/*
* Copyright (c) 2016 Thomas Pornin
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "inner.h"
/* see inner.h */
void
br_i31_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
const uint32_t *m, uint32_t m0i)
{
/*
* Each outer loop iteration computes:
* d <- (d + xu*y + f*m) / 2^31
* We have xu <= 2^31-1 and f <= 2^31-1.
* Thus, if d <= 2*m-1 on input, then:
* 2*m-1 + 2*(2^31-1)*m <= (2^32)*m-1
* and the new d value is less than 2*m.
*
* We represent d over 31-bit words, with an extra word 'dh'
* which can thus be only 0 or 1.
*/
size_t len, len4, u, v;
uint32_t dh;
len = (m[0] + 31) >> 5;
len4 = len & ~(size_t)3;
br_i31_zero(d, m[0]);
dh = 0;
for (u = 0; u < len; u ++) {
/*
* The carry for each operation fits on 32 bits:
* d[v+1] <= 2^31-1
* xu*y[v+1] <= (2^31-1)*(2^31-1)
* f*m[v+1] <= (2^31-1)*(2^31-1)
* r <= 2^32-1
* (2^31-1) + 2*(2^31-1)*(2^31-1) + (2^32-1) = 2^63 - 2^31
* After division by 2^31, the new r is then at most 2^32-1
*
* Using a 32-bit carry has performance benefits on 32-bit
* systems; however, on 64-bit architectures, we prefer to
* keep the carry (r) in a 64-bit register, thus avoiding some
* "clear high bits" operations.
*/
uint32_t f, xu;
#if BR_64
uint64_t r;
#else
uint32_t r;
#endif
xu = x[u + 1];
f = MUL31_lo((d[1] + MUL31_lo(x[u + 1], y[1])), m0i);
r = 0;
for (v = 0; v < len4; v += 4) {
uint64_t z;
z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
+ MUL31(f, m[v + 1]) + r;
r = z >> 31;
d[v + 0] = (uint32_t)z & 0x7FFFFFFF;
z = (uint64_t)d[v + 2] + MUL31(xu, y[v + 2])
+ MUL31(f, m[v + 2]) + r;
r = z >> 31;
d[v + 1] = (uint32_t)z & 0x7FFFFFFF;
z = (uint64_t)d[v + 3] + MUL31(xu, y[v + 3])
+ MUL31(f, m[v + 3]) + r;
r = z >> 31;
d[v + 2] = (uint32_t)z & 0x7FFFFFFF;
z = (uint64_t)d[v + 4] + MUL31(xu, y[v + 4])
+ MUL31(f, m[v + 4]) + r;
r = z >> 31;
d[v + 3] = (uint32_t)z & 0x7FFFFFFF;
}
for (; v < len; v ++) {
uint64_t z;
z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1])
+ MUL31(f, m[v + 1]) + r;
r = z >> 31;
d[v] = (uint32_t)z & 0x7FFFFFFF;
}
/*
* Since the new dh can only be 0 or 1, the addition of
* the old dh with the carry MUST fit on 32 bits, and
* thus can be done into dh itself.
*/
dh += r;
d[len] = dh & 0x7FFFFFFF;
dh >>= 31;
}
/*
* We must write back the bit length because it was overwritten in
* the loop (not overwriting it would require a test in the loop,
* which would yield bigger and slower code).
*/
d[0] = m[0];
/*
* d[] may still be greater than m[] at that point; notably, the
* 'dh' word may be non-zero.
*/
br_i31_sub(d, m, NEQ(dh, 0) | NOT(br_i31_sub(d, m, 0)));
}