use Ryu for number formatting

This commit is contained in:
dzaima 2022-12-30 20:08:12 +02:00
parent 99a82afec4
commit fd38a5b241
15 changed files with 1537 additions and 32 deletions

View File

@ -77,4 +77,7 @@ Additionally, CBQN is known to compile as-is on macOS (with [some extra options]
## License
Any file without an explicit copyright message is copyright (c) 2021 dzaima, GNU GPLv3 - see LICENSE
Most files here are copyright (c) 2021 dzaima & others, [GNU GPLv3 only](licenses/LICENSE-GPLv3).
Exceptions are:
- timsort implementation - `src/builtins/sortTemplate.h`: [MIT](licenses/LICENSE-MIT-sort); [original repo](https://github.com/swenson/sort/tree/f79f2a525d03f102034b5a197c395f046eb82708)
- Ryu - `src/utils/ryu.c` & files in `src/utils/ryu/`: [Apache 2.0](licenses/LICENSE-Apache2) or [Boost 1.0](licenses/LICENSE-Boost); [original repo](https://github.com/ulfjack/ryu/tree/75d5a85440ed356ad7b23e9e6002d71f62a6255c)

View File

@ -484,7 +484,7 @@ cachedBin‿linkerCache ← {
"src/core/", "tyarr.c", "harr.c", "fillarr.c", "stuff.c", "derv.c", "mm.c", "heap.c"
"src/", "load.c", "main.c", "rtwrap.c", "vm.c", "ns.c", "nfns.c", "ffi.c"
"src/jit/", "nvm.c"
"src/utils/", "utf.c", "hash.c", "file.c", "mut.c", "each.c", "bits.c"
"src/utils/", "ryu.c", "utf.c", "hash.c", "file.c", "mut.c", "each.c", "bits.c"
singeliMap {po.arch"aarch64"? 𝕩/˜(1¨𝕩)"cmp""bits""equal"; 𝕩}
"src/core/stuff.c""equal", "src/utils/mut.c""copy", "src/utils/bits.c""bits"

