1 /*
2 * Copyright (C) 2015 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 * http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17 #include "code_generator_utils.h"
18
19 #include "base/logging.h"
20
21 namespace art {
22
CalculateMagicAndShiftForDivRem(int64_t divisor,bool is_long,int64_t * magic,int * shift)23 void CalculateMagicAndShiftForDivRem(int64_t divisor, bool is_long,
24 int64_t* magic, int* shift) {
25 // It does not make sense to calculate magic and shift for zero divisor.
26 DCHECK_NE(divisor, 0);
27
28 /* Implementation according to H.S.Warren's "Hacker's Delight" (Addison Wesley, 2002)
29 * Chapter 10 and T.Grablund, P.L.Montogomery's "Division by Invariant Integers Using
30 * Multiplication" (PLDI 1994).
31 * The magic number M and shift S can be calculated in the following way:
32 * Let nc be the most positive value of numerator(n) such that nc = kd - 1,
33 * where divisor(d) >= 2.
34 * Let nc be the most negative value of numerator(n) such that nc = kd + 1,
35 * where divisor(d) <= -2.
36 * Thus nc can be calculated like:
37 * nc = exp + exp % d - 1, where d >= 2 and exp = 2^31 for int or 2^63 for long
38 * nc = -exp + (exp + 1) % d, where d >= 2 and exp = 2^31 for int or 2^63 for long
39 *
40 * So the shift p is the smallest p satisfying
41 * 2^p > nc * (d - 2^p % d), where d >= 2
42 * 2^p > nc * (d + 2^p % d), where d <= -2.
43 *
44 * The magic number M is calculated by
45 * M = (2^p + d - 2^p % d) / d, where d >= 2
46 * M = (2^p - d - 2^p % d) / d, where d <= -2.
47 *
48 * Notice that p is always bigger than or equal to 32 (resp. 64), so we just return 32 - p
49 * (resp. 64 - p) as the shift number S.
50 */
51
52 int64_t p = is_long ? 63 : 31;
53 const uint64_t exp = is_long ? (UINT64_C(1) << 63) : (UINT32_C(1) << 31);
54
55 // Initialize the computations.
56 uint64_t abs_d = (divisor >= 0) ? divisor : -divisor;
57 uint64_t sign_bit = is_long ? static_cast<uint64_t>(divisor) >> 63 :
58 static_cast<uint32_t>(divisor) >> 31;
59 uint64_t tmp = exp + sign_bit;
60 uint64_t abs_nc = tmp - 1 - (tmp % abs_d);
61 uint64_t quotient1 = exp / abs_nc;
62 uint64_t remainder1 = exp % abs_nc;
63 uint64_t quotient2 = exp / abs_d;
64 uint64_t remainder2 = exp % abs_d;
65
66 /*
67 * To avoid handling both positive and negative divisor, "Hacker's Delight"
68 * introduces a method to handle these 2 cases together to avoid duplication.
69 */
70 uint64_t delta;
71 do {
72 p++;
73 quotient1 = 2 * quotient1;
74 remainder1 = 2 * remainder1;
75 if (remainder1 >= abs_nc) {
76 quotient1++;
77 remainder1 = remainder1 - abs_nc;
78 }
79 quotient2 = 2 * quotient2;
80 remainder2 = 2 * remainder2;
81 if (remainder2 >= abs_d) {
82 quotient2++;
83 remainder2 = remainder2 - abs_d;
84 }
85 delta = abs_d - remainder2;
86 } while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
87
88 *magic = (divisor > 0) ? (quotient2 + 1) : (-quotient2 - 1);
89
90 if (!is_long) {
91 *magic = static_cast<int>(*magic);
92 }
93
94 *shift = is_long ? p - 64 : p - 32;
95 }
96
97 } // namespace art
98