1/*
2 * Copyright © 2010 Valve Software
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#include <stdint.h>
25
26/*
27 * Code for fast 32-bit unsigned remainder, based off of "Faster Remainder by
28 * Direct Computation: Applications to Compilers and Software Libraries,"
29 * available at https://arxiv.org/pdf/1902.01961.pdf.
30 *
31 * util_fast_urem32(n, d, REMAINDER_MAGIC(d)) returns the same thing as
32 * n % d for any unsigned n and d, however it compiles down to only a few
33 * multiplications, so it should be faster than plain uint32_t modulo if the
34 * same divisor is used many times.
35 */
36
37#define REMAINDER_MAGIC(divisor) \
38   ((uint64_t) ~0ull / (divisor) + 1)
39
40/*
41 * Get bits 64-96 of a 32x64-bit multiply. If __int128_t is available, we use
42 * it, which usually compiles down to one instruction on 64-bit architectures.
43 * Otherwise on 32-bit architectures we usually get four instructions (one
44 * 32x32->64 multiply, one 32x32->32 multiply, and one 64-bit add).
45 */
46
47static inline uint32_t
48_mul32by64_hi(uint32_t a, uint64_t b)
49{
50#ifdef HAVE_UINT128
51   return ((__uint128_t) b * a) >> 64;
52#else
53   /*
54    * Let b = b0 + 2^32 * b1. Then a * b = a * b0 + 2^32 * a * b1. We would
55    * have to do a 96-bit addition to get the full result, except that only
56    * one term has non-zero lower 32 bits, which means that to get the high 32
57    * bits, we only have to add the high 64 bits of each term. Unfortunately,
58    * we have to do the 64-bit addition in case the low 32 bits overflow.
59    */
60   uint32_t b0 = (uint32_t) b;
61   uint32_t b1 = b >> 32;
62   return ((((uint64_t) a * b0) >> 32) + (uint64_t) a * b1) >> 32;
63#endif
64}
65
66static inline uint32_t
67util_fast_urem32(uint32_t n, uint32_t d, uint64_t magic)
68{
69   uint64_t lowbits = magic * n;
70   uint32_t result = _mul32by64_hi(d, lowbits);
71   assert(result == n % d);
72   return result;
73}
74
75