f", ["not a number", 2.536_f32]) - end - - assert_sprintf "%12.2f %12.2f %6.2f %.2f", [2.0, 3.0, 4.0, 5.0], " 2.00 3.00 4.00 5.00" - - assert_sprintf "%f", 1e15, "1000000000000000.000000" end [Float32, Float64].each do |float| diff --git a/src/float/printer/ryu_printf.cr b/src/float/printer/ryu_printf.cr new file mode 100644 index 000000000000..d14ac70a831c --- /dev/null +++ b/src/float/printer/ryu_printf.cr @@ -0,0 +1,626 @@ +require "./ryu_printf_table" + +# Source port of Ryu Printf's reference implementation in C. +# +# The following is their license: +# +# Copyright 2018 Ulf Adams +# +# The contents of this file may be used under the terms of the Apache License, +# Version 2.0. +# +# (See accompanying file LICENSE-Apache or copy at +# http://www.apache.org/licenses/LICENSE-2.0) +# +# Alternatively, the contents of this file may be used under the terms of +# the Boost Software License, Version 1.0. +# (See accompanying file LICENSE-Boost or copy at +# https://www.boost.org/LICENSE_1_0.txt) +# +# Unless required by applicable law or agreed to in writing, this software +# is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. +module Float::Printer::RyuPrintf + # Current revision: https://github.com/ulfjack/ryu/tree/75d5a85440ed356ad7b23e9e6002d71f62a6255c + + # Returns the number of decimal digits in v, which must not contain more than 9 digits. + private def self.decimal_length9(v : UInt32) : UInt32 + # Function precondition: v is not a 10-digit number. + # (f2s: 9 digits are sufficient for round-tripping.) + # (d2fixed: We print 9-digit blocks.) + case v + when .>=(100000000) then 9_u32 + when .>=(10000000) then 8_u32 + when .>=(1000000) then 7_u32 + when .>=(100000) then 6_u32 + when .>=(10000) then 5_u32 + when .>=(1000) then 4_u32 + when .>=(100) then 3_u32 + when .>=(10) then 2_u32 + else + 1_u32 + end + end + + private def self.log10_pow2(e : Int32) : UInt32 + # The first value this approximation fails for is 2^1651 which is just greater than 10^297. + (e.to_u32! &* 78913) >> 18 + end + + M_INV_5 = 14757395258967641293u64 # 5 * m_inv_5 = 1 (mod 2^64) + N_DIV_5 = 3689348814741910323u64 # #{ n | n = 0 (mod 2^64) } = 2^64 / 5 + + private def self.pow5_factor(value : UInt64) : UInt32 + count = 0_u32 + while true + value &*= M_INV_5 + break if value > N_DIV_5 + count &+= 1 + end + count + end + + # Returns true if value is divisible by 5^p. + private def self.multiple_of_power_of_5?(value : UInt64, p : UInt32) + pow5_factor(value) >= p + end + + # Returns true if value is divisible by 2^p. + private def self.multiple_of_power_of_2?(value : UInt64, p : UInt32) + value & ~(UInt64::MAX << p) == 0 + end + + private def self.umul128(a : UInt64, b : UInt64) : {UInt64, UInt64} + a_lo = a.to_u32!.to_u64! + a_hi = (a >> 32).to_u32!.to_u64! + b_lo = b.to_u32! + b_hi = (b >> 32).to_u32! + + b00 = a_lo &* b_lo + b01 = a_lo &* b_hi + b10 = a_hi &* b_lo + b11 = a_hi &* b_hi + + b00_lo = b00.to_u32! + b00_hi = (b00 >> 32).to_u32! + + mid1 = b10 &+ b00_hi + mid1_lo = mid1.to_u32! + mid1_hi = (mid1 >> 32).to_u32! + + mid2 = b01 &+ mid1_lo + mid2_lo = mid2.to_u32! + mid2_hi = (mid2 >> 32).to_u32! + + {b11 &+ mid1_hi &+ mid2_hi, (mid2_lo.to_u64! << 32) | b00_lo} + end + + private def self.shiftright128(lo : UInt64, hi : UInt64, dist : UInt32) : UInt64 + # We don't need to handle the case dist >= 64 here + (hi << (64 &- dist)) | (lo >> dist) + end + + # Returns the low 64 bits of the high 128 bits of the 256-bit product of a and b. + private def self.umul256_hi128_lo64(a_hi : UInt64, a_lo : UInt64, b_hi : UInt64, b_lo : UInt64) + b00_hi, _ = umul128(a_lo, b_lo) + b01_hi, b01_lo = umul128(a_lo, b_hi) + b10_hi, b10_lo = umul128(a_hi, b_lo) + _, b11_lo = umul128(a_hi, b_hi) + + temp1_lo = b10_lo &+ b00_hi + temp1_hi = b10_hi &+ (temp1_lo < b10_lo ? 1 : 0) + temp2_lo = b01_lo &+ temp1_lo + temp2_hi = b01_hi &+ (temp2_lo < b01_lo ? 1 : 0) + b11_lo &+ temp1_hi &+ temp2_hi + end + + private def self.uint128_mod1e9(v_hi : UInt64, v_lo : UInt64) : UInt32 + # After multiplying, we're going to shift right by 29, then truncate to uint32_t. + # This means that we need only 29 + 32 = 61 bits, so we can truncate to uint64_t before shifting. + multiplied = umul256_hi128_lo64(v_hi, v_lo, 0x89705F4136B4A597u64, 0x31680A88F8953031u64) + + # For uint32_t truncation, see the mod1e9() comment in d2s_intrinsics.h. + shifted = (multiplied >> 29).to_u32! + + v_lo.to_u32! &- 1000000000_u32 &* shifted + end + + private def self.mulshift_mod1e9(m : UInt64, mul : {UInt64, UInt64, UInt64}, j : Int32) : UInt32 + high0, low0 = umul128(m, mul[0]) + high1, low1 = umul128(m, mul[1]) + high2, low2 = umul128(m, mul[2]) + + s0high = low1 &+ high0 # 64 + c1 = s0high < low1 ? 1 : 0 + s1low = low2 &+ high1 &+ c1 # 128 + c2 = s1low < low2 ? 1 : 0 # high1 + c1 can't overflow, so compare against low2 + s1high = high2 &+ c2 # 192 + dist = (j &- 128).to_u32! # dist: [0, 52] + shiftedhigh = s1high >> dist + shiftedlow = shiftright128(s1low, s1high, dist) + uint128_mod1e9(shiftedhigh, shiftedlow) + end + + private def self.index_for_exponent(e : UInt32) + (e &+ 15) // 16 + end + + private ADDITIONAL_BITS_2 = 120 + + private def self.pow10_bits_for_index(idx : UInt32) + idx &* 16 &+ ADDITIONAL_BITS_2 + end + + private def self.length_for_index(idx : UInt32) + # +1 for ceil, +16 for mantissa, +8 to round up when dividing by 9 + (log10_pow2(16 &* idx.to_i32!) &+ 25) // 9 + end + + # Convert `digits` to a sequence of decimal digits. Append the digits to the result. + # The caller has to guarantee that: + # 10^(olength-1) <= digits < 10^olength + # e.g., by passing `olength` as `decimalLength9(digits)`. + private def self.append_n_digits(olength : UInt32, digits : UInt32, result : UInt8*) + i = 0_u32 + while digits >= 10000 + c = digits &- 10000 &* (digits // 10000) + digits //= 10000 + c0 = (c % 100) << 1 + c1 = (c // 100) << 1 + (DIGIT_TABLE + c0).copy_to(result + olength - i - 2, 2) + (DIGIT_TABLE + c1).copy_to(result + olength - i - 4, 2) + i &+= 4 + end + if digits >= 100 + c = (digits % 100) << 1 + digits //= 100 + (DIGIT_TABLE + c).copy_to(result + olength - i - 2, 2) + i &+= 2 + end + if digits >= 10 + c = digits << 1 + (DIGIT_TABLE + c).copy_to(result + olength - i - 2, 2) + else + result.value = '0'.ord.to_u8! &+ digits + end + end + + # Convert `digits` to a sequence of decimal digits. Print the first digit, followed by a decimal + # dot '.' followed by the remaining digits. The caller has to guarantee that: + # 10^(olength-1) <= digits < 10^olength + # e.g., by passing `olength` as `decimalLength9(digits)`. + private def self.append_d_digits(olength : UInt32, digits : UInt32, result : UInt8*) + i = 0_u32 + while digits >= 10000 + c = digits &- 10000 &* (digits // 10000) + digits //= 10000 + c0 = (c % 100) << 1 + c1 = (c // 100) << 1 + (DIGIT_TABLE + c0).copy_to(result + olength + 1 - i - 2, 2) + (DIGIT_TABLE + c1).copy_to(result + olength + 1 - i - 4, 2) + i &+= 4 + end + if digits >= 100 + c = (digits % 100) << 1 + digits //= 100 + (DIGIT_TABLE + c).copy_to(result + olength + 1 - i - 2, 2) + i &+= 2 + end + if digits >= 10 + c = digits << 1 + result[2] = DIGIT_TABLE[c &+ 1] + result[1] = '.'.ord.to_u8! + result[0] = DIGIT_TABLE[c] + else + result[1] = '.'.ord.to_u8! + result[0] = '0'.ord.to_u8! &+ digits + end + end + + # Convert `digits` to decimal and write the last `count` decimal digits to result. + # If `digits` contains additional digits, then those are silently ignored. + private def self.append_c_digits(count : UInt32, digits : UInt32, result : UInt8*) + i = 0_u32 + + # Copy pairs of digits from DIGIT_TABLE. + while i < count &- 1 + c = (digits % 100) << 1 + digits //= 100 + (DIGIT_TABLE + c).copy_to(result + count - i - 2, 2) + i &+= 2 + end + + # Generate the last digit if count is odd. + if i < count + c = '0'.ord.to_u8! &+ (digits % 10) + result[count - i - 1] = c + end + end + + # Convert `digits` to decimal and write the last 9 decimal digits to result. + # If `digits` contains additional digits, then those are silently ignored. + private def self.append_nine_digits(digits : UInt32, result : UInt8*) + if digits == 0 + Slice.new(result, 9).fill('0'.ord.to_u8!) + return + end + + c = digits &- 10000 &* (digits // 10000) + digits //= 10000 + c0 = (c % 100) << 1 + c1 = (c // 100) << 1 + (DIGIT_TABLE + c0).copy_to(result + 7, 2) + (DIGIT_TABLE + c1).copy_to(result + 5, 2) + + c = digits &- 10000 &* (digits // 10000) + digits //= 10000 + c0 = (c % 100) << 1 + c1 = (c // 100) << 1 + (DIGIT_TABLE + c0).copy_to(result + 3, 2) + (DIGIT_TABLE + c1).copy_to(result + 1, 2) + + result.value = '0'.ord.to_u8! &+ digits + end + + MANTISSA_BITS = Float64::MANT_DIGITS - 1 + EXPONENT_BITS = 11 + + # NOTE: in Crystal *d* must be positive and finite + private def self.extract_float(d : Float64) + bits = d.unsafe_as(UInt64) + + ieee_mantissa = bits & ~(UInt64::MAX << MANTISSA_BITS) + ieee_exponent = (bits >> MANTISSA_BITS) & ~(UInt64::MAX << EXPONENT_BITS) + + if ieee_exponent == 0 + e2 = 1 &- 1023 &- MANTISSA_BITS + m2 = ieee_mantissa + else + e2 = ieee_exponent.to_i32! &- 1023 &- MANTISSA_BITS + m2 = (1_u64 << MANTISSA_BITS) | ieee_mantissa + end + + {e2, m2} + end + + def self.d2fixed_buffered_n(d : Float64, precision : UInt32, result : UInt8*) + e2, m2 = extract_float(d) + index = 0 + nonzero = false + + if e2 >= -MANTISSA_BITS + idx = e2 < 0 ? 0_u32 : index_for_exponent(e2.to_u32!) + p10bits = pow10_bits_for_index(idx) + len = length_for_index(idx).to_i32! + + (len - 1).downto(0) do |i| + j = p10bits &- e2 + # Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is + # a slightly faster code path in mulshift_mod1e9. Instead, we can just increase the multipliers. + digits = mulshift_mod1e9(m2 << 8, POW10_SPLIT[POW10_OFFSET[idx] &+ i], (j &+ 8).to_i32!) + if nonzero + append_nine_digits(digits, result + index) + index &+= 9 + elsif digits != 0 + olength = decimal_length9(digits) + append_n_digits(olength, digits, result + index) + index &+= olength + nonzero = true + end + end + end + + unless nonzero + result[index] = '0'.ord.to_u8! + index &+= 1 + end + + if precision > 0 + result[index] = '.'.ord.to_u8! + index &+= 1 + end + + if e2 >= 0 + Slice.new(result + index, precision).fill('0'.ord.to_u8!) + index &+= precision + return index + end + + idx = (0 &- e2) // 16 + blocks = precision // 9 &+ 1 + # 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd. + round_up = 0 + i = 0_u32 + + if blocks <= MIN_BLOCK_2[idx] + i = blocks + Slice.new(result + index, precision).fill('0'.ord.to_u8!) + index &+= precision + elsif i < MIN_BLOCK_2[idx] + i = MIN_BLOCK_2[idx].to_u32! + Slice.new(result + index, i &* 9).fill('0'.ord.to_u8!) + index &+= i &* 9 + end + + while i < blocks + j = ADDITIONAL_BITS_2 &- e2 &- 16 &* idx + p = POW10_OFFSET_2[idx] &+ i &- MIN_BLOCK_2[idx] + + if p >= POW10_OFFSET_2[idx + 1] + # If the remaining digits are all 0, then we might as well use memset. + # No rounding required in this case. + fill = precision &- 9 &* i + Slice.new(result + index, fill).fill('0'.ord.to_u8!) + index &+= fill + break + end + + # Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is + # a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers. + digits = mulshift_mod1e9(m2 << 8, POW10_SPLIT_2[p], j &+ 8) + if i < blocks &- 1 + append_nine_digits(digits, result + index) + index &+= 9 + else + maximum = precision &- 9 &* i + last_digit = 0_u32 + (9 &- maximum).times do + last_digit = digits % 10 + digits //= 10 + end + + if last_digit != 5 + round_up = last_digit > 5 ? 1 : 0 + else + # Is m * 10^(additionalDigits + 1) / 2^(-e2) integer? + required_twos = 0 &- e2 &- precision.to_i32! &- 1 + trailing_zeros = required_twos <= 0 || (required_twos < 60 && multiple_of_power_of_2?(m2, required_twos.to_u32!)) + round_up = trailing_zeros ? 2 : 1 + end + + if maximum > 0 + append_c_digits(maximum, digits, result + index) + index &+= maximum + end + break + end + + i &+= 1 + end + + if round_up != 0 + round_index = index + dot_index = 0 + while true + round_index &-= 1 + c = result[round_index] + if round_index == -1 || c === '-' + result[round_index &+ 1] = '1'.ord.to_u8! + if dot_index > 0 + result[dot_index] = '0'.ord.to_u8! + result[dot_index &+ 1] = '.'.ord.to_u8! + end + result[index] = '0'.ord.to_u8! + index &+= 1 + break + end + + if c === '.' + dot_index = round_index + next + elsif c === '9' + result[round_index] = '0'.ord.to_u8! + round_up = 1 + next + else + result[round_index] = c &+ 1 unless round_up == 2 && c % 2 == 0 + break + end + end + end + + index + end + + def self.d2exp_buffered_n(d : Float64, precision : UInt32, result : UInt8*) + if d == 0 + result[0] = '0'.ord.to_u8! + index = 1 + if precision > 0 + result[index] = '.'.ord.to_u8! + index &+= 1 + Slice.new(result + index, precision).fill('0'.ord.to_u8!) + index &+= precision + end + result[index] = 'e'.ord.to_u8! + result[index + 1] = '+'.ord.to_u8! + result[index + 2] = '0'.ord.to_u8! + return index &+ 3 + end + + e2, m2 = extract_float(d) + print_decimal_digit = precision > 0 + precision &+= 1 + index = 0 + digits = 0_u32 + printed_digits = 0_u32 + available_digits = 0_u32 + exp = 0 + + if e2 >= -MANTISSA_BITS + idx = e2 < 0 ? 0_u32 : index_for_exponent(e2.to_u32!) + p10bits = pow10_bits_for_index(idx) + len = length_for_index(idx).to_i32! + + (len - 1).downto(0) do |i| + j = p10bits &- e2 + # Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is + # a slightly faster code path in mulshift_mod1e9. Instead, we can just increase the multipliers. + digits = mulshift_mod1e9(m2 << 8, POW10_SPLIT[POW10_OFFSET[idx] &+ i], (j &+ 8).to_i32!) + if printed_digits != 0 + if printed_digits &+ 9 > precision + available_digits = 9_u32 + break + end + append_nine_digits(digits, result + index) + index &+= 9 + printed_digits &+= 9 + elsif digits != 0 + available_digits = decimal_length9(digits) + exp = i &* 9 &+ available_digits.to_i32! &- 1 + break if available_digits > precision + if print_decimal_digit + append_d_digits(available_digits, digits, result + index) + index &+= available_digits &+ 1 # +1 for decimal point + else + result[index] = '0'.ord.to_u8! &+ digits + index &+= 1 + end + printed_digits = available_digits + available_digits = 0_u32 + end + end + end + + if e2 < 0 && available_digits == 0 + idx = (0 &- e2) // 16 + (MIN_BLOCK_2[idx]..200).each do |i| + j = ADDITIONAL_BITS_2 &- e2 &- 16 &* idx + p = POW10_OFFSET_2[idx] &+ i &- MIN_BLOCK_2[idx] + # Temporary: j is usually around 128, and by shifting a bit, we push it to 128 or above, which is + # a slightly faster code path in mulShift_mod1e9. Instead, we can just increase the multipliers. + digits = p >= POW10_OFFSET_2[idx &+ 1] ? 0_u32 : mulshift_mod1e9(m2 << 8, POW10_SPLIT_2[p], j &+ 8) + + if printed_digits != 0 + if printed_digits &+ 9 > precision + available_digits = 9_u32 + break + end + append_nine_digits(digits, result + index) + index &+= 9 + printed_digits &+= 9 + elsif digits != 0 + available_digits = decimal_length9(digits) + exp = (-1 &- i) &* 9 &+ available_digits.to_i32! &- 1 + break if available_digits > precision + if print_decimal_digit + append_d_digits(available_digits, digits, result + index) + index &+= available_digits &+ 1 # +1 for decimal point + else + result[index] = '0'.ord.to_u8! &+ digits + index &+= 1 + end + printed_digits = available_digits + available_digits = 0_u32 + end + end + end + + maximum = precision &- printed_digits + digits = 0_u32 if available_digits == 0 + last_digit = 0_u32 + if available_digits > maximum + (available_digits &- maximum).times do + last_digit = digits % 10 + digits //= 10 + end + end + + # 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd. + round_up = 0 + if last_digit != 5 + round_up = last_digit > 5 ? 