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