From 9f9d7f7f55b4a67295398e0d6d6a53364f7d8cc0 Mon Sep 17 00:00:00 2001 From: Matthias Huerbe Date: Fri, 25 Sep 2026 11:55:36 +0200 Subject: [PATCH 1/3] ported Eisel-Lemire's fast float algorithm to odin also fixed string the float conversion producing wrong results. --- core/strconv/LICENSE_fast_float | 31 + core/strconv/fast_float.odin | 784 ++++++++++++++++++++++ core/strconv/strconv.odin | 112 +++- tests/core/strconv/test_core_strconv.odin | 111 ++- 4 files changed, 1003 insertions(+), 35 deletions(-) create mode 100644 core/strconv/LICENSE_fast_float create mode 100644 core/strconv/fast_float.odin diff --git a/core/strconv/LICENSE_fast_float b/core/strconv/LICENSE_fast_float new file mode 100644 index 000000000..8ddef69e7 --- /dev/null +++ b/core/strconv/LICENSE_fast_float @@ -0,0 +1,31 @@ +This license applies to the Eisel-Lemire code and the _POW5_128 table in +fast_float.odin, which are ported from ffc.h and fast_float. + + ffc.h: https://github.com/kolemannix/ffc.h + fast_float: https://github.com/fastfloat/fast_float + +Copyright (c) 2021 The fast_float authors + +Boost Software License - Version 1.0 - August 17th, 2003 + +Permission is hereby granted, free of charge, to any person or organization +obtaining a copy of the software and accompanying documentation covered by +this license (the "Software") to use, reproduce, display, distribute, +execute, and transmit the Software, and to prepare derivative works of the +Software, and to permit third-parties to whom the Software is furnished to +do so, all subject to the following: + +The copyright notices in the Software and this entire statement, including +the above license grant, this restriction and the following disclaimer, +must be included in all copies of the Software, in whole or in part, and +all derivative works of the Software, unless such copies or derivative +works are solely in the form of machine-executable object code generated by +a source language processor. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT +SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE +FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +DEALINGS IN THE SOFTWARE. diff --git a/core/strconv/fast_float.odin b/core/strconv/fast_float.odin new file mode 100644 index 000000000..a68184cad --- /dev/null +++ b/core/strconv/fast_float.odin @@ -0,0 +1,784 @@ +package strconv + +import "core:math/bits" + +/* + Eisel-Lemire decimal to binary conversion. + + Ported from ffc.h (https://github.com/kolemannix/ffc.h) + Made available under the Boost Software License 1.0, + see LICENSE_fast_float in this package. + + List of contributors: + Daniel Lemire, João Paulo Magalhaes: Original fast_float implementation + Koleman Nix: C port (ffc.h) +*/ + +/* + References: + - Daniel Lemire, "Number Parsing at a Gigabyte per Second", + Software: Practice and Experience 51 (8), 2021. https://arxiv.org/abs/2101.11408 + - Noble Mushtak, Daniel Lemire, "Fast Number Parsing Without Fallback", + Software: Practice and Experience 53 (7), 2023. https://arxiv.org/abs/2212.06644 +*/ + +@(private="file") +_POW5_128_MIN_EXP :: -342 + +/* +Computes the `T` closest to `w * 10^q`, rounding ties to even. + +`w` must be the exact decimal significand. When the input had more digits than fit +in a `u64`, call this with both the truncated significand `w` and `w + 1`: if both +calls return the same bits, the result is correct. Otherwise, use a slow path. + +**Inputs** +- T: `f32` or `f64` +- q: The decimal exponent +- w: The decimal significand + +**Returns** +- The IEEE-754 bit pattern of the result, without the sign bit. An overflow gives the bit pattern of infinity. +*/ +fast_float_compute_float :: proc "contextless" ($T: typeid, q: int, w: u64) -> u64 where T == f32 || T == f64 #no_bounds_check { + when T == f64 { + MANT_BITS :: 52 + MIN_EXPONENT :: -1023 + INFINITE_POWER :: 0x7ff + SMALLEST_POW10 :: -342 + LARGEST_POW10 :: 308 + MIN_EXP_ROUND_EVEN :: -4 + MAX_EXP_ROUND_EVEN :: 23 + } else { + MANT_BITS :: 23 + MIN_EXPONENT :: -127 + INFINITE_POWER :: 0xff + SMALLEST_POW10 :: -64 + LARGEST_POW10 :: 38 + MIN_EXP_ROUND_EVEN :: -17 + MAX_EXP_ROUND_EVEN :: 10 + } + + // w <= max(u64) and q < SMALLEST_POW10 always rounds to zero. + if w == 0 || q < SMALLEST_POW10 { + return 0 + } + if q > LARGEST_POW10 { + return INFINITE_POWER << MANT_BITS + } + + lz := bits.count_leading_zeros(w) + wn := w << lz // normalized so the top bit is set + + // Compute a 128-bit approximation of wn * 5^q. We need the product to be accurate + // to MANT_BITS+3 bits. If the lower bits of the high word are all ones, the error + // in the first product could affect them, so we refine the result with the lower + // half of the power of five. + PRECISION_MASK :: max(u64) >> (MANT_BITS + 3) + pow5 := &_POW5_128[q - _POW5_128_MIN_EXP] + hi, lo := bits.mul_u64(wn, pow5[0]) + if hi & PRECISION_MASK == PRECISION_MASK { + hi2, _ := bits.mul_u64(wn, pow5[1]) + lo += hi2 + if hi2 > lo { + hi += 1 + } + } + // Mushtak & Lemire (2023) prove that this product is always accurate enough. + + upperbit := int(hi >> 63) + shift := uint(upperbit + 64 - MANT_BITS - 3) + mantissa := hi >> shift + // ((152170 + 65536) * q) >> 16 is floor(q * log2(10)) for |q| < 1650. + power2 := (((152170 + 65536) * q) >> 16) + 63 + upperbit - int(lz) - MIN_EXPONENT + + if power2 <= 0 { + // Subnormal result. + if -power2 + 1 >= 64 { + return 0 + } + mantissa >>= uint(-power2 + 1) + mantissa += mantissa & 1 // round up + mantissa >>= 1 + // Rounding up can give the smallest normal number. Then the hidden bit + // is set, and it is also the lowest bit of the exponent. + return mantissa + } + + // We usually round up. If the value is exactly halfway between two floats, + // and the lower float is even, we must round down. An exact halfway value is + // possible only for a small range of exponents. + if lo <= 1 && q >= MIN_EXP_ROUND_EVEN && q <= MAX_EXP_ROUND_EVEN && mantissa & 3 == 1 { + if mantissa << shift == hi { + mantissa &~= 1 + } + } + mantissa += mantissa & 1 // round up + mantissa >>= 1 + if mantissa >= 2 << MANT_BITS { + mantissa = 1 << MANT_BITS + power2 += 1 + } + mantissa &~= 1 << MANT_BITS + if power2 >= INFINITE_POWER { + return INFINITE_POWER << MANT_BITS + } + return mantissa | u64(power2) << MANT_BITS +} + +// 128-bit truncated mantissas of 5^-342 to 5^308, with the most significant +// bit set. Generated by fast_float script/table_generation.py. +@(private="file", rodata) +_POW5_128 := [651][2]u64{ + {0xeef453d6923bd65a, 0x113faa2906a13b3f}, // 5^-342 + {0x9558b4661b6565f8, 0x4ac7ca59a424c507}, // 5^-341 + {0xbaaee17fa23ebf76, 0x5d79bcf00d2df649}, // 5^-340 + {0xe95a99df8ace6f53, 0xf4d82c2c107973dc}, // 5^-339 + {0x91d8a02bb6c10594, 0x79071b9b8a4be869}, // 5^-338 + {0xb64ec836a47146f9, 0x9748e2826cdee284}, // 5^-337 + {0xe3e27a444d8d98b7, 0xfd1b1b2308169b25}, // 5^-336 + {0x8e6d8c6ab0787f72, 0xfe30f0f5e50e20f7}, // 5^-335 + {0xb208ef855c969f4f, 0xbdbd2d335e51a935}, // 5^-334 + {0xde8b2b66b3bc4723, 0xad2c788035e61382}, // 5^-333 + {0x8b16fb203055ac76, 