1 : 0 + else + # Is m * 2^e2 * 10^(precision + 1 - exp) integer? + # precision was already increased by 1, so we don't need to write + 1 here. + rexp = precision.to_i32! &- exp + required_twos = 0 &- e2 &- rexp + trailing_zeros = required_twos <= 0 || (required_twos < 60 && multiple_of_power_of_2?(m2, required_twos.to_u32!)) + if rexp < 0 + required_fives = 0 &- rexp + trailing_zeros = trailing_zeros && multiple_of_power_of_5?(m2, required_fives.to_u32!) + end + round_up = trailing_zeros ? 2 : 1 + end + + if printed_digits != 0 + if digits == 0 + Slice.new(result + index, maximum).fill('0'.ord.to_u8!) + else + append_c_digits(maximum, digits, result + index) + end + index &+= maximum + else + if print_decimal_digit + append_d_digits(maximum, digits, result + index) + index &+= maximum &+ 1 # +1 for decimal point + else + result[index] = '0'.ord.to_u8! &+ digits + index &+= 1 + end + end + + if round_up != 0 + round_index = index + while true + round_index &-= 1 + c = result[round_index] + if round_index == -1 || c === '-' + result[round_index &+ 1] = '1'.ord.to_u8! + exp &+= 1 + break + end + + if c === '.' + next + elsif c === '9' + result[round_index] = '0'.ord.to_u8! + round_up = 1 + next + else + result[round_index] = c &+ 1 unless round_up == 2 && c % 2 == 0 + break + end + end + end + + result[index] = 'e'.ord.to_u8! + index &+= 1 + if exp < 0 + result[index] = '-'.ord.to_u8! + exp = 0 &- exp + else + result[index] = '+'.ord.to_u8! + end + index &+= 1 + + if exp >= 100 + c = exp % 10 + (DIGIT_TABLE + ((exp // 10) << 1)).copy_to(result + index, 2) + result[index &+ 2] = '0'.ord.to_u8! &+ c + index &+= 3 + elsif exp >= 10 + (DIGIT_TABLE + (exp << 1)).copy_to(result + index, 2) + index &+= 2 + else + result[index] = '0'.ord.to_u8! &+ exp + index &+= 1 + end + + index + end + + def self.d2fixed(d : Float64, precision : Int) + String.new(2000) do |buffer| + len = d2fixed_buffered_n(d, precision.to_u32, buffer) + {len, len} + end + end + + def self.d2exp(d : Float64, precision : Int) + String.new(2000) do |buffer| + len = d2exp_buffered_n(d, precision.to_u32, buffer) + {len, len} + end + end +end diff --git a/src/float/printer/ryu_printf_table.cr b/src/float/printer/ryu_printf_table.cr new file mode 100644 index 000000000000..c24d75a048f2 --- /dev/null +++ b/src/float/printer/ryu_printf_table.cr @@ -0,0 +1,4412 @@ +module Float::Printer::RyuPrintf + {% begin %} + # A table of all two-digit numbers. This is used to speed up decimal digit + # generation by copying pairs of digits into the final output. + DIGIT_TABLE = "{% for i in 0..9 %}0{{ i }}{% end %}{% for i in 10..99 %}{{ i }}{% end %}".to_unsafe + {% end %} + + # TODO: this is needed to avoid generating lots of allocas + # in LLVM, which makes LLVM really slow. The compiler should + # try to avoid/reuse temporary allocas. + # Explanation: https://github.com/crystal-lang/crystal/issues/4516#issuecomment-306226171 + private def self.put(array : Array, values) : Nil + array << values + end + + private POW10_OFFSET = [ + 0, 2, 5, 8, 12, 16, 21, 26, 32, 39, + 46, 54, 62, 71, 80, 90, 100, 111, 122, 134, + 146, 159, 173, 187, 202, 217, 233, 249, 266, 283, + 301, 319, 338, 357, 377, 397, 418, 440, 462, 485, + 508, 532, 556, 581, 606, 632, 658, 685, 712, 740, + 769, 798, 828, 858, 889, 920, 952, 984, 1017, 1050, + 1084, 1118, 1153, 1188, + ] of UInt16 + + private POW10_SPLIT = begin + data = Array({UInt64, UInt64, UInt64}).new(1224) + put(data, {1u64, 72057594037927936u64, 0u64}) + put(data, {699646928636035157u64, 72057594u64, 0u64}) + put(data, {1u64, 0u64, 256u64}) + put(data, {11902091922964236229u64, 4722366482869u64, 0u64}) + put(data, {6760415703743915872u64, 4722u64, 0u64}) + put(data, {1u64, 0u64, 16777216u64}) + put(data, {13369850649504950658u64, 309485009821345068u64, 0u64}) + put(data, {15151142278969419334u64, 309485009u64, 0u64}) + put(data, {1u64, 0u64, 75511627776u64}) + put(data, {4635408826454083567u64, 9437866644873197963u64, 1099u64}) + put(data, {12367138975830625353u64, 20282409603651u64, 0u64}) + put(data, {7555853734021184432u64, 20282u64, 0u64}) + put(data, {1u64, 0u64, 250037927936u64}) + put(data, {5171444645924616995u64, 699646928636035156u64, 72057594u64}) + put(data, {16672297533003297786u64, 1329227995784915872u64, 0u64}) + put(data, {14479142226848862515u64, 1329227995u64, 0u64}) + put(data, {1u64, 0u64, 181645213696u64}) + put(data, {12214193123817091081u64, 11902091922964236228u64, 114366482869u64}) + put(data, {16592893013671929435u64, 6760415703743915871u64, 4722u64}) + put(data, {4549827147718617003u64, 87112285931760u64, 0u64}) + put(data, {5274510003815168971u64, 87112u64, 0u64}) + put(data, {1u64, 0u64, 44724781056u64}) + put(data, {9794971998307800535u64, 13369850649504950657u64, 209821345068u64}) + put(data, {14720142899209240169u64, 15151142278969419333u64, 309485009u64}) + put(data, {4300745446091561535u64, 5708990770823839524u64, 0u64}) + put(data, {15197156861335443364u64, 5708990770u64, 0u64}) + put(data, {1u64, 0u64, 139251286016u64}) + put(data, {13484604155038683037u64, 4635408826454083566u64, 67670423947u64}) + put(data, {8356963862052375699u64, 12367138975830625352u64, 58409603651u64}) + put(data, {5850852848337610021u64, 7555853734021184431u64, 20282u64}) + put(data, {2712780827214982050u64, 374144419156711u64, 0u64}) + put(data, {7732076577307618052u64, 374144u64, 0u64}) + put(data, {1u64, 0u64, 84280344576u64}) + put(data, {17296309485351745867u64, 5171444645924616994u64, 160903807060u64}) + put(data, {16598859101615853088u64, 16672297533003297785u64, 219784915872u64}) + put(data, {7469952526870444257u64, 14479142226848862514u64, 1329227995u64}) + put(data, {13531654022114669524u64, 6073184580144670117u64, 1u64}) + put(data, {15757609704383306943u64, 24519928653u64, 0u64}) + put(data, {9590990814237149590u64, 24u64, 0u64}) + put(data, {1u64, 0u64, 196662132736u64}) + put(data, {15408590707489433890u64, 12214193123817091080u64, 95899502532u64}) + put(data, {18332056844289122710u64, 16592893013671929434u64, 240246646623u64}) + put(data, {11114572877353986193u64, 4549827147718617002u64, 72285931760u64}) + put(data, {1703393793997526525u64, 5274510003815168970u64, 87112u64}) + put(data, {5082852056285196265u64, 1606938044258990u64, 0u64}) + put(data, {816434266573722365u64, 1606938u64, 0u64}) + put(data, {1u64, 0u64, 129530986496u64}) + put(data, {5736523019264798742u64, 9794971998307800534u64, 69797980545u64}) + put(data, {10129314776268243339u64, 14720142899209240168u64, 36233143877u64}) + put(data, {16511595775483995364u64, 4300745446091561534u64, 50823839524u64}) + put(data, {12367293405401453325u64, 15197156861335443363u64, 5708990770u64}) + put(data, {16934621733248854291u64, 13078571300009428617u64, 5u64}) + put(data, {10278280417769171336u64, 105312291668u64, 0u64}) + put(data, {5760764486226151240u64, 105u64, 0u64}) + put(data, {1u64, 0u64, 238731001856u64}) + put(data, {4128368337188369761u64, 13484604155038683036u64, 72453031918u64}) + put(data, {10240941003671005056u64, 8356963862052375698u64, 175317175368u64}) + put(data, {17933378316822368251u64, 5850852848337610020u64, 231147060143u64}) + put(data, {8346249813075698616u64, 2712780827214982049u64, 128419156711u64}) + put(data, {15906203609160902695u64, 7732076577307618051u64, 374144u64}) + put(data, {14525607416135386328u64, 6901746346790563u64, 0u64}) + put(data, {6397156777364256320u64, 6901746u64, 0u64}) + put(data, {1u64, 0u64, 34937634816u64}) + put(data, {16798760952716600048u64, 17296309485351745866u64, 249899825954u64}) + put(data, {2419982808370854967u64, 16598859101615853087u64, 50404946937u64}) + put(data, {2922947087773078956u64, 7469952526870444256u64, 165733552434u64}) + put(data, {15419220167069510190u64, 13531654022114669523u64, 77854221733u64}) + put(data, {3452124642157173416u64, 15757609704383306942u64, 24519928653u64}) + put(data, {5979700067267186899u64, 9590990814237149589u64, 24u64}) + put(data, {4913998146922579597u64, 452312848583u64, 0u64}) + put(data, {5771037749337678924u64, 452u64, 0u64}) + put(data, {1u64, 0u64, 8835301376u64}) + put(data, {3464734175350698519u64, 15408590707489433889u64, 90993782792u64}) + put(data, {9334527711335850125u64, 18332056844289122709u64, 170602522202u64}) + put(data, {7269882896518450106u64, 11114572877353986192u64, 202092341162u64}) + put(data, {1372511258182263196u64, 1703393793997526524u64, 174275541962u64}) + put(data, {7571228438575951046u64, 5082852056285196264u64, 26044258990u64}) + put(data, {2992506536646070406u64, 816434266573722364u64, 1606938u64}) + put(data, {524517896824344606u64, 29642774844752946u64, 0u64}) + put(data, {15582941400898702773u64, 29642774u64, 0u64}) + put(data, {1u64, 0u64, 214310977536u64}) + put(data, {3846112492507251066u64, 5736523019264798741u64, 104549111254u64}) + put(data, {16681117750123089487u64, 10129314776268243338u64, 62895095400u64}) + put(data, {14986314536556547267u64, 16511595775483995363u64, 163670432318u64}) + put(data, {2573712825027107389u64, 12367293405401453324u64, 137918027683u64}) + put(data, {7504855874008324928u64, 16934621733248854290u64, 84557186697u64}) + put(data, {9572138030626879787u64, 10278280417769171335u64, 105312291668u64}) + put(data, {8520676959353394843u64, 5760764486226151239u64, 105u64}) + put(data, {13448984662897903496u64, 1942668892225u64, 0u64}) + put(data, {12338883700918130648u64, 1942u64, 0u64}) + put(data, {1u64, 0u64, 156223799296u64}) + put(data, {2517285787892561600u64, 4128368337188369760u64, 146555162524u64}) + put(data, {4338831817635138103u64, 10240941003671005055u64, 36972170386u64}) + put(data, {1561495325934523196u64, 17933378316822368250u64, 161452451108u64}) + put(data, {12262635050079398786u64, 8346249813075698615u64, 3862277025u64}) + put(data, {11144065765517284188u64, 15906203609160902694u64, 163787434755u64}) + put(data, {1212260522471875711u64, 14525607416135386327u64, 242346790563u64}) + put(data, {9695352922247418869u64, 6397156777364256319u64, 6901746u64}) + put(data, {7227025834627242948u64, 127314748520905380u64, 0u64}) + put(data, {9609008238705447829u64, 127314748u64, 0u64}) + put(data, {1u64, 0u64, 74910662656u64}) + put(data, {3609144142396852269u64, 16798760952716600047u64, 31131187530u64}) + put(data, {11568848377382068865u64, 2419982808370854966u64, 224158453279u64}) + put(data, {10068303578029323957u64, 2922947087773078955u64, 211835877600u64}) + put(data, {11645070846862630231u64, 15419220167069510189u64, 190187140051u64}) + put(data, {12449386705878485055u64, 3452124642157173415u64, 149324160190u64}) + put(data, {15025619323517318418u64, 5979700067267186898u64, 199266388373u64}) + put(data, {14996237555047131272u64, 4913998146922579596u64, 196312848583u64}) + put(data, {10211005638256058413u64, 5771037749337678923u64, 452u64}) + put(data, {1014743503555840530u64, 8343699359066u64, 0u64}) + put(data, {12900897707145290678u64, 8343u64, 0u64}) + put(data, {1u64, 0u64, 33187823616u64}) + put(data, {4718003016239473662u64, 3464734175350698518u64, 149506025761u64}) + put(data, {14865830648693666725u64, 9334527711335850124u64, 144394101141u64}) + put(data, {14754517212823091778u64, 7269882896518450105u64, 252074403984u64}) + put(data, {11113946551474911901u64, 1372511258182263195u64, 232410437116u64}) + put(data, {1963520352638130630u64, 7571228438575951045u64, 252162224104u64}) + put(data, {13342587341404964200u64, 2992506536646070405u64, 50028434172u64}) + put(data, {6240392545013573291u64, 524517896824344605u64, 22844752946u64}) + put(data, {14377490861349714758u64, 15582941400898702772u64, 29642774u64}) + put(data, {1717863312631397839u64, 546812681195752981u64, 0u64}) + put(data, {3611005143890591770u64, 546812681u64, 0u64}) + put(data, {1u64, 0u64, 21208498176u64}) + put(data, {13168252824351245504u64, 3846112492507251065u64, 138904285205u64}) + put(data, {735883891883379688u64, 16681117750123089486u64, 227812409738u64}) + put(data, {10609203866866106404u64, 14986314536556547266u64, 12139521251u64}) + put(data, {12358191111890306470u64, 2573712825027107388u64, 18406839052u64}) + put(data, {15229916368406413528u64, 7504855874008324927u64, 135518906642u64}) + put(data, {7241424335568075942u64, 9572138030626879786u64, 71461906823u64}) + put(data, {6049715868779871913u64, 8520676959353394842u64, 65729070919u64}) + put(data, {2000548404719336762u64, 13448984662897903495u64, 150668892225u64}) + put(data, {1410974761895205301u64, 12338883700918130647u64, 1942u64}) + put(data, {16000132467694084868u64, 35835915874844u64, 0u64}) + put(data, {16894908866816792556u64, 35835u64, 0u64}) + put(data, {1u64, 0u64, 96136462336u64}) + put(data, {589096329272056762u64, 2517285787892561599u64, 127235208544u64}) + put(data, {7097729792403256904u64, 4338831817635138102u64, 250084648831u64}) + put(data, {8553736750439287020u64, 1561495325934523195u64, 183664758778u64}) + put(data, {2114152625261065696u64, 12262635050079398785u64, 38604121015u64}) + put(data, {9817523680007641224u64, 11144065765517284187u64, 215065716774u64}) + put(data, {13047215537500048015u64, 1212260522471875710u64, 63525586135u64}) + put(data, {16755544192002345880u64, 9695352922247418868u64, 164391777855u64}) + put(data, {6930119832670648356u64, 7227025834627242947u64, 60520905380u64}) + put(data, {14560698131901886167u64, 9609008238705447828u64, 127314748u64}) + put(data, {16408020927503338035u64, 2348542582773833227u64, 0u64}) + put(data, {14274703510609809116u64, 2348542582u64, 0u64}) + put(data, {1u64, 0u64, 239195652096u64}) + put(data, {16428432973129962470u64, 3609144142396852268u64, 54627148527u64}) + put(data, {3721112279790863774u64, 11568848377382068864u64, 171545803830u64}) + put(data, {18032764903259620753u64, 10068303578029323956u64, 45631280555u64}) + put(data, {18058455550468776079u64, 11645070846862630230u64, 167674882605u64}) + put(data, {15692090139033993190u64, 12449386705878485054u64, 210814540455u64}) + put(data, {389416944300619393u64, 15025619323517318417u64, 140812947666u64}) + put(data, {12009691357260487293u64, 14996237555047131271u64, 75553539724u64}) + put(data, {13494259174449809900u64, 10211005638256058412u64, 90055009355u64}) + put(data, {18288583400616279877u64, 1014743503555840529u64, 151699359066u64}) + put(data, {7216107869057472u64, 12900897707145290677u64, 8343u64}) + put(data, {17237061291959073878u64, 153914086704665u64, 0u64}) + put(data, {1599418782488783273u64, 153914u64, 0u64}) + put(data, {1u64, 0u64, 22255763456u64}) + put(data, {9565464987240335777u64, 4718003016239473661u64, 140805878294u64}) + put(data, {857713933775880687u64, 14865830648693666724u64, 185799843980u64}) + put(data, {4621617820081363356u64, 14754517212823091777u64, 155602488249u64}) + put(data, {9630162611715632528u64, 11113946551474911900u64, 197106442651u64}) + put(data, {9283986497984645815u64, 1963520352638130629u64, 133723303109u64}) + put(data, {8981807745082630996u64, 13342587341404964199u64, 29338292357u64}) + put(data, {18350140531565934622u64, 