mirror of
https://github.com/ii64/sonic.git
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feat: optimize float-to-str encoding through the Ryu algorithm (#60)
Co-authored-by: liuqiang <liuqiang.06@bytedance.com> Co-authored-by: Oxygen <chenzhuoyu@users.noreply.github.com>
This commit is contained in:
liu
GitHub
parent
c2ea100389
commit
83208b7ac4
7 changed files with 5633 additions and 2754 deletions
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@ -14,21 +14,21 @@ func ___asm2asm_compiled_code__DO_NOT_CALL_THIS_SYMBOL___()
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var (
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_func__base = ___asm2asm_compiled_code__DO_NOT_CALL_THIS_SYMBOL___
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_subr__f64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 574
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_subr__i64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3638
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_subr__f64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 558
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_subr__i64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3541
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_subr__lspace = **(**uintptr)(unsafe.Pointer(&_func__base)) + 238
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_subr__lzero = **(**uintptr)(unsafe.Pointer(&_func__base)) + 0
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_subr__quote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 4951
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_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15993
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_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 16028
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_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13671
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_subr__u64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3731
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_subr__unquote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 5972
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_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 9426
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_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 12001
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_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13121
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_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11032
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_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13398
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_subr__quote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 4854
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_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15896
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_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15931
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_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13574
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_subr__u64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3634
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_subr__unquote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 5875
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_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 9329
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_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11904
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_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13024
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_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 10935
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_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13301
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)
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var (
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File diff suppressed because it is too large
Load diff
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@ -14,21 +14,21 @@ func ___asm2asm_compiled_code__DO_NOT_CALL_THIS_SYMBOL___()
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var (
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_func__base = ___asm2asm_compiled_code__DO_NOT_CALL_THIS_SYMBOL___
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_subr__f64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 822
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_subr__i64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3886
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_subr__f64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 806
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_subr__i64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3789
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_subr__lspace = **(**uintptr)(unsafe.Pointer(&_func__base)) + 366
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_subr__lzero = **(**uintptr)(unsafe.Pointer(&_func__base)) + 0
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_subr__quote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 5299
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_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 18413
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_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 18448
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_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15613
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_subr__u64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3979
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_subr__unquote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 7136
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_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11379
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_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13943
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_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15063
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_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13090
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_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15340
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_subr__quote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 5202
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_subr__skip_array = **(**uintptr)(unsafe.Pointer(&_func__base)) + 18316
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_subr__skip_object = **(**uintptr)(unsafe.Pointer(&_func__base)) + 18351
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_subr__skip_one = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15516
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_subr__u64toa = **(**uintptr)(unsafe.Pointer(&_func__base)) + 3882
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_subr__unquote = **(**uintptr)(unsafe.Pointer(&_func__base)) + 7039
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_subr__value = **(**uintptr)(unsafe.Pointer(&_func__base)) + 11282
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_subr__vnumber = **(**uintptr)(unsafe.Pointer(&_func__base)) + 13846
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_subr__vsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 14966
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_subr__vstring = **(**uintptr)(unsafe.Pointer(&_func__base)) + 12993
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_subr__vunsigned = **(**uintptr)(unsafe.Pointer(&_func__base)) + 15243
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)
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var (
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@ -1,437 +1,472 @@
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/*
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* Copyright 2021 ByteDance Inc.
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/* Copyright 2018 Ulf Adams.
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* Modifications copyright 2021 ByteDance Inc.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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* The contents of this file may be used under the terms of the Apache License,
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* Version 2.0.
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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* (See accompanying file LICENSE-Apache or copy at
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* http: *www.apache.org/licenses/LICENSE-2.0)
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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* Alternatively, the contents of this file may be used under the terms of
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* the Boost Software License, Version 1.0.
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* (See accompanying file LICENSE-Boost or copy at
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* https: *www.boost.org/LICENSE_1_0.txt)
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*
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* Unless required by applicable law or agreed to in writing, this software
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* is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
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* KIND, either express or implied.
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*/
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/** This is the Florian's Grisu2 Algorithm implemented in C.
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* See https://legacy.cs.indiana.edu/~dyb/pubs/FP-Printing-PLDI96.pdf for more info.
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*/
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#include "native.h"
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#include "ryu_tab.h"
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struct f64_t {
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int32_t e;
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uint64_t f;
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};
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/* use 128-bit type for performance */
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typedef __uint128_t uint128_t;
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#define FP_SSIZE 64
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#define DP_SSIZE 52
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#define DP_1_LG10 0.30102999566398114 // = 1 / log2(10)
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#define F64_EBIAS 1075
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#define F64_EXMIN -F64_EBIAS
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#define F64_HBIT 0x0010000000000000
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#define F64_EMASK 0x7ff0000000000000
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#define F64_SMASK 0x000fffffffffffff
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static const int16_t TabPowE[87] = {
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-1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980,
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-954, -927, -901, -874, -847, -821, -794, -768, -741, -715,
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-688, -661, -635, -608, -582, -555, -529, -502, -475, -449,
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-422, -396, -369, -343, -316, -289, -263, -236, -210, -183,
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-157, -130, -103, -77, -50, -24, 3, 30, 56, 83,
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109, 136, 162, 189, 216, 242, 269, 295, 322, 348,
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375, 402, 428, 455, 481, 508, 534, 561, 588, 614,
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641, 667, 694, 720, 747, 774, 800, 827, 853, 880,
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907, 933, 960, 986, 1013, 1039, 1066
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};
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static const uint64_t TabPowF[87] = {
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0xfa8fd5a0081c0288, 0xbaaee17fa23ebf76,
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0x8b16fb203055ac76, 0xcf42894a5dce35ea,
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0x9a6bb0aa55653b2d, 0xe61acf033d1a45df,
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0xab70fe17c79ac6ca, 0xff77b1fcbebcdc4f,
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0xbe5691ef416bd60c, 0x8dd01fad907ffc3c,
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0xd3515c2831559a83, 0x9d71ac8fada6c9b5,
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0xea9c227723ee8bcb, 0xaecc49914078536d,
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0x823c12795db6ce57, 0xc21094364dfb5637,
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0x9096ea6f3848984f, 0xd77485cb25823ac7,
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0xa086cfcd97bf97f4, 0xef340a98172aace5,
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0xb23867fb2a35b28e, 0x84c8d4dfd2c63f3b,
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0xc5dd44271ad3cdba, 0x936b9fcebb25c996,
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0xdbac6c247d62a584, 0xa3ab66580d5fdaf6,
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0xf3e2f893dec3f126, 0xb5b5ada8aaff80b8,
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0x87625f056c7c4a8b, 0xc9bcff6034c13053,
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0x964e858c91ba2655, 0xdff9772470297ebd,
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0xa6dfbd9fb8e5b88f, 0xf8a95fcf88747d94,
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0xb94470938fa89bcf, 0x8a08f0f8bf0f156b,
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0xcdb02555653131b6, 0x993fe2c6d07b7fac,
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0xe45c10c42a2b3b06, 0xaa242499697392d3,
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0xfd87b5f28300ca0e, 0xbce5086492111aeb,
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0x8cbccc096f5088cc, 0xd1b71758e219652c,
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0x9c40000000000000, 0xe8d4a51000000000,
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0xad78ebc5ac620000, 0x813f3978f8940984,
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0xc097ce7bc90715b3, 0x8f7e32ce7bea5c70,
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0xd5d238a4abe98068, 0x9f4f2726179a2245,
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0xed63a231d4c4fb27, 0xb0de65388cc8ada8,
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0x83c7088e1aab65db, 0xc45d1df942711d9a,
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0x924d692ca61be758, 0xda01ee641a708dea,
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0xa26da3999aef774a, 0xf209787bb47d6b85,
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0xb454e4a179dd1877, 0x865b86925b9bc5c2,
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0xc83553c5c8965d3d, 0x952ab45cfa97a0b3,
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0xde469fbd99a05fe3, 0xa59bc234db398c25,
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0xf6c69a72a3989f5c, 0xb7dcbf5354e9bece,
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0x88fcf317f22241e2, 0xcc20ce9bd35c78a5,
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0x98165af37b2153df, 0xe2a0b5dc971f303a,
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0xa8d9d1535ce3b396, 0xfb9b7cd9a4a7443c,
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0xbb764c4ca7a44410, 0x8bab8eefb6409c1a,
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0xd01fef10a657842c, 0x9b10a4e5e9913129,
