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>
16MagicNumbersForDivision<T> SignedDivisionByConstant(T d) {
17  STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1));
18  DCHECK(d != static_cast<T>(-1) && d != 0 && d != 1);
19  const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8;
20  const T min = (static_cast<T>(1) << (bits - 1));
21  const bool neg = (min & d) != 0;
22  const T ad = neg ? (0 - d) : d;
23  const T t = min + (d >> (bits - 1));
24  const T anc = t - 1 - t % ad;  // Absolute value of nc
25  unsigned p = bits - 1;         // Init. p.
26  T q1 = min / anc;              // Init. q1 = 2**p/|nc|.
27  T r1 = min - q1 * anc;         // Init. r1 = rem(2**p, |nc|).
28  T q2 = min / ad;               // Init. q2 = 2**p/|d|.
29  T r2 = min - q2 * ad;          // Init. r2 = rem(2**p, |d|).
30  T delta;
31  do {
32    p = p + 1;
33    q1 = 2 * q1;      // Update q1 = 2**p/|nc|.
34    r1 = 2 * r1;      // Update r1 = rem(2**p, |nc|).
35    if (r1 >= anc) {  // Must be an unsigned comparison here.
36      q1 = q1 + 1;
37      r1 = r1 - anc;
38    }
39    q2 = 2 * q2;     // Update q2 = 2**p/|d|.
40    r2 = 2 * r2;     // Update r2 = rem(2**p, |d|).
41    if (r2 >= ad) {  // Must be an unsigned comparison here.
42      q2 = q2 + 1;
43      r2 = r2 - ad;
44    }
45    delta = ad - r2;
46  } while (q1 < delta || (q1 == delta && r1 == 0));
47  T mul = q2 + 1;
48  return MagicNumbersForDivision<T>(neg ? (0 - mul) : mul, p - bits, false);
49}
50
51
52template <class T>
53MagicNumbersForDivision<T> UnsignedDivisionByConstant(T d,
54                                                      unsigned leading_zeros) {
55  STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1));
56  DCHECK_NE(d, 0);
57  const unsigned bits = static_cast<unsigned>(sizeof(T)) * 8;
58  const T ones = ~static_cast<T>(0) >> leading_zeros;
59  const T min = static_cast<T>(1) << (bits - 1);
60  const T max = ~static_cast<T>(0) >> 1;
61  const T nc = ones - (ones - d) % d;
62  bool a = false;         // Init. "add" indicator.
63  unsigned p = bits - 1;  // Init. p.
64  T q1 = min / nc;        // Init. q1 = 2**p/nc
65  T r1 = min - q1 * nc;   // Init. r1 = rem(2**p,nc)
66  T q2 = max / d;         // Init. q2 = (2**p - 1)/d.
67  T r2 = max - q2 * d;    // Init. r2 = rem(2**p - 1, d).
68  T delta;
69  do {
70    p = p + 1;
71    if (r1 >= nc - r1) {
72      q1 = 2 * q1 + 1;
73      r1 = 2 * r1 - nc;
74    } else {
75      q1 = 2 * q1;
76      r1 = 2 * r1;
77    }
78    if (r2 + 1 >= d - r2) {
79      if (q2 >= max) a = true;
80      q2 = 2 * q2 + 1;
81      r2 = 2 * r2 + 1 - d;
82    } else {
83      if (q2 >= min) a = true;
84      q2 = 2 * q2;
85      r2 = 2 * r2 + 1;
86    }
87    delta = d - 1 - r2;
88  } while (p < bits * 2 && (q1 < delta || (q1 == delta && r1 == 0)));
89  return MagicNumbersForDivision<T>(q2 + 1, p - bits, a);
90}
91
92
93// -----------------------------------------------------------------------------
94// Instantiations.
95
96template struct EXPORT_TEMPLATE_DEFINE(V8_BASE_EXPORT)
97    MagicNumbersForDivision<uint32_t>;
98template struct EXPORT_TEMPLATE_DEFINE(V8_BASE_EXPORT)
99    MagicNumbersForDivision<uint64_t>;
100
101template EXPORT_TEMPLATE_DEFINE(V8_BASE_EXPORT)
102    MagicNumbersForDivision<uint32_t> SignedDivisionByConstant(uint32_t d);
103template EXPORT_TEMPLATE_DEFINE(V8_BASE_EXPORT)
104    MagicNumbersForDivision<uint64_t> SignedDivisionByConstant(uint64_t d);
105
106template EXPORT_TEMPLATE_DEFINE(V8_BASE_EXPORT)
107    MagicNumbersForDivision<uint32_t> UnsignedDivisionByConstant(
108        uint32_t d, unsigned leading_zeros);
109template EXPORT_TEMPLATE_DEFINE(V8_BASE_EXPORT)
110    MagicNumbersForDivision<uint64_t> UnsignedDivisionByConstant(
111        uint64_t d, unsigned leading_zeros);
112
113}  // namespace base
114}  // namespace v8
115