0x4c3bcb5021afcc31}, // 5^-332 + {0xaddcb9e83c6b1793, 0xdf4abe242a1bbf3d}, // 5^-331 + {0xd953e8624b85dd78, 0xd71d6dad34a2af0d}, // 5^-330 + {0x87d4713d6f33aa6b, 0x8672648c40e5ad68}, // 5^-329 + {0xa9c98d8ccb009506, 0x680efdaf511f18c2}, // 5^-328 + {0xd43bf0effdc0ba48, 0x0212bd1b2566def2}, // 5^-327 + {0x84a57695fe98746d, 0x014bb630f7604b57}, // 5^-326 + {0xa5ced43b7e3e9188, 0x419ea3bd35385e2d}, // 5^-325 + {0xcf42894a5dce35ea, 0x52064cac828675b9}, // 5^-324 + {0x818995ce7aa0e1b2, 0x7343efebd1940993}, // 5^-323 + {0xa1ebfb4219491a1f, 0x1014ebe6c5f90bf8}, // 5^-322 + {0xca66fa129f9b60a6, 0xd41a26e077774ef6}, // 5^-321 + {0xfd00b897478238d0, 0x8920b098955522b4}, // 5^-320 + {0x9e20735e8cb16382, 0x55b46e5f5d5535b0}, // 5^-319 + {0xc5a890362fddbc62, 0xeb2189f734aa831d}, // 5^-318 + {0xf712b443bbd52b7b, 0xa5e9ec7501d523e4}, // 5^-317 + {0x9a6bb0aa55653b2d, 0x47b233c92125366e}, // 5^-316 + {0xc1069cd4eabe89f8, 0x999ec0bb696e840a}, // 5^-315 + {0xf148440a256e2c76, 0xc00670ea43ca250d}, // 5^-314 + {0x96cd2a865764dbca, 0x380406926a5e5728}, // 5^-313 + {0xbc807527ed3e12bc, 0xc605083704f5ecf2}, // 5^-312 + {0xeba09271e88d976b, 0xf7864a44c633682e}, // 5^-311 + {0x93445b8731587ea3, 0x7ab3ee6afbe0211d}, // 5^-310 + {0xb8157268fdae9e4c, 0x5960ea05bad82964}, // 5^-309 + {0xe61acf033d1a45df, 0x6fb92487298e33bd}, // 5^-308 + {0x8fd0c16206306bab, 0xa5d3b6d479f8e056}, // 5^-307 + {0xb3c4f1ba87bc8696, 0x8f48a4899877186c}, // 5^-306 + {0xe0b62e2929aba83c, 0x331acdabfe94de87}, // 5^-305 + {0x8c71dcd9ba0b4925, 0x9ff0c08b7f1d0b14}, // 5^-304 + {0xaf8e5410288e1b6f, 0x07ecf0ae5ee44dd9}, // 5^-303 + {0xdb71e91432b1a24a, 0xc9e82cd9f69d6150}, // 5^-302 + {0x892731ac9faf056e, 0xbe311c083a225cd2}, // 5^-301 + {0xab70fe17c79ac6ca, 0x6dbd630a48aaf406}, // 5^-300 + {0xd64d3d9db981787d, 0x092cbbccdad5b108}, // 5^-299 + {0x85f0468293f0eb4e, 0x25bbf56008c58ea5}, // 5^-298 + {0xa76c582338ed2621, 0xaf2af2b80af6f24e}, // 5^-297 + {0xd1476e2c07286faa, 0x1af5af660db4aee1}, // 5^-296 + {0x82cca4db847945ca, 0x50d98d9fc890ed4d}, // 5^-295 + {0xa37fce126597973c, 0xe50ff107bab528a0}, // 5^-294 + {0xcc5fc196fefd7d0c, 0x1e53ed49a96272c8}, // 5^-293 + {0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7a}, // 5^-292 + {0x9faacf3df73609b1, 0x77b191618c54e9ac}, // 5^-291 + {0xc795830d75038c1d, 0xd59df5b9ef6a2417}, // 5^-290 + {0xf97ae3d0d2446f25, 0x4b0573286b44ad1d}, // 5^-289 + {0x9becce62836ac577, 0x4ee367f9430aec32}, // 5^-288 + {0xc2e801fb244576d5, 0x229c41f793cda73f}, // 5^-287 + {0xf3a20279ed56d48a, 0x6b43527578c1110f}, // 5^-286 + {0x9845418c345644d6, 0x830a13896b78aaa9}, // 5^-285 + {0xbe5691ef416bd60c, 0x23cc986bc656d553}, // 5^-284 + {0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa8}, // 5^-283 + {0x94b3a202eb1c3f39, 0x7bf7d71432f3d6a9}, // 5^-282 + {0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc53}, // 5^-281 + {0xe858ad248f5c22c9, 0xd1b3400f8f9cff68}, // 5^-280 + {0x91376c36d99995be, 0x23100809b9c21fa1}, // 5^-279 + {0xb58547448ffffb2d, 0xabd40a0c2832a78a}, // 5^-278 + {0xe2e69915b3fff9f9, 0x16c90c8f323f516c}, // 5^-277 + {0x8dd01fad907ffc3b, 0xae3da7d97f6792e3}, // 5^-276 + {0xb1442798f49ffb4a, 0x99cd11cfdf41779c}, // 5^-275 + {0xdd95317f31c7fa1d, 0x40405643d711d583}, // 5^-274 + {0x8a7d3eef7f1cfc52, 0x482835ea666b2572}, // 5^-273 + {0xad1c8eab5ee43b66, 0xda3243650005eecf}, // 5^-272 + {0xd863b256369d4a40, 0x90bed43e40076a82}, // 5^-271 + {0x873e4f75e2224e68, 0x5a7744a6e804a291}, // 5^-270 + {0xa90de3535aaae202, 0x711515d0a205cb36}, // 5^-269 + {0xd3515c2831559a83, 0x0d5a5b44ca873e03}, // 5^-268 + {0x8412d9991ed58091, 0xe858790afe9486c2}, // 5^-267 + {0xa5178fff668ae0b6, 0x626e974dbe39a872}, // 5^-266 + {0xce5d73ff402d98e3, 0xfb0a3d212dc8128f}, // 5^-265 + {0x80fa687f881c7f8e, 0x7ce66634bc9d0b99}, // 5^-264 + {0xa139029f6a239f72, 0x1c1fffc1ebc44e80}, // 5^-263 + {0xc987434744ac874e, 0xa327ffb266b56220}, // 5^-262 + {0xfbe9141915d7a922, 0x4bf1ff9f0062baa8}, // 5^-261 + {0x9d71ac8fada6c9b5, 0x6f773fc3603db4a9}, // 5^-260 + {0xc4ce17b399107c22, 0xcb550fb4384d21d3}, // 5^-259 + {0xf6019da07f549b2b, 0x7e2a53a146606a48}, // 5^-258 + {0x99c102844f94e0fb, 0x2eda7444cbfc426d}, // 5^-257 + {0xc0314325637a1939, 0xfa911155fefb5308}, // 5^-256 + {0xf03d93eebc589f88, 0x793555ab7eba27ca}, // 5^-255 + {0x96267c7535b763b5, 0x4bc1558b2f3458de}, // 5^-254 + {0xbbb01b9283253ca2, 0x9eb1aaedfb016f16}, // 5^-253 + {0xea9c227723ee8bcb, 0x465e15a979c1cadc}, // 5^-252 + {0x92a1958a7675175f, 0x0bfacd89ec191ec9}, // 5^-251 + {0xb749faed14125d36, 0xcef980ec671f667b}, // 5^-250 + {0xe51c79a85916f484, 0x82b7e12780e7401a}, // 5^-249 + {0x8f31cc0937ae58d2, 0xd1b2ecb8b0908810}, // 5^-248 + {0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa15}, // 5^-247 + {0xdfbdcece67006ac9, 0x67a791e093e1d49a}, // 5^-246 + {0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e0}, // 5^-245 + {0xaecc49914078536d, 0x58fae9f773886e18}, // 5^-244 + {0xda7f5bf590966848, 0xaf39a475506a899e}, // 5^-243 + {0x888f99797a5e012d, 0x6d8406c952429603}, // 5^-242 + {0xaab37fd7d8f58178, 0xc8e5087ba6d33b83}, // 5^-241 + {0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a64}, // 5^-240 + {0x855c3be0a17fcd26, 0x5cf2eea09a55067f}, // 5^-239 + {0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481e}, // 5^-238 + {0xd0601d8efc57b08b, 0xf13b94daf124da26}, // 5^-237 + {0x823c12795db6ce57, 0x76c53d08d6b70858}, // 5^-236 + {0xa2cb1717b52481ed, 0x54768c4b0c64ca6e}, // 5^-235 + {0xcb7ddcdda26da268, 0xa9942f5dcf7dfd09}, // 5^-234 + {0xfe5d54150b090b02, 0xd3f93b35435d7c4c}, // 5^-233 + {0x9efa548d26e5a6e1, 0xc47bc5014a1a6daf}, // 5^-232 + {0xc6b8e9b0709f109a, 0x359ab6419ca1091b}, // 5^-231 + {0xf867241c8cc6d4c0, 0xc30163d203c94b62}, // 5^-230 + {0x9b407691d7fc44f8, 0x79e0de63425dcf1d}, // 5^-229 + {0xc21094364dfb5636, 0x985915fc12f542e4}, // 5^-228 + {0xf294b943e17a2bc4, 0x3e6f5b7b17b2939d}, // 5^-227 + {0x979cf3ca6cec5b5a, 0xa705992ceecf9c42}, // 5^-226 + {0xbd8430bd08277231, 0x50c6ff782a838353}, // 5^-225 + {0xece53cec4a314ebd, 0xa4f8bf5635246428}, // 5^-224 + {0x940f4613ae5ed136, 0x871b7795e136be99}, // 5^-223 + {0xb913179899f68584, 0x28e2557b59846e3f}, // 5^-222 + {0xe757dd7ec07426e5, 0x331aeada2fe589cf}, // 5^-221 + {0x9096ea6f3848984f, 0x3ff0d2c85def7621}, // 5^-220 + {0xb4bca50b065abe63, 0x0fed077a756b53a9}, // 5^-219 + {0xe1ebce4dc7f16dfb, 0xd3e8495912c62894}, // 5^-218 + {0x8d3360f09cf6e4bd, 0x64712dd7abbbd95c}, // 5^-217 + {0xb080392cc4349dec, 0xbd8d794d96aacfb3}, // 5^-216 + {0xdca04777f541c567, 0xecf0d7a0fc5583a0}, // 5^-215 + {0x89e42caaf9491b60, 0xf41686c49db57244}, // 5^-214 + {0xac5d37d5b79b6239, 0x311c2875c522ced5}, // 5^-213 + {0xd77485cb25823ac7, 0x7d633293366b828b}, // 5^-212 + {0x86a8d39ef77164bc, 0xae5dff9c02033197}, // 5^-211 + {0xa8530886b54dbdeb, 0xd9f57f830283fdfc}, // 5^-210 + {0xd267caa862a12d66, 0xd072df63c324fd7b}, // 5^-209 + {0x8380dea93da4bc60, 0x4247cb9e59f71e6d}, // 5^-208 + {0xa46116538d0deb78, 0x52d9be85f074e608}, // 5^-207 + {0xcd795be870516656, 0x67902e276c921f8b}, // 5^-206 + {0x806bd9714632dff6, 0x00ba1cd8a3db53b6}, // 5^-205 + {0xa086cfcd97bf97f3, 