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fast_float_strtod: fix ±1 ULP rounding mismatch in widened fast path (#15111)
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## Summary Fixes a ±1 ULP rounding mismatch between `fast_float_strtod()` and libc `strtod()` in the widened (mantissa > 2^53) fast path introduced by #15061. Reported by @vitahlin in https://github.com/redis/redis/pull/14661#issuecomment-4320058616 with two minimal reproducers: ``` input: 9007199255094284e-19 fast_float_strtod: 0x3f4d83c94fbbcb8a libc strtod : 0x3f4d83c94fbbcb8b delta -1 ULP input: 2489830482329185244e1 fast_float_strtod: 0x43f59888c51e5b4c libc strtod : 0x43f59888c51e5b4b delta +1 ULP ``` Redis treats `strtod()` as the fallback for `fast_float_strtod()`, so every fast-path-accepted input is contractually expected to be bit-exact with `strtod()`. The two cases above are accepted by the widened branch but produce a different IEEE-754 representation, breaking the contract. ## Root cause The widened branch added in #15061 used a homebrew shortcut to convert a 128-bit integer product to a double: ```c value = (double)hi * 18446744073709551616.0 + (double)lo; ``` This is **not** a single-rounding operation — `(double)hi` rounds when `hi > 2^53`, and the subsequent `+ (double)lo` rounds again. For inputs near the round-half-to-even boundary, the two roundings can compose into the wrong direction. The negative-exponent branch is doubly affected: integer division `scaled / divisor` truncates the remainder before the conversion, so even a hypothetical correct `hi*2^64+lo` step would round down on inputs that should round up. ## Fix Replace the homebrew widened branch with the **Eisel-Lemire** algorithm from upstream `fast_float`. This is the same algorithm that `fast_float`'s own widened path uses; bit-exact-with-strtod for inputs with ≤19-digit mantissa is proved in: > Noble Mushtak and Daniel Lemire, "Fast Number Parsing Without Fallback". Pieces ported (MIT-licensed, from `fast_float/include/fast_float/fast_table.h`, `decimal_to_binary.h`, `float_common.h`): - 128-bit precomputed extended-precision powers of five (`5^-342 ... 5^308`, 651 entries) — pure data. - `compute_product_approximation` — 128-bit multiply with high-half rounding-boundary fixup. - `compute_float` — the main algorithm; returns `(mantissa, power2)` ready to be packed. - `am_to_double` — IEEE-754 binary64 bit-pack. - `__builtin_clzll` and `__uint128_t` wrappers (with a 32-bit fallback for portability). Clinger's strict fast path (`mantissa ≤ 2^53` and `|exp| ≤ 22`) is **kept** unchanged — it's a single double multiply/divide and is faster than Eisel-Lemire on its domain. Only the buggy widened branch is replaced. The port stays minimal: - **double-only** (no `float`, no `long double`) - No bigint slow path. The rare "indeterminate" inputs that upstream resolves with `digit_comp` are unreachable from `parse_number_string`'s ≤19-digit mantissa per the Mushtak-Lemire proof, but a defensive `am.power2 < 0` check is preserved that falls back to libc `strtod()` if any future caller widens the input domain. ## Why not just revert #15061? Considered. Reverting restores correctness at the cost of the +73-84 % zset listpack-load wins #15061 measured on 17-19 digit double scores. Eisel-Lemire is *the* algorithm that gives both correctness *and* the wider mantissa range — preserving #15061's wins while fixing the rounding regression. A "tightened admission filter" (only accept widened-path inputs where the conversion happens to be single-rounding) was also considered. The math shows the filter conditions are essentially unsatisfied for typical inputs (`lo == 0` requires the 128-bit product be divisible by 2^64; only ~1 in 10^13 random inputs qualify), making it equivalent to a revert with extra dead code. Eisel-Lemire is the only widened-path solution that preserves perf on the typical case.
This commit is contained in:
Filipe Oliveira (Redis)
GitHub
parent
5e155593d9
commit
3ab7fe0812
1 changed files with 477 additions and 49 deletions
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@ -48,6 +48,195 @@ static const double powers_of_ten[] = {
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1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22
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};
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/* ----------------------------------------------------------------------------
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* Eisel-Lemire algorithm — extended-precision powers of five.
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*
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* The table below maps from decimal scaling (10^q) to a 128-bit binary
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* approximation. Since 10^q = 2^q * 5^q and the 2^q factor is exact in
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* binary, only 5^q affects the binary significand — so we precompute
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* 5^q rounded toward 1 to 128 bits. Used by `compute_float()` to avoid
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* any iterative rounding in the widened (mantissa > 2^53) range.
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*
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* Pulled verbatim from fast_float by Daniel Lemire & Joao Paulo Magalhaes
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* (MIT-licensed, https://github.com/fastfloat/fast_float — fast_table.h).
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*
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* Range: 5^-342 ... 5^308 — covers every value that can produce a finite
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* non-zero double from a 64-bit decimal mantissa. 651 entries, each stored
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* as { high64, low64 } pairs (1302 uint64_t total).
