1*0957b409SSimon J. Gerraty /*
2*0957b409SSimon J. Gerraty * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
3*0957b409SSimon J. Gerraty *
4*0957b409SSimon J. Gerraty * Permission is hereby granted, free of charge, to any person obtaining
5*0957b409SSimon J. Gerraty * a copy of this software and associated documentation files (the
6*0957b409SSimon J. Gerraty * "Software"), to deal in the Software without restriction, including
7*0957b409SSimon J. Gerraty * without limitation the rights to use, copy, modify, merge, publish,
8*0957b409SSimon J. Gerraty * distribute, sublicense, and/or sell copies of the Software, and to
9*0957b409SSimon J. Gerraty * permit persons to whom the Software is furnished to do so, subject to
10*0957b409SSimon J. Gerraty * the following conditions:
11*0957b409SSimon J. Gerraty *
12*0957b409SSimon J. Gerraty * The above copyright notice and this permission notice shall be
13*0957b409SSimon J. Gerraty * included in all copies or substantial portions of the Software.
14*0957b409SSimon J. Gerraty *
15*0957b409SSimon J. Gerraty * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16*0957b409SSimon J. Gerraty * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17*0957b409SSimon J. Gerraty * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18*0957b409SSimon J. Gerraty * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19*0957b409SSimon J. Gerraty * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20*0957b409SSimon J. Gerraty * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21*0957b409SSimon J. Gerraty * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22*0957b409SSimon J. Gerraty * SOFTWARE.
23*0957b409SSimon J. Gerraty */
24*0957b409SSimon J. Gerraty
25*0957b409SSimon J. Gerraty #include "inner.h"
26*0957b409SSimon J. Gerraty
27*0957b409SSimon J. Gerraty /* see inner.h */
28*0957b409SSimon J. Gerraty void
br_i31_montymul(uint32_t * d,const uint32_t * x,const uint32_t * y,const uint32_t * m,uint32_t m0i)29*0957b409SSimon J. Gerraty br_i31_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
30*0957b409SSimon J. Gerraty const uint32_t *m, uint32_t m0i)
31*0957b409SSimon J. Gerraty {
32*0957b409SSimon J. Gerraty /*
33*0957b409SSimon J. Gerraty * Each outer loop iteration computes:
34*0957b409SSimon J. Gerraty * d <- (d + xu*y + f*m) / 2^31
35*0957b409SSimon J. Gerraty * We have xu <= 2^31-1 and f <= 2^31-1.
36*0957b409SSimon J. Gerraty * Thus, if d <= 2*m-1 on input, then:
37*0957b409SSimon J. Gerraty * 2*m-1 + 2*(2^31-1)*m <= (2^32)*m-1
38*0957b409SSimon J. Gerraty * and the new d value is less than 2*m.
39*0957b409SSimon J. Gerraty *
40*0957b409SSimon J. Gerraty * We represent d over 31-bit words, with an extra word 'dh'
41*0957b409SSimon J. Gerraty * which can thus be only 0 or 1.
42*0957b409SSimon J. Gerraty */
43*0957b409SSimon J. Gerraty size_t len, len4, u, v;
44*0957b409SSimon J. Gerraty uint32_t dh;
45*0957b409SSimon J. Gerraty
46*0957b409SSimon J. Gerraty len = (m[0] + 31) >> 5;
47*0957b409SSimon J. Gerraty len4 = len & ~(size_t)3;
48*0957b409SSimon J. Gerraty br_i31_zero(d, m[0]);
49*0957b409SSimon J. Gerraty dh = 0;
50*0957b409SSimon J. Gerraty for (u = 0; u < len; u ++) {
51*0957b409SSimon J. Gerraty /*
52*0957b409SSimon J. Gerraty * The carry for each operation fits on 32 bits:
53*0957b409SSimon J. Gerraty * d[v+1] <= 2^31-1
54*0957b409SSimon J. Gerraty * xu*y[v+1] <= (2^31-1)*(2^31-1)
55*0957b409SSimon J. Gerraty * f*m[v+1] <= (2^31-1)*(2^31-1)
56*0957b409SSimon J. Gerraty * r <= 2^32-1
57*0957b409SSimon J. Gerraty * (2^31-1) + 2*(2^31-1)*(2^31-1) + (2^32-1) = 2^63 - 2^31
58*0957b409SSimon J. Gerraty * After division by 2^31, the new r is then at most 2^32-1
59*0957b409SSimon J. Gerraty *
60*0957b409SSimon J. Gerraty * Using a 32-bit carry has performance benefits on 32-bit
61*0957b409SSimon J. Gerraty * systems; however, on 64-bit architectures, we prefer to
62*0957b409SSimon J. Gerraty * keep the carry (r) in a 64-bit register, thus avoiding some
63*0957b409SSimon J. Gerraty * "clear high bits" operations.