201
licenses/LICENSE-Apache2 Normal file
View File

@ -0,0 +1,201 @@
Apache License
Version 2.0, January 2004
http://www.apache.org/licenses/
TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
1. Definitions.
"License" shall mean the terms and conditions for use, reproduction,
and distribution as defined by Sections 1 through 9 of this document.
"Licensor" shall mean the copyright owner or entity authorized by
the copyright owner that is granting the License.
"Legal Entity" shall mean the union of the acting entity and all
other entities that control, are controlled by, or are under common
control with that entity. For the purposes of this definition,
"control" means (i) the power, direct or indirect, to cause the
direction or management of such entity, whether by contract or
otherwise, or (ii) ownership of fifty percent (50%) or more of the
outstanding shares, or (iii) beneficial ownership of such entity.
"You" (or "Your") shall mean an individual or Legal Entity
exercising permissions granted by this License.
"Source" form shall mean the preferred form for making modifications,
including but not limited to software source code, documentation
source, and configuration files.
"Object" form shall mean any form resulting from mechanical
transformation or translation of a Source form, including but
not limited to compiled object code, generated documentation,
and conversions to other media types.
"Work" shall mean the work of authorship, whether in Source or
Object form, made available under the License, as indicated by a
copyright notice that is included in or attached to the work
(an example is provided in the Appendix below).
"Derivative Works" shall mean any work, whether in Source or Object
form, that is based on (or derived from) the Work and for which the
editorial revisions, annotations, elaborations, or other modifications
represent, as a whole, an original work of authorship. For the purposes
of this License, Derivative Works shall not include works that remain
separable from, or merely link (or bind by name) to the interfaces of,
the Work and Derivative Works thereof.
"Contribution" shall mean any work of authorship, including
the original version of the Work and any modifications or additions
to that Work or Derivative Works thereof, that is intentionally
submitted to Licensor for inclusion in the Work by the copyright owner
or by an individual or Legal Entity authorized to submit on behalf of
the copyright owner. For the purposes of this definition, "submitted"
means any form of electronic, verbal, or written communication sent
to the Licensor or its representatives, including but not limited to
communication on electronic mailing lists, source code control systems,
and issue tracking systems that are managed by, or on behalf of, the
Licensor for the purpose of discussing and improving the Work, but
excluding communication that is conspicuously marked or otherwise
designated in writing by the copyright owner as "Not a Contribution."
"Contributor" shall mean Licensor and any individual or Legal Entity
on behalf of whom a Contribution has been received by Licensor and
subsequently incorporated within the Work.
2. Grant of Copyright License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
copyright license to reproduce, prepare Derivative Works of,
publicly display, publicly perform, sublicense, and distribute the
Work and such Derivative Works in Source or Object form.
3. Grant of Patent License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
(except as stated in this section) patent license to make, have made,
use, offer to sell, sell, import, and otherwise transfer the Work,
where such license applies only to those patent claims licensable
by such Contributor that are necessarily infringed by their
Contribution(s) alone or by combination of their Contribution(s)
with the Work to which such Contribution(s) was submitted. If You
institute patent litigation against any entity (including a
cross-claim or counterclaim in a lawsuit) alleging that the Work
or a Contribution incorporated within the Work constitutes direct
or contributory patent infringement, then any patent licenses
granted to You under this License for that Work shall terminate
as of the date such litigation is filed.
4. Redistribution. You may reproduce and distribute copies of the
Work or Derivative Works thereof in any medium, with or without
modifications, and in Source or Object form, provided that You
meet the following conditions:
(a) You must give any other recipients of the Work or
Derivative Works a copy of this License; and
(b) You must cause any modified files to carry prominent notices
stating that You changed the files; and
(c) You must retain, in the Source form of any Derivative Works
that You distribute, all copyright, patent, trademark, and
attribution notices from the Source form of the Work,
excluding those notices that do not pertain to any part of
the Derivative Works; and
(d) If the Work includes a "NOTICE" text file as part of its
distribution, then any Derivative Works that You distribute must
include a readable copy of the attribution notices contained
within such NOTICE file, excluding those notices that do not
pertain to any part of the Derivative Works, in at least one
of the following places: within a NOTICE text file distributed
as part of the Derivative Works; within the Source form or
documentation, if provided along with the Derivative Works; or,
within a display generated by the Derivative Works, if and
wherever such third-party notices normally appear. The contents
of the NOTICE file are for informational purposes only and
do not modify the License. You may add Your own attribution
notices within Derivative Works that You distribute, alongside
or as an addendum to the NOTICE text from the Work, provided
that such additional attribution notices cannot be construed
as modifying the License.
You may add Your own copyright statement to Your modifications and
may provide additional or different license terms and conditions
for use, reproduction, or distribution of Your modifications, or
for any such Derivative Works as a whole, provided Your use,
reproduction, and distribution of the Work otherwise complies with
the conditions stated in this License.
5. Submission of Contributions. Unless You explicitly state otherwise,
any Contribution intentionally submitted for inclusion in the Work
by You to the Licensor shall be under the terms and conditions of
this License, without any additional terms or conditions.
Notwithstanding the above, nothing herein shall supersede or modify
the terms of any separate license agreement you may have executed
with Licensor regarding such Contributions.
6. Trademarks. This License does not grant permission to use the trade
names, trademarks, service marks, or product names of the Licensor,
except as required for reasonable and customary use in describing the
origin of the Work and reproducing the content of the NOTICE file.
7. Disclaimer of Warranty. Unless required by applicable law or
agreed to in writing, Licensor provides the Work (and each
Contributor provides its Contributions) on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
implied, including, without limitation, any warranties or conditions
of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
PARTICULAR PURPOSE. You are solely responsible for determining the
appropriateness of using or redistributing the Work and assume any
risks associated with Your exercise of permissions under this License.
8. Limitation of Liability. In no event and under no legal theory,
whether in tort (including negligence), contract, or otherwise,
unless required by applicable law (such as deliberate and grossly
negligent acts) or agreed to in writing, shall any Contributor be
liable to You for damages, including any direct, indirect, special,
incidental, or consequential damages of any character arising as a
result of this License or out of the use or inability to use the
Work (including but not limited to damages for loss of goodwill,
work stoppage, computer failure or malfunction, or any and all
other commercial damages or losses), even if such Contributor
has been advised of the possibility of such damages.
9. Accepting Warranty or Additional Liability. While redistributing
the Work or Derivative Works thereof, You may choose to offer,
and charge a fee for, acceptance of support, warranty, indemnity,
or other liability obligations and/or rights consistent with this
License. However, in accepting such obligations, You may act only
on Your own behalf and on Your sole responsibility, not on behalf
of any other Contributor, and only if You agree to indemnify,
defend, and hold each Contributor harmless for any liability
incurred by, or claims asserted against, such Contributor by reason
of your accepting any such warranty or additional liability.
END OF TERMS AND CONDITIONS
APPENDIX: How to apply the Apache License to your work.
To apply the Apache License to your work, attach the following
boilerplate notice, with the fields enclosed by brackets "[]"
replaced with your own identifying information. (Don't include
the brackets!) The text should be enclosed in the appropriate
comment syntax for the file format. We also recommend that a
file or class name and description of purpose be included on the
same "printed page" as the copyright notice for easier
identification within third-party archives.
Copyright [yyyy] [name of copyright owner]
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

23
licenses/LICENSE-Boost Normal file
View File

@ -0,0 +1,23 @@
Boost Software License - Version 1.0 - August 17th, 2003
Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
execute, and transmit the Software, and to prepare derivative works of the
Software, and to permit third-parties to whom the Software is furnished to
do so, all subject to the following:
The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
all derivative works of the Software, unless such copies or derivative
works are solely in the form of machine-executable object code generated by
a source language processor.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

40
licenses/LICENSE-MIT-sort Normal file
View File

@ -0,0 +1,40 @@
The MIT License (MIT)
Copyright (c) 2010-2019 Christopher Swenson and [others as listed in CONTRIBUTORS.md](CONTRIBUTORS.md)
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
contents of the respective CONTRIBUTORS.md:
List of contributors, in alphabetical order:
- Andrey Astrelin
- Antony Dovgal
- @[Baobaobear](https://github.com/Baobaobear)
- Christopher Swenson
- [@drfie](https://github.com/drfie)
- [@DrMarkS](https://github.com/DrMarkS)
- Emanuel Falkenauer
- Google Inc.
- Haneef Mubarak
- Matthieu Darbois
- Vojtech Fried

View File

@ -248,7 +248,7 @@ ${bd}/%.o: src/%.c
@echo $< | cut -c 5-
@$(CC_INC) $@.d -o $@ -c $<
utils: ${addprefix ${bd}/, utf.o hash.o file.o mut.o each.o bits.o}
utils: ${addprefix ${bd}/, ryu.o utf.o hash.o file.o mut.o each.o bits.o}
${bd}/%.o: src/utils/%.c
@echo $< | cut -c 5-
@$(CC_INC) $@.d -o $@ -c $<