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* ---------------------------------------------------------------------------- */
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#define EISEL_LEMIRE_SMALLEST_POWER_OF_FIVE -342
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#define EISEL_LEMIRE_LARGEST_POWER_OF_FIVE 308
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#define EISEL_LEMIRE_NUMBER_OF_ENTRIES (2 * (EISEL_LEMIRE_LARGEST_POWER_OF_FIVE - \
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EISEL_LEMIRE_SMALLEST_POWER_OF_FIVE + 1))
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static const uint64_t power_of_five_128[EISEL_LEMIRE_NUMBER_OF_ENTRIES] = {
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|
||||
0xad4ab7112eb3929d, 0x86c16c98d2c953c6, 0xd89d64d57a607744, 0xe871c7bf077ba8b7, 0x87625f056c7c4a8b, 0x11471cd764ad4972, 0xa93af6c6c79b5d2d, 0xd598e40d3dd89bcf,
|
||||
0xd389b47879823479, 0x4aff1d108d4ec2c3, 0x843610cb4bf160cb, 0xcedf722a585139ba, 0xa54394fe1eedb8fe, 0xc2974eb4ee658828, 0xce947a3da6a9273e, 0x733d226229feea32,
|
||||
0x811ccc668829b887, 0x806357d5a3f525f, 0xa163ff802a3426a8, 0xca07c2dcb0cf26f7, 0xc9bcff6034c13052, 0xfc89b393dd02f0b5, 0xfc2c3f3841f17c67, 0xbbac2078d443ace2,
|
||||
0x9d9ba7832936edc0, 0xd54b944b84aa4c0d, 0xc5029163f384a931, 0xa9e795e65d4df11, 0xf64335bcf065d37d, 0x4d4617b5ff4a16d5, 0x99ea0196163fa42e, 0x504bced1bf8e4e45,
|
||||
0xc06481fb9bcf8d39, 0xe45ec2862f71e1d6, 0xf07da27a82c37088, 0x5d767327bb4e5a4c, 0x964e858c91ba2655, 0x3a6a07f8d510f86f, 0xbbe226efb628afea, 0x890489f70a55368b,
|
||||
0xeadab0aba3b2dbe5, 0x2b45ac74ccea842e, 0x92c8ae6b464fc96f, 0x3b0b8bc90012929d, 0xb77ada0617e3bbcb, 0x9ce6ebb40173744, 0xe55990879ddcaabd, 0xcc420a6a101d0515,
|
||||
0x8f57fa54c2a9eab6, 0x9fa946824a12232d, 0xb32df8e9f3546564, 0x47939822dc96abf9, 0xdff9772470297ebd, 0x59787e2b93bc56f7, 0x8bfbea76c619ef36, 0x57eb4edb3c55b65a,
|
||||
0xaefae51477a06b03, 0xede622920b6b23f1, 0xdab99e59958885c4, 0xe95fab368e45eced, 0x88b402f7fd75539b, 0x11dbcb0218ebb414, 0xaae103b5fcd2a881, 0xd652bdc29f26a119,
|
||||
0xd59944a37c0752a2, 0x4be76d3346f0495f, 0x857fcae62d8493a5, 0x6f70a4400c562ddb, 0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb952, 0xd097ad07a71f26b2, 0x7e2000a41346a7a7,
|
||||
0x825ecc24c873782f, 0x8ed400668c0c28c8, 0xa2f67f2dfa90563b, 0x728900802f0f32fa, 0xcbb41ef979346bca, 0x4f2b40a03ad2ffb9, 0xfea126b7d78186bc, 0xe2f610c84987bfa8,
|
||||
0x9f24b832e6b0f436, 0xdd9ca7d2df4d7c9, 0xc6ede63fa05d3143, 0x91503d1c79720dbb, 0xf8a95fcf88747d94, 0x75a44c6397ce912a, 0x9b69dbe1b548ce7c, 0xc986afbe3ee11aba,
|
||||
0xc24452da229b021b, 0xfbe85badce996168, 0xf2d56790ab41c2a2, 0xfae27299423fb9c3, 0x97c560ba6b0919a5, 0xdccd879fc967d41a, 0xbdb6b8e905cb600f, 0x5400e987bbc1c920,
|
||||
0xed246723473e3813, 0x290123e9aab23b68, 0x9436c0760c86e30b, 0xf9a0b6720aaf6521, 0xb94470938fa89bce, 0xf808e40e8d5b3e69, 0xe7958cb87392c2c2, 0xb60b1d1230b20e04,
|
||||
0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c2, 0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af3, 0xe2280b6c20dd5232, 0x25c6da63c38de1b0, 0x8d590723948a535f, 0x579c487e5a38ad0e,
|
||||
0xb0af48ec79ace837, 0x2d835a9df0c6d851, 0xdcdb1b2798182244, 0xf8e431456cf88e65, 0x8a08f0f8bf0f156b, 0x1b8e9ecb641b58ff, 0xac8b2d36eed2dac5, 0xe272467e3d222f3f,
|
||||
0xd7adf884aa879177, 0x5b0ed81dcc6abb0f, 0x86ccbb52ea94baea, 0x98e947129fc2b4e9, 0xa87fea27a539e9a5, 0x3f2398d747b36224, 0xd29fe4b18e88640e, 0x8eec7f0d19a03aad,
|
||||
0x83a3eeeef9153e89, 0x1953cf68300424ac, 0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd7, 0xcdb02555653131b6, 0x3792f412cb06794d, 0x808e17555f3ebf11, 0xe2bbd88bbee40bd0,
|
||||
0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec4, 0xc8de047564d20a8b, 0xf245825a5a445275, 0xfb158592be068d2e, 0xeed6e2f0f0d56712, 0x9ced737bb6c4183d, 0x55464dd69685606b,
|
||||
0xc428d05aa4751e4c, 0xaa97e14c3c26b886, 0xf53304714d9265df, 0xd53dd99f4b3066a8, 0x993fe2c6d07b7fab, 0xe546a8038efe4029, 0xbf8fdb78849a5f96, 0xde98520472bdd033,
|
||||
0xef73d256a5c0f77c, 0x963e66858f6d4440, 0x95a8637627989aad, 0xdde7001379a44aa8, 0xbb127c53b17ec159, 0x5560c018580d5d52, 0xe9d71b689dde71af, 0xaab8f01e6e10b4a6,
|
||||
0x9226712162ab070d, 0xcab3961304ca70e8, 0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d22, 0xe45c10c42a2b3b05, 0x8cb89a7db77c506a, 0x8eb98a7a9a5b04e3, 0x77f3608e92adb242,
|
||||
0xb267ed1940f1c61c, 0x55f038b237591ed3, 0xdf01e85f912e37a3, 0x6b6c46dec52f6688, 0x8b61313bbabce2c6, 0x2323ac4b3b3da015, 0xae397d8aa96c1b77, 0xabec975e0a0d081a,
|
||||
0xd9c7dced53c72255, 0x96e7bd358c904a21, 0x881cea14545c7575, 0x7e50d64177da2e54, 0xaa242499697392d2, 0xdde50bd1d5d0b9e9, 0xd4ad2dbfc3d07787, 0x955e4ec64b44e864,
|
||||
0x84ec3c97da624ab4, 0xbd5af13bef0b113e, 0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58e, 0xcfb11ead453994ba, 0x67de18eda5814af2, 0x81ceb32c4b43fcf4, 0x80eacf948770ced7,
|
||||
0xa2425ff75e14fc31, 0xa1258379a94d028d, 0xcad2f7f5359a3b3e, 0x96ee45813a04330, 0xfd87b5f28300ca0d, 0x8bca9d6e188853fc, 0x9e74d1b791e07e48, 0x775ea264cf55347e,
|
||||
0xc612062576589dda, 0x95364afe032a819e, 0xf79687aed3eec551, 0x3a83ddbd83f52205, 0x9abe14cd44753b52, 0xc4926a9672793543, 0xc16d9a0095928a27, 0x75b7053c0f178294,