6240392545013573290u64, 180779405341u64}) + put(data, {4411619033127524143u64, 14377490861349714757u64, 21093125556u64}) + put(data, {1852297584111266889u64, 1717863312631397838u64, 9195752981u64}) + put(data, {11746243463811666096u64, 3611005143890591769u64, 546812681u64}) + put(data, {6335244004343789147u64, 10086913586276986678u64, 0u64}) + put(data, {5109502367228239844u64, 10086913586u64, 0u64}) + put(data, {1603272682579847821u64, 10u64, 0u64}) + put(data, {1u64, 0u64, 121713852416u64}) + put(data, {6609546910952910052u64, 13168252824351245503u64, 78039892345u64}) + put(data, {3911171343112928288u64, 735883891883379687u64, 194575126094u64}) + put(data, {5254510615100863555u64, 10609203866866106403u64, 60669938882u64}) + put(data, {3881927570803887650u64, 12358191111890306469u64, 63825615420u64}) + put(data, {6379348759607163190u64, 15229916368406413527u64, 42392558399u64}) + put(data, {14595733737222406466u64, 7241424335568075941u64, 154327955754u64}) + put(data, {14670223432002373542u64, 6049715868779871912u64, 135108449946u64}) + put(data, {4045087795619708513u64, 2000548404719336761u64, 215076489095u64}) + put(data, {12598467307137142718u64, 1410974761895205300u64, 28867368919u64}) + put(data, {734704388050777108u64, 16000132467694084867u64, 251915874844u64}) + put(data, {5682201693687285822u64, 16894908866816792555u64, 35835u64}) + put(data, {11048712694145438788u64, 661055968790248u64, 0u64}) + put(data, {17871025777010319485u64, 661055u64, 0u64}) + put(data, {1u64, 0u64, 191031934976u64}) + put(data, {15268761435931663695u64, 589096329272056761u64, 54384768703u64}) + put(data, {5016238054648555438u64, 7097729792403256903u64, 59463698998u64}) + put(data, {14236047313993899750u64, 8553736750439287019u64, 129114608443u64}) + put(data, {6957759675154690848u64, 2114152625261065695u64, 91532209025u64}) + put(data, {18439367135478514473u64, 9817523680007641223u64, 126707290971u64}) + put(data, {8539004472540641041u64, 13047215537500048014u64, 244908319870u64}) + put(data, {1908462039431738399u64, 16755544192002345879u64, 195375682548u64}) + put(data, {714690453250792146u64, 6930119832670648355u64, 148789337027u64}) + put(data, {13782189447673929633u64, 14560698131901886166u64, 11889480596u64}) + put(data, {3584742913798803164u64, 16408020927503338034u64, 118773833227u64}) + put(data, {4347581515245125291u64, 14274703510609809115u64, 2348542582u64}) + put(data, {16836742268156371392u64, 6429475823218628948u64, 2u64}) + put(data, {11764082328865615308u64, 43322963970u64, 0u64}) + put(data, {5957633711383291746u64, 43u64, 0u64}) + put(data, {1u64, 0u64, 44890587136u64}) + put(data, {9917186842884466953u64, 16428432973129962469u64, 128201721900u64}) + put(data, {4751011869809829335u64, 3721112279790863773u64, 180977558144u64}) + put(data, {11068497969931435029u64, 18032764903259620752u64, 86978950836u64}) + put(data, {17118056985122509954u64, 18058455550468776078u64, 62850669910u64}) + put(data, {14607066080907684459u64, 15692090139033993189u64, 17021110334u64}) + put(data, {11768892370493391107u64, 389416944300619392u64, 135651046673u64}) + put(data, {4043396447647747170u64, 12009691357260487292u64, 44731525255u64}) + put(data, {1670341095362518057u64, 13494259174449809899u64, 17991426092u64}) + put(data, {3190817644167043165u64, 18288583400616279876u64, 181000391185u64}) + put(data, {10425820027224322486u64, 7216107869057471u64, 25934422965u64}) + put(data, {13139964660506311565u64, 17237061291959073877u64, 58086704665u64}) + put(data, {2297772885416059937u64, 1599418782488783272u64, 153914u64}) + put(data, {7677687919964523763u64, 2839213766779714u64, 0u64}) + put(data, {14144589152747892828u64, 2839213u64, 0u64}) + put(data, {1u64, 0u64, 253518544896u64}) + put(data, {17069730341503660290u64, 9565464987240335776u64, 164046496765u64}) + put(data, {18167423787163077107u64, 857713933775880686u64, 65250538404u64}) + put(data, {3765746945827805904u64, 4621617820081363355u64, 156522052161u64}) + put(data, {10241734342430761691u64, 9630162611715632527u64, 197503285916u64}) + put(data, {13345717282537140784u64, 9283986497984645814u64, 103486904773u64}) + put(data, {9313926784816939953u64, 8981807745082630995u64, 170994763111u64}) + put(data, {550974205049535019u64, 18350140531565934621u64, 69239154346u64}) + put(data, {4494692285504086222u64, 4411619033127524142u64, 206100413253u64}) + put(data, {1134308559863725587u64, 1852297584111266888u64, 25636765134u64}) + put(data, {17587558045116130233u64, 11746243463811666095u64, 54343434265u64}) + put(data, {9817142032346161594u64, 6335244004343789146u64, 50276986678u64}) + put(data, 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1853093467828272926u64, 105799888670u64}) + put(data, {4553830511509832021u64, 14755341584803008676u64, 103254872681u64}) + put(data, {8869400642218174412u64, 4701571132542556620u64, 87332245607u64}) + put(data, {16570849151159054040u64, 6128849686644853850u64, 68651977815u64}) + put(data, {16127119334101797673u64, 12026867901170202093u64, 86970890052u64}) + put(data, {9686867250420930550u64, 17909760324981426302u64, 230157084246u64}) + put(data, {10678226869774428035u64, 2897692901883393663u64, 163499238u64}) + put(data, {7767227962910162068u64, 3016028602530220424u64, 0u64}) + put(data, {9780840471948993674u64, 3016028602u64, 0u64}) + put(data, {1u64, 0u64, 213668069376u64}) + put(data, {6288709332106746357u64, 12323704802554838153u64, 16386837205u64}) + put(data, {9066785620141948673u64, 7135886931147821731u64, 141831652624u64}) + put(data, {8442375916704414909u64, 15341283120292884946u64, 14167660429u64}) + put(data, {11604629218100425803u64, 3092789040392634165u64, 188477686542u64}) + put(data, {3877248044010875762u64, 8811761390822097864u64, 134914571196u64}) + put(data, {16435137704395217283u64, 16870860798610218168u64, 103946077062u64}) + put(data, {14994442577577813271u64, 17452041453591904832u64, 111559165543u64}) + put(data, {4410105917142436089u64, 10314783684009874907u64, 245267398767u64}) + put(data, {4632574728444936970u64, 4932636630789274902u64, 202983581941u64}) + put(data, {9117147535650050359u64, 18143884346082124479u64, 134153046474u64}) + put(data, {588939301256904809u64, 2823209155405527321u64, 69877954182u64}) + put(data, {324393982565305683u64, 16195396106620226250u64, 173062371141u64}) + put(data, {9380909186923521175u64, 1150544491807648943u64, 73421074605u64}) + put(data, {4463385697777230217u64, 7767455475523884823u64, 94824230985u64}) + put(data, {16378985502426333808u64, 15204378045683991807u64, 211934567774u64}) + put(data, {18210894922387834354u64, 17239732561718805621u64, 38698574803u64}) + put(data, {1555748035329493205u64, 12886430624522800061u64, 83984577574u64}) + put(data, {4277055533891898507u64, 18162250541178258135u64, 184923140435u64}) + put(data, {11574429772510874408u64, 17028935366700158083u64, 219871452856u64}) + put(data, {17391099253493808815u64, 16075467823964198636u64, 215531468251u64}) + put(data, {5791212393959129882u64, 9803858825574498303u64, 27946729175u64}) + put(data, {11254268231455680880u64, 17464070808143041816u64, 124958581275u64}) + put(data, {16355477587312235322u64, 17682703471239266775u64, 227983788156u64}) + put(data, {2411485149249320633u64, 18147688354161351335u64, 145361224931u64}) + put(data, {12763114642070638360u64, 6663423873348080050u64, 183510511249u64}) + put(data, {1147543073987366419u64, 9417270363716235132u64, 197503883703u64}) + put(data, {8410777835225272692u64, 9295013721571344178u64, 63336074437u64}) + put(data, {8134725822306818018u64, 6199479138350037782u64, 14048117055u64}) + put(data, {8899607004752328377u64, 887603005365085687u64, 232018105614u64}) + put(data, {690976506652396830u64, 333989628642975695u64, 140250490600u64}) + put(data, {12281570945595192074u64, 4620735991403939438u64, 54673209484u64}) + put(data, {12592957291365552899u64, 12418523063962801200u64, 219086071862u64}) + put(data, {13595807339013970272u64, 1587745622680169418u64, 10715u64}) + put(data, {9698096389749839992u64, 197658450495420u64, 0u64}) + put(data, {8310173728816391804u64, 197658u64, 0u64}) + data + end + + private POW10_OFFSET_2 = [ + 0, 2, 6, 12, 20, 29, 40, 52, 66, 80, + 95, 112, 130, 150, 170, 192, 215, 240, 265, 292, + 320, 350, 381, 413, 446, 480, 516, 552, 590, 629, + 670, 712, 755, 799, 845, 892, 940, 989, 1040, 1092, + 1145, 1199, 1254, 1311, 1369, 1428, 1488, 1550, 1613, 1678, + 1743, 1810, 1878, 1947, 2017, 2088, 2161, 2235, 2311, 2387, + 2465, 2544, 2625, 2706, 2789, 2873, 2959, 3046, 3133, + ] of UInt16 + + private MIN_BLOCK_2 = [ + 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, + 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, + 8, 9, 9, 10, 11, 11, 12, 12, 13, 13, + 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, + 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, + 24, 25, 26, 26, 27, 27, 28, 28, 29, 29, + 30, 30, 31, 31, 32, 32, 33, 34, 0, + ] of UInt8 + + private POW10_SPLIT_2 = begin + data = Array({UInt64, UInt64, UInt64}).new(3133) + put(data, {0u64, 0u64, 3906250u64}) + put(data, {0u64, 0u64, 202000000000u64}) + put(data, {0u64, 11153727427136454656u64, 59u64}) + put(data, {0u64, 7205759403792793600u64, 59604644775u64}) + put(data, {0u64, 0u64, 167390625000u64}) + put(data, {0u64, 0u64, 232000000000u64}) + put(data, {0u64, 16777216000000000u64, 0u64}) + put(data, {0u64, 12945425605062557696u64, 909494u64}) + put(data, {0u64, 4388757836872548352u64, 182701772928u64}) + put(data, {0u64, 1152921504606846976u64, 128237915039u64}) + put(data, {0u64, 0u64, 159062500000u64}) + put(data, {0u64, 0u64, 160000000000u64}) + put(data, {0u64, 256000000000u64, 0u64}) + put(data, {0u64, 16192327041775828992u64, 13u64}) + put(data, {0u64, 15024075324038053888u64, 13877787807u64}) + put(data, {0u64, 5449091666327633920u64, 159814456755u64}) + put(data, {0u64, 2494994193563254784u64, 179295395851u64}) + put(data, {0u64, 4611686018427387904u64, 11135253906u64}) + put(data, {0u64, 0u64, 146250000000u64}) + put(data, {0u64, 0u64, 128000000000u64}) + put(data, {0u64, 3906250u64, 0u64}) + put(data, {0u64, 3906250000000000u64, 0u64}) + put(data, {0u64, 4368439412768899072u64, 211758u64}) + put(data, {0u64, 1563676642168012800u64, 46236813575u64}) + put(data, {0u64, 11532349341402398720u64, 7084767080u64}) + put(data, {0u64, 9048364970084925440u64, 104625169910u64}) + put(data, {0u64, 16609275425742389248u64, 246490512847u64}) + put(data, {0u64, 0u64, 207900390625u64}) + put(data, {0u64, 0u64, 225000000000u64}) + put(data, {11153727427136454656u64, 59u64, 0u64}) + put(data, {7205759403792793600u64, 59604644775u64, 0u64}) + put(data, {0u64, 4264412554261970152u64, 3u64}) + put(data, {0u64, 14485570586272534528u64, 3231174267u64}) + put(data, {0u64, 17827675094632103936u64, 123785264354u64}) + put(data, {0u64, 7347197909193981952u64, 226966440203u64}) + put(data, {0u64, 13677404030777688064u64, 11398292396u64}) + put(data, {0u64, 3810326759732150272u64, 172741453558u64}) + put(data, {0u64, 9943947977234055168u64, 246206558227u64}) + put(data, {0u64, 0u64, 19539062500u64}) + put(data, {0u64, 0u64, 228000000000u64}) + put(data, {12945425605062557696u64, 909494u64, 0u64}) + put(data, {4388757836872548352u64, 909494701772928u64, 0u64}) + put(data, {1152921504606846976u64, 14878706826214591391u64, 49303u64}) + put(data, {0u64, 4387341015746028192u64, 151806576313u64}) + put(data, {0u64, 651726680428265472u64, 185237838233u64}) + put(data, {0u64, 2570638187944738816u64, 153035330174u64}) + put(data, {0u64, 7419175577111756800u64, 126139354575u64}) + put(data, {0u64, 17299322326264840192u64, 207402194313u64}) + put(data, {0u64, 7990511638862102528u64, 137937798142u64}) + put(data, {0u64, 16717361816799281152u64, 254433166503u64}) + put(data, {0u64, 0u64, 167906250000u64}) + put(data, {0u64, 0u64, 16000000000u64}) + put(data, {16192327041775828992u64, 13u64, 0u64}) + put(data, {15024075324038053888u64, 13877787807u64, 0u64}) + put(data, {5449091666327633920u64, 13877787807814456755u64, 0u64}) + put(data, {2494994193563254784u64, 9707857417284919307u64, 752316384u64}) + put(data, {4611686018427387904u64, 1844515466944871826u64, 224526264005u64}) + put(data, {0u64, 15167599819856275072u64, 197099991383u64}) + put(data, {0u64, 14830185305589481472u64, 87822237233u64}) + put(data, {0u64, 6163721531743535104u64, 49803945956u64}) + put(data, {0u64, 14122847407012052992u64, 228334136013u64}) + put(data, {0u64, 335491783960035328u64, 205765601092u64}) + put(data, {0u64, 941252322120433664u64, 68018187046u64}) + put(data, {0u64, 11529215046068469760u64, 38051025390u64}) + put(data, {0u64, 0u64, 238625000000u64}) + put(data, {0u64, 0u64, 64000000000u64}) + put(data, {4368439412768899072u64, 211758u64, 0u64}) + put(data, {1563676642168012800u64, 211758236813575u64, 0u64}) + put(data, {11532349341402398720u64, 8061591463141767016u64, 11479u64}) + put(data, {9048364970084925440u64, 16628725344207857142u64, 215437019748u64}) + put(data, {16609275425742389248u64, 3555541870038531535u64, 100901445007u64}) + put(data, {0u64, 18316647450161853665u64, 143192746310u64}) + put(data, {0u64, 16709574568378075648u64, 70992947447u64}) + put(data, {0u64, 7696022835795591168u64, 247905827852u64}) + put(data, {0u64, 16664449640376041472u64, 12417202233u64}) + put(data, {0u64, 3109186955116544000u64, 57903381625u64}) + put(data, {0u64, 10515518101817131008u64, 121168549362u64}) + put(data, {0u64, 9961962375743537152u64, 242570047378u64}) + put(data, {0u64, 9223372036854775808u64, 146540039062u64}) + put(data, {0u64, 0u64, 150500000000u64}) + put(data, {14485570586272534528u64, 3231174267u64, 0u64}) + put(data, {17827675094632103936u64, 3231174267785264354u64, 0u64}) + put(data, {7347197909193981952u64, 748977172262750475u64, 175162308u64}) + put(data, {13677404030777688064u64, 15965033457315095468u64, 196040602133u64}) + put(data, {3810326759732150272u64, 16809402149066729206u64, 21865466197u64}) + put(data, {9943947977234055168u64, 7563769067065700371u64, 85911239516u64}) + put(data, {0u64, 13550322810840051428u64, 92410032742u64}) + put(data, {0u64, 8663209637545764864u64, 102734564471u64}) + put(data, {0u64, 8969247575312957440u64, 119469633535u64}) + put(data, {0u64, 6193172891660451840u64, 255486223885u64}) + put(data, {0u64, 3427954273864908800u64, 13335732575u64}) + put(data, {0u64, 10058367555266936832u64, 95185829773u64}) + put(data, {0u64, 13907115649320091648u64, 141545265197u64}) + put(data, {0u64, 0u64, 45753906250u64}) + put(data, {0u64, 0u64, 74000000000u64}) + put(data, {14878706826214591391u64, 49303u64, 0u64}) + put(data, {4387341015746028192u64, 49303806576313u64, 0u64}) + put(data, {651726680428265472u64, 14106411361315920281u64, 2672u64}) + put(data, {2570638187944738816u64, 3609034283485221502u64, 112764710092u64}) + put(data, {7419175577111756800u64, 9896072247338192335u64, 204195646140u64}) + put(data, {17299322326264840192u64, 8889095178479228297u64, 188536467151u64}) + put(data, {7990511638862102528u64, 3631796911038383102u64, 207481878815u64}) + put(data, {16717361816799281152u64, 898318840772166823u64, 31196880105u64}) + put(data, {0u64, 17293677953982795024u64, 233048697961u64}) + put(data, {0u64, 7353628266884669440u64, 105937492160u64}) + put(data, {0u64, 2404693032470315008u64, 192398640987u64}) + put(data, {0u64, 9191155893041889280u64, 91130358670u64}) + put(data, {0u64, 