174 lines
4.6 KiB
C
174 lines
4.6 KiB
C
/*
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* Copyright (c) 2017 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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/*
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* Constant-time division. The divisor must not be larger than 16 bits,
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* and the quotient must fit on 17 bits.
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*/
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static uint32_t
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divrem16(uint32_t x, uint32_t d, uint32_t *r)
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{
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int i;
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uint32_t q;
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q = 0;
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d <<= 16;
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for (i = 16; i >= 0; i --) {
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uint32_t ctl;
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ctl = LE(d, x);
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q |= ctl << i;
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x -= (-ctl) & d;
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d >>= 1;
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}
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if (r != NULL) {
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*r = x;
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}
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return q;
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}
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/* see inner.h */
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void
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br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m)
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{
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/*
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* Constant-time: we accept to leak the exact bit length of the
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* modulus m.
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*/
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unsigned m_bitlen, mblr;
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size_t u, mlen;
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uint32_t hi, a0, a, b, q;
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uint32_t cc, tb, over, under;
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/*
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* Simple case: the modulus fits on one word.
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*/
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m_bitlen = m[0];
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if (m_bitlen == 0) {
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return;
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}
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if (m_bitlen <= 15) {
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uint32_t rem;
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divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem);
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x[1] = rem;
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return;
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}
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mlen = (m_bitlen + 15) >> 4;
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mblr = m_bitlen & 15;
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/*
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* Principle: we estimate the quotient (x*2^15+z)/m by
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* doing a 30/15 division with the high words.
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*
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* Let:
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* w = 2^15
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* a = (w*a0 + a1) * w^N + a2
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* b = b0 * w^N + b2
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* such that:
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* 0 <= a0 < w
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* 0 <= a1 < w
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* 0 <= a2 < w^N
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* w/2 <= b0 < w
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* 0 <= b2 < w^N
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* a < w*b
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* I.e. the two top words of a are a0:a1, the top word of b is
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* b0, we ensured that b0 is "full" (high bit set), and a is
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* such that the quotient q = a/b fits on one word (0 <= q < w).
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*
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* If a = b*q + r (with 0 <= r < q), then we can estimate q by
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* using a division on the top words:
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* a0*w + a1 = b0*u + v (with 0 <= v < b0)
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* Then the following holds:
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* 0 <= u <= w
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* u-2 <= q <= u
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*/
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hi = x[mlen];
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if (mblr == 0) {
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a0 = x[mlen];
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memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
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x[1] = z;
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a = (a0 << 15) + x[mlen];
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b = m[mlen];
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} else {
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a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr);
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memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
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x[1] = z;
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a = (a0 << 15) | (((x[mlen] << (15 - mblr))
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| (x[mlen - 1] >> mblr)) & 0x7FFF);
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b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr);
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}
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q = divrem16(a, b, NULL);
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/*
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* We computed an estimate for q, but the real one may be q,
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* q-1 or q-2; moreover, the division may have returned a value
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* 8000 or even 8001 if the two high words were identical, and
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* we want to avoid values beyond 7FFF. We thus adjust q so
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* that the "true" multiplier will be q+1, q or q-1, and q is
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* in the 0000..7FFF range.
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*/
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q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31));
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/*
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* We subtract q*m from x (x has an extra high word of value 'hi').
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* Since q may be off by 1 (in either direction), we may have to
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* add or subtract m afterwards.
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*
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* The 'tb' flag will be true (1) at the end of the loop if the
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* result is greater than or equal to the modulus (not counting
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* 'hi' or the carry).
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*/
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cc = 0;
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tb = 1;
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for (u = 1; u <= mlen; u ++) {
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uint32_t mw, zl, xw, nxw;
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mw = m[u];
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zl = MUL15(mw, q) + cc;
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cc = zl >> 15;
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zl &= 0x7FFF;
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xw = x[u];
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nxw = xw - zl;
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cc += nxw >> 31;
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nxw &= 0x7FFF;
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x[u] = nxw;
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tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
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}
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/*
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* If we underestimated q, then either cc < hi (one extra bit
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* beyond the top array word), or cc == hi and tb is true (no
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* extra bit, but the result is not lower than the modulus).
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*
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* If we overestimated q, then cc > hi.
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*/
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over = GT(cc, hi);
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under = ~over & (tb | LT(cc, hi));
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br_i15_add(x, m, over);
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br_i15_sub(x, m, under);
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}
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