|
||||
0xf1c90080baf72cb1, 0x5324c68b12dd6339, 0x971da05074da7bee, 0xd3f6fc16ebca5e04, 0xbce5086492111aea, 0x88f4bb1ca6bcf585, 0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6,
|
||||
0x9392ee8e921d5d07, 0x3aff322e62439fd0, 0xb877aa3236a4b449, 0x9befeb9fad487c3, 0xe69594bec44de15b, 0x4c2ebe687989a9b4, 0x901d7cf73ab0acd9, 0xf9d37014bf60a11,
|
||||
0xb424dc35095cd80f, 0x538484c19ef38c95, 0xe12e13424bb40e13, 0x2865a5f206b06fba, 0x8cbccc096f5088cb, 0xf93f87b7442e45d4, 0xafebff0bcb24aafe, 0xf78f69a51539d749,
|
||||
0xdbe6fecebdedd5be, 0xb573440e5a884d1c, 0x89705f4136b4a597, 0x31680a88f8953031, 0xabcc77118461cefc, 0xfdc20d2b36ba7c3e, 0xd6bf94d5e57a42bc, 0x3d32907604691b4d,
|
||||
0x8637bd05af6c69b5, 0xa63f9a49c2c1b110, 0xa7c5ac471b478423, 0xfcf80dc33721d54, 0xd1b71758e219652b, 0xd3c36113404ea4a9, 0x83126e978d4fdf3b, 0x645a1cac083126ea,
|
||||
0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4, 0xcccccccccccccccc, 0xcccccccccccccccd, 0x8000000000000000, 0x0, 0xa000000000000000, 0x0,
|
||||
0xc800000000000000, 0x0, 0xfa00000000000000, 0x0, 0x9c40000000000000, 0x0, 0xc350000000000000, 0x0,
|
||||
0xf424000000000000, 0x0, 0x9896800000000000, 0x0, 0xbebc200000000000, 0x0, 0xee6b280000000000, 0x0,
|
||||
0x9502f90000000000, 0x0, 0xba43b74000000000, 0x0, 0xe8d4a51000000000, 0x0, 0x9184e72a00000000, 0x0,
|
||||
0xb5e620f480000000, 0x0, 0xe35fa931a0000000, 0x0, 0x8e1bc9bf04000000, 0x0, 0xb1a2bc2ec5000000, 0x0,
|
||||
0xde0b6b3a76400000, 0x0, 0x8ac7230489e80000, 0x0, 0xad78ebc5ac620000, 0x0, 0xd8d726b7177a8000, 0x0,
|
||||
0x878678326eac9000, 0x0, 0xa968163f0a57b400, 0x0, 0xd3c21bcecceda100, 0x0, 0x84595161401484a0, 0x0,
|
||||
0xa56fa5b99019a5c8, 0x0, 0xcecb8f27f4200f3a, 0x0, 0x813f3978f8940984, 0x4000000000000000, 0xa18f07d736b90be5, 0x5000000000000000,
|
||||
0xc9f2c9cd04674ede, 0xa400000000000000, 0xfc6f7c4045812296, 0x4d00000000000000, 0x9dc5ada82b70b59d, 0xf020000000000000, 0xc5371912364ce305, 0x6c28000000000000,
|
||||
0xf684df56c3e01bc6, 0xc732000000000000, 0x9a130b963a6c115c, 0x3c7f400000000000, 0xc097ce7bc90715b3, 0x4b9f100000000000, 0xf0bdc21abb48db20, 0x1e86d40000000000,
|
||||
0x96769950b50d88f4, 0x1314448000000000, 0xbc143fa4e250eb31, 0x17d955a000000000, 0xeb194f8e1ae525fd, 0x5dcfab0800000000, 0x92efd1b8d0cf37be, 0x5aa1cae500000000,
|
||||
0xb7abc627050305ad, 0xf14a3d9e40000000, 0xe596b7b0c643c719, 0x6d9ccd05d0000000, 0x8f7e32ce7bea5c6f, 0xe4820023a2000000, 0xb35dbf821ae4f38b, 0xdda2802c8a800000,
|
||||
0xe0352f62a19e306e, 0xd50b2037ad200000, 0x8c213d9da502de45, 0x4526f422cc340000, 0xaf298d050e4395d6, 0x9670b12b7f410000, 0xdaf3f04651d47b4c, 0x3c0cdd765f114000,
|
||||
0x88d8762bf324cd0f, 0xa5880a69fb6ac800, 0xab0e93b6efee0053, 0x8eea0d047a457a00, 0xd5d238a4abe98068, 0x72a4904598d6d880, 0x85a36366eb71f041, 0x47a6da2b7f864750,
|
||||
0xa70c3c40a64e6c51, 0x999090b65f67d924, 0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d, 0x82818f1281ed449f, 0xbff8f10e7a8921a4, 0xa321f2d7226895c7, 0xaff72d52192b6a0d,
|
||||
0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490, 0xfee50b7025c36a08, 0x2f236d04753d5b4, 0x9f4f2726179a2245, 0x1d762422c946590, 0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5,
|
||||
0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2, 0x9b934c3b330c8577, 0x63cc55f49f88eb2f, 0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb, 0xf316271c7fc3908a, 0x8bef464e3945ef7a,
|
||||
0x97edd871cfda3a56, 0x97758bf0e3cbb5ac, 0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317, 0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd, 0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a,
|
||||
0xb975d6b6ee39e436, 0xb3e2fd538e122b44, 0xe7d34c64a9c85d44, 0x60dbbca87196b616, 0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd, 0xb51d13aea4a488dd, 0x6babab6398bdbe41,
|
||||
0xe264589a4dcdab14, 0xc696963c7eed2dd1, 0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2, 0xb0de65388cc8ada8, 0x3b25a55f43294bcb, 0xdd15fe86affad912, 0x49ef0eb713f39ebe,
|
||||
0x8a2dbf142dfcc7ab, 0x6e3569326c784337, 0xacb92ed9397bf996, 0x49c2c37f07965404, 0xd7e77a8f87daf7fb, 0xdc33745ec97be906, 0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3,
|
||||
0xa8acd7c0222311bc, 0xc40832ea0d68ce0c, 0xd2d80db02aabd62b, 0xf50a3fa490c30190, 0x83c7088e1aab65db, 0x792667c6da79e0fa, 0xa4b8cab1a1563f52, 0x577001b891185938,
|
||||
0xcde6fd5e09abcf26, 0xed4c0226b55e6f86, 0x80b05e5ac60b6178, 0x544f8158315b05b4, 0xa0dc75f1778e39d6, 0x696361ae3db1c721, 0xc913936dd571c84c, 0x3bc3a19cd1e38e9,
|
||||
0xfb5878494ace3a5f, 0x4ab48a04065c723, 0x9d174b2dcec0e47b, 0x62eb0d64283f9c76, 0xc45d1df942711d9a, 0x3ba5d0bd324f8394, 0xf5746577930d6500, 0xca8f44ec7ee36479,
|
||||
0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb, 0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e, 0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e, 0x95d04aee3b80ece5, 0xbba1f1d158724a12,
|
||||
0xbb445da9ca61281f, 0x2a8a6e45ae8edc97, 0xea1575143cf97226, 0xf52d09d71a3293bd, 0x924d692ca61be758, 0x593c2626705f9c56, 0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c,
|
||||
0xe498f455c38b997a, 0xb6dfb9c0f956447, 0x8edf98b59a373fec, 0x4724bd4189bd5eac, 0xb2977ee300c50fe7, 0x58edec91ec2cb657, 0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed,
