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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.
#ifndef ABSL_STRINGS_INTERNAL_CHARCONV_BIGINT_H_
#define ABSL_STRINGS_INTERNAL_CHARCONV_BIGINT_H_
#include <algorithm>
#include <cstdint>
#include <iostream>
#include <string>
#include "absl/base/config.h"
#include "absl/strings/ascii.h"
#include "absl/strings/internal/charconv_parse.h"
#include "absl/strings/string_view.h"
namespace absl {
ABSL_NAMESPACE_BEGIN
namespace strings_internal {
// The largest power that 5 that can be raised to, and still fit in a uint32_t.
constexpr int kMaxSmallPowerOfFive = 13;
// The largest power that 10 that can be raised to, and still fit in a uint32_t.
constexpr int kMaxSmallPowerOfTen = 9;
ABSL_DLL extern const uint32_t
kFiveToNth[kMaxSmallPowerOfFive + 1];
ABSL_DLL extern const uint32_t kTenToNth[kMaxSmallPowerOfTen + 1];
// Large, fixed-width unsigned integer.
//
// Exact rounding for decimal-to-binary floating point conversion requires very
// large integer math, but a design goal of absl::from_chars is to avoid
// allocating memory. The integer precision needed for decimal-to-binary
// conversions is large but bounded, so a huge fixed-width integer class
// suffices.
//
// This is an intentionally limited big integer class. Only needed operations
// are implemented. All storage lives in an array data member, and all
// arithmetic is done in-place, to avoid requiring separate storage for operand
// and result.
//
// This is an internal class. Some methods live in the .cc file, and are
// instantiated only for the values of max_words we need.
template <int max_words>
class BigUnsigned {
public:
static_assert(max_words == 4 || max_words == 84,
"unsupported max_words value");
BigUnsigned() : size_(0), words_{} {}
explicit constexpr BigUnsigned(uint64_t v)
: size_((v >> 32) ? 2 : v ? 1 : 0),
words_{static_cast<uint32_t>(v & 0xffffffffu),
static_cast<uint32_t>(v >> 32)} {}
// Constructs a BigUnsigned from the given string_view containing a decimal
// value. If the input string is not a decimal integer, constructs a 0
// instead.
explicit BigUnsigned(absl::string_view sv) : size_(0), words_{} {
// Check for valid input, returning a 0 otherwise. This is reasonable
// behavior only because this constructor is for unit tests.
if (std::find_if_not(sv.begin(), sv.end(), ascii_isdigit) != sv.end() ||
sv.empty()) {
return;
}
int exponent_adjust =
ReadDigits(sv.data(), sv.data() + sv.size(), Digits10() + 1);
if (exponent_adjust > 0) {
MultiplyByTenToTheNth(exponent_adjust);
}
}
// Loads the mantissa value of a previously-parsed float.
//
// Returns the associated decimal exponent. The value of the parsed float is
// exactly *this * 10**exponent.
int ReadFloatMantissa(const ParsedFloat& fp, int significant_digits);
// Returns the number of decimal digits of precision this type provides. All
// numbers with this many decimal digits or fewer are representable by this
// type.
//
// Analagous to std::numeric_limits<BigUnsigned>::digits10.
static constexpr int Digits10() {
// 9975007/1035508 is very slightly less than log10(2**32).
return static_cast<uint64_t>(max_words) * 9975007 / 1035508;
}
// Shifts left by the given number of bits.
void ShiftLeft(int count) {
if (count > 0) {
const int word_shift = count / 32;
if (word_shift >= max_words) {
SetToZero();
return;
}
size_ = (std::min)(size_ + word_shift, max_words);
count %= 32;
if (count == 0) {
std::copy_backward(words_, words_ + size_ - word_shift, words_ + size_);
} else {
for (int i = (std::min)(size_, max_words - 1); i > word_shift; --i) {
words_[i] = (words_[i - word_shift] << count) |
(words_[i - word_shift - 1] >> (32 - count));
}
words_[word_shift] = words_[0] << count;
// Grow size_ if necessary.
if (size_ < max_words && words_[size_]) {
++size_;
}
}
std::fill(words_, words_ + word_shift, 0u);
}
}
// Multiplies by v in-place.
void MultiplyBy(uint32_t v) {
if (size_ == 0 || v == 1) {
return;
}
if (v == 0) {
SetToZero();
return;
}
const uint64_t factor = v;
uint64_t window = 0;
for (int i = 0; i < size_; ++i) {
window += factor * words_[i];
words_[i] = window & 0xffffffff;
window >>= 32;
}
// If carry bits remain and there's space for them, grow size_.