64*0957b409SSimon J. Gerraty */
65*0957b409SSimon J. Gerraty uint32_t f, xu;
66*0957b409SSimon J. Gerraty #if BR_64
67*0957b409SSimon J. Gerraty uint64_t r;
68*0957b409SSimon J. Gerraty #else
69*0957b409SSimon J. Gerraty uint32_t r;
70*0957b409SSimon J. Gerraty #endif
71*0957b409SSimon J. Gerraty
72*0957b409SSimon J. Gerraty xu = x[u + 1];
73*0957b409SSimon J. Gerraty f = MUL31_lo((d[1] + MUL31_lo(x[u + 1], y[1])), m0i);
74*0957b409SSimon J. Gerraty
75*0957b409SSimon J. Gerraty r = 0;
76*0957b409SSimon J. Gerraty for (v = 0; v < len4; v += 4) {
77*0957b409SSimon J. Gerraty uint64_t z;
78*0957b409SSimon J. Gerraty
79*0957b409SSimon J. Gerraty z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
80*0957b409SSimon J. Gerraty + MUL31(f, m[v + 1]) + r;
81*0957b409SSimon J. Gerraty r = z >> 31;
82*0957b409SSimon J. Gerraty d[v + 0] = (uint32_t)z & 0x7FFFFFFF;
83*0957b409SSimon J. Gerraty z = (uint64_t)d[v + 2] + MUL31(xu, y[v + 2])
84*0957b409SSimon J. Gerraty + MUL31(f, m[v + 2]) + r;
85*0957b409SSimon J. Gerraty r = z >> 31;
86*0957b409SSimon J. Gerraty d[v + 1] = (uint32_t)z & 0x7FFFFFFF;
87*0957b409SSimon J. Gerraty z = (uint64_t)d[v + 3] + MUL31(xu, y[v + 3])
88*0957b409SSimon J. Gerraty + MUL31(f, m[v + 3]) + r;
89*0957b409SSimon J. Gerraty r = z >> 31;
90*0957b409SSimon J. Gerraty d[v + 2] = (uint32_t)z & 0x7FFFFFFF;
91*0957b409SSimon J. Gerraty z = (uint64_t)d[v + 4] + MUL31(xu, y[v + 4])
92*0957b409SSimon J. Gerraty + MUL31(f, m[v + 4]) + r;
93*0957b409SSimon J. Gerraty r = z >> 31;
94*0957b409SSimon J. Gerraty d[v + 3] = (uint32_t)z & 0x7FFFFFFF;
95*0957b409SSimon J. Gerraty }
96*0957b409SSimon J. Gerraty for (; v < len; v ++) {
97*0957b409SSimon J. Gerraty uint64_t z;
98*0957b409SSimon J. Gerraty
99*0957b409SSimon J. Gerraty z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
100*0957b409SSimon J. Gerraty + MUL31(f, m[v + 1]) + r;
101*0957b409SSimon J. Gerraty r = z >> 31;
102*0957b409SSimon J. Gerraty d[v] = (uint32_t)z & 0x7FFFFFFF;
103*0957b409SSimon J. Gerraty }
104*0957b409SSimon J. Gerraty
105*0957b409SSimon J. Gerraty /*
106*0957b409SSimon J. Gerraty * Since the new dh can only be 0 or 1, the addition of
107*0957b409SSimon J. Gerraty * the old dh with the carry MUST fit on 32 bits, and
108*0957b409SSimon J. Gerraty * thus can be done into dh itself.
109*0957b409SSimon J. Gerraty */
110*0957b409SSimon J. Gerraty dh += r;
111*0957b409SSimon J. Gerraty d[len] = dh & 0x7FFFFFFF;
112*0957b409SSimon J. Gerraty dh >>= 31;
113*0957b409SSimon J. Gerraty }
114*0957b409SSimon J. Gerraty
115*0957b409SSimon J. Gerraty /*
116*0957b409SSimon J. Gerraty * We must write back the bit length because it was overwritten in
117*0957b409SSimon J. Gerraty * the loop (not overwriting it would require a test in the loop,
118*0957b409SSimon J. Gerraty * which would yield bigger and slower code).
119*0957b409SSimon J. Gerraty */
120*0957b409SSimon J. Gerraty d[0] = m[0];
121*0957b409SSimon J. Gerraty
122*0957b409SSimon J. Gerraty /*
123*0957b409SSimon J. Gerraty * d[] may still be greater than m[] at that point; notably, the
124*0957b409SSimon J. Gerraty * 'dh' word may be non-zero.
125*0957b409SSimon J. Gerraty */
126*0957b409SSimon J. Gerraty br_i31_sub(d, m, NEQ(dh, 0) | NOT(br_i31_sub(d, m, 0)));
127*0957b409SSimon J. Gerraty }
128