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0xe7109bfba19c0c9d, 0xac2820d9623bf429,
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0x80444b5e7aa7cf85, 0xbf21e44003acdd2d,
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0x8e679c2f5e44ff8f, 0xd433179d9c8cb841,
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0x9e19db92b4e31ba9, 0xeb96bf6ebadf77d9,
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0xaf87023b9bf0ee6b
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};
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static const uint64_t TabPow10[10] = {
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1,
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10,
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100,
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1000,
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10000,
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100000,
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1000000,
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10000000,
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100000000,
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1000000000
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};
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/** FP-64 Helper **/
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static inline void f64_set(struct f64_t *r, double v) {
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uint64_t bv = *(uint64_t *)&v;
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uint64_t sv = bv & F64_SMASK;
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int32_t ev = (bv & F64_EMASK) >> DP_SSIZE;
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/* check for denormalized values */
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if (ev == 0) {
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r->f = sv;
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r->e = F64_EXMIN + 1;
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} else {
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r->f = sv + F64_HBIT;
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r->e = ev - F64_EBIAS;
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}
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/* Returns e == 0 ? 1 : ceil(log_2(5^e)) */
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static inline int32_t pow5bits(const int32_t e) {
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return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1);
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}
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static inline void f64_raw(struct f64_t *r, uint64_t f, int32_t e) {
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r->e = e;
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r->f = f;
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/* Returns floor(log_10(2^e)) */
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static inline uint32_t log10pow2(const int32_t e) {
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return (((uint32_t) e) * 78913) >> 18;
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}
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static inline void f64_sub(struct f64_t *r, const struct f64_t *a, const struct f64_t *b) {
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r->e = a->e;
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r->f = a->f - b->f;
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/* Returns floor(log_10(5^e)) */
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static inline uint32_t log10pow5(const int32_t e) {
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return (((uint32_t) e) * 732923) >> 20;
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}
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static inline void f64_mul(struct f64_t *r, const struct f64_t *a, const struct f64_t *b) {
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__int128_t v0 = a->f;
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__int128_t v1 = b->f;
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__int128_t v2 = v0 * v1;
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uint64_t vh = v2 >> 64;
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uint64_t vl = (uint64_t)v2;
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/* rounding */
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if (vl & (1ull << 63)) {
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vh++;
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}
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/* save the result */
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r->f = vh;
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r->e = a->e + b->e + 64;
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}
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static inline void f64_norm(struct f64_t *r, const struct f64_t *v) {
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uint64_t f = v->f;
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uint32_t s = __builtin_clzll(f);
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/* remove the leading zeros, and adjust the exponent */
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r->f = f << s;
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r->e = v->e - s;
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}
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static inline void f64_normb(struct f64_t *m, struct f64_t *p, const struct f64_t *v) {
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int32_t dv = v->f != F64_HBIT ? 1 : 2;
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int32_t e0 = v->e - 1;
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int32_t e1 = v->e - dv;
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uint64_t f0 = (v->f << 1) + 1;
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uint64_t f1 = (v->f << dv) - 1;
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uint32_t sh = __builtin_clzll(f0);
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/* calculate the m+ */
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p->e = e0 - sh;
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p->f = f0 << sh;
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/* calculate the m- */
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m->e = p->e;
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m->f = f1 << (e1 - p->e);
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}
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static inline void f64_power(struct f64_t *v, int e, int *k) {
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double dk = (-61 - e) * DP_1_LG10 + 347;
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int32_t ik = (int32_t)dk;
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uint32_t id;
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/* ceil the logrithmic result */
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if (dk - ik > 0.0) {
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ik++;
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}
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/* calculate the K value */
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id = (uint32_t)(ik >> 3) + 1;
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*k = 348 - (int32_t)(id << 3);
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/* lookup the power */
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v->e = TabPowE[id];
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v->f = TabPowF[id];
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}
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/** Florian's Grisu2 Algorithm **/
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static const char TabDigits[200] = {
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'0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
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'1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
|
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'2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
|
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'3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
|
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'4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
|
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'5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
|
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'6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
|
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'7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
|
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'8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
|
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'9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
|
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};
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|
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static inline int ctz10(uint64_t n) {
|
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if (n < 10) return 1;
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if (n < 100) return 2;
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if (n < 1000) return 3;
|
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if (n < 10000) return 4;
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if (n < 100000) return 5;
|
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if (n < 1000000) return 6;
|
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if (n < 10000000) return 7;
|
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if (n < 100000000) return 8;
|
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if (n < 1000000000) return 9;
|
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return 10;
|
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}
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|
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static inline int divmod(uint64_t *p1, int kp) {
|
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switch (kp) {
|
||||
case 10: kp = *p1 / 1000000000; *p1 %= 1000000000; return kp;
|
||||
case 9: kp = *p1 / 100000000; *p1 %= 100000000; return kp;
|
||||
case 8: kp = *p1 / 10000000; *p1 %= 10000000; return kp;
|
||||
case 7: kp = *p1 / 1000000; *p1 %= 1000000; return kp;
|
||||
case 6: kp = *p1 / 100000; *p1 %= 100000; return kp;
|
||||
case 5: kp = *p1 / 10000; *p1 %= 10000; return kp;
|
||||
case 4: kp = *p1 / 1000; *p1 %= 1000; return kp;
|
||||
case 3: kp = *p1 / 100; *p1 %= 100; return kp;
|
||||
case 2: kp = *p1 / 10; *p1 %= 10; return kp;
|
||||
case 1: kp = *p1; *p1 = 0; return kp;
|
||||
default: __builtin_unreachable();
|
||||
}
|
||||
}
|
||||
|
||||
static inline void roundg(char *p, uint64_t d, uint64_t r, uint64_t kp10, uint64_t dpw) {
|
||||
while (r < dpw && d - r >= kp10 && (r + kp10 < dpw || dpw - r > r + kp10 - dpw)) {
|
||||
r += kp10;
|
||||
p[-1] -= 1;
|
||||
}
|
||||
}
|
||||
|
||||
static inline int digits(char *p, int *k, const struct f64_t *w, const struct f64_t *m, uint64_t d) {
|
||||
uint32_t dv;
|
||||
uint64_t vt;
|
||||
struct f64_t dpw;
|
||||
struct f64_t one;
|
||||
|
||||
/* initial state */
|
||||
f64_sub(&dpw, m, w);
|
||||
f64_raw(&one, 1ull << -m->e, m->e);
|
||||
|
||||
/* m+ cutoff */
|
||||
uint64_t p1 = m->f >> -one.e;
|
||||
uint64_t p2 = m->f & (one.f - 1);
|
||||
|
||||
/* count the integer part length */
|
||||
char * pb = p;
|
||||
int32_t kp = ctz10(p1);
|
||||
|
||||
/* small values */
|
||||
while (kp > 0) {
|
||||
dv = divmod(&p1, kp);
|
||||
kp--;
|
||||
|
||||
/* write one digit */
|
||||
if (dv || p > pb) {
|
||||
*p++ = (char)(dv + '0');
|
||||
}
|
||||
|
||||
/* calculate the error */
|
||||
vt = p1 << -one.e;
|
||||
vt += p2;
|
||||
|
||||
/* check the precision */
|
||||
if (vt <= d) {
|
||||
*k += kp;
|
||||
roundg(p, d, vt, TabPow10[kp] << -one.e, dpw.f);
|
||||
return p - pb;
|
||||
}
|
||||
}
|
||||
|
||||
/* large values (longer than 6 leading digits) */
|
||||
static inline uint32_t pow5factor(uint64_t v) {
|
||||
uint64_t m_inv5 = 14757395258967641293u; // *5 = 1(mod 2^64)
|
||||
uint64_t n_div5 = 3689348814741910323u; // =2^64 / 5
|
||||
uint32_t cnt = 0;
|
||||
for (;;) {
|
||||
d *= 10;
|
||||
p2 *= 10;
|
||||
dv = (p2 >> -one.e) & 0xff;
|
||||
p2 &= one.f - 1;
|
||||
kp--;
|
||||
v *= m_inv5;
|
||||
if (v > n_div5)
|
||||
break;
|
||||
++cnt;
|
||||
}
|
||||
return cnt;
|
||||
}
|
||||
|
||||
/* write one digit */
|
||||
if (dv || p > pb) {
|
||||
*p++ = (char)(dv + '0');
|
||||
/* Returns true if value is divisible by 5^p */
|
||||
static inline bool ispow5(const uint64_t v, const uint32_t p) {
|
||||
return pow5factor(v) >= p;
|
||||
}
|
||||
|
||||
/* Returns true if value is divisible by 2^p */
|
||||
static inline bool ispow2(const uint64_t v, const uint32_t p) {
|
||||
return (v & ((1ull << p) - 1)) == 0;
|
||||
}
|
||||
|
||||
/* Requires 0 <= v < v < 100000000000000000L */
|
||||
static inline uint32_t ctz10(const uint64_t v) {
|
||||
if (v < 10) return 1;
|
||||
if (v < 100) return 2;
|
||||
if (v < 1000) return 3;
|
||||
if (v < 10000) return 4;
|
||||
if (v < 100000) return 5;
|
||||
if (v < 1000000) return 6;
|
||||
if (v < 10000000) return 7;
|
||||
if (v < 100000000) return 8;
|
||||
if (v < 1000000000) return 9;
|
||||
if (v < 10000000000) return 10;
|
||||
if (v < 100000000000) return 11;
|
||||
if (v < 1000000000000) return 12;
|
||||
if (v < 10000000000000) return 13;
|
||||
if (v < 100000000000000) return 14;
|
||||
if (v < 1000000000000000) return 15;
|
||||
if (v < 10000000000000000) return 16;
|
||||
return 17;
|
||||
}
|
||||
|
||||
/* Best case: use 128-bit type */
|
||||
static inline uint64_t mulshift(const uint64_t m, const uint64_t *mul, const int32_t j) {
|
||||
uint128_t lo = ((uint128_t) m) * mul[0];
|
||||
uint128_t hi = ((uint128_t) m) * mul[1];
|
||||
return (uint64_t) (((lo >> 64) + hi) >> (j - 64));
|
||||
}
|
||||
|
||||
#define mul_shift_all(m, mul, j, shift) \
|
||||
vp = mulshift(4 * m + 2, mul, j); \
|
||||
vm = mulshift(4 * m - 1 - shift, mul, j); \
|
||||
vr = mulshift(4 * m, mul, j);
|
||||
|
||||
#define copy_two_digs(dst, src) \
|
||||
*(dst) = *(src); \
|
||||
*(dst+1) = *(src+1);
|
||||
|
||||
/* A floating decimal representing man * 10^exp */
|
||||
typedef struct f64_d {
|
||||
uint64_t man;
|
||||
int32_t exp;
|
||||
} f64_d;
|
||||
|
||||
static inline f64_d f64tod(const uint64_t man,const uint32_t exp) {
|
||||
int32_t e2;
|
||||
uint64_t m2;
|
||||
if (exp == 0) {
|
||||
/* subtract 2 so that the bounds computation has 2 additional bits */
|
||||
e2 = 1 - 1023 - 52 - 2;
|
||||
m2 = man;
|
||||
} else {
|
||||
e2 = (int32_t) exp - 1023 - 52 - 2;
|
||||
m2 = (1ull << 52) | man;
|
||||
}
|
||||
bool even = (m2 & 1) == 0;
|
||||
|
||||
/* Step 2: Determine the interval of valid decimal representations */
|
||||
uint64_t mv = 4 * m2;
|
||||
/* Implicit bool -> int conversion. True is 1, false is 0 */
|
||||
uint32_t shift = man != 0 || exp <= 1;
|
||||
|
||||
/* Step 3: Convert to a decimal power base using 128-bit arithmetic */
|
||||
uint64_t vr, vp, vm;
|
||||
int32_t e10;
|
||||
bool vmzeros = false;
|
||||
bool vrzeros = false;
|
||||
if (e2 >= 0) {
|
||||
|
||||
uint32_t q = log10pow2(e2) - (e2 > 3); // max(0, log10pow2(e2) - 1)
|
||||
e10 = (int32_t) q;
|
||||
int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
|
||||
int32_t i = -e2 + (int32_t) q + k;
|
||||
uint64_t *mul = (uint64_t*)DOUBLE_POW5_INV_SPLIT[q];
|
||||
/* {vm, vr, vp} * 10^e10 = {mm, mv, mp} * 2^e2
|
||||
* mp = 4 * m2 + 2
|
||||
* mm = mv - 1 - shift
|
||||
*/
|
||||
mul_shift_all(m2, mul, i, shift)
|
||||
|
||||
if (q <= 21) {
|
||||
if (mv % 5 == 0) {
|
||||
vrzeros = ispow5(mv, q);
|
||||
} else if (even) {
|
||||
/* Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
|
||||
* <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
|
||||
* <=> true && pow5Factor(mm) >= q, since e2 >= q.
