Make Rules.mk more compatible with merges and local diffs.
[BearSSL] / src / int / i15_muladd.c
1 /*
2 * Copyright (c) 2017 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 /*
28 * Constant-time division. The divisor must not be larger than 16 bits,
29 * and the quotient must fit on 17 bits.
30 */
31 static uint32_t
32 divrem16(uint32_t x, uint32_t d, uint32_t *r)
33 {
34 int i;
35 uint32_t q;
36
37 q = 0;
38 d <<= 16;
39 for (i = 16; i >= 0; i --) {
40 uint32_t ctl;
41
42 ctl = LE(d, x);
43 q |= ctl << i;
44 x -= (-ctl) & d;
45 d >>= 1;
46 }
47 if (r != NULL) {
48 *r = x;
49 }
50 return q;
51 }
52
53 /* see inner.h */
54 void
55 br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m)
56 {
57 /*
58 * Constant-time: we accept to leak the exact bit length of the
59 * modulus m.
60 */
61 unsigned m_bitlen, mblr;
62 size_t u, mlen;
63 uint32_t hi, a0, a, b, q;
64 uint32_t cc, tb, over, under;
65
66 /*
67 * Simple case: the modulus fits on one word.
68 */
69 m_bitlen = m[0];
70 if (m_bitlen == 0) {
71 return;
72 }
73 if (m_bitlen <= 15) {
74 uint32_t rem;
75
76 divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem);
77 x[1] = rem;
78 return;
79 }
80 mlen = (m_bitlen + 15) >> 4;
81 mblr = m_bitlen & 15;
82
83 /*
84 * Principle: we estimate the quotient (x*2^15+z)/m by
85 * doing a 30/15 division with the high words.
86 *
87 * Let:
88 * w = 2^15
89 * a = (w*a0 + a1) * w^N + a2
90 * b = b0 * w^N + b2
91 * such that:
92 * 0 <= a0 < w
93 * 0 <= a1 < w
94 * 0 <= a2 < w^N
95 * w/2 <= b0 < w
96 * 0 <= b2 < w^N
97 * a < w*b
98 * I.e. the two top words of a are a0:a1, the top word of b is
99 * b0, we ensured that b0 is "full" (high bit set), and a is
100 * such that the quotient q = a/b fits on one word (0 <= q < w).
101 *
102 * If a = b*q + r (with 0 <= r < q), then we can estimate q by
103 * using a division on the top words:
104 * a0*w + a1 = b0*u + v (with 0 <= v < b0)
105 * Then the following holds:
106 * 0 <= u <= w
107 * u-2 <= q <= u
108 */
109 hi = x[mlen];
110 if (mblr == 0) {
111 a0 = x[mlen];
112 memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
113 x[1] = z;
114 a = (a0 << 15) + x[mlen];
115 b = m[mlen];
116 } else {
117 a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr);
118 memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
119 x[1] = z;
120 a = (a0 << 15) | (((x[mlen] << (15 - mblr))
121 | (x[mlen - 1] >> mblr)) & 0x7FFF);
122 b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr);
123 }
124 q = divrem16(a, b, NULL);
125
126 /*
127 * We computed an estimate for q, but the real one may be q,
128 * q-1 or q-2; moreover, the division may have returned a value
129 * 8000 or even 8001 if the two high words were identical, and
130 * we want to avoid values beyond 7FFF. We thus adjust q so
131 * that the "true" multiplier will be q+1, q or q-1, and q is
132 * in the 0000..7FFF range.
133 */
134 q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31));
135
136 /*
137 * We subtract q*m from x (x has an extra high word of value 'hi').
138 * Since q may be off by 1 (in either direction), we may have to
139 * add or subtract m afterwards.
140 *
141 * The 'tb' flag will be true (1) at the end of the loop if the
142 * result is greater than or equal to the modulus (not counting
143 * 'hi' or the carry).
144 */
145 cc = 0;
146 tb = 1;
147 for (u = 1; u <= mlen; u ++) {
148 uint32_t mw, zl, xw, nxw;
149
150 mw = m[u];
151 zl = MUL15(mw, q) + cc;
152 cc = zl >> 15;
153 zl &= 0x7FFF;
154 xw = x[u];
155 nxw = xw - zl;
156 cc += nxw >> 31;
157 nxw &= 0x7FFF;
158 x[u] = nxw;
159 tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
160 }
161
162 /*
163 * If we underestimated q, then either cc < hi (one extra bit
164 * beyond the top array word), or cc == hi and tb is true (no
165 * extra bit, but the result is not lower than the modulus).
166 *
167 * If we overestimated q, then cc > hi.
168 */
169 over = GT(cc, hi);
170 under = ~over & (tb | LT(cc, hi));
171 br_i15_add(x, m, over);
172 br_i15_sub(x, m, under);
173 }