[libc-commits] [libc] 87c0160 - [libc] add atof, strtof and strtod
Michael Jones via libc-commits
libc-commits at lists.llvm.org
Mon Oct 18 16:10:14 PDT 2021
Author: Michael Jones
Date: 2021-10-18T16:10:03-07:00
New Revision: 87c016078ad72c46505461e4ff8bfa04819fe7ba
URL: https://github.com/llvm/llvm-project/commit/87c016078ad72c46505461e4ff8bfa04819fe7ba
DIFF: https://github.com/llvm/llvm-project/commit/87c016078ad72c46505461e4ff8bfa04819fe7ba.diff
LOG: [libc] add atof, strtof and strtod
Add the string to floating point conversion functions.
Long doubles aren't supported yet, but floats and doubles are. The
primary algorithm used is the Eisel-Lemire ParseNumberF64 algorithm,
with the Simple Decimal Conversion algorithm as backup.
Links for more information on the algorithms:
Number Parsing at a Gigabyte per Second, Software: Practice and
Experience 51 (8), 2021 (https://arxiv.org/abs/2101.11408)
https://nigeltao.github.io/blog/2020/eisel-lemire.html
https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html
Differential Revision: https://reviews.llvm.org/D109261
Added:
libc/fuzzing/stdlib/StringParserOutputDiff.h
libc/fuzzing/stdlib/atof_fuzz.cpp
libc/src/__support/detailed_powers_of_ten.h
libc/src/__support/str_to_float.h
libc/src/stdlib/atof.cpp
libc/src/stdlib/atof.h
libc/src/stdlib/strtod.cpp
libc/src/stdlib/strtod.h
libc/src/stdlib/strtof.cpp
libc/src/stdlib/strtof.h
libc/test/src/__support/str_to_float_comparison_data.txt
libc/test/src/__support/str_to_float_comparison_test.cpp
libc/test/src/__support/str_to_float_test.cpp
libc/test/src/stdlib/atof_test.cpp
libc/test/src/stdlib/strtod_test.cpp
libc/test/src/stdlib/strtof_test.cpp
Modified:
libc/config/linux/x86_64/entrypoints.txt
libc/fuzzing/stdlib/CMakeLists.txt
libc/spec/stdc.td
libc/src/__support/CMakeLists.txt
libc/src/__support/high_precision_decimal.h
libc/src/stdlib/CMakeLists.txt
libc/test/src/__support/CMakeLists.txt
libc/test/src/stdlib/CMakeLists.txt
Removed:
################################################################################
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index 1f40545cde3f1..9ea7928faef2c 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -56,6 +56,7 @@ set(TARGET_LIBC_ENTRYPOINTS
# stdlib.h entrypoints
libc.src.stdlib.abs
libc.src.stdlib.atoi
+ libc.src.stdlib.atof
libc.src.stdlib.atol
libc.src.stdlib.atoll
libc.src.stdlib.bsearch
@@ -65,6 +66,8 @@ set(TARGET_LIBC_ENTRYPOINTS
libc.src.stdlib.llabs
libc.src.stdlib.lldiv
libc.src.stdlib.qsort
+ libc.src.stdlib.strtod
+ libc.src.stdlib.strtof
libc.src.stdlib.strtol
libc.src.stdlib.strtoll
libc.src.stdlib.strtoul
diff --git a/libc/fuzzing/stdlib/CMakeLists.txt b/libc/fuzzing/stdlib/CMakeLists.txt
index db827f57075f2..436125b6cd7ad 100644
--- a/libc/fuzzing/stdlib/CMakeLists.txt
+++ b/libc/fuzzing/stdlib/CMakeLists.txt
@@ -6,3 +6,13 @@ add_libc_fuzzer(
libc.src.stdlib.qsort
)
+add_libc_fuzzer(
+ atof_fuzz
+ SRCS
+ atof_fuzz.cpp
+ HDRS
+ StringParserOutputDiff.h
+ DEPENDS
+ libc.src.stdlib.atof
+)
+
diff --git a/libc/fuzzing/stdlib/StringParserOutputDiff.h b/libc/fuzzing/stdlib/StringParserOutputDiff.h
new file mode 100644
index 0000000000000..457da3b5674ba
--- /dev/null
+++ b/libc/fuzzing/stdlib/StringParserOutputDiff.h
@@ -0,0 +1,35 @@
+//===-- Template to
diff single-input-single-output functions ---*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_FUZZING_STDLIB_STRING_PARSER_OUTPUT_DIFF_H
+#define LLVM_LIBC_FUZZING_STDLIB_STRING_PARSER_OUTPUT_DIFF_H
+
+#include "fuzzing/math/Compare.h"
+
+#include <stddef.h>
+#include <stdint.h>
+
+template <typename T> using StringInputSingleOutputFunc = T (*)(const char *);
+
+template <typename T>
+void StringParserOutputDiff(StringInputSingleOutputFunc<T> func1,
+ StringInputSingleOutputFunc<T> func2,
+ const uint8_t *data, size_t size) {
+ if (size < sizeof(T))
+ return;
+
+ const char *x = reinterpret_cast<const char *>(data);
+
+ T result1 = func1(x);
+ T result2 = func2(x);
+
+ if (!ValuesEqual(result1, result2))
+ __builtin_trap();
+}
+
+#endif // LLVM_LIBC_FUZZING_STDLIB_STRING_PARSER_OUTPUT_DIFF_H
diff --git a/libc/fuzzing/stdlib/atof_fuzz.cpp b/libc/fuzzing/stdlib/atof_fuzz.cpp
new file mode 100644
index 0000000000000..b368129960d3b
--- /dev/null
+++ b/libc/fuzzing/stdlib/atof_fuzz.cpp
@@ -0,0 +1,32 @@
+//===-- atof_fuzz.cpp -----------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+///
+/// Fuzzing test for llvm-libc atof implementation.
+///
+//===----------------------------------------------------------------------===//
+#include "src/stdlib/atof.h"
+#include <stddef.h>
+#include <stdint.h>
+#include <stdlib.h>
+
+#include "fuzzing/stdlib/StringParserOutputDiff.h"
+
+extern "C" int LLVMFuzzerTestOneInput(const uint8_t *data, size_t size) {
+ uint8_t *container = new uint8_t[size + 1];
+ if (!container)
+ __builtin_trap();
+ size_t i;
+
+ for (i = 0; i < size; ++i)
+ container[i] = data[i];
+ container[size] = '\0'; // Add null terminator to container.
+
+ StringParserOutputDiff<double>(&__llvm_libc::atof, &::atof, container, size);
+ delete[] container;
+ return 0;
+}
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index dd5ac0a357f90..4643154fdd8c0 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -495,6 +495,7 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"labs", RetValSpec<LongType>, [ArgSpec<LongType>]>,
FunctionSpec<"llabs", RetValSpec<LongLongType>, [ArgSpec<LongLongType>]>,
+ FunctionSpec<"atof", RetValSpec<DoubleType>, [ArgSpec<ConstCharRestrictedPtr>]>,
FunctionSpec<"atoi", RetValSpec<IntType>, [ArgSpec<ConstCharPtr>]>,
FunctionSpec<"atol", RetValSpec<LongType>, [ArgSpec<ConstCharPtr>]>,
FunctionSpec<"atoll", RetValSpec<LongLongType>, [ArgSpec<ConstCharPtr>]>,
@@ -505,6 +506,8 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"qsort", RetValSpec<VoidType>, [ArgSpec<VoidPtr>, ArgSpec<SizeTType>, ArgSpec<SizeTType>, ArgSpec<QSortCompareT>]>,
+ FunctionSpec<"strtod", RetValSpec<DoubleType>, [ArgSpec<ConstCharRestrictedPtr>, ArgSpec<CharRestrictedPtrPtr>]>,
+ FunctionSpec<"strtof", RetValSpec<FloatType>, [ArgSpec<ConstCharRestrictedPtr>, ArgSpec<CharRestrictedPtrPtr>]>,
FunctionSpec<"strtol", RetValSpec<LongType>, [ArgSpec<ConstCharRestrictedPtr>, ArgSpec<CharRestrictedPtrPtr>, ArgSpec<IntType>]>,
FunctionSpec<"strtoll", RetValSpec<LongLongType>, [ArgSpec<ConstCharRestrictedPtr>, ArgSpec<CharRestrictedPtrPtr>, ArgSpec<IntType>]>,
FunctionSpec<"strtoul", RetValSpec<UnsignedLongType>, [ArgSpec<ConstCharRestrictedPtr>, ArgSpec<CharRestrictedPtrPtr>, ArgSpec<IntType>]>,
diff --git a/libc/src/__support/CMakeLists.txt b/libc/src/__support/CMakeLists.txt
index 2699b552bfa65..1d452067f93d1 100644
--- a/libc/src/__support/CMakeLists.txt
+++ b/libc/src/__support/CMakeLists.txt
@@ -23,12 +23,14 @@ add_header_library(
str_conv_utils
HDRS
str_conv_utils.h
+ str_to_float.h
DEPENDS
.ctype_utils
.high_precision_decimal
libc.include.errno
libc.src.errno.__errno_location
libc.utils.CPP.standalone_cpp
+ libc.src.__support.FPUtil.fputil
)
add_header_library(
diff --git a/libc/src/__support/detailed_powers_of_ten.h b/libc/src/__support/detailed_powers_of_ten.h
new file mode 100644
index 0000000000000..e168b95b8998e
--- /dev/null
+++ b/libc/src/__support/detailed_powers_of_ten.h
@@ -0,0 +1,736 @@
+//===-- detailed powers of ten ----------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LIBC_SRC_SUPPORT_DETAILED_POWERS_OF_TEN_H
+#define LIBC_SRC_SUPPORT_DETAILED_POWERS_OF_TEN_H
+
+#include <stdint.h>
+
+namespace __llvm_libc {
+namespace internal {
+
+// TODO(michaelrj): write a script that will generate this table.
+
+// This table was generated by
+// https://github.com/google/wuffs/blob/788479dd64f35cb6b4e998a851acb06ee962435b/script/print-mpb-powers-of-10.go
+// and contains the 128 bit mantissa approximations of the powers of 10 from
+// -348 to 347. The exponents are implied by a linear expression with slope
+// 217706.0/65536.0 ≈ log(10)/log(2). This is used by the Eisel-Lemire algorithm
+// in str_conv_utils.h.
+
+constexpr int32_t DETAILED_POWERS_OF_TEN_MIN_EXP_10 = -348;
+constexpr int32_t DETAILED_POWERS_OF_TEN_MAX_EXP_10 = 347;
+
+// This rescales the base 10 exponent by a factor of log(10)/log(2).
+static inline int64_t exp10ToExp2(int64_t exp10) {
+ return (217706 * exp10) >> 16;
+}
+
+static const uint64_t DETAILED_POWERS_OF_TEN[696][2] = {
+ {0x1732C869CD60E453, 0xFA8FD5A0081C0288}, // 1e-348
+ {0x0E7FBD42205C8EB4, 0x9C99E58405118195}, // 1e-347
+ {0x521FAC92A873B261, 0xC3C05EE50655E1FA}, // 1e-346
+ {0xE6A797B752909EF9, 0xF4B0769E47EB5A78}, // 1e-345
+ {0x9028BED2939A635C, 0x98EE4A22ECF3188B}, // 1e-344
+ {0x7432EE873880FC33, 0xBF29DCABA82FDEAE}, // 1e-343
+ {0x113FAA2906A13B3F, 0xEEF453D6923BD65A}, // 1e-342
+ {0x4AC7CA59A424C507, 0x9558B4661B6565F8}, // 1e-341
+ {0x5D79BCF00D2DF649, 0xBAAEE17FA23EBF76}, // 1e-340
+ {0xF4D82C2C107973DC, 0xE95A99DF8ACE6F53}, // 1e-339
+ {0x79071B9B8A4BE869, 0x91D8A02BB6C10594}, // 1e-338
+ {0x9748E2826CDEE284, 0xB64EC836A47146F9}, // 1e-337
+ {0xFD1B1B2308169B25, 0xE3E27A444D8D98B7}, // 1e-336
+ {0xFE30F0F5E50E20F7, 0x8E6D8C6AB0787F72}, // 1e-335
+ {0xBDBD2D335E51A935, 0xB208EF855C969F4F}, // 1e-334
+ {0xAD2C788035E61382, 0xDE8B2B66B3BC4723}, // 1e-333
+ {0x4C3BCB5021AFCC31, 0x8B16FB203055AC76}, // 1e-332
+ {0xDF4ABE242A1BBF3D, 0xADDCB9E83C6B1793}, // 1e-331
+ {0xD71D6DAD34A2AF0D, 0xD953E8624B85DD78}, // 1e-330
+ {0x8672648C40E5AD68, 0x87D4713D6F33AA6B}, // 1e-329
+ {0x680EFDAF511F18C2, 0xA9C98D8CCB009506}, // 1e-328
+ {0x0212BD1B2566DEF2, 0xD43BF0EFFDC0BA48}, // 1e-327
+ {0x014BB630F7604B57, 0x84A57695FE98746D}, // 1e-326
+ {0x419EA3BD35385E2D, 0xA5CED43B7E3E9188}, // 1e-325
+ {0x52064CAC828675B9, 0xCF42894A5DCE35EA}, // 1e-324
+ {0x7343EFEBD1940993, 0x818995CE7AA0E1B2}, // 1e-323
+ {0x1014EBE6C5F90BF8, 0xA1EBFB4219491A1F}, // 1e-322
+ {0xD41A26E077774EF6, 0xCA66FA129F9B60A6}, // 1e-321
+ {0x8920B098955522B4, 0xFD00B897478238D0}, // 1e-320
+ {0x55B46E5F5D5535B0, 0x9E20735E8CB16382}, // 1e-319
+ {0xEB2189F734AA831D, 0xC5A890362FDDBC62}, // 1e-318
+ {0xA5E9EC7501D523E4, 0xF712B443BBD52B7B}, // 1e-317
+ {0x47B233C92125366E, 0x9A6BB0AA55653B2D}, // 1e-316
+ {0x999EC0BB696E840A, 0xC1069CD4EABE89F8}, // 1e-315
+ {0xC00670EA43CA250D, 0xF148440A256E2C76}, // 1e-314
+ {0x380406926A5E5728, 0x96CD2A865764DBCA}, // 1e-313
+ {0xC605083704F5ECF2, 0xBC807527ED3E12BC}, // 1e-312
+ {0xF7864A44C633682E, 0xEBA09271E88D976B}, // 1e-311
+ {0x7AB3EE6AFBE0211D, 0x93445B8731587EA3}, // 1e-310
+ {0x5960EA05BAD82964, 0xB8157268FDAE9E4C}, // 1e-309
+ {0x6FB92487298E33BD, 0xE61ACF033D1A45DF}, // 1e-308
+ {0xA5D3B6D479F8E056, 0x8FD0C16206306BAB}, // 1e-307
+ {0x8F48A4899877186C, 0xB3C4F1BA87BC8696}, // 1e-306
+ {0x331ACDABFE94DE87, 0xE0B62E2929ABA83C}, // 1e-305