|
||||
*/
|
||||
vmzeros = ispow5(mv - 1 - shift, q);
|
||||
} else {
|
||||
/* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
|
||||
vp -= ispow5(mv + 2, q);
|
||||
}
|
||||
}
|
||||
} else {
|
||||
uint32_t q = log10pow5(-e2) - (-e2 > 1); // max(0, log10pow5(-e2) - 1)
|
||||
e10 = (int32_t) q + e2;
|
||||
int32_t i = -e2 - (int32_t) q;
|
||||
int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
|
||||
int32_t j = (int32_t) q - k;
|
||||
uint64_t *mul = (uint64_t*)DOUBLE_POW5_SPLIT[i];
|
||||
/* {vm, vr, vp} * 10^e10 = {mm, mv, mp} * 2^e2 */
|
||||
mul_shift_all(m2, mul, j, shift)
|
||||
|
||||
/* check the precision */
|
||||
if (p2 < d) {
|
||||
*k += kp;
|
||||
roundg(p, d, p2, one.f, dpw.f * TabPow10[-kp]);
|
||||
return p - pb;
|
||||
}
|
||||
if (q <= 1) {
|
||||
/* {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing
|
||||
* 0 bits. mv = 4 * m2, so it always has at least two trailing 0 bits.
|
||||
*/
|
||||
vrzeros = true;
|
||||
if (even) {
|
||||
/* mm = mv - 1 - shift, so it has 1 trailing 0 bit if shift = 1 */
|
||||
vmzeros = shift == 1;
|
||||
} else {
|
||||
/* mp = mv + 2, so it always has at least one trailing 0 bit */
|
||||
--vp;
|
||||
}
|
||||
} else if (q < 63) {
|
||||
vrzeros = ispow2(mv, q);
|
||||
}
|
||||
}
|
||||
|
||||
/* Step 4: Find the shortest decimal representation in the interval */
|
||||
int32_t removed = 0;
|
||||
uint8_t lastrmdig = 0;
|
||||
uint64_t dman;
|
||||
/* On average, we remove ~2 DIGs */
|
||||
if (vmzeros || vrzeros) {
|
||||
/* General case, which happens rarely (~0.7%) */
|
||||
for (;;) {
|
||||
uint64_t vpdiv10 = vp / 10;
|
||||
uint64_t vmdiv10 = vm / 10;
|
||||
if (vpdiv10 <= vmdiv10) {
|
||||
break;
|
||||
}
|
||||
uint32_t vmmod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmdiv10);
|
||||
uint64_t vrdiv10 = vr / 10;
|
||||
uint32_t vrmod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrdiv10);
|
||||
vmzeros &= vmmod10 == 0;
|
||||
vrzeros &= lastrmdig == 0;
|
||||
lastrmdig = (uint8_t) vrmod10;
|
||||
vr = vrdiv10;
|
||||
vp = vpdiv10;
|
||||
vm = vmdiv10;
|
||||
++removed;
|
||||
}
|
||||
if (vmzeros) {
|
||||
for (;;) {
|
||||
uint64_t vmdiv10 = vm / 10;
|
||||
uint32_t vmmod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmdiv10);
|
||||
if (vmmod10 != 0) {
|
||||
break;
|
||||
}
|
||||
uint64_t vpdiv10 = vp / 10;
|
||||
uint64_t vrdiv10 = vr / 10;
|
||||
uint32_t vrmod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrdiv10);
|
||||
vrzeros &= lastrmdig == 0;
|
||||
lastrmdig = (uint8_t) vrmod10;
|
||||
vr = vrdiv10;
|
||||
vp = vpdiv10;
|
||||
vm = vmdiv10;
|
||||
++removed;
|
||||
}
|
||||
}
|
||||
if (vrzeros && lastrmdig == 5 && vr % 2 == 0) {
|
||||
/* Round even if the exact number is .....50..0 */
|
||||
lastrmdig = 4;
|
||||
}
|
||||
/* We need to take vr + 1 if vr is outside bounds or we need to round up */
|
||||
dman = vr + ((vr == vm && (!even || !vmzeros)) || lastrmdig >= 5);
|
||||
} else {
|
||||
/* Specialized for the common case (~99.3%). Percentages below are relative to this */
|
||||
bool roundup= false;
|
||||
uint64_t vpdiv100 = vp / 100;
|
||||
uint64_t vmdiv100 = vm / 100;
|
||||
if (vpdiv100 > vmdiv100) { // Optimization: remove two DIGs at a time (~86.2%).
|
||||
uint64_t vrdiv100 = vr / 100;
|
||||
uint32_t vrmod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrdiv100);
|
||||
roundup = vrmod100 >= 50;
|
||||
vr = vrdiv100;
|
||||
vp = vpdiv100;
|
||||
vm = vmdiv100;
|
||||
removed += 2;
|
||||
}
|
||||
/* Loop iterations below (approximately), without optimization above:
|
||||
* 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
|
||||
* Loop iterations below (approximately), with optimization above:
|
||||
* 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
|
||||
*/
|
||||
for (;;) {
|
||||
uint64_t vpdiv10 = vp / 10;
|
||||
uint64_t vmdiv10 = vm / 10;
|
||||
if (vpdiv10 <= vmdiv10) {
|
||||
break;
|
||||
}
|
||||
uint64_t vrdiv10 = vr / 10;
|
||||
uint32_t vrmod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrdiv10);
|
||||
roundup = vrmod10 >= 5;
|
||||
vr = vrdiv10;
|
||||
vp = vpdiv10;
|
||||
vm = vmdiv10;
|
||||
++removed;
|
||||
}
|
||||
/* We need to take vr + 1 if vr is outside bounds or we need to round up */
|
||||
dman = vr + (vr == vm || roundup);
|
||||
}
|
||||
f64_d fd = {
|
||||
.exp = e10 + removed,
|
||||
.man = dman,
|
||||
};
|
||||
return fd;
|
||||
}
|
||||
|
||||
/* Print the decimal DIGs from mantissa */
|
||||
static inline void print_mantissa(uint64_t man, char *out, int mlen) {
|
||||
/* We have at most 17 DIGs, and uint32_t can store 9 DIGs.
|
||||
* If man doesn't fit into uint32_t, we cut off 8 DIGs,
|
||||
* so the rest will fit into uint32_t.
|
||||
*/
|
||||
char *r = out + mlen;
|
||||
if (man < 10) {}
|
||||
if ((man >> 32) != 0) {
|
||||
/* Expensive 64-bit division */
|
||||
uint64_t q = man / 100000000;
|
||||
uint32_t man2 = ((uint32_t) man) - 100000000 * ((uint32_t) q);
|
||||
man = q;
|
||||
|
||||
uint32_t c = man2 % 10000;
|
||||
man2 /= 10000;
|
||||
uint32_t d = man2 % 10000;
|
||||
uint32_t c0 = (c % 100) << 1;
|
||||
uint32_t c1 = (c / 100) << 1;
|
||||
uint32_t d0 = (d % 100) << 1;
|
||||
uint32_t d1 = (d / 100) << 1;
|
||||
copy_two_digs(r - 2, DIG_TAB + c0)
|
||||
copy_two_digs(r - 4, DIG_TAB + c1)
|
||||
copy_two_digs(r - 6, DIG_TAB + d0)
|
||||
copy_two_digs(r - 8, DIG_TAB + d1)
|
||||
r -= 8;
|
||||
}
|
||||
uint32_t man2 = (uint32_t) man;
|
||||
while (man2 >= 10000) {
|
||||
#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
|
||||
uint32_t c = man2 - 10000 * (man2 / 10000);
|
||||
#else
|
||||
uint32_t c = man2 % 10000;
|
||||
#endif
|
||||
man2 /= 10000;
|
||||
uint32_t c0 = (c % 100) << 1;
|
||||
uint32_t c1 = (c / 100) << 1;
|
||||
copy_two_digs(r - 2, DIG_TAB + c0)
|
||||
copy_two_digs(r - 4, DIG_TAB + c1)
|
||||
r -= 4;
|
||||
}
|
||||
if (man2 >= 100) {
|
||||
uint32_t c = (man2 % 100) << 1;
|
||||
man2 /= 100;
|
||||
copy_two_digs(r - 2, DIG_TAB + c)
|
||||
r -= 2;
|
||||
}
|
||||
if (man2 >= 10) {
|
||||
uint32_t c = man2 << 1;
|
||||
copy_two_digs(r - 2, DIG_TAB + c)
|
||||
} else {
|
||||
*out = (char) ('0' + man2);
|
||||
}
|
||||
}
|
||||
|
||||
static inline int grisu2(char *p, double v, int *k) {
|
||||
struct f64_t vv;
|
||||
struct f64_t mk;
|
||||
struct f64_t wm;
|
||||
struct f64_t wp;
|
||||
struct f64_t ww;
|
||||
static inline int print_exponent(f64_d v, char *out, int mlen) {
|
||||
int idx = 0;
|
||||
|
||||
/* calculate m+ and m- */
|
||||
f64_set (&vv, v);
|
||||
f64_normb (&wm, &wp, &vv);
|
||||
f64_power (&mk, wp.e, k);
|
||||
f64_norm (&ww, &vv);
|
||||
f64_mul (&ww, &ww, &mk);
|
||||
f64_mul (&wp, &wp, &mk);
|
||||
f64_mul (&wm, &wm, &mk);
|
||||
print_mantissa(v.man, out + idx + 1, mlen);
|
||||
|
||||
/* generate the digits */
|
||||
wm.f++;
|
||||
wp.f--;
|
||||
return digits(p, k, &ww, &wp, wp.f - wm.f);
|
||||
}
|
||||
|
||||
static inline void movchar(char *p, int n, int v, int d) {
|
||||
for (int i = n + d - 1; i >= v; i--) {
|
||||
p[i] = p[i - d];
|
||||
}
|
||||
}
|
||||
|
||||
static inline void setchar(char *p, char c, int n) {
|
||||
while (n--) {
|
||||
*p++ = c;
|
||||
}
|
||||
}
|
||||
|
||||
static inline void inschr1(char *p, char c, int n, int v) {
|
||||
movchar(p, n, v, 1);
|
||||
p[v] = c;
|
||||
}
|
||||
|
||||
static inline void inschr2(char *p, char c0, char c1, int n, int v, int d) {
|
||||
movchar(p, n, v, d + 2);
|
||||
p[v + 0] = c0;
|
||||
p[v + 1] = c1;
|
||||
}
|
||||
|
||||
static inline void setexpo(char *p, int *n, int k) {
|
||||
int ex = k;
|
||||
int n0 = *n;
|
||||
char * p0 = p;
|
||||
|
||||
