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