|
||||
0x8b865b215899f46c, 0xbd79e0d20082ee74, 0xae67f1e9aec07187, 0xecd8590680a3aa11, 0xda01ee641a708de9, 0xe80e6f4820cc9495, 0x884134fe908658b2, 0x3109058d147fdcdd,
|
||||
0xaa51823e34a7eede, 0xbd4b46f0599fd415, 0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a, 0x850fadc09923329e, 0x3e2cf6bc604ddb0, 0xa6539930bf6bff45, 0x84db8346b786151c,
|
||||
0xcfe87f7cef46ff16, 0xe612641865679a63, 0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e, 0xa26da3999aef7749, 0xe3be5e330f38f09d, 0xcb090c8001ab551c, 0x5cadf5bfd3072cc5,
|
||||
0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6, 0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa, 0xc646d63501a1511d, 0xb281e1fd541501b8, 0xf7d88bc24209a565, 0x1f225a7ca91a4226,
|
||||
0x9ae757596946075f, 0x3375788de9b06958, 0xc1a12d2fc3978937, 0x52d6b1641c83ae, 0xf209787bb47d6b84, 0xc0678c5dbd23a49a, 0x9745eb4d50ce6332, 0xf840b7ba963646e0,
|
||||
0xbd176620a501fbff, 0xb650e5a93bc3d898, 0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe, 0x93ba47c980e98cdf, 0xc66f336c36b10137, 0xb8a8d9bbe123f017, 0xb80b0047445d4184,
|
||||
0xe6d3102ad96cec1d, 0xa60dc059157491e5, 0x9043ea1ac7e41392, 0x87c89837ad68db2f, 0xb454e4a179dd1877, 0x29babe4598c311fb, 0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a,
|
||||
0x8ce2529e2734bb1d, 0x1899e4a65f58660c, 0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f, 0xdc21a1171d42645d, 0x76707543f4fa1f73, 0x899504ae72497eba, 0x6a06494a791c53a8,
|
||||
0xabfa45da0edbde69, 0x487db9d17636892, 0xd6f8d7509292d603, 0x45a9d2845d3c42b6, 0x865b86925b9bc5c2, 0xb8a2392ba45a9b2, 0xa7f26836f282b732, 0x8e6cac7768d7141e,
|
||||
0xd1ef0244af2364ff, 0x3207d795430cd926, 0x8335616aed761f1f, 0x7f44e6bd49e807b8, 0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6, 0xcd036837130890a1, 0x36dba887c37a8c0f,
|
||||
0x802221226be55a64, 0xc2494954da2c9789, 0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c, 0xc83553c5c8965d3d, 0x6f92829494e5acc7, 0xfa42a8b73abbf48c, 0xcb772339ba1f17f9,
|
||||
0x9c69a97284b578d7, 0xff2a760414536efb, 0xc38413cf25e2d70d, 0xfef5138519684aba, 0xf46518c2ef5b8cd1, 0x7eb258665fc25d69, 0x98bf2f79d5993802, 0xef2f773ffbd97a61,
|
||||
0xbeeefb584aff8603, 0xaafb550ffacfd8fa, 0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38, 0x952ab45cfa97a0b2, 0xdd945a747bf26183, 0xba756174393d88df, 0x94f971119aeef9e4,
|
||||
0xe912b9d1478ceb17, 0x7a37cd5601aab85d, 0x91abb422ccb812ee, 0xac62e055c10ab33a, 0xb616a12b7fe617aa, 0x577b986b314d6009, 0xe39c49765fdf9d94, 0xed5a7e85fda0b80b,
|
||||
0x8e41ade9fbebc27d, 0x14588f13be847307, 0xb1d219647ae6b31c, 0x596eb2d8ae258fc8, 0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb, 0x8aec23d680043bee, 0x25de7bb9480d5854,
|
||||
0xada72ccc20054ae9, 0xaf561aa79a10ae6a, 0xd910f7ff28069da4, 0x1b2ba1518094da04, 0x87aa9aff79042286, 0x90fb44d2f05d0842, 0xa99541bf57452b28, 0x353a1607ac744a53,
|
||||
0xd3fa922f2d1675f2, 0x42889b8997915ce8, 0x847c9b5d7c2e09b7, 0x69956135febada11, 0xa59bc234db398c25, 0x43fab9837e699095, 0xcf02b2c21207ef2e, 0x94f967e45e03f4bb,
|
||||
0x8161afb94b44f57d, 0x1d1be0eebac278f5, 0xa1ba1ba79e1632dc, 0x6462d92a69731732, 0xca28a291859bbf93, 0x7d7b8f7503cfdcfe, 0xfcb2cb35e702af78, 0x5cda735244c3d43e,
|
||||
0x9defbf01b061adab, 0x3a0888136afa64a7, 0xc56baec21c7a1916, 0x88aaa1845b8fdd0, 0xf6c69a72a3989f5b, 0x8aad549e57273d45, 0x9a3c2087a63f6399, 0x36ac54e2f678864b,
|
||||
0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd, 0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5, 0x969eb7c47859e743, 0x9f644ae5a4b1b325, 0xbc4665b596706114, 0x873d5d9f0dde1fee,
|
||||
0xeb57ff22fc0c7959, 0xa90cb506d155a7ea, 0x9316ff75dd87cbd8, 0x9a7f12442d588f2, 0xb7dcbf5354e9bece, 0xc11ed6d538aeb2f, 0xe5d3ef282a242e81, 0x8f1668c8a86da5fa,
|
||||
0x8fa475791a569d10, 0xf96e017d694487bc, 0xb38d92d760ec4455, 0x37c981dcc395a9ac, 0xe070f78d3927556a, 0x85bbe253f47b1417, 0x8c469ab843b89562, 0x93956d7478ccec8e,
|
||||
0xaf58416654a6babb, 0x387ac8d1970027b2, 0xdb2e51bfe9d0696a, 0x6997b05fcc0319e, 0x88fcf317f22241e2, 0x441fece3bdf81f03, 0xab3c2fddeeaad25a, 0xd527e81cad7626c3,
|
||||
0xd60b3bd56a5586f1, 0x8a71e223d8d3b074, 0x85c7056562757456, 0xf6872d5667844e49, 0xa738c6bebb12d16c, 0xb428f8ac016561db, 0xd106f86e69d785c7, 0xe13336d701beba52,
|
||||
0x82a45b450226b39c, 0xecc0024661173473, 0xa34d721642b06084, 0x27f002d7f95d0190, 0xcc20ce9bd35c78a5, 0x31ec038df7b441f4, 0xff290242c83396ce, 0x7e67047175a15271,
|
||||
0x9f79a169bd203e41, 0xf0062c6e984d386, 0xc75809c42c684dd1, 0x52c07b78a3e60868, 0xf92e0c3537826145, 0xa7709a56ccdf8a82, 0x9bbcc7a142b17ccb, 0x88a66076400bb691,
|
||||
0xc2abf989935ddbfe, 0x6acff893d00ea435, 0xf356f7ebf83552fe, 0x583f6b8c4124d43, 0x98165af37b2153de, 0xc3727a337a8b704a, 0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c,
|
||||
0xeda2ee1c7064130c, 0x1162def06f79df73, 0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8, 0xb9a74a0637ce2ee1, 0x6d953e2bd7173692, 0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437,
|
||||
0x910ab1d4db9914a0, 0x1d9c9892400a22a2, 0xb54d5e4a127f59c8, 0x2503beb6d00cab4b, 0xe2a0b5dc971f303a, 0x2e44ae64840fd61d, 0x8da471a9de737e24, 0x5ceaecfed289e5d2,
|
||||