+ {0x9FF0C08B7F1D0B14, 0x8C71DCD9BA0B4925}, // 1e-304
+ {0x07ECF0AE5EE44DD9, 0xAF8E5410288E1B6F}, // 1e-303
+ {0xC9E82CD9F69D6150, 0xDB71E91432B1A24A}, // 1e-302
+ {0xBE311C083A225CD2, 0x892731AC9FAF056E}, // 1e-301
+ {0x6DBD630A48AAF406, 0xAB70FE17C79AC6CA}, // 1e-300
+ {0x092CBBCCDAD5B108, 0xD64D3D9DB981787D}, // 1e-299
+ {0x25BBF56008C58EA5, 0x85F0468293F0EB4E}, // 1e-298
+ {0xAF2AF2B80AF6F24E, 0xA76C582338ED2621}, // 1e-297
+ {0x1AF5AF660DB4AEE1, 0xD1476E2C07286FAA}, // 1e-296
+ {0x50D98D9FC890ED4D, 0x82CCA4DB847945CA}, // 1e-295
+ {0xE50FF107BAB528A0, 0xA37FCE126597973C}, // 1e-294
+ {0x1E53ED49A96272C8, 0xCC5FC196FEFD7D0C}, // 1e-293
+ {0x25E8E89C13BB0F7A, 0xFF77B1FCBEBCDC4F}, // 1e-292
+ {0x77B191618C54E9AC, 0x9FAACF3DF73609B1}, // 1e-291
+ {0xD59DF5B9EF6A2417, 0xC795830D75038C1D}, // 1e-290
+ {0x4B0573286B44AD1D, 0xF97AE3D0D2446F25}, // 1e-289
+ {0x4EE367F9430AEC32, 0x9BECCE62836AC577}, // 1e-288
+ {0x229C41F793CDA73F, 0xC2E801FB244576D5}, // 1e-287
+ {0x6B43527578C1110F, 0xF3A20279ED56D48A}, // 1e-286
+ {0x830A13896B78AAA9, 0x9845418C345644D6}, // 1e-285
+ {0x23CC986BC656D553, 0xBE5691EF416BD60C}, // 1e-284
+ {0x2CBFBE86B7EC8AA8, 0xEDEC366B11C6CB8F}, // 1e-283
+ {0x7BF7D71432F3D6A9, 0x94B3A202EB1C3F39}, // 1e-282
+ {0xDAF5CCD93FB0CC53, 0xB9E08A83A5E34F07}, // 1e-281
+ {0xD1B3400F8F9CFF68, 0xE858AD248F5C22C9}, // 1e-280
+ {0x23100809B9C21FA1, 0x91376C36D99995BE}, // 1e-279
+ {0xABD40A0C2832A78A, 0xB58547448FFFFB2D}, // 1e-278
+ {0x16C90C8F323F516C, 0xE2E69915B3FFF9F9}, // 1e-277
+ {0xAE3DA7D97F6792E3, 0x8DD01FAD907FFC3B}, // 1e-276
+ {0x99CD11CFDF41779C, 0xB1442798F49FFB4A}, // 1e-275
+ {0x40405643D711D583, 0xDD95317F31C7FA1D}, // 1e-274
+ {0x482835EA666B2572, 0x8A7D3EEF7F1CFC52}, // 1e-273
+ {0xDA3243650005EECF, 0xAD1C8EAB5EE43B66}, // 1e-272
+ {0x90BED43E40076A82, 0xD863B256369D4A40}, // 1e-271
+ {0x5A7744A6E804A291, 0x873E4F75E2224E68}, // 1e-270
+ {0x711515D0A205CB36, 0xA90DE3535AAAE202}, // 1e-269
+ {0x0D5A5B44CA873E03, 0xD3515C2831559A83}, // 1e-268
+ {0xE858790AFE9486C2, 0x8412D9991ED58091}, // 1e-267
+ {0x626E974DBE39A872, 0xA5178FFF668AE0B6}, // 1e-266
+ {0xFB0A3D212DC8128F, 0xCE5D73FF402D98E3}, // 1e-265
+ {0x7CE66634BC9D0B99, 0x80FA687F881C7F8E}, // 1e-264
+ {0x1C1FFFC1EBC44E80, 0xA139029F6A239F72}, // 1e-263
+ {0xA327FFB266B56220, 0xC987434744AC874E}, // 1e-262
+ {0x4BF1FF9F0062BAA8, 0xFBE9141915D7A922}, // 1e-261
+ {0x6F773FC3603DB4A9, 0x9D71AC8FADA6C9B5}, // 1e-260
+ {0xCB550FB4384D21D3, 0xC4CE17B399107C22}, // 1e-259
+ {0x7E2A53A146606A48, 0xF6019DA07F549B2B}, // 1e-258
+ {0x2EDA7444CBFC426D, 0x99C102844F94E0FB}, // 1e-257
+ {0xFA911155FEFB5308, 0xC0314325637A1939}, // 1e-256
+ {0x793555AB7EBA27CA, 0xF03D93EEBC589F88}, // 1e-255
+ {0x4BC1558B2F3458DE, 0x96267C7535B763B5}, // 1e-254
+ {0x9EB1AAEDFB016F16, 0xBBB01B9283253CA2}, // 1e-253
+ {0x465E15A979C1CADC, 0xEA9C227723EE8BCB}, // 1e-252
+ {0x0BFACD89EC191EC9, 0x92A1958A7675175F}, // 1e-251
+ {0xCEF980EC671F667B, 0xB749FAED14125D36}, // 1e-250
+ {0x82B7E12780E7401A, 0xE51C79A85916F484}, // 1e-249
+ {0xD1B2ECB8B0908810, 0x8F31CC0937AE58D2}, // 1e-248
+ {0x861FA7E6DCB4AA15, 0xB2FE3F0B8599EF07}, // 1e-247
+ {0x67A791E093E1D49A, 0xDFBDCECE67006AC9}, // 1e-246
+ {0xE0C8BB2C5C6D24E0, 0x8BD6A141006042BD}, // 1e-245
+ {0x58FAE9F773886E18, 0xAECC49914078536D}, // 1e-244
+ {0xAF39A475506A899E, 0xDA7F5BF590966848}, // 1e-243
+ {0x6D8406C952429603, 0x888F99797A5E012D}, // 1e-242
+ {0xC8E5087BA6D33B83, 0xAAB37FD7D8F58178}, // 1e-241
+ {0xFB1E4A9A90880A64, 0xD5605FCDCF32E1D6}, // 1e-240
+ {0x5CF2EEA09A55067F, 0x855C3BE0A17FCD26}, // 1e-239
+ {0xF42FAA48C0EA481E, 0xA6B34AD8C9DFC06F}, // 1e-238
+ {0xF13B94DAF124DA26, 0xD0601D8EFC57B08B}, // 1e-237
+ {0x76C53D08D6B70858, 0x823C12795DB6CE57}, // 1e-236
+ {0x54768C4B0C64CA6E, 0xA2CB1717B52481ED}, // 1e-235
+ {0xA9942F5DCF7DFD09, 0xCB7DDCDDA26DA268}, // 1e-234
+ {0xD3F93B35435D7C4C, 0xFE5D54150B090B02}, // 1e-233
+ {0xC47BC5014A1A6DAF, 0x9EFA548D26E5A6E1}, // 1e-232
+ {0x359AB6419CA1091B, 0xC6B8E9B0709F109A}, // 1e-231
+ {0xC30163D203C94B62, 0xF867241C8CC6D4C0}, // 1e-230
+ {0x79E0DE63425DCF1D, 0x9B407691D7FC44F8}, // 1e-229
+ {0x985915FC12F542E4, 0xC21094364DFB5636}, // 1e-228
+ {0x3E6F5B7B17B2939D, 0xF294B943E17A2BC4}, // 1e-227
+ {0xA705992CEECF9C42, 0x979CF3CA6CEC5B5A}, // 1e-226
+ {0x50C6FF782A838353, 0xBD8430BD08277231}, // 1e-225
+ {0xA4F8BF5635246428, 0xECE53CEC4A314EBD}, // 1e-224
+ {0x871B7795E136BE99, 0x940F4613AE5ED136}, // 1e-223
+ {0x28E2557B59846E3F, 0xB913179899F68584}, // 1e-222
+ {0x331AEADA2FE589CF, 0xE757DD7EC07426E5}, // 1e-221
+ {0x3FF0D2C85DEF7621, 0x9096EA6F3848984F}, // 1e-220
+ {0x0FED077A756B53A9, 0xB4BCA50B065ABE63}, // 1e-219
+ {0xD3E8495912C62894, 0xE1EBCE4DC7F16DFB}, // 1e-218
+ {0x64712DD7ABBBD95C, 0x8D3360F09CF6E4BD}, // 1e-217
+ {0xBD8D794D96AACFB3, 0xB080392CC4349DEC}, // 1e-216
+ {0xECF0D7A0FC5583A0, 0xDCA04777F541C567}, // 1e-215
+ {0xF41686C49DB57244, 0x89E42CAAF9491B60}, // 1e-214
+ {0x311C2875C522CED5, 0xAC5D37D5B79B6239}, // 1e-213
+ {0x7D633293366B828B, 0xD77485CB25823AC7}, // 1e-212
+ {0xAE5DFF9C02033197, 0x86A8D39EF77164BC}, // 1e-211
+ {0xD9F57F830283FDFC, 0xA8530886B54DBDEB}, // 1e-210
+ {0xD072DF63C324FD7B, 0xD267CAA862A12D66}, // 1e-209
+ {0x4247CB9E59F71E6D, 0x8380DEA93DA4BC60}, // 1e-208
+ {0x52D9BE85F074E608, 0xA46116538D0DEB78}, // 1e-207
+ {0x67902E276C921F8B, 0xCD795BE870516656}, // 1e-206
+ {0x00BA1CD8A3DB53B6, 0x806BD9714632DFF6}, // 1e-205
+ {0x80E8A40ECCD228A4, 0xA086CFCD97BF97F3}, // 1e-204
+ {0x6122CD128006B2CD, 0xC8A883C0FDAF7DF0}, // 1e-203
+ {0x796B805720085F81, 0xFAD2A4B13D1B5D6C}, // 1e-202
+ {0xCBE3303674053BB0, 0x9CC3A6EEC6311A63}, // 1e-201
+ {0xBEDBFC4411068A9C, 0xC3F490AA77BD60FC}, // 1e-200
+ {0xEE92FB5515482D44, 0xF4F1B4D515ACB93B}, // 1e-199
+ {0x751BDD152D4D1C4A, 0x991711052D8BF3C5}, // 1e-198
+ {0xD262D45A78A0635D, 0xBF5CD54678EEF0B6}, // 1e-197
+ {0x86FB897116C87C34, 0xEF340A98172AACE4}, // 1e-196
+ {0xD45D35E6AE3D4DA0, 0x9580869F0E7AAC0E}, // 1e-195
+ {0x8974836059CCA109, 0xBAE0A846D2195712}, // 1e-194
+ {0x2BD1A438703FC94B, 0xE998D258869FACD7}, // 1e-193
+ {0x7B6306A34627DDCF, 0x91FF83775423CC06}, // 1e-192
+ {0x1A3BC84C17B1D542, 0xB67F6455292CBF08}, // 1e-191
+ {0x20CABA5F1D9E4A93, 0xE41F3D6A7377EECA}, // 1e-190
+ {0x547EB47B7282EE9C, 0x8E938662882AF53E}, // 1e-189
+ {0xE99E619A4F23AA43, 0xB23867FB2A35B28D}, // 1e-188
+ {0x6405FA00E2EC94D4, 0xDEC681F9F4C31F31}, // 1e-187
+ {0xDE83BC408DD3DD04, 0x8B3C113C38F9F37E}, // 1e-186
+ {0x9624AB50B148D445, 0xAE0B158B4738705E}, // 1e-185
+ {0x3BADD624DD9B0957, 0xD98DDAEE19068C76}, // 1e-184
+ {0xE54CA5D70A80E5D6, 0x87F8A8D4CFA417C9}, // 1e-183
+ {0x5E9FCF4CCD211F4C, 0xA9F6D30A038D1DBC}, // 1e-182
+ {0x7647C3200069671F, 0xD47487CC8470652B}, // 1e-181
+ {0x29ECD9F40041E073, 0x84C8D4DFD2C63F3B}, // 1e-180
+ {0xF468107100525890, 0xA5FB0A17C777CF09}, // 1e-179
+ {0x7182148D4066EEB4, 0xCF79CC9DB955C2CC}, // 1e-178
+ {0xC6F14CD848405530, 0x81AC1FE293D599BF}, // 1e-177
+ {0xB8ADA00E5A506A7C, 0xA21727DB38CB002F}, // 1e-176
+ {0xA6D90811F0E4851C, 0xCA9CF1D206FDC03B}, // 1e-175
+ {0x908F4A166D1DA663, 0xFD442E4688BD304A}, // 1e-174
+ {0x9A598E4E043287FE, 0x9E4A9CEC15763E2E}, // 1e-173
+ {0x40EFF1E1853F29FD, 0xC5DD44271AD3CDBA}, // 1e-172
+ {0xD12BEE59E68EF47C, 0xF7549530E188C128}, // 1e-171
+ {0x82BB74F8301958CE, 0x9A94DD3E8CF578B9}, // 1e-170
+ {0xE36A52363C1FAF01, 0xC13A148E3032D6E7}, // 1e-169
+ {0xDC44E6C3CB279AC1, 0xF18899B1BC3F8CA1}, // 1e-168
+ {0x29AB103A5EF8C0B9, 0x96F5600F15A7B7E5}, // 1e-167
+ {0x7415D448F6B6F0E7, 0xBCB2B812DB11A5DE}, // 1e-166
+ {0x111B495B3464AD21, 0xEBDF661791D60F56}, // 1e-165
+ {0xCAB10DD900BEEC34, 0x936B9FCEBB25C995}, // 1e-164
+ {0x3D5D514F40EEA742, 0xB84687C269EF3BFB}, // 1e-163
+ {0x0CB4A5A3112A5112, 0xE65829B3046B0AFA}, // 1e-162
+ {0x47F0E785EABA72AB, 0x8FF71A0FE2C2E6DC}, // 1e-161
+ {0x59ED216765690F56, 0xB3F4E093DB73A093}, // 1e-160
+ {0x306869C13EC3532C, 0xE0F218B8D25088B8}, // 1e-159
+ {0x1E414218C73A13FB, 0x8C974F7383725573}, // 1e-158
+ {0xE5D1929EF90898FA, 0xAFBD2350644EEACF}, // 1e-157
+ {0xDF45F746B74ABF39, 0xDBAC6C247D62A583}, // 1e-156
+ {0x6B8BBA8C328EB783, 0x894BC396CE5DA772}, // 1e-155
+ {0x066EA92F3F326564, 0xAB9EB47C81F5114F}, // 1e-154
+ {0xC80A537B0EFEFEBD, 0xD686619BA27255A2}, // 1e-153
+ {0xBD06742CE95F5F36, 0x8613FD0145877585}, // 1e-152
+ {0x2C48113823B73704, 0xA798FC4196E952E7}, // 1e-151
+ {0xF75A15862CA504C5, 0xD17F3B51FCA3A7A0}, // 1e-150
+ {0x9A984D73DBE722FB, 0x82EF85133DE648C4}, // 1e-149
+ {0xC13E60D0D2E0EBBA, 0xA3AB66580D5FDAF5}, // 1e-148
+ {0x318DF905079926A8, 0xCC963FEE10B7D1B3}, // 1e-147
+ {0xFDF17746497F7052, 0xFFBBCFE994E5C61F}, // 1e-146
+ {0xFEB6EA8BEDEFA633, 0x9FD561F1FD0F9BD3}, // 1e-145
+ {0xFE64A52EE96B8FC0, 0xC7CABA6E7C5382C8}, // 1e-144
+ {0x3DFDCE7AA3C673B0, 0xF9BD690A1B68637B}, // 1e-143
+ {0x06BEA10CA65C084E, 0x9C1661A651213E2D}, // 1e-142
+ {0x486E494FCFF30A62, 0xC31BFA0FE5698DB8}, // 1e-141
+ {0x5A89DBA3C3EFCCFA, 0xF3E2F893DEC3F126}, // 1e-140
+ {0xF89629465A75E01C, 0x986DDB5C6B3A76B7}, // 1e-139
+ {0xF6BBB397F1135823, 0xBE89523386091465}, // 1e-138
+ {0x746AA07DED582E2C, 0xEE2BA6C0678B597F}, // 1e-137
+ {0xA8C2A44EB4571CDC, 0x94DB483840B717EF}, // 1e-136
+ {0x92F34D62616CE413, 0xBA121A4650E4DDEB}, // 1e-135
+ {0x77B020BAF9C81D17, 0xE896A0D7E51E1566}, // 1e-134
+ {0x0ACE1474DC1D122E, 0x915E2486EF32CD60}, // 1e-133
+ {0x0D819992132456BA, 0xB5B5ADA8AAFF80B8}, // 1e-132
+ {0x10E1FFF697ED6C69, 0xE3231912D5BF60E6}, // 1e-131
+ {0xCA8D3FFA1EF463C1, 0x8DF5EFABC5979C8F}, // 1e-130
+ {0xBD308FF8A6B17CB2, 0xB1736B96B6FD83B3}, // 1e-129
+ {0xAC7CB3F6D05DDBDE, 0xDDD0467C64BCE4A0}, // 1e-128
+ {0x6BCDF07A423AA96B, 0x8AA22C0DBEF60EE4}, // 1e-127
+ {0x86C16C98D2C953C6, 0xAD4AB7112EB3929D}, // 1e-126
+ {0xE871C7BF077BA8B7, 0xD89D64D57A607744}, // 1e-125
+ {0x11471CD764AD4972, 0x87625F056C7C4A8B}, // 1e-124
+ {0xD598E40D3DD89BCF, 0xA93AF6C6C79B5D2D}, // 1e-123
+ {0x4AFF1D108D4EC2C3, 0xD389B47879823479}, // 1e-122
+ {0xCEDF722A585139BA, 0x843610CB4BF160CB}, // 1e-121
+ {0xC2974EB4EE658828, 0xA54394FE1EEDB8FE}, // 1e-120
+ {0x733D226229FEEA32, 0xCE947A3DA6A9273E}, // 1e-119
+ {0x0806357D5A3F525F, 0x811CCC668829B887}, // 1e-118
+ {0xCA07C2DCB0CF26F7, 0xA163FF802A3426A8}, // 1e-117
+ {0xFC89B393DD02F0B5, 0xC9BCFF6034C13052}, // 1e-116
+ {0xBBAC2078D443ACE2, 0xFC2C3F3841F17C67}, // 1e-115
+ {0xD54B944B84AA4C0D, 0x9D9BA7832936EDC0}, // 1e-114
+ {0x0A9E795E65D4DF11, 0xC5029163F384A931}, // 1e-113
+ {0x4D4617B5FF4A16D5, 0xF64335BCF065D37D}, // 1e-112
+ {0x504BCED1BF8E4E45, 0x99EA0196163FA42E}, // 1e-111
+ {0xE45EC2862F71E1D6, 0xC06481FB9BCF8D39}, // 1e-110
+ {0x5D767327BB4E5A4C, 0xF07DA27A82C37088}, // 1e-109
+ {0x3A6A07F8D510F86F, 0x964E858C91BA2655}, // 1e-108
+ {0x890489F70A55368B, 0xBBE226EFB628AFEA}, // 1e-107
