1 /*
2 * Copyright © 2018 Advanced Micro Devices, Inc.
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining a
5 * copy of this software and associated documentation files (the "Software"),
6 * to deal in the Software without restriction, including without limitation
7 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
8 * and/or sell copies of the Software, and to permit persons to whom the
9 * Software is furnished to do so, subject to the following conditions:
10 *
11 * The above copyright notice and this permission notice (including the next
12 * paragraph) shall be included in all copies or substantial portions of the
13 * Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
18 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
20 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
21 * IN THE SOFTWARE.
22 */
23
24 /* Imported from:
25 * https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c
26 * Paper:
27 * http://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf
28 *
29 * The author, ridiculous_fish, wrote:
30 *
31 * ''Reference implementations of computing and using the "magic number"
32 * approach to dividing by constants, including codegen instructions.
33 * The unsigned division incorporates the "round down" optimization per
34 * ridiculous_fish.
35 *
36 * This is free and unencumbered software. Any copyright is dedicated
37 * to the Public Domain.''
38 */
39
40 #include "fast_idiv_by_const.h"
41 #include "u_math.h"
42 #include "util/macros.h"
43 #include <limits.h>
44 #include <assert.h>
45
46 struct util_fast_udiv_info
util_compute_fast_udiv_info(uint64_t D,unsigned num_bits,unsigned UINT_BITS)47 util_compute_fast_udiv_info(uint64_t D, unsigned num_bits, unsigned UINT_BITS)
48 {
49 /* The numerator must fit in a uint64_t */
50 assert(num_bits > 0 && num_bits <= UINT_BITS);
51 assert(D != 0);
52
53 /* The eventual result */
54 struct util_fast_udiv_info result;
55
56 if (util_is_power_of_two_or_zero64(D)) {
57 unsigned div_shift = util_logbase2_64(D);
58
59 if (div_shift) {
60 /* Dividing by a power of two. */
61 result.multiplier = 1ull << (UINT_BITS - div_shift);
62 result.pre_shift = 0;
63 result.post_shift = 0;
64 result.increment = 0;
65 return result;
66 } else {
67 /* Dividing by 1. */
68 /* Assuming: floor((num + 1) * (2^32 - 1) / 2^32) = num */
69 result.multiplier = u_uintN_max(UINT_BITS);
70 result.pre_shift = 0;
71 result.post_shift = 0;
72 result.increment = 1;
73 return result;
74 }
75 }
76
77 /* The extra shift implicit in the difference between UINT_BITS and num_bits
78 */
79 const unsigned extra_shift = UINT_BITS - num_bits;
80
81 /* The initial power of 2 is one less than the first one that can possibly
82 * work.
83 */
84 const uint64_t initial_power_of_2 = (uint64_t)1 << (UINT_BITS-1);
85
86 /* The remainder and quotient of our power of 2 divided by d */
87 uint64_t quotient = initial_power_of_2 / D;
88 uint64_t remainder = initial_power_of_2 % D;
89
90 /* ceil(log_2 D) */
91 unsigned ceil_log_2_D;
92
93 /* The magic info for the variant "round down" algorithm */
94 uint64_t down_multiplier = 0;
95 unsigned down_exponent = 0;
96 int has_magic_down = 0;
97
98 /* Compute ceil(log_2 D) */
99 ceil_log_2_D = 0;
100 uint64_t tmp;
101 for (tmp = D; tmp > 0; tmp >>= 1)
102 ceil_log_2_D += 1;
103
104
105 /* Begin a loop that increments the exponent, until we find a power of 2
106 * that works.
107 */
108 unsigned exponent;
109 for (exponent = 0; ; exponent++) {
110 /* Quotient and remainder is from previous exponent; compute it for this
111 * exponent.
112 */
113 if (remainder >= D - remainder) {
114 /* Doubling remainder will wrap around D */
115 quotient = quotient * 2 + 1;
116 remainder = remainder * 2 - D;
117 } else {
118 /* Remainder will not wrap */
119 quotient = quotient * 2;
120 remainder = remainder * 2;
121 }
122
123 /* We're done if this exponent works for the round_up algorithm.
124 * Note that exponent may be larger than the maximum shift supported,
125 * so the check for >= ceil_log_2_D is critical.