View File

@ -1,32 +1,7 @@
// modified version of https://github.com/swenson/sort/tree/f79f2a525d03f102034b5a197c395f046eb82708
// modified version of https://github.com/swenson/sort/tree/f79f2a525d03f102034b5a197c395f046eb82708; see licenses/LICENSE-MIT-sort
/* Copyright (c) 2010-2019 Christopher Swenson. */
/* Copyright (c) 2012 Vojtech Fried. */
/* Copyright (c) 2012 Google Inc. All Rights Reserved. */
/*
The MIT License (MIT)
Copyright (c) 2010-2019 Christopher Swenson and [others as listed in CONTRIBUTORS.md](CONTRIBUTORS.md)
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
(contributors list, as this isn't markdown in the original repo: https://github.com/swenson/sort/blob/f79f2a525d03f102034b5a197c395f046eb82708/CONTRIBUTORS.md)
*/
#include <stdlib.h>
#include <stdio.h>

View File

@ -81,10 +81,18 @@ B glyph_c1(B t, B x) {
return m_c32vec_0(U"(•Glyph: given object with unexpected type)");
}
#if !NO_RYU
B ryu_d2s(double f);
#endif
B repr_c1(B t, B x) {
if (isF64(x)) {
#if NO_RYU
NUM_FMT_BUF(buf, x.f);
return utf8Decode(buf, strlen(buf));
#else
return ryu_d2s(o2fG(x));
#endif
} else {
#if FORMATTER
return bqn_repr(x);

View File

@ -8,7 +8,7 @@
#define PRECOMPILED_FILE1(X) PRECOMPILED_FILE0(X)
#define PRECOMPILED_FILE(END) PRECOMPILED_FILE1(../build/BYTECODE_DIR/gen/END)
#define FOR_INIT(F) F(base) F(harr) F(mutF) F(cmpA) F(fillarr) F(tyarr) F(hash) F(sfns) F(fns) F(arith) F(md1) F(md2) F(derv) F(comp) F(rtWrap) F(ns) F(nfn) F(sysfn) F(inverse) F(slash) F(search) F(load) F(sysfnPost) F(dervPost) F(ffi) F(mmap) F(typesFinished)
#define FOR_INIT(F) F(base) F(harr) F(mutF) F(cmpA) F(fillarr) F(tyarr) F(hash) F(sfns) F(fns) F(arith) F(md1) F(md2) F(derv) F(comp) F(rtWrap) F(ns) F(nfn) F(sysfn) F(inverse) F(slash) F(search) F(load) F(sysfnPost) F(dervPost) F(ryu) F(ffi) F(mmap) F(typesFinished)
#define F(X) NOINLINE void X##_init(void);
FOR_INIT(F)
#undef F

View File

@ -15,6 +15,7 @@
#include "../utils/mut.c"
#include "../utils/each.c"
#include "../utils/bits.c"
#include "../utils/ryu.c"
#include "../builtins/fns.c"
#include "../builtins/sfns.c"
#include "../builtins/select.c"

