Added intermediate casts to void* to prevent spurious warnings (with Clang and -Wcast...
[BearSSL] / src / int / i31_muladd.c
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
29 br_i31_muladd_small(uint32_t *x, uint32_t z, const uint32_t *m)
30 {
31 uint32_t m_bitlen;
32 unsigned mblr;
33 size_t u, mlen;
34 uint32_t a0, a1, b0, hi, g, q, tb;
35 uint32_t under, over;
36 uint32_t cc;
37
38 /*
39 * We can test on the modulus bit length since we accept to
40 * leak that length.
41 */
42 m_bitlen = m[0];
43 if (m_bitlen == 0) {
44 return;
45 }
46 if (m_bitlen <= 31) {
47 uint32_t lo;
48
49 hi = x[1] >> 1;
50 lo = (x[1] << 31) | z;
51 x[1] = br_rem(hi, lo, m[1]);
52 return;
53 }
54 mlen = (m_bitlen + 31) >> 5;
55 mblr = (unsigned)m_bitlen & 31;
56
57 /*
58 * Principle: we estimate the quotient (x*2^31+z)/m by
59 * doing a 64/32 division with the high words.
60 *
61 * Let:
62 * w = 2^31
63 * a = (w*a0 + a1) * w^N + a2
64 * b = b0 * w^N + b2
65 * such that:
66 * 0 <= a0 < w
67 * 0 <= a1 < w
68 * 0 <= a2 < w^N
69 * w/2 <= b0 < w
70 * 0 <= b2 < w^N
71 * a < w*b
72 * I.e. the two top words of a are a0:a1, the top word of b is
73 * b0, we ensured that b0 is "full" (high bit set), and a is
74 * such that the quotient q = a/b fits on one word (0 <= q < w).
75 *
76 * If a = b*q + r (with 0 <= r < q), we can estimate q by
77 * doing an Euclidean division on the top words:
78 * a0*w+a1 = b0*u + v (with 0 <= v < b0)
79 * Then the following holds:
80 * 0 <= u <= w
81 * u-2 <= q <= u
82 */
83 hi = x[mlen];
84 if (mblr == 0) {
85 a0 = x[mlen];
86 memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
87 x[1] = z;
88 a1 = x[mlen];
89 b0 = m[mlen];
90 } else {
91 a0 = ((x[mlen] << (31 - mblr)) | (x[mlen - 1] >> mblr))
92 & 0x7FFFFFFF;
93 memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
94 x[1] = z;
95 a1 = ((x[mlen] << (31 - mblr)) | (x[mlen - 1] >> mblr))
96 & 0x7FFFFFFF;
97 b0 = ((m[mlen] << (31 - mblr)) | (m[mlen - 1] >> mblr))
98 & 0x7FFFFFFF;
99 }
100
101 /*
102 * We estimate a divisor q. If the quotient returned by br_div()
103 * is g:
104 * -- If a0 == b0 then g == 0; we want q = 0x7FFFFFFF.
105 * -- Otherwise:
106 * -- if g == 0 then we set q = 0;
107 * -- otherwise, we set q = g - 1.
108 * The properties described above then ensure that the true
109 * quotient is q-1, q or q+1.
110 *
111 * Take care that a0, a1 and b0 are 31-bit words, not 32-bit. We
112 * must adjust the parameters to br_div() accordingly.
113 */
114 g = br_div(a0 >> 1, a1 | (a0 << 31), b0);
115 q = MUX(EQ(a0, b0), 0x7FFFFFFF, MUX(EQ(g, 0), 0, g - 1));
116
117 /*
118 * We subtract q*m from x (with the extra high word of value 'hi').
119 * Since q may be off by 1 (in either direction), we may have to
120 * add or subtract m afterwards.
121 *
122 * The 'tb' flag will be true (1) at the end of the loop if the
123 * result is greater than or equal to the modulus (not counting
124 * 'hi' or the carry).
125 */
126 cc = 0;
127 tb = 1;
128 for (u = 1; u <= mlen; u ++) {
129 uint32_t mw, zw, xw, nxw;
130 uint64_t zl;
131
132 mw = m[u];
133 zl = MUL31(mw, q) + cc;
134 cc = (uint32_t)(zl >> 31);
135 zw = (uint32_t)zl & (uint32_t)0x7FFFFFFF;
136 xw = x[u];
137 nxw = xw - zw;
138 cc += nxw >> 31;
139 nxw &= 0x7FFFFFFF;
140 x[u] = nxw;
141 tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
142 }
143
144 /*
145 * If we underestimated q, then either cc < hi (one extra bit
146 * beyond the top array word), or cc == hi and tb is true (no
147 * extra bit, but the result is not lower than the modulus). In
148 * these cases we must subtract m once.
149 *
150 * Otherwise, we may have overestimated, which will show as
151 * cc > hi (thus a negative result). Correction is adding m once.
152 */
153 over = GT(cc, hi);
154 under = ~over & (tb | LT(cc, hi));
155 br_i31_add(x, m, over);
156 br_i31_sub(x, m, under);
157 }