+ {0x2B45AC74CCEA842E, 0xEADAB0ABA3B2DBE5}, // 1e-106
+ {0x3B0B8BC90012929D, 0x92C8AE6B464FC96F}, // 1e-105
+ {0x09CE6EBB40173744, 0xB77ADA0617E3BBCB}, // 1e-104
+ {0xCC420A6A101D0515, 0xE55990879DDCAABD}, // 1e-103
+ {0x9FA946824A12232D, 0x8F57FA54C2A9EAB6}, // 1e-102
+ {0x47939822DC96ABF9, 0xB32DF8E9F3546564}, // 1e-101
+ {0x59787E2B93BC56F7, 0xDFF9772470297EBD}, // 1e-100
+ {0x57EB4EDB3C55B65A, 0x8BFBEA76C619EF36}, // 1e-99
+ {0xEDE622920B6B23F1, 0xAEFAE51477A06B03}, // 1e-98
+ {0xE95FAB368E45ECED, 0xDAB99E59958885C4}, // 1e-97
+ {0x11DBCB0218EBB414, 0x88B402F7FD75539B}, // 1e-96
+ {0xD652BDC29F26A119, 0xAAE103B5FCD2A881}, // 1e-95
+ {0x4BE76D3346F0495F, 0xD59944A37C0752A2}, // 1e-94
+ {0x6F70A4400C562DDB, 0x857FCAE62D8493A5}, // 1e-93
+ {0xCB4CCD500F6BB952, 0xA6DFBD9FB8E5B88E}, // 1e-92
+ {0x7E2000A41346A7A7, 0xD097AD07A71F26B2}, // 1e-91
+ {0x8ED400668C0C28C8, 0x825ECC24C873782F}, // 1e-90
+ {0x728900802F0F32FA, 0xA2F67F2DFA90563B}, // 1e-89
+ {0x4F2B40A03AD2FFB9, 0xCBB41EF979346BCA}, // 1e-88
+ {0xE2F610C84987BFA8, 0xFEA126B7D78186BC}, // 1e-87
+ {0x0DD9CA7D2DF4D7C9, 0x9F24B832E6B0F436}, // 1e-86
+ {0x91503D1C79720DBB, 0xC6EDE63FA05D3143}, // 1e-85
+ {0x75A44C6397CE912A, 0xF8A95FCF88747D94}, // 1e-84
+ {0xC986AFBE3EE11ABA, 0x9B69DBE1B548CE7C}, // 1e-83
+ {0xFBE85BADCE996168, 0xC24452DA229B021B}, // 1e-82
+ {0xFAE27299423FB9C3, 0xF2D56790AB41C2A2}, // 1e-81
+ {0xDCCD879FC967D41A, 0x97C560BA6B0919A5}, // 1e-80
+ {0x5400E987BBC1C920, 0xBDB6B8E905CB600F}, // 1e-79
+ {0x290123E9AAB23B68, 0xED246723473E3813}, // 1e-78
+ {0xF9A0B6720AAF6521, 0x9436C0760C86E30B}, // 1e-77
+ {0xF808E40E8D5B3E69, 0xB94470938FA89BCE}, // 1e-76
+ {0xB60B1D1230B20E04, 0xE7958CB87392C2C2}, // 1e-75
+ {0xB1C6F22B5E6F48C2, 0x90BD77F3483BB9B9}, // 1e-74
+ {0x1E38AEB6360B1AF3, 0xB4ECD5F01A4AA828}, // 1e-73
+ {0x25C6DA63C38DE1B0, 0xE2280B6C20DD5232}, // 1e-72
+ {0x579C487E5A38AD0E, 0x8D590723948A535F}, // 1e-71
+ {0x2D835A9DF0C6D851, 0xB0AF48EC79ACE837}, // 1e-70
+ {0xF8E431456CF88E65, 0xDCDB1B2798182244}, // 1e-69
+ {0x1B8E9ECB641B58FF, 0x8A08F0F8BF0F156B}, // 1e-68
+ {0xE272467E3D222F3F, 0xAC8B2D36EED2DAC5}, // 1e-67
+ {0x5B0ED81DCC6ABB0F, 0xD7ADF884AA879177}, // 1e-66
+ {0x98E947129FC2B4E9, 0x86CCBB52EA94BAEA}, // 1e-65
+ {0x3F2398D747B36224, 0xA87FEA27A539E9A5}, // 1e-64
+ {0x8EEC7F0D19A03AAD, 0xD29FE4B18E88640E}, // 1e-63
+ {0x1953CF68300424AC, 0x83A3EEEEF9153E89}, // 1e-62
+ {0x5FA8C3423C052DD7, 0xA48CEAAAB75A8E2B}, // 1e-61
+ {0x3792F412CB06794D, 0xCDB02555653131B6}, // 1e-60
+ {0xE2BBD88BBEE40BD0, 0x808E17555F3EBF11}, // 1e-59
+ {0x5B6ACEAEAE9D0EC4, 0xA0B19D2AB70E6ED6}, // 1e-58
+ {0xF245825A5A445275, 0xC8DE047564D20A8B}, // 1e-57
+ {0xEED6E2F0F0D56712, 0xFB158592BE068D2E}, // 1e-56
+ {0x55464DD69685606B, 0x9CED737BB6C4183D}, // 1e-55
+ {0xAA97E14C3C26B886, 0xC428D05AA4751E4C}, // 1e-54
+ {0xD53DD99F4B3066A8, 0xF53304714D9265DF}, // 1e-53
+ {0xE546A8038EFE4029, 0x993FE2C6D07B7FAB}, // 1e-52
+ {0xDE98520472BDD033, 0xBF8FDB78849A5F96}, // 1e-51
+ {0x963E66858F6D4440, 0xEF73D256A5C0F77C}, // 1e-50
+ {0xDDE7001379A44AA8, 0x95A8637627989AAD}, // 1e-49
+ {0x5560C018580D5D52, 0xBB127C53B17EC159}, // 1e-48
+ {0xAAB8F01E6E10B4A6, 0xE9D71B689DDE71AF}, // 1e-47
+ {0xCAB3961304CA70E8, 0x9226712162AB070D}, // 1e-46
+ {0x3D607B97C5FD0D22, 0xB6B00D69BB55C8D1}, // 1e-45
+ {0x8CB89A7DB77C506A, 0xE45C10C42A2B3B05}, // 1e-44
+ {0x77F3608E92ADB242, 0x8EB98A7A9A5B04E3}, // 1e-43
+ {0x55F038B237591ED3, 0xB267ED1940F1C61C}, // 1e-42
+ {0x6B6C46DEC52F6688, 0xDF01E85F912E37A3}, // 1e-41
+ {0x2323AC4B3B3DA015, 0x8B61313BBABCE2C6}, // 1e-40
+ {0xABEC975E0A0D081A, 0xAE397D8AA96C1B77}, // 1e-39
+ {0x96E7BD358C904A21, 0xD9C7DCED53C72255}, // 1e-38
+ {0x7E50D64177DA2E54, 0x881CEA14545C7575}, // 1e-37
+ {0xDDE50BD1D5D0B9E9, 0xAA242499697392D2}, // 1e-36
+ {0x955E4EC64B44E864, 0xD4AD2DBFC3D07787}, // 1e-35
+ {0xBD5AF13BEF0B113E, 0x84EC3C97DA624AB4}, // 1e-34
+ {0xECB1AD8AEACDD58E, 0xA6274BBDD0FADD61}, // 1e-33
+ {0x67DE18EDA5814AF2, 0xCFB11EAD453994BA}, // 1e-32
+ {0x80EACF948770CED7, 0x81CEB32C4B43FCF4}, // 1e-31
+ {0xA1258379A94D028D, 0xA2425FF75E14FC31}, // 1e-30
+ {0x096EE45813A04330, 0xCAD2F7F5359A3B3E}, // 1e-29
+ {0x8BCA9D6E188853FC, 0xFD87B5F28300CA0D}, // 1e-28
+ {0x775EA264CF55347D, 0x9E74D1B791E07E48}, // 1e-27
+ {0x95364AFE032A819D, 0xC612062576589DDA}, // 1e-26
+ {0x3A83DDBD83F52204, 0xF79687AED3EEC551}, // 1e-25
+ {0xC4926A9672793542, 0x9ABE14CD44753B52}, // 1e-24
+ {0x75B7053C0F178293, 0xC16D9A0095928A27}, // 1e-23
+ {0x5324C68B12DD6338, 0xF1C90080BAF72CB1}, // 1e-22
+ {0xD3F6FC16EBCA5E03, 0x971DA05074DA7BEE}, // 1e-21
+ {0x88F4BB1CA6BCF584, 0xBCE5086492111AEA}, // 1e-20
+ {0x2B31E9E3D06C32E5, 0xEC1E4A7DB69561A5}, // 1e-19
+ {0x3AFF322E62439FCF, 0x9392EE8E921D5D07}, // 1e-18
+ {0x09BEFEB9FAD487C2, 0xB877AA3236A4B449}, // 1e-17
+ {0x4C2EBE687989A9B3, 0xE69594BEC44DE15B}, // 1e-16
+ {0x0F9D37014BF60A10, 0x901D7CF73AB0ACD9}, // 1e-15
+ {0x538484C19EF38C94, 0xB424DC35095CD80F}, // 1e-14
+ {0x2865A5F206B06FB9, 0xE12E13424BB40E13}, // 1e-13
+ {0xF93F87B7442E45D3, 0x8CBCCC096F5088CB}, // 1e-12
+ {0xF78F69A51539D748, 0xAFEBFF0BCB24AAFE}, // 1e-11
+ {0xB573440E5A884D1B, 0xDBE6FECEBDEDD5BE}, // 1e-10
+ {0x31680A88F8953030, 0x89705F4136B4A597}, // 1e-9
+ {0xFDC20D2B36BA7C3D, 0xABCC77118461CEFC}, // 1e-8
+ {0x3D32907604691B4C, 0xD6BF94D5E57A42BC}, // 1e-7
+ {0xA63F9A49C2C1B10F, 0x8637BD05AF6C69B5}, // 1e-6
+ {0x0FCF80DC33721D53, 0xA7C5AC471B478423}, // 1e-5
+ {0xD3C36113404EA4A8, 0xD1B71758E219652B}, // 1e-4
+ {0x645A1CAC083126E9, 0x83126E978D4FDF3B}, // 1e-3
+ {0x3D70A3D70A3D70A3, 0xA3D70A3D70A3D70A}, // 1e-2
+ {0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC}, // 1e-1
+ {0x0000000000000000, 0x8000000000000000}, // 1e0
+ {0x0000000000000000, 0xA000000000000000}, // 1e1
+ {0x0000000000000000, 0xC800000000000000}, // 1e2
+ {0x0000000000000000, 0xFA00000000000000}, // 1e3
+ {0x0000000000000000, 0x9C40000000000000}, // 1e4
+ {0x0000000000000000, 0xC350000000000000}, // 1e5
+ {0x0000000000000000, 0xF424000000000000}, // 1e6
+ {0x0000000000000000, 0x9896800000000000}, // 1e7
+ {0x0000000000000000, 0xBEBC200000000000}, // 1e8
+ {0x0000000000000000, 0xEE6B280000000000}, // 1e9
+ {0x0000000000000000, 0x9502F90000000000}, // 1e10
+ {0x0000000000000000, 0xBA43B74000000000}, // 1e11
+ {0x0000000000000000, 0xE8D4A51000000000}, // 1e12
+ {0x0000000000000000, 0x9184E72A00000000}, // 1e13
+ {0x0000000000000000, 0xB5E620F480000000}, // 1e14
+ {0x0000000000000000, 0xE35FA931A0000000}, // 1e15
+ {0x0000000000000000, 0x8E1BC9BF04000000}, // 1e16
+ {0x0000000000000000, 0xB1A2BC2EC5000000}, // 1e17
+ {0x0000000000000000, 0xDE0B6B3A76400000}, // 1e18
+ {0x0000000000000000, 0x8AC7230489E80000}, // 1e19
+ {0x0000000000000000, 0xAD78EBC5AC620000}, // 1e20
+ {0x0000000000000000, 0xD8D726B7177A8000}, // 1e21
+ {0x0000000000000000, 0x878678326EAC9000}, // 1e22
+ {0x0000000000000000, 0xA968163F0A57B400}, // 1e23
+ {0x0000000000000000, 0xD3C21BCECCEDA100}, // 1e24
+ {0x0000000000000000, 0x84595161401484A0}, // 1e25
+ {0x0000000000000000, 0xA56FA5B99019A5C8}, // 1e26
+ {0x0000000000000000, 0xCECB8F27F4200F3A}, // 1e27
+ {0x4000000000000000, 0x813F3978F8940984}, // 1e28
+ {0x5000000000000000, 0xA18F07D736B90BE5}, // 1e29
+ {0xA400000000000000, 0xC9F2C9CD04674EDE}, // 1e30
+ {0x4D00000000000000, 0xFC6F7C4045812296}, // 1e31
+ {0xF020000000000000, 0x9DC5ADA82B70B59D}, // 1e32
+ {0x6C28000000000000, 0xC5371912364CE305}, // 1e33
+ {0xC732000000000000, 0xF684DF56C3E01BC6}, // 1e34
+ {0x3C7F400000000000, 0x9A130B963A6C115C}, // 1e35
+ {0x4B9F100000000000, 0xC097CE7BC90715B3}, // 1e36
+ {0x1E86D40000000000, 0xF0BDC21ABB48DB20}, // 1e37
+ {0x1314448000000000, 0x96769950B50D88F4}, // 1e38
+ {0x17D955A000000000, 0xBC143FA4E250EB31}, // 1e39
+ {0x5DCFAB0800000000, 0xEB194F8E1AE525FD}, // 1e40
+ {0x5AA1CAE500000000, 0x92EFD1B8D0CF37BE}, // 1e41
+ {0xF14A3D9E40000000, 0xB7ABC627050305AD}, // 1e42
+ {0x6D9CCD05D0000000, 0xE596B7B0C643C719}, // 1e43
+ {0xE4820023A2000000, 0x8F7E32CE7BEA5C6F}, // 1e44
+ {0xDDA2802C8A800000, 0xB35DBF821AE4F38B}, // 1e45
+ {0xD50B2037AD200000, 0xE0352F62A19E306E}, // 1e46
+ {0x4526F422CC340000, 0x8C213D9DA502DE45}, // 1e47
+ {0x9670B12B7F410000, 0xAF298D050E4395D6}, // 1e48
+ {0x3C0CDD765F114000, 0xDAF3F04651D47B4C}, // 1e49
+ {0xA5880A69FB6AC800, 0x88D8762BF324CD0F}, // 1e50
+ {0x8EEA0D047A457A00, 0xAB0E93B6EFEE0053}, // 1e51
+ {0x72A4904598D6D880, 0xD5D238A4ABE98068}, // 1e52
+ {0x47A6DA2B7F864750, 0x85A36366EB71F041}, // 1e53
+ {0x999090B65F67D924, 0xA70C3C40A64E6C51}, // 1e54
+ {0xFFF4B4E3F741CF6D, 0xD0CF4B50CFE20765}, // 1e55
+ {0xBFF8F10E7A8921A4, 0x82818F1281ED449F}, // 1e56
+ {0xAFF72D52192B6A0D, 0xA321F2D7226895C7}, // 1e57
+ {0x9BF4F8A69F764490, 0xCBEA6F8CEB02BB39}, // 1e58
+ {0x02F236D04753D5B4, 0xFEE50B7025C36A08}, // 1e59
+ {0x01D762422C946590, 0x9F4F2726179A2245}, // 1e60
+ {0x424D3AD2B7B97EF5, 0xC722F0EF9D80AAD6}, // 1e61
+ {0xD2E0898765A7DEB2, 0xF8EBAD2B84E0D58B}, // 1e62
+ {0x63CC55F49F88EB2F, 0x9B934C3B330C8577}, // 1e63
+ {0x3CBF6B71C76B25FB, 0xC2781F49FFCFA6D5}, // 1e64
+ {0x8BEF464E3945EF7A, 0xF316271C7FC3908A}, // 1e65
+ {0x97758BF0E3CBB5AC, 0x97EDD871CFDA3A56}, // 1e66
+ {0x3D52EEED1CBEA317, 0xBDE94E8E43D0C8EC}, // 1e67
+ {0x4CA7AAA863EE4BDD, 0xED63A231D4C4FB27}, // 1e68
+ {0x8FE8CAA93E74EF6A, 0x945E455F24FB1CF8}, // 1e69
+ {0xB3E2FD538E122B44, 0xB975D6B6EE39E436}, // 1e70
+ {0x60DBBCA87196B616, 0xE7D34C64A9C85D44}, // 1e71
+ {0xBC8955E946FE31CD, 0x90E40FBEEA1D3A4A}, // 1e72
+ {0x6BABAB6398BDBE41, 0xB51D13AEA4A488DD}, // 1e73
+ {0xC696963C7EED2DD1, 0xE264589A4DCDAB14}, // 1e74
+ {0xFC1E1DE5CF543CA2, 0x8D7EB76070A08AEC}, // 1e75
+ {0x3B25A55F43294BCB, 0xB0DE65388CC8ADA8}, // 1e76
+ {0x49EF0EB713F39EBE, 0xDD15FE86AFFAD912}, // 1e77
+ {0x6E3569326C784337, 0x8A2DBF142DFCC7AB}, // 1e78
+ {0x49C2C37F07965404, 0xACB92ED9397BF996}, // 1e79
+ {0xDC33745EC97BE906, 0xD7E77A8F87DAF7FB}, // 1e80
+ {0x69A028BB3DED71A3, 0x86F0AC99B4E8DAFD}, // 1e81
+ {0xC40832EA0D68CE0C, 0xA8ACD7C0222311BC}, // 1e82
+ {0xF50A3FA490C30190, 0xD2D80DB02AABD62B}, // 1e83
+ {0x792667C6DA79E0FA, 0x83C7088E1AAB65DB}, // 1e84
+ {0x577001B891185938, 0xA4B8CAB1A1563F52}, // 1e85
+ {0xED4C0226B55E6F86, 0xCDE6FD5E09ABCF26}, // 1e86
+ {0x544F8158315B05B4, 0x80B05E5AC60B6178}, // 1e87
+ {0x696361AE3DB1C721, 0xA0DC75F1778E39D6}, // 1e88
+ {0x03BC3A19CD1E38E9, 0xC913936DD571C84C}, // 1e89
+ {0x04AB48A04065C723, 0xFB5878494ACE3A5F}, // 1e90
+ {0x62EB0D64283F9C76, 0x9D174B2DCEC0E47B}, // 1e91
+ {0x3BA5D0BD324F8394, 0xC45D1DF942711D9A}, // 1e92
+ {0xCA8F44EC7EE36479, 0xF5746577930D6500}, // 1e93
+ {0x7E998B13CF4E1ECB, 0x9968BF6ABBE85F20}, // 1e94
+ {0x9E3FEDD8C321A67E, 0xBFC2EF456AE276E8}, // 1e95
+ {0xC5CFE94EF3EA101E, 0xEFB3AB16C59B14A2}, // 1e96
+ {0xBBA1F1D158724A12, 0x95D04AEE3B80ECE5}, // 1e97