6353946855033798656u64, 142498253559u64}) + put(data, {0u64, 3767824038248841216u64, 247344448149u64}) + put(data, {0u64, 7205759403792793600u64, 149204254150u64}) + put(data, {0u64, 0u64, 198390625000u64}) + put(data, {0u64, 0u64, 232000000000u64}) + put(data, {9707857417284919307u64, 752316384u64, 0u64}) + put(data, {1844515466944871826u64, 752316384526264005u64, 0u64}) + put(data, {15167599819856275072u64, 17063068157692817751u64, 40783152u64}) + put(data, {14830185305589481472u64, 5385330256507239985u64, 48924990778u64}) + put(data, {6163721531743535104u64, 3373050282752075748u64, 58291939338u64}) + put(data, {14122847407012052992u64, 4116064001262906061u64, 10182853422u64}) + put(data, {335491783960035328u64, 11306582046748043076u64, 46223132276u64}) + put(data, {941252322120433664u64, 17035410946089626406u64, 116612931040u64}) + put(data, {11529215046068469760u64, 15618595715183448558u64, 224923491477u64}) + put(data, {0u64, 5141740092277295680u64, 149846685770u64}) + put(data, {0u64, 16973644291514990592u64, 74278734288u64}) + put(data, {0u64, 14625255268443750400u64, 208920143100u64}) + put(data, {0u64, 14021170507320131584u64, 252792836676u64}) + put(data, {0u64, 4451355232865091584u64, 68760089176u64}) + put(data, {0u64, 12891553933348044800u64, 88241308450u64}) + put(data, {0u64, 1152921504606846976u64, 34698852539u64}) + put(data, {0u64, 0u64, 187062500000u64}) + put(data, {0u64, 0u64, 160000000000u64}) + put(data, {8061591463141767016u64, 11479u64, 0u64}) + put(data, {16628725344207857142u64, 11479437019748u64, 0u64}) + put(data, {3555541870038531535u64, 5562205901560339855u64, 622u64}) + put(data, {18316647450161853665u64, 2106077949367544134u64, 110301527786u64}) + put(data, {16709574568378075648u64, 7496855998374373623u64, 234114170714u64}) + put(data, {7696022835795591168u64, 229183437194837004u64, 90406405378u64}) + put(data, {16664449640376041472u64, 465169186276472889u64, 2012424059u64}) + put(data, {3109186955116544000u64, 2152980561625316473u64, 123025216872u64}) + put(data, {10515518101817131008u64, 2059790725449340402u64, 104116713310u64}) + put(data, {9961962375743537152u64, 17891190926410198930u64, 94111661478u64}) + put(data, {9223372036854775808u64, 9930696175609809814u64, 166969883403u64}) + put(data, {0u64, 7276914261609005312u64, 11538344118u64}) + put(data, {0u64, 10539762974036983808u64, 182394482312u64}) + put(data, {0u64, 12851089458992250880u64, 136571361695u64}) + put(data, {0u64, 9449311677678878720u64, 159696658955u64}) + put(data, {0u64, 8699564697382289408u64, 11512248212u64}) + put(data, {0u64, 4224376450473525248u64, 148471604347u64}) + put(data, {0u64, 4611686018427387904u64, 123229003906u64}) + put(data, {0u64, 0u64, 130250000000u64}) + put(data, {0u64, 0u64, 128000000000u64}) + put(data, {748977172262750475u64, 175162308u64, 0u64}) + put(data, {15965033457315095468u64, 175162308040602133u64, 0u64}) + put(data, {16809402149066729206u64, 13756840147955779925u64, 9495567u64}) + put(data, {7563769067065700371u64, 13788447602092505948u64, 15745759798u64}) + put(data, {13550322810840051428u64, 4972540435632173670u64, 54747473242u64}) + put(data, {8663209637545764864u64, 2844874687533091959u64, 90269561957u64}) + put(data, {8969247575312957440u64, 15377573779532804095u64, 101154220965u64}) + put(data, {6193172891660451840u64, 17824715805091194381u64, 165833619944u64}) + put(data, {3427954273864908800u64, 18277569135638159711u64, 232966279779u64}) + put(data, {10058367555266936832u64, 4254645803379752845u64, 99990829008u64}) + put(data, {13907115649320091648u64, 2933643244178200621u64, 208230644811u64}) + put(data, {0u64, 17188148801879487562u64, 75159033118u64}) + put(data, {0u64, 11069762501163246592u64, 30931771413u64}) + put(data, {0u64, 11676570643941818368u64, 21600093027u64}) + put(data, {0u64, 17840016768744030208u64, 99632988162u64}) + put(data, {0u64, 16463817321652158464u64, 2967109246u64}) + put(data, {0u64, 6954191143357644800u64, 126892505325u64}) + put(data, {0u64, 5080060379673919488u64, 237376987457u64}) + put(data, {0u64, 0u64, 65275390625u64}) + put(data, {0u64, 0u64, 161000000000u64}) + put(data, {14106411361315920281u64, 2672u64, 0u64}) + put(data, {3609034283485221502u64, 2672764710092u64, 0u64}) + put(data, {9896072247338192335u64, 16433563478020213436u64, 144u64}) + put(data, {8889095178479228297u64, 4194750497955655375u64, 144890865261u64}) + put(data, {3631796911038383102u64, 2691539602252904735u64, 109227397880u64}) + put(data, {898318840772166823u64, 3775467271962795241u64, 248145908654u64}) + put(data, {17293677953982795024u64, 16980212613224918121u64, 174204668490u64}) + put(data, {7353628266884669440u64, 4172857038337333440u64, 74920499170u64}) + put(data, {2404693032470315008u64, 5936867627376461659u64, 226226211033u64}) + put(data, {9191155893041889280u64, 17856837443266866062u64, 217321838238u64}) + put(data, {6353946855033798656u64, 8956297047799810807u64, 158968021097u64}) + put(data, {3767824038248841216u64, 15356974049716912789u64, 105485521835u64}) + put(data, {7205759403792793600u64, 6923608913322982854u64, 171832503231u64}) + put(data, {0u64, 4855902993563955944u64, 191375329591u64}) + put(data, {0u64, 13835893222288330752u64, 55263239028u64}) + put(data, {0u64, 9114973913760137216u64, 116750045274u64}) + put(data, {0u64, 17937099003422310400u64, 90494123725u64}) + put(data, {0u64, 7007960010734960640u64, 205972372085u64}) + put(data, {0u64, 7683422439270776832u64, 117379902273u64}) + put(data, {0u64, 720575940379279360u64, 65416519165u64}) + put(data, {0u64, 0u64, 253039062500u64}) + put(data, {0u64, 0u64, 228000000000u64}) + put(data, {17063068157692817751u64, 40783152u64, 0u64}) + put(data, {5385330256507239985u64, 40783152924990778u64, 0u64}) + put(data, {3373050282752075748u64, 2768933352715741194u64, 2210859u64}) + put(data, {4116064001262906061u64, 15201941611824153390u64, 43150104177u64}) + put(data, {11306582046748043076u64, 1418128541727000180u64, 113824098906u64}) + put(data, {17035410946089626406u64, 5353350204565757408u64, 90076876902u64}) + put(data, {15618595715183448558u64, 1721001680354286741u64, 102290205696u64}) + put(data, {5141740092277295680u64, 637631411660453962u64, 93295688u64}) + put(data, {16973644291514990592u64, 1630012588870568400u64, 72034566068u64}) + put(data, 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6917194446u64}) + put(data, {9204796763694620958u64, 12365301604512770359u64, 206937619100u64}) + put(data, {7826260310402107021u64, 2814271599679204744u64, 156670324343u64}) + put(data, {10122690201685169383u64, 2154994415780170517u64, 119152561969u64}) + put(data, {7438455564568110133u64, 6717373824370072839u64, 49116822481u64}) + put(data, {2805412574380520817u64, 12709155755801344060u64, 209364149564u64}) + put(data, {7250965427231182867u64, 826847911966403896u64, 60688964714u64}) + put(data, {8136242944826085924u64, 2277322703890025383u64, 106044823515u64}) + put(data, {15357191647956011780u64, 2774508958389496437u64, 219123453911u64}) + put(data, {7369614426695395460u64, 245697774950120915u64, 215150406432u64}) + put(data, {10886957545142526638u64, 1268929063431863950u64, 32013319303u64}) + put(data, {2030047207417538097u64, 6735665673159411439u64, 135068788782u64}) + put(data, {11557093828502314355u64, 14734771742997073207u64, 46365141167u64}) + put(data, {15201062539664128543u64, 13683287077957612495u64, 175798773576u64}) + put(data, {8846936323343880674u64, 15370263741354826803u64, 72741772478u64}) + put(data, {1485291750116245364u64, 48035913070297507u64, 190833223667u64}) + put(data, {2076024439668322013u64, 1206547475966802115u64, 243002604032u64}) + put(data, {7029497773682748741u64, 13512340386605768006u64, 65407069u64}) + put(data, {16333533921668749881u64, 2325760467700278797u64, 93732505440u64}) + put(data, {2065057316131928423u64, 10848110652847753816u64, 96126079727u64}) + put(data, {7800502648925570223u64, 15846378960784301285u64, 239588077256u64}) + put(data, {17011619967093802015u64, 14121839924449844911u64, 200859033924u64}) + put(data, {5368819344429198672u64, 5147613424753296550u64, 68765546476u64}) + put(data, {15598879366754275267u64, 16817040482828810167u64, 236279052682u64}) + put(data, {16393893486035835647u64, 5773528746119363888u64, 138911653591u64}) + put(data, {12042046205096920307u64, 8716201595536184826u64, 215312983620u64}) + put(data, {15437070428008474344u64, 5259122109038474872u64, 68472506235u64}) + put(data, {13704569163204647509u64, 14744540084230155984u64, 123285097580u64}) + put(data, {18192483750856993350u64, 10719345477982635878u64, 108799303119u64}) + put(data, {5152535865317963250u64, 13698037261310555208u64, 207581096882u64}) + put(data, {17512614083933854680u64, 16141171632951976936u64, 178742572087u64}) + put(data, {14481918350603613536u64, 10060790174955808839u64, 55875014667u64}) + put(data, {16124419709964004915u64, 4250043307981877118u64, 11545396528u64}) + put(data, {18088011566435813579u64, 7075646198054337199u64, 48230395309u64}) + put(data, {15008862380698848893u64, 18141738384245531503u64, 173383571548u64}) + put(data, {18160498644611827812u64, 8174370508376809531u64, 92983465608u64}) + put(data, {3604680497457231965u64, 3581964982731575596u64, 136443133513u64}) + put(data, {5957615565551495921u64, 14798509948722114761u64, 73194178710u64}) + put(data, {17528455034961565995u64, 14713923334885122090u64, 150802228831u64}) + put(data, {8503772325120113809u64, 5042978054260414139u64, 95797643382u64}) + put(data, {8501492578048509537u64, 2052996319372883413u64, 118273380388u64}) + put(data, {2296237701094386060u64, 8825683007899981588u64, 36111293153u64}) + put(data, {3753593040591076946u64, 9992196755378745151u64, 225478441234u64}) + put(data, {8518075399775653155u64, 9301073417573669950u64, 18541678071u64}) + put(data, {12757855675959554597u64, 5331614769144850592u64, 247504212200u64}) + put(data, {121631169379748595u64, 14354009428310052102u64, 232289027415u64}) + put(data, {16679062494579173314u64, 5581221063029119078u64, 87778132410u64}) + put(data, {10739912744743898054u64, 1529260335339476189u64, 186302558600u64}) + put(data, {9367340677776287570u64, 16483061525949201148u64, 136082901368u64}) + put(data, {12227321512794715397u64, 14431217812333089675u64, 120893548555u64}) + put(data, {7241061891859170651u64, 3452349151135392267u64, 11782317885u64}) + put(data, {13148571323079237489u64, 9075317899834447999u64, 61187152222u64}) + put(data, {12509763434355012654u64, 2764331337978901575u64, 94491973969u64}) + put(data, {11812768946960181977u64, 1942890683708857202u64, 81149854702u64}) + put(data, {14170358803552564832u64, 165089169728028447u64, 238105324315u64}) + put(data, {18179989524780635952u64, 15193620741871233073u64, 27008949501u64}) + put(data, {17091718978514754901u64, 14995000835194145926u64, 253823647830u64}) + put(data, {7394768384359232459u64, 1788823614552255558u64, 86812880624u64}) + put(data, {6778628272692852803u64, 8384901184618498845u64, 240096972322u64}) + put(data, {18193335045875234320u64, 405511217862281310u64, 34454546404u64}) + put(data, {1378519212560967521u64, 3111530463755196557u64, 228021982807u64}) + put(data, {4677732610631043584u64, 7893558450035460812u64, 87168676404u64}) + put(data, {17296098591070486528u64, 156573858237402216u64, 52427910661u64}) + put(data, {7343735382392963072u64, 15915324019419451223u64, 5008487885u64}) + put(data, {14525996728454217728u64, 16293363012778802804u64, 205862771443u64}) + put(data, {9691359370008330240u64, 14342105318291351412u64, 243883264978u64}) + put(data, {3044433348102455296u64, 3788398842525387052u64, 210777487087u64}) + put(data, {9223372036854775808u64, 14118764407048307670u64, 239205369512u64}) + put(data, {0u64, 2705021334614720768u64, 168765379752u64}) + put(data, {0u64, 7017988973805568000u64, 168146639500u64}) + put(data, {0u64, 10956732053634154496u64, 140380445944u64}) + put(data, {0u64, 14657517938546835456u64, 248593965634u64}) + put(data, {0u64, 11268868284797157376u64, 66794585639u64}) + put(data, {0u64, 14600669991935148032u64, 39610886573u64}) + put(data, {0u64, 4611686018427387904u64, 173791503906u64}) + put(data, {0u64, 0u64, 34250000000u64}) + put(data, {0u64, 0u64, 128000000000u64}) + put(data, {8201586317771250746u64, 1424047269u64, 0u64}) + put(data, {3278889188817135834u64, 1424047269444608885u64, 0u64}) + put(data, {1710725240251040430u64, 3001188830946823627u64, 77197757u64}) + put(data, {1850175733663425006u64, 9732296932705387049u64, 189162694772u64}) + put(data, {9147599666163914249u64, 16337535782679529459u64, 116527588873u64}) + put(data, {10221885933644344166u64, 7969742269895046547u64, 9885659589u64}) + put(data, {14901479793736678101u64, 2923592083903829642u64, 197432040594u64}) + put(data, {5181831442059703136u64, 8144196241160608534u64, 146158488244u64}) + put(data, {6396246577759793483u64, 16431078457793424253u64, 180441497762u64}) + put(data, {14167229556464870447u64, 202362949592775653u64, 162890730548u64}) + put(data, {2969982933326311854u64, 8835125248522947981u64, 52010970117u64}) + put(data, {7892677766222018881u64, 7959873808777345113u64, 5478953099u64}) + put(data, {798698968922663621u64, 14929747122315126151u64, 139431505623u64}) + put(data, {15926812109043458972u64, 4310328817360515349u64, 215809343213u64}) + put(data, {8663842590352697437u64, 7294899422760201126u64, 237233663393u64}) + put(data, {17093523026636671168u64, 2047461597291187207u64, 161395457290u64}) + put(data, {839764004742743203u64, 10942374468813517900u64, 10110993115u64}) + put(data, {16894643909298232323u64, 10364795403063433969u64, 219593187308u64}) + put(data, {9066702926218949317u64, 12330859528790939137u64, 236561876684u64}) + put(data, {9119392417260546810u64, 8973160144879916806u64, 204668457234u64}) + put(data, {9723021096578315109u64, 2895354388547509877u64, 18486435986u64}) + put(data, {14787464248751217597u64, 16766844772497556429u64, 146156957475u64}) + put(data, {3733434565920249133u64, 7442407174620948827u64, 35908932476u64}) + put(data, {6643788868836820841u64, 6683013428676659077u64, 124403453701u64}) + put(data, {4729646697422664063u64, 16713703375071907588u64, 5362286883u64}) + put(data, {4090144564201555829u64, 8791044883080637861u64, 35906051675u64}) + put(data, {2109480737093400002u64, 602844107089214413u64, 91476563498u64}) + put(data, {16577155033369419739u64, 9754832281172880875u64, 42032680244u64}) + put(data, {745377248603805917u64, 10587846778003503903u64, 52528810517u64}) + put(data, {11305561465807999667u64, 17206244172922947013u64, 21573968323u64}) + put(data, {2211245518782892177u64, 11620628420699303875u64, 195932752365u64}) + put(data, {14170095199249735666u64, 17864732368219338611u64, 237629955528u64}) + put(data, {17849973668116118927u64, 4146383014621345887u64, 200968449082u64}) + put(data, {9020960204585720001u64, 11445705075042688243u64, 58224775873u64}) + put(data, {10807134002871850916u64, 7369147888966546592u64, 193620472915u64}) + put(data, {3925122626254791201u64, 9762476865090597796u64, 83399482307u64}) + put(data, {17208463291312718997u64, 5507001428194242827u64, 195529224931u64}) + put(data, {5145077219589447653u64, 11371471148365328344u64, 227298535145u64}) + put(data, {17602397765035489468u64, 3148788104946538618u64, 233616448686u64}) + put(data, {16422643262490753377u64, 3762722308424507574u64, 