about summary refs log tree commit diff
path: root/absl/numeric/int128.cc
blob: b605a87042c166bfcac7eb46111e13ad626e9aa0 (plain) (blame)
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
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
// 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
//
//      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/numeric/int128.h"

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

namespace absl {
ABSL_NAMESPACE_BEGIN

ABSL_DLL 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:
// https://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));
}

#if defined(__clang__) && !defined(__SSE3__)
// Workaround for clang bug: https://bugs.llvm.org/show_bug.cgi?id=38289
// Casting from long double to uint64_t is miscompiled and drops bits.
// It is more work, so only use when we need the workaround.
uint128 MakeUint128FromFloat(long double v) {
  // Go 50 bits at a time, that fits in a double
  static_assert(std::numeric_limits<double>::digits >= 50, "");
  static_assert(std::numeric_limits<long double>::digits <= 150, "");
  // Undefined behavior if v is not finite or cannot fit into uint128.
  assert(std::isfinite(v) && v > -1 && v < std::ldexp(1.0L, 128));

  v = std::ldexp(v, -100);
  uint64_t w0 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
  v = std::ldexp(v - static_cast<double>(w0), 50);
  uint64_t w1 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
  v = std::ldexp(v - static_cast<double>(w1), 50);
  uint64_t w2 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
  return (static_cast<uint128>(w0) << 100) | (static_cast<uint128>(w1) << 50) |
         static_cast<uint128>(w2);
}
#endif  // __clang__ && !__SSE3__
}  // 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 {

uint128 UnsignedAbsoluteValue(int128 v) {
  // Cast to uint128 before possibly negating because -Int128Min() is undefined.
  return Int128High64(v) < 0 ? -uint128(v) : uint128(v);
}

}  // namespace

#if !defined(ABSL_HAVE_INTRINSIC_INT128)
namespace {

template <typename T>
int128 MakeInt128FromFloat(T v) {
  // Conversion when v is NaN or cannot fit into int128 would be undefined
  // behavior if using an intrinsic 128-bit integer.
  assert(std::isfinite(v) && (std::numeric_limits<T>::max_exponent <= 127 ||
                              (v >= -std::ldexp(static_cast<T>(1), 127) &&
                               v < std::ldexp(static_cast<T>(1), 127))));

  // We must convert the absolute value and then negate as needed, because
  // floating point types are typically sign-magnitude. Otherwise, the
  // difference between the high and low 64 bits when interpreted as two's
  // complement overwhelms the precision of the mantissa.
  uint128 result = v < 0 ? -MakeUint128FromFloat(-v) : MakeUint128FromFloat(v);
  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(result)),
                    Uint128Low64(result));
}

}  // namespace

int128::int128(float v) : int128(MakeInt128FromFloat(v)) {}
int128::int128(double v) : int128(MakeInt128FromFloat(v)) {}
int128::int128(long double v) : int128(MakeInt128FromFloat(v)) {}

int128 operator/(int128 lhs, int128 rhs) {
  assert(lhs != Int128Min() || rhs != -1);  // UB on two's complement.

  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
             &quotient, &remainder);
  if ((Int128High64(lhs) < 0) != (Int128High64(rhs) < 0)) quotient = -quotient;
  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(quotient)),
                    Uint128Low64(quotient));
}

int128 operator%(int128 lhs, int128 rhs) {
  assert(lhs != Int128Min() || rhs != -1);  // UB on two's complement.

  uint128 quotient = 0;
  uint128 remainder = 0;
  DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
             &quotient, &remainder);
  if (Int128High64(lhs) < 0) remainder = -remainder;
  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(remainder)),
                    Uint128Low64(remainder));
}
#endif  // ABSL_HAVE_INTRINSIC_INT128

std::ostream& operator<<(std::ostream& os, int128 v) {
  std::ios_base::fmtflags flags = os.flags();
  std::string rep;

  // Add the sign if needed.
  bool print_as_decimal =
      (flags & std::ios::basefield) == std::ios::dec ||
      (flags & std::ios::basefield) == std::ios_base::fmtflags();
  if (print_as_decimal) {
    if (Int128High64(v) < 0) {
      rep = "-";
    } else if (flags & std::ios::showpos) {
      rep = "+";
    }
  }

  rep.append(Uint128ToFormattedString(
      print_as_decimal ? UnsignedAbsoluteValue(v) : uint128(v), os.flags()));

  // Add the requisite padding.
  std::streamsize width = os.width(0);
  if (static_cast<size_t>(width) > rep.size()) {
    switch (flags & std::ios::adjustfield) {
      case std::ios::left:
        rep.append(width - rep.size(), os.fill());
        break;
      case std::ios::internal:
        if (print_as_decimal && (rep[0] == '+' || rep[0] == '-')) {
          rep.insert(1, width - rep.size(), os.fill());
        } else if ((flags & std::ios::basefield) == std::ios::hex &&
                   (flags & std::ios::showbase) && v != 0) {
          rep.insert(2, width - rep.size(), os.fill());
        } else {
          rep.insert(0, width - rep.size(), os.fill());
        }
        break;
      default:  // std::ios::right
        rep.insert(0, width - rep.size(), os.fill());
        break;
    }
  }

  return os << rep;
}

ABSL_NAMESPACE_END
}  // 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;

constexpr bool numeric_limits<absl::int128>::is_specialized;
constexpr bool numeric_limits<absl::int128>::is_signed;
constexpr bool numeric_limits<absl::int128>::is_integer;
constexpr bool numeric_limits<absl::int128>::is_exact;
constexpr bool numeric_limits<absl::int128>::has_infinity;
constexpr bool numeric_limits<absl::int128>::has_quiet_NaN;
constexpr bool numeric_limits<absl::int128>::has_signaling_NaN;
constexpr float_denorm_style numeric_limits<absl::int128>::has_denorm;
constexpr bool numeric_limits<absl::int128>::has_denorm_loss;
constexpr float_round_style numeric_limits<absl::int128>::round_style;
constexpr bool numeric_limits<absl::int128>::is_iec559;
constexpr bool numeric_limits<absl::int128>::is_bounded;
constexpr bool numeric_limits<absl::int128>::is_modulo;
constexpr int numeric_limits<absl::int128>::digits;
constexpr int numeric_limits<absl::int128>::digits10;
constexpr int numeric_limits<absl::int128>::max_digits10;
constexpr int numeric_limits<absl::int128>::radix;
constexpr int numeric_limits<absl::int128>::min_exponent;
constexpr int numeric_limits<absl::int128>::min_exponent10;
constexpr int numeric_limits<absl::int128>::max_exponent;
constexpr int numeric_limits<absl::int128>::max_exponent10;
constexpr bool numeric_limits<absl::int128>::traps;
constexpr bool numeric_limits<absl::int128>::tinyness_before;
}  // namespace std