0xb10d8e1456105dad, 0x7425a83e872c5f47, 0xdd50f1996b947518, 0xd12f124e28f77719, 0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f, 0xace73cbfdc0bfb7b, 0x636cc64d1001550b,
|
||||
0xd8210befd30efa5a, 0x3c47f7e05401aa4e, 0x8714a775e3e95c78, 0x65acfaec34810a71, 0xa8d9d1535ce3b396, 0x7f1839a741a14d0d, 0xd31045a8341ca07c, 0x1ede48111209a050,
|
||||
0x83ea2b892091e44d, 0x934aed0aab460432, 0xa4e4b66b68b65d60, 0xf81da84d5617853f, 0xce1de40642e3f4b9, 0x36251260ab9d668e, 0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019,
|
||||
0xa1075a24e4421730, 0xb24cf65b8612f81f, 0xc94930ae1d529cfc, 0xdee033f26797b627, 0xfb9b7cd9a4a7443c, 0x169840ef017da3b1, 0x9d412e0806e88aa5, 0x8e1f289560ee864e,
|
||||
0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2, 0xf5b5d7ec8acb58a2, 0xae10af696774b1db, 0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29, 0xbff610b0cc6edd3f, 0x17fd090a58d32af3,
|
||||
0xeff394dcff8a948e, 0xddfc4b4cef07f5b0, 0x95f83d0a1fb69cd9, 0x4abdaf101564f98e, 0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1, 0xea53df5fd18d5513, 0x84c86189216dc5ed,
|
||||
0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4, 0xb7118682dbb66a77, 0x3fbc8c33221dc2a1, 0xe4d5e82392a40515, 0xfabaf3feaa5334a, 0x8f05b1163ba6832d, 0x29cb4d87f2a7400e,
|
||||
0xb2c71d5bca9023f8, 0x743e20e9ef511012, 0xdf78e4b2bd342cf6, 0x914da9246b255416, 0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e, 0xae9672aba3d0c320, 0xa184ac2473b529b1,
|
||||
0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e, 0x8865899617fb1871, 0x7e2fa67c7a658892, 0xaa7eebfb9df9de8d, 0xddbb901b98feeab7, 0xd51ea6fa85785631, 0x552a74227f3ea565,
|
||||
0x8533285c936b35de, 0xd53a88958f87275f, 0xa67ff273b8460356, 0x8a892abaf368f137, 0xd01fef10a657842c, 0x2d2b7569b0432d85, 0x8213f56a67f6b29b, 0x9c3b29620e29fc73,
|
||||
0xa298f2c501f45f42, 0x8349f3ba91b47b8f, 0xcb3f2f7642717713, 0x241c70a936219a73, 0xfe0efb53d30dd4d7, 0xed238cd383aa0110, 0x9ec95d1463e8a506, 0xf4363804324a40aa,
|
||||
0xc67bb4597ce2ce48, 0xb143c6053edcd0d5, 0xf81aa16fdc1b81da, 0xdd94b7868e94050a, 0x9b10a4e5e9913128, 0xca7cf2b4191c8326, 0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0,
|
||||
0xf24a01a73cf2dccf, 0xbc633b39673c8cec, 0x976e41088617ca01, 0xd5be0503e085d813, 0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18, 0xec9c459d51852ba2, 0xddf8e7d60ed1219e,
|
||||
0x93e1ab8252f33b45, 0xcabb90e5c942b503, 0xb8da1662e7b00a17, 0x3d6a751f3b936243, 0xe7109bfba19c0c9d, 0xcc512670a783ad4, 0x906a617d450187e2, 0x27fb2b80668b24c5,
|
||||
0xb484f9dc9641e9da, 0xb1f9f660802dedf6, 0xe1a63853bbd26451, 0x5e7873f8a0396973, 0x8d07e33455637eb2, 0xdb0b487b6423e1e8, 0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62,
|
||||
0xdc5c5301c56b75f7, 0x7641a140cc7810fb, 0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d, 0xac2820d9623bf429, 0x546345fa9fbdcd44, 0xd732290fbacaf133, 0xa97c177947ad4095,
|
||||
0x867f59a9d4bed6c0, 0x49ed8eabcccc485d, 0xa81f301449ee8c70, 0x5c68f256bfff5a74, 0xd226fc195c6a2f8c, 0x73832eec6fff3111, 0x83585d8fd9c25db7, 0xc831fd53c5ff7eab,
|
||||
0xa42e74f3d032f525, 0xba3e7ca8b77f5e55, 0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb, 0x80444b5e7aa7cf85, 0x7980d163cf5b81b3, 0xa0555e361951c366, 0xd7e105bcc332621f,
|
||||
0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7, 0xfa856334878fc150, 0xb14f98f6f0feb951, 0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3, 0xc3b8358109e84f07, 0xa862f80ec4700c8,
|
||||
0xf4a642e14c6262c8, 0xcd27bb612758c0fa, 0x98e7e9cccfbd7dbd, 0x8038d51cb897789c, 0xbf21e44003acdd2c, 0xe0470a63e6bd56c3, 0xeeea5d5004981478, 0x1858ccfce06cac74,
|
||||
0x95527a5202df0ccb, 0xf37801e0c43ebc8, 0xbaa718e68396cffd, 0xd30560258f54e6ba, 0xe950df20247c83fd, 0x47c6b82ef32a2069, 0x91d28b7416cdd27e, 0x4cdc331d57fa5441,
|
||||
0xb6472e511c81471d, 0xe0133fe4adf8e952, 0xe3d8f9e563a198e5, 0x58180fddd97723a6, 0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648,
|
||||
};
|
||||
|
||||
|
||||
/* Maximum mantissa for fast path: 2^53 */
|
||||
#define MAX_MANTISSA_FAST_PATH 9007199254740992ULL /* 2^53 */
|
||||
|
||||
|
|
@ -159,6 +348,190 @@ static inline uint32_t parse_eight_digits_swar(uint64_t val) {
|
|||
return (uint32_t)val;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------------
|
||||
* Eisel-Lemire algorithm — core (compute_float / am_to_double).
|
||||
*
|
||||
* Given a decimal mantissa `w` (≤ 19 digits, fits in uint64) and exponent `q`,
|
||||
* compute the correctly-rounded `double` representing `w * 10^q`. Internally:
|
||||
*
|
||||
* 1. Shift `w` so its leading bit is set (full 64-bit mantissa).
|
||||
* 2. Multiply by the 128-bit precomputed power-of-five entry above.
|
||||
* 3. Extract the 53-bit mantissa from the high 64 bits of the product, with
|
||||
* one extra bit for round-to-nearest-even.
|
||||
* 4. Apply the round-half-to-even rule, including the rare power-of-2 tie
|
||||
* case that needs a second-pass check.
|
||||
*
|
||||
* For the 19-digit / |q| ≤ 22 input range the result is provably bit-exact
|
||||
* with strtod() (Mushtak & Lemire, "Fast Number Parsing Without Fallback").
|
||||
* The caller falls back to strtod() if compute_float() signals indeterminate
|
||||
* (we never trigger that branch with parse_number_string's bounded inputs).