174170696145u64}) + put(data, {2902509461400906224u64, 1156171244825745915u64, 209203977585u64}) + put(data, {3422418805967265206u64, 14208921674868257865u64, 113062676168u64}) + put(data, {4228874576277237392u64, 7903080886897905503u64, 200770267187u64}) + put(data, {2553488530807495751u64, 6367240794154270982u64, 51428426873u64}) + put(data, {11546099176912486413u64, 1623672396662369850u64, 121345168815u64}) + put(data, {10460791037534167991u64, 18323231215381674394u64, 175088019456u64}) + put(data, {8127117908566000904u64, 9842279843006544554u64, 993304354u64}) + put(data, {11541304458088287306u64, 7376839231308610600u64, 34533551059u64}) + put(data, {6249718665174839700u64, 609751749293657672u64, 211399899256u64}) + put(data, {13102508413386290995u64, 10386457966860989799u64, 120033054708u64}) + put(data, {6274675218640661911u64, 11160336020836149780u64, 244563051014u64}) + put(data, {3404497118599817167u64, 17947559933847409193u64, 6605003027u64}) + put(data, {11258566093988562335u64, 10229787001712704590u64, 19972939173u64}) + put(data, {16762592482501635397u64, 10441677090043619866u64, 165554557864u64}) + put(data, {5550125446725071998u64, 4996681336392922375u64, 168566044449u64}) + put(data, {6370033225258510318u64, 124497102381021895u64, 33270870638u64}) + put(data, {1503521728674735398u64, 8180812057779384577u64, 110006749001u64}) + put(data, {4250415082606384364u64, 5294232873532946716u64, 73443482710u64}) + put(data, {6020091901030562974u64, 2885620189169448039u64, 86287000939u64}) + put(data, {16288222967151527138u64, 16662526875008170507u64, 107156429783u64}) + put(data, {6377016228656203782u64, 15663095032402672480u64, 215903277391u64}) + put(data, {8378856515587563750u64, 1824281504410546614u64, 79849098083u64}) + put(data, {15812881490200838483u64, 9506565509584809953u64, 99098894498u64}) + put(data, {4548570371183413652u64, 16941136942345070055u64, 162515351948u64}) + put(data, {16731431495283420383u64, 15924115693705937725u64, 140918380873u64}) + put(data, {14737727629551135532u64, 9247807690406628462u64, 73863248041u64}) + put(data, {12413722258104293893u64, 7993916633864834871u64, 169501324659u64}) + put(data, {800899742400762438u64, 1018504409177639408u64, 115433351089u64}) + put(data, {603197008376033550u64, 12097800686634130718u64, 177055213234u64}) + put(data, {6380777281587743935u64, 6221488888422637551u64, 178655823089u64}) + put(data, {10001440249018225388u64, 8229322865256080421u64, 241337267588u64}) + put(data, {5505914461980436708u64, 7927745108183101786u64, 132446112486u64}) + put(data, {1105464290051876864u64, 8488683721235326653u64, 230429763923u64}) + put(data, {4500443576769970176u64, 11165516518170922283u64, 83460172466u64}) + put(data, {2843045143185981440u64, 5463648141113596927u64, 178605283863u64}) + put(data, {660949699682893824u64, 3958440403860778042u64, 23296184959u64}) + put(data, {276549164618219520u64, 5091534813990256011u64, 127214587484u64}) + put(data, {4683743612465315840u64, 6100166970623291280u64, 92276012655u64}) + put(data, {0u64, 1913011027739012426u64, 111330690714u64}) + put(data, {0u64, 11310957650604221440u64, 154103704535u64}) + put(data, {0u64, 16303817257009020928u64, 215613168242u64}) + put(data, {0u64, 9090406322154766336u64, 114883831704u64}) + put(data, {0u64, 3003279315069566976u64, 152492791914u64}) + put(data, {0u64, 16582887146675765248u64, 106162808097u64}) + put(data, {0u64, 9691746398101307392u64, 33898960113u64}) + put(data, {0u64, 0u64, 241525390625u64}) + put(data, {0u64, 0u64, 33000000000u64}) + data + end +end diff --git a/src/string/formatter.cr b/src/string/formatter.cr index 8ff32cf2ada0..e39ecbaa87a6 100644 --- a/src/string/formatter.cr +++ b/src/string/formatter.cr @@ -219,6 +219,7 @@ struct String::Formatter(A) int flags, arg when 'a', 'A', 'e', 'E', 'f', 'g', 'G' flags.type = char + flags.float = true float flags, arg else raise ArgumentError.new("Malformed format string - %#{char.inspect}") @@ -297,7 +298,6 @@ struct String::Formatter(A) end end - # We don't actually format the float ourselves, we delegate to snprintf def float(flags, arg) : Nil if arg.responds_to?(:to_f64) float = arg.is_a?(Float64) ? arg : arg.to_f64 @@ -307,13 +307,18 @@ struct String::Formatter(A) elsif float.nan? float_special("nan", 1, flags) else - format_buf = recreate_float_format_string(flags) - - len = LibC.snprintf(nil, 0, format_buf, float) + 1 - temp_buf = temp_buf(len) - LibC.snprintf(temp_buf, len, format_buf, float) - - @io.write_string Slice.new(temp_buf, len - 1) + case flags.type + when 'f' + float_fixed(float, flags) + when 'e', 'E' + float_scientific(float, flags) + when 'g', 'G' + float_general(float, flags) + when 'a', 'A' + float_hex(float, flags) + else + raise "BUG: Unknown format type '#{flags.type}'" + end end else raise ArgumentError.new("Expected a float, not #{arg.inspect}") @@ -334,6 +339,73 @@ struct String::Formatter(A) pad(str_size, flags) if flags.right_padding? end + # Formats floats with `%f` + private def float_fixed(float, flags) + # the longest string possible is due to `Float64::MIN_SUBNORMAL`, which + # produces `0.` followed by 1074 nonzero digits; there is also no need + # for any precision > 1074 because all trailing digits will be zeros + if precision = flags.precision + printf_precision = {precision.to_u32, 1074_u32}.min + trailing_zeros = {precision - printf_precision, 0}.max + else + # default precision for C's `%f` + printf_precision = 6_u32 + trailing_zeros = 0 + end + + printf_buf = uninitialized UInt8[1076] + printf_size = Float::Printer::RyuPrintf.d2fixed_buffered_n(float, printf_precision, printf_buf.to_unsafe) + printf_slice = printf_buf.to_slice[0, printf_size] + dot_index = printf_slice.index('.'.ord) + sign = Math.copysign(1.0, float) + + str_size = printf_size + trailing_zeros + str_size += 1 if sign < 0 || flags.plus || flags.space + str_size += 1 if flags.sharp && dot_index.nil? + + pad(str_size, flags) if flags.left_padding? && flags.padding_char != '0' + + # this preserves -0.0's sign correctly + write_plus_or_space(sign, flags) + @io << '-' if sign < 0 + + pad(str_size, flags) if flags.left_padding? && flags.padding_char == '0' + @io.write_string(printf_slice) + trailing_zeros.times { @io << '0' } + @io << '.' if flags.sharp && dot_index.nil? + + pad(str_size, flags) if flags.right_padding? + end + + # Formats floats with `%e` or `%E` + private def float_scientific(float, flags) + # TODO: implement using `Float::Printer::RyuPrintf` + float_fallback(float, flags) + end + + # Formats floats with `%g` or `%G` + private def float_general(float, flags) + # TODO: implement using `Float::Printer::RyuPrintf` + float_fallback(float, flags) + end + + # Formats floats with `%a` or `%A` + private def float_hex(float, flags) + # TODO: implement using `Float::Printer::Hexfloat` + float_fallback(float, flags) + end + + # Delegate to `LibC.snprintf` for float formats not yet ported to Crystal + private def float_fallback(float, flags) + format_buf = recreate_float_format_string(flags) + + len = LibC.snprintf(nil, 0, format_buf, float) + 1 + temp_buf = temp_buf(len) + LibC.snprintf(temp_buf, len, format_buf, float) + + @io.write_string Slice.new(temp_buf, len - 1) + end + # Here we rebuild the original format string, like %f or %.2g and use snprintf def recreate_float_format_string(flags) capacity = 3 # percent + type + \0 @@ -451,13 +523,13 @@ struct String::Formatter(A) end struct Flags - property space : Bool, sharp : Bool, plus : Bool, minus : Bool, zero : Bool, base : Int32 + property space : Bool, sharp : Bool, plus : Bool, minus : Bool, zero : Bool, float : Bool, base : Int32 property width : Int32, width_size : Int32 property type : Char, precision : Int32?, precision_size : Int32 property index : Int32? def initialize - @space = @sharp = @plus = @minus = @zero = false + @space = @sharp = @plus = @minus = @zero = @float = false @width = 0 @width_size = 0 @base = 10 @@ -475,7 +547,7 @@ struct String::Formatter(A) end def padding_char : Char - @zero && !right_padding? && !@precision ? '0' : ' ' + @zero && !right_padding? && (@float || !@precision) ? '0' : ' ' end end end From ca5447e7f1f5b66983604118659edecb392a31ad Mon Sep 17 00:00:00 2001 From: Quinton Miller Date: Thu, 7 Dec 2023 21:11:14 +0800 Subject: [PATCH 2/5] disable on wasm32 --- spec/std/float_printer/ryu_printf_spec.cr | 2 + src/float/printer/ryu_printf.cr | 2 + src/float/printer/ryu_printf_table.cr | 2 + src/string/formatter.cr | 125 ++++++++++++---------- 4 files changed, 73 insertions(+), 58 deletions(-) diff --git a/spec/std/float_printer/ryu_printf_spec.cr b/spec/std/float_printer/ryu_printf_spec.cr index f8e80d1a33dd..a175d826eb99 100644 --- a/spec/std/float_printer/ryu_printf_spec.cr +++ b/spec/std/float_printer/ryu_printf_spec.cr @@ -1,3 +1,5 @@ +{% skip_file if flag?(:wasm32) %} + # This file contains test cases derived from: # # * https://github.com/ulfjack/ryu diff --git a/src/float/printer/ryu_printf.cr b/src/float/printer/ryu_printf.cr index d14ac70a831c..40b9ddb2c1d5 100644 --- a/src/float/printer/ryu_printf.cr +++ b/src/float/printer/ryu_printf.cr @@ -1,3 +1,5 @@ +{% skip_file if flag?(:wasm32) %} + require "./ryu_printf_table" # Source port of Ryu Printf's reference implementation in C. diff --git a/src/float/printer/ryu_printf_table.cr b/src/float/printer/ryu_printf_table.cr index c24d75a048f2..c8e78f6e49e0 100644 --- a/src/float/printer/ryu_printf_table.cr +++ b/src/float/printer/ryu_printf_table.cr @@ -1,3 +1,5 @@ +{% skip_file if flag?(:wasm32) %} + module Float::Printer::RyuPrintf {% begin %} # A table of all two-digit numbers. This is used to speed up decimal digit diff --git a/src/string/formatter.cr b/src/string/formatter.cr index e39ecbaa87a6..cdf5710b45f4 100644 --- a/src/string/formatter.cr +++ b/src/string/formatter.cr @@ -307,18 +307,25 @@ struct String::Formatter(A) elsif float.nan? float_special("nan", 1, flags) else - case flags.type - when 'f' - float_fixed(float, flags) - when 'e', 'E' - float_scientific(float, flags) - when 'g', 'G' - float_general(float, flags) - when 'a', 'A' - float_hex(float, flags) - else - raise "BUG: Unknown format type '#{flags.type}'" - end + # FIXME: wasm32 appears to run out of memory if we use Ryu Printf, which + # initializes very large lookup tables, so we always fall back to + # `LibC.snprintf` (#13918) + {% if flag?(:wasm32) %} + float_fallback(float, flags) + {% else %} + case flags.type + when 'f' + float_fixed(float, flags) + when 'e', 'E' + float_scientific(float, flags) + when 'g', 'G' + float_general(float, flags) + when 'a', 'A' + float_hex(float, flags) + else + raise "BUG: Unknown format type '#{flags.type}'" + end + {% end %} end else raise ArgumentError.new("Expected a float, not #{arg.inspect}") @@ -339,61 +346,63 @@ struct String::Formatter(A) pad(str_size, flags) if flags.right_padding? end - # Formats floats with `%f` - private def float_fixed(float, flags) - # the longest string possible is due to `Float64::MIN_SUBNORMAL`, which - # produces `0.` followed by 1074 nonzero digits; there is also no need - # for any precision > 1074 because all trailing digits will be zeros - if precision = flags.precision - printf_precision = {precision.to_u32, 1074_u32}.min - trailing_zeros = {precision - printf_precision, 0}.max - else - # default precision for C's `%f` - printf_precision = 6_u32 - trailing_zeros = 0 - end + {% unless flag?(:wasm32) %} + # Formats floats with `%f` + private def float_fixed(float, flags) + # the longest string possible is due to `Float64::MIN_SUBNORMAL`, which + # produces `0.` followed by 1074 nonzero digits; there is also no need + # for any precision > 1074 because all trailing digits will be zeros + if precision = flags.precision + printf_precision = {precision.to_u32, 1074_u32}.min + trailing_zeros = {precision - printf_precision, 0}.max + else + # default precision for C's `%f` + printf_precision = 6_u32 + trailing_zeros = 0 + end - printf_buf = uninitialized UInt8[1076] - printf_size = Float::Printer::RyuPrintf.d2fixed_buffered_n(float, printf_precision, printf_buf.to_unsafe) - printf_slice = printf_buf.to_slice[0, printf_size] - dot_index = printf_slice.index('.'.ord) - sign = Math.copysign(1.0, float) + printf_buf = uninitialized UInt8[1076] + printf_size = Float::Printer::RyuPrintf.d2fixed_buffered_n(float, printf_precision, printf_buf.to_unsafe) + printf_slice = printf_buf.to_slice[0, printf_size] + dot_index = printf_slice.index('.'.ord) + sign = Math.copysign(1.0, float) - str_size = printf_size + trailing_zeros - str_size += 1 if sign < 0 || flags.plus || flags.space - str_size += 1 if flags.sharp && dot_index.nil? + str_size = printf_size + trailing_zeros + str_size += 1 if sign < 0 || flags.plus || flags.space + str_size += 1 if flags.sharp && dot_index.nil? - pad(str_size, flags) if flags.left_padding? && flags.padding_char != '0' + pad(str_size, flags) if flags.left_padding? && flags.padding_char != '0' - # this preserves -0.0's sign correctly - write_plus_or_space(sign, flags) - @io << '-' if sign < 0 + # this preserves -0.0's sign correctly + write_plus_or_space(sign, flags) + @io << '-' if sign < 0 - pad(str_size, flags) if flags.left_padding? && flags.padding_char == '0' - @io.write_string(printf_slice) - trailing_zeros.times { @io << '0' } - @io << '.' if flags.sharp && dot_index.nil? + pad(str_size, flags) if flags.left_padding? && flags.padding_char == '0' + @io.write_string(printf_slice) + trailing_zeros.times { @io << '0' } + @io << '.' if flags.sharp && dot_index.nil? - pad(str_size, flags) if flags.right_padding? - end + pad(str_size, flags) if flags.right_padding? + end - # Formats floats with `%e` or `%E` - private def float_scientific(float, flags) - # TODO: implement using `Float::Printer::RyuPrintf` - float_fallback(float, flags) - end + # Formats floats with `%e` or `%E` + private def float_scientific(float, flags) + # TODO: implement using `Float::Printer::RyuPrintf` + float_fallback(float, flags) + end - # Formats floats with `%g` or `%G` - private def float_general(float, flags) - # TODO: implement using `Float::Printer::RyuPrintf` - float_fallback(float, flags) - end + # Formats floats with `%g` or `%G` + private def float_general(float, flags) + # TODO: implement using `Float::Printer::RyuPrintf` + float_fallback(float, flags) + end - # Formats floats with `%a` or `%A` - private def float_hex(float, flags) - # TODO: implement using `Float::Printer::Hexfloat` - float_fallback(float, flags) - end + # Formats floats with `%a` or `%A` + private def float_hex(float, flags) + # TODO: implement using `Float::Printer::Hexfloat` + float_fallback(float, flags) + end + {% end %} # Delegate to `LibC.snprintf` for float formats not yet ported to Crystal private def float_fallback(float, flags) From 1c2966c05ffb02f5f1bfaba621b9c5306496cc6e Mon Sep 17 00:00:00 2001 From: Quinton Miller Date: Fri, 8 Dec 2023 13:58:19 +0800 Subject: [PATCH 3/5] fixme --- spec/std/float_printer/ryu_printf_spec.cr | 1 + src/float/printer/ryu_printf.cr | 1 + src/float/printer/ryu_printf_table.cr | 1 + 3 files changed, 3 insertions(+) diff --git a/spec/std/float_printer/ryu_printf_spec.cr b/spec/std/float_printer/ryu_printf_spec.cr index a175d826eb99..15d28bd3bf1f 100644 --- a/spec/std/float_printer/ryu_printf_spec.cr +++ b/spec/std/float_printer/ryu_printf_spec.cr @@ -1,3 +1,4 @@ +# FIXME: this leads to an OOB on wasm32 (#13918) {% skip_file if flag?