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#ifndef FAST_IDIV_BY_CONST_H
25#define FAST_IDIV_BY_CONST_H
26
27/* Imported from:
28 *   https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c
29 */
30
31#include <inttypes.h>
32#include <limits.h>
33#include <assert.h>
34
35#ifdef __cplusplus
36extern "C" {
37#endif
38
39/* Computes "magic info" for performing signed division by a fixed integer D.
40 * The type 'sint_t' is assumed to be defined as a signed integer type large
41 * enough to hold both the dividend and the divisor.
42 * Here >> is arithmetic (signed) shift, and >>> is logical shift.
43 *
44 * To emit code for n/d, rounding towards zero, use the following sequence:
45 *
46 *   m = compute_signed_magic_info(D)
47 *   emit("result = (m.multiplier * n) >> SINT_BITS");
48 *   if d > 0 and m.multiplier < 0: emit("result += n")
49 *   if d < 0 and m.multiplier > 0: emit("result -= n")
50 *   if m.post_shift > 0: emit("result >>= m.shift")
51 *   emit("result += (result < 0)")
52 *
53 * The shifts by SINT_BITS may be "free" if the high half of the full multiply
54 * is put in a separate register.
55 *
56 * The final add can of course be implemented via the sign bit, e.g.
57 *    result += (result >>> (SINT_BITS - 1))
58 * or
59 *    result -= (result >> (SINT_BITS - 1))
60 *
61 * This code is heavily indebted to Hacker's Delight by Henry Warren.
62 * See http://www.hackersdelight.org/HDcode/magic.c.txt
63 * Used with permission from http://www.hackersdelight.org/permissions.htm
64 */
65
66struct util_fast_sdiv_info {
67   int64_t multiplier; /* the "magic number" multiplier */
68   unsigned shift; /* shift for the dividend after multiplying */
69};
70
71struct util_fast_sdiv_info
72util_compute_fast_sdiv_info(int64_t D, unsigned SINT_BITS);
73
74/* Computes "magic info" for performing unsigned division by a fixed positive
75 * integer D.  UINT_BITS is the bit size at which the final "magic"
76 * calculation will be performed; it is assumed to be large enough to hold
77 * both the dividand and the divisor.  num_bits can be set appropriately if n
78 * is known to be smaller than calc_bits; if this is not known then UINT_BITS
79 * for num_bits.
80 *
81 * Assume we have a hardware register of width UINT_BITS, a known constant D
82 * which is not zero and not a power of 2, and a variable n of width num_bits
83 * (which may be up to UINT_BITS). To emit code for n/d, use one of the two
84 * following sequences (here >>> refers to a logical bitshift):
85 *
86 *   m = compute_unsigned_magic_info(D, num_bits)
87 *   if m.pre_shift > 0: emit("n >>>= m.pre_shift")
88 *   if m.increment: emit("n = saturated_increment(n)")
89 *   emit("result = (m.multiplier * n) >>> UINT_BITS")
90 *   if m.post_shift > 0: emit("result >>>= m.post_shift")
91 *
92 * or
93 *
94 *   m = compute_unsigned_magic_info(D, num_bits)
95 *   if m.pre_shift > 0: emit("n >>>= m.pre_shift")
96 *   emit("result = m.multiplier * n")
97 *   if m.increment: emit("result = result + m.multiplier")
98 *   emit("result >>>= UINT_BITS")
99 *   if m.post_shift > 0: emit("result >>>= m.post_shift")
100 *
101 * This second version works even if D is 1.  The shifts by UINT_BITS may be
102 * "free" if the high half of the full multiply is put in a separate register.
103 *
104 * saturated_increment(n) means "increment n unless it would wrap to 0," i.e.
105 *   if n == (1 << UINT_BITS)-1: result = n
106 *   else: result = n+1
107 * A common way to implement this is with the carry bit. For example, on x86:
108 *   add 1
109 *   sbb 0
110 *
111 * Some invariants:
112 *   1: At least one of pre_shift and increment is zero
113 *   2: multiplier is never zero
114 *
115 * This code incorporates the "round down" optimization per ridiculous_fish.
116 */
117
118struct util_fast_udiv_info {
119   uint64_t multiplier; /* the "magic number" multiplier */
120   unsigned pre_shift; /* shift for the dividend before multiplying */
121   unsigned post_shift; /* shift for the dividend after multiplying */
122   int increment; /* 0 or 1; if set then increment the numerator, using one of
123                     the two strategies */
124};
125
126struct util_fast_udiv_info
127util_compute_fast_udiv_info(uint64_t D, unsigned num_bits, unsigned UINT_BITS);
128
129/* Below are possible options for dividing by a uniform in a shader where
130 * the divisor is constant but not known at compile time.
131 */
132
133/* Full version. */
134static inline uint32_t
135util_fast_udiv32(uint32_t n, struct util_fast_udiv_info info)
136{
137   n = n >> info.pre_shift;
138   /* If the divisor is not 1, you can instead use a 32-bit ADD that clamps
139    * to UINT_MAX. Dividing by 1 needs the full 64-bit ADD.
140    *
141    * If you have unsigned 64-bit MAD with 32-bit inputs, you can do:
142    *    increment = increment ? multiplier : 0; // on the CPU
143    *    (n * multiplier + increment) // on the GPU using unsigned 64-bit MAD
144    */
145   n = (((uint64_t)n + info.increment) * info.multiplier) >> 32;
146   n = n >> info.post_shift;
147   return n;
148}
149
150/* A little more efficient version if n != UINT_MAX, i.e. no unsigned
151 * wraparound in the computation.
152 */
153static inline uint32_t
154util_fast_udiv32_nuw(uint32_t n, struct util_fast_udiv_info info)
155{
156   assert(n != UINT32_MAX);
157   n = n >> info.pre_shift;
158   n = n + info.increment;
159   n = ((uint64_t)n * info.multiplier) >> 32;
160   n = n >> info.post_shift;
161   return n;
162}
163
164/* Even faster version but both operands must be 31-bit unsigned integers
165 * and the divisor must be greater than 1.
166 *
167 * info must be computed with num_bits == 31.
168 */
169static inline uint32_t
170util_fast_udiv32_u31_d_not_one(uint32_t n, struct util_fast_udiv_info info)
171{
172   assert(info.pre_shift == 0);
173   assert(info.increment == 0);
174   n = ((uint64_t)n * info.multiplier) >> 32;
175   n = n >> info.post_shift;
176   return n;
177}
178
179#ifdef __cplusplus
180} /* extern C */
181#endif
182
183#endif /* FAST_IDIV_BY_CONST_H */
184