/* negative exponent */
|
||||
if (ex < 0) {
|
||||
ex = -ex;
|
||||
*p++ = '-';
|
||||
/* Print decimal point if needed */
|
||||
out[idx] = out[idx + 1];
|
||||
if (mlen > 1) {
|
||||
out[idx + 1] = '.';
|
||||
idx += mlen + 1;
|
||||
} else {
|
||||
++idx;
|
||||
}
|
||||
|
||||
/* single digit exponent */
|
||||
if (ex < 10) {
|
||||
*n = p - p0 + n0 + 1;
|
||||
*p = (char)(ex + '0');
|
||||
return;
|
||||
/* Print the exponent */
|
||||
out[idx++] = 'e';
|
||||
int32_t exp = v.exp + (int32_t) mlen - 1;
|
||||
if (exp < 0) {
|
||||
out[idx++] = '-';
|
||||
exp = -exp;
|
||||
}
|
||||
|
||||
/* 2-digit exponent */
|
||||
if (ex < 100) {
|
||||
*n = p - p0 + n0 + 2;
|
||||
*p++ = TabDigits[ex * 2];
|
||||
*p++ = TabDigits[ex * 2 + 1];
|
||||
return;
|
||||
}
|
||||
if (exp >= 100) {
|
||||
int32_t c = exp % 10;
|
||||
copy_two_digs(out + idx, DIG_TAB + 2 * (exp / 10))
|
||||
out[idx + 2] = (char) ('0' + c);
|
||||
idx += 3;
|
||||
} else if (exp >= 10) {
|
||||
copy_two_digs(out + idx, DIG_TAB + 2 * exp)
|
||||
idx += 2;
|
||||
} else {
|
||||
out[idx++] = (char) ('0' + exp);
|
||||
}
|
||||
|
||||
/* 3-digit exponent */
|
||||
*n = p - p0 + n0 + 3;
|
||||
*p++ = (char)(ex / 100 + '0');
|
||||
*p++ = TabDigits[(ex % 100) * 2];
|
||||
*p++ = TabDigits[(ex % 100) * 2 + 1];
|
||||
return idx;
|
||||
}
|
||||
|
||||
static inline void normalize(char *p, int *np, int k) {
|
||||
int n = *np;
|
||||
int nk = n + k;
|
||||
static inline int print_decimal(const f64_d v, char *out, int mlen) {
|
||||
int idx = 0;
|
||||
int lzeros = 0;
|
||||
int rzeros = 0;
|
||||
int point = 0;
|
||||
int exp10 = mlen - 1 + v.exp;
|
||||
|
||||
/* case 1: p = "1234", k = 7 -> "12340000000" */
|
||||
if (n <= nk && nk <= 21) {
|
||||
*np = nk;
|
||||
setchar(p + n, '0', k);
|
||||
return;
|
||||
/* parse the point idx and additional zeros */
|
||||
if (exp10 < 0) {
|
||||
lzeros = -exp10;
|
||||
point = 1;
|
||||
} else if (exp10 < mlen - 1) {
|
||||
point = 1 + exp10;
|
||||
} else {
|
||||
rzeros = exp10 - mlen + 1;
|
||||
}
|
||||
|
||||
/* case 2: p = "1234", k = -2 -> "12.34" */
|
||||
if (0 < nk && nk <= 21) {
|
||||
*np = n + 1;
|
||||
inschr1(p, '.', n, nk);
|
||||
return;
|
||||
}
|
||||
|
||||
/* case 3: p = "1234", k = -6 -> "0.001234" */
|
||||
if (-6 < nk && nk <= 0) {
|
||||
*np = 2 - k;
|
||||
inschr2(p, '0', '.', n, 0, -nk);
|
||||
setchar(p + 2, '0', -nk);
|
||||
return;
|
||||
}
|
||||
|
||||
/* case 4: p = "1", k = 30 -> "1e30" */
|
||||
if (n == 1) {
|
||||
(*np)++;
|
||||
p[1] = 'e';
|
||||
setexpo(p + 2, np, nk - 1);
|
||||
return;
|
||||
int i = 0;
|
||||
/* add left zeros */
|
||||
if (lzeros) {
|
||||
out[idx++] = '0';
|
||||
out[idx++] = '.';
|
||||
point = 0;
|
||||
}
|
||||
for (i = 1; i < lzeros; ++i) {
|
||||
out[idx++] = '0';
|
||||
}
|
||||
|
||||
/* case 5 (final case): p = "1234", k = 30 -> "1.234e33" */
|
||||
*np += 2;
|
||||
inschr1(p, '.', n, 1);
|
||||
setchar(p + n + 1, 'e', 1);
|
||||
setexpo(p + n + 2, np, nk - 1);
|
||||
/* add the mantissa DIGs */
|
||||
print_mantissa(v.man, out + idx, mlen);
|
||||
if (point) {
|
||||
for (i = idx + mlen; i > idx + point; --i) {
|
||||
out[i] = out[i-1];
|
||||
}
|
||||
out[idx + point] = '.';
|
||||
idx += 1;
|
||||
}
|
||||
|
||||
/* add right zeros */
|
||||
idx += mlen;
|
||||
for (i = 0; i < rzeros; ++i) {
|
||||
out[idx++] = '0';
|
||||
}
|
||||
|
||||
return idx;
|
||||
}
|
||||
|
||||
static inline bool f64tod_exct_int(const uint64_t man, const uint32_t exp,
|
||||
f64_d* v) {
|
||||
uint64_t m2 = (1ull << 52) | man; // implicit 1
|
||||
int32_t e2 = (int32_t) exp - 1023 - 52;
|
||||
|
||||
if (e2 > 0 || e2 < -52) {
|
||||
return false;
|
||||
}
|
||||
|
||||
uint64_t mask = (1ull << -e2) - 1;
|
||||
if ((m2 & mask) != 0) { // with fraction
|
||||
return false;
|
||||
}
|
||||
|
||||
v->man = m2 >> -e2;
|
||||
v->exp = 0;
|
||||
return true;
|
||||
}
|
||||
|
||||
static int inline ryu(double val, char *out) {
|
||||
/* Step 1: Decode the floating-point number */
|
||||
uint64_t bits = *(uint64_t *)(&val);
|
||||
uint64_t man = bits & ((1ull << 52) - 1);
|
||||
uint32_t exp = (uint32_t) ((bits >> 52) & ((1u << 11) - 1));
|
||||
|
||||
/* Skip when Infinity */
|
||||
if (exp == ((1u << 11) - 1u)) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
f64_d v;
|
||||
/* for integer from [1, 2^53], can be resepensated exactly by double */
|
||||
bool is_exact_int = f64tod_exct_int(man, exp, &v);
|
||||
if (!is_exact_int){ // find the shortest decimal representation
|
||||
v = f64tod(man, exp);
|
||||
}
|
||||
|
||||
/* Step 5: Print the decimal representation */
|
||||
int idx = 0;
|
||||
uint32_t mlen = ctz10(v.man);
|
||||
int exp10 = mlen - 1 + v.exp;
|
||||
/* The format as Go encoding/json package */
|
||||
bool isexp = exp10 < -6 || exp10 >= 21;
|
||||
|
||||
if (isexp) // exponent format
|
||||
idx += print_exponent(v, out + idx, mlen);
|
||||
else // decimal format
|
||||
idx += print_decimal(v, out + idx, mlen);
|
||||
|
||||
/* Terminate the string */
|
||||
out[idx] = '\0';
|
||||
return idx;
|
||||
}
|
||||
|
||||
int f64toa(char *out, double val) {
|
||||
int i = 0;
|
||||
char * p = out;
|
||||
int i = 0;
|
||||
char *p = out;
|
||||
|
||||
/* simple case of 0.0 */
|
||||
if (val == 0.0) {
|
||||
|
|
@ -441,16 +476,12 @@ int f64toa(char *out, double val) {
|
|||
|
||||
/* negative numbers */
|
||||
if (val < 0.0) {
|
||||
i = 1;
|
||||
val = -val;
|
||||
i = 1;
|
||||
val = -val;
|
||||
*p++ = '-';
|
||||
}
|
||||
|
||||
/* print the number with Grisu2 algorithm */
|
||||
int k;
|
||||
int n = grisu2(p, val, &k);
|
||||
|
||||
/* normalize the output, and adjust the length */
|
||||
normalize(p, &n, k);
|
||||
/* print the number with Ryu algorithm */
|
||||
int n = ryu(val, p);
|
||||
return n + i;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -20,6 +20,7 @@
|
|||
#include <stdint.h>
|
||||
#include <sys/types.h>
|
||||
#include <immintrin.h>
|
||||
#include <stdbool.h>
|
||||
|
||||
#define V_EOF 1
|
||||
#define V_NULL 2
|
||||
|
|
@ -116,4 +117,4 @@ long skip_positive(const GoString *src, long *p);
|
|||
int atof_eisel_lemire64(uint64_t mant, int exp10, int sgn, double *val);
|
||||
double atof_native_decimal(const char *buf, int len);
|
||||
|
||||
#endif
|
||||
#endif
|
||||
|
|
|
|||
385
native/ryu_tab.h
Normal file
385
native/ryu_tab.h
Normal file
|
|
@ -0,0 +1,385 @@
|
|||
/* Copyright 2018 Ulf Adams.
|
||||
* Modifications copyright 2021 ByteDance Inc.
|
||||
*
|
||||
* The contents of this file may be used under the terms of the Apache License,
|
||||
* Version 2.0.
|
||||
*
|
||||
* (See accompanying file LICENSE-Apache or copy at
|
||||
* http: *www.apache.org/licenses/LICENSE-2.0)
|
||||
*
|
||||
* Alternatively, the contents of this file may be used under the terms of
|
||||
* the Boost Software License, Version 1.0.
|
||||
* (See accompanying file LICENSE-Boost or copy at
|
||||
* https: *www.boost.org/LICENSE_1_0.txt)
|
||||
*
|
||||
* Unless required by applicable law or agreed to in writing, this software
|
||||
* is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
|
||||
* KIND, either express or implied.
|
||||
*/
|
||||
#ifndef RYU_TAB_H
|
||||
#define RYU_TAB_H
|
||||
|
||||
/* These tables are generated by PrintDoubleLookupTable */
|
||||
#define DOUBLE_POW5_INV_BITCOUNT 125
|
||||
#define DOUBLE_POW5_BITCOUNT 125
|
||||
|
||||
#define DOUBLE_POW5_INV_TABLE_SIZE 342
|
||||
#define DOUBLE_POW5_TABLE_SIZE 326
|
||||
|
||||
/* A table of all two-digit numbers. This is used to speed up decimal digit
|
||||
* generation by copying pairs of digits into the final output.
