int128.cc 8.29 KB
Newer Older
wangdawei's avatar
wangdawei committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251
// Copyright 2017 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.

#include "absl/numeric/int128.h"

#include <stddef.h>
#include <cassert>
#include <iomanip>
#include <ostream>  // NOLINT(readability/streams)
#include <sstream>
#include <string>
#include <type_traits>

namespace absl {

const uint128 kuint128max = MakeUint128(std::numeric_limits<uint64_t>::max(),
                                        std::numeric_limits<uint64_t>::max());

namespace {

// Returns the 0-based position of the last set bit (i.e., most significant bit)
// in the given uint64_t. The argument may not be 0.
//
// For example:
//   Given: 5 (decimal) == 101 (binary)
//   Returns: 2
#define STEP(T, n, pos, sh)                   \
  do {                                        \
    if ((n) >= (static_cast<T>(1) << (sh))) { \
      (n) = (n) >> (sh);                      \
      (pos) |= (sh);                          \
    }                                         \
  } while (0)
static inline int Fls64(uint64_t n) {
  assert(n != 0);
  int pos = 0;
  STEP(uint64_t, n, pos, 0x20);
  uint32_t n32 = static_cast<uint32_t>(n);
  STEP(uint32_t, n32, pos, 0x10);
  STEP(uint32_t, n32, pos, 0x08);
  STEP(uint32_t, n32, pos, 0x04);
  return pos + ((uint64_t{0x3333333322221100} >> (n32 << 2)) & 0x3);
}
#undef STEP

// Like Fls64() above, but returns the 0-based position of the last set bit
// (i.e., most significant bit) in the given uint128. The argument may not be 0.
static inline int Fls128(uint128 n) {
  if (uint64_t hi = Uint128High64(n)) {
    return Fls64(hi) + 64;
  }
  return Fls64(Uint128Low64(n));
}

// Long division/modulo for uint128 implemented using the shift-subtract
// division algorithm adapted from:
// http://stackoverflow.com/questions/5386377/division-without-using
void DivModImpl(uint128 dividend, uint128 divisor, uint128* quotient_ret,
                uint128* remainder_ret) {
  assert(divisor != 0);

  if (divisor > dividend) {
    *quotient_ret = 0;
    *remainder_ret = dividend;
    return;
  }

  if (divisor == dividend) {
    *quotient_ret = 1;
    *remainder_ret = 0;
    return;
  }

  uint128 denominator = divisor;
  uint128 quotient = 0;

  // Left aligns the MSB of the denominator and the dividend.
  const int shift = Fls128(dividend) - Fls128(denominator);
  denominator <<= shift;

  // Uses shift-subtract algorithm to divide dividend by denominator. The
  // remainder will be left in dividend.
  for (int i = 0; i <= shift; ++i) {
    quotient <<= 1;
    if (dividend >= denominator) {
      dividend -= denominator;
      quotient |= 1;
    }
    denominator >>= 1;
  }

  *quotient_ret = quotient;
  *remainder_ret = dividend;
}

template <typename T>
uint128 MakeUint128FromFloat(T v) {
  static_assert(std::is_floating_point<T>::value, "");

  // Rounding behavior is towards zero, same as for built-in types.

  // Undefined behavior if v is NaN or cannot fit into uint128.
  assert(std::isfinite(v) && v > -1 &&
         (std::numeric_limits<T>::max_exponent <= 128 ||
          v < std::ldexp(static_cast<T>(1), 128)));

  if (v >= std::ldexp(static_cast<T>(1), 64)) {
    uint64_t hi = static_cast<uint64_t>(std::ldexp(v, -64));
    uint64_t lo = static_cast<uint64_t>(v - std::ldexp(static_cast<T>(hi), 64));
    return MakeUint128(hi, lo);
  }

  return MakeUint128(0, static_cast<uint64_t>(v));
}
}  // namespace

uint128::uint128(float v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(double v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(long double v) : uint128(MakeUint128FromFloat(v)) {}

uint128 operator/(uint128 lhs, uint128 rhs) {
#if defined(ABSL_HAVE_INTRINSIC_INT128)
  return static_cast<unsigned __int128>(lhs) /
         static_cast<unsigned __int128>(rhs);
#else  // ABSL_HAVE_INTRINSIC_INT128
  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(lhs, rhs, &quotient, &remainder);
  return quotient;
#endif  // ABSL_HAVE_INTRINSIC_INT128
}
uint128 operator%(uint128 lhs, uint128 rhs) {
#if defined(ABSL_HAVE_INTRINSIC_INT128)
  return static_cast<unsigned __int128>(lhs) %
         static_cast<unsigned __int128>(rhs);
#else  // ABSL_HAVE_INTRINSIC_INT128
  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(lhs, rhs, &quotient, &remainder);
  return remainder;
#endif  // ABSL_HAVE_INTRINSIC_INT128
}

