Abseil Common Libraries (C++) (grcp 依赖) https://abseil.io/
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Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
// Copyright 2018 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "absl/strings/charconv.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstring>
#include "absl/base/casts.h"
Export of internal Abseil changes -- dab5caab05d89d03066ef92584660688595a3aaf by Mark Barolak <mbar@google.com>: Add absl::Status and absl::StatusOr to absl/README.md Import of https://github.com/abseil/abseil-cpp/pull/863 PiperOrigin-RevId: 347857368 -- 1ca3c7a96417cd6e6d62f4dc36fd5ddaa61cfa20 by Chris Kennelly <ckennelly@google.com>: Leverage integer power-of-2 functions and bit counting library in Abseil. PiperOrigin-RevId: 347816486 -- e5cbe05879fd65dce7875e2e0105331a1615d89b by Chris Kennelly <ckennelly@google.com>: Mitigate narrowing warning on MSVC. If sizeof(x) <= sizeof(uint32_t), no truncation occurs when casting to uint32_t, but the compiler cannot always determine this. PiperOrigin-RevId: 347696526 -- 079dff64cb175d282d9e22dfb4a522199ffdae2e by Benjamin Barenblat <bbaren@google.com>: Avoid libgcc -NaN narrowing bug When testing -NaN parsing, avoid narrowing -NaN from double to float. This avoids a bug in libgcc (https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98251). PiperOrigin-RevId: 347654751 -- 2e78a7634865aeef6765e1f447e96cf8d9985059 by Chris Kennelly <ckennelly@google.com>: Mark popcount helpers as inline. These are conditionally constexpr, so we need to add inline to cover the non-constexpr builds to avoid ODR violations. PiperOrigin-RevId: 347620138 -- 437fbb363aea1654179f102dcdd607ec33c1af1e by Chris Kennelly <ckennelly@google.com>: Use explicit narrowing cast. This is never invoked in practice, but compilers with -Wimplicit-int-conversion may trigger when sizeof(T) > sizeof(uint16_t) prior to determining this never runs. PiperOrigin-RevId: 347609857 GitOrigin-RevId: dab5caab05d89d03066ef92584660688595a3aaf Change-Id: I6296ddffe7ec646f8ce121138f21e1e85a2cff4b
4 years ago
#include "absl/numeric/bits.h"
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
#include "absl/numeric/int128.h"
#include "absl/strings/internal/charconv_bigint.h"
#include "absl/strings/internal/charconv_parse.h"
// The macro ABSL_BIT_PACK_FLOATS is defined on x86-64, where IEEE floating
// point numbers have the same endianness in memory as a bitfield struct
// containing the corresponding parts.
//
// When set, we replace calls to ldexp() with manual bit packing, which is
// faster and is unaffected by floating point environment.
#ifdef ABSL_BIT_PACK_FLOATS
#error ABSL_BIT_PACK_FLOATS cannot be directly set
#elif defined(__x86_64__) || defined(_M_X64)
#define ABSL_BIT_PACK_FLOATS 1
#endif
// A note about subnormals:
//
// The code below talks about "normals" and "subnormals". A normal IEEE float
// has a fixed-width mantissa and power of two exponent. For example, a normal
// `double` has a 53-bit mantissa. Because the high bit is always 1, it is not
// stored in the representation. The implicit bit buys an extra bit of
// resolution in the datatype.
//
// The downside of this scheme is that there is a large gap between DBL_MIN and
// zero. (Large, at least, relative to the different between DBL_MIN and the
// next representable number). This gap is softened by the "subnormal" numbers,
// which have the same power-of-two exponent as DBL_MIN, but no implicit 53rd
// bit. An all-bits-zero exponent in the encoding represents subnormals. (Zero
// is represented as a subnormal with an all-bits-zero mantissa.)
//
// The code below, in calculations, represents the mantissa as a uint64_t. The
// end result normally has the 53rd bit set. It represents subnormals by using
// narrower mantissas.
namespace absl {
ABSL_NAMESPACE_BEGIN
namespace {
template <typename FloatType>
struct FloatTraits;
template <>
struct FloatTraits<double> {
// The number of mantissa bits in the given float type. This includes the
// implied high bit.
static constexpr int kTargetMantissaBits = 53;
// The largest supported IEEE exponent, in our integral mantissa
// representation.
//
// If `m` is the largest possible int kTargetMantissaBits bits wide, then
// m * 2**kMaxExponent is exactly equal to DBL_MAX.
static constexpr int kMaxExponent = 971;
// The smallest supported IEEE normal exponent, in our integral mantissa
// representation.
//
// If `m` is the smallest possible int kTargetMantissaBits bits wide, then
// m * 2**kMinNormalExponent is exactly equal to DBL_MIN.
static constexpr int kMinNormalExponent = -1074;
static double MakeNan(const char* tagp) {
// Support nan no matter which namespace it's in. Some platforms
// incorrectly don't put it in namespace std.
using namespace std; // NOLINT
return nan(tagp);
}
// Builds a nonzero floating point number out of the provided parts.
//
// This is intended to do the same operation as ldexp(mantissa, exponent),
// but using purely integer math, to avoid -ffastmath and floating
// point environment issues. Using type punning is also faster. We fall back
// to ldexp on a per-platform basis for portability.
//
// `exponent` must be between kMinNormalExponent and kMaxExponent.
//
// `mantissa` must either be exactly kTargetMantissaBits wide, in which case
// a normal value is made, or it must be less narrow than that, in which case
// `exponent` must be exactly kMinNormalExponent, and a subnormal value is
// made.
static double Make(uint64_t mantissa, int exponent, bool sign) {
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
#ifndef ABSL_BIT_PACK_FLOATS
// Support ldexp no matter which namespace it's in. Some platforms
// incorrectly don't put it in namespace std.
using namespace std; // NOLINT
return sign ? -ldexp(mantissa, exponent) : ldexp(mantissa, exponent);
#else
constexpr uint64_t kMantissaMask =
(uint64_t{1} << (kTargetMantissaBits - 1)) - 1;
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
uint64_t dbl = static_cast<uint64_t>(sign) << 63;
if (mantissa > kMantissaMask) {
// Normal value.
// Adjust by 1023 for the exponent representation bias, and an additional
// 52 due to the implied decimal point in the IEEE mantissa represenation.
dbl += uint64_t{exponent + 1023u + kTargetMantissaBits - 1} << 52;
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
mantissa &= kMantissaMask;
} else {
// subnormal value
assert(exponent == kMinNormalExponent);
}
dbl += mantissa;
return absl::bit_cast<double>(dbl);
#endif // ABSL_BIT_PACK_FLOATS
}
};
// Specialization of floating point traits for the `float` type. See the
// FloatTraits<double> specialization above for meaning of each of the following
// members and methods.
template <>
struct FloatTraits<float> {
static constexpr int kTargetMantissaBits = 24;
static constexpr int kMaxExponent = 104;
static constexpr int kMinNormalExponent = -149;
static float MakeNan(const char* tagp) {
// Support nanf no matter which namespace it's in. Some platforms
// incorrectly don't put it in namespace std.
using namespace std; // NOLINT
return nanf(tagp);
}
static float Make(uint32_t mantissa, int exponent, bool sign) {
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
#ifndef ABSL_BIT_PACK_FLOATS
// Support ldexpf no matter which namespace it's in. Some platforms
// incorrectly don't put it in namespace std.
using namespace std; // NOLINT
return sign ? -ldexpf(mantissa, exponent) : ldexpf(mantissa, exponent);
#else
constexpr uint32_t kMantissaMask =
(uint32_t{1} << (kTargetMantissaBits - 1)) - 1;
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
uint32_t flt = static_cast<uint32_t>(sign) << 31;
if (mantissa > kMantissaMask) {
// Normal value.