439
src/utils/ryu.c Normal file
View File

@ -0,0 +1,439 @@
// Copyright 2019 Ulf Adams
//
// The contents of this file may be used under the terms of the Apache License,
// Version 2.0.
//
// (See accompanying file LICENSE-Apache or copy at
// http://www.apache.org/licenses/LICENSE-2.0)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
#define INT_SCIENTIFIC_START 1e15 // integer scientific representation start; only applies to integers with 2⋆53>|𝕩
#define POS_SCIENTIFIC_START 15 // positive scientific representation start; as-is can't be greater than 15 because only the small_int case provides trailing zeroes
#define NEG_SCIENTIFIC_START 5 // negative scientific representation start
#if NO_RYU
void ryu_init() { }
#else
#include "../core.h"
#include "ryu/ryu_common.h"
// Include either the small or the full lookup tables depending on the mode.
#if defined(RYU_OPTIMIZE_SIZE)
#include "ryu/d2s_small_table.h"
#else
#include "ryu/d2s_full_table.h"
#endif
#define DOUBLE_MANTISSA_BITS 52
#define DOUBLE_EXPONENT_BITS 11
#define DOUBLE_BIAS 1023
// A floating decimal representing m * 10^e.
typedef struct floating_decimal_64 {
uint64_t mantissa;
// Decimal exponent's range is -324 to 308
// inclusive, and can fit in a short if needed.
int32_t exponent;
} floating_decimal_64;
static inline floating_decimal_64 d2d(const uint64_t mantissa, const uint32_t exponent) {
int32_t e2;
uint64_t m2;
if (exponent == 0) {
// We subtract 2 so that the bounds computation has 2 additional bits.
e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
m2 = mantissa;
} else {
e2 = (int32_t) exponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
m2 = (1ull << DOUBLE_MANTISSA_BITS) | mantissa;
}
const bool even = (m2 & 1) == 0;
const bool acceptBounds = even;
#ifdef RYU_DEBUG
printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2);
#endif
// Step 2: Determine the interval of valid decimal representations.
const uint64_t mv = 4 * m2;
const uint32_t mmShift = mantissa!=0 || exponent<=1; // Implicit bool -> int conversion. True is 1, false is 0.
// We would compute mp and mm like this:
// uint64_t mp = 4 * m2 + 2;
// uint64_t mm = mv - 1 - mmShift;
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
uint64_t vr, vp, vm;
int32_t e10;
bool vmIsTrailingZeros = false;
bool vrIsTrailingZeros = false;
if (e2 >= 0) {
// I tried special-casing q == 0, but there was no effect on performance.
// This expression is slightly faster than max(0, log10Pow2(e2) - 1).
const uint32_t q = log10Pow2(e2) - (e2 > 3);
e10 = (int32_t) q;
const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1;
const int32_t i = -e2 + (int32_t) q + k;
#if defined(RYU_OPTIMIZE_SIZE)
uint64_t pow5[2];
double_computeInvPow5(q, pow5);
vr = mulShiftAll64(m2, pow5, i, &vp, &vm, mmShift);
#else
vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
#endif
#ifdef RYU_DEBUG
printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q);
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
#endif
if (q <= 21) {
// This should use q <= 22, but I think 21 is also safe. Smaller values
// may still be safe, but it's more difficult to reason about them.
// Only one of mp, mv, and mm can be a multiple of 5, if any.
const uint32_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) div5(mv));
if (mvMod5 == 0) {
vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
} else if (acceptBounds) {
// Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
// <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
// <=> true && pow5Factor(mm) >= q, since e2 >= q.
vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
} else {
// Same as min(e2 + 1, pow5Factor(mp)) >= q.
vp -= multipleOfPowerOf5(mv + 2, q);
}
}
} else {
// This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
const uint32_t q = log10Pow5(-e2) - (-e2 > 1);
e10 = (int32_t) q + e2;
const int32_t i = -e2 - (int32_t) q;
const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
const int32_t j = (int32_t) q - k;
#if defined(RYU_OPTIMIZE_SIZE)
uint64_t pow5[2];
double_computePow5(i, pow5);
vr = mulShiftAll64(m2, pow5, j, &vp, &vm, mmShift);
#else
vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
#endif
#ifdef RYU_DEBUG
printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q);
printf("%u %d %d %d\n", q, i, k, j);
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
#endif
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.
vrIsTrailingZeros = true;
if (acceptBounds) {
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
vmIsTrailingZeros = mmShift == 1;
} else {
// mp = mv + 2, so it always has at least one trailing 0 bit.
--vp;
}
} else if (q < 63) { // TODO(ulfjack): Use a tighter bound here.
// We want to know if the full product has at least q trailing zeros.
// We need to compute min(p2(mv), p5(mv) - e2) >= q
// <=> p2(mv) >= q && p5(mv) - e2 >= q
// <=> p2(mv) >= q (because -e2 >= q)
vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
#ifdef RYU_DEBUG
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
}
}
#ifdef RYU_DEBUG
printf("e10=%d\n", e10);
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
// Step 4: Find the shortest decimal representation in the interval of valid representations.
int32_t removed = 0;
uint8_t lastRemovedDigit = 0;
uint64_t output;
// On average, we remove ~2 digits.
if (vmIsTrailingZeros || vrIsTrailingZeros) {
// General case, which happens rarely (~0.7%).
for (;;) {
const uint64_t vpDiv10 = div10(vp);
const uint64_t vmDiv10 = div10(vm);
if (vpDiv10 <= vmDiv10) {
break;
}
const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
vmIsTrailingZeros &= vmMod10 == 0;
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t) vrMod10;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
#ifdef RYU_DEBUG
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
#endif
if (vmIsTrailingZeros) {
for (;;) {
const uint64_t vmDiv10 = div10(vm);
const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10);
if (vmMod10 != 0) {
break;
}
const uint64_t vpDiv10 = div10(vp);
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t) vrMod10;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
}
#ifdef RYU_DEBUG
printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) {
// Round even if the exact number is .....50..0.