0x80e8a40eccd228a4}, // 5^-204 + {0xc8a883c0fdaf7df0, 0x6122cd128006b2cd}, // 5^-203 + {0xfad2a4b13d1b5d6c, 0x796b805720085f81}, // 5^-202 + {0x9cc3a6eec6311a63, 0xcbe3303674053bb0}, // 5^-201 + {0xc3f490aa77bd60fc, 0xbedbfc4411068a9c}, // 5^-200 + {0xf4f1b4d515acb93b, 0xee92fb5515482d44}, // 5^-199 + {0x991711052d8bf3c5, 0x751bdd152d4d1c4a}, // 5^-198 + {0xbf5cd54678eef0b6, 0xd262d45a78a0635d}, // 5^-197 + {0xef340a98172aace4, 0x86fb897116c87c34}, // 5^-196 + {0x9580869f0e7aac0e, 0xd45d35e6ae3d4da0}, // 5^-195 + {0xbae0a846d2195712, 0x8974836059cca109}, // 5^-194 + {0xe998d258869facd7, 0x2bd1a438703fc94b}, // 5^-193 + {0x91ff83775423cc06, 0x7b6306a34627ddcf}, // 5^-192 + {0xb67f6455292cbf08, 0x1a3bc84c17b1d542}, // 5^-191 + {0xe41f3d6a7377eeca, 0x20caba5f1d9e4a93}, // 5^-190 + {0x8e938662882af53e, 0x547eb47b7282ee9c}, // 5^-189 + {0xb23867fb2a35b28d, 0xe99e619a4f23aa43}, // 5^-188 + {0xdec681f9f4c31f31, 0x6405fa00e2ec94d4}, // 5^-187 + {0x8b3c113c38f9f37e, 0xde83bc408dd3dd04}, // 5^-186 + {0xae0b158b4738705e, 0x9624ab50b148d445}, // 5^-185 + {0xd98ddaee19068c76, 0x3badd624dd9b0957}, // 5^-184 + {0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d6}, // 5^-183 + {0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4c}, // 5^-182 + {0xd47487cc8470652b, 0x7647c3200069671f}, // 5^-181 + {0x84c8d4dfd2c63f3b, 0x29ecd9f40041e073}, // 5^-180 + {0xa5fb0a17c777cf09, 0xf468107100525890}, // 5^-179 + {0xcf79cc9db955c2cc, 0x7182148d4066eeb4}, // 5^-178 + {0x81ac1fe293d599bf, 0xc6f14cd848405530}, // 5^-177 + {0xa21727db38cb002f, 0xb8ada00e5a506a7c}, // 5^-176 + {0xca9cf1d206fdc03b, 0xa6d90811f0e4851c}, // 5^-175 + {0xfd442e4688bd304a, 0x908f4a166d1da663}, // 5^-174 + {0x9e4a9cec15763e2e, 0x9a598e4e043287fe}, // 5^-173 + {0xc5dd44271ad3cdba, 0x40eff1e1853f29fd}, // 5^-172 + {0xf7549530e188c128, 0xd12bee59e68ef47c}, // 5^-171 + {0x9a94dd3e8cf578b9, 0x82bb74f8301958ce}, // 5^-170 + {0xc13a148e3032d6e7, 0xe36a52363c1faf01}, // 5^-169 + {0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac1}, // 5^-168 + {0x96f5600f15a7b7e5, 0x29ab103a5ef8c0b9}, // 5^-167 + {0xbcb2b812db11a5de, 0x7415d448f6b6f0e7}, // 5^-166 + {0xebdf661791d60f56, 0x111b495b3464ad21}, // 5^-165 + {0x936b9fcebb25c995, 0xcab10dd900beec34}, // 5^-164 + {0xb84687c269ef3bfb, 0x3d5d514f40eea742}, // 5^-163 + {0xe65829b3046b0afa, 0x0cb4a5a3112a5112}, // 5^-162 + {0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ab}, // 5^-161 + {0xb3f4e093db73a093, 0x59ed216765690f56}, // 5^-160 + {0xe0f218b8d25088b8, 0x306869c13ec3532c}, // 5^-159 + {0x8c974f7383725573, 0x1e414218c73a13fb}, // 5^-158 + {0xafbd2350644eeacf, 0xe5d1929ef90898fa}, // 5^-157 + {0xdbac6c247d62a583, 0xdf45f746b74abf39}, // 5^-156 + {0x894bc396ce5da772, 0x6b8bba8c328eb783}, // 5^-155 + {0xab9eb47c81f5114f, 0x066ea92f3f326564}, // 5^-154 + {0xd686619ba27255a2, 0xc80a537b0efefebd}, // 5^-153 + {0x8613fd0145877585, 0xbd06742ce95f5f36}, // 5^-152 + {0xa798fc4196e952e7, 0x2c48113823b73704}, // 5^-151 + {0xd17f3b51fca3a7a0, 0xf75a15862ca504c5}, // 5^-150 + {0x82ef85133de648c4, 0x9a984d73dbe722fb}, // 5^-149 + {0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebba}, // 5^-148 + {0xcc963fee10b7d1b3, 0x318df905079926a8}, // 5^-147 + {0xffbbcfe994e5c61f, 0xfdf17746497f7052}, // 5^-146 + {0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa633}, // 5^-145 + {0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc0}, // 5^-144 + {0xf9bd690a1b68637b, 0x3dfdce7aa3c673b0}, // 5^-143 + {0x9c1661a651213e2d, 0x06bea10ca65c084e}, // 5^-142 + {0xc31bfa0fe5698db8, 0x486e494fcff30a62}, // 5^-141 + {0xf3e2f893dec3f126, 0x5a89dba3c3efccfa}, // 5^-140 + {0x986ddb5c6b3a76b7, 0xf89629465a75e01c}, // 5^-139 + {0xbe89523386091465, 0xf6bbb397f1135823}, // 5^-138 + {0xee2ba6c0678b597f, 0x746aa07ded582e2c}, // 5^-137 + {0x94db483840b717ef, 0xa8c2a44eb4571cdc}, // 5^-136 + {0xba121a4650e4ddeb, 0x92f34d62616ce413}, // 5^-135 + {0xe896a0d7e51e1566, 0x77b020baf9c81d17}, // 5^-134 + {0x915e2486ef32cd60, 0x0ace1474dc1d122e}, // 5^-133 + {0xb5b5ada8aaff80b8, 0x0d819992132456ba}, // 5^-132 + {0xe3231912d5bf60e6, 0x10e1fff697ed6c69}, // 5^-131 + {0x8df5efabc5979c8f, 0xca8d3ffa1ef463c1}, // 5^-130 + {0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb2}, // 5^-129 + {0xddd0467c64bce4a0, 0xac7cb3f6d05ddbde}, // 5^-128 + {0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96b}, // 5^-127 + {0xad4ab7112eb3929d, 0x86c16c98d2c953c6}, // 5^-126 + {0xd89d64d57a607744, 0xe871c7bf077ba8b7}, // 5^-125 + {0x87625f056c7c4a8b, 0x11471cd764ad4972}, // 5^-124 + {0xa93af6c6c79b5d2d, 0xd598e40d3dd89bcf}, // 5^-123 + {0xd389b47879823479, 0x4aff1d108d4ec2c3}, // 5^-122 + {0x843610cb4bf160cb, 0xcedf722a585139ba}, // 5^-121 + {0xa54394fe1eedb8fe, 0xc2974eb4ee658828}, // 5^-120 + {0xce947a3da6a9273e, 0x733d226229feea32}, // 5^-119 + {0x811ccc668829b887, 0x0806357d5a3f525f}, // 5^-118 + {0xa163ff802a3426a8, 0xca07c2dcb0cf26f7}, // 5^-117 + {0xc9bcff6034c13052, 0xfc89b393dd02f0b5}, // 5^-116 + {0xfc2c3f3841f17c67, 0xbbac2078d443ace2}, // 5^-115 + {0x9d9ba7832936edc0, 0xd54b944b84aa4c0d}, // 5^-114 + {0xc5029163f384a931, 0x0a9e795e65d4df11}, // 5^-113 + {0xf64335bcf065d37d, 0x4d4617b5ff4a16d5}, // 5^-112 + {0x99ea0196163fa42e, 0x504bced1bf8e4e45}, // 5^-111 + {0xc06481fb9bcf8d39, 0xe45ec2862f71e1d6}, // 5^-110 + {0xf07da27a82c37088, 0x5d767327bb4e5a4c}, // 5^-109 + {0x964e858c91ba2655, 0x3a6a07f8d510f86f}, // 5^-108 + {0xbbe226efb628afea, 0x890489f70a55368b}, // 5^-107 + {0xeadab0aba3b2dbe5, 0x2b45ac74ccea842e}, // 5^-106 + {0x92c8ae6b464fc96f, 0x3b0b8bc90012929d}, // 5^-105 + {0xb77ada0617e3bbcb, 0x09ce6ebb40173744}, // 5^-104 + {0xe55990879ddcaabd, 0xcc420a6a101d0515}, // 5^-103 + {0x8f57fa54c2a9eab6, 0x9fa946824a12232d}, // 5^-102 + {0xb32df8e9f3546564, 0x47939822dc96abf9}, // 5^-101 + {0xdff9772470297ebd, 0x59787e2b93bc56f7}, // 5^-100 + {0x8bfbea76c619ef36, 0x57eb4edb3c55b65a}, // 5^-99 + {0xaefae51477a06b03, 0xede622920b6b23f1}, // 5^-98 + {0xdab99e59958885c4, 0xe95fab368e45eced}, // 5^-97 + {0x88b402f7fd75539b, 0x11dbcb0218ebb414}, // 5^-96 + {0xaae103b5fcd2a881, 0xd652bdc29f26a119}, // 5^-95 + {0xd59944a37c0752a2, 0x4be76d3346f0495f}, // 5^-94 + {0x857fcae62d8493a5, 0x6f70a4400c562ddb}, // 5^-93 + {0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb952}, // 5^-92 + {0xd097ad07a71f26b2, 0x7e2000a41346a7a7}, // 5^-91 + {0x825ecc24c873782f, 0x8ed400668c0c28c8}, // 5^-90 + {0xa2f67f2dfa90563b, 0x728900802f0f32fa}, // 5^-89 + {0xcbb41ef979346bca, 0x4f2b40a03ad2ffb9}, // 5^-88 + {0xfea126b7d78186bc, 0xe2f610c84987bfa8}, // 5^-87 + {0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7c9}, // 5^-86 + {0xc6ede63fa05d3143, 0x91503d1c79720dbb}, // 5^-85 + {0xf8a95fcf88747d94, 0x75a44c6397ce912a}, // 5^-84 + {0x9b69dbe1b548ce7c, 0xc986afbe3ee11aba}, // 5^-83 + {0xc24452da229b021b, 0xfbe85badce996168}, // 5^-82 + {0xf2d56790ab41c2a2, 0xfae27299423fb9c3}, // 5^-81 + {0x97c560ba6b0919a5, 0xdccd879fc967d41a}, // 5^-80 + {0xbdb6b8e905cb600f, 0x5400e987bbc1c920}, // 5^-79 + {0xed246723473e3813, 0x290123e9aab23b68}, // 5^-78 + {0x9436c0760c86e30b, 0xf9a0b6720aaf6521}, // 