// Adjust by 127 for the exponent representation bias, and an additional
// 23 due to the implied decimal point in the IEEE mantissa represenation.
flt += uint32_t{exponent + 127u + kTargetMantissaBits - 1} << 23;
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
mantissa &= kMantissaMask;
} else {
// subnormal value
assert(exponent == kMinNormalExponent);
}
flt += mantissa;
return absl::bit_cast<float>(flt);
#endif // ABSL_BIT_PACK_FLOATS
}
};
// Decimal-to-binary conversions require coercing powers of 10 into a mantissa
// and a power of 2. The two helper functions Power10Mantissa(n) and
// Power10Exponent(n) perform this task. Together, these represent a hand-
// rolled floating point value which is equal to or just less than 10**n.
//
// The return values satisfy two range guarantees:
//
// Power10Mantissa(n) * 2**Power10Exponent(n) <= 10**n
// < (Power10Mantissa(n) + 1) * 2**Power10Exponent(n)
//
// 2**63 <= Power10Mantissa(n) < 2**64.
//
// Lookups into the power-of-10 table must first check the Power10Overflow() and
// Power10Underflow() functions, to avoid out-of-bounds table access.
//
// Indexes into these tables are biased by -kPower10TableMin, and the table has
// values in the range [kPower10TableMin, kPower10TableMax].
extern const uint64_t kPower10MantissaTable[];
extern const int16_t kPower10ExponentTable[];
// The smallest allowed value for use with the Power10Mantissa() and
// Power10Exponent() functions below. (If a smaller exponent is needed in
// calculations, the end result is guaranteed to underflow.)
constexpr int kPower10TableMin = -342;
// The largest allowed value for use with the Power10Mantissa() and
// Power10Exponent() functions below. (If a smaller exponent is needed in
// calculations, the end result is guaranteed to overflow.)
constexpr int kPower10TableMax = 308;
uint64_t Power10Mantissa(int n) {
return kPower10MantissaTable[n - kPower10TableMin];
}
int Power10Exponent(int n) {
return kPower10ExponentTable[n - kPower10TableMin];
}
// Returns true if n is large enough that 10**n always results in an IEEE
// overflow.
bool Power10Overflow(int n) { return n > kPower10TableMax; }
// Returns true if n is small enough that 10**n times a ParsedFloat mantissa
// always results in an IEEE underflow.
bool Power10Underflow(int n) { return n < kPower10TableMin; }
// Returns true if Power10Mantissa(n) * 2**Power10Exponent(n) is exactly equal
// to 10**n numerically. Put another way, this returns true if there is no
// truncation error in Power10Mantissa(n).
bool Power10Exact(int n) { return n >= 0 && n <= 27; }
// Sentinel exponent values for representing numbers too large or too close to
// zero to represent in a double.
constexpr int kOverflow = 99999;
constexpr int kUnderflow = -99999;
// Struct representing the calculated conversion result of a positive (nonzero)
// floating point number.
//
// The calculated number is mantissa * 2**exponent (mantissa is treated as an
// integer.) `mantissa` is chosen to be the correct width for the IEEE float
// representation being calculated. (`mantissa` will always have the same bit
// width for normal values, and narrower bit widths for subnormals.)
//
// If the result of conversion was an underflow or overflow, exponent is set
// to kUnderflow or kOverflow.
struct CalculatedFloat {
uint64_t mantissa = 0;
int exponent = 0;
};
// Returns the bit width of the given uint128. (Equivalently, returns 128
// minus the number of leading zero bits.)
unsigned BitWidth(uint128 value) {
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
if (Uint128High64(value) == 0) {
return static_cast<unsigned>(bit_width(Uint128Low64(value)));
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
}
Export of internal Abseil changes -- dab5caab05d89d03066ef92584660688595a3aaf by Mark Barolak <mbar@google.com>: Add absl::Status and absl::StatusOr to absl/README.md Import of https://github.com/abseil/abseil-cpp/pull/863 PiperOrigin-RevId: 347857368 -- 1ca3c7a96417cd6e6d62f4dc36fd5ddaa61cfa20 by Chris Kennelly <ckennelly@google.com>: Leverage integer power-of-2 functions and bit counting library in Abseil. PiperOrigin-RevId: 347816486 -- e5cbe05879fd65dce7875e2e0105331a1615d89b by Chris Kennelly <ckennelly@google.com>: Mitigate narrowing warning on MSVC. If sizeof(x) <= sizeof(uint32_t), no truncation occurs when casting to uint32_t, but the compiler cannot always determine this. PiperOrigin-RevId: 347696526 -- 079dff64cb175d282d9e22dfb4a522199ffdae2e by Benjamin Barenblat <bbaren@google.com>: Avoid libgcc -NaN narrowing bug When testing -NaN parsing, avoid narrowing -NaN from double to float. This avoids a bug in libgcc (https://gcc.gnu.org/bugzilla/show_bug.cgi?id=98251). PiperOrigin-RevId: 347654751 -- 2e78a7634865aeef6765e1f447e96cf8d9985059 by Chris Kennelly <ckennelly@google.com>: Mark popcount helpers as inline. These are conditionally constexpr, so we need to add inline to cover the non-constexpr builds to avoid ODR violations. PiperOrigin-RevId: 347620138 -- 437fbb363aea1654179f102dcdd607ec33c1af1e by Chris Kennelly <ckennelly@google.com>: Use explicit narrowing cast. This is never invoked in practice, but compilers with -Wimplicit-int-conversion may trigger when sizeof(T) > sizeof(uint16_t) prior to determining this never runs. PiperOrigin-RevId: 347609857 GitOrigin-RevId: dab5caab05d89d03066ef92584660688595a3aaf Change-Id: I6296ddffe7ec646f8ce121138f21e1e85a2cff4b
4 years ago
return 128 - countl_zero(Uint128High64(value));
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
}
// Calculates how far to the right a mantissa needs to be shifted to create a
// properly adjusted mantissa for an IEEE floating point number.
//
// `mantissa_width` is the bit width of the mantissa to be shifted, and
// `binary_exponent` is the exponent of the number before the shift.
//
// This accounts for subnormal values, and will return a larger-than-normal
// shift if binary_exponent would otherwise be too low.
template <typename FloatType>
int NormalizedShiftSize(int mantissa_width, int binary_exponent) {
const int normal_shift =
mantissa_width - FloatTraits<FloatType>::kTargetMantissaBits;
const int minimum_shift =
FloatTraits<FloatType>::kMinNormalExponent - binary_exponent;
return std::max(normal_shift, minimum_shift);
}
// Right shifts a uint128 so that it has the requested bit width. (The
// resulting value will have 128 - bit_width leading zeroes.) The initial
// `value` must be wider than the requested bit width.
//
// Returns the number of bits shifted.
int TruncateToBitWidth(int bit_width, uint128* value) {
const int current_bit_width = BitWidth(*value);
const int shift = current_bit_width - bit_width;
*value >>= shift;
return shift;
}
// Checks if the given ParsedFloat represents one of the edge cases that are
// not dependent on number base: zero, infinity, or NaN. If so, sets *value
// the appropriate double, and returns true.
template <typename FloatType>
bool HandleEdgeCase(const strings_internal::ParsedFloat& input, bool negative,
FloatType* value) {
if (input.type == strings_internal::FloatType::kNan) {
// A bug in both clang and gcc would cause the compiler to optimize away the
// buffer we are building below. Declaring the buffer volatile avoids the
// issue, and has no measurable performance impact in microbenchmarks.
//
// https://bugs.llvm.org/show_bug.cgi?id=37778
// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=86113
constexpr ptrdiff_t kNanBufferSize = 128;
volatile char n_char_sequence[kNanBufferSize];
if (input.subrange_begin == nullptr) {
n_char_sequence[0] = '\0';
} else {
ptrdiff_t nan_size = input.subrange_end - input.subrange_begin;
nan_size = std::min(nan_size, kNanBufferSize - 1);
std::copy_n(input.subrange_begin, nan_size, n_char_sequence);
n_char_sequence[nan_size] = '\0';
}
char* nan_argument = const_cast<char*>(n_char_sequence);
*value = negative ? -FloatTraits<FloatType>::MakeNan(nan_argument)
: FloatTraits<FloatType>::MakeNan(nan_argument);
return true;
}
if (input.type == strings_internal::FloatType::kInfinity) {
*value = negative ? -std::numeric_limits<FloatType>::infinity()
: std::numeric_limits<FloatType>::infinity();
return true;
}
if (input.mantissa == 0) {
*value = negative ? -0.0 : 0.0;
return true;
}
return false;
}
// Given a CalculatedFloat result of a from_chars conversion, generate the
// correct output values.