lastRemovedDigit = 4;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
} else {
// Specialized for the common case (~99.3%). Percentages below are relative to this.
bool roundUp = false;
const uint64_t vpDiv100 = div100(vp);
const uint64_t vmDiv100 = div100(vm);
if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
const uint64_t vrDiv100 = div100(vr);
const 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 (;;) {
const uint64_t vpDiv10 = div10(vp);
const uint64_t vmDiv10 = div10(vm);
if (vpDiv10 <= vmDiv10) {
break;
}
const uint64_t vrDiv10 = div10(vr);
const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10);
roundUp = vrMod10 >= 5;
vr = vrDiv10;
vp = vpDiv10;
vm = vmDiv10;
++removed;
}
#ifdef RYU_DEBUG
printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
#endif
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr + (vr == vm || roundUp);
}
const int32_t exp = e10 + removed;
#ifdef RYU_DEBUG
printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
printf("O=%" PRIu64 "\n", output);
printf("EXP=%d\n", exp);
#endif
floating_decimal_64 fd;
fd.exponent = exp;
fd.mantissa = output;
return fd;
}
#define W2D(RES, NUM) memcpy((RES), DIGIT_TABLE + (NUM)*2, 2)
#define W4D(RES, NUM) ({ char* r4_ = (RES); AUTO n4_ = (NUM); W2D(r4_, n4_/100 ); W2D(r4_+2, n4_%100 ); })
#ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
#define mod1e4(X) ((X) - 10000 * ((X)/10000))
#else
#define mod1e4(X) ((X)%10000)
#endif
static inline bool d2d_small_int(const uint64_t mantissa, const uint32_t exponent, floating_decimal_64* const v) {
const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | mantissa;
const int32_t e2 = (int32_t) exponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
if (e2 > 0) return false; // f = m2 * 2^e2 >= 2^53 is an integer. Ignore this case for now.
if (e2 < -52) return false; // f < 1.
// Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53.
// Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0.
const uint64_t mask = (1ull << -e2) - 1;
const uint64_t fraction = m2 & mask;
if (fraction != 0) return false;
// f is an integer in the range [1, 2^53).
v->mantissa = m2 >> -e2; // Note: mantissa contains trailing (decimal) 0's for numbers with such.
v->exponent = 0;
return true;
}
static inline B to_chars(const floating_decimal_64 v, const bool sign, const bool forcePositional) {
char buf[25];
char* dec = buf+25;
// decode all digits to temporary buffer
uint64_t o64 = v.mantissa;
if ((o64 >> 32) != 0) {
uint64_t q = div1e8(o64);
uint32_t o32 = ((uint32_t) o64) - 100000000 * ((uint32_t) q);
o64 = q;
uint32_t c = o32%10000; o32/= 10000;
uint32_t d = o32%10000;
W4D(dec-4, c);
W4D(dec-8, d);
dec-= 8;
}
uint32_t o32 = (uint32_t) o64;
while (o32 >= 10000) { uint32_t c = mod1e4(o32); o32/= 10000; dec-= 4; W4D(dec, c); }
if (o32 >= 100 ) { uint32_t c = o32%100; o32/= 100; dec-= 2; W2D(dec, c); }
if (o32 >= 10 ) { uint32_t c = o32; dec-= 2; W2D(dec, c); }
else *(--dec) = '0'+o32;
int dlen = buf+25 - dec; // number of digits
int32_t expRaw = v.exponent; // exponent relative to decimal mantissa
int exp = expRaw+dlen-1; // proper decimal exponent
#if RYU_DEBUG
printf("mantissa=" N64u " exp=%d expRaw=%d dlen=%d\n", v.mantissa, exp, expRaw, dlen);
#endif
bool positional = forcePositional;
positional|= exp>-NEG_SCIENTIFIC_START && exp<POS_SCIENTIFIC_START;
int rlen = dlen + sign;
if (positional) {
rlen+= exp<0? 1-exp : expRaw!=0; // exp<0? 0.00000001234 : expRaw==0? 1234 : 12.34
// 123400000 is handled by caller by already having trailing zeroes in mantissa and expRaw==0
} else {
int expAbs = exp;
rlen+= dlen!=1; // 1e99 vs 1.2e99
if (expAbs<0) { expAbs = -expAbs; rlen++; } // 1e9 vs 1e¯9
rlen+= expAbs>=100? 4 : expAbs>=10? 3 : 2; // 1e9 vs 1e99 vs 1e299
}
u8* rp;
B r = m_c8arrv(&rp, rlen);
if (sign) rp++[0] = U'¯';
if (positional) {
if (exp<0) {
rp[0] = '0';
rp[1] = '.';
PLAINLOOP for (int i = 0; i < -exp-1; i++) rp[i+2] = '0';
memcpy(rp-exp+1, dec, dlen);
} else {
memcpy(rp, dec, exp+1);
if (expRaw!=0) {
rp[exp+1] = '.';
memcpy(rp+exp+2, dec+exp+1, dlen-exp-1);
}
}
} else {
rp[0] = dec[0];
int epos;
if (dlen!=1) {
rp[1] = '.';
memcpy(rp+2, dec+1, dlen-1);
epos = dlen+1;
} else epos = dlen;
rp[epos] = 'e';
if (exp<0) { exp = -exp; rp[++epos] = U'¯'; }
if (exp>=100) { W2D(rp+epos+1, exp/10); rp[epos+3] = '0' + exp%10; }
else if (exp>=10) { W2D(rp+epos+1, exp); }
else rp[epos+1] = '0' + exp;
}
return r;
}
static B fmt_nan, fmt_inf[2], fmt_zero[2];
B ryu_d2s(double f) {
const uint64_t bits = double_to_bits(f); // decode the floating-point number, and unify normalized and subnormal cases.
#ifdef RYU_DEBUG
printf("IN=");
for (int32_t bit = 64; bit-->0; ) printf("%d", (int) ((bits >> bit) & 1));
printf("\n");
#endif
// Decode bits into sign, mantissa, and exponent.
const bool sign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
const uint64_t mantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
const uint32_t exponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
// Case distinction; exit early for the easy cases.
if (exponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (exponent == 0 && mantissa == 0)) {
B r;
if (mantissa) r = fmt_nan;
if (exponent) r = fmt_inf[sign];
else r = fmt_zero[sign];
return incG(r);
}
floating_decimal_64 v;
// For small numbers, we want non-scientific.
// isSmallInt handles the case of trailing zeroes, everything else is just moving "." & "e" around
bool isSmallInt = d2d_small_int(mantissa, exponent, &v); // "small" ≡ <2⋆53
bool forcePositional;
if (isSmallInt) {
forcePositional = v.mantissa < (uint64_t)(INT_SCIENTIFIC_START);
if (!forcePositional) {
for (;;) { // remove trailing zeroes, as to_chars doesn't handle those unless forcePositional
uint64_t q = div10(v.mantissa);
uint32_t r = (uint32_t)v.mantissa - 10 * (uint32_t)q;
if (r!=0) break;
v.mantissa = q;
++v.exponent;
}
}
} else {
forcePositional = false;
v = d2d(mantissa, exponent);
}
return to_chars(v, sign, forcePositional);
}
void ryu_init() {
gc_add(fmt_nan = m_c8vec("NaN", 3));
gc_add(fmt_zero[0] = m_c8vec("0", 1));
{ u16* d; B c = m_c16arrv(&d, 1); d[0]=U''; gc_add(c); fmt_inf[0] = c; }
{ u16* d; B c = m_c16arrv(&d, 2); d[0]=U'¯'; d[1]=U''; gc_add(c); fmt_inf[1] = c; }
{ u8* d; B c = m_c8arrv (&d, 2); d[0]=U'¯'; d[1]=U'0'; gc_add(c); fmt_zero[1] = c; }
}
#endif