|
||||
*/
|
||||
static const char DIG_TAB[200] = {
|
||||
'0','0','0','1','0','2','0','3','0','4','0','5','0','6','0','7','0','8','0','9',
|
||||
'1','0','1','1','1','2','1','3','1','4','1','5','1','6','1','7','1','8','1','9',
|
||||
'2','0','2','1','2','2','2','3','2','4','2','5','2','6','2','7','2','8','2','9',
|
||||
'3','0','3','1','3','2','3','3','3','4','3','5','3','6','3','7','3','8','3','9',
|
||||
'4','0','4','1','4','2','4','3','4','4','4','5','4','6','4','7','4','8','4','9',
|
||||
'5','0','5','1','5','2','5','3','5','4','5','5','5','6','5','7','5','8','5','9',
|
||||
'6','0','6','1','6','2','6','3','6','4','6','5','6','6','6','7','6','8','6','9',
|
||||
'7','0','7','1','7','2','7','3','7','4','7','5','7','6','7','7','7','8','7','9',
|
||||
'8','0','8','1','8','2','8','3','8','4','8','5','8','6','8','7','8','8','8','9',
|
||||
'9','0','9','1','9','2','9','3','9','4','9','5','9','6','9','7','9','8','9','9'
|
||||
};
|
||||
|
||||
static const uint64_t DOUBLE_POW5_INV_SPLIT[DOUBLE_POW5_INV_TABLE_SIZE][2] = {
|
||||
{ 1u, 2305843009213693952u }, { 11068046444225730970u, 1844674407370955161u },
|
||||
{ 5165088340638674453u, 1475739525896764129u }, { 7821419487252849886u, 1180591620717411303u },
|
||||
{ 8824922364862649494u, 1888946593147858085u }, { 7059937891890119595u, 1511157274518286468u },
|
||||
{ 13026647942995916322u, 1208925819614629174u }, { 9774590264567735146u, 1934281311383406679u },
|
||||
{ 11509021026396098440u, 1547425049106725343u }, { 16585914450600699399u, 1237940039285380274u },
|
||||
{ 15469416676735388068u, 1980704062856608439u }, { 16064882156130220778u, 1584563250285286751u },
|
||||
{ 9162556910162266299u, 1267650600228229401u }, { 7281393426775805432u, 2028240960365167042u },
|
||||
{ 16893161185646375315u, 1622592768292133633u }, { 2446482504291369283u, 1298074214633706907u },
|
||||
{ 7603720821608101175u, 2076918743413931051u }, { 2393627842544570617u, 1661534994731144841u },
|
||||
{ 16672297533003297786u, 1329227995784915872u }, { 11918280793837635165u, 2126764793255865396u },
|
||||
{ 5845275820328197809u, 1701411834604692317u }, { 15744267100488289217u, 1361129467683753853u },
|
||||
{ 3054734472329800808u, 2177807148294006166u }, { 17201182836831481939u, 1742245718635204932u },
|
||||
{ 6382248639981364905u, 1393796574908163946u }, { 2832900194486363201u, 2230074519853062314u },
|
||||
{ 5955668970331000884u, 1784059615882449851u }, { 1075186361522890384u, 1427247692705959881u },
|
||||
{ 12788344622662355584u, 2283596308329535809u }, { 13920024512871794791u, 1826877046663628647u },
|
||||
{ 3757321980813615186u, 1461501637330902918u }, { 10384555214134712795u, 1169201309864722334u },
|
||||
{ 5547241898389809503u, 1870722095783555735u }, { 4437793518711847602u, 1496577676626844588u },
|
||||
{ 10928932444453298728u, 1197262141301475670u }, { 17486291911125277965u, 1915619426082361072u },
|
||||
{ 6610335899416401726u, 1532495540865888858u }, { 12666966349016942027u, 1225996432692711086u },
|
||||
{ 12888448528943286597u, 1961594292308337738u }, { 17689456452638449924u, 1569275433846670190u },
|
||||
{ 14151565162110759939u, 1255420347077336152u }, { 7885109000409574610u, 2008672555323737844u },
|
||||
{ 9997436015069570011u, 1606938044258990275u }, { 7997948812055656009u, 1285550435407192220u },
|
||||
{ 12796718099289049614u, 2056880696651507552u }, { 2858676849947419045u, 1645504557321206042u },
|
||||
{ 13354987924183666206u, 1316403645856964833u }, { 17678631863951955605u, 2106245833371143733u },
|
||||
{ 3074859046935833515u, 1684996666696914987u }, { 13527933681774397782u, 1347997333357531989u },
|
||||
{ 10576647446613305481u, 2156795733372051183u }, { 15840015586774465031u, 1725436586697640946u },
|
||||
{ 8982663654677661702u, 1380349269358112757u }, { 18061610662226169046u, 2208558830972980411u },
|
||||
{ 10759939715039024913u, 1766847064778384329u }, { 12297300586773130254u, 1413477651822707463u },
|
||||
{ 15986332124095098083u, 2261564242916331941u }, { 9099716884534168143u, 1809251394333065553u },
|
||||
{ 14658471137111155161u, 1447401115466452442u }, { 4348079280205103483u, 1157920892373161954u },
|
||||
{ 14335624477811986218u, 1852673427797059126u }, { 7779150767507678651u, 1482138742237647301u },
|
||||
{ 2533971799264232598u, 1185710993790117841u }, { 15122401323048503126u, 1897137590064188545u },
|
||||
{ 12097921058438802501u, 1517710072051350836u }, { 5988988032009131678u, 1214168057641080669u },
|
||||
{ 16961078480698431330u, 1942668892225729070u }, { 13568862784558745064u, 1554135113780583256u },
|
||||
{ 7165741412905085728u, 1243308091024466605u }, { 11465186260648137165u, 1989292945639146568u },
|
||||
{ 16550846638002330379u, 1591434356511317254u }, { 16930026125143774626u, 1273147485209053803u },
|
||||
{ 4951948911778577463u, 2037035976334486086u }, { 272210314680951647u, 1629628781067588869u },
|
||||
{ 3907117066486671641u, 1303703024854071095u }, { 6251387306378674625u, 2085924839766513752u },
|
||||
{ 16069156289328670670u, 1668739871813211001u }, { 9165976216721026213u, 1334991897450568801u },
|
||||
{ 7286864317269821294u, 2135987035920910082u }, { 16897537898041588005u, 1708789628736728065u },
|
||||
{ 13518030318433270404u, 1367031702989382452u }, { 6871453250525591353u, 2187250724783011924u },
|
||||
{ 9186511415162383406u, 1749800579826409539u }, { 11038557946871817048u, 1399840463861127631u },
|
||||
{ 10282995085511086630u, 2239744742177804210u }, { 8226396068408869304u, 1791795793742243368u },
|
||||
{ 13959814484210916090u, 1433436634993794694u }, { 11267656730511734774u, 2293498615990071511u },
|
||||
{ 5324776569667477496u, 1834798892792057209u }, { 7949170070475892320u, 1467839114233645767u },
|
||||
{ 17427382500606444826u, 1174271291386916613u }, { 5747719112518849781u, 1878834066219066582u },
|
||||
{ 15666221734240810795u, 1503067252975253265u }, { 12532977387392648636u, 1202453802380202612u },
|
||||
{ 5295368560860596524u, 1923926083808324180u }, { 4236294848688477220u, 1539140867046659344u },
|
||||
{ 7078384693692692099u, 1231312693637327475u }, { 11325415509908307358u, 1970100309819723960u },
|
||||
{ 9060332407926645887u, 1576080247855779168u }, { 14626963555825137356u, 1260864198284623334u },
|
||||
{ 12335095245094488799u, 2017382717255397335u }, { 9868076196075591040u, 1613906173804317868u },
|
||||
{ 15273158586344293478u, 1291124939043454294u }, { 13369007293925138595u, 2065799902469526871u },
|
||||
{ 7005857020398200553u, 1652639921975621497u }, { 16672732060544291412u, 1322111937580497197u },
|
||||
{ 11918976037903224966u, 2115379100128795516u }, { 5845832015580669650u, 1692303280103036413u },
|
||||
{ 12055363241948356366u, 1353842624082429130u }, { 841837113407818570u, 2166148198531886609u },
|
||||
{ 4362818505468165179u, 1732918558825509287u }, { 14558301248600263113u, 1386334847060407429u },
|
||||
{ 12225235553534690011u, 2218135755296651887u }, { 2401490813343931363u, 1774508604237321510u },
|
||||
{ 1921192650675145090u, 1419606883389857208u }, { 17831303500047873437u, 2271371013423771532u },
|
||||
{ 6886345170554478103u, 1817096810739017226u }, { 1819727321701672159u, 1453677448591213781u },
|
||||
{ 16213177116328979020u, 1162941958872971024u }, { 14873036941900635463u, 1860707134196753639u },
|
||||
{ 15587778368262418694u, 1488565707357402911u }, { 8780873879868024632u, 1190852565885922329u },
|
||||
{ 2981351763563108441u, 1905364105417475727u }, { 13453127855076217722u, 1524291284333980581u },
|
||||
{ 7073153469319063855u, 1219433027467184465u }, { 11317045550910502167u, 1951092843947495144u },
|
||||
{ 12742985255470312057u, 1560874275157996115u }, { 10194388204376249646u, 1248699420126396892u },
|
||||
{ 1553625868034358140u, 1997919072202235028u }, { 8621598323911307159u, 1598335257761788022u },
|
||||
{ 17965325103354776697u, 1278668206209430417u }, { 13987124906400001422u, 2045869129935088668u },
|
||||
{ 121653480894270168u, 1636695303948070935u }, { 97322784715416134u, 1309356243158456748u },
|
||||
{ 14913111714512307107u, 2094969989053530796u }, { 8241140556867935363u, 1675975991242824637u },
|
||||
{ 17660958889720079260u, 1340780792994259709u }, { 17189487779326395846u, 2145249268790815535u },
|
||||
{ 13751590223461116677u, 1716199415032652428u }, { 18379969808252713988u, 1372959532026121942u },
|
||||
{ 14650556434236701088u, 2196735251241795108u }, { 652398703163629901u, 1757388200993436087u },
|
||||
{ 11589965406756634890u, 1405910560794748869u }, { 7475898206584884855u, 2249456897271598191u },
|
||||
{ 2291369750525997561u, 1799565517817278553u }, { 9211793429904618695u, 1439652414253822842u },
|
||||
{ 18428218302589300235u, 2303443862806116547u }, { 7363877012587619542u, 1842755090244893238u },
|
||||
{ 13269799239553916280u, 1474204072195914590u }, { 10615839391643133024u, 1179363257756731672u },
|
||||
