1// Copyright 2014 the V8 project authors. All rights reserved.
2// Use of this source code is governed by a BSD-style license that can be
3// found in the LICENSE file.
4
5#include "src/base/division-by-constant.h"
6
7#include <stdint.h>
8
9#include "src/base/logging.h"
10#include "src/base/macros.h"
11
12namespace v8 {
13namespace base {
14
15template <class T>
16bool MagicNumbersForDivision<T>::operator==(
17    const MagicNumbersForDivision& rhs) const {
18  return multiplier == rhs.multiplier && shift == rhs.shift && add == rhs.add;
19}
20
21
22template <class T>
23MagicNumbersForDivision<T> SignedDivisionByConstant(T d) {
24  STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1));
25  DCHECK(d != static_cast<T>(-1) && d != 0 && d != 1);
26  const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8;
27  const T min = (static_cast<T>(1) << (bits - 1));
28  const bool neg = (min & d) != 0;
29  const T ad = neg ? (0 - d) : d;
30  const T t = min + (d >> (bits - 1));
31  const T anc = t - 1 - t % ad;  // Absolute value of nc
32  unsigned p = bits - 1;         // Init. p.
33  T q1 = min / anc;              // Init. q1 = 2**p/|nc|.
34  T r1 = min - q1 * anc;         // Init. r1 = rem(2**p, |nc|).
35  T q2 = min / ad;               // Init. q2 = 2**p/|d|.
36  T r2 = min - q2 * ad;          // Init. r2 = rem(2**p, |d|).
37  T delta;
38  do {
39    p = p + 1;
40    q1 = 2 * q1;      // Update q1 = 2**p/|nc|.
41    r1 = 2 * r1;      // Update r1 = rem(2**p, |nc|).
42    if (r1 >= anc) {  // Must be an unsigned comparison here.
43      q1 = q1 + 1;
44      r1 = r1 - anc;
45    }
46    q2 = 2 * q2;     // Update q2 = 2**p/|d|.
47    r2 = 2 * r2;     // Update r2 = rem(2**p, |d|).
48    if (r2 >= ad) {  // Must be an unsigned comparison here.
49      q2 = q2 + 1;
50      r2 = r2 - ad;
51    }
52    delta = ad - r2;
53  } while (q1 < delta || (q1 == delta && r1 == 0));
54  T mul = q2 + 1;
55  return {neg ? (0 - mul) : mul, p - bits, false};
56}
57
58
59template <class T>
60MagicNumbersForDivision<T> UnsignedDivisionByConstant(T d,
61                                                      unsigned leading_zeros) {
62  STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1));
63  DCHECK(d != 0);
64  const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8;
65  const T ones = ~static_cast<T>(0) >> leading_zeros;
66  const T min = static_cast<T>(1) << (bits - 1);
67  const T max = ~static_cast<T>(0) >> 1;
68  const T nc = ones - (ones - d) % d;
69  bool a = false;         // Init. "add" indicator.
70  unsigned p = bits - 1;  // Init. p.
71  T q1 = min / nc;        // Init. q1 = 2**p/nc
72  T r1 = min - q1 * nc;   // Init. r1 = rem(2**p,nc)
73  T q2 = max / d;         // Init. q2 = (2**p - 1)/d.
74  T r2 = max - q2 * d;    // Init. r2 = rem(2**p - 1, d).
75  T delta;
76  do {
77    p = p + 1;
78    if (r1 >= nc - r1) {
79      q1 = 2 * q1 + 1;
80      r1 = 2 * r1 - nc;
81    } else {
82      q1 = 2 * q1;
83      r1 = 2 * r1;
84    }
85    if (r2 + 1 >= d - r2) {
86      if (q2 >= max) a = true;
87      q2 = 2 * q2 + 1;
88      r2 = 2 * r2 + 1 - d;
89    } else {
90      if (q2 >= min) a = true;
91      q2 = 2 * q2;
92      r2 = 2 * r2 + 1;
93    }
94    delta = d - 1 - r2;
95  } while (p < bits * 2 && (q1 < delta || (q1 == delta && r1 == 0)));
96  return {q2 + 1, p - bits, a};
97}
98
99
100// -----------------------------------------------------------------------------
101// Instantiations.
102
103template struct MagicNumbersForDivision<uint32_t>;
104template struct MagicNumbersForDivision<uint64_t>;
105
106template MagicNumbersForDivision<uint32_t> SignedDivisionByConstant(uint32_t d);
107template MagicNumbersForDivision<uint64_t> SignedDivisionByConstant(uint64_t d);
108
109template MagicNumbersForDivision<uint32_t> UnsignedDivisionByConstant(
110    uint32_t d, unsigned leading_zeros);
111template MagicNumbersForDivision<uint64_t> UnsignedDivisionByConstant(
112    uint64_t d, unsigned leading_zeros);
113
114}  // namespace base
115}  // namespace v8
116