126 */
127 if ((exponent + extra_shift >= ceil_log_2_D) ||
128 (D - remainder) <= ((uint64_t)1 << (exponent + extra_shift)))
129 break;
130
131 /* Set magic_down if we have not set it yet and this exponent works for
132 * the round_down algorithm
133 */
134 if (!has_magic_down &&
135 remainder <= ((uint64_t)1 << (exponent + extra_shift))) {
136 has_magic_down = 1;
137 down_multiplier = quotient;
138 down_exponent = exponent;
139 }
140 }
141
142 if (exponent < ceil_log_2_D) {
143 /* magic_up is efficient */
144 result.multiplier = quotient + 1;
145 result.pre_shift = 0;
146 result.post_shift = exponent;
147 result.increment = 0;
148 } else if (D & 1) {
149 /* Odd divisor, so use magic_down, which must have been set */
150 assert(has_magic_down);
151 result.multiplier = down_multiplier;
152 result.pre_shift = 0;
153 result.post_shift = down_exponent;
154 result.increment = 1;
155 } else {
156 /* Even divisor, so use a prefix-shifted dividend */
157 unsigned pre_shift = 0;
158 uint64_t shifted_D = D;
159 while ((shifted_D & 1) == 0) {
160 shifted_D >>= 1;
161 pre_shift += 1;
162 }
163 result = util_compute_fast_udiv_info(shifted_D, num_bits - pre_shift,
164 UINT_BITS);
165 /* expect no increment or pre_shift in this path */
166 assert(result.increment == 0 && result.pre_shift == 0);
167 result.pre_shift = pre_shift;
168 }
169 return result;
170 }
171
172 struct util_fast_sdiv_info
util_compute_fast_sdiv_info(int64_t D,unsigned SINT_BITS)173 util_compute_fast_sdiv_info(int64_t D, unsigned SINT_BITS)
174 {
175 /* D must not be zero. */
176 assert(D != 0);
177 /* The result is not correct for these divisors. */
178 assert(D != 1 && D != -1);
179
180 /* Our result */
181 struct util_fast_sdiv_info result;
182
183 /* Absolute value of D (we know D is not the most negative value since
184 * that's a power of 2)
185 */
186 const uint64_t abs_d = (D < 0 ? -D : D);
187
188 /* The initial power of 2 is one less than the first one that can possibly
189 * work */
190 /* "two31" in Warren */
191 unsigned exponent = SINT_BITS - 1;
192 const uint64_t initial_power_of_2 = (uint64_t)1 << exponent;
193
194 /* Compute the absolute value of our "test numerator,"
195 * which is the largest dividend whose remainder with d is d-1.
196 * This is called anc in Warren.
197 */
198 const uint64_t tmp = initial_power_of_2 + (D < 0);
199 const uint64_t abs_test_numer = tmp - 1 - tmp % abs_d;
200
201 /* Initialize our quotients and remainders (q1, r1, q2, r2 in Warren) */
202 uint64_t quotient1 = initial_power_of_2 / abs_test_numer;
203 uint64_t remainder1 = initial_power_of_2 % abs_test_numer;
204 uint64_t quotient2 = initial_power_of_2 / abs_d;
205 uint64_t remainder2 = initial_power_of_2 % abs_d;
206 uint64_t delta;
207
208 /* Begin our loop */
209 do {
210 /* Update the exponent */
211 exponent++;
212
213 /* Update quotient1 and remainder1 */
214 quotient1 *= 2;
215 remainder1 *= 2;
216 if (remainder1 >= abs_test_numer) {
217 quotient1 += 1;
218 remainder1 -= abs_test_numer;
219 }
220
221 /* Update quotient2 and remainder2 */
222 quotient2 *= 2;
223 remainder2 *= 2;
224 if (remainder2 >= abs_d) {
225 quotient2 += 1;
226 remainder2 -= abs_d;
227 }
228
229 /* Keep going as long as (2**exponent) / abs_d <= delta */
230 delta = abs_d - remainder2;
231 } while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
232
233 result.multiplier = util_sign_extend(quotient2 + 1, SINT_BITS);
234 if (D < 0) result.multiplier = -result.multiplier;
235 result.shift = exponent - SINT_BITS;
236 return result;
237 }
238