5^-77 + {0xb94470938fa89bce, 0xf808e40e8d5b3e69}, // 5^-76 + {0xe7958cb87392c2c2, 0xb60b1d1230b20e04}, // 5^-75 + {0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c2}, // 5^-74 + {0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af3}, // 5^-73 + {0xe2280b6c20dd5232, 0x25c6da63c38de1b0}, // 5^-72 + {0x8d590723948a535f, 0x579c487e5a38ad0e}, // 5^-71 + {0xb0af48ec79ace837, 0x2d835a9df0c6d851}, // 5^-70 + {0xdcdb1b2798182244, 0xf8e431456cf88e65}, // 5^-69 + {0x8a08f0f8bf0f156b, 0x1b8e9ecb641b58ff}, // 5^-68 + {0xac8b2d36eed2dac5, 0xe272467e3d222f3f}, // 5^-67 + {0xd7adf884aa879177, 0x5b0ed81dcc6abb0f}, // 5^-66 + {0x86ccbb52ea94baea, 0x98e947129fc2b4e9}, // 5^-65 + {0xa87fea27a539e9a5, 0x3f2398d747b36224}, // 5^-64 + {0xd29fe4b18e88640e, 0x8eec7f0d19a03aad}, // 5^-63 + {0x83a3eeeef9153e89, 0x1953cf68300424ac}, // 5^-62 + {0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd7}, // 5^-61 + {0xcdb02555653131b6, 0x3792f412cb06794d}, // 5^-60 + {0x808e17555f3ebf11, 0xe2bbd88bbee40bd0}, // 5^-59 + {0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec4}, // 5^-58 + {0xc8de047564d20a8b, 0xf245825a5a445275}, // 5^-57 + {0xfb158592be068d2e, 0xeed6e2f0f0d56712}, // 5^-56 + {0x9ced737bb6c4183d, 0x55464dd69685606b}, // 5^-55 + {0xc428d05aa4751e4c, 0xaa97e14c3c26b886}, // 5^-54 + {0xf53304714d9265df, 0xd53dd99f4b3066a8}, // 5^-53 + {0x993fe2c6d07b7fab, 0xe546a8038efe4029}, // 5^-52 + {0xbf8fdb78849a5f96, 0xde98520472bdd033}, // 5^-51 + {0xef73d256a5c0f77c, 0x963e66858f6d4440}, // 5^-50 + {0x95a8637627989aad, 0xdde7001379a44aa8}, // 5^-49 + {0xbb127c53b17ec159, 0x5560c018580d5d52}, // 5^-48 + {0xe9d71b689dde71af, 0xaab8f01e6e10b4a6}, // 5^-47 + {0x9226712162ab070d, 0xcab3961304ca70e8}, // 5^-46 + {0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d22}, // 5^-45 + {0xe45c10c42a2b3b05, 0x8cb89a7db77c506a}, // 5^-44 + {0x8eb98a7a9a5b04e3, 0x77f3608e92adb242}, // 5^-43 + {0xb267ed1940f1c61c, 0x55f038b237591ed3}, // 5^-42 + {0xdf01e85f912e37a3, 0x6b6c46dec52f6688}, // 5^-41 + {0x8b61313bbabce2c6, 0x2323ac4b3b3da015}, // 5^-40 + {0xae397d8aa96c1b77, 0xabec975e0a0d081a}, // 5^-39 + {0xd9c7dced53c72255, 0x96e7bd358c904a21}, // 5^-38 + {0x881cea14545c7575, 0x7e50d64177da2e54}, // 5^-37 + {0xaa242499697392d2, 0xdde50bd1d5d0b9e9}, // 5^-36 + {0xd4ad2dbfc3d07787, 0x955e4ec64b44e864}, // 5^-35 + {0x84ec3c97da624ab4, 0xbd5af13bef0b113e}, // 5^-34 + {0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58e}, // 5^-33 + {0xcfb11ead453994ba, 0x67de18eda5814af2}, // 5^-32 + {0x81ceb32c4b43fcf4, 0x80eacf948770ced7}, // 5^-31 + {0xa2425ff75e14fc31, 0xa1258379a94d028d}, // 5^-30 + {0xcad2f7f5359a3b3e, 0x096ee45813a04330}, // 5^-29 + {0xfd87b5f28300ca0d, 0x8bca9d6e188853fc}, // 5^-28 + {0x9e74d1b791e07e48, 0x775ea264cf55347e}, // 5^-27 + {0xc612062576589dda, 0x95364afe032a819e}, // 5^-26 + {0xf79687aed3eec551, 0x3a83ddbd83f52205}, // 5^-25 + {0x9abe14cd44753b52, 0xc4926a9672793543}, // 5^-24 + {0xc16d9a0095928a27, 0x75b7053c0f178294}, // 5^-23 + {0xf1c90080baf72cb1, 0x5324c68b12dd6339}, // 5^-22 + {0x971da05074da7bee, 0xd3f6fc16ebca5e04}, // 5^-21 + {0xbce5086492111aea, 0x88f4bb1ca6bcf585}, // 5^-20 + {0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6}, // 5^-19 + {0x9392ee8e921d5d07, 0x3aff322e62439fd0}, // 5^-18 + {0xb877aa3236a4b449, 0x09befeb9fad487c3}, // 5^-17 + {0xe69594bec44de15b, 0x4c2ebe687989a9b4}, // 5^-16 + {0x901d7cf73ab0acd9, 0x0f9d37014bf60a11}, // 5^-15 + {0xb424dc35095cd80f, 0x538484c19ef38c95}, // 5^-14 + {0xe12e13424bb40e13, 0x2865a5f206b06fba}, // 5^-13 + {0x8cbccc096f5088cb, 0xf93f87b7442e45d4}, // 5^-12 + {0xafebff0bcb24aafe, 0xf78f69a51539d749}, // 5^-11 + {0xdbe6fecebdedd5be, 0xb573440e5a884d1c}, // 5^-10 + {0x89705f4136b4a597, 0x31680a88f8953031}, // 5^-9 + {0xabcc77118461cefc, 0xfdc20d2b36ba7c3e}, // 5^-8 + {0xd6bf94d5e57a42bc, 0x3d32907604691b4d}, // 5^-7 + {0x8637bd05af6c69b5, 0xa63f9a49c2c1b110}, // 5^-6 + {0xa7c5ac471b478423, 0x0fcf80dc33721d54}, // 5^-5 + {0xd1b71758e219652b, 0xd3c36113404ea4a9}, // 5^-4 + {0x83126e978d4fdf3b, 0x645a1cac083126ea}, // 5^-3 + {0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4}, // 5^-2 + {0xcccccccccccccccc, 0xcccccccccccccccd}, // 5^-1 + {0x8000000000000000, 0x0000000000000000}, // 5^0 + {0xa000000000000000, 0x0000000000000000}, // 5^1 + {0xc800000000000000, 0x0000000000000000}, // 5^2 + {0xfa00000000000000, 0x0000000000000000}, // 5^3 + {0x9c40000000000000, 0x0000000000000000}, // 5^4 + {0xc350000000000000, 0x0000000000000000}, // 5^5 + {0xf424000000000000, 0x0000000000000000}, // 5^6 + {0x9896800000000000, 0x0000000000000000}, // 5^7 + {0xbebc200000000000, 0x0000000000000000}, // 5^8 + {0xee6b280000000000, 0x0000000000000000}, // 5^9 + {0x9502f90000000000, 0x0000000000000000}, // 5^10 + {0xba43b74000000000, 0x0000000000000000}, // 5^11 + {0xe8d4a51000000000, 0x0000000000000000}, // 5^12 + {0x9184e72a00000000, 0x0000000000000000}, // 5^13 + {0xb5e620f480000000, 0x0000000000000000}, // 5^14 + {0xe35fa931a0000000, 0x0000000000000000}, // 5^15 + {0x8e1bc9bf04000000, 0x0000000000000000}, // 5^16 + {0xb1a2bc2ec5000000, 0x0000000000000000}, // 5^17 + {0xde0b6b3a76400000, 0x0000000000000000}, // 5^18 + {0x8ac7230489e80000, 0x0000000000000000}, // 5^19 + {0xad78ebc5ac620000, 0x0000000000000000}, // 5^20 + {0xd8d726b7177a8000, 0x0000000000000000}, // 5^21 + {0x878678326eac9000, 0x0000000000000000}, // 5^22 + {0xa968163f0a57b400, 0x0000000000000000}, // 5^23 + {0xd3c21bcecceda100, 0x0000000000000000}, // 5^24 + {0x84595161401484a0, 0x0000000000000000}, // 5^25 + {0xa56fa5b99019a5c8, 0x0000000000000000}, // 5^26 + {0xcecb8f27f4200f3a, 0x0000000000000000}, // 5^27 + {0x813f3978f8940984, 0x4000000000000000}, // 5^28 + {0xa18f07d736b90be5, 0x5000000000000000}, // 5^29 + {0xc9f2c9cd04674ede, 0xa400000000000000}, // 5^30 + {0xfc6f7c4045812296, 0x4d00000000000000}, // 5^31 + {0x9dc5ada82b70b59d, 0xf020000000000000}, // 5^32 + {0xc5371912364ce305, 0x6c28000000000000}, // 5^33 + {0xf684df56c3e01bc6, 0xc732000000000000}, // 5^34 + {0x9a130b963a6c115c, 0x3c7f400000000000}, // 5^35 + {0xc097ce7bc90715b3, 0x4b9f100000000000}, // 5^36 + {0xf0bdc21abb48db20, 0x1e86d40000000000}, // 5^37 + {0x96769950b50d88f4, 0x1314448000000000}, // 5^38 + {0xbc143fa4e250eb31, 0x17d955a000000000}, // 5^39 + {0xeb194f8e1ae525fd, 0x5dcfab0800000000}, // 5^40 + {0x92efd1b8d0cf37be, 0x5aa1cae500000000}, // 5^41 + {0xb7abc627050305ad, 0xf14a3d9e40000000}, // 5^42 + {0xe596b7b0c643c719, 0x6d9ccd05d0000000}, // 5^43 + {0x8f7e32ce7bea5c6f, 0xe4820023a2000000}, // 5^44 + {0xb35dbf821ae4f38b, 0xdda2802c8a800000}, // 5^45 + {0xe0352f62a19e306e, 0xd50b2037ad200000}, // 5^46 + {0x8c213d9da502de45, 0x4526f422cc340000}, // 5^47 + {0xaf298d050e4395d6, 0x9670b12b7f410000}, // 5^48 + {0xdaf3f04651d47b4c, 0x3c0cdd765f114000}, // 5^49 + {0x88d8762bf324cd0f, 0xa5880a69fb6ac800}, // 5^50 + {0xab0e93b6efee0053, 0x8eea0d047a457a00}, // 5^51 + {0xd5d238a4abe98068, 0x72a4904598d6d880}, // 5^52 + {0x85a36366eb71f041, 0x47a6da2b7f864750}, // 5^53 + {0xa70c3c40a64e6c51, 0x999090b65f67d924}, // 5^54 + {0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d}, // 5^55 + {0x82818f1281ed449f, 0xbff8f10e7a8921a4}, // 5^56 + {0xa321f2d7226895c7, 0xaff72d52192b6a0d}, // 5^57 + {0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490}, // 5^58 + {0xfee50b7025c36a08, 0x02f236d04753d5b4}, // 5^59 + {0x9f4f2726179a2245, 0x01d762422c946590}, // 5^60 + {0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5}, // 5^61 + {0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2}, // 5^62 + {0x9b934c3b330c8577, 0x63cc55f49f88eb2f}, // 5^63 + {0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb}, // 5^64 + {0xf316271c7fc3908a, 0x8bef464e3945ef7a}, // 5^65 + {0x97edd871cfda3a56, 0x97758bf0e3cbb5ac}, // 5^66 + {0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317}, // 5^67 + {0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd}, // 5^68 + {0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a}, // 5^69 + {0xb975d6b6ee39e436, 0xb3e2fd538e122b44}, // 5^70 + {0xe7d34c64a9c85d44, 0x60dbbca87196b616}, // 5^71 + {0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd}, // 5^72 + {0xb51d13aea4a488dd, 0x6babab6398bdbe41}, // 5^73 + {0xe264589a4dcdab14, 0xc696963c7eed2dd1}, // 5^74 + {0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2}, // 5^75 + {0xb0de65388cc8ada8, 0x3b25a55f43294bcb}, // 5^76 + {0xdd15fe86affad912, 0x49ef0eb713f39ebe}, // 5^77 + {0x8a2dbf142dfcc7ab, 0x6e3569326c784337}, // 5^78 + {0xacb92ed9397bf996, 0x49c2c37f07965404}, // 5^79 + {0xd7e77a8f87daf7fb, 0xdc33745ec97be906}, // 5^80 + {0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3}, // 5^81 + {0xa8acd7c0222311bc, 0xc40832ea0d68ce0c}, // 5^82 + {0xd2d80db02aabd62b, 0xf50a3fa490c30190}, // 5^83 + {0x83c7088e1aab65db, 0x792667c6da79e0fa}, // 5^84 + {0xa4b8cab1a1563f52, 0x577001b891185938}, // 5^85 + {0xcde6fd5e09abcf26, 0xed4c0226b55e6f86}, // 5^86 + {0x80b05e5ac60b6178, 0x544f8158315b05b4}, // 5^87 + {0xa0dc75f1778e39d6, 0x696361ae3db1c721}, // 5^88 + {0xc913936dd571c84c, 0x03bc3a19cd1e38e9}, // 5^89 + {0xfb5878494ace3a5f, 0x04ab48a04065c723}, // 5^90 + {0x9d174b2dcec0e47b, 0x62eb0d64283f9c76}, // 5^91 + {0xc45d1df942711d9a, 0x3ba5d0bd324f8394}, // 5^92 + {0xf5746577930d6500, 0xca8f44ec7ee36479}, // 5^93 + {0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb}, // 5^94 + {0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e}, // 5^95 + {0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e}, // 5^96 + {0x95d04aee3b80ece5, 0xbba1f1d158724a12}, // 5^97 + {0xbb445da9ca61281f, 0x2a8a6e45ae8edc97}, // 5^98 + {0xea1575143cf97226, 0xf52d09d71a3293bd}, // 5^99 + {0x924d692ca61be758, 0x593c2626705f9c56}, // 5^100 + {0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c}, // 5^101 + {0xe498f455c38b997a, 0x0b6dfb9c0f956447}, // 5^102 + {0x8edf98b59a373fec, 0x4724bd4189bd5eac}, // 5^103 + {0xb2977ee300c50fe7, 0x58edec91ec2cb657}, // 5^104 + {0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed}, // 5^105 + {0x8b865b215899f46c, 0xbd79e0d20082ee74}, // 5^106 + {0xae67f1e9aec07187, 0xecd8590680a3aa11}, // 5^107 + {0xda01ee641a708de9, 0xe80e6f4820cc9495}, // 5^108 + {0x884134fe908658b2, 0x3109058d147fdcdd}, // 5^109 + {0xaa51823e34a7eede, 0xbd4b46f0599fd415}, // 5^110 + {0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a}, // 5^111 + {0x850fadc09923329e, 0x03e2cf6bc604ddb0}, // 5^112 + {0xa6539930bf6bff45, 0x84db8346b786151c}, // 5^113 + {0xcfe87f7cef46ff16, 0xe612641865679a63}, // 5^114 + {0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e}, // 5^115 + {0xa26da3999aef7749, 0xe3be5e330f38f09d}, // 5^116 + {0xcb090c8001ab551c, 0x5cadf5bfd3072cc5}, // 5^117 + {0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6}, // 5^118 + {0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa}, // 5^119 + {0xc646d63501a1511d, 0xb281e1fd541501b8}, // 5^120 + {0xf7d88bc24209a565, 0x1f225a7ca91a4226}, // 5^121 + {0x9ae757596946075f, 0x3375788de9b06958}, // 5^122 + {0xc1a12d2fc3978937, 0x0052d6b1641c83ae}, // 5^123 + {0xf209787bb47d6b84, 0xc0678c5dbd23a49a}, // 5^124 + {0x9745eb4d50ce6332, 0xf840b7ba963646e0}, // 5^125 + {0xbd176620a501fbff, 0xb650e5a93bc3d898}, // 5^126 + {0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe}, // 5^127 + {0x93ba47c980e98cdf, 0xc66f336c36b10137}, // 5^128 + {0xb8a8d9bbe123f017, 0xb80b0047445d4184}, // 5^129 + {0xe6d3102ad96cec1d, 0xa60dc059157491e5}, // 5^130 + {0x9043ea1ac7e41392, 0x87c89837ad68db2f}, // 5^131 + {0xb454e4a179dd1877, 0x29babe4598c311fb}, // 5^132 + {0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a}, // 5^133 + {0x8ce2529e2734bb1d, 0x1899e4a65f58660c}, // 5^134 + {0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f}, // 5^135 + {0xdc21a1171d42645d, 0x76707543f4fa1f73}, // 5^136 + {0x899504ae72497eba, 0x6a06494a791c53a8}, // 5^137 + {0xabfa45da0edbde69, 0x0487db9d17636892}, // 5^138 + {0xd6f8d7509292d603, 0x45a9d2845d3c42b6}, // 5^139 + {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2}, // 5^140 + {0xa7f26836f282b732, 0x8e6cac7768d7141e}, // 5^141 + {0xd1ef0244af2364ff, 0x3207d795430cd926}, // 5^142 + {0x8335616aed761f1f, 0x7f44e6bd49e807b8}, // 5^143 + {0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6}, // 5^144 + {0xcd036837130890a1, 0x36dba887c37a8c0f}, // 5^145 + {0x802221226be55a64, 0xc2494954da2c9789}, // 5^146 + {0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c}, // 5^147 + {0xc83553c5c8965d3d, 0x6f92829494e5acc7}, // 5^148 + {0xfa42a8b73abbf48c, 0xcb772339ba1f17f9}, // 5^149 + {0x9c69a97284b578d7, 0xff2a760414536efb}, // 5^150 + {0xc38413cf25e2d70d, 0xfef5138519684aba}, // 5^151 + {0xf46518c2ef5b8cd1, 0x7eb258665fc25d69}, // 5^152 + {0x98bf2f79d5993802, 0xef2f773ffbd97a61}, // 5^153 + {0xbeeefb584aff8603, 0xaafb550ffacfd8fa}, // 5^154 + {0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38}, // 5^155 + {0x952ab45cfa97a0b2, 0xdd945a747bf26183}, // 5^156 + {0xba756174393d88df, 0x94f971119aeef9e4}, // 5^157 + {0xe912b9d1478ceb17, 0x7a37cd5601aab85d}, // 5^158 + {0x91abb422ccb812ee, 0xac62e055c10ab33a}, // 5^159 + {0xb616a12b7fe617aa, 0x577b986b314d6009}, // 5^160 + {0xe39c49765fdf9d94, 0xed5a7e85fda0b80b}, // 5^161 + {0x8e41ade9fbebc27d, 0x14588f13be847307}, // 5^162 + {0xb1d219647ae6b31c, 0x596eb2d8ae258fc8}, // 5^163 + {0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb}, // 5^164 + {0x8aec23d680043bee, 0x25de7bb9480d5854}, // 5^165 + {0xada72ccc20054ae9, 0xaf561aa79a10ae6a}, // 5^166 + {0xd910f7ff28069da4, 0x1b2ba1518094da04}, // 5^167 + {0x87aa9aff79042286, 0x90fb44d2f05d0842}, // 5^168 + {0xa99541bf57452b28, 0x353a1607ac744a53}, // 5^169 + {0xd3fa922f2d1675f2, 0x42889b8997915ce8}, // 5^170 + {0x847c9b5d7c2e09b7, 0x69956135febada11}, // 5^171 + {0xa59bc234db398c25, 0x43fab9837e699095}, // 5^172 + {0xcf02b2c21207ef2e, 0x94f967e45e03f4bb}, // 5^173 + {0x8161afb94b44f57d, 0x1d1be0eebac278f5}, // 5^174 + {0xa1ba1ba79e1632dc, 0x6462d92a69731732}, // 5^175 + {0xca28a291859bbf93, 0x7d7b8f7503cfdcfe}, // 5^176 + {0xfcb2cb35e702af78, 0x5cda735244c3d43e}, // 5^177 + {0x9defbf01b061adab, 0x3a0888136afa64a7}, // 5^178 + {0xc56baec21c7a1916, 0x088aaa1845b8fdd0}, // 5^179 + {0xf6c69a72a3989f5b, 