{ 2227947767661371545u, 1886981212410770676u }, { 16539753473096738529u, 1509584969928616540u },
|
||||
{ 13231802778477390823u, 1207667975942893232u }, { 6413489186596184024u, 1932268761508629172u },
|
||||
{ 16198837793502678189u, 1545815009206903337u }, { 5580372605318321905u, 1236652007365522670u },
|
||||
{ 8928596168509315048u, 1978643211784836272u }, { 18210923379033183008u, 1582914569427869017u },
|
||||
{ 7190041073742725760u, 1266331655542295214u }, { 436019273762630246u, 2026130648867672343u },
|
||||
{ 7727513048493924843u, 1620904519094137874u }, { 9871359253537050198u, 1296723615275310299u },
|
||||
{ 4726128361433549347u, 2074757784440496479u }, { 7470251503888749801u, 1659806227552397183u },
|
||||
{ 13354898832594820487u, 1327844982041917746u }, { 13989140502667892133u, 2124551971267068394u },
|
||||
{ 14880661216876224029u, 1699641577013654715u }, { 11904528973500979224u, 1359713261610923772u },
|
||||
{ 4289851098633925465u, 2175541218577478036u }, { 18189276137874781665u, 1740432974861982428u },
|
||||
{ 3483374466074094362u, 1392346379889585943u }, { 1884050330976640656u, 2227754207823337509u },
|
||||
{ 5196589079523222848u, 1782203366258670007u }, { 15225317707844309248u, 1425762693006936005u },
|
||||
{ 5913764258841343181u, 2281220308811097609u }, { 8420360221814984868u, 1824976247048878087u },
|
||||
{ 17804334621677718864u, 1459980997639102469u }, { 17932816512084085415u, 1167984798111281975u },
|
||||
{ 10245762345624985047u, 1868775676978051161u }, { 4507261061758077715u, 1495020541582440929u },
|
||||
{ 7295157664148372495u, 1196016433265952743u }, { 7982903447895485668u, 1913626293225524389u },
|
||||
{ 10075671573058298858u, 1530901034580419511u }, { 4371188443704728763u, 1224720827664335609u },
|
||||
{ 14372599139411386667u, 1959553324262936974u }, { 15187428126271019657u, 1567642659410349579u },
|
||||
{ 15839291315758726049u, 1254114127528279663u }, { 3206773216762499739u, 2006582604045247462u },
|
||||
{ 13633465017635730761u, 1605266083236197969u }, { 14596120828850494932u, 1284212866588958375u },
|
||||
{ 4907049252451240275u, 2054740586542333401u }, { 236290587219081897u, 1643792469233866721u },
|
||||
{ 14946427728742906810u, 1315033975387093376u }, { 16535586736504830250u, 2104054360619349402u },
|
||||
{ 5849771759720043554u, 1683243488495479522u }, { 15747863852001765813u, 1346594790796383617u },
|
||||
{ 10439186904235184007u, 2154551665274213788u }, { 15730047152871967852u, 1723641332219371030u },
|
||||
{ 12584037722297574282u, 1378913065775496824u }, { 9066413911450387881u, 2206260905240794919u },
|
||||
{ 10942479943902220628u, 1765008724192635935u }, { 8753983955121776503u, 1412006979354108748u },
|
||||
{ 10317025513452932081u, 2259211166966573997u }, { 874922781278525018u, 1807368933573259198u },
|
||||
{ 8078635854506640661u, 1445895146858607358u }, { 13841606313089133175u, 1156716117486885886u },
|
||||
{ 14767872471458792434u, 1850745787979017418u }, { 746251532941302978u, 1480596630383213935u },
|
||||
{ 597001226353042382u, 1184477304306571148u }, { 15712597221132509104u, 1895163686890513836u },
|
||||
{ 8880728962164096960u, 1516130949512411069u }, { 10793931984473187891u, 1212904759609928855u },
|
||||
{ 17270291175157100626u, 1940647615375886168u }, { 2748186495899949531u, 1552518092300708935u },
|
||||
{ 2198549196719959625u, 1242014473840567148u }, { 18275073973719576693u, 1987223158144907436u },
|
||||
{ 10930710364233751031u, 1589778526515925949u }, { 12433917106128911148u, 1271822821212740759u },
|
||||
{ 8826220925580526867u, 2034916513940385215u }, { 7060976740464421494u, 1627933211152308172u },
|
||||
{ 16716827836597268165u, 1302346568921846537u }, { 11989529279587987770u, 2083754510274954460u },
|
||||
{ 9591623423670390216u, 1667003608219963568u }, { 15051996368420132820u, 1333602886575970854u },
|
||||
{ 13015147745246481542u, 2133764618521553367u }, { 3033420566713364587u, 1707011694817242694u },
|
||||
{ 6116085268112601993u, 1365609355853794155u }, { 9785736428980163188u, 2184974969366070648u },
|
||||
{ 15207286772667951197u, 1747979975492856518u }, { 1097782973908629988u, 1398383980394285215u },
|
||||
{ 1756452758253807981u, 2237414368630856344u }, { 5094511021344956708u, 1789931494904685075u },
|
||||
{ 4075608817075965366u, 1431945195923748060u }, { 6520974107321544586u, 2291112313477996896u },
|
||||
{ 1527430471115325346u, 1832889850782397517u }, { 12289990821117991246u, 1466311880625918013u },
|
||||
{ 17210690286378213644u, 1173049504500734410u }, { 9090360384495590213u, 1876879207201175057u },
|
||||
{ 18340334751822203140u, 1501503365760940045u }, { 14672267801457762512u, 1201202692608752036u },
|
||||
{ 16096930852848599373u, 1921924308174003258u }, { 1809498238053148529u, 1537539446539202607u },
|
||||
{ 12515645034668249793u, 1230031557231362085u }, { 1578287981759648052u, 1968050491570179337u },
|
||||
{ 12330676829633449412u, 1574440393256143469u }, { 13553890278448669853u, 1259552314604914775u },
|
||||
{ 3239480371808320148u, 2015283703367863641u }, { 17348979556414297411u, 1612226962694290912u },
|
||||
{ 6500486015647617283u, 1289781570155432730u }, { 10400777625036187652u, 2063650512248692368u },
|
||||
{ 15699319729512770768u, 1650920409798953894u }, { 16248804598352126938u, 1320736327839163115u },
|
||||
{ 7551343283653851484u, 2113178124542660985u }, { 6041074626923081187u, 1690542499634128788u },
|
||||
{ 12211557331022285596u, 1352433999707303030u }, { 1091747655926105338u, 2163894399531684849u },
|
||||
{ 4562746939482794594u, 1731115519625347879u }, { 7339546366328145998u, 1384892415700278303u },
|
||||
{ 8053925371383123274u, 2215827865120445285u }, { 6443140297106498619u, 1772662292096356228u },
|
||||
{ 12533209867169019542u, 1418129833677084982u }, { 5295740528502789974u, 2269007733883335972u },
|
||||
{ 15304638867027962949u, 1815206187106668777u }, { 4865013464138549713u, 1452164949685335022u },
|
||||
{ 14960057215536570740u, 1161731959748268017u }, { 9178696285890871890u, 1858771135597228828u },
|
||||
{ 14721654658196518159u, 1487016908477783062u }, { 4398626097073393881u, 1189613526782226450u },
|
||||
{ 7037801755317430209u, 1903381642851562320u }, { 5630241404253944167u, 1522705314281249856u },
|
||||
{ 814844308661245011u, 1218164251424999885u }, { 1303750893857992017u, 1949062802279999816u },
|
||||
{ 15800395974054034906u, 1559250241823999852u }, { 5261619149759407279u, 1247400193459199882u },
|
||||
{ 12107939454356961969u, 1995840309534719811u }, { 5997002748743659252u, 1596672247627775849u },
|
||||
{ 8486951013736837725u, 1277337798102220679u }, { 2511075177753209390u, 2043740476963553087u },
|
||||
{ 13076906586428298482u, 1634992381570842469u }, { 14150874083884549109u, 1307993905256673975u },
|
||||
{ 4194654460505726958u, 2092790248410678361u }, { 18113118827372222859u, 1674232198728542688u },
|
||||
{ 3422448617672047318u, 1339385758982834151u }, { 16543964232501006678u, 2143017214372534641u },
|
||||
{ 9545822571258895019u, 1714413771498027713u }, { 15015355686490936662u, 1371531017198422170u },
|
||||
{ 5577825024675947042u, 2194449627517475473u }, { 11840957649224578280u, 1755559702013980378u },
|
||||
{ 16851463748863483271u, 1404447761611184302u }, { 12204946739213931940u, 2247116418577894884u },
|
||||
{ 13453306206113055875u, 1797693134862315907u }, { 3383947335406624054u, 1438154507889852726u },
|
||||
{ 16482362180876329456u, 2301047212623764361u }, { 9496540929959153242u, 1840837770099011489u },
|
||||
{ 11286581558709232917u, 1472670216079209191u }, { 5339916432225476010u, 1178136172863367353u },
|
||||
{ 4854517476818851293u, 1885017876581387765u }, { 3883613981455081034u, 1508014301265110212u },
|
||||
{ 14174937629389795797u, 1206411441012088169u }, { 11611853762797942306u, 1930258305619341071u },
|
||||
{ 5600134195496443521u, 1544206644495472857u }, { 15548153800622885787u, 1235365315596378285u },
|
||||
{ 6430302007287065643u, 1976584504954205257u }, { 16212288050055383484u, 1581267603963364205u },
|
||||
{ 12969830440044306787u, 1265014083170691364u }, { 9683682259845159889u, 2024022533073106183u },
|
||||
{ 15125643437359948558u, 1619218026458484946u }, { 8411165935146048523u, 1295374421166787957u },
|
||||
{ 17147214310975587960u, 2072599073866860731u }, { 10028422634038560045u, 1658079259093488585u },
|
||||
{ 8022738107230848036u, 1326463407274790868u }, { 9147032156827446534u, 2122341451639665389u },
|
||||
{ 11006974540203867551u, 1697873161311732311u }, { 5116230817421183718u, 1358298529049385849u },
|
||||
{ 15564666937357714594u, 2173277646479017358u }, { 1383687105660440706u, 1738622117183213887u },
|
||||
{ 12174996128754083534u, 1390897693746571109u }, { 8411947361780802685u, 2225436309994513775u },
|
||||
{ 6729557889424642148u, 1780349047995611020u }, { 5383646311539713719u, 1424279238396488816u },
|
||||
