_ Git - BearSSL/blob - src/int/i31_montmul.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_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
  30         const uint32_t *m, uint32_t m0i)
  31 {
  32         /*
  33          * Each outer loop iteration computes:
  34          *   d <- (d + xu*y + f*m) / 2^31
  35          * We have xu <= 2^31-1 and f <= 2^31-1.
  36          * Thus, if d <= 2*m-1 on input, then:
  37          *   2*m-1 + 2*(2^31-1)*m <= (2^32)*m-1
  38          * and the new d value is less than 2*m.
  39          *
  40          * We represent d over 31-bit words, with an extra word 'dh'
  41          * which can thus be only 0 or 1.
  42          */
  43         size_t len, len4, u, v;
  44         uint32_t dh;
  45
  46         len = (m[0] + 31) >> 5;
  47         len4 = len & ~(size_t)3;
  48         br_i31_zero(d, m[0]);
  49         dh = 0;
  50         for (u = 0; u < len; u ++) {
  51                 /*
  52                  * The carry for each operation fits on 32 bits:
  53                  *   d[v+1] <= 2^31-1
  54                  *   xu*y[v+1] <= (2^31-1)*(2^31-1)
  55                  *   f*m[v+1] <= (2^31-1)*(2^31-1)
  56                  *   r <= 2^32-1
  57                  *   (2^31-1) + 2*(2^31-1)*(2^31-1) + (2^32-1) = 2^63 - 2^31
  58                  * After division by 2^31, the new r is then at most 2^32-1
  59                  *
  60                  * Using a 32-bit carry has performance benefits on 32-bit
  61                  * systems; however, on 64-bit architectures, we prefer to
  62                  * keep the carry (r) in a 64-bit register, thus avoiding some
  63                  * "clear high bits" operations.
  64                  */
  65                 uint32_t f, xu;
  66 #if BR_64
  67                 uint64_t r;
  68 #else
  69                 uint32_t r;
  70 #endif
  71
  72                 xu = x[u + 1];
  73                 f = MUL31_lo((d[1] + MUL31_lo(x[u + 1], y[1])), m0i);
  74
  75                 r = 0;
  76                 for (v = 0; v < len4; v += 4) {
  77                         uint64_t z;
  78
  79                         z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
  80                                 + MUL31(f, m[v + 1]) + r;
  81                         r = z >> 31;
  82                         d[v + 0] = (uint32_t)z & 0x7FFFFFFF;
  83                         z = (uint64_t)d[v + 2] + MUL31(xu, y[v + 2])
  84                                 + MUL31(f, m[v + 2]) + r;
  85                         r = z >> 31;
  86                         d[v + 1] = (uint32_t)z & 0x7FFFFFFF;
  87                         z = (uint64_t)d[v + 3] + MUL31(xu, y[v + 3])
  88                                 + MUL31(f, m[v + 3]) + r;
  89                         r = z >> 31;
  90                         d[v + 2] = (uint32_t)z & 0x7FFFFFFF;
  91                         z = (uint64_t)d[v + 4] + MUL31(xu, y[v + 4])
  92                                 + MUL31(f, m[v + 4]) + r;
  93                         r = z >> 31;
  94                         d[v + 3] = (uint32_t)z & 0x7FFFFFFF;
  95                 }
  96                 for (; v < len; v ++) {
  97                         uint64_t z;
  98
  99                         z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
 100                                 + MUL31(f, m[v + 1]) + r;
 101                         r = z >> 31;
 102                         d[v] = (uint32_t)z & 0x7FFFFFFF;
 103                 }
 104
 105                 /*
 106                  * Since the new dh can only be 0 or 1, the addition of
 107                  * the old dh with the carry MUST fit on 32 bits, and
 108                  * thus can be done into dh itself.
 109                  */
 110                 dh += r;
 111                 d[len] = dh & 0x7FFFFFFF;
 112                 dh >>= 31;
 113         }
 114
 115         /*
 116          * We must write back the bit length because it was overwritten in
 117          * the loop (not overwriting it would require a test in the loop,
 118          * which would yield bigger and slower code).
 119          */
 120         d[0] = m[0];
 121
 122         /*
 123          * d[] may still be greater than m[] at that point; notably, the
 124          * 'dh' word may be non-zero.
 125          */
 126         br_i31_sub(d, m, NEQ(dh, 0) | NOT(br_i31_sub(d, m, 0)));
 127 }