//
// CalculatedFloat can represent an underflow or overflow, in which case the
// error code in *result is set. Otherwise, the calculated floating point
// number is stored in *value.
template <typename FloatType>
void EncodeResult(const CalculatedFloat& calculated, bool negative,
absl::from_chars_result* result, FloatType* value) {
if (calculated.exponent == kOverflow) {
result->ec = std::errc::result_out_of_range;
*value = negative ? -std::numeric_limits<FloatType>::max()
: std::numeric_limits<FloatType>::max();
return;
} else if (calculated.mantissa == 0 || calculated.exponent == kUnderflow) {
result->ec = std::errc::result_out_of_range;
*value = negative ? -0.0 : 0.0;
return;
}
*value = FloatTraits<FloatType>::Make(calculated.mantissa,
calculated.exponent, negative);
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
}
// Returns the given uint128 shifted to the right by `shift` bits, and rounds
// the remaining bits using round_to_nearest logic. The value is returned as a
// uint64_t, since this is the type used by this library for storing calculated
// floating point mantissas.
//
// It is expected that the width of the input value shifted by `shift` will
// be the correct bit-width for the target mantissa, which is strictly narrower
// than a uint64_t.
//
// If `input_exact` is false, then a nonzero error epsilon is assumed. For
// rounding purposes, the true value being rounded is strictly greater than the
// input value. The error may represent a single lost carry bit.
//
// When input_exact, shifted bits of the form 1000000... represent a tie, which
// is broken by rounding to even -- the rounding direction is chosen so the low
// bit of the returned value is 0.
//
// When !input_exact, shifted bits of the form 10000000... represent a value
// strictly greater than one half (due to the error epsilon), and so ties are
// always broken by rounding up.
//
// When !input_exact, shifted bits of the form 01111111... are uncertain;
// the true value may or may not be greater than 10000000..., due to the
// possible lost carry bit. The correct rounding direction is unknown. In this
// case, the result is rounded down, and `output_exact` is set to false.
//
// Zero and negative values of `shift` are accepted, in which case the word is
// shifted left, as necessary.
uint64_t ShiftRightAndRound(uint128 value, int shift, bool input_exact,
bool* output_exact) {
if (shift <= 0) {
*output_exact = input_exact;
return static_cast<uint64_t>(value << -shift);
}
if (shift >= 128) {
// Exponent is so small that we are shifting away all significant bits.
// Answer will not be representable, even as a subnormal, so return a zero
// mantissa (which represents underflow).
*output_exact = true;
return 0;
}
*output_exact = true;
const uint128 shift_mask = (uint128(1) << shift) - 1;
const uint128 halfway_point = uint128(1) << (shift - 1);
const uint128 shifted_bits = value & shift_mask;
value >>= shift;
if (shifted_bits > halfway_point) {
// Shifted bits greater than 10000... require rounding up.
return static_cast<uint64_t>(value + 1);
}
if (shifted_bits == halfway_point) {
// In exact mode, shifted bits of 10000... mean we're exactly halfway
// between two numbers, and we must round to even. So only round up if
// the low bit of `value` is set.
//
// In inexact mode, the nonzero error means the actual value is greater
// than the halfway point and we must alway round up.
if ((value & 1) == 1 || !input_exact) {
++value;
}
return static_cast<uint64_t>(value);
}
if (!input_exact && shifted_bits == halfway_point - 1) {
// Rounding direction is unclear, due to error.
*output_exact = false;
}
// Otherwise, round down.
return static_cast<uint64_t>(value);
}
// Checks if a floating point guess needs to be rounded up, using high precision
// math.
//
// `guess_mantissa` and `guess_exponent` represent a candidate guess for the
// number represented by `parsed_decimal`.
//
// The exact number represented by `parsed_decimal` must lie between the two
// numbers:
// A = `guess_mantissa * 2**guess_exponent`
// B = `(guess_mantissa + 1) * 2**guess_exponent`
//
// This function returns false if `A` is the better guess, and true if `B` is
// the better guess, with rounding ties broken by rounding to even.
bool MustRoundUp(uint64_t guess_mantissa, int guess_exponent,
const strings_internal::ParsedFloat& parsed_decimal) {
// 768 is the number of digits needed in the worst case. We could determine a
// better limit dynamically based on the value of parsed_decimal.exponent.
// This would optimize pathological input cases only. (Sane inputs won't have
// hundreds of digits of mantissa.)
absl::strings_internal::BigUnsigned<84> exact_mantissa;
int exact_exponent = exact_mantissa.ReadFloatMantissa(parsed_decimal, 768);
// Adjust the `guess` arguments to be halfway between A and B.
guess_mantissa = guess_mantissa * 2 + 1;
guess_exponent -= 1;
// In our comparison:
// lhs = exact = exact_mantissa * 10**exact_exponent
// = exact_mantissa * 5**exact_exponent * 2**exact_exponent
// rhs = guess = guess_mantissa * 2**guess_exponent
//
// Because we are doing integer math, we can't directly deal with negative
// exponents. We instead move these to the other side of the inequality.
absl::strings_internal::BigUnsigned<84>& lhs = exact_mantissa;
int comparison;
if (exact_exponent >= 0) {
lhs.MultiplyByFiveToTheNth(exact_exponent);
absl::strings_internal::BigUnsigned<84> rhs(guess_mantissa);
// There are powers of 2 on both sides of the inequality; reduce this to
// a single bit-shift.
if (exact_exponent > guess_exponent) {
lhs.ShiftLeft(exact_exponent - guess_exponent);
} else {
rhs.ShiftLeft(guess_exponent - exact_exponent);
}
comparison = Compare(lhs, rhs);
} else {
// Move the power of 5 to the other side of the equation, giving us:
// lhs = exact_mantissa * 2**exact_exponent
// rhs = guess_mantissa * 5**(-exact_exponent) * 2**guess_exponent
absl::strings_internal::BigUnsigned<84> rhs =
absl::strings_internal::BigUnsigned<84>::FiveToTheNth(-exact_exponent);
rhs.MultiplyBy(guess_mantissa);
if (exact_exponent > guess_exponent) {
lhs.ShiftLeft(exact_exponent - guess_exponent);
} else {
rhs.ShiftLeft(guess_exponent - exact_exponent);
}
comparison = Compare(lhs, rhs);
}
if (comparison < 0) {
return false;
} else if (comparison > 0) {
return true;
} else {
// When lhs == rhs, the decimal input is exactly between A and B.
// Round towards even -- round up only if the low bit of the initial
// `guess_mantissa` was a 1. We shifted guess_mantissa left 1 bit at
// the beginning of this function, so test the 2nd bit here.
return (guess_mantissa & 2) == 2;
}
}
// Constructs a CalculatedFloat from a given mantissa and exponent, but
// with the following normalizations applied:
//
// If rounding has caused mantissa to increase just past the allowed bit
// width, shift and adjust exponent.
//
// If exponent is too high, sets kOverflow.