(:wasm32) %} # This file contains test cases derived from: diff --git a/src/float/printer/ryu_printf.cr b/src/float/printer/ryu_printf.cr index 40b9ddb2c1d5..d44a2fa8739b 100644 --- a/src/float/printer/ryu_printf.cr +++ b/src/float/printer/ryu_printf.cr @@ -1,3 +1,4 @@ +# FIXME: this leads to an OOB on wasm32 (#13918) {% skip_file if flag?(:wasm32) %} require "./ryu_printf_table" diff --git a/src/float/printer/ryu_printf_table.cr b/src/float/printer/ryu_printf_table.cr index c8e78f6e49e0..dc733c492991 100644 --- a/src/float/printer/ryu_printf_table.cr +++ b/src/float/printer/ryu_printf_table.cr @@ -1,3 +1,4 @@ +# FIXME: this leads to an OOB on wasm32 (#13918) {% skip_file if flag?(:wasm32) %} module Float::Printer::RyuPrintf From 06bc918fa0b24b7a7f24fe93b743be4c51f03900 Mon Sep 17 00:00:00 2001 From: Quinton Miller Date: Tue, 12 Dec 2023 19:18:52 +0800 Subject: [PATCH 4/5] fix todo --- spec/std/float_printer/ryu_printf_spec.cr | 80 ++++++++++++----------- 1 file changed, 41 insertions(+), 39 deletions(-) diff --git a/spec/std/float_printer/ryu_printf_spec.cr b/spec/std/float_printer/ryu_printf_spec.cr index 15d28bd3bf1f..21bed0087be3 100644 --- a/spec/std/float_printer/ryu_printf_spec.cr +++ b/spec/std/float_printer/ryu_printf_spec.cr @@ -361,29 +361,29 @@ ALL_POWERS_OF_TEN = [ {1e-3, 60, 57}, {1e-2, 59, 57}, {1e-1, 55, 54}, - {1e0, 0, 1}, # TODO: fix exp_reference - {1e1, 0, 1}, - {1e2, 0, 1}, - {1e3, 0, 1}, - {1e4, 0, 1}, - {1e5, 0, 1}, - {1e6, 0, 1}, - {1e7, 0, 1}, - {1e8, 0, 1}, - {1e9, 0, 1}, - {1e10, 0, 1}, - {1e11, 0, 1}, - {1e12, 0, 1}, - {1e13, 0, 1}, - {1e14, 0, 1}, - {1e15, 0, 1}, - {1e16, 0, 1}, - {1e17, 0, 1}, - {1e18, 0, 1}, - {1e19, 0, 1}, - {1e20, 0, 1}, - {1e21, 0, 1}, - {1e22, 0, 1}, + {1e0, 0, 0}, + {1e1, 0, 0}, + {1e2, 0, 0}, + {1e3, 0, 0}, + {1e4, 0, 0}, + {1e5, 0, 0}, + {1e6, 0, 0}, + {1e7, 0, 0}, + {1e8, 0, 0}, + {1e9, 0, 0}, + {1e10, 0, 0}, + {1e11, 0, 0}, + {1e12, 0, 0}, + {1e13, 0, 0}, + {1e14, 0, 0}, + {1e15, 0, 0}, + {1e16, 0, 0}, + {1e17, 0, 0}, + {1e18, 0, 0}, + {1e19, 0, 0}, + {1e20, 0, 0}, + {1e21, 0, 0}, + {1e22, 0, 0}, {1e23, 0, 22}, {1e24, 0, 23}, {1e25, 0, 25}, @@ -2725,13 +2725,13 @@ ALL_BINARY_EXPONENTS = [ ] struct BigFloat - def to_s(*, point_range : Range = -3..15) + def to_s_with_range(*, point_range : Range = -3..15) String.build do |io| - to_s(io, point_range: point_range) + to_s_with_range(io, point_range: point_range) end end - def to_s(io : IO, *, point_range : Range = -3..15) : Nil + def to_s_with_range(io : IO, *, point_range : Range = -3..15) : Nil cstr = LibGMP.mpf_get_str(nil, out decimal_exponent, 10, 0, self) length = LibC.strlen(cstr) buffer = Slice.new(cstr, length) @@ -2762,20 +2762,22 @@ struct BigFloat buffer = buffer[point...] end - # TODO: allow this to be not written at all - io << '.' + # skip `.0000...` + unless buffer.all?(&.=== '0') + io << '.' - # add leading zeros after point - if point < 0 - (-point).times { io << '0' } - end + # add leading zeros after point + if point < 0 + (-point).times { io << '0' } + end - # add fractional part digits - io.write_string buffer + # add fractional part digits + io.write_string buffer - # print trailing 0 if whole number or exp notation of power of ten - if (decimal_exponent >= length && !exp_mode) || ((exp != point || exp_mode) && length == 1) - io << '0' + # print trailing 0 if whole number or exp notation of power of ten + if (decimal_exponent >= length && !exp_mode) || ((exp != point || exp_mode) && length == 1) + io << '0' + end end # exp notation @@ -2791,12 +2793,12 @@ private def fixed_reference(value, precision) if precision == 0 value.to_big_i.to_s else - BigFloat.new(value, 4096).to_s(point_range: ..) + BigFloat.new(value, 4096).to_s_with_range(point_range: ..) end end private def exp_reference(value, precision) - BigFloat.new(value, 4096).to_s(point_range: 0...0) + BigFloat.new(value, 4096).to_s_with_range(point_range: 0...0) end private def ieee_parts_to_f64(sign, exponent, mantissa) From 6f0e9e0b3ca9df74803c3848232f6d26d092149a Mon Sep 17 00:00:00 2001 From: Quinton Miller Date: Tue, 12 Dec 2023 19:20:12 +0800 Subject: [PATCH 5/5] split --- spec/std/float_printer/ryu_printf_spec.cr | 2697 +---------------- .../float_printer/ryu_printf_test_cases.cr | 2697 +++++++++++++++++ 2 files changed, 2698 insertions(+), 2696 deletions(-) create mode 100644 spec/std/float_printer/ryu_printf_test_cases.cr diff --git a/spec/std/float_printer/ryu_printf_spec.cr b/spec/std/float_printer/ryu_printf_spec.cr index 21bed0087be3..d4ba77bffd94 100644 --- a/spec/std/float_printer/ryu_printf_spec.cr +++ b/spec/std/float_printer/ryu_printf_spec.cr @@ -27,2702 +27,7 @@ require "spec" require "float/printer/ryu_printf" require "big" - -# The following two lists store: {value, fixed_precision, exp_precision} -# Iterate over them via macros only, otherwise the entire array literal will be -# materialized! -# The original specs contain also the full expected results which would have -# increased the file size by over 18x. Here we assume that `BigFloat#to_s` and -# `BigDecimal#to_s` are always correct, so that we don't have to write the long -# results in the source code. - -# These values test every power of ten that's within the range of doubles. -ALL_POWERS_OF_TEN = [ - {1e-323, 1073, 749}, - {1e-322, 1072, 749}, - {1e-321, 1073, 751}, - {1e-320, 1071, 750}, - {1e-319, 1070, 750}, - {1e-318, 1073, 754}, - {1e-317, 1074, 757}, - {1e-316, 1074, 757}, - {1e-315, 1074, 758}, - {1e-314, 1074, 759}, - {1e-313, 1074, 761}, - {1e-312, 1074, 761}, - {1e-311, 1074, 762}, - {1e-310, 1074, 763}, - {1e-309, 1074, 765}, - {1e-308, 1073, 764}, - {1e-307, 1072, 764}, - {1e-306, 1069, 763}, - {1e-305, 1066, 760}, - {1e-304, 1062, 757}, - {1e-303, 1059, 755}, - {1e-302, 1054, 751}, - {1e-301, 1052, 751}, - {1e-300, 1049, 749}, - {1e-299, 1046, 746}, - {1e-298, 1042, 743}, - {1e-297, 1039, 742}, - {1e-296, 1035, 739}, - {1e-295, 1032, 737}, - {1e-294, 1029, 735}, - {1e-293, 1022, 729}, - {1e-292, 1021, 729}, - {1e-291, 1019, 727}, - {1e-290, 1015, 725}, - {1e-289, 1012, 723}, - {1e-288, 1009, 721}, - {1e-287, 1006, 719}, - {1e-286, 1003, 717}, - {1e-285, 999, 714}, - {1e-284, 996, 712}, - {1e-283, 993, 709}, - {1e-282, 986, 704}, - {1e-281, 985, 704}, - {1e-280, 981, 700}, - {1e-279, 979, 700}, - {1e-278, 976, 697}, - {1e-277, 973, 695}, - {1e-276, 957, 681}, - {1e-275, 966, 690}, - {1e-274, 963, 688}, - {1e-273, 954, 681}, - {1e-272, 956, 683}, - {1e-271, 953, 681}, - {1e-270, 948, 678}, - {1e-269, 944, 674}, - {1e-268, 943, 674}, - {1e-267, 935, 667}, - {1e-266, 934, 667}, - {1e-265, 933, 667}, - {1e-264, 925, 661}, - {1e-263, 924, 661}, - {1e-262, 923, 661}, - {1e-261, 920, 658}, - {1e-260, 916, 655}, - {1e-259, 909, 650}, - {1e-258, 910, 651}, - {1e-257, 904, 646}, - {1e-256, 903, 646}, - {1e-255, 898, 643}, - {1e-254, 894, 639}, - {1e-253, 890, 637}, - {1e-252, 890, 637}, - {1e-251, 886, 635}, - {1e-250, 881, 631}, - {1e-249, 880, 631}, - {1e-248, 876, 627}, - {1e-247, 872, 625}, - {1e-246, 870, 623}, - {1e-245, 863, 617}, - {1e-244, 862, 617}, - {1e-243, 860, 616}, - {1e-242, 850, 607}, - {1e-241, 849, 607}, - {1e-240, 848, 607}, - {1e-239, 845, 606}, - {1e-238, 840, 601}, - {1e-237, 839, 601}, - {1e-236, 835, 599}, - {1e-235, 829, 593}, - {1e-234, 828, 593}, - {1e-233, 827, 593}, - {1e-232, 823, 591}, - {1e-231, 819, 587}, - {1e-230, 817, 587}, - {1e-229, 813, 584}, - {1e-228, 810, 582}, - {1e-227, 807, 579}, - {1e-226, 803, 576}, - {1e-225, 799, 573}, - {1e-224, 796, 572}, - {1e-223, 792, 568}, - {1e-222, 790, 568}, - {1e-221, 787, 566}, - {1e-220, 783, 562}, - {1e-219, 777, 558}, - {1e-218, 776, 558}, - {1e-217, 773, 556}, - {1e-216, 768, 552}, - {1e-215, 767, 552}, - {1e-214, 763, 548}, - {1e-213, 758, 544}, - {1e-212, 757, 544}, - {1e-211, 753, 542}, - {1e-210, 747, 537}, - {1e-209, 746, 537}, - {1e-208, 740, 532}, - {1e-207, 740, 532}, - {1e-206, 737, 531}, - {1e-205, 731, 526}, - {1e-204, 730, 526}, - {1e-203, 723, 520}, - {1e-202, 722, 520}, - {1e-201, 720, 518}, - {1e-200, 715, 514}, - {1e-199, 714, 514}, - {1e-198, 709, 510}, - {1e-197, 706, 508}, - {1e-196, 703, 507}, - {1e-195, 699, 504}, - {1e-194, 697, 503}, - {1e-193, 693, 500}, - {1e-192, 689, 497}, - {1e-191, 684, 493}, - {1e-190, 683, 493}, - {1e-189, 680, 491}, - {1e-188, 676, 487}, - {1e-187, 672, 485}, - {1e-186, 669, 482}, - {1e-185, 666, 480}, - {1e-184, 663, 479}, - {1e-183, 660, 477}, - {1e-182, 655, 473}, - {1e-181, 654, 473}, - {1e-180, 647, 467}, - {1e-179, 646, 467}, - {1e-178, 641, 462}, - {1e-177, 640, 462}, - {1e-176, 632, 455}, - {1e-175, 631, 455}, - {1e-174, 630, 455}, - {1e-173, 624, 451}, - {1e-172, 623, 451}, - {1e-171, 618, 446}, - {1e-170, 617, 446}, - {1e-169, 614, 445}, - {1e-168, 610, 442}, - {1e-167, 607, 440}, - {1e-166, 604, 438}, - {1e-165, 600, 435}, - {1e-164, 597, 432}, - {1e-163, 594, 430}, - {1e-162, 591, 428}, - {1e-161, 587, 426}, - {1e-160, 582, 421}, - {1e-159, 581, 421}, - {1e-158, 577, 419}, - {1e-157, 574, 416}, - {1e-156, 571, 415}, - {1e-155, 567, 412}, - {1e-154, 563, 408}, - {1e-153, 561, 408}, - {1e-152, 557, 405}, - {1e-151, 553, 401}, - {1e-150, 551, 401}, - {1e-149, 547, 397}, - {1e-148, 544, 395}, - {1e-147, 540, 392}, - {1e-146, 538, 392}, - {1e-145, 534, 388}, - {1e-144, 527, 382}, - {1e-143, 526, 382}, - {1e-142, 521, 379}, - {1e-141, 520, 379}, - {1e-140, 517, 376}, - {1e-139, 514, 375}, - {1e-138, 511, 373}, - {1e-137, 508, 370}, - {1e-136, 504, 368}, - {1e-135, 499, 364}, - {1e-134, 498, 364}, - {1e-133, 493, 360}, - {1e-132, 487, 354}, - {1e-131, 486, 354}, - {1e-130, 482, 352}, - {1e-129, 477, 347}, - {1e-128, 478, 350}, - {1e-127, 473, 346}, - {1e-126, 470, 343}, - {1e-125, 468, 343}, - {1e-124, 464, 339}, - {1e-123, 459, 336}, - {1e-122, 458, 336}, - {1e-121, 452, 330}, - {1e-120, 451, 330}, - {1e-119, 448, 329}, - {1e-118, 444, 325}, - {1e-117, 441, 324}, - {1e-116, 437, 320}, - {1e-115, 431, 316}, - {1e-114, 430, 316}, - {1e-113, 428, 314}, - {1e-112, 424, 311}, - {1e-111, 421, 310}, - {1e-110, 417, 307}, - {1e-109, 414, 304}, - {1e-108, 411, 303}, - {1e-107, 407, 300}, - {1e-106, 405, 298}, - {1e-105, 401, 295}, - {1e-104, 398, 293}, - {1e-103, 395, 291}, - {1e-102, 391, 288}, - {1e-101, 388, 287}, - {1e-100, 381, 281}, - {1e-99, 380, 281}, - {1e-98, 378, 279}, - {1e-97, 375, 278}, - {1e-96, 370, 273}, - {1e-95, 368, 272}, - {1e-94, 364, 269}, - {1e-93, 360, 266}, - {1e-92, 358, 265}, - {1e-91, 355, 264}, - {1e-90, 351, 260}, - {1e-89, 348, 259}, - {1e-88, 345, 256}, - {1e-87, 342, 255}, - {1e-86, 338, 252}, - {1e-85, 334, 248}, - {1e-84, 328, 244}, - {1e-83, 327, 244}, - {1e-82, 320, 237}, - {1e-81, 319, 237}, - {1e-80, 318, 237}, - {1e-79, 313, 233}, - {1e-78, 312, 233}, - {1e-77, 306, 228}, - {1e-76, 305, 228}, - {1e-75, 299, 223}, - {1e-74, 298, 223}, - {1e-73, 295, 221}, - {1e-72, 291, 218}, - {1e-71, 287, 215}, - {1e-70, 285, 214}, - {1e-69, 280, 210}, - {1e-68, 278, 210}, - {1e-67, 275, 207}, - {1e-66, 271, 204}, - {1e-65, 268, 202}, - {1e-64, 265, 200}, - {1e-63, 262, 199}, - {1e-62, 255, 193}, - {1e-61, 254, 193}, - {1e-60, 251, 190}, - {1e-59, 245, 186}, - {1e-58, 244, 186}, - {1e-57, 242, 184}, - {1e-56, 238, 182}, - {1e-55, 235, 179}, - {1e-54, 230, 176}, - {1e-53, 229, 176}, - {1e-52, 221, 169}, - {1e-51, 220, 169}, - {1e-50, 219, 169}, - {1e-49, 215, 165}, - {1e-48, 209, 160}, - {1e-47, 208, 160}, - {1e-46, 205, 159}, - {1e-45, 202, 156}, - {1e-44, 199, 154}, - {1e-43, 195, 152}, - {1e-42, 192, 150}, - {1e-41, 189, 148}, - {1e-40, 183, 142}, - {1e-39, 182, 142}, - {1e-38, 177, 138}, - {1e-37, 175, 138}, - {1e-36, 171, 134}, - {1e-35, 169, 134}, - {1e-34, 165, 130}, - {1e-33, 160, 127}, - {1e-32, 159, 127}, - {1e-31, 148, 117}, - {1e-30, 147, 117}, - {1e-29, 149, 119}, - {1e-28, 146, 117}, - {1e-27, 138, 111}, - {1e-26, 137, 111}, - {1e-25, 136, 111}, - {1e-24, 132, 107}, - {1e-23, 129, 105}, - {1e-22, 125, 103}, - {1e-21, 122, 100}, - {1e-20, 119, 98}, - {1e-19, 114, 94}, - {1e-18, 110, 92}, - {1e-17, 109, 92}, - {1e-16, 104, 87}, - {1e-15, 101, 86}, - {1e-14, 99, 84}, - {1e-13, 95, 82}, - {1e-12, 92, 79}, - {1e-11, 89, 77}, - {1e-10, 86, 76}, - {1e-9, 82, 73}, - {1e-8, 78, 70}, - {1e-7, 73, 65}, - {1e-6, 72, 65}, - {1e-5, 69, 64}, - {1e-4, 66, 62}, - {1e-3, 60, 57}, - {1e-2, 59, 57}, - {1e-1, 55, 54}, - {1e0, 0, 0}, - {1e1, 0, 0}, - {1e2, 0, 0}, - {1e3, 0, 0}, - {1e4, 0, 0}, - {1e5, 0, 0}, - {1e6, 0, 0}, - {1e7, 0, 0}, - {1e8, 0, 0}, - {1e9, 0, 0}, - {1e10, 0, 0}, - {1e11, 0, 0}, - {1e12, 0, 0}, - {1e13, 0, 0}, - {1e14, 0, 0}, - {1e15, 0, 0}, - {1e16, 0, 0}, - {1e17, 0, 0}, - {1e18, 0, 0}, - {1e19, 0, 0}, - {1e20, 0, 0}, - {1e21, 0, 0}, - {1e22, 0, 0}, - {1e23, 0, 22}, - {1e24, 0, 23}, - {1e25, 0, 25}, - {1e26, 0, 26}, - {1e27, 0, 27}, - {1e28, 0, 27}, - {1e29, 0, 28}, - {1e30, 0, 30}, - {1e31, 0, 30}, - {1e32, 0, 32}, - {1e33, 0, 32}, - {1e34, 0, 32}, - {1e35, 0, 34}, - {1e36, 0, 36}, - {1e37, 0, 36}, - {1e38, 0, 37}, - {1e39, 0, 38}, - {1e40, 0, 40}, - {1e41, 0, 41}, - {1e42, 0, 42}, - {1e43, 0, 43}, - {1e44, 0, 44}, - {1e45, 0, 44}, - {1e46, 0, 45}, - {1e47, 0, 47}, - {1e48, 0, 47}, - {1e49, 0, 48}, - {1e50, 0, 49}, - {1e51, 0, 50}, - {1e52, 0, 50}, - {1e53, 0, 50}, - {1e54, 0, 54}, - {1e55, 0, 55}, - {1e56, 0, 56}, - {1e57, 0, 57}, - {1e58, 0, 57}, - {1e59, 0, 58}, - {1e60, 0, 59}, - {1e61, 0, 59}, - {1e62, 0, 62}, - {1e63, 0, 63}, - {1e64, 0, 64}, - {1e65, 0, 64}, - {1e66, 0, 65}, - {1e67, 0, 66}, - {1e68, 0, 67}, - {1e69, 0, 68}, - {1e70, 0, 68}, - {1e71, 0, 71}, - {1e72, 0, 71}, - {1e73, 0, 72}, - {1e74, 0, 73}, - {1e75, 0, 74}, - {1e76, 0, 76}, - {1e77, 0, 76}, - {1e78, 0, 78}, - {1e79, 0, 78}, - {1e80, 0, 80}, - {1e81, 0, 80}, - {1e82, 0, 81}, - {1e83, 0, 83}, - {1e84, 0, 84}, - {1e85, 0, 85}, - {1e86, 0, 85}, - {1e87, 0, 86}, - {1e88, 0, 86}, - {1e89, 0, 88}, - {1e90, 0, 89}, - {1e91, 0, 90}, - {1e92, 0, 92}, - {1e93, 0, 92}, - {1e94, 0, 94}, - {1e95, 0, 94}, - {1e96, 0, 96}, - {1e97, 0, 97}, - {1e98, 0, 97}, - {1e99, 0, 98}, - {1e100, 0, 100}, - {1e101, 0, 100}, - {1e102, 0, 100}, - {1e103, 0, 103}, - {1e104, 0, 103}, - {1e105, 0, 104}, - {1e106, 0, 106}, - {1e107, 0, 106}, - {1e108, 0, 108}, - {1e109, 0, 108}, - {1e110, 0, 110}, - {1e111, 0, 110}, - {1e112, 0, 111}, - {1e113, 0, 113}, - {1e114, 0, 113}, - {1e115, 0, 113}, - {1e116, 0, 113}, - {1e117, 0, 117}, - {1e118, 0, 117}, - {1e119, 0, 118}, - {1e120, 0, 119}, - {1e121, 0, 121}, - {1e122, 0, 122}, - {1e123, 0, 122}, - {1e124, 0, 123}, - {1e125, 0, 124}, - {1e126, 0, 124}, - {1e127, 0, 126}, - {1e128, 0, 126}, - {1e129, 0, 128}, - {1e130, 0, 130}, - {1e131, 0, 130}, - {1e132, 0, 131}, - {1e133, 0, 133}, - {1e134, 0, 133}, - {1e135, 0, 134}, - {1e136, 0, 136}, - {1e137, 0, 137}, - {1e138, 0, 137}, - {1e139, 0, 137}, - {1e140, 0, 140}, - {1e141, 0, 141}, - {1e142, 0, 142}, - {1e143, 0, 143}, - {1e144, 0, 143}, - {1e145, 0, 144}, - {1e146, 0, 145}, - {1e147, 0, 146}, - {1e148, 0, 148}, - {1e149, 0, 148}, - {1e150, 0, 149}, - {1e151, 0, 151}, - {1e152, 0, 152}, - {1e153, 0, 152}, - {1e154, 0, 154}, - {1e155, 0, 155}, - {1e156, 0, 155}, - {1e157, 0, 155}, - {1e158, 0, 157}, - {1e159, 0, 158}, - {1e160, 0, 160}, - {1e161, 0, 161}, - {1e162, 0, 161}, - {1e163, 0, 161}, - {1e164, 0, 164}, - {1e165, 0, 164}, - {1e166, 0, 165}, - {1e167, 0, 167}, - {1e168, 0, 167}, - {1e169, 