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+// 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
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef ABSL_STRINGS_INTERNAL_CHARCONV_BIGINT_H_
+#define ABSL_STRINGS_INTERNAL_CHARCONV_BIGINT_H_
+
+#include <algorithm>
+#include <cstdint>
+#include <iostream>
+#include <string>
+
+#include "absl/strings/ascii.h"
+#include "absl/strings/internal/charconv_parse.h"
+#include "absl/strings/string_view.h"
+
+namespace absl {
+inline namespace lts_2018_06_20 {
+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;
+
+extern const uint32_t kFiveToNth[kMaxSmallPowerOfFive + 1];
+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 BigUnsigned(uint32_t v) : size_(v > 0 ? 1 : 0), words_{v} {}
+ explicit BigUnsigned(uint64_t v)
+ : size_(0),
+ words_{static_cast<uint32_t>(v & 0xffffffff),
+ static_cast<uint32_t>(v >> 32)} {
+ if (words_[1]) {
+ size_ = 2;
+ } else if (words_[0]) {
+ size_ = 1;
+ }
+ }
+
+ // Constructs a BigUnsigned from the given string_view containing a decimal
+ // value. If the input std::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 std::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
+} // inline namespace lts_2018_06_20
+} // namespace absl
+
+#endif // ABSL_STRINGS_INTERNAL_CHARCONV_BIGINT_H_
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