1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
|
/*
* gen_crc32_multipliers.c
*
* Copyright 2016 Eric Biggers
*
* 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 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 <inttypes.h>
#include <stdio.h>
/* generator polynomial G(x) */
#define CRCPOLY 0xEDB88320 /* G(x) without x^32 term */
#define CRCPOLY_FULL (((uint64_t)CRCPOLY << 1) | 1) /* G(x) */
/* Compute x^D mod G(x) */
static uint32_t
compute_multiplier(int D)
{
/* Start with x^0 mod G(x) */
uint32_t remainder = 0x80000000;
/* Each iteration, 'remainder' becomes x^i mod G(x) */
for (int i = 1; i <= D; i++)
remainder = (remainder >> 1) ^ ((remainder & 1) ? CRCPOLY : 0);
/* Now 'remainder' is x^D mod G(x) */
return remainder;
}
/* Compute floor(x^64 / G(x)) */
static uint64_t
compute_barrett_reduction_constant(void)
{
uint64_t quotient = 0;
uint64_t dividend = 0x1;
for (int i = 0; i < 64 - 32 + 1; i++) {
if ((dividend >> i) & 1) {
quotient |= (uint64_t)1 << i;
dividend ^= CRCPOLY_FULL << i;
}
}
return quotient;
}
/*
* This program computes the constant multipliers needed for carryless
* multiplication accelerated CRC-32. It assumes 128-bit vectors divided into
* two 64-bit halves which are multiplied separately with different 32-bit
* multipliers, producing two 95-bit products. For a given number of 128-bit
* vectors per iteration, the program outputs a pair of multipliers, one for
* each 64-bit half.
*
* Careful: all polynomials are "bit-reversed", meaning that the low-order bits
* have the highest degree and the high-order bits have the lowest degree!
*/
int
main(void)
{
printf("\t/* Constants precomputed by gen_crc32_multipliers.c. "
"Do not edit! */\n");
/* High and low multipliers for each needed vector count */
for (int order = 2; order >= 0; order--) {
int vecs_per_iteration = 1 << order;
int right = (128 * vecs_per_iteration) + 95;
printf("\tconst __v2di multipliers_%d = (__v2di)"
"{ 0x%08"PRIX32", 0x%08"PRIX32" };\n",
vecs_per_iteration,
compute_multiplier(right - 64) /* higher degree half */,
compute_multiplier(right - 128) /* lower degree half */);
}
/* Multiplier for final 96 => 64 bit fold */
printf("\tconst __v2di final_multiplier = (__v2di){ 0x%08"PRIX32" };\n",
compute_multiplier(63));
/* 32-bit mask */
printf("\tconst __m128i mask32 = (__m128i)(__v4si){ 0xFFFFFFFF };\n");
/* Constants for final 64 => 32 bit reduction */
printf("\tconst __v2di barrett_reduction_constants =\n"
"\t\t\t(__v2di){ 0x%016"PRIX64", 0x%016"PRIX64" };\n",
compute_barrett_reduction_constant(), CRCPOLY_FULL);
return 0;
}
|
