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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