//
// If mantissa is zero (representing a non-zero value not representable, even
// as a subnormal), sets kUnderflow.
template <typename FloatType>
CalculatedFloat CalculatedFloatFromRawValues(uint64_t mantissa, int exponent) {
CalculatedFloat result;
if (mantissa == uint64_t{1} << FloatTraits<FloatType>::kTargetMantissaBits) {
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
mantissa >>= 1;
exponent += 1;
}
if (exponent > FloatTraits<FloatType>::kMaxExponent) {
result.exponent = kOverflow;
} else if (mantissa == 0) {
result.exponent = kUnderflow;
} else {
result.exponent = exponent;
result.mantissa = mantissa;
}
return result;
}
template <typename FloatType>
CalculatedFloat CalculateFromParsedHexadecimal(
const strings_internal::ParsedFloat& parsed_hex) {
uint64_t mantissa = parsed_hex.mantissa;
int exponent = parsed_hex.exponent;
auto mantissa_width = static_cast<unsigned>(bit_width(mantissa));
Export of internal Abseil changes -- f012012ef78234a6a4585321b67d7b7c92ebc266 by Laramie Leavitt <lar@google.com>: Slight restructuring of absl/random/internal randen implementation. Convert round-keys.inc into randen_round_keys.cc file. Consistently use a 128-bit pointer type for internal method parameters. This allows simpler pointer arithmetic in C++ & permits removal of some constants and casts. Remove some redundancy in comments & constexpr variables. Specifically, all references to Randen algorithm parameters use RandenTraits; duplication in RandenSlow removed. PiperOrigin-RevId: 312190313 -- dc8b42e054046741e9ed65335bfdface997c6063 by Abseil Team <absl-team@google.com>: Internal change. PiperOrigin-RevId: 312167304 -- f13d248fafaf206492c1362c3574031aea3abaf7 by Matthew Brown <matthewbr@google.com>: Cleanup StrFormat extensions a little. PiperOrigin-RevId: 312166336 -- 9d9117589667afe2332bb7ad42bc967ca7c54502 by Derek Mauro <dmauro@google.com>: Internal change PiperOrigin-RevId: 312105213 -- 9a12b9b3aa0e59b8ee6cf9408ed0029045543a9b by Abseil Team <absl-team@google.com>: Complete IGNORE_TYPE macro renaming. PiperOrigin-RevId: 311999699 -- 64756f20d61021d999bd0d4c15e9ad3857382f57 by Gennadiy Rozental <rogeeff@google.com>: Switch to fixed bytes specific default value. This fixes the Abseil Flags for big endian platforms. PiperOrigin-RevId: 311844448 -- bdbe6b5b29791dbc3816ada1828458b3010ff1e9 by Laramie Leavitt <lar@google.com>: Change many distribution tests to use pcg_engine as a deterministic source of entropy. It's reasonable to test that the BitGen itself has good entropy, however when testing the cross product of all random distributions x all the architecture variations x all submitted changes results in a large number of tests. In order to account for these failures while still using good entropy requires that our allowed sigma need to account for all of these independent tests. Our current sigma values are too restrictive, and we see a lot of failures, so we have to either relax the sigma values or convert some of the statistical tests to use deterministic values. This changelist does the latter. PiperOrigin-RevId: 311840096 GitOrigin-RevId: f012012ef78234a6a4585321b67d7b7c92ebc266 Change-Id: Ic84886f38ff30d7d72c126e9b63c9a61eb729a1a
5 years ago
const int shift = NormalizedShiftSize<FloatType>(mantissa_width, exponent);
bool result_exact;
exponent += shift;
mantissa = ShiftRightAndRound(mantissa, shift,
/* input exact= */ true, &result_exact);
// ParseFloat handles rounding in the hexadecimal case, so we don't have to
// check `result_exact` here.
return CalculatedFloatFromRawValues<FloatType>(mantissa, exponent);
}
template <typename FloatType>
CalculatedFloat CalculateFromParsedDecimal(
const strings_internal::ParsedFloat& parsed_decimal) {
CalculatedFloat result;
// Large or small enough decimal exponents will always result in overflow
// or underflow.
if (Power10Underflow(parsed_decimal.exponent)) {
result.exponent = kUnderflow;
return result;
} else if (Power10Overflow(parsed_decimal.exponent)) {
result.exponent = kOverflow;
return result;
}
// Otherwise convert our power of 10 into a power of 2 times an integer
// mantissa, and multiply this by our parsed decimal mantissa.
uint128 wide_binary_mantissa = parsed_decimal.mantissa;
wide_binary_mantissa *= Power10Mantissa(parsed_decimal.exponent);
int binary_exponent = Power10Exponent(parsed_decimal.exponent);
// Discard bits that are inaccurate due to truncation error. The magic
// `mantissa_width` constants below are justified in
// https://abseil.io/about/design/charconv. They represent the number of bits
// in `wide_binary_mantissa` that are guaranteed to be unaffected by error
// propagation.
bool mantissa_exact;
int mantissa_width;
if (parsed_decimal.subrange_begin) {
// Truncated mantissa
mantissa_width = 58;
mantissa_exact = false;
binary_exponent +=
TruncateToBitWidth(mantissa_width, &wide_binary_mantissa);
} else if (!Power10Exact(parsed_decimal.exponent)) {
// Exact mantissa, truncated power of ten
mantissa_width = 63;
mantissa_exact = false;
binary_exponent +=
TruncateToBitWidth(mantissa_width, &wide_binary_mantissa);
} else {
// Product is exact
mantissa_width = BitWidth(wide_binary_mantissa);
mantissa_exact = true;
}
// Shift into an FloatType-sized mantissa, and round to nearest.
const int shift =
NormalizedShiftSize<FloatType>(mantissa_width, binary_exponent);
bool result_exact;
binary_exponent += shift;
uint64_t binary_mantissa = ShiftRightAndRound(wide_binary_mantissa, shift,
mantissa_exact, &result_exact);
if (!result_exact) {
// We could not determine the rounding direction using int128 math. Use
// full resolution math instead.
if (MustRoundUp(binary_mantissa, binary_exponent, parsed_decimal)) {
binary_mantissa += 1;
}
}
return CalculatedFloatFromRawValues<FloatType>(binary_mantissa,
binary_exponent);
}
template <typename FloatType>
from_chars_result FromCharsImpl(const char* first, const char* last,
FloatType& value, chars_format fmt_flags) {
from_chars_result result;
result.ptr = first; // overwritten on successful parse
result.ec = std::errc();
bool negative = false;
if (first != last && *first == '-') {
++first;
negative = true;
}
// If the `hex` flag is *not* set, then we will accept a 0x prefix and try
// to parse a hexadecimal float.
if ((fmt_flags & chars_format::hex) == chars_format{} && last - first >= 2 &&
*first == '0' && (first[1] == 'x' || first[1] == 'X')) {
const char* hex_first = first + 2;
strings_internal::ParsedFloat hex_parse =
strings_internal::ParseFloat<16>(hex_first, last, fmt_flags);
if (hex_parse.end == nullptr ||
hex_parse.type != strings_internal::FloatType::kNumber) {
// Either we failed to parse a hex float after the "0x", or we read
// "0xinf" or "0xnan" which we don't want to match.
//
// However, a string that begins with "0x" also begins with "0", which
// is normally a valid match for the number zero. So we want these
// strings to match zero unless fmt_flags is `scientific`. (This flag
// means an exponent is required, which the string "0" does not have.)
if (fmt_flags == chars_format::scientific) {
result.ec = std::errc::invalid_argument;
} else {
result.ptr = first + 1;
value = negative ? -0.0 : 0.0;
}
return result;
}
// We matched a value.
result.ptr = hex_parse.end;
if (HandleEdgeCase(hex_parse, negative, &value)) {
return result;
}
CalculatedFloat calculated =
CalculateFromParsedHexadecimal<FloatType>(hex_parse);
EncodeResult(calculated, negative, &result, &value);
return result;
}
// Otherwise, we choose the number base based on the flags.
if ((fmt_flags & chars_format::hex) == chars_format::hex) {
strings_internal::ParsedFloat hex_parse =
strings_internal::ParseFloat<16>(first, last, fmt_flags);
if (hex_parse.end == nullptr) {
result.ec = std::errc::invalid_argument;
return result;
}
result.ptr = hex_parse.end;
if (HandleEdgeCase(hex_parse, negative, &value)) {
return result;
}
CalculatedFloat calculated =
CalculateFromParsedHexadecimal<FloatType>(hex_parse);
EncodeResult(calculated, negative, &result, &value);
return result;
} else {
strings_internal::ParsedFloat decimal_parse =
strings_internal::ParseFloat<10>(first, last, fmt_flags);
if (decimal_parse.end == nullptr) {
result.ec = std::errc::invalid_argument;
return result;
}
result.ptr = decimal_parse.end;
if (HandleEdgeCase(decimal_parse, negative, &value)) {
return result;
}
CalculatedFloat calculated =
CalculateFromParsedDecimal<FloatType>(decimal_parse);
EncodeResult(calculated, negative, &result, &value);
return result;
}
}
} // namespace
from_chars_result from_chars(const char* first, const char* last, double& value,
chars_format fmt) {
return FromCharsImpl(first, last, value, fmt);
}
from_chars_result from_chars(const char* first, const char* last, float& value,
chars_format fmt) {
return FromCharsImpl(first, last, value, fmt);
}
namespace {
// Table of powers of 10, from kPower10TableMin to kPower10TableMax.
