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>
SignedDivisionByConstant(T d)16 MagicNumbersForDivision<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
52 template <class T>
UnsignedDivisionByConstant(T d,unsigned leading_zeros)53 MagicNumbersForDivision<T> UnsignedDivisionByConstant(T d,
54 unsigned leading_zeros) {
55 STATIC_ASSERT(static_cast<T>(0) < static_cast<T>(-1));
56 DCHECK(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
96 template struct V8_BASE_EXPORT MagicNumbersForDivision<uint32_t>;
97 template struct V8_BASE_EXPORT MagicNumbersForDivision<uint64_t>;
98
99 template MagicNumbersForDivision<uint32_t> SignedDivisionByConstant(uint32_t d);
100 template MagicNumbersForDivision<uint64_t> SignedDivisionByConstant(uint64_t d);
101
102 template MagicNumbersForDivision<uint32_t> UnsignedDivisionByConstant(
103 uint32_t d, unsigned leading_zeros);
104 template MagicNumbersForDivision<uint64_t> UnsignedDivisionByConstant(
105 uint64_t d, unsigned leading_zeros);
106
107 } // namespace base
108 } // namespace v8
109