use Ryu for number formatting
This commit is contained in:
parent
99a82afec4
commit
fd38a5b241
@ -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)
|
||||
@ -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
201
licenses/LICENSE-Apache2
Normal 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
23
licenses/LICENSE-Boost
Normal 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
40
licenses/LICENSE-MIT-sort
Normal 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
|
||||
2
makefile
2
makefile
@ -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 $<
|
||||
|
||||
@ -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>
|
||||
|
||||
@ -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)) {
|
||||
NUM_FMT_BUF(buf, x.f);
|
||||
return utf8Decode(buf, strlen(buf));
|
||||
#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);
|
||||
|
||||
@ -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
|
||||
|
||||
@ -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
439
src/utils/ryu.c
Normal 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
|
||||
367
src/utils/ryu/d2s_full_table.h
Normal file
367
src/utils/ryu/d2s_full_table.h
Normal 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
|
||||
182
src/utils/ryu/d2s_small_table.h
Normal file
182
src/utils/ryu/d2s_small_table.h
Normal 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
266
src/utils/ryu/ryu_common.h
Normal 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
|
||||
Loading…
Reference in New Issue
Block a user