|
||||
*
|
||||
* Ported from fast_float by Daniel Lemire & Joao Paulo Magalhaes
|
||||
* (MIT-licensed, https://github.com/fastfloat/fast_float — decimal_to_binary.h
|
||||
* and float_common.h). C++ template machinery dropped in favour of a
|
||||
* double-only specialisation; struct layouts kept to ease future review.
|
||||
* ---------------------------------------------------------------------------- */
|
||||
|
||||
/* IEEE-754 binary64 constants (mirrors fast_float's binary_format<double>). */
|
||||
#define DOUBLE_MANTISSA_EXPLICIT_BITS 52
|
||||
#define DOUBLE_MIN_EXPONENT_ROUND_EVEN -4
|
||||
#define DOUBLE_MAX_EXPONENT_ROUND_EVEN 23
|
||||
#define DOUBLE_MINIMUM_EXPONENT -1023
|
||||
#define DOUBLE_INFINITE_POWER 0x7FF
|
||||
|
||||
/* 128-bit unsigned, little-endian: low holds bits [0..63]. */
|
||||
typedef struct {
|
||||
uint64_t low;
|
||||
uint64_t high;
|
||||
} value128;
|
||||
|
||||
/* Result of compute_float(): a 53-bit mantissa and a biased binary exponent.
|
||||
* power2 < 0 signals indeterminate (caller should fall back to strtod()). */
|
||||
typedef struct {
|
||||
uint64_t mantissa;
|
||||
int32_t power2;
|
||||
} adjusted_mantissa;
|
||||
|
||||
/* `__builtin_clzll` is undefined on input 0 — caller guarantees v > 0. */
|
||||
static inline int leading_zeroes_u64(uint64_t v) {
|
||||
return __builtin_clzll(v);
|
||||
}
|
||||
|
||||
/* 64x64 -> 128 multiplication. __uint128_t is available on every 64-bit
|
||||
* target Redis supports (gated explicitly in the call site). */
|
||||
static inline value128 full_multiplication(uint64_t a, uint64_t b) {
|
||||
value128 r;
|
||||
#ifdef __SIZEOF_INT128__
|
||||
__uint128_t prod = (__uint128_t)a * (__uint128_t)b;
|
||||
r.low = (uint64_t)prod;
|
||||
r.high = (uint64_t)(prod >> 64);
|
||||
#else
|
||||
/* 32-bit fallback: split each operand into two 32-bit halves. */
|
||||
uint64_t a_lo = (uint32_t)a, a_hi = a >> 32;
|
||||
uint64_t b_lo = (uint32_t)b, b_hi = b >> 32;
|
||||
uint64_t ll = a_lo * b_lo;
|
||||
uint64_t lh = a_lo * b_hi;
|
||||
uint64_t hl = a_hi * b_lo;
|
||||
uint64_t hh = a_hi * b_hi;
|
||||
uint64_t mid = (ll >> 32) + (uint32_t)lh + (uint32_t)hl;
|
||||
r.low = (mid << 32) | (uint32_t)ll;
|
||||
r.high = hh + (lh >> 32) + (hl >> 32) + (mid >> 32);
|
||||
#endif
|
||||
return r;
|
||||
}
|
||||
|
||||
/* For q in (-400, 350), this approximates floor(log2(5^q)) + q + 63
|
||||
* (or -ceil(log2(5^|q|)) + q + 63 for negative q). Used to derive power2. */
|
||||
static inline int32_t eisel_lemire_power(int32_t q) {
|
||||
return (((152170 + 65536) * q) >> 16) + 63;
|
||||
}
|
||||
|
||||
/* 128-bit approximation of `w * 5^q`. The optional fixup multiplies by the
|
||||
* second (extension) entry of the power-of-five table when the high half is
|
||||
* close to a rounding boundary. Mathematical proof of sufficiency: see
|
||||
* Mushtak & Lemire, "Fast Number Parsing Without Fallback". */
|
||||
static inline value128 compute_product_approximation_d(int64_t q, uint64_t w) {
|
||||
int index = 2 * (int)(q - EISEL_LEMIRE_SMALLEST_POWER_OF_FIVE);
|
||||
value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
|
||||
/* For double, bit_precision = mantissa_explicit_bits (52) + 3 = 55. */
|
||||
const uint64_t precision_mask =
|
||||
(uint64_t)0xFFFFFFFFFFFFFFFFULL >> 55;
|
||||
if ((firstproduct.high & precision_mask) == precision_mask) {
|
||||
value128 secondproduct =
|
||||
full_multiplication(w, power_of_five_128[index + 1]);
|
||||
firstproduct.low += secondproduct.high;
|
||||
if (secondproduct.high > firstproduct.low) {
|
||||
firstproduct.high++;
|
||||
}
|
||||
}
|
||||
return firstproduct;
|
||||
}
|
||||
|
||||
/* Eisel-Lemire main: compute a correctly-rounded representation of w * 10^q.
|
||||
* Returns an `adjusted_mantissa`. Special outputs:
|
||||
* - mantissa == 0 && power2 == 0: result is +/-0
|
||||
* - power2 == DOUBLE_INFINITE_POWER && mantissa == 0: result is infinity
|
||||
* - power2 < 0: indeterminate (caller should fall back to strtod()). With
|
||||
* parse_number_string()'s bounded mantissa (<= 19 digits), this branch
|
||||
* is unreachable, but we keep the signature for safety.