View File

@ -0,0 +1,367 @@
// Copyright 2018 Ulf Adams
//
// The contents of this file may be used under the terms of the Apache License,
// Version 2.0.
//
// (See accompanying file LICENSE-Apache or copy at
// http://www.apache.org/licenses/LICENSE-2.0)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
#ifndef RYU_D2S_FULL_TABLE_H
#define RYU_D2S_FULL_TABLE_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
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_D2S_FULL_TABLE_H

View File

@ -0,0 +1,182 @@
// Copyright 2018 Ulf Adams
//
// The contents of this file may be used under the terms of the Apache License,
// Version 2.0.
//
// (See accompanying file LICENSE-Apache or copy at
// http://www.apache.org/licenses/LICENSE-2.0)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
#ifndef RYU_D2S_SMALL_TABLE_H
#define RYU_D2S_SMALL_TABLE_H
// Defines HAS_UINT128 and uint128_t if applicable.
#include "ryu_common.h"
// These tables are generated by PrintDoubleLookupTable.
#define DOUBLE_POW5_INV_BITCOUNT 125
#define DOUBLE_POW5_BITCOUNT 125
static const uint64_t DOUBLE_POW5_INV_SPLIT2[15][2] = {
{ 1u, 2305843009213693952u },
{ 5955668970331000884u, 1784059615882449851u },
{ 8982663654677661702u, 1380349269358112757u },
{ 7286864317269821294u, 2135987035920910082u },
{ 7005857020398200553u, 1652639921975621497u },
{ 17965325103354776697u, 1278668206209430417u },
{ 8928596168509315048u, 1978643211784836272u },
{ 10075671573058298858u, 1530901034580419511u },
{ 597001226353042382u, 1184477304306571148u },
{ 1527430471115325346u, 1832889850782397517u },
{ 12533209867169019542u, 1418129833677084982u },
{ 5577825024675947042u, 2194449627517475473u },
{ 11006974540203867551u, 1697873161311732311u },
{ 10313493231639821582u, 1313665730009899186u },
{ 12701016819766672773u, 2032799256770390445u }
};
static const uint32_t POW5_INV_OFFSETS[19] = {
0x54544554, 0x04055545, 0x10041000, 0x00400414, 0x40010000, 0x41155555,
0x00000454, 0x00010044, 0x40000000, 0x44000041, 0x50454450, 0x55550054,
0x51655554, 0x40004000, 0x01000001, 0x00010500, 0x51515411, 0x05555554,
0x00000000
};
static const uint64_t DOUBLE_POW5_SPLIT2[13][2] = {
{ 0u, 1152921504606846976u },
{ 0u, 1490116119384765625u },
{ 1032610780636961552u, 1925929944387235853u },
{ 7910200175544436838u, 1244603055572228341u },
{ 16941905809032713930u, 1608611746708759036u },
{ 13024893955298202172u, 2079081953128979843u },
{ 6607496772837067824u, 1343575221513417750u },
{ 17332926989895652603u, 1736530273035216783u },
{ 13037379183483547984u, 2244412773384604712u },
{ 1605989338741628675u, 1450417759929778918u },
{ 9630225068416591280u, 1874621017369538693u },
{ 665883850346957067u, 1211445438634777304u },
{ 14931890668723713708u, 1565756531257009982u }
};
static const uint32_t POW5_OFFSETS[21] = {
0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x40000000, 0x59695995,
0x55545555, 0x56555515, 0x41150504, 0x40555410, 0x44555145, 0x44504540,
0x45555550, 0x40004000, 0x96440440, 0x55565565, 0x54454045, 0x40154151,
0x55559155, 0x51405555, 0x00000105
};
#define POW5_TABLE_SIZE 26
static const uint64_t DOUBLE_POW5_TABLE[POW5_TABLE_SIZE] = {
1ull, 5ull, 25ull, 125ull, 625ull, 3125ull, 15625ull, 78125ull, 390625ull,
1953125ull, 9765625ull, 48828125ull, 244140625ull, 1220703125ull, 6103515625ull,
30517578125ull, 152587890625ull, 762939453125ull, 3814697265625ull,
19073486328125ull, 95367431640625ull, 476837158203125ull,
2384185791015625ull, 11920928955078125ull, 59604644775390625ull,
298023223876953125ull //, 1490116119384765625ull
};
#if defined(HAS_UINT128)
// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
static inline void double_computePow5(const uint32_t i, uint64_t* const result) {
const uint32_t base = i / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = i - base2;
const uint64_t* const mul = DOUBLE_POW5_SPLIT2[base];
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset];
const uint128_t b0 = ((uint128_t) m) * mul[0];
const uint128_t b2 = ((uint128_t) m) * mul[1];
const uint32_t delta = pow5bits(i) - pow5bits(base2);
const uint128_t shiftedSum = (b0 >> delta) + (b2 << (64 - delta)) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[0] = (uint64_t) shiftedSum;
result[1] = (uint64_t) (shiftedSum >> 64);
}
// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
static inline void double_computeInvPow5(const uint32_t i, uint64_t* const result) {
const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = base2 - i;
const uint64_t* const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset]; // 5^offset
const uint128_t b0 = ((uint128_t) m) * (mul[0] - 1);
const uint128_t b2 = ((uint128_t) m) * mul[1]; // 1/5^base2 * 5^offset = 1/5^(base2-offset) = 1/5^i
const uint32_t delta = pow5bits(base2) - pow5bits(i);
const uint128_t shiftedSum =
((b0 >> delta) + (b2 << (64 - delta))) + 1 + ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[0] = (uint64_t) shiftedSum;
result[1] = (uint64_t) (shiftedSum >> 64);
}
#else // defined(HAS_UINT128)
// Computes 5^i in the form required by Ryu, and stores it in the given pointer.
static inline void double_computePow5(const uint32_t i, uint64_t* const result) {
const uint32_t base = i / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = i - base2;
const uint64_t* const mul = DOUBLE_POW5_SPLIT2[base];
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset];
uint64_t high1;
const uint64_t low1 = umul128(m, mul[1], &high1);
uint64_t high0;
const uint64_t low0 = umul128(m, mul[0], &high0);
const uint64_t sum = high0 + low1;
if (sum < high0) {
++high1; // overflow into high1
}
// high1 | sum | low0
const uint32_t delta = pow5bits(i) - pow5bits(base2);
result[0] = shiftright128(low0, sum, delta) + ((POW5_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[1] = shiftright128(sum, high1, delta);
}
// Computes 5^-i in the form required by Ryu, and stores it in the given pointer.
static inline void double_computeInvPow5(const uint32_t i, uint64_t* const result) {
const uint32_t base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
const uint32_t base2 = base * POW5_TABLE_SIZE;
const uint32_t offset = base2 - i;
const uint64_t* const mul = DOUBLE_POW5_INV_SPLIT2[base]; // 1/5^base2
if (offset == 0) {
result[0] = mul[0];
result[1] = mul[1];
return;
}
const uint64_t m = DOUBLE_POW5_TABLE[offset];
uint64_t high1;
const uint64_t low1 = umul128(m, mul[1], &high1);
uint64_t high0;
const uint64_t low0 = umul128(m, mul[0] - 1, &high0);
const uint64_t sum = high0 + low1;
if (sum < high0) {
++high1; // overflow into high1
}
// high1 | sum | low0
const uint32_t delta = pow5bits(base2) - pow5bits(i);
result[0] = shiftright128(low0, sum, delta) + 1 + ((POW5_INV_OFFSETS[i / 16] >> ((i % 16) << 1)) & 3);
result[1] = shiftright128(sum, high1, delta);
}
#endif // defined(HAS_UINT128)
#endif // RYU_D2S_SMALL_TABLE_H

