tor-browser

charconv_bigint.h (15130B)

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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
//
//      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 <ostream>
#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.
 //
 // Analogous 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) {
// https://gcc.gnu.org/bugzilla/show_bug.cgi?id=warray-bounds
// shows a lot of bogus -Warray-bounds warnings under GCC.
// This is not the only one in Abseil.
#if ABSL_INTERNAL_HAVE_MIN_GNUC_VERSION(14, 0)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Warray-bounds"
#endif
       std::copy_backward(words_, words_ + size_ - word_shift, words_ + size_);
#if ABSL_INTERNAL_HAVE_MIN_GNUC_VERSION(14, 0)
#pragma GCC diagnostic pop
#endif
     } 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_n(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_n(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_