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Remove division from matrix multiplication

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This change reduces llama.com CPU cycles systemically by 2.5% according
to the Linux Kernel `perf stat -Bddd` utility.
This commit is contained in:
Justine Tunney 2023-05-10 21:19:54 -07:00
parent a88290e595
commit 1f6f9e6701
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GPG key ID: BE714B4575D6E328
7 changed files with 191 additions and 70 deletions
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65
libc/tinymath/magicu.c Normal file
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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│
╞══════════════════════════════════════════════════════════════════════════════╡
│ Copyright 2023 Justine Alexandra Roberts Tunney │
│ │
│ Permission to use, copy, modify, and/or distribute this software for │
│ any purpose with or without fee is hereby granted, provided that the │
│ above copyright notice and this permission notice appear in all copies. │
│ │
│ THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL │
│ WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED │
│ WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE │
│ AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL │
│ DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR │
│ PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER │
│ TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR │
│ PERFORMANCE OF THIS SOFTWARE. │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/tinymath/magicu.h"
/**
* Precomputes magic numbers for unsigned division by constant.
*
* The returned divisor may be passed to __magic_div() to perform
* unsigned integer division way faster than normal division e.g.
*
* assert(77 / 7 == __magicu_div(77, __magicu_get(7)));
*
* @param d is intended divisor, which must not be zero
* @return magic divisor
*/
struct magicu __magicu_get(uint32_t d) {
// From Hacker's Delight by Henry S. Warren Jr., 9780321842688
// Figure 10–3. Simplified algorithm for magic number unsigned
int a, p;
struct magicu magu;
uint32_t p32, q, r, delta;
p32 = 0; // Avoid compiler warning.
a = 0; // Initialize "add" indicator.
p = 31; // Initialize p.
q = 0x7FFFFFFF / d; // Initialize q = (2**p - 1)/d.
r = 0x7FFFFFFF - q * d; // Init. r = rem(2**p - 1, d).
do {
p = p + 1;
if (p == 32) {
p32 = 1; // Set p32 = 2**(p-32).
} else {
p32 = 2 * p32;
}
if (r + 1 >= d - r) {
if (q >= 0x7FFFFFFF) a = 1;
q = 2 * q + 1; // Update q.
r = 2 * r + 1 - d; // Update r.
} else {
if (q >= 0x80000000) a = 1;
q = 2 * q;
r = 2 * r + 1;
}
delta = d - 1 - r;
} while (p < 64 && p32 < delta);
magu.M = q + 1; // Magic number and
magu.s = p - 32; // Shift amount to return
if (a) magu.s |= 64; // Sets "add" indicator
return magu;
}

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libc/tinymath/magicu.h Normal file
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#ifndef COSMOPOLITAN_LIBC_TINYMATH_MAGICU_H_
#define COSMOPOLITAN_LIBC_TINYMATH_MAGICU_H_
#if !(__ASSEMBLER__ + __LINKER__ + 0)
COSMOPOLITAN_C_START_
struct magicu {
uint32_t M;
uint32_t s;
};
struct magicu __magicu_get(uint32_t);
/**
* Performs fast division using precomputed magic for constant divisor.
*
* @param x is unsigned integer that shall be divided
* @param d should be `__magicu_get(y)` if computing `x / y`
* @return result of unsigned integer division
*/
static inline uint32_t __magicu_div(uint32_t x, struct magicu d) {
return ((((uint64_t)x * d.M) >> 32) + ((d.s & 64) ? x : 0)) >> (d.s & 63);
}
COSMOPOLITAN_C_END_
#endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */
#endif /* COSMOPOLITAN_LIBC_TINYMATH_MAGICU_H_ */