COMBINATORIAL_BLAS 1.6
 
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mod_arith_xmt.h
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1/* Copyright (C) 2010 The Trustees of Indiana University. */
2/* */
3/* Use, modification and distribution is subject to the Boost Software */
4/* License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at */
5/* http://www.boost.org/LICENSE_1_0.txt) */
6/* */
7/* Authors: Jeremiah Willcock */
8/* Andrew Lumsdaine */
9
10#ifndef MOD_ARITH_XMT_H
11#define MOD_ARITH_XMT_H
12
13#include <stdint.h>
14#include <assert.h>
15#include <machine/mtaops.h>
16
17/* Various modular arithmetic operations for modulus 2^31-1 (0x7FFFFFFF).
18 * These may need to be tweaked to get acceptable performance on some platforms
19 * (especially ones without conditional moves). */
20
21/* MTA code is based on description in
22 * http://www.hackersdelight.org/divcMore.pdf and experimentation based on
23 * that. */
24
25#pragma mta inline
26static inline uint_fast32_t mod_add(uint_fast32_t a, uint_fast32_t b) {
27 uint_fast32_t x;
28 assert (a <= 0x7FFFFFFE);
29 assert (b <= 0x7FFFFFFE);
30 x = a + b; /* x <= 0xFFFFFFFC */
31 return (x + MTA_UNS_ADD_MUL_UPPER(0x0000000200000003, 0x0000000200000004, x)) & 0x7FFFFFFF;
32}
33
34#pragma mta inline
35static inline uint_fast32_t mod_mul(uint_fast32_t a, uint_fast32_t b) {
36 uint_fast64_t temp;
37 uint_fast32_t temp2;
38 assert (a <= 0x7FFFFFFE);
39 assert (b <= 0x7FFFFFFE);
40 temp = MTA_INT_ADD_MUL(0, a, b);
41 return (temp + MTA_UNS_ADD_MUL_UPPER(0x0000000200000003, 0x0000000200000004, temp)) & 0x7FFFFFFF;
42}
43
44#pragma mta inline
45static inline uint_fast32_t mod_mac(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b) {
46 uint_fast64_t temp;
47 uint_fast32_t temp2;
48 assert (sum <= 0x7FFFFFFE);
49 assert (a <= 0x7FFFFFFE);
50 assert (b <= 0x7FFFFFFE);
51 temp = MTA_INT_ADD_MUL(sum, a, b);
52 return (temp + MTA_UNS_ADD_MUL_UPPER(0x0000000200000003, 0x0000000200000004, temp)) & 0x7FFFFFFF;
53}
54
55#pragma mta inline
56static inline uint_fast32_t mod_mac2(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b, uint_fast32_t c, uint_fast32_t d) {
57 uint_fast64_t temp;
58 assert (sum <= 0x7FFFFFFE);
59 assert (a <= 0x7FFFFFFE);
60 assert (b <= 0x7FFFFFFE);
61 assert (c <= 0x7FFFFFFE);
62 assert (d <= 0x7FFFFFFE);
63 temp = MTA_INT_ADD_MUL(MTA_INT_ADD_MUL(sum, a, b), c, d);
64 return (temp + MTA_UNS_ADD_MUL_UPPER(0x0000000200000003, 0x0000000200000004, temp)) & 0x7FFFFFFF;
65}
66
67#pragma mta inline
68static inline uint_fast32_t mod_mac3(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b, uint_fast32_t c, uint_fast32_t d, uint_fast32_t e, uint_fast32_t f) {
69 uint_fast64_t temp;
70 assert (sum <= 0x7FFFFFFE);
71 assert (a <= 0x7FFFFFFE);
72 assert (b <= 0x7FFFFFFE);
73 assert (c <= 0x7FFFFFFE);
74 assert (d <= 0x7FFFFFFE);
75 assert (e <= 0x7FFFFFFE);
76 assert (f <= 0x7FFFFFFE);
77 temp = MTA_INT_ADD_MUL(MTA_INT_ADD_MUL(MTA_INT_ADD_MUL(sum, a, b), c, d), e, f);
78 return (temp + MTA_UNS_ADD_MUL_UPPER(0x0000000200000003, 0x0000000200000004, temp)) & 0x7FFFFFFF;
79}
80
81#pragma mta inline
82static inline uint_fast32_t mod_mac4(uint_fast32_t sum, uint_fast32_t a, uint_fast32_t b, uint_fast32_t c, uint_fast32_t d, uint_fast32_t e, uint_fast32_t f, uint_fast32_t g, uint_fast32_t h) {
83 uint_fast64_t temp;
84 assert (sum <= 0x7FFFFFFE);
85 assert (a <= 0x7FFFFFFE);
86 assert (b <= 0x7FFFFFFE);
87 assert (c <= 0x7FFFFFFE);
88 assert (d <= 0x7FFFFFFE);
89 assert (e <= 0x7FFFFFFE);
90 assert (f <= 0x7FFFFFFE);
91 assert (g <= 0x7FFFFFFE);
92 assert (h <= 0x7FFFFFFE);
93 temp = MTA_INT_ADD_MUL(MTA_INT_ADD_MUL(MTA_INT_ADD_MUL(MTA_INT_ADD_MUL(sum, a, b), c, d), e, f), g, h);
94 return (temp + MTA_UNS_ADD_MUL_UPPER(0x0000000200000003, 0x0000000200000004, temp)) & 0x7FFFFFFF;
95}
96
97static inline uint_fast64_t mod_down(uint_fast64_t x);
98
99#pragma mta inline
100static inline uint_fast64_t mod_down_fast(uint_fast64_t x) {
101 return (x >> 31) + (x & 0x7FFFFFFF);
102}
103
104#pragma mta inline
105static inline uint_fast64_t mod_down(uint_fast64_t x) {
106 return ((x + MTA_UNS_ADD_MUL_UPPER(0x0000000200000003, 0x0000000200000004, x)) & 0x7FFFFFFF);
107 // x = mod_down_fast(mod_down_fast(x));
108 // x = (x + (x >= 0x7FFFFFFF)) & 0x7FFFFFFF;
109 // return x;
110}
111
112/* The two constants x and y are special cases because they are easier to
113 * multiply by on 32-bit systems. They are used as multipliers in the random
114 * number generator. The techniques for fast multiplication by these
115 * particular values are in L'Ecuyer's papers; we don't use them yet. */
116
117#pragma mta inline
118static inline uint_fast32_t mod_mul_x(uint_fast32_t a) {
119 return mod_mul(a, 107374182);
120}
121
122#pragma mta inline
123static inline uint_fast32_t mod_mul_y(uint_fast32_t a) {
124 return mod_mul(a, 104480);
125}
126
127#pragma mta inline
128static inline uint_fast32_t mod_mac_y(uint_fast32_t sum, uint_fast32_t a) {
129 return mod_mac(sum, a, 104480);
130}
131
132#endif /* MOD_ARITH_XMT_H */
uint_fast64_t
uint64_t uint_fast64_t
Definition stdint.h:111
uint_fast32_t
uint32_t uint_fast32_t
Definition stdint.h:110