{ 1235136468979721303u, 2278846781434382106u }, { 15745504434151418335u, 1823077425147505684u },
|
||||
{ 16285752362063044992u, 1458461940118004547u }, { 5649904260166615347u, 1166769552094403638u },
|
||||
{ 5350498001524674232u, 1866831283351045821u }, { 591049586477829062u, 1493465026680836657u },
|
||||
{ 11540886113407994219u, 1194772021344669325u }, { 18673707743239135u, 1911635234151470921u },
|
||||
{ 14772334225162232601u, 1529308187321176736u }, { 8128518565387875758u, 1223446549856941389u },
|
||||
{ 1937583260394870242u, 1957514479771106223u }, { 8928764237799716840u, 1566011583816884978u },
|
||||
{ 14521709019723594119u, 1252809267053507982u }, { 8477339172590109297u, 2004494827285612772u },
|
||||
{ 17849917782297818407u, 1603595861828490217u }, { 6901236596354434079u, 1282876689462792174u },
|
||||
{ 18420676183650915173u, 2052602703140467478u }, { 3668494502695001169u, 1642082162512373983u },
|
||||
{ 10313493231639821582u, 1313665730009899186u }, { 9122891541139893884u, 2101865168015838698u },
|
||||
{ 14677010862395735754u, 1681492134412670958u }, { 673562245690857633u, 1345193707530136767u }
|
||||
};
|
||||
|
||||
static const uint64_t DOUBLE_POW5_SPLIT[DOUBLE_POW5_TABLE_SIZE][2] = {
|
||||
{ 0u, 1152921504606846976u }, { 0u, 1441151880758558720u },
|
||||
{ 0u, 1801439850948198400u }, { 0u, 2251799813685248000u },
|
||||
{ 0u, 1407374883553280000u }, { 0u, 1759218604441600000u },
|
||||
{ 0u, 2199023255552000000u }, { 0u, 1374389534720000000u },
|
||||
{ 0u, 1717986918400000000u }, { 0u, 2147483648000000000u },
|
||||
{ 0u, 1342177280000000000u }, { 0u, 1677721600000000000u },
|
||||
{ 0u, 2097152000000000000u }, { 0u, 1310720000000000000u },
|
||||
{ 0u, 1638400000000000000u }, { 0u, 2048000000000000000u },
|
||||
{ 0u, 1280000000000000000u }, { 0u, 1600000000000000000u },
|
||||
{ 0u, 2000000000000000000u }, { 0u, 1250000000000000000u },
|
||||
{ 0u, 1562500000000000000u }, { 0u, 1953125000000000000u },
|
||||
{ 0u, 1220703125000000000u }, { 0u, 1525878906250000000u },
|
||||
{ 0u, 1907348632812500000u }, { 0u, 1192092895507812500u },
|
||||
{ 0u, 1490116119384765625u }, { 4611686018427387904u, 1862645149230957031u },
|
||||
{ 9799832789158199296u, 1164153218269348144u }, { 12249790986447749120u, 1455191522836685180u },
|
||||
{ 15312238733059686400u, 1818989403545856475u }, { 14528612397897220096u, 2273736754432320594u },
|
||||
{ 13692068767113150464u, 1421085471520200371u }, { 12503399940464050176u, 1776356839400250464u },
|
||||
{ 15629249925580062720u, 2220446049250313080u }, { 9768281203487539200u, 1387778780781445675u },
|
||||
{ 7598665485932036096u, 1734723475976807094u }, { 274959820560269312u, 2168404344971008868u },
|
||||
{ 9395221924704944128u, 1355252715606880542u }, { 2520655369026404352u, 1694065894508600678u },
|
||||
{ 12374191248137781248u, 2117582368135750847u }, { 14651398557727195136u, 1323488980084844279u },
|
||||
{ 13702562178731606016u, 1654361225106055349u }, { 3293144668132343808u, 2067951531382569187u },
|
||||
{ 18199116482078572544u, 1292469707114105741u }, { 8913837547316051968u, 1615587133892632177u },
|
||||
{ 15753982952572452864u, 2019483917365790221u }, { 12152082354571476992u, 1262177448353618888u },
|
||||
{ 15190102943214346240u, 1577721810442023610u }, { 9764256642163156992u, 1972152263052529513u },
|
||||
{ 17631875447420442880u, 1232595164407830945u }, { 8204786253993389888u, 1540743955509788682u },
|
||||
{ 1032610780636961552u, 1925929944387235853u }, { 2951224747111794922u, 1203706215242022408u },
|
||||
{ 3689030933889743652u, 1504632769052528010u }, { 13834660704216955373u, 1880790961315660012u },
|
||||
{ 17870034976990372916u, 1175494350822287507u }, { 17725857702810578241u, 1469367938527859384u },
|
||||
{ 3710578054803671186u, 1836709923159824231u }, { 26536550077201078u, 2295887403949780289u },
|
||||
{ 11545800389866720434u, 1434929627468612680u }, { 14432250487333400542u, 1793662034335765850u },
|
||||
{ 8816941072311974870u, 2242077542919707313u }, { 17039803216263454053u, 1401298464324817070u },
|
||||
{ 12076381983474541759u, 1751623080406021338u }, { 5872105442488401391u, 2189528850507526673u },
|
||||
{ 15199280947623720629u, 1368455531567204170u }, { 9775729147674874978u, 1710569414459005213u },
|
||||
{ 16831347453020981627u, 2138211768073756516u }, { 1296220121283337709u, 1336382355046097823u },
|
||||
{ 15455333206886335848u, 1670477943807622278u }, { 10095794471753144002u, 2088097429759527848u },
|
||||
{ 6309871544845715001u, 1305060893599704905u }, { 12499025449484531656u, 1631326116999631131u },
|
||||
{ 11012095793428276666u, 2039157646249538914u }, { 11494245889320060820u, 1274473528905961821u },
|
||||
{ 532749306367912313u, 1593091911132452277u }, { 5277622651387278295u, 1991364888915565346u },
|
||||
{ 7910200175544436838u, 1244603055572228341u }, { 14499436237857933952u, 1555753819465285426u },
|
||||
{ 8900923260467641632u, 1944692274331606783u }, { 12480606065433357876u, 1215432671457254239u },
|
||||
{ 10989071563364309441u, 1519290839321567799u }, { 9124653435777998898u, 1899113549151959749u },
|
||||
{ 8008751406574943263u, 1186945968219974843u }, { 5399253239791291175u, 1483682460274968554u },
|
||||
{ 15972438586593889776u, 1854603075343710692u }, { 759402079766405302u, 1159126922089819183u },
|
||||
{ 14784310654990170340u, 1448908652612273978u }, { 9257016281882937117u, 1811135815765342473u },
|
||||
{ 16182956370781059300u, 2263919769706678091u }, { 7808504722524468110u, 1414949856066673807u },
|
||||
{ 5148944884728197234u, 1768687320083342259u }, { 1824495087482858639u, 2210859150104177824u },
|
||||
{ 1140309429676786649u, 1381786968815111140u }, { 1425386787095983311u, 1727233711018888925u },
|
||||
{ 6393419502297367043u, 2159042138773611156u }, { 13219259225790630210u, 1349401336733506972u },
|
||||
{ 16524074032238287762u, 1686751670916883715u }, { 16043406521870471799u, 2108439588646104644u },
|
||||
{ 803757039314269066u, 1317774742903815403u }, { 14839754354425000045u, 1647218428629769253u },
|
||||
{ 4714634887749086344u, 2059023035787211567u }, { 9864175832484260821u, 1286889397367007229u },
|
||||
{ 16941905809032713930u, 1608611746708759036u }, { 2730638187581340797u, 2010764683385948796u },
|
||||
{ 10930020904093113806u, 1256727927116217997u }, { 18274212148543780162u, 1570909908895272496u },
|
||||
{ 4396021111970173586u, 1963637386119090621u }, { 5053356204195052443u, 1227273366324431638u },
|
||||
{ 15540067292098591362u, 1534091707905539547u }, { 14813398096695851299u, 1917614634881924434u },
|
||||
{ 13870059828862294966u, 1198509146801202771u }, { 12725888767650480803u, 1498136433501503464u },
|
||||
{ 15907360959563101004u, 1872670541876879330u }, { 14553786618154326031u, 1170419088673049581u },
|
||||
{ 4357175217410743827u, 1463023860841311977u }, { 10058155040190817688u, 1828779826051639971u },
|
||||
{ 7961007781811134206u, 2285974782564549964u }, { 14199001900486734687u, 1428734239102843727u },
|
||||
{ 13137066357181030455u, 1785917798878554659u }, { 11809646928048900164u, 2232397248598193324u },
|
||||
{ 16604401366885338411u, 1395248280373870827u }, { 16143815690179285109u, 1744060350467338534u },
|
||||
{ 10956397575869330579u, 2180075438084173168u }, { 6847748484918331612u, 1362547148802608230u },
|
||||
{ 17783057643002690323u, 1703183936003260287u }, { 17617136035325974999u, 2128979920004075359u },
|
||||
{ 17928239049719816230u, 1330612450002547099u }, { 17798612793722382384u, 1663265562503183874u },
|
||||
{ 13024893955298202172u, 2079081953128979843u }, { 5834715712847682405u, 1299426220705612402u },
|
||||
{ 16516766677914378815u, 1624282775882015502u }, { 11422586310538197711u, 2030353469852519378u },
|
||||
{ 11750802462513761473u, 1268970918657824611u }, { 10076817059714813937u, 1586213648322280764u },
|
||||
{ 12596021324643517422u, 1982767060402850955u }, { 5566670318688504437u, 1239229412751781847u },
|
||||
{ 2346651879933242642u, 1549036765939727309u }, { 7545000868343941206u, 1936295957424659136u },
|
||||
{ 4715625542714963254u, 1210184973390411960u }, { 5894531928393704067u, 1512731216738014950u },
|
||||
{ 16591536947346905892u, 1890914020922518687u }, { 17287239619732898039u, 1181821263076574179u },
|
||||
{ 16997363506238734644u, 1477276578845717724u }, { 2799960309088866689u, 1846595723557147156u },
|
||||
{ 10973347230035317489u, 1154122327223216972u }, { 13716684037544146861u, 1442652909029021215u },
|
||||
{ 12534169028502795672u, 1803316136286276519u }, { 11056025267201106687u, 2254145170357845649u },
|
||||
{ 18439230838069161439u, 1408840731473653530u }, { 13825666510731675991u, 1761050914342066913u },
|
||||
{ 3447025083132431277u, 2201313642927583642u }, { 6766076695385157452u, 1375821026829739776u },
|
||||
{ 8457595869231446815u, 1719776283537174720u }, { 10571994836539308519u, 2149720354421468400u },
|
||||