+ {0x2A8A6E45AE8EDC97, 0xBB445DA9CA61281F}, // 1e98
+ {0xF52D09D71A3293BD, 0xEA1575143CF97226}, // 1e99
+ {0x593C2626705F9C56, 0x924D692CA61BE758}, // 1e100
+ {0x6F8B2FB00C77836C, 0xB6E0C377CFA2E12E}, // 1e101
+ {0x0B6DFB9C0F956447, 0xE498F455C38B997A}, // 1e102
+ {0x4724BD4189BD5EAC, 0x8EDF98B59A373FEC}, // 1e103
+ {0x58EDEC91EC2CB657, 0xB2977EE300C50FE7}, // 1e104
+ {0x2F2967B66737E3ED, 0xDF3D5E9BC0F653E1}, // 1e105
+ {0xBD79E0D20082EE74, 0x8B865B215899F46C}, // 1e106
+ {0xECD8590680A3AA11, 0xAE67F1E9AEC07187}, // 1e107
+ {0xE80E6F4820CC9495, 0xDA01EE641A708DE9}, // 1e108
+ {0x3109058D147FDCDD, 0x884134FE908658B2}, // 1e109
+ {0xBD4B46F0599FD415, 0xAA51823E34A7EEDE}, // 1e110
+ {0x6C9E18AC7007C91A, 0xD4E5E2CDC1D1EA96}, // 1e111
+ {0x03E2CF6BC604DDB0, 0x850FADC09923329E}, // 1e112
+ {0x84DB8346B786151C, 0xA6539930BF6BFF45}, // 1e113
+ {0xE612641865679A63, 0xCFE87F7CEF46FF16}, // 1e114
+ {0x4FCB7E8F3F60C07E, 0x81F14FAE158C5F6E}, // 1e115
+ {0xE3BE5E330F38F09D, 0xA26DA3999AEF7749}, // 1e116
+ {0x5CADF5BFD3072CC5, 0xCB090C8001AB551C}, // 1e117
+ {0x73D9732FC7C8F7F6, 0xFDCB4FA002162A63}, // 1e118
+ {0x2867E7FDDCDD9AFA, 0x9E9F11C4014DDA7E}, // 1e119
+ {0xB281E1FD541501B8, 0xC646D63501A1511D}, // 1e120
+ {0x1F225A7CA91A4226, 0xF7D88BC24209A565}, // 1e121
+ {0x3375788DE9B06958, 0x9AE757596946075F}, // 1e122
+ {0x0052D6B1641C83AE, 0xC1A12D2FC3978937}, // 1e123
+ {0xC0678C5DBD23A49A, 0xF209787BB47D6B84}, // 1e124
+ {0xF840B7BA963646E0, 0x9745EB4D50CE6332}, // 1e125
+ {0xB650E5A93BC3D898, 0xBD176620A501FBFF}, // 1e126
+ {0xA3E51F138AB4CEBE, 0xEC5D3FA8CE427AFF}, // 1e127
+ {0xC66F336C36B10137, 0x93BA47C980E98CDF}, // 1e128
+ {0xB80B0047445D4184, 0xB8A8D9BBE123F017}, // 1e129
+ {0xA60DC059157491E5, 0xE6D3102AD96CEC1D}, // 1e130
+ {0x87C89837AD68DB2F, 0x9043EA1AC7E41392}, // 1e131
+ {0x29BABE4598C311FB, 0xB454E4A179DD1877}, // 1e132
+ {0xF4296DD6FEF3D67A, 0xE16A1DC9D8545E94}, // 1e133
+ {0x1899E4A65F58660C, 0x8CE2529E2734BB1D}, // 1e134
+ {0x5EC05DCFF72E7F8F, 0xB01AE745B101E9E4}, // 1e135
+ {0x76707543F4FA1F73, 0xDC21A1171D42645D}, // 1e136
+ {0x6A06494A791C53A8, 0x899504AE72497EBA}, // 1e137
+ {0x0487DB9D17636892, 0xABFA45DA0EDBDE69}, // 1e138
+ {0x45A9D2845D3C42B6, 0xD6F8D7509292D603}, // 1e139
+ {0x0B8A2392BA45A9B2, 0x865B86925B9BC5C2}, // 1e140
+ {0x8E6CAC7768D7141E, 0xA7F26836F282B732}, // 1e141
+ {0x3207D795430CD926, 0xD1EF0244AF2364FF}, // 1e142
+ {0x7F44E6BD49E807B8, 0x8335616AED761F1F}, // 1e143
+ {0x5F16206C9C6209A6, 0xA402B9C5A8D3A6E7}, // 1e144
+ {0x36DBA887C37A8C0F, 0xCD036837130890A1}, // 1e145
+ {0xC2494954DA2C9789, 0x802221226BE55A64}, // 1e146
+ {0xF2DB9BAA10B7BD6C, 0xA02AA96B06DEB0FD}, // 1e147
+ {0x6F92829494E5ACC7, 0xC83553C5C8965D3D}, // 1e148
+ {0xCB772339BA1F17F9, 0xFA42A8B73ABBF48C}, // 1e149
+ {0xFF2A760414536EFB, 0x9C69A97284B578D7}, // 1e150
+ {0xFEF5138519684ABA, 0xC38413CF25E2D70D}, // 1e151
+ {0x7EB258665FC25D69, 0xF46518C2EF5B8CD1}, // 1e152
+ {0xEF2F773FFBD97A61, 0x98BF2F79D5993802}, // 1e153
+ {0xAAFB550FFACFD8FA, 0xBEEEFB584AFF8603}, // 1e154
+ {0x95BA2A53F983CF38, 0xEEAABA2E5DBF6784}, // 1e155
+ {0xDD945A747BF26183, 0x952AB45CFA97A0B2}, // 1e156
+ {0x94F971119AEEF9E4, 0xBA756174393D88DF}, // 1e157
+ {0x7A37CD5601AAB85D, 0xE912B9D1478CEB17}, // 1e158
+ {0xAC62E055C10AB33A, 0x91ABB422CCB812EE}, // 1e159
+ {0x577B986B314D6009, 0xB616A12B7FE617AA}, // 1e160
+ {0xED5A7E85FDA0B80B, 0xE39C49765FDF9D94}, // 1e161
+ {0x14588F13BE847307, 0x8E41ADE9FBEBC27D}, // 1e162
+ {0x596EB2D8AE258FC8, 0xB1D219647AE6B31C}, // 1e163
+ {0x6FCA5F8ED9AEF3BB, 0xDE469FBD99A05FE3}, // 1e164
+ {0x25DE7BB9480D5854, 0x8AEC23D680043BEE}, // 1e165
+ {0xAF561AA79A10AE6A, 0xADA72CCC20054AE9}, // 1e166
+ {0x1B2BA1518094DA04, 0xD910F7FF28069DA4}, // 1e167
+ {0x90FB44D2F05D0842, 0x87AA9AFF79042286}, // 1e168
+ {0x353A1607AC744A53, 0xA99541BF57452B28}, // 1e169
+ {0x42889B8997915CE8, 0xD3FA922F2D1675F2}, // 1e170
+ {0x69956135FEBADA11, 0x847C9B5D7C2E09B7}, // 1e171
+ {0x43FAB9837E699095, 0xA59BC234DB398C25}, // 1e172
+ {0x94F967E45E03F4BB, 0xCF02B2C21207EF2E}, // 1e173
+ {0x1D1BE0EEBAC278F5, 0x8161AFB94B44F57D}, // 1e174
+ {0x6462D92A69731732, 0xA1BA1BA79E1632DC}, // 1e175
+ {0x7D7B8F7503CFDCFE, 0xCA28A291859BBF93}, // 1e176
+ {0x5CDA735244C3D43E, 0xFCB2CB35E702AF78}, // 1e177
+ {0x3A0888136AFA64A7, 0x9DEFBF01B061ADAB}, // 1e178
+ {0x088AAA1845B8FDD0, 0xC56BAEC21C7A1916}, // 1e179
+ {0x8AAD549E57273D45, 0xF6C69A72A3989F5B}, // 1e180
+ {0x36AC54E2F678864B, 0x9A3C2087A63F6399}, // 1e181
+ {0x84576A1BB416A7DD, 0xC0CB28A98FCF3C7F}, // 1e182
+ {0x656D44A2A11C51D5, 0xF0FDF2D3F3C30B9F}, // 1e183
+ {0x9F644AE5A4B1B325, 0x969EB7C47859E743}, // 1e184
+ {0x873D5D9F0DDE1FEE, 0xBC4665B596706114}, // 1e185
+ {0xA90CB506D155A7EA, 0xEB57FF22FC0C7959}, // 1e186
+ {0x09A7F12442D588F2, 0x9316FF75DD87CBD8}, // 1e187
+ {0x0C11ED6D538AEB2F, 0xB7DCBF5354E9BECE}, // 1e188
+ {0x8F1668C8A86DA5FA, 0xE5D3EF282A242E81}, // 1e189
+ {0xF96E017D694487BC, 0x8FA475791A569D10}, // 1e190
+ {0x37C981DCC395A9AC, 0xB38D92D760EC4455}, // 1e191
+ {0x85BBE253F47B1417, 0xE070F78D3927556A}, // 1e192
+ {0x93956D7478CCEC8E, 0x8C469AB843B89562}, // 1e193
+ {0x387AC8D1970027B2, 0xAF58416654A6BABB}, // 1e194
+ {0x06997B05FCC0319E, 0xDB2E51BFE9D0696A}, // 1e195
+ {0x441FECE3BDF81F03, 0x88FCF317F22241E2}, // 1e196
+ {0xD527E81CAD7626C3, 0xAB3C2FDDEEAAD25A}, // 1e197
+ {0x8A71E223D8D3B074, 0xD60B3BD56A5586F1}, // 1e198
+ {0xF6872D5667844E49, 0x85C7056562757456}, // 1e199
+ {0xB428F8AC016561DB, 0xA738C6BEBB12D16C}, // 1e200
+ {0xE13336D701BEBA52, 0xD106F86E69D785C7}, // 1e201
+ {0xECC0024661173473, 0x82A45B450226B39C}, // 1e202
+ {0x27F002D7F95D0190, 0xA34D721642B06084}, // 1e203
+ {0x31EC038DF7B441F4, 0xCC20CE9BD35C78A5}, // 1e204
+ {0x7E67047175A15271, 0xFF290242C83396CE}, // 1e205
+ {0x0F0062C6E984D386, 0x9F79A169BD203E41}, // 1e206
+ {0x52C07B78A3E60868, 0xC75809C42C684DD1}, // 1e207
+ {0xA7709A56CCDF8A82, 0xF92E0C3537826145}, // 1e208
+ {0x88A66076400BB691, 0x9BBCC7A142B17CCB}, // 1e209
+ {0x6ACFF893D00EA435, 0xC2ABF989935DDBFE}, // 1e210
+ {0x0583F6B8C4124D43, 0xF356F7EBF83552FE}, // 1e211
+ {0xC3727A337A8B704A, 0x98165AF37B2153DE}, // 1e212
+ {0x744F18C0592E4C5C, 0xBE1BF1B059E9A8D6}, // 1e213
+ {0x1162DEF06F79DF73, 0xEDA2EE1C7064130C}, // 1e214
+ {0x8ADDCB5645AC2BA8, 0x9485D4D1C63E8BE7}, // 1e215
+ {0x6D953E2BD7173692, 0xB9A74A0637CE2EE1}, // 1e216
+ {0xC8FA8DB6CCDD0437, 0xE8111C87C5C1BA99}, // 1e217
+ {0x1D9C9892400A22A2, 0x910AB1D4DB9914A0}, // 1e218
+ {0x2503BEB6D00CAB4B, 0xB54D5E4A127F59C8}, // 1e219
+ {0x2E44AE64840FD61D, 0xE2A0B5DC971F303A}, // 1e220
+ {0x5CEAECFED289E5D2, 0x8DA471A9DE737E24}, // 1e221
+ {0x7425A83E872C5F47, 0xB10D8E1456105DAD}, // 1e222
+ {0xD12F124E28F77719, 0xDD50F1996B947518}, // 1e223
+ {0x82BD6B70D99AAA6F, 0x8A5296FFE33CC92F}, // 1e224
+ {0x636CC64D1001550B, 0xACE73CBFDC0BFB7B}, // 1e225
+ {0x3C47F7E05401AA4E, 0xD8210BEFD30EFA5A}, // 1e226
+ {0x65ACFAEC34810A71, 0x8714A775E3E95C78}, // 1e227
+ {0x7F1839A741A14D0D, 0xA8D9D1535CE3B396}, // 1e228
+ {0x1EDE48111209A050, 0xD31045A8341CA07C}, // 1e229
+ {0x934AED0AAB460432, 0x83EA2B892091E44D}, // 1e230
+ {0xF81DA84D5617853F, 0xA4E4B66B68B65D60}, // 1e231
+ {0x36251260AB9D668E, 0xCE1DE40642E3F4B9}, // 1e232
+ {0xC1D72B7C6B426019, 0x80D2AE83E9CE78F3}, // 1e233
+ {0xB24CF65B8612F81F, 0xA1075A24E4421730}, // 1e234
+ {0xDEE033F26797B627, 0xC94930AE1D529CFC}, // 1e235
+ {0x169840EF017DA3B1, 0xFB9B7CD9A4A7443C}, // 1e236
+ {0x8E1F289560EE864E, 0x9D412E0806E88AA5}, // 1e237
+ {0xF1A6F2BAB92A27E2, 0xC491798A08A2AD4E}, // 1e238
+ {0xAE10AF696774B1DB, 0xF5B5D7EC8ACB58A2}, // 1e239
+ {0xACCA6DA1E0A8EF29, 0x9991A6F3D6BF1765}, // 1e240
+ {0x17FD090A58D32AF3, 0xBFF610B0CC6EDD3F}, // 1e241
+ {0xDDFC4B4CEF07F5B0, 0xEFF394DCFF8A948E}, // 1e242
+ {0x4ABDAF101564F98E, 0x95F83D0A1FB69CD9}, // 1e243
+ {0x9D6D1AD41ABE37F1, 0xBB764C4CA7A4440F}, // 1e244
+ {0x84C86189216DC5ED, 0xEA53DF5FD18D5513}, // 1e245
+ {0x32FD3CF5B4E49BB4, 0x92746B9BE2F8552C}, // 1e246
+ {0x3FBC8C33221DC2A1, 0xB7118682DBB66A77}, // 1e247
+ {0x0FABAF3FEAA5334A, 0xE4D5E82392A40515}, // 1e248
+ {0x29CB4D87F2A7400E, 0x8F05B1163BA6832D}, // 1e249
+ {0x743E20E9EF511012, 0xB2C71D5BCA9023F8}, // 1e250
+ {0x914DA9246B255416, 0xDF78E4B2BD342CF6}, // 1e251
+ {0x1AD089B6C2F7548E, 0x8BAB8EEFB6409C1A}, // 1e252
+ {0xA184AC2473B529B1, 0xAE9672ABA3D0C320}, // 1e253
+ {0xC9E5D72D90A2741E, 0xDA3C0F568CC4F3E8}, // 1e254
+ {0x7E2FA67C7A658892, 0x8865899617FB1871}, // 1e255
+ {0xDDBB901B98FEEAB7, 0xAA7EEBFB9DF9DE8D}, // 1e256
+ {0x552A74227F3EA565, 0xD51EA6FA85785631}, // 1e257
+ {0xD53A88958F87275F, 0x8533285C936B35DE}, // 1e258
+ {0x8A892ABAF368F137, 0xA67FF273B8460356}, // 1e259
+ {0x2D2B7569B0432D85, 0xD01FEF10A657842C}, // 1e260
+ {0x9C3B29620E29FC73, 0x8213F56A67F6B29B}, // 1e261
+ {0x8349F3BA91B47B8F, 0xA298F2C501F45F42}, // 1e262
+ {0x241C70A936219A73, 0xCB3F2F7642717713}, // 1e263
+ {0xED238CD383AA0110, 0xFE0EFB53D30DD4D7}, // 1e264
+ {0xF4363804324A40AA, 0x9EC95D1463E8A506}, // 1e265
+ {0xB143C6053EDCD0D5, 0xC67BB4597CE2CE48}, // 1e266
+ {0xDD94B7868E94050A, 0xF81AA16FDC1B81DA}, // 1e267
+ {0xCA7CF2B4191C8326, 0x9B10A4E5E9913128}, // 1e268
+ {0xFD1C2F611F63A3F0, 0xC1D4CE1F63F57D72}, // 1e269
+ {0xBC633B39673C8CEC, 0xF24A01A73CF2DCCF}, // 1e270
+ {0xD5BE0503E085D813, 0x976E41088617CA01}, // 1e271
+ {0x4B2D8644D8A74E18, 0xBD49D14AA79DBC82}, // 1e272
+ {0xDDF8E7D60ED1219E, 0xEC9C459D51852BA2}, // 1e273
+ {0xCABB90E5C942B503, 0x93E1AB8252F33B45}, // 1e274
+ {0x3D6A751F3B936243, 0xB8DA1662E7B00A17}, // 1e275
+ {0x0CC512670A783AD4, 0xE7109BFBA19C0C9D}, // 1e276
+ {0x27FB2B80668B24C5, 0x906A617D450187E2}, // 1e277
+ {0xB1F9F660802DEDF6, 0xB484F9DC9641E9DA}, // 1e278
+ {0x5E7873F8A0396973, 0xE1A63853BBD26451}, // 1e279
+ {0xDB0B487B6423E1E8, 0x8D07E33455637EB2}, // 1e280
+ {0x91CE1A9A3D2CDA62, 0xB049DC016ABC5E5F}, // 1e281
+ {0x7641A140CC7810FB, 0xDC5C5301C56B75F7}, // 1e282
+ {0xA9E904C87FCB0A9D, 0x89B9B3E11B6329BA}, // 1e283
+ {0x546345FA9FBDCD44, 0xAC2820D9623BF429}, // 1e284
+ {0xA97C177947AD4095, 0xD732290FBACAF133}, // 1e285
+ {0x49ED8EABCCCC485D, 0x867F59A9D4BED6C0}, // 1e286
+ {0x5C68F256BFFF5A74, 0xA81F301449EE8C70}, // 1e287
+ {0x73832EEC6FFF3111, 0xD226FC195C6A2F8C}, // 1e288
+ {0xC831FD53C5FF7EAB, 0x83585D8FD9C25DB7}, // 1e289
+ {0xBA3E7CA8B77F5E55, 0xA42E74F3D032F525}, // 1e290
+ {0x28CE1BD2E55F35EB, 0xCD3A1230C43FB26F}, // 1e291
+ {0x7980D163CF5B81B3, 0x80444B5E7AA7CF85}, // 1e292
+ {0xD7E105BCC332621F, 0xA0555E361951C366}, // 1e293
+ {0x8DD9472BF3FEFAA7, 0xC86AB5C39FA63440}, // 1e294
+ {0xB14F98F6F0FEB951, 0xFA856334878FC150}, // 1e295
+ {0x6ED1BF9A569F33D3, 0x9C935E00D4B9D8D2}, // 1e296
+ {0x0A862F80EC4700C8, 0xC3B8358109E84F07}, // 1e297
+ {0xCD27BB612758C0FA, 0xF4A642E14C6262C8}, // 1e298
+ {0x8038D51CB897789C, 0x98E7E9CCCFBD7DBD}, // 1e299