|
||||
*/
|
||||
static adjusted_mantissa compute_float_d(int64_t q, uint64_t w) {
|
||||
adjusted_mantissa answer;
|
||||
|
||||
if (w == 0 || q < EISEL_LEMIRE_SMALLEST_POWER_OF_FIVE) {
|
||||
answer.power2 = 0;
|
||||
answer.mantissa = 0;
|
||||
return answer;
|
||||
}
|
||||
if (q > EISEL_LEMIRE_LARGEST_POWER_OF_FIVE) {
|
||||
answer.power2 = DOUBLE_INFINITE_POWER;
|
||||
answer.mantissa = 0;
|
||||
return answer;
|
||||
}
|
||||
|
||||
/* Renormalise w so its top bit is set. */
|
||||
int lz = leading_zeroes_u64(w);
|
||||
w <<= lz;
|
||||
|
||||
value128 product = compute_product_approximation_d(q, w);
|
||||
|
||||
int upperbit = (int)(product.high >> 63);
|
||||
int shift = upperbit + 64 - DOUBLE_MANTISSA_EXPLICIT_BITS - 3;
|
||||
|
||||
answer.mantissa = product.high >> shift;
|
||||
answer.power2 = (int32_t)(eisel_lemire_power((int32_t)q) + upperbit - lz - DOUBLE_MINIMUM_EXPONENT);
|
||||
|
||||
if (answer.power2 <= 0) {
|
||||
/* Subnormal path. */
|
||||
if (-answer.power2 + 1 >= 64) {
|
||||
/* More than 64 bits below minimum exponent — definitely zero. */
|
||||
answer.power2 = 0;
|
||||
answer.mantissa = 0;
|
||||
return answer;
|
||||
}
|
||||
/* Safe: -answer.power2 + 1 < 64. */
|
||||
answer.mantissa >>= -answer.power2 + 1;
|
||||
answer.mantissa += (answer.mantissa & 1); /* round up */
|
||||
answer.mantissa >>= 1;
|
||||
/* If post-rounding the value crosses back into the normal range, mark
|
||||
* it normal (power2 = 1) rather than subnormal (power2 = 0). */
|
||||
answer.power2 = (answer.mantissa < ((uint64_t)1 << DOUBLE_MANTISSA_EXPLICIT_BITS)) ? 0 : 1;
|
||||
return answer;
|
||||
}
|
||||
|
||||
/* Normal path: handle the round-half-to-even tie case. */
|
||||
if ((product.low <= 1) &&
|
||||
(q >= DOUBLE_MIN_EXPONENT_ROUND_EVEN) &&
|
||||
(q <= DOUBLE_MAX_EXPONENT_ROUND_EVEN) &&
|
||||
((answer.mantissa & 3) == 1)) {
|
||||
if ((answer.mantissa << shift) == product.high) {
|
||||
answer.mantissa &= ~(uint64_t)1; /* clear LSB so we round down */
|
||||
}
|
||||
}
|
||||
answer.mantissa += (answer.mantissa & 1);
|
||||
answer.mantissa >>= 1;
|
||||
if (answer.mantissa >= ((uint64_t)2 << DOUBLE_MANTISSA_EXPLICIT_BITS)) {
|
||||
answer.mantissa = (uint64_t)1 << DOUBLE_MANTISSA_EXPLICIT_BITS;
|
||||
answer.power2++;
|
||||
}
|
||||
answer.mantissa &= ~((uint64_t)1 << DOUBLE_MANTISSA_EXPLICIT_BITS);
|
||||
if (answer.power2 >= DOUBLE_INFINITE_POWER) {
|
||||
answer.power2 = DOUBLE_INFINITE_POWER;
|
||||
answer.mantissa = 0;
|
||||
}
|
||||
return answer;
|
||||
}
|
||||
|
||||
/* Pack adjusted_mantissa back to a double via IEEE-754 bit layout. */
|
||||
static inline double am_to_double(int negative, adjusted_mantissa am) {
|
||||
uint64_t word = am.mantissa;
|
||||
word |= (uint64_t)am.power2 << DOUBLE_MANTISSA_EXPLICIT_BITS;
|
||||
if (negative) word |= (uint64_t)1 << 63;
|
||||
double value;
|
||||
memcpy(&value, &word, sizeof(value));
|
||||
return value;
|
||||
}
|
||||
|
||||
/* Parse a decimal number string into components.
|
||||
* This follows the fast_float algorithm closely. */
|
||||
static inline int parse_number_string(const char *p, const char *pend, double *result, const char **endptr) {
|
||||
|
|
@ -261,65 +634,42 @@ static inline int parse_number_string(const char *p, const char *pend, double *r
|
|||
if (digit_count > MAX_DIGITS) return 0;
|
||||
}
|
||||
|
||||
/* Check if we're within fast path bounds */
|
||||
if (exponent < MIN_EXPONENT_FAST_PATH) return 0;
|
||||
if (exponent > MAX_EXPONENT_FAST_PATH) return 0;
|
||||
|
||||
/* Pick the conversion path. Two regimes:
|
||||
* Clinger fast path: small mantissa (<= 2^53) and small |exp| (<= 22).
|
||||
* One double multiply or divide; cheapest, exact by construction.
|
||||
* Eisel-Lemire: large mantissa or wide exponent range (full double
|
||||
* domain). Slightly slower per call (128-bit multiply + table lookup)
|
||||
* but correctly-rounded by the Mushtak-Lemire proof.
|
||||
* Inputs outside both ranges fall back to strtod() (caller of this fn). */
|
||||
double value;
|
||||
if (mantissa <= MAX_MANTISSA_FAST_PATH) {
|
||||
if (mantissa <= MAX_MANTISSA_FAST_PATH &&
|
||||
exponent >= MIN_EXPONENT_FAST_PATH &&
|
||||
exponent <= MAX_EXPONENT_FAST_PATH)
|
||||
{
|
||||
/* Clinger fast path: all operands exact in double precision,
|
||||
* single multiply/divide produces a correctly-rounded result. */
|
||||
value = (double)mantissa;
|
||||
if (exponent < 0) value = value / powers_of_ten[-exponent];
|
||||
else if (exponent > 0) value = value * powers_of_ten[exponent];
|
||||
if (negative) value = -value;
|
||||
} else {
|
||||
#ifdef __SIZEOF_INT128__
|
||||
/* Widened fast path for 17-19 significant-digit mantissas.
|
||||
*
|
||||
* (double)mantissa alone loses up to 11 bits when mantissa > 2^53,
|
||||
* so the existing Clinger path would yield up to 1 ULP vs strtod.
|
||||
* We recover full precision by doing the multiply/divide in 128-bit
|
||||
* integer arithmetic (correctly-rounded by construction). Cases
|
||||
* outside the supported exponent range fall through to strtod.
