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 } 158