0x8aad549e57273d45}, // 5^180 + {0x9a3c2087a63f6399, 0x36ac54e2f678864b}, // 5^181 + {0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd}, // 5^182 + {0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5}, // 5^183 + {0x969eb7c47859e743, 0x9f644ae5a4b1b325}, // 5^184 + {0xbc4665b596706114, 0x873d5d9f0dde1fee}, // 5^185 + {0xeb57ff22fc0c7959, 0xa90cb506d155a7ea}, // 5^186 + {0x9316ff75dd87cbd8, 0x09a7f12442d588f2}, // 5^187 + {0xb7dcbf5354e9bece, 0x0c11ed6d538aeb2f}, // 5^188 + {0xe5d3ef282a242e81, 0x8f1668c8a86da5fa}, // 5^189 + {0x8fa475791a569d10, 0xf96e017d694487bc}, // 5^190 + {0xb38d92d760ec4455, 0x37c981dcc395a9ac}, // 5^191 + {0xe070f78d3927556a, 0x85bbe253f47b1417}, // 5^192 + {0x8c469ab843b89562, 0x93956d7478ccec8e}, // 5^193 + {0xaf58416654a6babb, 0x387ac8d1970027b2}, // 5^194 + {0xdb2e51bfe9d0696a, 0x06997b05fcc0319e}, // 5^195 + {0x88fcf317f22241e2, 0x441fece3bdf81f03}, // 5^196 + {0xab3c2fddeeaad25a, 0xd527e81cad7626c3}, // 5^197 + {0xd60b3bd56a5586f1, 0x8a71e223d8d3b074}, // 5^198 + {0x85c7056562757456, 0xf6872d5667844e49}, // 5^199 + {0xa738c6bebb12d16c, 0xb428f8ac016561db}, // 5^200 + {0xd106f86e69d785c7, 0xe13336d701beba52}, // 5^201 + {0x82a45b450226b39c, 0xecc0024661173473}, // 5^202 + {0xa34d721642b06084, 0x27f002d7f95d0190}, // 5^203 + {0xcc20ce9bd35c78a5, 0x31ec038df7b441f4}, // 5^204 + {0xff290242c83396ce, 0x7e67047175a15271}, // 5^205 + {0x9f79a169bd203e41, 0x0f0062c6e984d386}, // 5^206 + {0xc75809c42c684dd1, 0x52c07b78a3e60868}, // 5^207 + {0xf92e0c3537826145, 0xa7709a56ccdf8a82}, // 5^208 + {0x9bbcc7a142b17ccb, 0x88a66076400bb691}, // 5^209 + {0xc2abf989935ddbfe, 0x6acff893d00ea435}, // 5^210 + {0xf356f7ebf83552fe, 0x0583f6b8c4124d43}, // 5^211 + {0x98165af37b2153de, 0xc3727a337a8b704a}, // 5^212 + {0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c}, // 5^213 + {0xeda2ee1c7064130c, 0x1162def06f79df73}, // 5^214 + {0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8}, // 5^215 + {0xb9a74a0637ce2ee1, 0x6d953e2bd7173692}, // 5^216 + {0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437}, // 5^217 + {0x910ab1d4db9914a0, 0x1d9c9892400a22a2}, // 5^218 + {0xb54d5e4a127f59c8, 0x2503beb6d00cab4b}, // 5^219 + {0xe2a0b5dc971f303a, 0x2e44ae64840fd61d}, // 5^220 + {0x8da471a9de737e24, 0x5ceaecfed289e5d2}, // 5^221 + {0xb10d8e1456105dad, 0x7425a83e872c5f47}, // 5^222 + {0xdd50f1996b947518, 0xd12f124e28f77719}, // 5^223 + {0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f}, // 5^224 + {0xace73cbfdc0bfb7b, 0x636cc64d1001550b}, // 5^225 + {0xd8210befd30efa5a, 0x3c47f7e05401aa4e}, // 5^226 + {0x8714a775e3e95c78, 0x65acfaec34810a71}, // 5^227 + {0xa8d9d1535ce3b396, 0x7f1839a741a14d0d}, // 5^228 + {0xd31045a8341ca07c, 0x1ede48111209a050}, // 5^229 + {0x83ea2b892091e44d, 0x934aed0aab460432}, // 5^230 + {0xa4e4b66b68b65d60, 0xf81da84d5617853f}, // 5^231 + {0xce1de40642e3f4b9, 0x36251260ab9d668e}, // 5^232 + {0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019}, // 5^233 + {0xa1075a24e4421730, 0xb24cf65b8612f81f}, // 5^234 + {0xc94930ae1d529cfc, 0xdee033f26797b627}, // 5^235 + {0xfb9b7cd9a4a7443c, 0x169840ef017da3b1}, // 5^236 + {0x9d412e0806e88aa5, 0x8e1f289560ee864e}, // 5^237 + {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2}, // 5^238 + {0xf5b5d7ec8acb58a2, 0xae10af696774b1db}, // 5^239 + {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29}, // 5^240 + {0xbff610b0cc6edd3f, 0x17fd090a58d32af3}, // 5^241 + {0xeff394dcff8a948e, 0xddfc4b4cef07f5b0}, // 5^242 + {0x95f83d0a1fb69cd9, 0x4abdaf101564f98e}, // 5^243 + {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1}, // 5^244 + {0xea53df5fd18d5513, 0x84c86189216dc5ed}, // 5^245 + {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4}, // 5^246 + {0xb7118682dbb66a77, 0x3fbc8c33221dc2a1}, // 5^247 + {0xe4d5e82392a40515, 0x0fabaf3feaa5334a}, // 5^248 + {0x8f05b1163ba6832d, 0x29cb4d87f2a7400e}, // 5^249 + {0xb2c71d5bca9023f8, 0x743e20e9ef511012}, // 5^250 + {0xdf78e4b2bd342cf6, 0x914da9246b255416}, // 5^251 + {0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e}, // 5^252 + {0xae9672aba3d0c320, 0xa184ac2473b529b1}, // 5^253 + {0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e}, // 5^254 + {0x8865899617fb1871, 0x7e2fa67c7a658892}, // 5^255 + {0xaa7eebfb9df9de8d, 0xddbb901b98feeab7}, // 5^256 + {0xd51ea6fa85785631, 0x552a74227f3ea565}, // 5^257 + {0x8533285c936b35de, 0xd53a88958f87275f}, // 5^258 + {0xa67ff273b8460356, 0x8a892abaf368f137}, // 5^259 + {0xd01fef10a657842c, 0x2d2b7569b0432d85}, // 5^260 + {0x8213f56a67f6b29b, 0x9c3b29620e29fc73}, // 5^261 + {0xa298f2c501f45f42, 0x8349f3ba91b47b8f}, // 5^262 + {0xcb3f2f7642717713, 0x241c70a936219a73}, // 5^263 + {0xfe0efb53d30dd4d7, 0xed238cd383aa0110}, // 5^264 + {0x9ec95d1463e8a506, 0xf4363804324a40aa}, // 5^265 + {0xc67bb4597ce2ce48, 0xb143c6053edcd0d5}, // 5^266 + {0xf81aa16fdc1b81da, 0xdd94b7868e94050a}, // 5^267 + {0x9b10a4e5e9913128, 0xca7cf2b4191c8326}, // 5^268 + {0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0}, // 5^269 + {0xf24a01a73cf2dccf, 0xbc633b39673c8cec}, // 5^270 + {0x976e41088617ca01, 0xd5be0503e085d813}, // 5^271 + {0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18}, // 5^272 + {0xec9c459d51852ba2, 0xddf8e7d60ed1219e}, // 5^273 + {0x93e1ab8252f33b45, 0xcabb90e5c942b503}, // 5^274 + {0xb8da1662e7b00a17, 0x3d6a751f3b936243}, // 5^275 + {0xe7109bfba19c0c9d, 0x0cc512670a783ad4}, // 5^276 + {0x906a617d450187e2, 0x27fb2b80668b24c5}, // 5^277 + {0xb484f9dc9641e9da, 0xb1f9f660802dedf6}, // 5^278 + {0xe1a63853bbd26451, 0x5e7873f8a0396973}, // 5^279 + {0x8d07e33455637eb2, 0xdb0b487b6423e1e8}, // 5^280 + {0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62}, // 5^281 + {0xdc5c5301c56b75f7, 0x7641a140cc7810fb}, // 5^282 + {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d}, // 5^283 + {0xac2820d9623bf429, 0x546345fa9fbdcd44}, // 5^284 + {0xd732290fbacaf133, 0xa97c177947ad4095}, // 5^285 + {0x867f59a9d4bed6c0, 0x49ed8eabcccc485d}, // 5^286 + {0xa81f301449ee8c70, 0x5c68f256bfff5a74}, // 5^287 + {0xd226fc195c6a2f8c, 0x73832eec6fff3111}, // 5^288 + {0x83585d8fd9c25db7, 0xc831fd53c5ff7eab}, // 5^289 + {0xa42e74f3d032f525, 0xba3e7ca8b77f5e55}, // 5^290 + {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb}, // 5^291 + {0x80444b5e7aa7cf85, 0x7980d163cf5b81b3}, // 5^292 + {0xa0555e361951c366, 0xd7e105bcc332621f}, // 5^293 + {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7}, // 5^294 + {0xfa856334878fc150, 0xb14f98f6f0feb951}, // 5^295 + {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3}, // 5^296 + {0xc3b8358109e84f07, 0x0a862f80ec4700c8}, // 5^297 + {0xf4a642e14c6262c8, 0xcd27bb612758c0fa}, // 5^298 + {0x98e7e9cccfbd7dbd, 0x8038d51cb897789c}, // 5^299 + {0xbf21e44003acdd2c, 0xe0470a63e6bd56c3}, // 5^300 + {0xeeea5d5004981478, 0x1858ccfce06cac74}, // 5^301 + {0x95527a5202df0ccb, 0x0f37801e0c43ebc8}, // 5^302 + {0xbaa718e68396cffd, 0xd30560258f54e6ba}, // 5^303 + {0xe950df20247c83fd, 0x47c6b82ef32a2069}, // 5^304 + {0x91d28b7416cdd27e, 0x4cdc331d57fa5441}, // 5^305 + {0xb6472e511c81471d, 0xe0133fe4adf8e952}, // 