_ Git - BearSSL/blob - src/int/i32_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_i32_muladd_small(uint32_t *x, uint32_t z, const uint32_t *m)
  30 {
  31         uint32_t m_bitlen;
  32         size_t u, mlen;
  33         uint32_t a0, a1, b0, hi, g, q, tb;
  34         uint32_t chf, clow, under, over;
  35         uint64_t cc;
  36
  37         /*
  38          * We can test on the modulus bit length since we accept to
  39          * leak that length.
  40          */
  41         m_bitlen = m[0];
  42         if (m_bitlen == 0) {
  43                 return;
  44         }
  45         if (m_bitlen <= 32) {
  46                 x[1] = br_rem(x[1], z, m[1]);
  47                 return;
  48         }
  49         mlen = (m_bitlen + 31) >> 5;
  50
  51         /*
  52          * Principle: we estimate the quotient (x*2^32+z)/m by
  53          * doing a 64/32 division with the high words.
  54          *
  55          * Let:
  56          *   w = 2^32
  57          *   a = (w*a0 + a1) * w^N + a2
  58          *   b = b0 * w^N + b2
  59          * such that:
  60          *   0 <= a0 < w
  61          *   0 <= a1 < w
  62          *   0 <= a2 < w^N
  63          *   w/2 <= b0 < w
  64          *   0 <= b2 < w^N
  65          *   a < w*b
  66          * I.e. the two top words of a are a0:a1, the top word of b is
  67          * b0, we ensured that b0 is "full" (high bit set), and a is
  68          * such that the quotient q = a/b fits on one word (0 <= q < w).
  69          *
  70          * If a = b*q + r (with 0 <= r < q), we can estimate q by
  71          * doing an Euclidean division on the top words:
  72          *   a0*w+a1 = b0*u + v  (with 0 <= v < w)
  73          * Then the following holds:
  74          *   0 <= u <= w
  75          *   u-2 <= q <= u
  76          */
  77         a0 = br_i32_word(x, m_bitlen - 32);
  78         hi = x[mlen];
  79         memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
  80         x[1] = z;
  81         a1 = br_i32_word(x, m_bitlen - 32);
  82         b0 = br_i32_word(m, m_bitlen - 32);
  83
  84         /*
  85          * We estimate a divisor q. If the quotient returned by br_div()
  86          * is g:
  87          * -- If a0 == b0 then g == 0; we want q = 0xFFFFFFFF.
  88          * -- Otherwise:
  89          *    -- if g == 0 then we set q = 0;
  90          *    -- otherwise, we set q = g - 1.
  91          * The properties described above then ensure that the true
  92          * quotient is q-1, q or q+1.
  93          */
  94         g = br_div(a0, a1, b0);
  95         q = MUX(EQ(a0, b0), 0xFFFFFFFF, MUX(EQ(g, 0), 0, g - 1));
  96
  97         /*
  98          * We subtract q*m from x (with the extra high word of value 'hi').
  99          * Since q may be off by 1 (in either direction), we may have to
 100          * add or subtract m afterwards.
 101          *
 102          * The 'tb' flag will be true (1) at the end of the loop if the
 103          * result is greater than or equal to the modulus (not counting
 104          * 'hi' or the carry).
 105          */
 106         cc = 0;
 107         tb = 1;
 108         for (u = 1; u <= mlen; u ++) {
 109                 uint32_t mw, zw, xw, nxw;
 110                 uint64_t zl;
 111
 112                 mw = m[u];
 113                 zl = MUL(mw, q) + cc;
 114                 cc = (uint32_t)(zl >> 32);
 115                 zw = (uint32_t)zl;
 116                 xw = x[u];
 117                 nxw = xw - zw;
 118                 cc += (uint64_t)GT(nxw, xw);
 119                 x[u] = nxw;
 120                 tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
 121         }
 122
 123         /*
 124          * If we underestimated q, then either cc < hi (one extra bit
 125          * beyond the top array word), or cc == hi and tb is true (no
 126          * extra bit, but the result is not lower than the modulus). In
 127          * these cases we must subtract m once.
 128          *
 129          * Otherwise, we may have overestimated, which will show as
 130          * cc > hi (thus a negative result). Correction is adding m once.
 131          */
 132         chf = (uint32_t)(cc >> 32);
 133         clow = (uint32_t)cc;
 134         over = chf | GT(clow, hi);
 135         under = ~over & (tb | (~chf & LT(clow, hi)));
 136         br_i32_add(x, m, over);
 137         br_i32_sub(x, m, under);
 138 }