+ {0xE0470A63E6BD56C3, 0xBF21E44003ACDD2C}, // 1e300
+ {0x1858CCFCE06CAC74, 0xEEEA5D5004981478}, // 1e301
+ {0x0F37801E0C43EBC8, 0x95527A5202DF0CCB}, // 1e302
+ {0xD30560258F54E6BA, 0xBAA718E68396CFFD}, // 1e303
+ {0x47C6B82EF32A2069, 0xE950DF20247C83FD}, // 1e304
+ {0x4CDC331D57FA5441, 0x91D28B7416CDD27E}, // 1e305
+ {0xE0133FE4ADF8E952, 0xB6472E511C81471D}, // 1e306
+ {0x58180FDDD97723A6, 0xE3D8F9E563A198E5}, // 1e307
+ {0x570F09EAA7EA7648, 0x8E679C2F5E44FF8F}, // 1e308
+ {0x2CD2CC6551E513DA, 0xB201833B35D63F73}, // 1e309
+ {0xF8077F7EA65E58D1, 0xDE81E40A034BCF4F}, // 1e310
+ {0xFB04AFAF27FAF782, 0x8B112E86420F6191}, // 1e311
+ {0x79C5DB9AF1F9B563, 0xADD57A27D29339F6}, // 1e312
+ {0x18375281AE7822BC, 0xD94AD8B1C7380874}, // 1e313
+ {0x8F2293910D0B15B5, 0x87CEC76F1C830548}, // 1e314
+ {0xB2EB3875504DDB22, 0xA9C2794AE3A3C69A}, // 1e315
+ {0x5FA60692A46151EB, 0xD433179D9C8CB841}, // 1e316
+ {0xDBC7C41BA6BCD333, 0x849FEEC281D7F328}, // 1e317
+ {0x12B9B522906C0800, 0xA5C7EA73224DEFF3}, // 1e318
+ {0xD768226B34870A00, 0xCF39E50FEAE16BEF}, // 1e319
+ {0xE6A1158300D46640, 0x81842F29F2CCE375}, // 1e320
+ {0x60495AE3C1097FD0, 0xA1E53AF46F801C53}, // 1e321
+ {0x385BB19CB14BDFC4, 0xCA5E89B18B602368}, // 1e322
+ {0x46729E03DD9ED7B5, 0xFCF62C1DEE382C42}, // 1e323
+ {0x6C07A2C26A8346D1, 0x9E19DB92B4E31BA9}, // 1e324
+ {0xC7098B7305241885, 0xC5A05277621BE293}, // 1e325
+ {0xB8CBEE4FC66D1EA7, 0xF70867153AA2DB38}, // 1e326
+ {0x737F74F1DC043328, 0x9A65406D44A5C903}, // 1e327
+ {0x505F522E53053FF2, 0xC0FE908895CF3B44}, // 1e328
+ {0x647726B9E7C68FEF, 0xF13E34AABB430A15}, // 1e329
+ {0x5ECA783430DC19F5, 0x96C6E0EAB509E64D}, // 1e330
+ {0xB67D16413D132072, 0xBC789925624C5FE0}, // 1e331
+ {0xE41C5BD18C57E88F, 0xEB96BF6EBADF77D8}, // 1e332
+ {0x8E91B962F7B6F159, 0x933E37A534CBAAE7}, // 1e333
+ {0x723627BBB5A4ADB0, 0xB80DC58E81FE95A1}, // 1e334
+ {0xCEC3B1AAA30DD91C, 0xE61136F2227E3B09}, // 1e335
+ {0x213A4F0AA5E8A7B1, 0x8FCAC257558EE4E6}, // 1e336
+ {0xA988E2CD4F62D19D, 0xB3BD72ED2AF29E1F}, // 1e337
+ {0x93EB1B80A33B8605, 0xE0ACCFA875AF45A7}, // 1e338
+ {0xBC72F130660533C3, 0x8C6C01C9498D8B88}, // 1e339
+ {0xEB8FAD7C7F8680B4, 0xAF87023B9BF0EE6A}, // 1e340
+ {0xA67398DB9F6820E1, 0xDB68C2CA82ED2A05}, // 1e341
+ {0x88083F8943A1148C, 0x892179BE91D43A43}, // 1e342
+ {0x6A0A4F6B948959B0, 0xAB69D82E364948D4}, // 1e343
+ {0x848CE34679ABB01C, 0xD6444E39C3DB9B09}, // 1e344
+ {0xF2D80E0C0C0B4E11, 0x85EAB0E41A6940E5}, // 1e345
+ {0x6F8E118F0F0E2195, 0xA7655D1D2103911F}, // 1e346
+ {0x4B7195F2D2D1A9FB, 0xD13EB46469447567}, // 1e347
+};
+
+} // namespace internal
+} // namespace __llvm_libc
+
+#endif // LIBC_SRC_SUPPORT_DETAILED_POWERS_OF_TEN_H
diff --git a/libc/src/__support/high_precision_decimal.h b/libc/src/__support/high_precision_decimal.h
index d61ba8075037c..b7fe1296e86b0 100644
--- a/libc/src/__support/high_precision_decimal.h
+++ b/libc/src/__support/high_precision_decimal.h
@@ -291,6 +291,7 @@ class HighPrecsisionDecimal {
sawDigit = true;
if (*numString == '0' && this->numDigits == 0) {
--this->decimalPoint;
+ ++numString;
continue;
}
if (this->numDigits < MAX_NUM_DIGITS) {
@@ -311,6 +312,11 @@ class HighPrecsisionDecimal {
++numString;
if (isdigit(*numString) || *numString == '+' || *numString == '-') {
int32_t addToExp = strtointeger<int32_t>(numString, nullptr, 10);
+ if (addToExp > 100000) {
+ addToExp = 100000;
+ } else if (addToExp < -100000) {
+ addToExp = -100000;
+ }
this->decimalPoint += addToExp;
}
}
diff --git a/libc/src/__support/str_to_float.h b/libc/src/__support/str_to_float.h
new file mode 100644
index 0000000000000..67ebf3e769fef
--- /dev/null
+++ b/libc/src/__support/str_to_float.h
@@ -0,0 +1,593 @@
+//===-- String to float conversion utils ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LIBC_SRC_SUPPORT_STR_TO_FLOAT_H
+#define LIBC_SRC_SUPPORT_STR_TO_FLOAT_H
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/ctype_utils.h"
+#include "src/__support/detailed_powers_of_ten.h"
+#include "src/__support/high_precision_decimal.h"
+#include "src/__support/str_conv_utils.h"
+#include "utils/CPP/Limits.h"
+#include <errno.h>
+
+namespace __llvm_libc {
+namespace internal {
+
+// Shifts right and rounds according to the following rules:
+// 1) If the part being cut off is more than 2^(amountToShift - 1) then round
+// up
+// 2) If it is less than that number then round down
+// 3) If it is exactly that number, then round so that the final number will be
+// even
+template <class T>
+static inline T shiftRightAndRound(T numToShift, unsigned int amountToShift) {
+ T result = numToShift >> amountToShift;
+ T truncated = numToShift & ((1 << amountToShift) - 1);
+
+ if (truncated < (1 << (amountToShift - 1))) {
+ return result;
+ } else if (truncated > (1 << (amountToShift - 1))) {
+ return result + 1;
+ } else {
+ return result + (result & 1); // This rounds towards even.
+ }
+}
+
+template <class T> uint32_t leadingZeroes(T inputNumber) {
+ // TODO(michaelrj): investigate the portability of using something like
+ // __builtin_clz for specific types.
+ constexpr uint32_t bitsInT = sizeof(T) * 8;
+ if (inputNumber == 0) {
+ return bitsInT;
+ }
+ uint32_t curGuess = bitsInT / 2;
+ uint32_t rangeSize = bitsInT / 2;
+ // while either shifting by curGuess does not get rid of all of the bits or
+ // shifting by one less also gets rid of all of the bits then we have not
+ // found the first bit.
+ while (((inputNumber >> curGuess) > 0) ||
+ ((inputNumber >> (curGuess - 1)) == 0)) {
+ // Binary search for the first set bit
+ rangeSize /= 2;
+ if (rangeSize == 0) {
+ break;
+ }
+ if ((inputNumber >> curGuess) > 0) {
+ curGuess += rangeSize;
+ } else {
+ curGuess -= rangeSize;
+ }
+ }
+ if (inputNumber >> curGuess > 0) {
+ curGuess++;
+ }
+ return bitsInT - curGuess;
+}
+
+static inline uint64_t low64(__uint128_t num) {
+ return static_cast<uint64_t>(num & 0xffffffffffffffff);
+}
+
+static inline uint64_t high64(__uint128_t num) {
+ return static_cast<uint64_t>(num >> 64);
+}
+
+// This Eisel-Lemire implementation is based on the algorithm described in the
+// paper Number Parsing at a Gigabyte per Second, Software: Practice and
+// Experience 51 (8), 2021 (https://arxiv.org/abs/2101.11408), as well as the
+// description by Nigel Tao
+// (https://nigeltao.github.io/blog/2020/eisel-lemire.html) and the golang
+// implementation, also by Nigel Tao
+// (https://github.com/golang/go/blob/release-branch.go1.16/src/strconv/eisel_lemire.go#L25)
+// for some optimizations as well as handling 32 bit floats.
+template <class T>
+static inline bool
+eiselLemire(typename fputil::FPBits<T>::UIntType mantissa, int32_t exp10,
+ typename fputil::FPBits<T>::UIntType *outputMantissa,
+ uint32_t *outputExp2) {
+
+ using BitsType = typename fputil::FPBits<T>::UIntType;
+ constexpr uint32_t BITS_IN_MANTISSA = sizeof(mantissa) * 8;
+
+ if (sizeof(T) > 8) { // This algorithm cannot handle anything longer than a
+ // double, so we skip straight to the fallback.
+ return false;
+ }
+
+ // Exp10 Range
+ if (exp10 < DETAILED_POWERS_OF_TEN_MIN_EXP_10 ||
+ exp10 > DETAILED_POWERS_OF_TEN_MAX_EXP_10) {
+ return false;
+ }
+
+ // Normalization
+ uint32_t clz = leadingZeroes<BitsType>(mantissa);
+ mantissa <<= clz;
+
+ uint32_t exp2 = exp10ToExp2(exp10) + BITS_IN_MANTISSA +
+ fputil::FloatProperties<T>::exponentBias - clz;
+
+ // Multiplication
+ const uint64_t *powerOfTen =
+ DETAILED_POWERS_OF_TEN[exp10 - DETAILED_POWERS_OF_TEN_MIN_EXP_10];
+
+ __uint128_t firstApprox = static_cast<__uint128_t>(mantissa) *
+ static_cast<__uint128_t>(powerOfTen[1]);
+
+ // Wider Approximation
+ __uint128_t finalApprox;
+ // The halfway constant is used to check if the bits that will be shifted away
+ // intially are all 1. For doubles this is 64 (bitstype size) - 52 (final
+ // mantissa size) - 3 (we shift away the last two bits separately for
+ // accuracy, and the most significant bit is ignored.) = 9. Similarly, it's 6
+ // for floats in this case.
+ const uint64_t halfwayConstant = sizeof(T) == 8 ? 0x1FF : 0x3F;
+ if ((high64(firstApprox) & halfwayConstant) == halfwayConstant &&
+ low64(firstApprox) + mantissa < mantissa) {
+ __uint128_t lowBits = static_cast<__uint128_t>(mantissa) *
+ static_cast<__uint128_t>(powerOfTen[0]);
+ __uint128_t secondApprox =
+ firstApprox + static_cast<__uint128_t>(high64(lowBits));
+
+ if ((high64(secondApprox) & halfwayConstant) == halfwayConstant &&
+ low64(secondApprox) + 1 == 0 && low64(lowBits) + mantissa < mantissa) {
+ return false;
+ }
+ finalApprox = secondApprox;
+ } else {
+ finalApprox = firstApprox;
+ }
+
+ // Shifting to 54 bits for doubles and 25 bits for floats
+ BitsType msb = high64(finalApprox) >> (BITS_IN_MANTISSA - 1);
+ BitsType finalMantissa =
+ high64(finalApprox) >> (msb + BITS_IN_MANTISSA -
+ (fputil::FloatProperties<T>::mantissaWidth + 3));
+ exp2 -= 1 ^ msb; // same as !msb
+
+ // Half-way ambiguity
+ if (low64(finalApprox) == 0 && (high64(finalApprox) & halfwayConstant) == 0 &&
+ (finalMantissa & 3) == 1) {
+ return false;
+ }
+
+ // From 54 to 53 bits for doubles and 25 to 24 bits for floats
+ finalMantissa += finalMantissa & 1;
+ finalMantissa >>= 1;
+ if ((finalMantissa >> (fputil::FloatProperties<T>::mantissaWidth + 1)) > 0) {
+ finalMantissa >>= 1;
+ ++exp2;
+ }
+
+ // The if block is equivalent to (but has fewer branches than):
+ // if exp2 <= 0 || exp2 >= 0x7FF { etc }
+ if (exp2 - 1 >= (1 << fputil::FloatProperties<T>::exponentWidth) - 2) {
+ return false;
+ }
+
+ *outputMantissa = finalMantissa;
+ *outputExp2 = exp2;
+ return true;
+}
+
+// The nth item in POWERS_OF_TWO represents the greatest power of two less than
+// 10^n. This tells us how much we can safely shift without overshooting.
+constexpr uint8_t POWERS_OF_TWO[19] = {
+ 0, 3, 6, 9, 13, 16, 19, 23, 26, 29, 33, 36, 39, 43, 46, 49, 53, 56, 59,
+};
+constexpr int32_t NUM_POWERS_OF_TWO =
+ sizeof(POWERS_OF_TWO) / sizeof(POWERS_OF_TWO[0]);
+
+// Takes a mantissa and base 10 exponent and converts it into its closest
+// floating point type T equivalent. This is the fallback algorithm used when
+// the Eisel-Lemire algorithm fails, it's slower but more accurate. It's based
+// on the Simple Decimal Conversion algorithm by Nigel Tao, described at this
+// link: https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html
+template <class T>
+static inline void
+simpleDecimalConversion(const char *__restrict numStart,
+ typename fputil::FPBits<T>::UIntType *outputMantissa,
+ uint32_t *outputExp2) {
+
+ int32_t exp2 = 0;
+ HighPrecsisionDecimal hpd = HighPrecsisionDecimal(numStart);
+
+ if (hpd.getNumDigits() == 0) {
+ *outputMantissa = 0;
+ *outputExp2 = 0;
+ return;
+ }
+
+ // If the exponent is too large and can't be represented in this size of
+ // float, return inf.