0, 167}, - {1e170, 0, 170}, - {1e171, 0, 170}, - {1e172, 0, 172}, - {1e173, 0, 173}, - {1e174, 0, 174}, - {1e175, 0, 174}, - {1e176, 0, 176}, - {1e177, 0, 176}, - {1e178, 0, 178}, - {1e179, 0, 178}, - {1e180, 0, 180}, - {1e181, 0, 180}, - {1e182, 0, 182}, - {1e183, 0, 182}, - {1e184, 0, 184}, - {1e185, 0, 184}, - {1e186, 0, 184}, - {1e187, 0, 186}, - {1e188, 0, 188}, - {1e189, 0, 188}, - {1e190, 0, 190}, - {1e191, 0, 190}, - {1e192, 0, 192}, - {1e193, 0, 193}, - {1e194, 0, 193}, - {1e195, 0, 194}, - {1e196, 0, 195}, - {1e197, 0, 195}, - {1e198, 0, 198}, - {1e199, 0, 199}, - {1e200, 0, 199}, - {1e201, 0, 201}, - {1e202, 0, 200}, - {1e203, 0, 202}, - {1e204, 0, 202}, - {1e205, 0, 205}, - {1e206, 0, 206}, - {1e207, 0, 206}, - {1e208, 0, 207}, - {1e209, 0, 209}, - {1e210, 0, 209}, - {1e211, 0, 210}, - {1e212, 0, 211}, - {1e213, 0, 212}, - {1e214, 0, 213}, - {1e215, 0, 214}, - {1e216, 0, 216}, - {1e217, 0, 216}, - {1e218, 0, 217}, - {1e219, 0, 218}, - {1e220, 0, 219}, - {1e221, 0, 221}, - {1e222, 0, 221}, - {1e223, 0, 221}, - {1e224, 0, 223}, - {1e225, 0, 224}, - {1e226, 0, 225}, - {1e227, 0, 225}, - {1e228, 0, 227}, - {1e229, 0, 228}, - {1e230, 0, 230}, - {1e231, 0, 231}, - {1e232, 0, 231}, - {1e233, 0, 232}, - {1e234, 0, 234}, - {1e235, 0, 235}, - {1e236, 0, 235}, - {1e237, 0, 235}, - {1e238, 0, 238}, - {1e239, 0, 238}, - {1e240, 0, 240}, - {1e241, 0, 241}, - {1e242, 0, 241}, - {1e243, 0, 243}, - {1e244, 0, 243}, - {1e245, 0, 245}, - {1e246, 0, 246}, - {1e247, 0, 246}, - {1e248, 0, 248}, - {1e249, 0, 247}, - {1e250, 0, 247}, - {1e251, 0, 251}, - {1e252, 0, 252}, - {1e253, 0, 252}, - {1e254, 0, 252}, - {1e255, 0, 254}, - {1e256, 0, 256}, - {1e257, 0, 256}, - {1e258, 0, 258}, - {1e259, 0, 258}, - {1e260, 0, 260}, - {1e261, 0, 258}, - {1e262, 0, 262}, - {1e263, 0, 262}, - {1e264, 0, 264}, - {1e265, 0, 265}, - {1e266, 0, 266}, - {1e267, 0, 266}, - {1e268, 0, 266}, - {1e269, 0, 269}, - {1e270, 0, 269}, - {1e271, 0, 270}, - {1e272, 0, 272}, - {1e273, 0, 272}, - {1e274, 0, 273}, - {1e275, 0, 274}, - {1e276, 0, 276}, - {1e277, 0, 277}, - {1e278, 0, 277}, - {1e279, 0, 279}, - {1e280, 0, 280}, - {1e281, 0, 280}, - {1e282, 0, 280}, - {1e283, 0, 282}, - {1e284, 0, 284}, - {1e285, 0, 284}, - {1e286, 0, 286}, - {1e287, 0, 287}, - {1e288, 0, 288}, - {1e289, 0, 289}, - {1e290, 0, 289}, - {1e291, 0, 290}, - {1e292, 0, 292}, - {1e293, 0, 292}, - {1e294, 0, 294}, - {1e295, 0, 294}, - {1e296, 0, 294}, - {1e297, 0, 297}, - {1e298, 0, 297}, - {1e299, 0, 299}, - {1e300, 0, 299}, - {1e301, 0, 299}, - {1e302, 0, 302}, - {1e303, 0, 303}, - {1e304, 0, 303}, - {1e305, 0, 303}, - {1e306, 0, 306}, - {1e307, 0, 306}, - {1e308, 0, 308}, -] - -# These values test every binary exponent (which would be more obvious with hexfloats). -# The mantissas were randomly generated. -ALL_BINARY_EXPONENTS = [ - {8.667315560151837e-309, 1074, 765}, - {3.402496288854889e-308, 1072, 764}, - {5.674095874064163e-308, 1068, 760}, - {1.5540526173622352e-307, 1072, 765}, - {1.990320005135143e-307, 1071, 764}, - {5.107418539046847e-307, 1070, 763}, - {9.580341507134765e-307, 1068, 761}, - {2.7686246461533843e-306, 1067, 761}, - {4.123539674247709e-306, 1066, 760}, - {1.0292523314007669e-305, 1065, 760}, - {1.869562966771459e-305, 1065, 760}, - {2.83258275754601e-305, 1063, 758}, - {6.143575467580988e-305, 1061, 756}, - {1.4317575812076783e-304, 1062, 758}, - {1.8736954404407843e-304, 1061, 757}, - {3.8678085703767116e-304, 1060, 756}, - {7.635297514304952e-304, 1058, 754}, - {1.9931833457401843e-303, 1056, 753}, - {5.7104439440441904e-303, 1057, 754}, - {5.845773229837182e-303, 1056, 753}, - {1.6446596413123796e-302, 1054, 752}, - {3.571334515579776e-302, 1054, 752}, - {5.226450761688444e-302, 1053, 751}, - {1.0747997253788843e-301, 1051, 750}, - {1.90892926200005e-301, 1051, 750}, - {6.786272682763782e-301, 1047, 746}, - {1.2172372613102281e-300, 1044, 744}, - {1.7966676643662128e-300, 1042, 742}, - {5.462819694528703e-300, 1047, 747}, - {6.961706248722051e-300, 1043, 743}, - {1.5112507155402445e-299, 1045, 746}, - {2.673980873749012e-299, 1044, 745}, - {8.503369157355244e-299, 1043, 744}, - {1.3233106901096892e-298, 1042, 744}, - {2.129178977672023e-298, 1041, 743}, - {4.178648615235546e-298, 1036, 738}, - {9.216189377840373e-298, 1038, 740}, - {2.0166542228894894e-297, 1036, 739}, - {3.5449747515908894e-297, 1034, 737}, - {8.064939085743458e-297, 1036, 739}, - {2.1182119864764602e-296, 1035, 739}, - {3.820427653349436e-296, 1034, 738}, - {9.166969936802109e-296, 1033, 737}, - {1.0587007370833377e-295, 1031, 736}, - {2.5617734189585968e-295, 1030, 735}, - {6.117667163341597e-295, 1030, 735}, - {1.2442918509206014e-294, 1028, 734}, - {3.100051235126117e-294, 1027, 733}, - {5.514599643126014e-294, 1026, 732}, - {8.019518080011996e-294, 1025, 731}, - {2.2148549407571022e-293, 1022, 729}, - {4.20911452464387e-293, 1024, 731}, - {6.673970944986261e-293, 1022, 729}, - {1.746546364023377e-292, 1021, 729}, - {2.5532945426002905e-292, 1021, 729}, - {7.167199051004838e-292, 1020, 728}, - {1.4331413352279302e-291, 1018, 727}, - {1.6537479214140957e-291, 1018, 727}, - {4.290843909020547e-291, 1017, 726}, - {9.634563122144926e-291, 1014, 723}, - {2.1086057222075156e-290, 1010, 720}, - {3.4206800637910767e-290, 1013, 723}, - {6.629016758967737e-290, 1013, 723}, - {1.352094685757577e-289, 1011, 722}, - {3.065153212531983e-289, 1011, 722}, - {5.074022975467963e-289, 1006, 717}, - {1.5066401531008766e-288, 1009, 721}, - {2.8015937941494583e-288, 1008, 720}, - {5.38303645298669e-288, 1007, 719}, - {8.441234238050258e-288, 1006, 718}, - {1.7229963037415354e-287, 1004, 717}, - {4.998022788892795e-287, 1004, 717}, - {8.728697912491584e-287, 1003, 716}, - {1.9042271010497776e-286, 1002, 716}, - {2.9003728382951163e-286, 1000, 714}, - {6.030230011480532e-286, 999, 713}, - {1.2707290656410452e-285, 997, 712}, - {3.3470583063356332e-285, 998, 713}, - {6.5966578537292035e-285, 997, 712}, - {7.427398668320939e-285, 995, 710}, - {2.5312725644714646e-284, 994, 710}, - {4.7441324100905746e-284, 994, 710}, - {7.352811059453878e-284, 992, 708}, - {1.2773195914029405e-283, 990, 707}, - {3.1336514683809336e-283, 991, 708}, - {4.624339948076099e-283, 990, 707}, - {8.894087772740341e-283, 989, 706}, - {2.3953652083727512e-282, 988, 706}, - {3.761567466326268e-282, 985, 703}, - {1.2928212167160486e-281, 985, 704}, - {2.2480352182123753e-281, 982, 701}, - {3.154850939942071e-281, 983, 702}, - {6.071363984983044e-281, 982, 701}, - {2.1910202165183368e-280, 981, 701}, - {4.3370603492214e-280, 980, 700}, - {6.968471572869319e-280, 980, 700}, - {1.473331115243779e-279, 979, 700}, - {2.66044060949483e-279, 971, 692}, - {5.683973436284207e-279, 976, 697}, - {1.4089452631685327e-278, 976, 698}, - {2.2755564362864927e-278, 973, 695}, - {3.821906858286435e-278, 973, 695}, - {8.103117627864485e-278, 973, 695}, - {1.832473425427903e-277, 970, 693}, - {2.727222054531752e-277, 970, 693}, - {7.882910515028218e-277, 964, 687}, - {1.479332526434952e-276, 966, 690}, - 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{6.842765724941906e+292, 0, 291}, - {1.249825938708993e+293, 0, 293}, - {2.392791615385826e+293, 0, 293}, - {4.152722646899415e+293, 0, 293}, - {6.790906283978802e+293, 0, 293}, - {1.3561785760749324e+294, 0, 294}, - {3.341059095259842e+294, 0, 293}, - {9.977930881477503e+294, 0, 294}, - {1.515106038250912e+295, 0, 294}, - {3.002184910089352e+295, 0, 295}, - {5.876579596327993e+295, 0, 295}, - {1.4003917488295084e+296, 0, 296}, - {3.1684232621942047e+296, 0, 296}, - {3.4747005896842154e+296, 0, 296}, - {7.669723855021269e+296, 0, 296}, - {1.3614131925096533e+297, 0, 297}, - {3.191738550947262e+297, 0, 297}, - {8.888378843987562e+297, 0, 297}, - {1.5112090835975456e+298, 0, 298}, - {2.3682327923940456e+298, 0, 298}, - {5.099780421145732e+298, 0, 298}, - {1.0673033377644726e+299, 0, 298}, - {2.378013021177001e+299, 0, 299}, - {6.554057728282088e+299, 0, 299}, - {8.318933161474208e+299, 0, 299}, - {1.3614082701057758e+300, 0, 300}, - {5.35086581101499e+300, 0, 300}, - {8.494089296675853e+300, 0, 299}, - {1.0890134027784214e+301, 0, 301}, - {2.358927877102592e+301, 0, 301}, - {8.117690363105265e+301, 0, 301}, - {9.341511426794588e+301, 0, 301}, - {2.64210043201936e+302, 0, 302}, - {6.847933389378864e+302, 0, 302}, - {1.1002556200184007e+303, 0, 303}, - {2.5611530892094995e+303, 0, 303}, - {5.076344585537476e+303, 0, 303}, - {8.304487832500949e+303, 0, 303}, - {1.1230804446665463e+304, 0, 304}, - {4.2777559220816043e+304, 0, 304}, - {6.283260967439312e+304, 0, 304}, - {1.3747215164191865e+305, 0, 305}, - {3.3096929273918684e+305, 0, 305}, - {6.171133478197849e+305, 0, 305}, - {1.2292521010494213e+306, 0, 306}, - {2.2862202954633178e+306, 0, 305}, - {3.5065941308845355e+306, 0, 306}, - {1.0940422247589228e+307, 0, 307}, - {2.0068458193014486e+307, 0, 306}, - {2.7914963723745636e+307, 0, 307}, - {6.123699292104195e+307, 0, 307}, - {1.7026387749989901e+308, 0, 308}, -] +require "./ryu_printf_test_cases" struct BigFloat def to_s_with_range(*, point_range : Range = -3..15) diff --git a/spec/std/float_printer/ryu_printf_test_cases.cr b/spec/std/float_printer/ryu_printf_test_cases.cr new file mode 100644 index 000000000000..6c1a3a155692 --- /dev/null +++ b/spec/std/float_printer/ryu_printf_test_cases.cr @@ -0,0 +1,2697 @@ +# Test cases used by `./ryu_printf_spec.cr` + +# The following two lists store: {value, fixed_precision, exp_precision} +# Iterate over them via macros only, otherwise the entire array literal will be +# materialized! +# The original specs contain also the full expected results which would have +# increased the file size by over 18x. Here we assume that `BigFloat#to_s` and +# `BigDecimal#to_s` are always correct, so that we don't have to write the long +# results in the source code. + +# These values test every power of ten that's within the range of doubles. +ALL_POWERS_OF_TEN = [ + {1e-323, 1073, 749}, + {1e-322, 1072, 749}, + {1e-321, 1073, 751}, + {1e-320, 1071, 750}, + {1e-319, 1070, 750}, + {1e-318, 1073, 754}, + {1e-317, 1074, 757}, + {1e-316, 1074, 757}, + {1e-315, 1074, 758}, + {1e-314, 1074, 759}, + {1e-313, 1074, 761}, + {1e-312, 1074, 761}, + {1e-311, 1074, 762}, + {1e-310, 1074, 763}, + {1e-309, 1074, 765}, + {1e-308, 1073, 764}, + {1e-307, 1072, 764}, + {1e-306, 1069, 763}, + {1e-305, 1066, 760}, + {1e-304, 1062, 757}, + {1e-303, 1059, 755}, + {1e-302, 1054, 751}, + {1e-301, 1052, 751}, + {1e-300, 1049, 749}, + {1e-299, 1046, 746}, + {1e-298, 1042, 743}, + {1e-297, 1039, 742}, + {1e-296, 1035, 739}, + {1e-295, 1032, 737}, + {1e-294, 1029, 735}, + {1e-293, 1022, 729}, + {1e-292, 1021, 729}, + {1e-291, 1019, 727}, + {1e-290, 1015, 725}, + {1e-289, 1012, 723}, + {1e-288, 1009, 721}, + {1e-287, 1006, 719}, + {1e-286, 1003, 717}, + {1e-285, 999, 714}, + {1e-284, 996, 712}, + {1e-283, 993, 709}, + {1e-282, 986, 704}, + {1e-281, 985, 704}, + {1e-280, 981, 700}, + {1e-279, 979, 700}, + {1e-278, 976, 697}, + {1e-277, 973, 695}, + {1e-276, 957, 681}, + {1e-275, 966, 690}, + {1e-274, 963, 688}, + {1e-273, 954, 681}, + {1e-272, 956, 683}, + {1e-271, 953, 681}, + {1e-270, 948, 678}, + {1e-269, 944, 674}, + {1e-268, 943, 674}, + {1e-267, 935, 667}, + {1e-266, 934, 667}, + {1e-265, 933, 667}, + {1e-264, 925, 661}, + {1e-263, 924, 661}, + {1e-262, 923, 661}, + {1e-261, 920, 658}, + {1e-260, 916, 655}, + {1e-259, 909, 650}, + {1e-258, 910, 651}, + {1e-257, 904, 646}, + {1e-256, 903, 646}, + {1e-255, 898, 643}, + {1e-254, 894, 639}, + {1e-253, 890, 637}, + {1e-252, 890, 637}, + {1e-251, 886, 635}, + {1e-250, 881, 631}, + {1e-249, 880, 631}, + {1e-248, 876, 627}, + {1e-247, 872, 625}, + {1e-246, 870, 623}, + {1e-245, 863, 617}, + {1e-244, 862, 617}, + {1e-243, 860, 616}, + {1e-242, 850, 607}, + {1e-241, 849, 607}, + {1e-240, 848, 607}, + {1e-239, 845, 606}, + {1e-238, 840, 601}, + {1e-237, 839, 601}, + {1e-236, 835, 599}, + {1e-235, 829, 593}, + {1e-234, 828, 593}, + {1e-233, 827, 593}, + {1e-232, 823, 591}, + {1e-231, 819, 587}, + {1e-230, 817, 587}, + {1e-229, 813, 584}, + {1e-228, 810, 582}, + {1e-227, 807, 579}, + {1e-226, 803, 576}, + {1e-225, 799, 573}, + {1e-224, 796, 572}, + {1e-223, 792, 568}, + {1e-222, 790, 568}, + {1e-221, 787, 566}, + {1e-220, 783, 562}, + {1e-219, 777, 558}, + {1e-218, 776, 558}, + {1e-217, 773, 556}, + {1e-216, 768, 552}, + {1e-215, 767, 552}, + {1e-214, 763, 548}, + {1e-213, 758, 544}, + {1e-212, 757, 544}, + {1e-211, 753, 542}, + {1e-210, 747, 537}, + {1e-209, 746, 537}, + {1e-208, 740, 532}, + {1e-207, 740, 532}, + {1e-206, 737, 531}, + {1e-205, 731, 526}, + {1e-204, 730, 526}, + {1e-203, 723, 520}, + {1e-202, 722, 520}, + {1e-201, 720, 518}, + {1e-200, 715, 514}, + {1e-199, 714, 514}, + {1e-198, 709, 510}, + {1e-197, 706, 508}, + {1e-196, 703, 507}, + {1e-195, 699, 504}, + {1e-194, 697, 503}, + {1e-193, 693, 500}, + {1e-192, 689, 497}, + {1e-191, 684, 493}, + {1e-190, 683, 493}, + {1e-189, 680, 491}, + {1e-188, 676, 487}, + {1e-187, 672, 485}, + {1e-186, 669, 482}, + {1e-185, 666, 480}, + {1e-184, 663, 479}, + {1e-183, 660, 477}, + {1e-182, 655, 473}, + {1e-181, 654, 473}, + {1e-180, 647, 467}, + {1e-179, 646, 467}, + {1e-178, 641, 462}, + {1e-177, 640, 462}, + {1e-176, 632, 455}, + {1e-175, 631, 455}, + {1e-174, 630, 455}, + {1e-173, 624, 451}, + {1e-172, 623, 451}, + {1e-171, 618, 446}, + {1e-170, 617, 446}, + {1e-169, 614, 445}, + {1e-168, 610, 442}, + {1e-167, 607, 440}, + {1e-166, 604, 438}, + {1e-165, 600, 435}, + {1e-164, 597, 432}, + {1e-163, 594, 430}, + {1e-162, 591, 428}, + {1e-161, 587, 426}, + {1e-160, 582, 421}, + {1e-159, 581, 421}, + {1e-158, 577, 419}, + {1e-157, 574, 416}, + {1e-156, 571, 415}, + {1e-155, 567, 412}, + {1e-154, 563, 408}, + {1e-153, 561, 408}, + {1e-152, 557, 405}, + {1e-151, 553, 401}, + {1e-150, 551, 401}, + {1e-149, 547, 397}, + {1e-148, 544, 395}, + {1e-147, 540, 392}, + {1e-146, 538, 392}, + {1e-145, 534, 388}, + {1e-144, 527, 382}, + {1e-143, 526, 382}, + {1e-142, 521, 379}, + {1e-141, 520, 379}, + {1e-140, 517, 376}, + {1e-139, 514, 375}, + {1e-138, 511, 373}, + {1e-137, 508, 370}, + {1e-136, 504, 368}, + {1e-135, 499, 364}, + {1e-134, 498, 364}, + {1e-133, 493, 360}, + {1e-132, 487, 354}, + {1e-131, 486, 354}, + {1e-130, 482, 352}, + {1e-129, 477, 347}, + {1e-128, 478, 350}, + {1e-127, 473, 346}, + {1e-126, 470, 343}, + {1e-125, 468, 343}, + {1e-124, 464, 339}, + {1e-123, 459, 336}, + {1e-122, 458, 336}, + {1e-121, 452, 330}, + {1e-120, 451, 330}, + {1e-119, 448, 329}, + {1e-118, 444, 325}, + {1e-117, 441, 324}, + {1e-116, 437, 320}, + {1e-115, 431, 316}, + {1e-114, 430, 316}, + {1e-113, 428, 314}, + {1e-112, 424, 311}, + {1e-111, 421, 310}, + {1e-110, 417, 307}, + {1e-109, 414, 304}, + {1e-108, 411, 303}, + {1e-107, 407, 300}, + {1e-106, 405, 298}, + {1e-105, 401, 295}, + {1e-104, 398, 293}, + {1e-103, 395, 291}, + {1e-102, 391, 288}, + {1e-101, 388, 287}, + {1e-100, 381, 281}, + {1e-99, 380, 281}, + {1e-98, 378, 279}, + {1e-97, 375, 278}, + {1e-96, 370, 273}, + {1e-95, 368, 272}, + {1e-94, 364, 269}, + {1e-93, 360, 266}, + {1e-92, 358, 265}, + {1e-91, 355, 264}, + {1e-90, 351, 260}, + {1e-89, 348, 259}, + {1e-88, 345, 256}, + {1e-87, 342, 255}, + {1e-86, 338, 252}, + {1e-85, 334, 248}, + {1e-84, 328, 244}, + {1e-83, 327, 244}, + {1e-82, 320, 237}, + {1e-81, 319, 237}, + {1e-80, 318, 237}, + {1e-79, 313, 233}, + {1e-78, 312, 233}, + {1e-77, 