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
46struct util_fast_udiv_info
47util_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
172struct util_fast_sdiv_info
173util_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