1 /*
2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25 #include "inner.h"
26
27 /* see inner.h */
28 void
br_i31_montymul(uint32_t * d,const uint32_t * x,const uint32_t * y,const uint32_t * m,uint32_t m0i)29 br_i31_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
30 const uint32_t *m, uint32_t m0i)
31 {
32 /*
33 * Each outer loop iteration computes:
34 * d <- (d + xu*y + f*m) / 2^31
35 * We have xu <= 2^31-1 and f <= 2^31-1.
36 * Thus, if d <= 2*m-1 on input, then:
37 * 2*m-1 + 2*(2^31-1)*m <= (2^32)*m-1
38 * and the new d value is less than 2*m.
39 *
40 * We represent d over 31-bit words, with an extra word 'dh'
41 * which can thus be only 0 or 1.
42 */
43 size_t len, len4, u, v;
44 uint32_t dh;
45
46 len = (m[0] + 31) >> 5;
47 len4 = len & ~(size_t)3;
48 br_i31_zero(d, m[0]);
49 dh = 0;
50 for (u = 0; u < len; u ++) {
51 /*
52 * The carry for each operation fits on 32 bits:
53 * d[v+1] <= 2^31-1
54 * xu*y[v+1] <= (2^31-1)*(2^31-1)
55 * f*m[v+1] <= (2^31-1)*(2^31-1)
56 * r <= 2^32-1
57 * (2^31-1) + 2*(2^31-1)*(2^31-1) + (2^32-1) = 2^63 - 2^31
58 * After division by 2^31, the new r is then at most 2^32-1
59 *
60 * Using a 32-bit carry has performance benefits on 32-bit
61 * systems; however, on 64-bit architectures, we prefer to
62 * keep the carry (r) in a 64-bit register, thus avoiding some
63 * "clear high bits" operations.
64 */
65 uint32_t f, xu;
66 #if BR_64
67 uint64_t r;
68 #else
69 uint32_t r;
70 #endif
71
72 xu = x[u + 1];
73 f = MUL31_lo((d[1] + MUL31_lo(x[u + 1], y[1])), m0i);
74
75 r = 0;
76 for (v = 0; v < len4; v += 4) {
77 uint64_t z;
78
79 z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
80 + MUL31(f, m[v + 1]) + r;
81 r = z >> 31;
82 d[v + 0] = (uint32_t)z & 0x7FFFFFFF;
83 z = (uint64_t)d[v + 2] + MUL31(xu, y[v + 2])
84 + MUL31(f, m[v + 2]) + r;
85 r = z >> 31;
86 d[v + 1] = (uint32_t)z & 0x7FFFFFFF;
87 z = (uint64_t)d[v + 3] + MUL31(xu, y[v + 3])
88 + MUL31(f, m[v + 3]) + r;
89 r = z >> 31;
90 d[v + 2] = (uint32_t)z & 0x7FFFFFFF;
91 z = (uint64_t)d[v + 4] + MUL31(xu, y[v + 4])
92 + MUL31(f, m[v + 4]) + r;
93 r = z >> 31;
94 d[v + 3] = (uint32_t)z & 0x7FFFFFFF;
95 }
96 for (; v < len; v ++) {
97 uint64_t z;
98
99 z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
100 + MUL31(f, m[v + 1]) + r;
101 r = z >> 31;
102 d[v] = (uint32_t)z & 0x7FFFFFFF;
103 }
104
105 /*
106 * Since the new dh can only be 0 or 1, the addition of
107 * the old dh with the carry MUST fit on 32 bits, and
108 * thus can be done into dh itself.
109 */
110 dh += r;
111 d[len] = dh & 0x7FFFFFFF;
112 dh >>= 31;
113 }
114
115 /*
116 * We must write back the bit length because it was overwritten in
117 * the loop (not overwriting it would require a test in the loop,
118 * which would yield bigger and slower code).
119 */
120 d[0] = m[0];
121
122 /*
123 * d[] may still be greater than m[] at that point; notably, the
124 * 'dh' word may be non-zero.
125 */
126 br_i31_sub(d, m, NEQ(dh, 0) | NOT(br_i31_sub(d, m, 0)));
127 }
128