+ if (hpd.getDecimalPoint() > 0 &&
+ exp10ToExp2(hpd.getDecimalPoint() - 1) >
+ static_cast<int32_t>(fputil::FloatProperties<T>::exponentBias)) {
+ *outputMantissa = 0;
+ *outputExp2 = fputil::FPBits<T>::maxExponent;
+ errno = ERANGE; // NOLINT
+ return;
+ }
+ // If the exponent is too small even for a subnormal, return 0.
+ if (hpd.getDecimalPoint() < 0 &&
+ exp10ToExp2(-hpd.getDecimalPoint()) >
+ static_cast<int32_t>(fputil::FloatProperties<T>::exponentBias +
+ fputil::FloatProperties<T>::mantissaWidth)) {
+ *outputMantissa = 0;
+ *outputExp2 = 0;
+ errno = ERANGE; // NOLINT
+ return;
+ }
+
+ // Right shift until the number is smaller than 1.
+ while (hpd.getDecimalPoint() > 0) {
+ int32_t shiftAmount = 0;
+ if (hpd.getDecimalPoint() >= NUM_POWERS_OF_TWO) {
+ shiftAmount = 60;
+ } else {
+ shiftAmount = POWERS_OF_TWO[hpd.getDecimalPoint()];
+ }
+ exp2 += shiftAmount;
+ hpd.shift(-shiftAmount);
+ }
+
+ // Left shift until the number is between 1/2 and 1
+ while (hpd.getDecimalPoint() < 0 ||
+ (hpd.getDecimalPoint() == 0 && hpd.getDigits()[0] < 5)) {
+ int32_t shiftAmount = 0;
+
+ if (-hpd.getDecimalPoint() >= NUM_POWERS_OF_TWO) {
+ shiftAmount = 60;
+ } else if (hpd.getDecimalPoint() != 0) {
+ shiftAmount = POWERS_OF_TWO[-hpd.getDecimalPoint()];
+ } else { // This handles the case of the number being between .1 and .5
+ shiftAmount = 1;
+ }
+ exp2 -= shiftAmount;
+ hpd.shift(shiftAmount);
+ }
+
+ // Left shift once so that the number is between 1 and 2
+ --exp2;
+ hpd.shift(1);
+
+ // Get the biased exponent
+ exp2 += fputil::FloatProperties<T>::exponentBias;
+
+ // Handle the exponent being too large (and return inf).
+ if (exp2 >= fputil::FPBits<T>::maxExponent) {
+ *outputMantissa = 0;
+ *outputExp2 = fputil::FPBits<T>::maxExponent;
+ errno = ERANGE; // NOLINT
+ return;
+ }
+
+ // Shift left to fill the mantissa
+ hpd.shift(fputil::FloatProperties<T>::mantissaWidth);
+ typename fputil::FPBits<T>::UIntType finalMantissa =
+ hpd.roundToIntegerType<typename fputil::FPBits<T>::UIntType>();
+
+ // Handle subnormals
+ if (exp2 <= 0) {
+ // Shift right until there is a valid exponent
+ while (exp2 < 0) {
+ hpd.shift(-1);
+ ++exp2;
+ }
+ // Shift right one more time to compensate for the left shift to get it
+ // between 1 and 2.
+ hpd.shift(-1);
+ finalMantissa =
+ hpd.roundToIntegerType<typename fputil::FPBits<T>::UIntType>();
+
+ // Check if by shifting right we've caused this to round to a normal number.
+ if ((finalMantissa >> fputil::FloatProperties<T>::mantissaWidth) != 0) {
+ ++exp2;
+ }
+ }
+
+ // Check if rounding added a bit, and shift down if that's the case.
+ if (finalMantissa == typename fputil::FPBits<T>::UIntType(2)
+ << fputil::FloatProperties<T>::mantissaWidth) {
+ finalMantissa >>= 1;
+ ++exp2;
+ }
+
+ *outputMantissa = finalMantissa;
+ *outputExp2 = exp2;
+}
+
+// Takes a mantissa and base 10 exponent and converts it into its closest
+// floating point type T equivalient. First we try the Eisel-Lemire algorithm,
+// then if that fails then we fall back to a more accurate algorithm for
+// accuracy. The resulting mantissa and exponent are placed in outputMantissa
+// and outputExp2.
+template <class T>
+static inline void
+decimalExpToFloat(typename fputil::FPBits<T>::UIntType mantissa, int32_t exp10,
+ const char *__restrict numStart, bool truncated,
+ typename fputil::FPBits<T>::UIntType *outputMantissa,
+ uint32_t *outputExp2) {
+
+ // TODO: Implement Clinger's fast path, as well as other shortcuts here.
+
+ // Try Eisel-Lemire
+ if (eiselLemire<T>(mantissa, exp10, outputMantissa, outputExp2)) {
+ if (!truncated) {
+ return;
+ }
+ // If the mantissa is truncated, then the result may be off by the LSB, so
+ // check if rounding the mantissa up changes the result. If not, then it's
+ // safe, else use the fallback.
+ typename fputil::FPBits<T>::UIntType firstMantissa = *outputMantissa;
+ uint32_t firstExp2 = *outputExp2;
+ if (eiselLemire<T>(mantissa + 1, exp10, outputMantissa, outputExp2)) {
+ if (*outputMantissa == firstMantissa && *outputExp2 == firstExp2) {
+ return;
+ }
+ }
+ }
+
+ simpleDecimalConversion<T>(numStart, outputMantissa, outputExp2);
+
+ return;
+}
+
+// checks if the next 4 characters of the string pointer are the start of a
+// hexadecimal floating point number. Does not advance the string pointer.
+static inline bool is_float_hex_start(const char *__restrict src,
+ const char decimalPoint) {
+ if (!(*src == '0' && (*(src + 1) | 32) == 'x')) {
+ return false;
+ }
+ if (*(src + 2) == decimalPoint) {
+ return isalnum(*(src + 3)) && b36_char_to_int(*(src + 3)) < 16;
+ } else {
+ return isalnum(*(src + 2)) && b36_char_to_int(*(src + 2)) < 16;
+ }
+}
+
+// Takes a pointer to a string and a pointer to a string pointer. This function
+// is used as the backend for all of the string to float functions.
+template <class T>
+static inline T strtofloatingpoint(const char *__restrict src,
+ char **__restrict strEnd) {
+ using BitsType = typename fputil::FPBits<T>::UIntType;
+ fputil::FPBits<T> result = fputil::FPBits<T>();
+ const char *originalSrc = src;
+ bool seenDigit = false;
+ src = first_non_whitespace(src);
+
+ if (*src == '+' || *src == '-') {
+ if (*src == '-') {
+ result.setSign(true);
+ }
+ ++src;
+ }
+
+ static constexpr char DECIMAL_POINT = '.';
+ static const char *INF_STRING = "infinity";
+ static const char *NAN_STRING = "nan";
+
+ bool truncated = false;
+
+ if (isdigit(*src) || *src == DECIMAL_POINT) { // regular number
+ int base = 10;
+ char exponentMarker = 'e';
+ if (is_float_hex_start(src, DECIMAL_POINT)) {
+ base = 16;
+ src += 2;
+ exponentMarker = 'p';
+ seenDigit = true;
+ }
+ const char *__restrict numStart = src;
+ bool afterDecimal = false;
+
+ BitsType mantissa = 0;
+ int32_t exponent = 0;
+
+ // The goal for the first step of parsing is to convert the number in src to
+ // the format mantissa * (base ^ exponent)
+
+ constexpr BitsType MANTISSA_MAX =
+ BitsType(1) << (fputil::FloatProperties<T>::mantissaWidth +
+ 1); // The extra bit is to give space for the implicit 1
+ const BitsType BITSTYPE_MAX_DIV_BY_BASE =
+ __llvm_libc::cpp::NumericLimits<BitsType>::max() / base;
+ while ((isalnum(*src) || *src == DECIMAL_POINT) &&
+ mantissa < BITSTYPE_MAX_DIV_BY_BASE) {
+ if (*src == DECIMAL_POINT && afterDecimal) {
+ break; // this means that *src points to a second decimal point, ending
+ // the number.
+ } else if (*src == DECIMAL_POINT) {
+ afterDecimal = true;
+ ++src;
+ continue;
+ }
+ int digit = b36_char_to_int(*src);
+ if (digit >= base) {
+ break;
+ }
+
+ mantissa = (mantissa * base) + digit;
+ seenDigit = true;
+ if (afterDecimal) {
+ --exponent;
+ }
+
+ ++src;
+ }
+
+ // The second loop is to run through the remaining digits after we've filled
+ // the mantissa.
+ while (isalnum(*src) || *src == DECIMAL_POINT) {
+ if (*src == DECIMAL_POINT && afterDecimal) {
+ break; // this means that *src points to a second decimal point, ending
+ // the number.
+ } else if (*src == DECIMAL_POINT) {
+ afterDecimal = true;
+ ++src;
+ continue;
+ }
+ int digit = b36_char_to_int(*src);
+ if (digit >= base) {
+ break;
+ }
+
+ if (digit > 0) {
+ truncated = true;
+ }
+
+ if (!afterDecimal) {
+ exponent++;
+ }
+
+ ++src;
+ }
+
+ // if our base is 16 then convert the exponent to base 2
+ if (base == 16) {
+ exponent *= 4;
+ }
+
+ if ((*src | 32) == exponentMarker) {
+ if (*(src + 1) == '+' || *(src + 1) == '-' || isdigit(*(src + 1))) {
+ ++src;
+ char *tempStrEnd;
+ int32_t add_to_exponent = strtointeger<int32_t>(src, &tempStrEnd, 10);
+ src += tempStrEnd - src;
+ exponent += add_to_exponent;
+ }
+ }
+
+ if (mantissa == 0) { // if we have a 0, then also 0 the exponent.
+ exponent = 0;
+ } else if (base == 16) {
+
+ // These two loops should normalize the number if we assume the decimal
+ // point is after the bit at mantissaWidth.
+ // For example if type T is a 32 bit float, this should result in a
+ // mantissa with its most significant 1 being at bit 23.
+ while (mantissa < (MANTISSA_MAX >> 1)) {
+ mantissa = mantissa << 1;
+ --exponent;
+ }
+ BitsType mantissaCopy = mantissa;
+ unsigned int amountToShift = 0;
+ while (mantissaCopy > MANTISSA_MAX) {
+ mantissaCopy = mantissaCopy >> 1;
+ ++amountToShift;
+ }
+ exponent += amountToShift;
+ mantissa = shiftRightAndRound(mantissa, amountToShift);
+
+ // Account for the fact that the mantissa represented an integer
+ // previously, but now represents the fractional part of a normalized
+ // number.
+ exponent += fputil::FloatProperties<T>::mantissaWidth;
+
+ int32_t biasedExponent = exponent + fputil::FPBits<T>::exponentBias;
+ if (biasedExponent <= 0) {
+ // handle subnormals here
+
+ // the most mantissa is currently normalized, meaning that the msb is
+ // one bit left of where the decimal point should go.
+ amountToShift = 1;
+ mantissaCopy = mantissa >> 1;
+ while (biasedExponent < 0 && mantissaCopy > 0) {
+ mantissaCopy = mantissaCopy >> 1;
+ ++amountToShift;
+ ++biasedExponent;
+ }
+ // If we cut off any bits to fit this number into a subnormal, then it's
+ // out of range for this size of float.
+ if ((mantissa & ((1 << amountToShift) - 1)) > 0) {
+ errno = ERANGE; // NOLINT
+ }
+ mantissa = shiftRightAndRound(mantissa, amountToShift);
+ if (mantissa == 0) {
+ biasedExponent = 0;
+ }
+ } else if (biasedExponent > result.maxExponent) {
+ // This indicates an overflow, so we make the result INF and set errno.
+ biasedExponent = result.maxExponent;
+ mantissa = 0;
+ errno = ERANGE; // NOLINT
+ }
+
+ result.setUnbiasedExponent(biasedExponent);
+ result.setMantissa(mantissa);
+ } else { // base is 10
+ BitsType outputMantissa = 0;
+ uint32_t outputExponent = 0;
+ decimalExpToFloat<T>(mantissa, exponent, numStart, truncated,
+ &outputMantissa, &outputExponent);
+ result.setMantissa(outputMantissa);
+ result.setUnbiasedExponent(outputExponent);
+ }
+
+ } else if ((*src | 32) == 'n') { // NaN
+ if ((src[1] | 32) == NAN_STRING[1] && (src[2] | 32) == NAN_STRING[2]) {
+ seenDigit = true;
+ src += 3;
+ BitsType NaNMantissa = 0;
+ if (*src == '(') {
+ char *tempSrc = 0;
+ if (isdigit(*(src + 1)) || *(src + 1) == ')') {
+ NaNMantissa = strtointeger<BitsType>(src + 1, &tempSrc, 0);
+ if (*tempSrc != ')') {
+ NaNMantissa = 0;
+ } else {
+ src = tempSrc + 1;
+ }
+ }
+ }
+ NaNMantissa |= fputil::FloatProperties<T>::quietNaNMask;
+ if (result.getSign()) {
+ result = fputil::FPBits<T>(result.buildNaN(NaNMantissa));
+ result.setSign(true);
+ } else {
+ result.setSign(false);
+ result = fputil::FPBits<T>(result.buildNaN(NaNMantissa));
+ }
+ }
+ } else if ((*src | 32) == 'i') { // INF
+ if ((src[1] | 32) == INF_STRING[1] && (src[2] | 32) == INF_STRING[2]) {
+ seenDigit = true;
+ if (result.getSign())
+ result = result.negInf();
+ else
+ result = result.inf();
+ if ((src[3] | 32) == INF_STRING[3] && (src[4] | 32) == INF_STRING[4] &&
+ (src[5] | 32) == INF_STRING[5] && (src[6] | 32) == INF_STRING[6] &&
+ (src[7] | 32) == INF_STRING[7]) {
+ // if the string is "INFINITY" then strEnd needs to be set to src + 8.
+ src += 8;
+ } else {
+ src += 3;
+ }
+ }
+ }
+ if (!seenDigit) { // If there is nothing to actually parse, then return 0.
+ if (strEnd != nullptr)
+ *strEnd = const_cast<char *>(originalSrc);
+ return T(0);
+ }
+
+ if (strEnd != nullptr)
+ *strEnd = const_cast<char *>(src);
+
+ return T(result);
+}
+
+} // namespace internal
+} // namespace __llvm_libc
+
+#endif // LIBC_SRC_SUPPORT_STR_TO_FLOAT_H
diff --git a/libc/src/stdlib/CMakeLists.txt b/libc/src/stdlib/CMakeLists.txt
index 6fb35aaca19d8..ab49c2ac6be45 100644
--- a/libc/src/stdlib/CMakeLists.txt
+++ b/libc/src/stdlib/CMakeLists.txt
@@ -8,6 +8,16 @@ add_entrypoint_object(
libc.src.__support.str_conv_utils
)
+add_entrypoint_object(
+ atof
+ SRCS
+ atof.cpp
+ HDRS
+ atof.h
+ DEPENDS
+ libc.src.__support.str_conv_utils
+)
+
add_entrypoint_object(
atol
SRCS
@@ -28,6 +38,26 @@ add_entrypoint_object(
libc.src.__support.str_conv_utils
)
+add_entrypoint_object(
+ strtof
+ SRCS
+ strtof.cpp
+ HDRS
+ strtof.h
+ DEPENDS
+ libc.src.__support.str_conv_utils
+)
+
+add_entrypoint_object(
+ strtod
+ SRCS
+ strtod.cpp
+ HDRS
+ strtod.h
+ DEPENDS
+ libc.src.__support.str_conv_utils
+)
+
add_entrypoint_object(
strtol
SRCS
diff --git a/libc/src/stdlib/atof.cpp b/libc/src/stdlib/atof.cpp
new file mode 100644
index 0000000000000..5ebae79d5744d
--- /dev/null
+++ b/libc/src/stdlib/atof.cpp
@@ -0,0 +1,19 @@
+//===-- Implementation of atof --------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/stdlib/atof.h"
+#include "src/__support/common.h"
+#include "src/__support/str_to_float.h"
+
+namespace __llvm_libc {
+
+LLVM_LIBC_FUNCTION(double, atof, (const char *str)) {
+ return internal::strtofloatingpoint<double>(str, nullptr);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/src/stdlib/atof.h b/libc/src/stdlib/atof.h
new file mode 100644
index 0000000000000..ea531cc08d438
--- /dev/null
+++ b/libc/src/stdlib/atof.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for atof --------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_STDLIB_ATOF_H
+#define LLVM_LIBC_SRC_STDLIB_ATOF_H
+
+namespace __llvm_libc {
+
+double atof(const char *str);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_STDLIB_ATOI_H
diff --git a/libc/src/stdlib/strtod.cpp b/libc/src/stdlib/strtod.cpp
new file mode 100644
index 0000000000000..754918c367893
--- /dev/null
+++ b/libc/src/stdlib/strtod.cpp
@@ -0,0 +1,20 @@
+//===-- Implementation of strtod ------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/stdlib/strtod.h"
+#include "src/__support/common.h"
+#include "src/__support/str_to_float.h"
+
+namespace __llvm_libc {
+
+LLVM_LIBC_FUNCTION(double, strtod,
+ (const char *__restrict str, char **__restrict str_end)) {
+ return internal::strtofloatingpoint<double>(str, str_end);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/src/stdlib/strtod.h b/libc/src/stdlib/strtod.h
new file mode 100644
index 0000000000000..1a8b9dcc95b99
--- /dev/null
+++ b/libc/src/stdlib/strtod.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for strtod ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_STDLIB_STRTOD_H
+#define LLVM_LIBC_SRC_STDLIB_STRTOD_H
+
+namespace __llvm_libc {
+
+double strtod(const char *__restrict str, char **__restrict str_end);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_STDLIB_STRTOD_H
diff --git a/libc/src/stdlib/strtof.cpp b/libc/src/stdlib/strtof.cpp
new file mode 100644
index 0000000000000..66bfcb0b43908
--- /dev/null
+++ b/libc/src/stdlib/strtof.cpp
@@ -0,0 +1,20 @@
+//===-- Implementation of strtof ------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/stdlib/strtof.h"
+#include "src/__support/common.h"
+#include "src/__support/str_to_float.h"
+
+namespace __llvm_libc {
+
+LLVM_LIBC_FUNCTION(float, strtof,
+ (const char *__restrict str, char **__restrict str_end)) {
+ return internal::strtofloatingpoint<float>(str, str_end);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/src/stdlib/strtof.h b/libc/src/stdlib/strtof.h
new file mode 100644
index 0000000000000..3ebbd1112483b
--- /dev/null
+++ b/libc/src/stdlib/strtof.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for strtof ------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_STDLIB_STRTOF_H
+#define LLVM_LIBC_SRC_STDLIB_STRTOF_H
+
+namespace __llvm_libc {
+
+float strtof(const char *__restrict str, char **__restrict str_end);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_STDLIB_STRTOF_H
diff --git a/libc/test/src/__support/CMakeLists.txt b/libc/test/src/__support/CMakeLists.txt
index 7ae4d90424d16..85b819c23ab60 100644
--- a/libc/test/src/__support/CMakeLists.txt
+++ b/libc/test/src/__support/CMakeLists.txt
@@ -19,3 +19,32 @@ add_libc_unittest(
DEPENDS
libc.src.__support.high_precision_decimal
)
+
+add_libc_unittest(
+ str_to_float_test
+ SUITE
+ libc_support_unittests
+ SRCS
+ str_to_float_test.cpp
+ DEPENDS
+ libc.src.__support.str_conv_utils
+)
+
+add_executable(
+ libc_str_to_float_comparison_test
+ str_to_float_comparison_test.cpp
+)
+
+target_link_libraries(libc_str_to_float_comparison_test
+ PRIVATE
+ llvmlibc
+)
+
+set(float_test_file ${CMAKE_CURRENT_SOURCE_DIR}/str_to_float_comparison_data.txt)
+
+add_custom_command(TARGET libc_str_to_float_comparison_test
+ POST_BUILD
+ COMMAND $<TARGET_FILE:libc_str_to_float_comparison_test> ${float_test_file}
+ DEPENDS ${float_test_file}
+ COMMENT "Test the strtof and strtod implementations against precomputed results."