|
||||
*
|
||||
* Requires __uint128_t (GCC/Clang builtin, available on every 64-bit
|
||||
* target Redis supports). 32-bit builds take the strtod() fallback. */
|
||||
if (exponent < -19 || exponent > 19) return 0;
|
||||
/* Eisel-Lemire path. Replaces a previously hand-rolled widened branch
|
||||
* (`(double)hi * 2^64 + (double)lo` shortcut) that produced ±1 ULP
|
||||
* mismatches vs strtod() on inputs like 9007199255094284e-19 and
|
||||
* 2489830482329185244e1. compute_float_d is bit-exact with strtod()
|
||||
* for every input parse_number_string can produce. */
|
||||
if (exponent < EISEL_LEMIRE_SMALLEST_POWER_OF_FIVE || exponent > EISEL_LEMIRE_LARGEST_POWER_OF_FIVE)
|
||||
return 0;
|
||||
|
||||
if (exponent >= 0) {
|
||||
/* (mantissa * 10^e) fits in 128 bits. Convert exactly: the
|
||||
* single (double) cast from __uint128_t rounds to nearest. */
|
||||
__uint128_t prod = (__uint128_t)mantissa * (uint64_t)powers_of_ten[exponent];
|
||||
uint64_t hi = (uint64_t)(prod >> 64);
|
||||
uint64_t lo = (uint64_t)prod;
|
||||
/* (double)hi * 2^64 has no rounding error (hi up to 2^64-1 rounds
|
||||
* once, then * 2^64 is exact). Adding lo rounds once. Total:
|
||||
* matches strtod on every tested case with e in [0,19]. */
|
||||
value = (double)hi * 18446744073709551616.0 + (double)lo;
|
||||
} else {
|
||||
/* mantissa / 10^|e|: scale numerator up by 2^64 before integer
|
||||
* division to preserve precision, then descale by multiplying by
|
||||
* 2^-64 (exact power-of-two scaling, does not round). The single
|
||||
* (double) cast of the integer quotient produces IEEE round-to-
|
||||
* nearest-even, matching strtod() bit-exactly for every tested
|
||||
* 16-19 significant digit case. */
|
||||
uint64_t divisor = (uint64_t)powers_of_ten[-exponent];
|
||||
__uint128_t scaled = (__uint128_t)mantissa << 64;
|
||||
__uint128_t q = scaled / divisor;
|
||||
uint64_t hi = (uint64_t)(q >> 64);
|
||||
uint64_t lo = (uint64_t)q;
|
||||
value = ((double)hi * 18446744073709551616.0 + (double)lo)
|
||||
* 5.421010862427522170037e-20; /* 2^-64 */
|
||||
}
|
||||
#else
|
||||
/* 32-bit target without __uint128_t: fall through to the strtod()
|
||||
* fallback. Correctness is preserved (it's the same path that shipped
|
||||
* in 8.8-M02); only the perf gain is 64-bit-target-specific. */
|
||||
return 0;
|
||||
#endif
|
||||
adjusted_mantissa am = compute_float_d(exponent, mantissa);
|
||||
/* power2 < 0 would mean indeterminate (caller should fall back to
|
||||
* strtod). With our bounded mantissa (<= 19 digits) this branch is
|
||||
* unreachable per the Mushtak-Lemire proof, but we keep the guard so
|
||||
* any future caller that supplies a larger mantissa stays correct. */
|
||||
if (am.power2 < 0) return 0;
|
||||
value = am_to_double(negative, am);
|
||||
}
|
||||
|
||||
if (negative) value = -value;
|
||||
*result = value;
|
||||
return 1;
|
||||
}
|
||||
|
|
@ -524,9 +874,87 @@ int fastFloatTest(int argc, char **argv, int flags) {
|
|||
/* Negative numbers exercising the widened path */
|
||||
{"-0.49606648747577575", -0.49606648747577575},
|
||||
{"-9007199254740993", -9007199254740992.0},
|
||||
|
||||
/* Eisel-Lemire rounding-boundary cases.
|
||||
* Reported by @vitahlin on #14661 against the previous
|
||||
* `(double)hi * 2^64 + (double)lo` widened branch which
|
||||
* double-rounded the 128-bit product. Both must now match
|
||||
* strtod() exactly. */
|
||||
{"9007199255094284e-19", 9007199255094284e-19}, /* was -1 ULP */
|
||||
{"2489830482329185244e1", 2489830482329185244e1}, /* was +1 ULP */
|
||||
|
||||
/* Subnormal boundaries (Eisel-Lemire's subnormal branch). */
|
||||
{"5e-324", 5e-324}, /* smallest pos subnormal */
|
||||
{"4.9e-324", 5e-324}, /* below half: rounds up */
|
||||
{"2.2250738585072009e-308", 2.2250738585072009e-308}, /* largest subnormal */
|
||||
{"2.2250738585072014e-308", 2.2250738585072014e-308}, /* smallest normal */
|
||||
{"1e-323", 1e-323},
|
||||
|
||||
/* Round-half-to-even ties: post-Clinger range, hits compute_float_d
|
||||
* tie path (product.low <= 1, q in [-4, 23], mantissa & 3 == 1). */
|
||||
{"5497558138880", 5497558138880.0}, /* 2^42 + 2^33 boundary */
|
||||
{"5e-22", 5e-22},
|
||||
{"7.038531e-26", 7.038531e-26},
|
||||
{"4503599627475501e-10", 4503599627475501e-10}, /* near 2^52 */
|
||||
|
||||
/* Largest finite double + overflow. */
|
||||
{"1.7976931348623157e308", 1.7976931348623157e308}, /* DBL_MAX */
|
||||
{"1.7976931348623158e308", 1.7976931348623157e308}, /* nearest is DBL_MAX */
|
||||
{"1e308", 1e308},
|
||||
|
||||
/* Wide exponent range now reachable via Eisel-Lemire (previously
|
||||
* fell to strtod). */
|
||||
{"1.234567890123456e100", 1.234567890123456e100},
|
||||
{"9.999999999999999e99", 9.999999999999999e99},
|
||||
{"1e-300", 1e-300},
|
||||
{"1.7e-300", 1.7e-300},
|
||||
|
||||
/* Repunit / many-9 mantissas — adjacent-double tie territory. */
|
||||
{"9999999999999998", 9999999999999998.0},
|
||||
{"99999999999999999", 1e17},
|
||||
};
|
||||
run_ff_tests(decimal_ok, COUNTOF(decimal_ok), 0);
|
||||
|
||||
/* Differential cross-check: every accepted input must produce the
|
||||
* exact same bits as libc strtod(). Hand-picked hard cases covering
|
||||
* every code path in compute_float_d (subnormal branch, round-half-
|
||||
* to-even tie path, near-infinity, repunit mantissa, wide exponent). */
|
||||
{
|
||||
static const char *diff_inputs[] = {
|
||||
/* Boundary classics around 2^53. */
|
||||
"9007199254740992", "9007199254740993", "9007199254740994",
|
||||
"9007199254740995", "9007199254740996",
|
||||
/* Limits of finite double. */
|
||||
"1.7976931348623157e308", "2.2250738585072014e-308",
|
||||
"5e-324", "1e-323", "4.9406564584124654e-324",
|
||||
/* The two reproducer inputs the previous widened branch missed. */
|
||||
"9007199255094284e-19", "2489830482329185244e1",
|
||||
/* Mushtak-Lemire stress range — 19-digit mantissas. */
|
||||
"1234567890123456789e0", "1234567890123456789e-5",
|
||||
"1234567890123456789e5", "9999999999999999e19",
|
||||
/* Common scientific constants — mid-exponent sanity. */
|
||||
"3.141592653589793", "2.718281828459045",
|
||||
"1.4142135623730951e150", "6.022140857e23",
|
||||
"1.602176634e-19", "9.10938356e-31",
|
||||
};
|
||||
for (int i = 0; i < COUNTOF(diff_inputs); i++) {
|
||||
const char *s = diff_inputs[i];
|
||||
char *fend, *lend;
|
||||
errno = 0;
|
||||
double got = fast_float_strtod(s, strlen(s), &fend);
|
||||
errno = 0;
|
||||
double libc = strtod(s, &lend);
|
||||
uint64_t gb, lb;
|
||||
memcpy(&gb, &got, sizeof(gb));
|
||||
memcpy(&lb, &libc, sizeof(lb));
|
||||
char descr[160];
|
||||
snprintf(descr, sizeof(descr),
|
||||
"differential vs strtod: \"%s\" ff=0x%016llx libc=0x%016llx",
|
||||
s, (unsigned long long)gb, (unsigned long long)lb);
|
||||
test_cond(descr, gb == lb);
|
||||
}
|
||||
}
|
||||
|
||||
/* No valid prefix for full buffer, or trailing junk. */
|
||||
ff_testcase decimal_bad[] = {
|
||||
{"1abc", 1.0},
|
||||
|
|
|
|||
Loading…
Reference in a new issue