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
12 namespace v8 {
13 namespace base {
14
15 template <class T>
operator ==(const MagicNumbersForDivision & rhs) const16 bool MagicNumbersForDivision<T>::operator==(
17 const MagicNumbersForDivision& rhs) const {
18 return multiplier == rhs.multiplier && shift == rhs.shift && add == rhs.add;
19 }
20
21
22 template <class T>
SignedDivisionByConstant(T d)23 MagicNumbersForDivision<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
59 template <class T>
UnsignedDivisionByConstant(T d,unsigned leading_zeros)60 MagicNumbersForDivision<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
103 template struct MagicNumbersForDivision<uint32_t>;
104 template struct MagicNumbersForDivision<uint64_t>;
105
106 template MagicNumbersForDivision<uint32_t> SignedDivisionByConstant(uint32_t d);
107 template MagicNumbersForDivision<uint64_t> SignedDivisionByConstant(uint64_t d);
108
109 template MagicNumbersForDivision<uint32_t> UnsignedDivisionByConstant(
110 uint32_t d, unsigned leading_zeros);
111 template MagicNumbersForDivision<uint64_t> UnsignedDivisionByConstant(
112 uint64_t d, unsigned leading_zeros);
113
114 } // namespace base
115 } // namespace v8
116