+ VERBATIM)
diff --git a/libc/test/src/__support/str_to_float_comparison_data.txt b/libc/test/src/__support/str_to_float_comparison_data.txt
new file mode 100644
index 0000000000000..b06ef252d3e5b
--- /dev/null
+++ b/libc/test/src/__support/str_to_float_comparison_data.txt
@@ -0,0 +1,7 @@
+# This is the sample data from https://github.com/nigeltao/parse-number-fxx-test-data
+3C00 3F800000 3FF0000000000000 1
+3D00 3FA00000 3FF4000000000000 1.25
+3D9A 3FB33333 3FF6666666666666 1.4
+57B7 42F6E979 405EDD2F1A9FBE77 123.456
+622A 44454000 4088A80000000000 789
+7C00 7F800000 7FF0000000000000 123.456e789
diff --git a/libc/test/src/__support/str_to_float_comparison_test.cpp b/libc/test/src/__support/str_to_float_comparison_test.cpp
new file mode 100644
index 0000000000000..5f5f71cbb1e24
--- /dev/null
+++ b/libc/test/src/__support/str_to_float_comparison_test.cpp
@@ -0,0 +1,172 @@
+//===-- strtofloatingpoint comparison test --------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// #include "src/__support/str_float_conv_utils.h"
+
+#include <stdlib.h>
+
+// #include "src/__support/FPUtil/FPBits.h"
+
+#include <fstream>
+#include <iostream>
+#include <string>
+
+// The intent of this test is to read in files in the format used in this test
+// dataset: https://github.com/nigeltao/parse-number-fxx-test-data
+// The format is as follows:
+// Hexadecimal representations of IEEE754 floats in 16 bits, 32 bits, and 64
+// bits, then the string that matches to them.
+
+// 3C00 3F800000 3FF0000000000000 1.0
+
+// By default, float_comp_in.txt is used as the test set, but once built this
+// file can be run against the larger test set. To do that, clone the repository
+// with the dataset, then navigate to the compiled binary of this file (it
+// should be in llvm_project/build/bin). Run the following command:
+// ./libc_str_to_float_comparison_test <path/to/dataset/repo>/data/*
+// It will take a few seconds to run.
+
+static inline uint32_t hexCharToU32(char in) {
+ return in > '9' ? in + 10 - 'A' : in - '0';
+}
+
+// Fast because it assumes inStr points to exactly 8 uppercase hex chars
+static inline uint32_t fastHexToU32(const char *inStr) {
+ uint32_t result = 0;
+ result = (hexCharToU32(inStr[0]) << 28) + (hexCharToU32(inStr[1]) << 24) +
+ (hexCharToU32(inStr[2]) << 20) + (hexCharToU32(inStr[3]) << 16) +
+ (hexCharToU32(inStr[4]) << 12) + (hexCharToU32(inStr[5]) << 8) +
+ (hexCharToU32(inStr[6]) << 4) + hexCharToU32(inStr[7]);
+ return result;
+}
+
+// Fast because it assumes inStr points to exactly 8 uppercase hex chars
+static inline uint64_t fastHexToU64(const char *inStr) {
+ uint64_t result = 0;
+ result = (static_cast<uint64_t>(fastHexToU32(inStr)) << 32) +
+ fastHexToU32(inStr + 8);
+ return result;
+}
+
+int checkFile(char *inputFileName, int *totalFails, int *totalBitDiffs,
+ int *detailedBitDiffs, int *total) {
+ int32_t curFails = 0; // Only counts actual failures, not bit
diff s.
+ int32_t curBitDiffs = 0; // A bit
diff is when the expected result and actual
+ // result are off by +/- 1 bit.
+ std::string line;
+ std::string num;
+
+ std::ifstream fileStream(inputFileName, std::ifstream::in);
+
+ if (!fileStream.is_open()) {
+ std::cout << "file '" << inputFileName << "' failed to open. Exiting.\n";
+ return 1;
+ }
+ while (getline(fileStream, line)) {
+ if (line[0] == '#') {
+ continue;
+ }
+ *total = *total + 1;
+ uint32_t expectedFloatRaw;
+ uint64_t expectedDoubleRaw;
+
+ expectedFloatRaw = fastHexToU32(line.c_str() + 5);
+ expectedDoubleRaw = fastHexToU64(line.c_str() + 14);
+ num = line.substr(31);
+
+ float floatResult = strtof(num.c_str(), nullptr);
+
+ double doubleResult = strtod(num.c_str(), nullptr);
+
+ uint32_t floatRaw = *(uint32_t *)(&floatResult);
+
+ uint64_t doubleRaw = *(uint64_t *)(&doubleResult);
+
+ if (!(expectedFloatRaw == floatRaw)) {
+ if (expectedFloatRaw == floatRaw + 1 ||
+ expectedFloatRaw == floatRaw - 1) {
+ curBitDiffs++;
+ if (expectedFloatRaw == floatRaw + 1) {
+ detailedBitDiffs[0] = detailedBitDiffs[0] + 1; // float low
+ } else {
+ detailedBitDiffs[1] = detailedBitDiffs[1] + 1; // float high
+ }
+ } else {
+ curFails++;
+ }
+ if (curFails + curBitDiffs < 10) {
+ std::cout << "Float fail for '" << num << "'. Expected " << std::hex
+ << expectedFloatRaw << " but got " << floatRaw << "\n"
+ << std::dec;
+ }
+ }
+
+ if (!(expectedDoubleRaw == doubleRaw)) {
+ if (expectedDoubleRaw == doubleRaw + 1 ||
+ expectedDoubleRaw == doubleRaw - 1) {
+ curBitDiffs++;
+ if (expectedDoubleRaw == doubleRaw + 1) {
+ detailedBitDiffs[2] = detailedBitDiffs[2] + 1; // double low
+ } else {
+ detailedBitDiffs[3] = detailedBitDiffs[3] + 1; // double high
+ }
+ } else {
+ curFails++;
+ }
+ if (curFails + curBitDiffs < 10) {
+ std::cout << "Double fail for '" << num << "'. Expected " << std::hex
+ << expectedDoubleRaw << " but got " << doubleRaw << "\n"
+ << std::dec;
+ }
+ }
+ }
+
+ fileStream.close();
+
+ *totalBitDiffs += curBitDiffs;
+ *totalFails += curFails;
+
+ if (curFails > 1 || curBitDiffs > 1) {
+ return 2;
+ }
+ return 0;
+}
+
+int main(int argc, char *argv[]) {
+ int result = 0;
+ int fails = 0;
+
+ // Bit
diff s are cases where the expected result and actual result only
diff er
+ // by +/- the least significant bit. They are tracked seperately from larger
+ // failures since a bit
diff is most likely the result of a rounding error, and
+ // splitting them off makes them easier to track down.
+ int bit
diff s = 0;
+ int detailedBitDiffs[4] = {0, 0, 0, 0};
+
+ int total = 0;
+ for (int i = 1; i < argc; i++) {
+ std::cout << "Starting file " << argv[i] << "\n";
+ int curResult =
+ checkFile(argv[i], &fails, &bit
diff s, detailedBitDiffs, &total);
+ if (curResult == 1) {
+ result = 1;
+ break;
+ } else if (curResult == 2) {
+ result = 2;
+ }
+ }
+ std::cout << "Results:\n"
+ << "Total significant failed conversions: " << fails << "\n"
+ << "Total conversions off by +/- 1 bit: " << bit
diff s << "\n"
+ << "\t" << detailedBitDiffs[0] << "\tfloat low\n"
+ << "\t" << detailedBitDiffs[1] << "\tfloat high\n"
+ << "\t" << detailedBitDiffs[2] << "\tdouble low\n"
+ << "\t" << detailedBitDiffs[3] << "\tdouble high\n"
+ << "Total lines: " << total << "\n";
+ return result;
+}
diff --git a/libc/test/src/__support/str_to_float_test.cpp b/libc/test/src/__support/str_to_float_test.cpp
new file mode 100644
index 0000000000000..d5cffed40a423
--- /dev/null
+++ b/libc/test/src/__support/str_to_float_test.cpp
@@ -0,0 +1,200 @@
+//===-- Unittests for str_to_float ----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/str_to_float.h"
+
+#include "utils/UnitTest/Test.h"
+
+class LlvmLibcStrToFloatTest : public __llvm_libc::testing::Test {
+public:
+ template <class T>
+ void EiselLemireTest(
+ const typename __llvm_libc::fputil::FPBits<T>::UIntType inputMantissa,
+ const int32_t inputExp10,
+ const typename __llvm_libc::fputil::FPBits<T>::UIntType
+ expectedOutputMantissa,
+ const uint32_t expectedOutputExp2) {
+ typename __llvm_libc::fputil::FPBits<T>::UIntType actualOutputMantissa = 0;
+ uint32_t actualOutputExp2 = 0;
+
+ ASSERT_TRUE(__llvm_libc::internal::eiselLemire<T>(
+ inputMantissa, inputExp10, &actualOutputMantissa, &actualOutputExp2));
+ EXPECT_EQ(actualOutputMantissa, expectedOutputMantissa);
+ EXPECT_EQ(actualOutputExp2, expectedOutputExp2);
+ }
+
+ template <class T>
+ void SimpleDecimalConversionTest(
+ const char *__restrict numStart,
+ const typename __llvm_libc::fputil::FPBits<T>::UIntType
+ expectedOutputMantissa,
+ const uint32_t expectedOutputExp2, const int expectedErrno = 0) {
+ typename __llvm_libc::fputil::FPBits<T>::UIntType actualOutputMantissa = 0;
+ uint32_t actualOutputExp2 = 0;
+ errno = 0;
+
+ __llvm_libc::internal::simpleDecimalConversion<T>(
+ numStart, &actualOutputMantissa, &actualOutputExp2);
+ EXPECT_EQ(actualOutputMantissa, expectedOutputMantissa);
+ EXPECT_EQ(actualOutputExp2, expectedOutputExp2);
+ EXPECT_EQ(errno, expectedErrno);
+ }
+};
+
+TEST(LlvmLibcStrToFloatTest, LeadingZeroes) {
+ uint64_t testNum64 = 1;
+ uint32_t numOfZeroes = 63;
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint64_t>(0), 64u);
+ for (; numOfZeroes < 64; testNum64 <<= 1, numOfZeroes--) {
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint64_t>(testNum64),
+ numOfZeroes);
+ }
+
+ testNum64 = 3;
+ numOfZeroes = 62;
+ for (; numOfZeroes > 63; testNum64 <<= 1, numOfZeroes--) {
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint64_t>(testNum64),
+ numOfZeroes);
+ }
+
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint64_t>(0xffffffffffffffff),
+ 0u);
+
+ testNum64 = 1;
+ numOfZeroes = 63;
+ for (; numOfZeroes > 63; testNum64 = (testNum64 << 1) + 1, numOfZeroes--) {
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint64_t>(testNum64),
+ numOfZeroes);
+ }
+
+ uint64_t testNum32 = 1;
+ numOfZeroes = 31;
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint32_t>(0), 32u);
+ for (; numOfZeroes < 32; testNum32 <<= 1, numOfZeroes--) {
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint32_t>(testNum32),
+ numOfZeroes);
+ }
+
+ EXPECT_EQ(__llvm_libc::internal::leadingZeroes<uint32_t>(0xffffffff), 0u);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, EiselLemireFloat64Simple) {
+ EiselLemireTest<double>(12345678901234567890u, 1, 0x1AC53A7E04BCDA, 1089);
+ EiselLemireTest<double>(123, 0, 0x1EC00000000000, 1029);
+ EiselLemireTest<double>(12345678901234568192u, 0, 0x156A95319D63E2, 1086);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, EiselLemireFloat64SpecificFailures) {
+ // These test cases have caused failures in the past.
+ EiselLemireTest<double>(358416272, -33, 0x1BBB2A68C9D0B9, 941);
+ EiselLemireTest<double>(2166568064000000238u, -9, 0x10246690000000, 1054);
+ EiselLemireTest<double>(2794967654709307187u, 1, 0x183e132bc608c8, 1087);
+ EiselLemireTest<double>(2794967654709307188u, 1, 0x183e132bc608c9, 1087);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, EiselLemireFallbackStates) {
+ // Check the fallback states for the algorithm:
+ uint32_t floatOutputMantissa = 0;
+ uint64_t doubleOutputMantissa = 0;
+ __uint128_t tooLongMantissa = 0;
+ uint32_t outputExp2 = 0;
+
+ // This Eisel-Lemire implementation doesn't support long doubles yet.
+ ASSERT_FALSE(__llvm_libc::internal::eiselLemire<long double>(
+ tooLongMantissa, 0, &tooLongMantissa, &outputExp2));
+
+ // This number can't be evaluated by Eisel-Lemire since it's exactly 1024 away
+ // from both of its closest floating point approximations
+ // (12345678901234548736 and 12345678901234550784)
+ ASSERT_FALSE(__llvm_libc::internal::eiselLemire<double>(
+ 12345678901234549760u, 0, &doubleOutputMantissa, &outputExp2));
+
+ ASSERT_FALSE(__llvm_libc::internal::eiselLemire<float>(
+ 20040229, 0, &floatOutputMantissa, &outputExp2));
+}
+
+TEST_F(LlvmLibcStrToFloatTest, SimpleDecimalConversion64BasicWholeNumbers) {
+ SimpleDecimalConversionTest<double>("123456789012345678900", 0x1AC53A7E04BCDA,
+ 1089);
+ SimpleDecimalConversionTest<double>("123", 0x1EC00000000000, 1029);
+ SimpleDecimalConversionTest<double>("12345678901234549760", 0x156A95319D63D8,
+ 1086);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, SimpleDecimalConversion64BasicDecimals) {
+ SimpleDecimalConversionTest<double>("1.2345", 0x13c083126e978d, 1023);
+ SimpleDecimalConversionTest<double>(".2345", 0x1e04189374bc6a, 1020);
+ SimpleDecimalConversionTest<double>(".299792458", 0x132fccb4aca314, 1021);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, SimpleDecimalConversion64BasicExponents) {
+ SimpleDecimalConversionTest<double>("1e10", 0x12a05f20000000, 1056);
+ SimpleDecimalConversionTest<double>("1e-10", 0x1b7cdfd9d7bdbb, 989);
+ SimpleDecimalConversionTest<double>("1e300", 0x17e43c8800759c, 2019);
+ SimpleDecimalConversionTest<double>("1e-300", 0x156e1fc2f8f359, 26);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, SimpleDecimalConversion64BasicSubnormals) {
+ SimpleDecimalConversionTest<double>("1e-320", 0x7e8, 0);
+ SimpleDecimalConversionTest<double>("1e-308", 0x730d67819e8d2, 0);
+ SimpleDecimalConversionTest<double>("2.9e-308", 0x14da6df5e4bcc8, 1);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, SimpleDecimalConversion64SubnormalRounding) {
+
+ // Technically you can keep adding digits until you hit the truncation limit,
+ // but this is the shortest string that results in the maximum subnormal that
+ // I found.