306, 228}, + {1e-76, 305, 228}, + {1e-75, 299, 223}, + {1e-74, 298, 223}, + {1e-73, 295, 221}, + {1e-72, 291, 218}, + {1e-71, 287, 215}, + {1e-70, 285, 214}, + {1e-69, 280, 210}, + {1e-68, 278, 210}, + {1e-67, 275, 207}, + {1e-66, 271, 204}, + {1e-65, 268, 202}, + {1e-64, 265, 200}, + {1e-63, 262, 199}, + {1e-62, 255, 193}, + {1e-61, 254, 193}, + {1e-60, 251, 190}, + {1e-59, 245, 186}, + {1e-58, 244, 186}, + {1e-57, 242, 184}, + {1e-56, 238, 182}, + {1e-55, 235, 179}, + {1e-54, 230, 176}, + {1e-53, 229, 176}, + {1e-52, 221, 169}, + {1e-51, 220, 169}, + {1e-50, 219, 169}, + {1e-49, 215, 165}, + {1e-48, 209, 160}, + {1e-47, 208, 160}, + {1e-46, 205, 159}, + {1e-45, 202, 156}, + {1e-44, 199, 154}, + {1e-43, 195, 152}, + {1e-42, 192, 150}, + {1e-41, 189, 148}, + {1e-40, 183, 142}, + {1e-39, 182, 142}, + {1e-38, 177, 138}, + {1e-37, 175, 138}, + {1e-36, 171, 134}, + {1e-35, 169, 134}, + {1e-34, 165, 130}, + {1e-33, 160, 127}, + {1e-32, 159, 127}, + {1e-31, 148, 117}, + {1e-30, 147, 117}, + {1e-29, 149, 119}, + {1e-28, 146, 117}, + {1e-27, 138, 111}, + {1e-26, 137, 111}, + {1e-25, 136, 111}, + {1e-24, 132, 107}, + {1e-23, 129, 105}, + {1e-22, 125, 103}, + {1e-21, 122, 100}, + {1e-20, 119, 98}, + {1e-19, 114, 94}, + {1e-18, 110, 92}, + {1e-17, 109, 92}, + {1e-16, 104, 87}, + {1e-15, 101, 86}, + {1e-14, 99, 84}, + {1e-13, 95, 82}, + {1e-12, 92, 79}, + {1e-11, 89, 77}, + {1e-10, 86, 76}, + {1e-9, 82, 73}, + {1e-8, 78, 70}, + {1e-7, 73, 65}, + {1e-6, 72, 65}, + {1e-5, 69, 64}, + {1e-4, 66, 62}, + {1e-3, 60, 57}, + {1e-2, 59, 57}, + {1e-1, 55, 54}, + {1e0, 0, 0}, + {1e1, 0, 0}, + {1e2, 0, 0}, + {1e3, 0, 0}, + {1e4, 0, 0}, + {1e5, 0, 0}, + {1e6, 0, 0}, + {1e7, 0, 0}, + {1e8, 0, 0}, + {1e9, 0, 0}, + {1e10, 0, 0}, + {1e11, 0, 0}, + {1e12, 0, 0}, + {1e13, 0, 0}, + {1e14, 0, 0}, + {1e15, 0, 0}, + {1e16, 0, 0}, + {1e17, 0, 0}, + {1e18, 0, 0}, + {1e19, 0, 0}, + {1e20, 0, 0}, + {1e21, 0, 0}, + {1e22, 0, 0}, + {1e23, 0, 22}, + {1e24, 0, 23}, + {1e25, 0, 25}, + {1e26, 0, 26}, + {1e27, 0, 27}, + {1e28, 0, 27}, + {1e29, 0, 28}, + {1e30, 0, 30}, + {1e31, 0, 30}, + {1e32, 0, 32}, + {1e33, 0, 32}, + {1e34, 0, 32}, + {1e35, 0, 34}, + {1e36, 0, 36}, + {1e37, 0, 36}, + {1e38, 0, 37}, + {1e39, 0, 38}, + {1e40, 0, 40}, + {1e41, 0, 41}, + {1e42, 0, 42}, + {1e43, 0, 43}, + {1e44, 0, 44}, + {1e45, 0, 44}, + {1e46, 0, 45}, + {1e47, 0, 47}, + {1e48, 0, 47}, + {1e49, 0, 48}, + {1e50, 0, 49}, + {1e51, 0, 50}, + {1e52, 0, 50}, + {1e53, 0, 50}, + {1e54, 0, 54}, + {1e55, 0, 55}, + {1e56, 0, 56}, + {1e57, 0, 57}, + {1e58, 0, 57}, + {1e59, 0, 58}, + {1e60, 0, 59}, + {1e61, 0, 59}, + {1e62, 0, 62}, + {1e63, 0, 63}, + {1e64, 0, 64}, + {1e65, 0, 64}, + {1e66, 0, 65}, + {1e67, 0, 66}, + {1e68, 0, 67}, + {1e69, 0, 68}, + {1e70, 0, 68}, + {1e71, 0, 71}, + {1e72, 0, 71}, + {1e73, 0, 72}, + {1e74, 0, 73}, + {1e75, 0, 74}, + {1e76, 0, 76}, + {1e77, 0, 76}, + {1e78, 0, 78}, + {1e79, 0, 78}, + {1e80, 0, 80}, + {1e81, 0, 80}, + {1e82, 0, 81}, + {1e83, 0, 83}, + {1e84, 0, 84}, + {1e85, 0, 85}, + {1e86, 0, 85}, + {1e87, 0, 86}, + {1e88, 0, 86}, + {1e89, 0, 88}, + {1e90, 0, 89}, + {1e91, 0, 90}, + {1e92, 0, 92}, + {1e93, 0, 92}, + {1e94, 0, 94}, + {1e95, 0, 94}, + {1e96, 0, 96}, + {1e97, 0, 97}, + {1e98, 0, 97}, + {1e99, 0, 98}, + {1e100, 0, 100}, + {1e101, 0, 100}, + {1e102, 0, 100}, + {1e103, 0, 103}, + {1e104, 0, 103}, + {1e105, 0, 104}, + {1e106, 0, 106}, + {1e107, 0, 106}, + {1e108, 0, 108}, + {1e109, 0, 108}, + {1e110, 0, 110}, + {1e111, 0, 110}, + {1e112, 0, 111}, + {1e113, 0, 113}, + {1e114, 0, 113}, + {1e115, 0, 113}, + {1e116, 0, 113}, + {1e117, 0, 117}, + {1e118, 0, 117}, + {1e119, 0, 118}, + {1e120, 0, 119}, + {1e121, 0, 121}, + {1e122, 0, 122}, + {1e123, 0, 122}, + {1e124, 0, 123}, + {1e125, 0, 124}, + {1e126, 0, 124}, + {1e127, 0, 126}, + {1e128, 0, 126}, + {1e129, 0, 128}, + {1e130, 0, 130}, + {1e131, 0, 130}, + {1e132, 0, 131}, + {1e133, 0, 133}, + {1e134, 0, 133}, + {1e135, 0, 134}, + {1e136, 0, 136}, + {1e137, 0, 137}, + {1e138, 0, 137}, + {1e139, 0, 137}, + {1e140, 0, 140}, + {1e141, 0, 141}, + {1e142, 0, 142}, + {1e143, 0, 143}, + {1e144, 0, 143}, + {1e145, 0, 144}, + {1e146, 0, 145}, + {1e147, 0, 146}, + {1e148, 0, 148}, + {1e149, 0, 148}, + {1e150, 0, 149}, + {1e151, 0, 151}, + {1e152, 0, 152}, + {1e153, 0, 152}, + {1e154, 0, 154}, + {1e155, 0, 155}, + {1e156, 0, 155}, + {1e157, 0, 155}, + {1e158, 0, 157}, + {1e159, 0, 158}, + {1e160, 0, 160}, + {1e161, 0, 161}, + {1e162, 0, 161}, + {1e163, 0, 161}, + {1e164, 0, 164}, + {1e165, 0, 164}, + {1e166, 0, 165}, + {1e167, 0, 167}, + {1e168, 0, 167}, + {1e169, 0, 167}, + {1e170, 0, 170}, + {1e171, 0, 170}, + {1e172, 0, 172}, + {1e173, 0, 173}, + {1e174, 0, 174}, + {1e175, 0, 174}, + {1e176, 0, 176}, + {1e177, 0, 176}, + {1e178, 0, 178}, + {1e179, 0, 178}, + {1e180, 0, 180}, + {1e181, 0, 180}, + {1e182, 0, 182}, + {1e183, 0, 182}, + {1e184, 0, 184}, + {1e185, 0, 184}, + {1e186, 0, 184}, + {1e187, 0, 186}, + {1e188, 0, 188}, + {1e189, 0, 188}, + {1e190, 0, 190}, + {1e191, 0, 190}, + {1e192, 0, 192}, + {1e193, 0, 193}, + {1e194, 0, 193}, + {1e195, 0, 194}, + {1e196, 0, 195}, + {1e197, 0, 195}, + {1e198, 0, 198}, + {1e199, 0, 199}, + {1e200, 0, 199}, + {1e201, 0, 201}, + {1e202, 0, 200}, + {1e203, 0, 202}, + {1e204, 0, 202}, + {1e205, 0, 205}, + {1e206, 0, 206}, + {1e207, 0, 206}, + {1e208, 0, 207}, + {1e209, 0, 209}, + {1e210, 0, 209}, + {1e211, 0, 210}, + {1e212, 0, 211}, + {1e213, 0, 212}, + {1e214, 0, 213}, + {1e215, 0, 214}, + {1e216, 0, 216}, + {1e217, 0, 216}, + {1e218, 0, 217}, + {1e219, 0, 218}, + {1e220, 0, 219}, + {1e221, 0, 221}, + {1e222, 0, 221}, + {1e223, 0, 221}, + {1e224, 0, 223}, + {1e225, 0, 224}, + {1e226, 0, 225}, + {1e227, 0, 225}, + {1e228, 0, 227}, + {1e229, 0, 228}, + {1e230, 0, 230}, + {1e231, 0, 231}, + {1e232, 0, 231}, + {1e233, 0, 232}, + {1e234, 0, 234}, + {1e235, 0, 235}, + {1e236, 0, 235}, + {1e237, 0, 235}, + {1e238, 0, 238}, + {1e239, 0, 238}, + {1e240, 0, 240}, + {1e241, 0, 241}, + {1e242, 0, 241}, + {1e243, 0, 243}, + {1e244, 0, 243}, + {1e245, 0, 245}, + {1e246, 0, 246}, + {1e247, 0, 246}, + {1e248, 0, 248}, + {1e249, 0, 247}, + {1e250, 0, 247}, + {1e251, 0, 251}, + {1e252, 0, 252}, + {1e253, 0, 252}, + {1e254, 0, 252}, + {1e255, 0, 254}, + {1e256, 0, 256}, + {1e257, 0, 256}, + {1e258, 0, 258}, + {1e259, 0, 258}, + {1e260, 0, 260}, + {1e261, 0, 258}, + {1e262, 0, 262}, + {1e263, 0, 262}, + {1e264, 0, 264}, + {1e265, 0, 265}, + {1e266, 0, 266}, + {1e267, 0, 266}, + {1e268, 0, 266}, + {1e269, 0, 269}, + {1e270, 0, 269}, + {1e271, 0, 270}, + {1e272, 0, 272}, + {1e273, 0, 272}, + {1e274, 0, 273}, + {1e275, 0, 274}, + {1e276, 0, 276}, + {1e277, 0, 277}, + {1e278, 0, 277}, + {1e279, 0, 279}, + {1e280, 0, 280}, + {1e281, 0, 280}, + {1e282, 0, 280}, + {1e283, 0, 282}, + {1e284, 0, 284}, + {1e285, 0, 284}, + {1e286, 0, 286}, + {1e287, 0, 287}, + {1e288, 0, 288}, + {1e289, 0, 289}, + {1e290, 0, 289}, + {1e291, 0, 290}, + {1e292, 0, 292}, + {1e293, 0, 292}, + {1e294, 0, 294}, + {1e295, 0, 294}, + {1e296, 0, 294}, + {1e297, 0, 297}, + {1e298, 0, 297}, + {1e299, 0, 299}, + {1e300, 0, 299}, + {1e301, 0, 299}, + {1e302, 0, 302}, + {1e303, 0, 303}, + {1e304, 0, 303}, + {1e305, 0, 303}, + {1e306, 0, 306}, + {1e307, 0, 306}, + {1e308, 0, 308}, +] of _ + +# These values test every binary exponent (which would be more obvious with hexfloats). +# The mantissas were randomly generated. +ALL_BINARY_EXPONENTS = [ + {8.667315560151837e-309, 1074, 765}, + {3.402496288854889e-308, 1072, 764}, + {5.674095874064163e-308, 1068, 760}, + {1.5540526173622352e-307, 1072, 765}, + {1.990320005135143e-307, 1071, 764}, + {5.107418539046847e-307, 1070, 763}, + {9.580341507134765e-307, 1068, 761}, + {2.7686246461533843e-306, 1067, 761}, + {4.123539674247709e-306, 1066, 760}, + {1.0292523314007669e-305, 1065, 760}, + {1.869562966771459e-305, 1065, 760}, + {2.83258275754601e-305, 1063, 758}, + {6.143575467580988e-305, 1061, 756}, + {1.4317575812076783e-304, 1062, 758}, + {1.8736954404407843e-304, 1061, 757}, + {3.8678085703767116e-304, 1060, 756}, + {7.635297514304952e-304, 1058, 754}, + {1.9931833457401843e-303, 1056, 753}, + {5.7104439440441904e-303, 1057, 754}, + {5.845773229837182e-303, 1056, 753}, + {1.6446596413123796e-302, 1054, 752}, + {3.571334515579776e-302, 1054, 752}, + {5.226450761688444e-302, 1053, 751}, + {1.0747997253788843e-301, 1051, 750}, + {1.90892926200005e-301, 1051, 750}, + {6.786272682763782e-301, 1047, 746}, + {1.2172372613102281e-300, 1044, 744}, + {1.7966676643662128e-300, 1042, 742}, + {5.462819694528703e-300, 1047, 747}, + {6.961706248722051e-300, 1043, 743}, + {1.5112507155402445e-299, 1045, 746}, + {2.673980873749012e-299, 1044, 745}, + {8.503369157355244e-299, 1043, 744}, + {1.3233106901096892e-298, 1042, 744}, + {2.129178977672023e-298, 1041, 743}, + {4.178648615235546e-298, 1036, 738}, + {9.216189377840373e-298, 1038, 740}, + {2.0166542228894894e-297, 1036, 739}, + {3.5449747515908894e-297, 1034, 737}, + {8.064939085743458e-297, 1036, 739}, + {2.1182119864764602e-296, 1035, 739}, + {3.820427653349436e-296, 1034, 738}, + {9.166969936802109e-296, 1033, 737}, + {1.0587007370833377e-295, 1031, 736}, + {2.5617734189585968e-295, 1030, 735}, + {6.117667163341597e-295, 1030, 735}, + {1.2442918509206014e-294, 1028, 734}, + {3.100051235126117e-294, 1027, 733}, + {5.514599643126014e-294, 1026, 732}, + {8.019518080011996e-294, 1025, 731}, + {2.2148549407571022e-293, 1022, 729}, + {4.20911452464387e-293, 1024, 731}, + {6.673970944986261e-293, 1022, 729}, + {1.746546364023377e-292, 1021, 729}, + {2.5532945426002905e-292, 1021, 729}, + {7.167199051004838e-292, 1020, 728}, + {1.4331413352279302e-291, 1018, 727}, + {1.6537479214140957e-291, 1018, 727}, + {4.290843909020547e-291, 1017, 726}, + {9.634563122144926e-291, 1014, 723}, + {2.1086057222075156e-290, 1010, 720}, + {3.4206800637910767e-290, 1013, 723}, + {6.629016758967737e-290, 1013, 723}, + {1.352094685757577e-289, 1011, 722}, + {3.065153212531983e-289, 1011, 722}, + {5.074022975467963e-289, 1006, 717}, + {1.5066401531008766e-288, 1009, 721}, + {2.8015937941494583e-288, 1008, 720}, + {5.38303645298669e-288, 1007, 719}, + {8.441234238050258e-288, 1006, 718}, + {1.7229963037415354e-287, 1004, 717}, + {4.998022788892795e-287, 1004, 717}, + {8.728697912491584e-287, 1003, 716}, + {1.9042271010497776e-286, 1002, 716}, + {2.9003728382951163e-286, 1000, 714}, + {6.030230011480532e-286, 999, 713}, + {1.2707290656410452e-285, 997, 712}, + {3.3470583063356332e-285, 998, 713}, + {6.5966578537292035e-285, 997, 712}, + {7.427398668320939e-285, 995, 710}, + {2.5312725644714646e-284, 994, 710}, + {4.7441324100905746e-284, 994, 710}, + {7.352811059453878e-284, 992, 708}, + {1.2773195914029405e-283, 990, 707}, + {3.1336514683809336e-283, 991, 708}, + {4.624339948076099e-283, 990, 707}, + {8.894087772740341e-283, 989, 706}, + {2.3953652083727512e-282, 988, 706}, + {3.761567466326268e-282, 985, 703}, + {1.2928212167160486e-281, 985, 704}, + {2.2480352182123753e-281, 982, 701}, + {3.154850939942071e-281, 983, 702}, + {6.071363984983044e-281, 982, 701}, + {2.1910202165183368e-280, 981, 701}, + {4.3370603492214e-280, 980, 700}, + {6.968471572869319e-280, 980, 700}, + {1.473331115243779e-279, 979, 700}, + {2.66044060949483e-279, 971, 692}, + {5.683973436284207e-279, 976, 697}, + {1.4089452631685327e-278, 976, 698}, + {2.2755564362864927e-278, 973, 695}, + {3.821906858286435e-278, 973, 695}, + {8.103117627864485e-278, 973, 695}, + {1.832473425427903e-277, 970, 693}, + {2.727222054531752e-277, 970, 693}, + {7.882910515028218e-277, 964, 687}, + {1.479332526434952e-276, 966, 690}, + {2.2180410620430226e-276, 968, 692}, + {5.690649743658698e-276, 966, 690}, + {1.4121156100358157e-275, 966, 691}, + {2.6685811370633676e-275, 965, 690}, + {4.6692815012344967e-275, 963, 688}, + {9.834548098669551e-275, 958, 683}, + {1.8600057734718372e-274, 962, 688}, + {2.811775675630843e-274, 961, 687}, + {6.27142702954425e-274, 959, 685}, + {1.0250975871333601e-273, 959, 686}, + {2.5253325080332935e-273, 958, 685}, + {6.913296125147658e-273, 957, 684}, + {9.747372287629775e-273, 956, 683}, + {1.9721670909138485e-272, 953, 681}, + {4.469048372679605e-272, 953, 681}, + {1.0205638445192075e-271, 952, 681}, + {1.5594946591458144e-271, 952, 681}, + {2.3721122629194564e-271, 949, 678}, + {5.551135919284155e-271, 944, 673}, + {1.0734739674446298e-270, 947, 677}, + {2.4398554262702667e-270, 948, 678}, + {6.8642158764630495e-270, 942, 672}, + {1.2055339469240307e-269, 941, 672}, + {1.5235738192618518e-269, 945, 676}, + {4.043876497442965e-269, 944, 675}, + {8.743556251142875e-269, 941, 672}, + {1.4649312749107113e-268, 941, 673}, + {3.98040680032538e-268, 941, 673}, + {8.586286660615516e-268, 938, 670}, + {1.657418018730156e-267, 939, 672}, + {3.613106834542997e-267, 937, 670}, + {5.9183241751764955e-267, 936, 669}, + {1.1798475245572565e-266, 935, 669}, + {3.084511928870661e-266, 934, 668}, + {4.1367697432326765e-266, 930, 664}, + {1.1356367562498619e-265, 933, 668}, + {1.5494624584252724e-265, 928, 663}, + {3.028575537095104e-265, 931, 666}, + {9.42740333348115e-265, 930, 665}, + {1.729174836691517e-264, 929, 665}, + {2.1531241335994103e-264, 928, 664}, + {7.094381157920946e-264, 927, 663}, + {1.037244238361319e-263, 922, 659}, + {1.6682266784627316e-263, 925, 662}, + {5.516139500818587e-263, 924, 661}, + {1.1456020464232508e-262, 919, 657}, + {2.066981873698563e-262, 919, 657}, + {2.7219184652406806e-262, 921, 659}, + {5.081283542674735e-262, 918, 656}, + {1.6876650530578208e-261, 917, 656}, + {2.276883127404377e-261, 916, 655}, + {6.29191834725416e-261, 917, 656}, + {9.114070309202437e-261, 915, 654}, + {2.5433112499173348e-260, 909, 649}, + {4.8383034142174994e-260, 914, 654}, + {9.557162041008455e-260, 913, 653}, + {2.3218163991190385e-259, 912, 653}, + {4.4322942901196377e-259, 911, 652}, + {7.248624545665186e-259, 904, 645}, + {1.4667081257360905e-258, 909, 651}, + {3.832202635359104e-258, 908, 650}, + {6.943148025853397e-258, 905, 647}, + {9.18729939902564e-258, 906, 648}, + {3.0584908958671776e-257, 905, 648}, + {3.332730679024704e-257, 901, 644}, + {7.495951055510854e-257, 902, 645}, + {1.6420266726944826e-256, 900, 644}, + {3.9297951542678785e-256, 900, 644}, + {8.581799124622545e-256, 896, 640}, + {1.3408011506316038e-255, 899, 644}, + {3.074598537137766e-255, 898, 643}, + {8.304947313449564e-255, 893, 638}, + {1.4474411243713317e-254, 893, 639}, + {1.9586457971591685e-254, 895, 641}, + {4.686715367492042e-254, 894, 640}, + {1.3394037849881335e-253, 893, 640}, + {2.3636119615931954e-253, 892, 639}, + {2.941610445695594e-253, 891, 638}, + {5.910628843543644e-253, 890, 637}, + {1.6810396848558274e-252, 889, 637}, + {3.105977744955943e-252, 887, 635}, + {5.296557380144569e-252, 886, 634}, + {1.4534181673457758e-251, 886, 635}, + {2.3938479247234097e-251, 885, 634}, + {5.13191114201037e-251, 884, 633}, + {8.74142907505523e-251, 883, 632}, + {2.0810847152471556e-250, 881, 631}, + {3.470210840000035e-250, 879, 629}, + {7.63186683615216e-250, 879, 629}, + {1.5834019337617896e-249, 872, 623}, + {2.760497402953147e-249, 876, 627}, + {4.645119455324602e-249, 877, 628}, + {9.91990200069646e-249, 874, 625}, + {2.5293584256227207e-248, 874, 626}, + {6.890528046616735e-248, 874, 626}, + {9.9700406511611e-248, 870, 622}, + {2.0741563200652303e-247, 872, 625}, + 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