{ 6607496772837067824u, 1343575221513417750u }, { 17482743002901110588u, 1679469026891772187u },
|
||||
{ 17241742735199000331u, 2099336283614715234u }, { 15387775227926763111u, 1312085177259197021u },
|
||||
{ 5399660979626290177u, 1640106471573996277u }, { 11361262242960250625u, 2050133089467495346u },
|
||||
{ 11712474920277544544u, 1281333180917184591u }, { 10028907631919542777u, 1601666476146480739u },
|
||||
{ 7924448521472040567u, 2002083095183100924u }, { 14176152362774801162u, 1251301934489438077u },
|
||||
{ 3885132398186337741u, 1564127418111797597u }, { 9468101516160310080u, 1955159272639746996u },
|
||||
{ 15140935484454969608u, 1221974545399841872u }, { 479425281859160394u, 1527468181749802341u },
|
||||
{ 5210967620751338397u, 1909335227187252926u }, { 17091912818251750210u, 1193334516992033078u },
|
||||
{ 12141518985959911954u, 1491668146240041348u }, { 15176898732449889943u, 1864585182800051685u },
|
||||
{ 11791404716994875166u, 1165365739250032303u }, { 10127569877816206054u, 1456707174062540379u },
|
||||
{ 8047776328842869663u, 1820883967578175474u }, { 836348374198811271u, 2276104959472719343u },
|
||||
{ 7440246761515338900u, 1422565599670449589u }, { 13911994470321561530u, 1778206999588061986u },
|
||||
{ 8166621051047176104u, 2222758749485077483u }, { 2798295147690791113u, 1389224218428173427u },
|
||||
{ 17332926989895652603u, 1736530273035216783u }, { 17054472718942177850u, 2170662841294020979u },
|
||||
{ 8353202440125167204u, 1356664275808763112u }, { 10441503050156459005u, 1695830344760953890u },
|
||||
{ 3828506775840797949u, 2119787930951192363u }, { 86973725686804766u, 1324867456844495227u },
|
||||
{ 13943775212390669669u, 1656084321055619033u }, { 3594660960206173375u, 2070105401319523792u },
|
||||
{ 2246663100128858359u, 1293815875824702370u }, { 12031700912015848757u, 1617269844780877962u },
|
||||
{ 5816254103165035138u, 2021587305976097453u }, { 5941001823691840913u, 1263492066235060908u },
|
||||
{ 7426252279614801142u, 1579365082793826135u }, { 4671129331091113523u, 1974206353492282669u },
|
||||
{ 5225298841145639904u, 1233878970932676668u }, { 6531623551432049880u, 1542348713665845835u },
|
||||
{ 3552843420862674446u, 1927935892082307294u }, { 16055585193321335241u, 1204959932551442058u },
|
||||
{ 10846109454796893243u, 1506199915689302573u }, { 18169322836923504458u, 1882749894611628216u },
|
||||
{ 11355826773077190286u, 1176718684132267635u }, { 9583097447919099954u, 1470898355165334544u },
|
||||
{ 11978871809898874942u, 1838622943956668180u }, { 14973589762373593678u, 2298278679945835225u },
|
||||
{ 2440964573842414192u, 1436424174966147016u }, { 3051205717303017741u, 1795530218707683770u },
|
||||
{ 13037379183483547984u, 2244412773384604712u }, { 8148361989677217490u, 1402757983365377945u },
|
||||
{ 14797138505523909766u, 1753447479206722431u }, { 13884737113477499304u, 2191809349008403039u },
|
||||
{ 15595489723564518921u, 1369880843130251899u }, { 14882676136028260747u, 1712351053912814874u },
|
||||
{ 9379973133180550126u, 2140438817391018593u }, { 17391698254306313589u, 1337774260869386620u },
|
||||
{ 3292878744173340370u, 1672217826086733276u }, { 4116098430216675462u, 2090272282608416595u },
|
||||
{ 266718509671728212u, 1306420176630260372u }, { 333398137089660265u, 1633025220787825465u },
|
||||
{ 5028433689789463235u, 2041281525984781831u }, { 10060300083759496378u, 1275800953740488644u },
|
||||
{ 12575375104699370472u, 1594751192175610805u }, { 1884160825592049379u, 1993438990219513507u },
|
||||
{ 17318501580490888525u, 1245899368887195941u }, { 7813068920331446945u, 1557374211108994927u },
|
||||
{ 5154650131986920777u, 1946717763886243659u }, { 915813323278131534u, 1216698602428902287u },
|
||||
{ 14979824709379828129u, 1520873253036127858u }, { 9501408849870009354u, 1901091566295159823u },
|
||||
{ 12855909558809837702u, 1188182228934474889u }, { 2234828893230133415u, 1485227786168093612u },
|
||||
{ 2793536116537666769u, 1856534732710117015u }, { 8663489100477123587u, 1160334207943823134u },
|
||||
{ 1605989338741628675u, 1450417759929778918u }, { 11230858710281811652u, 1813022199912223647u },
|
||||
{ 9426887369424876662u, 2266277749890279559u }, { 12809333633531629769u, 1416423593681424724u },
|
||||
{ 16011667041914537212u, 1770529492101780905u }, { 6179525747111007803u, 2213161865127226132u },
|
||||
{ 13085575628799155685u, 1383226165704516332u }, { 16356969535998944606u, 1729032707130645415u },
|
||||
{ 15834525901571292854u, 2161290883913306769u }, { 2979049660840976177u, 1350806802445816731u },
|
||||
{ 17558870131333383934u, 1688508503057270913u }, { 8113529608884566205u, 2110635628821588642u },
|
||||
{ 9682642023980241782u, 1319147268013492901u }, { 16714988548402690132u, 1648934085016866126u },
|
||||
{ 11670363648648586857u, 2061167606271082658u }, { 11905663298832754689u, 1288229753919426661u },
|
||||
{ 1047021068258779650u, 1610287192399283327u }, { 15143834390605638274u, 2012858990499104158u },
|
||||
{ 4853210475701136017u, 1258036869061940099u }, { 1454827076199032118u, 1572546086327425124u },
|
||||
{ 1818533845248790147u, 1965682607909281405u }, { 3442426662494187794u, 1228551629943300878u },
|
||||
{ 13526405364972510550u, 1535689537429126097u }, { 3072948650933474476u, 1919611921786407622u },
|
||||
{ 15755650962115585259u, 1199757451116504763u }, { 15082877684217093670u, 1499696813895630954u },
|
||||
{ 9630225068416591280u, 1874621017369538693u }, { 8324733676974063502u, 1171638135855961683u },
|
||||
{ 5794231077790191473u, 1464547669819952104u }, { 7242788847237739342u, 1830684587274940130u },
|
||||
{ 18276858095901949986u, 2288355734093675162u }, { 16034722328366106645u, 1430222333808546976u },
|
||||
{ 1596658836748081690u, 1787777917260683721u }, { 6607509564362490017u, 2234722396575854651u },
|
||||
{ 1823850468512862308u, 1396701497859909157u }, { 6891499104068465790u, 1745876872324886446u },
|
||||
{ 17837745916940358045u, 2182346090406108057u }, { 4231062170446641922u, 1363966306503817536u },
|
||||
{ 5288827713058302403u, 1704957883129771920u }, { 6611034641322878003u, 2131197353912214900u },
|
||||
{ 13355268687681574560u, 1331998346195134312u }, { 16694085859601968200u, 1664997932743917890u },
|
||||
{ 11644235287647684442u, 2081247415929897363u }, { 4971804045566108824u, 1300779634956185852u },
|
||||
{ 6214755056957636030u, 1625974543695232315u }, { 3156757802769657134u, 2032468179619040394u },
|
||||
{ 6584659645158423613u, 1270292612261900246u }, { 17454196593302805324u, 1587865765327375307u },
|
||||
{ 17206059723201118751u, 1984832206659219134u }, { 6142101308573311315u, 1240520129162011959u },
|
||||
{ 3065940617289251240u, 1550650161452514949u }, { 8444111790038951954u, 1938312701815643686u },
|
||||
{ 665883850346957067u, 1211445438634777304u }, { 832354812933696334u, 1514306798293471630u },
|
||||
{ 10263815553021896226u, 1892883497866839537u }, { 17944099766707154901u, 1183052186166774710u },
|
||||
{ 13206752671529167818u, 1478815232708468388u }, { 16508440839411459773u, 1848519040885585485u },
|
||||
{ 12623618533845856310u, 1155324400553490928u }, { 15779523167307320387u, 1444155500691863660u },
|
||||
{ 1277659885424598868u, 1805194375864829576u }, { 1597074856780748586u, 2256492969831036970u },
|
||||
{ 5609857803915355770u, 1410308106144398106u }, { 16235694291748970521u, 1762885132680497632u },
|
||||
{ 1847873790976661535u, 2203606415850622041u }, { 12684136165428883219u, 1377254009906638775u },
|
||||
{ 11243484188358716120u, 1721567512383298469u }, { 219297180166231438u, 2151959390479123087u },
|
||||
{ 7054589765244976505u, 1344974619049451929u }, { 13429923224983608535u, 1681218273811814911u },
|
||||
{ 12175718012802122765u, 2101522842264768639u }, { 14527352785642408584u, 1313451776415480399u },
|
||||
{ 13547504963625622826u, 1641814720519350499u }, { 12322695186104640628u, 2052268400649188124u },
|
||||
{ 16925056528170176201u, 1282667750405742577u }, { 7321262604930556539u, 1603334688007178222u },
|
||||
{ 18374950293017971482u, 2004168360008972777u }, { 4566814905495150320u, 1252605225005607986u },
|
||||
{ 14931890668723713708u, 1565756531257009982u }, { 9441491299049866327u, 1957195664071262478u },
|
||||
{ 1289246043478778550u, 1223247290044539049u }, { 6223243572775861092u, 1529059112555673811u },
|
||||
{ 3167368447542438461u, 1911323890694592264u }, { 1979605279714024038u, 1194577431684120165u },
|
||||
{ 7086192618069917952u, 1493221789605150206u }, { 18081112809442173248u, 1866527237006437757u },
|
||||
{ 13606538515115052232u, 1166579523129023598u }, { 7784801107039039482u, 1458224403911279498u },
|
||||
{ 507629346944023544u, 1822780504889099373u }, { 5246222702107417334u, 2278475631111374216u },
|
||||
{ 3278889188817135834u, 1424047269444608885u }, { 8710297504448807696u, 1780059086805761106u }
|
||||
};
|
||||
|
||||
#endif // RYU_TAB_H
|
||||
Loading…
Reference in a new issue