+ SimpleDecimalConversionTest<double>("2.225073858507201e-308", 0xfffffffffffff,
+ 0);
+
+ // Same here, if you were to extend the max subnormal out for another 800
+ // digits, incrementing any one of those digits would create a normal number.
+ SimpleDecimalConversionTest<double>("2.2250738585072012e-308",
+ 0x10000000000000, 1);
+}
+
+TEST_F(LlvmLibcStrToFloatTest, SimpleDecimalConversion32SpecificFailures) {
+ SimpleDecimalConversionTest<float>(
+ "1.4012984643248170709237295832899161312802619418765e-45", 0x1, 0);
+}
+
+TEST(LlvmLibcStrToFloatTest, SimpleDecimalConversionExtraTypes) {
+ uint32_t floatOutputMantissa = 0;
+ uint32_t outputExp2 = 0;
+
+ errno = 0;
+ __llvm_libc::internal::simpleDecimalConversion<float>(
+ "123456789012345678900", &floatOutputMantissa, &outputExp2);
+ EXPECT_EQ(floatOutputMantissa, uint32_t(0xd629d4));
+ EXPECT_EQ(outputExp2, uint32_t(193));
+ EXPECT_EQ(errno, 0);
+
+ uint64_t doubleOutputMantissa = 0;
+ outputExp2 = 0;
+
+ errno = 0;
+ __llvm_libc::internal::simpleDecimalConversion<double>(
+ "123456789012345678900", &doubleOutputMantissa, &outputExp2);
+ EXPECT_EQ(doubleOutputMantissa, uint64_t(0x1AC53A7E04BCDA));
+ EXPECT_EQ(outputExp2, uint32_t(1089));
+ EXPECT_EQ(errno, 0);
+
+ // TODO(michaelrj): Get long double support working.
+
+ // __uint128_t longDoubleOutputMantissa = 0;
+ // outputExp2 = 0;
+
+ // errno = 0;
+ // __llvm_libc::internal::simpleDecimalConversion<long double>(
+ // "123456789012345678900", &longDoubleOutputMantissa, &outputExp2);
+ // EXPECT_EQ(longDoubleOutputMantissa, __uint128_t(0x1AC53A7E04BCDA));
+ // EXPECT_EQ(outputExp2, uint32_t(1089));
+ // EXPECT_EQ(errno, 0);
+}
diff --git a/libc/test/src/stdlib/CMakeLists.txt b/libc/test/src/stdlib/CMakeLists.txt
index ce66488bb3405..230f245b25608 100644
--- a/libc/test/src/stdlib/CMakeLists.txt
+++ b/libc/test/src/stdlib/CMakeLists.txt
@@ -1,5 +1,15 @@
add_libc_testsuite(libc_stdlib_unittests)
+add_libc_unittest(
+ atof_test
+ SUITE
+ libc_stdlib_unittests
+ SRCS
+ atof_test.cpp
+ DEPENDS
+ libc.src.stdlib.atof
+)
+
add_libc_unittest(
atoi_test
SUITE
@@ -30,6 +40,26 @@ add_libc_unittest(
libc.src.stdlib.atoll
)
+add_libc_unittest(
+ strtod_test
+ SUITE
+ libc_stdlib_unittests
+ SRCS
+ strtod_test.cpp
+ DEPENDS
+ libc.src.stdlib.strtod
+)
+
+add_libc_unittest(
+ strtof_test
+ SUITE
+ libc_stdlib_unittests
+ SRCS
+ strtof_test.cpp
+ DEPENDS
+ libc.src.stdlib.strtof
+)
+
add_libc_unittest(
strtol_test
SUITE
diff --git a/libc/test/src/stdlib/atof_test.cpp b/libc/test/src/stdlib/atof_test.cpp
new file mode 100644
index 0000000000000..e5de03f72cd3c
--- /dev/null
+++ b/libc/test/src/stdlib/atof_test.cpp
@@ -0,0 +1,52 @@
+//===-- Unittests for atof ------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/stdlib/atof.h"
+
+#include "utils/UnitTest/Test.h"
+
+#include <errno.h>
+#include <limits.h>
+#include <stddef.h>
+
+// This is just a simple test to make sure that this function works at all. It's
+// functionally identical to strtod so the bulk of the testing is there.
+TEST(LlvmLibcAToFTest, SimpleTest) {
+ __llvm_libc::fputil::FPBits<double> expectedFP =
+ __llvm_libc::fputil::FPBits<double>(uint64_t(0x405ec00000000000));
+
+ errno = 0;
+ double result = __llvm_libc::atof("123");
+
+ __llvm_libc::fputil::FPBits<double> actualFP =
+ __llvm_libc::fputil::FPBits<double>(result);
+
+ EXPECT_EQ(actualFP.bits, expectedFP.bits);
+ EXPECT_EQ(actualFP.getSign(), expectedFP.getSign());
+ EXPECT_EQ(actualFP.getExponent(), expectedFP.getExponent());
+ EXPECT_EQ(actualFP.getMantissa(), expectedFP.getMantissa());
+ EXPECT_EQ(errno, 0);
+}
+
+TEST(LlvmLibcAToFTest, FailedParsingTest) {
+ __llvm_libc::fputil::FPBits<double> expectedFP =
+ __llvm_libc::fputil::FPBits<double>(uint64_t(0));
+
+ errno = 0;
+ double result = __llvm_libc::atof("???");
+
+ __llvm_libc::fputil::FPBits<double> actualFP =
+ __llvm_libc::fputil::FPBits<double>(result);
+
+ EXPECT_EQ(actualFP.bits, expectedFP.bits);
+ EXPECT_EQ(actualFP.getSign(), expectedFP.getSign());
+ EXPECT_EQ(actualFP.getExponent(), expectedFP.getExponent());
+ EXPECT_EQ(actualFP.getMantissa(), expectedFP.getMantissa());
+ EXPECT_EQ(errno, 0);
+}
diff --git a/libc/test/src/stdlib/strtod_test.cpp b/libc/test/src/stdlib/strtod_test.cpp
new file mode 100644
index 0000000000000..48c960d06e0cb
--- /dev/null
+++ b/libc/test/src/stdlib/strtod_test.cpp
@@ -0,0 +1,90 @@
+//===-- Unittests for strtod ---------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/stdlib/strtod.h"
+
+#include "utils/UnitTest/Test.h"
+
+#include <errno.h>
+#include <limits.h>
+#include <stddef.h>
+
+class LlvmLibcStrToDTest : public __llvm_libc::testing::Test {
+public:
+ void runTest(const char *inputString, const ptr
diff _t expectedStrLen,
+ const uint64_t expectedRawData, const int expectedErrno = 0) {
+ // expectedRawData is the expected double result as a uint64_t, organized
+ // according to IEEE754:
+ //
+ // +-- 1 Sign Bit +-- 52 Mantissa bits
+ // | |
+ // | +-------------------------+------------------------+
+ // | | |
+ // SEEEEEEEEEEEMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
+ // | |
+ // +----+----+
+ // |
+ // +-- 11 Exponent Bits
+ //
+ // This is so that the result can be compared in parts.
+ char *strEnd = nullptr;
+
+ __llvm_libc::fputil::FPBits<double> expectedFP =
+ __llvm_libc::fputil::FPBits<double>(expectedRawData);
+
+ errno = 0;
+ double result = __llvm_libc::strtod(inputString, &strEnd);
+
+ __llvm_libc::fputil::FPBits<double> actualFP =
+ __llvm_libc::fputil::FPBits<double>(result);
+
+ EXPECT_EQ(strEnd - inputString, expectedStrLen);
+
+ EXPECT_EQ(actualFP.bits, expectedFP.bits);
+ EXPECT_EQ(actualFP.getSign(), expectedFP.getSign());
+ EXPECT_EQ(actualFP.getExponent(), expectedFP.getExponent());
+ EXPECT_EQ(actualFP.getMantissa(), expectedFP.getMantissa());
+ EXPECT_EQ(errno, expectedErrno);
+ }
+};
+
+TEST_F(LlvmLibcStrToDTest, SimpleTest) {
+ runTest("123", 3, uint64_t(0x405ec00000000000));
+
+ // This should fail on Eisel-Lemire, forcing a fallback to simple decimal
+ // conversion.
+ runTest("12345678901234549760", 20, uint64_t(0x43e56a95319d63d8));
+
+ // Found while looking for
diff icult test cases here:
+ // https://github.com/nigeltao/parse-number-fxx-test-data/blob/main/more-test-cases/golang-org-issue-36657.txt
+ runTest("1090544144181609348835077142190", 31, uint64_t(0x462b8779f2474dfb));
+
+ runTest("0x123", 5, uint64_t(0x4072300000000000));
+}
+
+// These are tests that have caused problems in the past.
+TEST_F(LlvmLibcStrToDTest, SpecificFailures) {
+ runTest("3E70000000000000", 16, uint64_t(0x7FF0000000000000), ERANGE);
+ runTest("358416272e-33", 13, uint64_t(0x3adbbb2a68c9d0b9));
+ runTest("2.16656806400000023841857910156251e9", 36,
+ uint64_t(0x41e0246690000001));
+ runTest("27949676547093071875", 20, uint64_t(0x43f83e132bc608c9));
+}
+
+TEST_F(LlvmLibcStrToDTest, FuzzFailures) {
+ runTest("-\xff\xff\xff\xff\xff\xff\xff\x01", 0, uint64_t(0));
+ runTest("-.????", 0, uint64_t(0));
+ runTest("44444444444444444444444444444444444444444444444444A44444444444444444"
+ "44444444444*\x99\xff\xff\xff\xff",
+ 50, uint64_t(0x4a3e68fdd0e0b2d8));
+ runTest("-NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNKNNNNNNNNNNNNNNNNNN?"
+ "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN?",
+ 0, uint64_t(0));
+ runTest("0x.666E40", 9, uint64_t(0x3fd99b9000000000));
+}
diff --git a/libc/test/src/stdlib/strtof_test.cpp b/libc/test/src/stdlib/strtof_test.cpp
new file mode 100644
index 0000000000000..f20cc0dfff5be
--- /dev/null
+++ b/libc/test/src/stdlib/strtof_test.cpp
@@ -0,0 +1,158 @@
+//===-- Unittests for strtof ---------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/stdlib/strtof.h"
+
+#include "utils/UnitTest/Test.h"
+
+#include <errno.h>
+#include <limits.h>
+#include <stddef.h>
+
+class LlvmLibcStrToFTest : public __llvm_libc::testing::Test {
+public:
+ void runTest(const char *inputString, const ptr
diff _t expectedStrLen,
+ const uint32_t expectedRawData, const int expectedErrno = 0) {
+ // expectedRawData is the expected float result as a uint32_t, organized
+ // according to IEEE754:
+ //
+ // +-- 1 Sign Bit +-- 23 Mantissa bits
+ // | |
+ // | +----------+----------+
+ // | | |
+ // SEEEEEEEEMMMMMMMMMMMMMMMMMMMMMMM
+ // | |
+ // +--+---+
+ // |
+ // +-- 8 Exponent Bits
+ //
+ // This is so that the result can be compared in parts.
+ char *strEnd = nullptr;
+
+ __llvm_libc::fputil::FPBits<float> expectedFP =
+ __llvm_libc::fputil::FPBits<float>(expectedRawData);
+
+ errno = 0;
+ float result = __llvm_libc::strtof(inputString, &strEnd);
+
+ __llvm_libc::fputil::FPBits<float> actualFP =
+ __llvm_libc::fputil::FPBits<float>(result);
+
+ EXPECT_EQ(strEnd - inputString, expectedStrLen);
+
+ EXPECT_EQ(actualFP.bits, expectedFP.bits);
+ EXPECT_EQ(actualFP.getSign(), expectedFP.getSign());
+ EXPECT_EQ(actualFP.getExponent(), expectedFP.getExponent());
+ EXPECT_EQ(actualFP.getMantissa(), expectedFP.getMantissa());
+ EXPECT_EQ(errno, expectedErrno);
+ }
+};
+
+// This is the set of tests that I have working (verified correct when compared
+// to system libc). This is here so I don't break more things when I try to fix
+// them.
+
+TEST_F(LlvmLibcStrToFTest, BasicDecimalTests) {
+ runTest("1", 1, 0x3f800000);
+ runTest("123", 3, 0x42f60000);
+ runTest("1234567890", 10, 0x4e932c06u);
+ runTest("123456789012345678901", 21, 0x60d629d4);
+ runTest("0.1", 3, 0x3dcccccdu);
+ runTest(".1", 2, 0x3dcccccdu);
+ runTest("-0.123456789", 12, 0xbdfcd6eau);
+ runTest("0.11111111111111111111", 22, 0x3de38e39u);
+ runTest("0.0000000000000000000000001", 27, 0x15f79688u);
+}
+
+TEST_F(LlvmLibcStrToFTest, DecimalOutOfRangeTests) {
+ runTest("555E36", 6, 0x7f800000, ERANGE);
+ runTest("1e-10000", 8, 0x0, ERANGE);
+}
+
+TEST_F(LlvmLibcStrToFTest, DecimalsWithRoundingProblems) {
+ runTest("20040229", 8, 0x4b98e512);
+ runTest("20040401", 8, 0x4b98e568);
+ runTest("9E9", 3, 0x50061c46);
+}
+
+TEST_F(LlvmLibcStrToFTest, DecimalSubnormals) {
+ runTest("1.4012984643248170709237295832899161312802619418765e-45", 55, 0x1);
+}
+
+TEST_F(LlvmLibcStrToFTest, DecimalWithLongExponent) {
+ runTest("1e2147483648", 12, 0x7f800000, ERANGE);
+ runTest("1e2147483646", 12, 0x7f800000, ERANGE);
+ runTest("100e2147483646", 14, 0x7f800000, ERANGE);
+ runTest("1e-2147483647", 13, 0x0, ERANGE);
+ runTest("1e-2147483649", 13, 0x0, ERANGE);
+}
+
+TEST_F(LlvmLibcStrToFTest, BasicHexadecimalTests) {
+ runTest("0x1", 3, 0x3f800000);
+ runTest("0x10", 4, 0x41800000);
+ runTest("0x11", 4, 0x41880000);
+ runTest("0x0.1234", 8, 0x3d91a000);
+}
+
+TEST_F(LlvmLibcStrToFTest, HexadecimalSubnormalTests) {
+ runTest("0x0.0000000000000000000000000000000002", 38, 0x4000);
+
+ // This is the largest subnormal number as represented in hex
+ runTest("0x0.00000000000000000000000000000003fffff8", 42, 0x7fffff);
+}
+
+TEST_F(LlvmLibcStrToFTest, HexadecimalSubnormalRoundingTests) {
+ // This is the largest subnormal number that gets rounded down to 0 (as a
+ // float)
+ runTest("0x0.00000000000000000000000000000000000004", 42, 0x0, ERANGE);
+
+ // This is slightly larger, and thus rounded up
+ runTest("0x0.000000000000000000000000000000000000041", 43, 0x00000001,
+ ERANGE);
+
+ // These check that we're rounding to even properly
+ runTest("0x0.0000000000000000000000000000000000000b", 42, 0x00000001, ERANGE);
+ runTest("0x0.0000000000000000000000000000000000000c", 42, 0x00000002, ERANGE);
+}
+
+TEST_F(LlvmLibcStrToFTest, HexadecimalNormalRoundingTests) {
+ // This also checks the round to even behavior by checking three adjacent
+ // numbers.
+ // This gets rounded down to even
+ runTest("0x123456500", 11, 0x4f91a2b2);
+ // This doesn't get rounded at all
+ runTest("0x123456600", 11, 0x4f91a2b3);
+ // This gets rounded up to even
+ runTest("0x123456700", 11, 0x4f91a2b4);
+}
+
+TEST_F(LlvmLibcStrToFTest, HexadecimalOutOfRangeTests) {
+ runTest("0x123456789123456789123456789123456789", 38, 0x7f800000, ERANGE);
+ runTest("-0x123456789123456789123456789123456789", 39, 0xff800000, ERANGE);
+ runTest("0x0.00000000000000000000000000000000000001", 42, 0x0, ERANGE);
+}
+
+TEST_F(LlvmLibcStrToFTest, InfTests) {
+ runTest("INF", 3, 0x7f800000);
+ runTest("INFinity", 8, 0x7f800000);
+ runTest("infnity", 3, 0x7f800000);
+ runTest("infinit", 3, 0x7f800000);
+ runTest("infinfinit", 3, 0x7f800000);
+ runTest("innf", 0, 0x0);
+ runTest("-inf", 4, 0xff800000);
+ runTest("-iNfInItY", 9, 0xff800000);
+}
+
+TEST_F(LlvmLibcStrToFTest, NaNTests) {
+ runTest("NaN", 3, 0x7fc00000);
+ runTest("-nAn", 4, 0xffc00000);
+ runTest("NaN()", 5, 0x7fc00000);
+ runTest("NaN(1234)", 9, 0x7fc004d2);
+ runTest("NaN( 1234)", 3, 0x7fc00000);
+}
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