if (window && size_ < max_words) {
words_[size_] = window & 0xffffffff;
++size_;
}
}
void MultiplyBy(uint64_t v) {
uint32_t words[2];
words[0] = static_cast<uint32_t>(v);
words[1] = static_cast<uint32_t>(v >> 32);
if (words[1] == 0) {
MultiplyBy(words[0]);
} else {
MultiplyBy(2, words);
}
}
// Multiplies in place by 5 to the power of n. n must be non-negative.
void MultiplyByFiveToTheNth(int n) {
while (n >= kMaxSmallPowerOfFive) {
MultiplyBy(kFiveToNth[kMaxSmallPowerOfFive]);
n -= kMaxSmallPowerOfFive;
}
if (n > 0) {
MultiplyBy(kFiveToNth[n]);
}
}
// Multiplies in place by 10 to the power of n. n must be non-negative.
void MultiplyByTenToTheNth(int n) {
if (n > kMaxSmallPowerOfTen) {
// For large n, raise to a power of 5, then shift left by the same amount.
// (10**n == 5**n * 2**n.) This requires fewer multiplications overall.
MultiplyByFiveToTheNth(n);
ShiftLeft(n);
} else if (n > 0) {
// We can do this more quickly for very small N by using a single
// multiplication.
MultiplyBy(kTenToNth[n]);
}
}
// Returns the value of 5**n, for non-negative n. This implementation uses
// a lookup table, and is faster then seeding a BigUnsigned with 1 and calling
// MultiplyByFiveToTheNth().
static BigUnsigned FiveToTheNth(int n);
// Multiplies by another BigUnsigned, in-place.
template <int M>
void MultiplyBy(const BigUnsigned<M>& other) {
MultiplyBy(other.size(), other.words());
}
void SetToZero() {
std::fill(words_, words_ + size_, 0u);
size_ = 0;
}
// Returns the value of the nth word of this BigUnsigned. This is
// range-checked, and returns 0 on out-of-bounds accesses.
uint32_t GetWord(int index) const {
if (index < 0 || index >= size_) {
return 0;
}
return words_[index];
}
// Returns this integer as a decimal string. This is not used in the decimal-
// to-binary conversion; it is intended to aid in testing.
std::string ToString() const;
int size() const { return size_; }
const uint32_t* words() const { return words_; }
private:
// Reads the number between [begin, end), possibly containing a decimal point,
// into this BigUnsigned.
//
// Callers are required to ensure [begin, end) contains a valid number, with
// one or more decimal digits and at most one decimal point. This routine
// will behave unpredictably if these preconditions are not met.
//
// Only the first `significant_digits` digits are read. Digits beyond this
// limit are "sticky": If the final significant digit is 0 or 5, and if any
// dropped digit is nonzero, then that final significant digit is adjusted up
// to 1 or 6. This adjustment allows for precise rounding.
//
// Returns `exponent_adjustment`, a power-of-ten exponent adjustment to
// account for the decimal point and for dropped significant digits. After
// this function returns,
// actual_value_of_parsed_string ~= *this * 10**exponent_adjustment.
int ReadDigits(const char* begin, const char* end, int significant_digits);
// Performs a step of big integer multiplication. This computes the full
// (64-bit-wide) values that should be added at the given index (step), and
// adds to that location in-place.
//
// Because our math all occurs in place, we must multiply starting from the
// highest word working downward. (This is a bit more expensive due to the
// extra carries involved.)
//
// This must be called in steps, for each word to be calculated, starting from
// the high end and working down to 0. The first value of `step` should be
// `std::min(original_size + other.size_ - 2, max_words - 1)`.
// The reason for this expression is that multiplying the i'th word from one
// multiplicand and the j'th word of another multiplicand creates a
// two-word-wide value to be stored at the (i+j)'th element. The highest
// word indices we will access are `original_size - 1` from this object, and
// `other.size_ - 1` from our operand. Therefore,
// `original_size + other.size_ - 2` is the first step we should calculate,
// but limited on an upper bound by max_words.
// Working from high-to-low ensures that we do not overwrite the portions of
// the initial value of *this which are still needed for later steps.
//
// Once called with step == 0, *this contains the result of the
// multiplication.