//
// kPower10MantissaTable[i - kPower10TableMin] stores the 64-bit mantissa (high
// bit always on), and kPower10ExponentTable[i - kPower10TableMin] stores the
// power-of-two exponent. For a given number i, this gives the unique mantissa
// and exponent such that mantissa * 2**exponent <= 10**i < (mantissa + 1) *
// 2**exponent.
const uint64_t kPower10MantissaTable[] = {
0xeef453d6923bd65aU, 0x9558b4661b6565f8U, 0xbaaee17fa23ebf76U,
0xe95a99df8ace6f53U, 0x91d8a02bb6c10594U, 0xb64ec836a47146f9U,
0xe3e27a444d8d98b7U, 0x8e6d8c6ab0787f72U, 0xb208ef855c969f4fU,
0xde8b2b66b3bc4723U, 0x8b16fb203055ac76U, 0xaddcb9e83c6b1793U,
0xd953e8624b85dd78U, 0x87d4713d6f33aa6bU, 0xa9c98d8ccb009506U,
0xd43bf0effdc0ba48U, 0x84a57695fe98746dU, 0xa5ced43b7e3e9188U,
0xcf42894a5dce35eaU, 0x818995ce7aa0e1b2U, 0xa1ebfb4219491a1fU,
0xca66fa129f9b60a6U, 0xfd00b897478238d0U, 0x9e20735e8cb16382U,
0xc5a890362fddbc62U, 0xf712b443bbd52b7bU, 0x9a6bb0aa55653b2dU,
0xc1069cd4eabe89f8U, 0xf148440a256e2c76U, 0x96cd2a865764dbcaU,
0xbc807527ed3e12bcU, 0xeba09271e88d976bU, 0x93445b8731587ea3U,
0xb8157268fdae9e4cU, 0xe61acf033d1a45dfU, 0x8fd0c16206306babU,
0xb3c4f1ba87bc8696U, 0xe0b62e2929aba83cU, 0x8c71dcd9ba0b4925U,
0xaf8e5410288e1b6fU, 0xdb71e91432b1a24aU, 0x892731ac9faf056eU,
0xab70fe17c79ac6caU, 0xd64d3d9db981787dU, 0x85f0468293f0eb4eU,
0xa76c582338ed2621U, 0xd1476e2c07286faaU, 0x82cca4db847945caU,
0xa37fce126597973cU, 0xcc5fc196fefd7d0cU, 0xff77b1fcbebcdc4fU,
0x9faacf3df73609b1U, 0xc795830d75038c1dU, 0xf97ae3d0d2446f25U,
0x9becce62836ac577U, 0xc2e801fb244576d5U, 0xf3a20279ed56d48aU,
0x9845418c345644d6U, 0xbe5691ef416bd60cU, 0xedec366b11c6cb8fU,
0x94b3a202eb1c3f39U, 0xb9e08a83a5e34f07U, 0xe858ad248f5c22c9U,
0x91376c36d99995beU, 0xb58547448ffffb2dU, 0xe2e69915b3fff9f9U,
0x8dd01fad907ffc3bU, 0xb1442798f49ffb4aU, 0xdd95317f31c7fa1dU,
0x8a7d3eef7f1cfc52U, 0xad1c8eab5ee43b66U, 0xd863b256369d4a40U,
0x873e4f75e2224e68U, 0xa90de3535aaae202U, 0xd3515c2831559a83U,
0x8412d9991ed58091U, 0xa5178fff668ae0b6U, 0xce5d73ff402d98e3U,
0x80fa687f881c7f8eU, 0xa139029f6a239f72U, 0xc987434744ac874eU,
0xfbe9141915d7a922U, 0x9d71ac8fada6c9b5U, 0xc4ce17b399107c22U,
0xf6019da07f549b2bU, 0x99c102844f94e0fbU, 0xc0314325637a1939U,
0xf03d93eebc589f88U, 0x96267c7535b763b5U, 0xbbb01b9283253ca2U,
0xea9c227723ee8bcbU, 0x92a1958a7675175fU, 0xb749faed14125d36U,
0xe51c79a85916f484U, 0x8f31cc0937ae58d2U, 0xb2fe3f0b8599ef07U,
0xdfbdcece67006ac9U, 0x8bd6a141006042bdU, 0xaecc49914078536dU,
0xda7f5bf590966848U, 0x888f99797a5e012dU, 0xaab37fd7d8f58178U,
0xd5605fcdcf32e1d6U, 0x855c3be0a17fcd26U, 0xa6b34ad8c9dfc06fU,
0xd0601d8efc57b08bU, 0x823c12795db6ce57U, 0xa2cb1717b52481edU,
0xcb7ddcdda26da268U, 0xfe5d54150b090b02U, 0x9efa548d26e5a6e1U,
0xc6b8e9b0709f109aU, 0xf867241c8cc6d4c0U, 0x9b407691d7fc44f8U,
0xc21094364dfb5636U, 0xf294b943e17a2bc4U, 0x979cf3ca6cec5b5aU,
0xbd8430bd08277231U, 0xece53cec4a314ebdU, 0x940f4613ae5ed136U,
0xb913179899f68584U, 0xe757dd7ec07426e5U, 0x9096ea6f3848984fU,
0xb4bca50b065abe63U, 0xe1ebce4dc7f16dfbU, 0x8d3360f09cf6e4bdU,
0xb080392cc4349decU, 0xdca04777f541c567U, 0x89e42caaf9491b60U,
0xac5d37d5b79b6239U, 0xd77485cb25823ac7U, 0x86a8d39ef77164bcU,
0xa8530886b54dbdebU, 0xd267caa862a12d66U, 0x8380dea93da4bc60U,
0xa46116538d0deb78U, 0xcd795be870516656U, 0x806bd9714632dff6U,
0xa086cfcd97bf97f3U, 0xc8a883c0fdaf7df0U, 0xfad2a4b13d1b5d6cU,
0x9cc3a6eec6311a63U, 0xc3f490aa77bd60fcU, 0xf4f1b4d515acb93bU,
0x991711052d8bf3c5U, 0xbf5cd54678eef0b6U, 0xef340a98172aace4U,
0x9580869f0e7aac0eU, 0xbae0a846d2195712U, 0xe998d258869facd7U,
0x91ff83775423cc06U, 0xb67f6455292cbf08U, 0xe41f3d6a7377eecaU,
0x8e938662882af53eU, 0xb23867fb2a35b28dU, 0xdec681f9f4c31f31U,
0x8b3c113c38f9f37eU, 0xae0b158b4738705eU, 0xd98ddaee19068c76U,
0x87f8a8d4cfa417c9U, 0xa9f6d30a038d1dbcU, 0xd47487cc8470652bU,
0x84c8d4dfd2c63f3bU, 0xa5fb0a17c777cf09U, 0xcf79cc9db955c2ccU,
0x81ac1fe293d599bfU, 0xa21727db38cb002fU, 0xca9cf1d206fdc03bU,
0xfd442e4688bd304aU, 0x9e4a9cec15763e2eU, 0xc5dd44271ad3cdbaU,
0xf7549530e188c128U, 0x9a94dd3e8cf578b9U, 0xc13a148e3032d6e7U,
0xf18899b1bc3f8ca1U, 0x96f5600f15a7b7e5U, 0xbcb2b812db11a5deU,
0xebdf661791d60f56U, 0x936b9fcebb25c995U, 0xb84687c269ef3bfbU,
0xe65829b3046b0afaU, 0x8ff71a0fe2c2e6dcU, 0xb3f4e093db73a093U,
0xe0f218b8d25088b8U, 0x8c974f7383725573U, 0xafbd2350644eeacfU,
0xdbac6c247d62a583U, 0x894bc396ce5da772U, 0xab9eb47c81f5114fU,
0xd686619ba27255a2U, 0x8613fd0145877585U, 0xa798fc4196e952e7U,
0xd17f3b51fca3a7a0U, 0x82ef85133de648c4U, 0xa3ab66580d5fdaf5U,