266
src/utils/ryu/ryu_common.h Normal file
View File

@ -0,0 +1,266 @@
// Copyright 2019 Ulf Adams
//
// The contents of this file may be used under the terms of the Apache License,
// Version 2.0.
//
// (See accompanying file LICENSE-Apache or copy at
// http://www.apache.org/licenses/LICENSE-2.0)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
// original file: digit_table.h
static const char DIGIT_TABLE[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'
};
// original file: common.h
#if defined(_M_IX86) || defined(_M_ARM)
#define RYU_32_BIT_PLATFORM
#endif
// Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528.
static inline int32_t pow5bits(const int32_t e) {
// This approximation works up to the point that the multiplication overflows at e = 3529.
// If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater
// than 2^9297.
assert(e >= 0);
assert(e <= 3528);
return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1);
}
// Returns floor(log_10(2^e)); requires 0 <= e <= 1650.
static inline uint32_t log10Pow2(const int32_t e) {
// The first value this approximation fails for is 2^1651 which is just greater than 10^297.
assert(e >= 0);
assert(e <= 1650);
return (((uint32_t) e) * 78913) >> 18;
}
// Returns floor(log_10(5^e)); requires 0 <= e <= 2620.
static inline uint32_t log10Pow5(const int32_t e) {
// The first value this approximation fails for is 5^2621 which is just greater than 10^1832.
assert(e >= 0);
assert(e <= 2620);
return (((uint32_t) e) * 732923) >> 20;
}
static inline uint64_t double_to_bits(const double d) {
uint64_t bits = 0;
memcpy(&bits, &d, sizeof(double));
return bits;
}
// original file: d2s_intrinsics.h
#if defined(__SIZEOF_INT128__) && !defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS)
#define HAS_UINT128
#elif defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
#define HAS_64_BIT_INTRINSICS
#endif
#if defined(HAS_UINT128)
typedef __uint128_t uint128_t;
#endif
#if defined(HAS_64_BIT_INTRINSICS)
#include <intrin.h>
static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
return _umul128(a, b, productHi);
}
// Returns the lower 64 bits of (hi*2^64 + lo) >> dist, with 0 < dist < 64.
static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
assert(dist < 64);
return __shiftright128(lo, hi, (unsigned char) dist);
}
#else // defined(HAS_64_BIT_INTRINSICS)
static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) {
// The casts here help MSVC to avoid calls to the __allmul library function.
const uint32_t aLo = (uint32_t)a; const uint32_t aHi = (uint32_t)(a >> 32);
const uint32_t bLo = (uint32_t)b; const uint32_t bHi = (uint32_t)(b >> 32);
const uint64_t b00 = (uint64_t)aLo * bLo; const uint64_t b01 = (uint64_t)aLo * bHi;
const uint64_t b10 = (uint64_t)aHi * bLo; const uint64_t b11 = (uint64_t)aHi * bHi;
const uint32_t b00Lo = (uint32_t)b00;
const uint32_t b00Hi = (uint32_t)(b00 >> 32);
const uint64_t mid1 = b10 + b00Hi;
const uint32_t mid1Lo = (uint32_t)(mid1);
const uint32_t mid1Hi = (uint32_t)(mid1 >> 32);
const uint64_t mid2 = b01 + mid1Lo;
const uint32_t mid2Lo = (uint32_t)(mid2);
const uint32_t mid2Hi = (uint32_t)(mid2 >> 32);
const uint64_t pHi = b11 + mid1Hi + mid2Hi;
const uint64_t pLo = ((uint64_t)mid2Lo << 32) | b00Lo;
*productHi = pHi;
return pLo;
}
static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) {
// We don't need to handle the case dist >= 64 here (see above).
assert(dist < 64);
assert(dist > 0);
return (hi << (64 - dist)) | (lo >> dist);
}
#endif // defined(HAS_64_BIT_INTRINSICS)
#if defined(RYU_32_BIT_PLATFORM)
// Returns the high 64 bits of the 128-bit product of a and b.
static inline uint64_t umulh(const uint64_t a, const uint64_t b) {
// Reuse the umul128 implementation.
// Optimizers will likely eliminate the instructions used to compute the
// low part of the product.
uint64_t hi;
umul128(a, b, &hi);
return hi;
}
static inline uint64_t div5(const uint64_t x) { return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2; }
static inline uint64_t div10(const uint64_t x) { return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3; }
static inline uint64_t div100(const uint64_t x) { return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2; }
static inline uint64_t div1e8(const uint64_t x) { return umulh(x, 0xABCC77118461CEFDu) >> 26; }