//
// `original_size` is the size_ of *this before the first call to
// MultiplyStep(). `other_words` and `other_size` are the contents of our
// operand. `step` is the step to perform, as described above.
void MultiplyStep(int original_size, const uint32_t* other_words,
int other_size, int step);
void MultiplyBy(int other_size, const uint32_t* other_words) {
const int original_size = size_;
const int first_step =
(std::min)(original_size + other_size - 2, max_words - 1);
for (int step = first_step; step >= 0; --step) {
MultiplyStep(original_size, other_words, other_size, step);
}
}
// Adds a 32-bit value to the index'th word, with carry.
void AddWithCarry(int index, uint32_t value) {
if (value) {
while (index < max_words && value > 0) {
words_[index] += value;
// carry if we overflowed in this word:
if (value > words_[index]) {
value = 1;
++index;
} else {
value = 0;
}
}
size_ = (std::min)(max_words, (std::max)(index + 1, size_));
}
}
void AddWithCarry(int index, uint64_t value) {
if (value && index < max_words) {
uint32_t high = value >> 32;
uint32_t low = value & 0xffffffff;
words_[index] += low;
if (words_[index] < low) {
++high;
if (high == 0) {
// Carry from the low word caused our high word to overflow.
// Short circuit here to do the right thing.
AddWithCarry(index + 2, static_cast<uint32_t>(1));
return;
}
}
if (high > 0) {
AddWithCarry(index + 1, high);
} else {
// Normally 32-bit AddWithCarry() sets size_, but since we don't call
// it when `high` is 0, do it ourselves here.
size_ = (std::min)(max_words, (std::max)(index + 1, size_));
}
}
}
// Divide this in place by a constant divisor. Returns the remainder of the
// division.
template <uint32_t divisor>
uint32_t DivMod() {
uint64_t accumulator = 0;
for (int i = size_ - 1; i >= 0; --i) {
accumulator <<= 32;
accumulator += words_[i];
// accumulator / divisor will never overflow an int32_t in this loop
words_[i] = static_cast<uint32_t>(accumulator / divisor);
accumulator = accumulator % divisor;
}
while (size_ > 0 && words_[size_ - 1] == 0) {
--size_;
}
return static_cast<uint32_t>(accumulator);
}
// The number of elements in words_ that may carry significant values.
// All elements beyond this point are 0.
//
// When size_ is 0, this BigUnsigned stores the value 0.
// When size_ is nonzero, is *not* guaranteed that words_[size_ - 1] is
// nonzero. This can occur due to overflow truncation.
// In particular, x.size_ != y.size_ does *not* imply x != y.
int size_;
uint32_t words_[max_words];
};
// Compares two big integer instances.
//
// Returns -1 if lhs < rhs, 0 if lhs == rhs, and 1 if lhs > rhs.
template <int N, int M>
int Compare(const BigUnsigned<N>& lhs, const BigUnsigned<M>& rhs) {
int limit = (std::max)(lhs.size(), rhs.size());
for (int i = limit - 1; i >= 0; --i) {
const uint32_t lhs_word = lhs.GetWord(i);
const uint32_t rhs_word = rhs.GetWord(i);
if (lhs_word < rhs_word) {
return -1;
} else if (lhs_word > rhs_word) {
return 1;
}
}
return 0;
}
template <int N, int M>
bool operator==(const BigUnsigned<N>& lhs, const BigUnsigned<M>& rhs) {
int limit = (std::max)(lhs.size(), rhs.size());
for (int i = 0; i < limit; ++i) {
if (lhs.GetWord(i) != rhs.GetWord(i)) {
return false;
}
}
return true;
}
template <int N, int M>
bool operator!=(const BigUnsigned<N>& lhs, const BigUnsigned<M>& rhs) {
return !(lhs == rhs);
}
template <int N, int M>
bool operator<(const BigUnsigned<N>& lhs, const BigUnsigned<M>& rhs) {
return Compare(lhs, rhs) == -1;
}
template <int N, int M>
bool operator>(const BigUnsigned<N>& lhs, const BigUnsigned<M>& rhs) {
return rhs < lhs;
}
template <int N, int M>
bool operator<=(const BigUnsigned<N>& lhs, const BigUnsigned<M>& rhs) {
return !(rhs < lhs);
}
template <int N, int M>
bool operator>=(const BigUnsigned<N>& lhs, const BigUnsigned<M>& rhs) {
return !(lhs < rhs);
}
// Output operator for BigUnsigned, for testing purposes only.
template <int N>
std::ostream& operator<<(std::ostream& os, const BigUnsigned<N>& num) {
return os << num.ToString();
}
// Explicit instantiation declarations for the sizes of BigUnsigned that we
// are using.
//
// For now, the choices of 4 and 84 are arbitrary; 4 is a small value that is
// still bigger than an int128, and 84 is a large value we will want to use
// in the from_chars implementation.
//
// Comments justifying the use of 84 belong in the from_chars implementation,
// and will be added in a follow-up CL.
extern template class BigUnsigned<4>;
extern template class BigUnsigned<84>;
} // namespace strings_internal
ABSL_NAMESPACE_END
} // namespace absl
#endif // ABSL_STRINGS_INTERNAL_CHARCONV_BIGINT_H_