0xcc963fee10b7d1b3U, 0xffbbcfe994e5c61fU, 0x9fd561f1fd0f9bd3U,
0xc7caba6e7c5382c8U, 0xf9bd690a1b68637bU, 0x9c1661a651213e2dU,
0xc31bfa0fe5698db8U, 0xf3e2f893dec3f126U, 0x986ddb5c6b3a76b7U,
0xbe89523386091465U, 0xee2ba6c0678b597fU, 0x94db483840b717efU,
0xba121a4650e4ddebU, 0xe896a0d7e51e1566U, 0x915e2486ef32cd60U,
0xb5b5ada8aaff80b8U, 0xe3231912d5bf60e6U, 0x8df5efabc5979c8fU,
0xb1736b96b6fd83b3U, 0xddd0467c64bce4a0U, 0x8aa22c0dbef60ee4U,
0xad4ab7112eb3929dU, 0xd89d64d57a607744U, 0x87625f056c7c4a8bU,
0xa93af6c6c79b5d2dU, 0xd389b47879823479U, 0x843610cb4bf160cbU,
0xa54394fe1eedb8feU, 0xce947a3da6a9273eU, 0x811ccc668829b887U,
0xa163ff802a3426a8U, 0xc9bcff6034c13052U, 0xfc2c3f3841f17c67U,
0x9d9ba7832936edc0U, 0xc5029163f384a931U, 0xf64335bcf065d37dU,
0x99ea0196163fa42eU, 0xc06481fb9bcf8d39U, 0xf07da27a82c37088U,
0x964e858c91ba2655U, 0xbbe226efb628afeaU, 0xeadab0aba3b2dbe5U,
0x92c8ae6b464fc96fU, 0xb77ada0617e3bbcbU, 0xe55990879ddcaabdU,
0x8f57fa54c2a9eab6U, 0xb32df8e9f3546564U, 0xdff9772470297ebdU,
0x8bfbea76c619ef36U, 0xaefae51477a06b03U, 0xdab99e59958885c4U,
0x88b402f7fd75539bU, 0xaae103b5fcd2a881U, 0xd59944a37c0752a2U,
0x857fcae62d8493a5U, 0xa6dfbd9fb8e5b88eU, 0xd097ad07a71f26b2U,
0x825ecc24c873782fU, 0xa2f67f2dfa90563bU, 0xcbb41ef979346bcaU,
0xfea126b7d78186bcU, 0x9f24b832e6b0f436U, 0xc6ede63fa05d3143U,
0xf8a95fcf88747d94U, 0x9b69dbe1b548ce7cU, 0xc24452da229b021bU,
0xf2d56790ab41c2a2U, 0x97c560ba6b0919a5U, 0xbdb6b8e905cb600fU,
0xed246723473e3813U, 0x9436c0760c86e30bU, 0xb94470938fa89bceU,
0xe7958cb87392c2c2U, 0x90bd77f3483bb9b9U, 0xb4ecd5f01a4aa828U,
0xe2280b6c20dd5232U, 0x8d590723948a535fU, 0xb0af48ec79ace837U,
0xdcdb1b2798182244U, 0x8a08f0f8bf0f156bU, 0xac8b2d36eed2dac5U,
0xd7adf884aa879177U, 0x86ccbb52ea94baeaU, 0xa87fea27a539e9a5U,
0xd29fe4b18e88640eU, 0x83a3eeeef9153e89U, 0xa48ceaaab75a8e2bU,
0xcdb02555653131b6U, 0x808e17555f3ebf11U, 0xa0b19d2ab70e6ed6U,
0xc8de047564d20a8bU, 0xfb158592be068d2eU, 0x9ced737bb6c4183dU,
0xc428d05aa4751e4cU, 0xf53304714d9265dfU, 0x993fe2c6d07b7fabU,
0xbf8fdb78849a5f96U, 0xef73d256a5c0f77cU, 0x95a8637627989aadU,
0xbb127c53b17ec159U, 0xe9d71b689dde71afU, 0x9226712162ab070dU,
0xb6b00d69bb55c8d1U, 0xe45c10c42a2b3b05U, 0x8eb98a7a9a5b04e3U,
0xb267ed1940f1c61cU, 0xdf01e85f912e37a3U, 0x8b61313bbabce2c6U,
0xae397d8aa96c1b77U, 0xd9c7dced53c72255U, 0x881cea14545c7575U,
0xaa242499697392d2U, 0xd4ad2dbfc3d07787U, 0x84ec3c97da624ab4U,
0xa6274bbdd0fadd61U, 0xcfb11ead453994baU, 0x81ceb32c4b43fcf4U,
0xa2425ff75e14fc31U, 0xcad2f7f5359a3b3eU, 0xfd87b5f28300ca0dU,
0x9e74d1b791e07e48U, 0xc612062576589ddaU, 0xf79687aed3eec551U,
0x9abe14cd44753b52U, 0xc16d9a0095928a27U, 0xf1c90080baf72cb1U,
0x971da05074da7beeU, 0xbce5086492111aeaU, 0xec1e4a7db69561a5U,
0x9392ee8e921d5d07U, 0xb877aa3236a4b449U, 0xe69594bec44de15bU,
0x901d7cf73ab0acd9U, 0xb424dc35095cd80fU, 0xe12e13424bb40e13U,
0x8cbccc096f5088cbU, 0xafebff0bcb24aafeU, 0xdbe6fecebdedd5beU,
0x89705f4136b4a597U, 0xabcc77118461cefcU, 0xd6bf94d5e57a42bcU,
0x8637bd05af6c69b5U, 0xa7c5ac471b478423U, 0xd1b71758e219652bU,
0x83126e978d4fdf3bU, 0xa3d70a3d70a3d70aU, 0xccccccccccccccccU,
0x8000000000000000U, 0xa000000000000000U, 0xc800000000000000U,
0xfa00000000000000U, 0x9c40000000000000U, 0xc350000000000000U,
0xf424000000000000U, 0x9896800000000000U, 0xbebc200000000000U,
0xee6b280000000000U, 0x9502f90000000000U, 0xba43b74000000000U,
0xe8d4a51000000000U, 0x9184e72a00000000U, 0xb5e620f480000000U,
0xe35fa931a0000000U, 0x8e1bc9bf04000000U, 0xb1a2bc2ec5000000U,
0xde0b6b3a76400000U, 0x8ac7230489e80000U, 0xad78ebc5ac620000U,
0xd8d726b7177a8000U, 0x878678326eac9000U, 0xa968163f0a57b400U,
0xd3c21bcecceda100U, 0x84595161401484a0U, 0xa56fa5b99019a5c8U,
0xcecb8f27f4200f3aU, 0x813f3978f8940984U, 0xa18f07d736b90be5U,
0xc9f2c9cd04674edeU, 0xfc6f7c4045812296U, 0x9dc5ada82b70b59dU,
0xc5371912364ce305U, 0xf684df56c3e01bc6U, 0x9a130b963a6c115cU,
0xc097ce7bc90715b3U, 0xf0bdc21abb48db20U, 0x96769950b50d88f4U,
0xbc143fa4e250eb31U, 0xeb194f8e1ae525fdU, 0x92efd1b8d0cf37beU,
0xb7abc627050305adU, 0xe596b7b0c643c719U, 0x8f7e32ce7bea5c6fU,
0xb35dbf821ae4f38bU, 0xe0352f62a19e306eU, 0x8c213d9da502de45U,
0xaf298d050e4395d6U, 0xdaf3f04651d47b4cU, 0x88d8762bf324cd0fU,
0xab0e93b6efee0053U, 0xd5d238a4abe98068U, 0x85a36366eb71f041U,
0xa70c3c40a64e6c51U, 0xd0cf4b50cfe20765U, 0x82818f1281ed449fU,
0xa321f2d7226895c7U, 0xcbea6f8ceb02bb39U, 0xfee50b7025c36a08U,
0x9f4f2726179a2245U, 0xc722f0ef9d80aad6U, 0xf8ebad2b84e0d58bU,