namespace {

std::string Uint128ToFormattedString(uint128 v, std::ios_base::fmtflags flags) {
  // Select a divisor which is the largest power of the base < 2^64.
  uint128 div;
  int div_base_log;
  switch (flags & std::ios::basefield) {
    case std::ios::hex:
      div = 0x1000000000000000;  // 16^15
      div_base_log = 15;
      break;
    case std::ios::oct:
      div = 01000000000000000000000;  // 8^21
      div_base_log = 21;
      break;
    default:  // std::ios::dec
      div = 10000000000000000000u;  // 10^19
      div_base_log = 19;
      break;
  }

  // Now piece together the uint128 representation from three chunks of the
  // original value, each less than "div" and therefore representable as a
  // uint64_t.
  std::ostringstream os;
  std::ios_base::fmtflags copy_mask =
      std::ios::basefield | std::ios::showbase | std::ios::uppercase;
  os.setf(flags & copy_mask, copy_mask);
  uint128 high = v;
  uint128 low;
  DivModImpl(high, div, &high, &low);
  uint128 mid;
  DivModImpl(high, div, &high, &mid);
  if (Uint128Low64(high) != 0) {
    os << Uint128Low64(high);
    os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
    os << Uint128Low64(mid);
    os << std::setw(div_base_log);
  } else if (Uint128Low64(mid) != 0) {
    os << Uint128Low64(mid);
    os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
  }
  os << Uint128Low64(low);
  return os.str();
}

}  // namespace

std::ostream& operator<<(std::ostream& os, uint128 v) {
  std::ios_base::fmtflags flags = os.flags();
  std::string rep = Uint128ToFormattedString(v, flags);

  // Add the requisite padding.
  std::streamsize width = os.width(0);
  if (static_cast<size_t>(width) > rep.size()) {
    std::ios::fmtflags adjustfield = flags & std::ios::adjustfield;
    if (adjustfield == std::ios::left) {
      rep.append(width - rep.size(), os.fill());
    } else if (adjustfield == std::ios::internal &&
               (flags & std::ios::showbase) &&
               (flags & std::ios::basefield) == std::ios::hex && v != 0) {
      rep.insert(2, width - rep.size(), os.fill());
    } else {
      rep.insert(0, width - rep.size(), os.fill());
    }
  }

  return os << rep;
}

}  // namespace absl

namespace std {
constexpr bool numeric_limits<absl::uint128>::is_specialized;
constexpr bool numeric_limits<absl::uint128>::is_signed;
constexpr bool numeric_limits<absl::uint128>::is_integer;
constexpr bool numeric_limits<absl::uint128>::is_exact;
constexpr bool numeric_limits<absl::uint128>::has_infinity;
constexpr bool numeric_limits<absl::uint128>::has_quiet_NaN;
constexpr bool numeric_limits<absl::uint128>::has_signaling_NaN;
constexpr float_denorm_style numeric_limits<absl::uint128>::has_denorm;
constexpr bool numeric_limits<absl::uint128>::has_denorm_loss;
constexpr float_round_style numeric_limits<absl::uint128>::round_style;
constexpr bool numeric_limits<absl::uint128>::is_iec559;
constexpr bool numeric_limits<absl::uint128>::is_bounded;
constexpr bool numeric_limits<absl::uint128>::is_modulo;
constexpr int numeric_limits<absl::uint128>::digits;
constexpr int numeric_limits<absl::uint128>::digits10;
constexpr int numeric_limits<absl::uint128>::max_digits10;
constexpr int numeric_limits<absl::uint128>::radix;
constexpr int numeric_limits<absl::uint128>::min_exponent;
constexpr int numeric_limits<absl::uint128>::min_exponent10;
constexpr int numeric_limits<absl::uint128>::max_exponent;
constexpr int numeric_limits<absl::uint128>::max_exponent10;
constexpr bool numeric_limits<absl::uint128>::traps;
constexpr bool numeric_limits<absl::uint128>::tinyness_before;
}  // namespace std