75 lines
2.8 KiB
C
75 lines
2.8 KiB
C
/*
|
|
* Copyright © 2010 Valve Software
|
|
*
|
|
* Permission is hereby granted, free of charge, to any person obtaining a
|
|
* copy of this software and associated documentation files (the "Software"),
|
|
* to deal in the Software without restriction, including without limitation
|
|
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
|
|
* and/or sell copies of the Software, and to permit persons to whom the
|
|
* Software is furnished to do so, subject to the following conditions:
|
|
*
|
|
* The above copyright notice and this permission notice (including the next
|
|
* paragraph) shall be included in all copies or substantial portions of the
|
|
* Software.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
|
|
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
|
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
|
* IN THE SOFTWARE.
|
|
*/
|
|
|
|
#include <stdint.h>
|
|
|
|
/*
|
|
* Code for fast 32-bit unsigned remainder, based off of "Faster Remainder by
|
|
* Direct Computation: Applications to Compilers and Software Libraries,"
|
|
* available at https://arxiv.org/pdf/1902.01961.pdf.
|
|
*
|
|
* util_fast_urem32(n, d, REMAINDER_MAGIC(d)) returns the same thing as
|
|
* n % d for any unsigned n and d, however it compiles down to only a few
|
|
* multiplications, so it should be faster than plain uint32_t modulo if the
|
|
* same divisor is used many times.
|
|
*/
|
|
|
|
#define REMAINDER_MAGIC(divisor) \
|
|
((uint64_t) ~0ull / (divisor) + 1)
|
|
|
|
/*
|
|
* Get bits 64-96 of a 32x64-bit multiply. If __int128_t is available, we use
|
|
* it, which usually compiles down to one instruction on 64-bit architectures.
|
|
* Otherwise on 32-bit architectures we usually get four instructions (one
|
|
* 32x32->64 multiply, one 32x32->32 multiply, and one 64-bit add).
|
|
*/
|
|
|
|
static inline uint32_t
|
|
_mul32by64_hi(uint32_t a, uint64_t b)
|
|
{
|
|
#ifdef HAVE_UINT128
|
|
return ((__uint128_t) b * a) >> 64;
|
|
#else
|
|
/*
|
|
* Let b = b0 + 2^32 * b1. Then a * b = a * b0 + 2^32 * a * b1. We would
|
|
* have to do a 96-bit addition to get the full result, except that only
|
|
* one term has non-zero lower 32 bits, which means that to get the high 32
|
|
* bits, we only have to add the high 64 bits of each term. Unfortunately,
|
|
* we have to do the 64-bit addition in case the low 32 bits overflow.
|
|
*/
|
|
uint32_t b0 = (uint32_t) b;
|
|
uint32_t b1 = b >> 32;
|
|
return ((((uint64_t) a * b0) >> 32) + (uint64_t) a * b1) >> 32;
|
|
#endif
|
|
}
|
|
|
|
static inline uint32_t
|
|
util_fast_urem32(uint32_t n, uint32_t d, uint64_t magic)
|
|
{
|
|
uint64_t lowbits = magic * n;
|
|
uint32_t result = _mul32by64_hi(d, lowbits);
|
|
assert(result == n % d);
|
|
return result;
|
|
}
|
|
|