0x9b934c3b330c8577U, 0xc2781f49ffcfa6d5U, 0xf316271c7fc3908aU,
0x97edd871cfda3a56U, 0xbde94e8e43d0c8ecU, 0xed63a231d4c4fb27U,
0x945e455f24fb1cf8U, 0xb975d6b6ee39e436U, 0xe7d34c64a9c85d44U,
0x90e40fbeea1d3a4aU, 0xb51d13aea4a488ddU, 0xe264589a4dcdab14U,
0x8d7eb76070a08aecU, 0xb0de65388cc8ada8U, 0xdd15fe86affad912U,
0x8a2dbf142dfcc7abU, 0xacb92ed9397bf996U, 0xd7e77a8f87daf7fbU,
0x86f0ac99b4e8dafdU, 0xa8acd7c0222311bcU, 0xd2d80db02aabd62bU,
0x83c7088e1aab65dbU, 0xa4b8cab1a1563f52U, 0xcde6fd5e09abcf26U,
0x80b05e5ac60b6178U, 0xa0dc75f1778e39d6U, 0xc913936dd571c84cU,
0xfb5878494ace3a5fU, 0x9d174b2dcec0e47bU, 0xc45d1df942711d9aU,
0xf5746577930d6500U, 0x9968bf6abbe85f20U, 0xbfc2ef456ae276e8U,
0xefb3ab16c59b14a2U, 0x95d04aee3b80ece5U, 0xbb445da9ca61281fU,
0xea1575143cf97226U, 0x924d692ca61be758U, 0xb6e0c377cfa2e12eU,
0xe498f455c38b997aU, 0x8edf98b59a373fecU, 0xb2977ee300c50fe7U,
0xdf3d5e9bc0f653e1U, 0x8b865b215899f46cU, 0xae67f1e9aec07187U,
0xda01ee641a708de9U, 0x884134fe908658b2U, 0xaa51823e34a7eedeU,
0xd4e5e2cdc1d1ea96U, 0x850fadc09923329eU, 0xa6539930bf6bff45U,
0xcfe87f7cef46ff16U, 0x81f14fae158c5f6eU, 0xa26da3999aef7749U,
0xcb090c8001ab551cU, 0xfdcb4fa002162a63U, 0x9e9f11c4014dda7eU,
0xc646d63501a1511dU, 0xf7d88bc24209a565U, 0x9ae757596946075fU,
0xc1a12d2fc3978937U, 0xf209787bb47d6b84U, 0x9745eb4d50ce6332U,
0xbd176620a501fbffU, 0xec5d3fa8ce427affU, 0x93ba47c980e98cdfU,
0xb8a8d9bbe123f017U, 0xe6d3102ad96cec1dU, 0x9043ea1ac7e41392U,
0xb454e4a179dd1877U, 0xe16a1dc9d8545e94U, 0x8ce2529e2734bb1dU,
0xb01ae745b101e9e4U, 0xdc21a1171d42645dU, 0x899504ae72497ebaU,
0xabfa45da0edbde69U, 0xd6f8d7509292d603U, 0x865b86925b9bc5c2U,
0xa7f26836f282b732U, 0xd1ef0244af2364ffU, 0x8335616aed761f1fU,
0xa402b9c5a8d3a6e7U, 0xcd036837130890a1U, 0x802221226be55a64U,
0xa02aa96b06deb0fdU, 0xc83553c5c8965d3dU, 0xfa42a8b73abbf48cU,
0x9c69a97284b578d7U, 0xc38413cf25e2d70dU, 0xf46518c2ef5b8cd1U,
0x98bf2f79d5993802U, 0xbeeefb584aff8603U, 0xeeaaba2e5dbf6784U,
0x952ab45cfa97a0b2U, 0xba756174393d88dfU, 0xe912b9d1478ceb17U,
0x91abb422ccb812eeU, 0xb616a12b7fe617aaU, 0xe39c49765fdf9d94U,
0x8e41ade9fbebc27dU, 0xb1d219647ae6b31cU, 0xde469fbd99a05fe3U,
0x8aec23d680043beeU, 0xada72ccc20054ae9U, 0xd910f7ff28069da4U,
0x87aa9aff79042286U, 0xa99541bf57452b28U, 0xd3fa922f2d1675f2U,
0x847c9b5d7c2e09b7U, 0xa59bc234db398c25U, 0xcf02b2c21207ef2eU,
0x8161afb94b44f57dU, 0xa1ba1ba79e1632dcU, 0xca28a291859bbf93U,
0xfcb2cb35e702af78U, 0x9defbf01b061adabU, 0xc56baec21c7a1916U,
0xf6c69a72a3989f5bU, 0x9a3c2087a63f6399U, 0xc0cb28a98fcf3c7fU,
0xf0fdf2d3f3c30b9fU, 0x969eb7c47859e743U, 0xbc4665b596706114U,
0xeb57ff22fc0c7959U, 0x9316ff75dd87cbd8U, 0xb7dcbf5354e9beceU,
0xe5d3ef282a242e81U, 0x8fa475791a569d10U, 0xb38d92d760ec4455U,
0xe070f78d3927556aU, 0x8c469ab843b89562U, 0xaf58416654a6babbU,
0xdb2e51bfe9d0696aU, 0x88fcf317f22241e2U, 0xab3c2fddeeaad25aU,
0xd60b3bd56a5586f1U, 0x85c7056562757456U, 0xa738c6bebb12d16cU,
0xd106f86e69d785c7U, 0x82a45b450226b39cU, 0xa34d721642b06084U,
0xcc20ce9bd35c78a5U, 0xff290242c83396ceU, 0x9f79a169bd203e41U,
0xc75809c42c684dd1U, 0xf92e0c3537826145U, 0x9bbcc7a142b17ccbU,
0xc2abf989935ddbfeU, 0xf356f7ebf83552feU, 0x98165af37b2153deU,
0xbe1bf1b059e9a8d6U, 0xeda2ee1c7064130cU, 0x9485d4d1c63e8be7U,
0xb9a74a0637ce2ee1U, 0xe8111c87c5c1ba99U, 0x910ab1d4db9914a0U,
0xb54d5e4a127f59c8U, 0xe2a0b5dc971f303aU, 0x8da471a9de737e24U,
0xb10d8e1456105dadU, 0xdd50f1996b947518U, 0x8a5296ffe33cc92fU,
0xace73cbfdc0bfb7bU, 0xd8210befd30efa5aU, 0x8714a775e3e95c78U,
0xa8d9d1535ce3b396U, 0xd31045a8341ca07cU, 0x83ea2b892091e44dU,
0xa4e4b66b68b65d60U, 0xce1de40642e3f4b9U, 0x80d2ae83e9ce78f3U,
0xa1075a24e4421730U, 0xc94930ae1d529cfcU, 0xfb9b7cd9a4a7443cU,
0x9d412e0806e88aa5U, 0xc491798a08a2ad4eU, 0xf5b5d7ec8acb58a2U,
0x9991a6f3d6bf1765U, 0xbff610b0cc6edd3fU, 0xeff394dcff8a948eU,
0x95f83d0a1fb69cd9U, 0xbb764c4ca7a4440fU, 0xea53df5fd18d5513U,
0x92746b9be2f8552cU, 0xb7118682dbb66a77U, 0xe4d5e82392a40515U,
0x8f05b1163ba6832dU, 0xb2c71d5bca9023f8U, 0xdf78e4b2bd342cf6U,
0x8bab8eefb6409c1aU, 0xae9672aba3d0c320U, 0xda3c0f568cc4f3e8U,
0x8865899617fb1871U, 0xaa7eebfb9df9de8dU, 0xd51ea6fa85785631U,
0x8533285c936b35deU, 0xa67ff273b8460356U, 0xd01fef10a657842cU,
0x8213f56a67f6b29bU, 0xa298f2c501f45f42U, 0xcb3f2f7642717713U,
0xfe0efb53d30dd4d7U, 0x9ec95d1463e8a506U, 0xc67bb4597ce2ce48U,
0xf81aa16fdc1b81daU, 0x9b10a4e5e9913128U, 0xc1d4ce1f63f57d72U,
0xf24a01a73cf2dccfU, 0x976e41088617ca01U, 0xbd49d14aa79dbc82U,