static inline uint64_t div1e9(const uint64_t x) { return umulh(x >> 9, 0x44B82FA09B5A53u) >> 11; }
static inline uint32_t mod1e9(const uint64_t x) { return ((uint32_t) x) - 1000000000 * ((uint32_t) div1e9(x)); }
#else // defined(RYU_32_BIT_PLATFORM)
static inline uint64_t div5(const uint64_t x) { return x / 5; }
static inline uint64_t div10(const uint64_t x) { return x / 10; }
static inline uint64_t div100(const uint64_t x) { return x / 100; }
static inline uint64_t div1e8(const uint64_t x) { return x / 100000000; }
static inline uint64_t div1e9(const uint64_t x) { return x / 1000000000; }
static inline uint32_t mod1e9(const uint64_t x) { return (uint32_t) (x - 1000000000 * div1e9(x)); }
#endif // defined(RYU_32_BIT_PLATFORM)
static inline uint32_t pow5Factor(uint64_t value) {
const uint64_t m_inv_5 = 14757395258967641293u; // 5 * m_inv_5 = 1 (mod 2^64)
const uint64_t n_div_5 = 3689348814741910323u; // #{ n | n = 0 (mod 2^64) } = 2^64 / 5
uint32_t count = 0;
for (;;) {
assert(value != 0);
value *= m_inv_5;
if (value > n_div_5)
break;
++count;
}
return count;
}
// Returns true if value is divisible by 5^p.
static inline bool multipleOfPowerOf5(const uint64_t value, const uint32_t p) {
// I tried a case distinction on p, but there was no performance difference.
return pow5Factor(value) >= p;
}
// Returns true if value is divisible by 2^p.
static inline bool multipleOfPowerOf2(const uint64_t value, const uint32_t p) {
assert(value != 0);
assert(p < 64);
// __builtin_ctzll doesn't appear to be faster here.
return (value & ((1ull << p) - 1)) == 0;
}
#if defined(HAS_UINT128)
// Best case: use 128-bit type.
static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
const uint128_t b0 = ((uint128_t) m) * mul[0];
const uint128_t b2 = ((uint128_t) m) * mul[1];
return (uint64_t) (((b0 >> 64) + b2) >> (j - 64));
}
static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j, uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
*vp = mulShift64(4 * m + 2, mul, j);
*vm = mulShift64(4 * m - 1 - mmShift, mul, j);
return mulShift64(4 * m, mul, j);
}
#elif defined(HAS_64_BIT_INTRINSICS)
static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
// m is maximum 55 bits
uint64_t high1; // 128
const uint64_t low1 = umul128(m, mul[1], &high1); // 64
uint64_t high0; // 64
umul128(m, mul[0], &high0); // 0
const uint64_t sum = high0 + low1;
if (sum < high0) {
++high1; // overflow into high1
}
return shiftright128(sum, high1, j - 64);
}
static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j,
uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
*vp = mulShift64(4 * m + 2, mul, j);
*vm = mulShift64(4 * m - 1 - mmShift, mul, j);
return mulShift64(4 * m, mul, j);
}
#else // !defined(HAS_UINT128) && !defined(HAS_64_BIT_INTRINSICS)
static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) {
// m is maximum 55 bits
uint64_t high1; // 128
const uint64_t low1 = umul128(m, mul[1], &high1); // 64
uint64_t high0; // 64
umul128(m, mul[0], &high0); // 0
const uint64_t sum = high0 + low1;
if (sum < high0) {
++high1; // overflow into high1
}
return shiftright128(sum, high1, j - 64);
}
// This is faster if we don't have a 64x64->128-bit multiplication.
static inline uint64_t mulShiftAll64(uint64_t m, const uint64_t* const mul, const int32_t j,
uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) {
m <<= 1;
// m is maximum 55 bits
uint64_t tmp;
const uint64_t lo = umul128(m, mul[0], &tmp);
uint64_t hi;
const uint64_t mid = tmp + umul128(m, mul[1], &hi);
hi += mid < tmp; // overflow into hi
const uint64_t lo2 = lo + mul[0];
const uint64_t mid2 = mid + mul[1] + (lo2 < lo);
const uint64_t hi2 = hi + (mid2 < mid);
*vp = shiftright128(mid2, hi2, (uint32_t) (j - 64 - 1));
if (mmShift == 1) {
const uint64_t lo3 = lo - mul[0];
const uint64_t mid3 = mid - mul[1] - (lo3 > lo);
const uint64_t hi3 = hi - (mid3 > mid);
*vm = shiftright128(mid3, hi3, (uint32_t) (j - 64 - 1));
} else {
const uint64_t lo3 = lo + lo;
const uint64_t mid3 = mid + mid + (lo3 < lo);
const uint64_t hi3 = hi + hi + (mid3 < mid);
const uint64_t lo4 = lo3 - mul[0];
const uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3);
const uint64_t hi4 = hi3 - (mid4 > mid3);
*vm = shiftright128(mid4, hi4, (uint32_t) (j - 64));
}
return shiftright128(mid, hi, (uint32_t) (j - 64 - 1));
}
#endif // HAS_64_BIT_INTRINSICS