5^306 + {0xe3d8f9e563a198e5, 0x58180fddd97723a6}, // 5^307 + {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648}, // 5^308 +} diff --git a/core/strconv/strconv.odin b/core/strconv/strconv.odin index f2450dcbd..f6fe48e8d 100644 --- a/core/strconv/strconv.odin +++ b/core/strconv/strconv.odin @@ -746,9 +746,13 @@ Output: - ok: `false` if a base 10 float could not be found, or if the input string contained more than just the number. */ parse_f32 :: proc(s: string, n: ^int = nil) -> (value: f32, ok: bool) { - v: f64 = --- - v, ok = parse_f64(s, n) - return f32(v), ok + nr: int + value, nr, ok = parse_f32_prefix(s) + if ok && len(s) != nr { + ok = false + } + if n != nil { n^ = nr } + return } /* Parses a 64-bit floating point number from a string @@ -817,10 +821,7 @@ Output: - ok: A boolean indicating whether the parsing was successful. */ parse_f32_prefix :: proc(str: string) -> (value: f32, nr: int, ok: bool) { - f: f64 - f, nr, ok = parse_f64_prefix(str) - value = f32(f) - return + return parse_float_prefix_generic(f32, str) } /* Parses a 64-bit floating point number from a string and returns the parsed number, the length of the parsed substring, and a boolean indicating whether the parsing was successful @@ -855,6 +856,11 @@ Output: - ok: `false` if a base 10 float could not be found */ parse_f64_prefix :: proc(str: string) -> (value: f64, nr: int, ok: bool) { + return parse_float_prefix_generic(f64, str) +} + +// Parses directly to `T`, so the result is correctly rounded for both `f32` and `f64`. +parse_float_prefix_generic :: proc($T: typeid, str: string) -> (value: T, nr: int, ok: bool) where T == f32 || T == f64 { common_prefix_len_ignore_case :: proc "contextless" (s, prefix: string) -> int { n := len(prefix) if n > len(s) { @@ -1122,19 +1128,27 @@ parse_f64_prefix :: proc(str: string) -> (value: f64, nr: int, ok: bool) { switch digits { case 4: - value = cast(f64)transmute(f16)cast(u16)as_int + value = cast(T)transmute(f16)cast(u16)as_int case 8: - value = cast(f64)transmute(f32)cast(u32)as_int + value = cast(T)transmute(f32)cast(u32)as_int case 16: - value = transmute(f64)as_int + value = cast(T)transmute(f64)as_int case: ok = false } return } - if value, nr, ok = check_special(str); ok { - return + if f, n, special := check_special(str); special { + return T(f), n, true + } + + when T == f64 { + Bits :: u64 + info := &_f64_info + } else { + Bits :: u32 + info := &_f32_info } mantissa: u64 @@ -1143,11 +1157,18 @@ parse_f64_prefix :: proc(str: string) -> (value: f64, nr: int, ok: bool) { mantissa, exp, neg, trunc, hex, nr = parse_components(str) or_return if hex { - value, ok = parse_hex(str, mantissa, exp, neg, trunc) + f: f64 + f, ok = parse_hex(str, mantissa, exp, neg, trunc) + value = T(f) + when T == f32 { + // A finite f64 can be too large for f32. + ok = ok && transmute(u32)value & 0x7f80_0000 != 0x7f80_0000 + } return } - trunc_block: if !trunc { + // Clinger's fast path algorithm + clinger_fast_path: if !trunc && !(ODIN_ARCH == .i386 && ODIN_OS != .Windows) { @(static, rodata) pow10 := [?]f64{ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, @@ -1155,33 +1176,58 @@ parse_f64_prefix :: proc(str: string) -> (value: f64, nr: int, ok: bool) { } if mantissa>>_f64_info.mantbits != 0 { - break trunc_block + break clinger_fast_path } f := f64(mantissa) - f_abs := f + switch { + case exp == 0: + case exp > 0 && exp <= 15+22: + e := exp + if e > 22 { + f *= pow10[e-22] + e = 22 + if f > 1e15 { + break clinger_fast_path + } + } + f *= pow10[e] + case -22 <= exp && exp < 0: + f /= pow10[-exp] + case: + break clinger_fast_path + } + when T == f32 { + // Every f32 midpoint is an f64 value, so rounding to f64 cannot + // move the result past a midpoint. The conversion to f32 is then + // correct, unless the f64 result is exactly a midpoint. + if transmute(u64)f & (1<<29 - 1) == 1<<28 { + break clinger_fast_path + } + } if neg { f = -f } - switch { - case exp == 0: - return f, nr, true - case exp > 0 && exp <= 15+22: - if exp > 22 { - f *= pow10[exp-22] - exp = 22 - } - if f_abs > 1e15 || f_abs < 1e-15 { - break trunc_block - } - return f * pow10[exp], nr, true - case -22 <= exp && exp < 0: - return f / pow10[-exp], nr, true - } + return T(f), nr, true } + + // Eisel-Lemire's fast float algorithm + fast_float: { + b := fast_float_compute_float(T, exp, mantissa) + if trunc && b != fast_float_compute_float(T, exp, mantissa+1) { + break fast_float + } + ok = b >> info.mantbits != 1< Date: Sun, 27 Sep 2026 13:56:41 +0200 Subject: [PATCH 2/3] changed variable names to be more descriptive --- core/strconv/LICENSE_fast_float | 2 +- core/strconv/fast_float.odin | 93 +++++++++++++++++---------------- 2 files changed, 48 insertions(+), 47 deletions(-) diff --git a/core/strconv/LICENSE_fast_float b/core/strconv/LICENSE_fast_float index 8ddef69e7..70afbb92d 100644 --- a/core/strconv/LICENSE_fast_float +++ b/core/strconv/LICENSE_fast_float @@ -1,4 +1,4 @@ -This license applies to the Eisel-Lemire code and the _POW5_128 table in +This license applies to the Eisel-Lemire code and the _POWER_OF_FIVE_128 table in fast_float.odin, which are ported from ffc.h and fast_float. ffc.h: https://github.com/kolemannix/ffc.h diff --git a/core/strconv/fast_float.odin b/core/strconv/fast_float.odin index a68184cad..568766e72 100644 --- a/core/strconv/fast_float.odin +++ b/core/strconv/fast_float.odin @@ -22,8 +22,7 @@ import "core:math/bits" Software: Practice and Experience 53 (7), 2023. https://arxiv.org/abs/2212.06644 */ -@(private="file") -_POW5_128_MIN_EXP :: -342 +_SMALLEST_POWER_OF_FIVE :: -342 /* Computes the `T` closest to `w * 10^q`, rounding ties to even. @@ -42,55 +41,57 @@ calls return the same bits, the result is correct. Otherwise, use a slow path. */ fast_float_compute_float :: proc "contextless" ($T: typeid, q: int, w: u64) -> u64 where T == f32 || T == f64 #no_bounds_check { when T == f64 { - MANT_BITS :: 52 - MIN_EXPONENT :: -1023 - INFINITE_POWER :: 0x7ff - SMALLEST_POW10 :: -342 - LARGEST_POW10 :: 308 - MIN_EXP_ROUND_EVEN :: -4 - MAX_EXP_ROUND_EVEN :: 23 + MANTISSA_EXPLICIT_BITS :: 52 + MINIMUM_EXPONENT :: -1023 + INFINITE_POWER :: 0x7ff + SMALLEST_POWER_OF_TEN :: -342 + LARGEST_POWER_OF_TEN :: 308 + MIN_EXPONENT_ROUND_TO_EVEN :: -4 + MAX_EXPONENT_ROUND_TO_EVEN :: 23 } else { - MANT_BITS :: 23 - MIN_EXPONENT :: -127 - INFINITE_POWER :: 0xff - SMALLEST_POW10 :: -64 - LARGEST_POW10 :: 38 - MIN_EXP_ROUND_EVEN :: -17 - MAX_EXP_ROUND_EVEN :: 10 + MANTISSA_EXPLICIT_BITS :: 23 + MINIMUM_EXPONENT :: -127 + INFINITE_POWER :: 0xff + SMALLEST_POWER_OF_TEN :: -64 + LARGEST_POWER_OF_TEN :: 38 + MIN_EXPONENT_ROUND_TO_EVEN :: -17 + MAX_EXPONENT_ROUND_TO_EVEN :: 10 } - // w <= max(u64) and q < SMALLEST_POW10 always rounds to zero. - if w == 0 || q < SMALLEST_POW10 { + // w <= max(u64) and q < SMALLEST_POWER_OF_TEN always rounds to zero. + if w == 0 || q < SMALLEST_POWER_OF_TEN { return 0 } - if q > LARGEST_POW10 { - return INFINITE_POWER << MANT_BITS + if q > LARGEST_POWER_OF_TEN { + return INFINITE_POWER << MANTISSA_EXPLICIT_BITS } + // Set the most significant bit of w. lz := bits.count_leading_zeros(w) - wn := w << lz // normalized so the top bit is set + w := w + w <<= lz - // Compute a 128-bit approximation of wn * 5^q. We need the product to be accurate - // to MANT_BITS+3 bits. If the lower bits of the high word are all ones, the error - // in the first product could affect them, so we refine the result with the lower - // half of the power of five. - PRECISION_MASK :: max(u64) >> (MANT_BITS + 3) - pow5 := &_POW5_128[q - _POW5_128_MIN_EXP] - hi, lo := bits.mul_u64(wn, pow5[0]) - if hi & PRECISION_MASK == PRECISION_MASK { - hi2, _ := bits.mul_u64(wn, pow5[1]) - lo += hi2 - if hi2 > lo { - hi += 1 + // Compute a 128-bit approximation of w * 5^q. We need the product to be accurate + // to MANTISSA_EXPLICIT_BITS+3 bits. If the lower bits of the high word are all ones, + // the error in the first product could affect them, so we refine the result with + // the lower half of the power of five. + PRECISION_MASK :: max(u64) >> (MANTISSA_EXPLICIT_BITS + 3) + pow5 := &_POWER_OF_FIVE_128[q - _SMALLEST_POWER_OF_FIVE] + high, low := bits.mul_u64(w, pow5[0]) + if high & PRECISION_MASK == PRECISION_MASK { + second_high, _ := bits.mul_u64(w, pow5[1]) + low += second_high + if second_high > low { + high += 1 } } // Mushtak & Lemire (2023) prove that this product is always accurate enough. - upperbit := int(hi >> 63) - shift := uint(upperbit + 64 - MANT_BITS - 3) - mantissa := hi >> shift + upperbit := int(high >> 63) + shift := uint(upperbit + 64 - MANTISSA_EXPLICIT_BITS - 3) + mantissa := high >> shift // ((152170 + 65536) * q) >> 16 is floor(q * log2(10)) for |q| < 1650. - power2 := (((152170 + 65536) * q) >> 16) + 63 + upperbit - int(lz) - MIN_EXPONENT + power2 := (((152170 + 65536) * q) >> 16) + 63 + upperbit - int(lz) - MINIMUM_EXPONENT if power2 <= 0 { // Subnormal result. @@ -108,28 +109,28 @@ fast_float_compute_float :: proc "contextless" ($T: typeid, q: int, w: u64) -> u // We usually round up. If the value is exactly halfway between two floats, // and the lower float is even, we must round down. An exact halfway value is // possible only for a small range of exponents. - if lo <= 1 && q >= MIN_EXP_ROUND_EVEN && q <= MAX_EXP_ROUND_EVEN && mantissa & 3 == 1 { - if mantissa << shift == hi { + if low <= 1 && q >= MIN_EXPONENT_ROUND_TO_EVEN && q <= MAX_EXPONENT_ROUND_TO_EVEN && mantissa & 3 == 1 { + if mantissa << shift == high { mantissa &~= 1 } } mantissa += mantissa & 1 // round up mantissa >>= 1 - if mantissa >= 2 << MANT_BITS { - mantissa = 1 << MANT_BITS + if mantissa >= 2 << MANTISSA_EXPLICIT_BITS { + mantissa = 1 << MANTISSA_EXPLICIT_BITS power2 += 1 } - mantissa &~= 1 << MANT_BITS + mantissa &~= 1 << MANTISSA_EXPLICIT_BITS if power2 >= INFINITE_POWER { - return INFINITE_POWER << MANT_BITS + return INFINITE_POWER << MANTISSA_EXPLICIT_BITS } - return mantissa | u64(power2) << MANT_BITS + return mantissa | u64(power2) << MANTISSA_EXPLICIT_BITS } // 128-bit truncated mantissas of 5^-342 to 5^308, with the most significant // bit set. Generated by fast_float script/table_generation.py. -@(private="file", rodata) -_POW5_128 := [651][2]u64{ +@(rodata) +_POWER_OF_FIVE_128 := [651][2]u64{ {0xeef453d6923bd65a, 0x113faa2906a13b3f}, // 5^-342 {0x9558b4661b6565f8, 0x4ac7ca59a424c507}, // 5^-341 {0xbaaee17fa23ebf76, 0x5d79bcf00d2df649}, // 5^-340 From 4269f09236cbcf46531998045edf2495802a58ff Mon Sep 17 00:00:00 2001 From: Matthias Huerbe Date: Mon, 28 Sep 2026 16:00:01 +0200 Subject: [PATCH 3/3] moved license notice into fast_float.odin --- core/strconv/LICENSE_fast_float | 31 ------------------------------- core/strconv/fast_float.odin | 33 +++++++++++++++++++++++++++++++++ 2 files changed, 33 insertions(+), 31 deletions(-) delete mode 100644 core/strconv/LICENSE_fast_float diff --git a/core/strconv/LICENSE_fast_float b/core/strconv/LICENSE_fast_float deleted file mode 100644 index 70afbb92d..000000000 --- a/core/strconv/LICENSE_fast_float +++ /dev/null @@ -1,31 +0,0 @@ -This license applies to the Eisel-Lemire code and the _POWER_OF_FIVE_128 table in -fast_float.odin, which are ported from ffc.h and fast_float. - - ffc.h: https://github.com/kolemannix/ffc.h - fast_float: https://github.com/fastfloat/fast_float - -Copyright (c) 2021 The fast_float authors - -Boost Software License - Version 1.0 - August 17th, 2003 - -Permission is hereby granted, free of charge, to any person or organization -obtaining a copy of the software and accompanying documentation covered by -this license (the "Software") to use, reproduce, display, distribute, -execute, and transmit the Software, and to prepare derivative works of the -Software, and to permit third-parties to whom the Software is furnished to -do so, all subject to the following: - -The copyright notices in the Software and this entire statement, including -the above license grant, this restriction and the following disclaimer, -must be included in all copies of the Software, in whole or in part, and -all derivative works of the Software, unless such copies or derivative -works are solely in the form of machine-executable object code generated by -a source language processor. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT -SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE -FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, -ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER -DEALINGS IN THE SOFTWARE. diff --git a/core/strconv/fast_float.odin b/core/strconv/fast_float.odin index 568766e72..83e63b2a5 100644 --- a/core/strconv/fast_float.odin +++ b/core/strconv/fast_float.odin @@ -783,3 +783,36 @@ _POWER_OF_FIVE_128 := [651][2]u64{ {0xe3d8f9e563a198e5, 0x58180fddd97723a6}, // 5^307 {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648}, // 5^308 } + +/* +Ported from ffc.h and fast_float. + + ffc.h: https://github.com/kolemannix/ffc.h + fast_float: https://github.com/fastfloat/fast_float + +Copyright (c) 2021 The fast_float authors + +Boost Software License - Version 1.0 - August 17th, 2003 + +Permission is hereby granted, free of charge, to any person or organization +obtaining a copy of the software and accompanying documentation covered by +this license (the "Software") to use, reproduce, display, distribute, +execute, and transmit the Software, and to prepare derivative works of the +Software, and to permit third-parties to whom the Software is furnished to +do so, all subject to the following: + +The copyright notices in the Software and this entire statement, including +the above license grant, this restriction and the following disclaimer, +must be included in all copies of the Software, in whole or in part, and +all derivative works of the Software, unless such copies or derivative +works are solely in the form of machine-executable object code generated by +a source language processor. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT +SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE +FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +DEALINGS IN THE SOFTWARE. +*/