0xec9c459d51852ba2U, 0x93e1ab8252f33b45U, 0xb8da1662e7b00a17U,
0xe7109bfba19c0c9dU, 0x906a617d450187e2U, 0xb484f9dc9641e9daU,
0xe1a63853bbd26451U, 0x8d07e33455637eb2U, 0xb049dc016abc5e5fU,
0xdc5c5301c56b75f7U, 0x89b9b3e11b6329baU, 0xac2820d9623bf429U,
0xd732290fbacaf133U, 0x867f59a9d4bed6c0U, 0xa81f301449ee8c70U,
0xd226fc195c6a2f8cU, 0x83585d8fd9c25db7U, 0xa42e74f3d032f525U,
0xcd3a1230c43fb26fU, 0x80444b5e7aa7cf85U, 0xa0555e361951c366U,
0xc86ab5c39fa63440U, 0xfa856334878fc150U, 0x9c935e00d4b9d8d2U,
0xc3b8358109e84f07U, 0xf4a642e14c6262c8U, 0x98e7e9cccfbd7dbdU,
0xbf21e44003acdd2cU, 0xeeea5d5004981478U, 0x95527a5202df0ccbU,
0xbaa718e68396cffdU, 0xe950df20247c83fdU, 0x91d28b7416cdd27eU,
0xb6472e511c81471dU, 0xe3d8f9e563a198e5U, 0x8e679c2f5e44ff8fU,
};
const int16_t kPower10ExponentTable[] = {
-1200, -1196, -1193, -1190, -1186, -1183, -1180, -1176, -1173, -1170, -1166,
-1163, -1160, -1156, -1153, -1150, -1146, -1143, -1140, -1136, -1133, -1130,
-1127, -1123, -1120, -1117, -1113, -1110, -1107, -1103, -1100, -1097, -1093,
-1090, -1087, -1083, -1080, -1077, -1073, -1070, -1067, -1063, -1060, -1057,
-1053, -1050, -1047, -1043, -1040, -1037, -1034, -1030, -1027, -1024, -1020,
-1017, -1014, -1010, -1007, -1004, -1000, -997, -994, -990, -987, -984,
-980, -977, -974, -970, -967, -964, -960, -957, -954, -950, -947,
-944, -940, -937, -934, -931, -927, -924, -921, -917, -914, -911,
-907, -904, -901, -897, -894, -891, -887, -884, -881, -877, -874,
-871, -867, -864, -861, -857, -854, -851, -847, -844, -841, -838,
-834, -831, -828, -824, -821, -818, -814, -811, -808, -804, -801,
-798, -794, -791, -788, -784, -781, -778, -774, -771, -768, -764,
-761, -758, -754, -751, -748, -744, -741, -738, -735, -731, -728,
-725, -721, -718, -715, -711, -708, -705, -701, -698, -695, -691,
-688, -685, -681, -678, -675, -671, -668, -665, -661, -658, -655,
-651, -648, -645, -642, -638, -635, -632, -628, -625, -622, -618,
-615, -612, -608, -605, -602, -598, -595, -592, -588, -585, -582,
-578, -575, -572, -568, -565, -562, -558, -555, -552, -549, -545,
-542, -539, -535, -532, -529, -525, -522, -519, -515, -512, -509,
-505, -502, -499, -495, -492, -489, -485, -482, -479, -475, -472,
-469, -465, -462, -459, -455, -452, -449, -446, -442, -439, -436,
-432, -429, -426, -422, -419, -416, -412, -409, -406, -402, -399,
-396, -392, -389, -386, -382, -379, -376, -372, -369, -366, -362,
-359, -356, -353, -349, -346, -343, -339, -336, -333, -329, -326,
-323, -319, -316, -313, -309, -306, -303, -299, -296, -293, -289,
-286, -283, -279, -276, -273, -269, -266, -263, -259, -256, -253,
-250, -246, -243, -240, -236, -233, -230, -226, -223, -220, -216,
-213, -210, -206, -203, -200, -196, -193, -190, -186, -183, -180,
-176, -173, -170, -166, -163, -160, -157, -153, -150, -147, -143,
-140, -137, -133, -130, -127, -123, -120, -117, -113, -110, -107,
-103, -100, -97, -93, -90, -87, -83, -80, -77, -73, -70,
-67, -63, -60, -57, -54, -50, -47, -44, -40, -37, -34,
-30, -27, -24, -20, -17, -14, -10, -7, -4, 0, 3,
6, 10, 13, 16, 20, 23, 26, 30, 33, 36, 39,
43, 46, 49, 53, 56, 59, 63, 66, 69, 73, 76,
79, 83, 86, 89, 93, 96, 99, 103, 106, 109, 113,
116, 119, 123, 126, 129, 132, 136, 139, 142, 146, 149,
152, 156, 159, 162, 166, 169, 172, 176, 179, 182, 186,
189, 192, 196, 199, 202, 206, 209, 212, 216, 219, 222,
226, 229, 232, 235, 239, 242, 245, 249, 252, 255, 259,
262, 265, 269, 272, 275, 279, 282, 285, 289, 292, 295,
299, 302, 305, 309, 312, 315, 319, 322, 325, 328, 332,
335, 338, 342, 345, 348, 352, 355, 358, 362, 365, 368,
372, 375, 378, 382, 385, 388, 392, 395, 398, 402, 405,
408, 412, 415, 418, 422, 425, 428, 431, 435, 438, 441,
445, 448, 451, 455, 458, 461, 465, 468, 471, 475, 478,
481, 485, 488, 491, 495, 498, 501, 505, 508, 511, 515,
518, 521, 524, 528, 531, 534, 538, 541, 544, 548, 551,
554, 558, 561, 564, 568, 571, 574, 578, 581, 584, 588,
591, 594, 598, 601, 604, 608, 611, 614, 617, 621, 624,
627, 631, 634, 637, 641, 644, 647, 651, 654, 657, 661,
664, 667, 671, 674, 677, 681, 684, 687, 691, 694, 697,
701, 704, 707, 711, 714, 717, 720, 724, 727, 730, 734,
737, 740, 744, 747, 750, 754, 757, 760, 764, 767, 770,
774, 777, 780, 784, 787, 790, 794, 797, 800, 804, 807,
810, 813, 817, 820, 823, 827, 830, 833, 837, 840, 843,
847, 850, 853, 857, 860, 863, 867, 870, 873, 877, 880,
883, 887, 890, 893, 897, 900, 903, 907, 910, 913, 916,
920, 923, 926, 930, 933, 936, 940, 943, 946, 950, 953,
956, 960,
};
} // namespace
ABSL_NAMESPACE_END
} // namespace absl