Some cleanups (removed unused files, split i15 code into per-function files).
This commit is contained in:
Thomas Pornin
parent
bd3036844b
commit
2f454aad57
22 changed files with 945 additions and 843 deletions
46
src/int/i15_add.c
Normal file
46
src/int/i15_add.c
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@ -0,0 +1,46 @@
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/*
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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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/* see inner.h */
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uint32_t
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br_i15_add(uint16_t *a, const uint16_t *b, uint32_t ctl)
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{
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uint32_t cc;
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size_t u, m;
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cc = 0;
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m = (a[0] + 31) >> 4;
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for (u = 1; u < m; u ++) {
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uint32_t aw, bw, naw;
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aw = a[u];
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bw = b[u];
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naw = aw + bw + cc;
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cc = naw >> 15;
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a[u] = MUX(ctl, naw & 0x7FFF, aw);
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}
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return cc;
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}
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44
src/int/i15_bitlen.c
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44
src/int/i15_bitlen.c
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@ -0,0 +1,44 @@
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/*
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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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/* see inner.h */
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uint32_t
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br_i15_bit_length(uint16_t *x, size_t xlen)
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{
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uint32_t tw, twk;
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tw = 0;
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twk = 0;
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while (xlen -- > 0) {
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uint32_t w, c;
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c = EQ(tw, 0);
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w = x[xlen];
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tw = MUX(c, w, tw);
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twk = MUX(c, (uint32_t)xlen, twk);
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}
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return (twk << 4) + BIT_LENGTH(tw);
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}
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@ -1,480 +0,0 @@
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/*
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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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* This file contains the core "big integer" functions for the i15
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* implementation, that represents integers as sequences of 15-bit
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* words.
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*/
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/* see inner.h */
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uint32_t
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br_i15_iszero(const uint16_t *x)
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{
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uint32_t z;
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size_t u;
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z = 0;
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for (u = (x[0] + 15) >> 4; u > 0; u --) {
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z |= x[u];
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}
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return ~(z | -z) >> 31;
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}
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/* see inner.h */
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uint16_t
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br_i15_ninv15(uint16_t x)
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{
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uint32_t y;
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y = 2 - x;
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y = MUL15(y, 2 - MUL15(x, y));
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y = MUL15(y, 2 - MUL15(x, y));
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y = MUL15(y, 2 - MUL15(x, y));
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return MUX(x & 1, -y, 0) & 0x7FFF;
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}
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/* see inner.h */
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uint32_t
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br_i15_add(uint16_t *a, const uint16_t *b, uint32_t ctl)
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{
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uint32_t cc;
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size_t u, m;
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cc = 0;
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m = (a[0] + 31) >> 4;
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for (u = 1; u < m; u ++) {
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uint32_t aw, bw, naw;
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aw = a[u];
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bw = b[u];
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naw = aw + bw + cc;
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cc = naw >> 15;
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a[u] = MUX(ctl, naw & 0x7FFF, aw);
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}
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return cc;
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}
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/* see inner.h */
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uint32_t
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br_i15_sub(uint16_t *a, const uint16_t *b, uint32_t ctl)
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{
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uint32_t cc;
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size_t u, m;
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cc = 0;
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m = (a[0] + 31) >> 4;
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for (u = 1; u < m; u ++) {
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uint32_t aw, bw, naw;
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aw = a[u];
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bw = b[u];
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naw = aw - bw - cc;
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cc = naw >> 31;
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a[u] = MUX(ctl, naw & 0x7FFF, aw);
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}
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return cc;
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}
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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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/* see inner.h */
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void
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br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
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const uint16_t *m, uint16_t m0i)
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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] + 15) >> 4;
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len4 = len & ~(size_t)3;
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br_i15_zero(d, m[0]);
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dh = 0;
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for (u = 0; u < len; u ++) {
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uint32_t f, xu, r, zh;
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xu = x[u + 1];
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f = MUL15((d[1] + MUL15(x[u + 1], y[1])) & 0x7FFF, m0i)
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& 0x7FFF;
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r = 0;
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for (v = 0; v < len4; v += 4) {
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uint32_t z;
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z = d[v + 1] + MUL15(xu, y[v + 1])
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+ MUL15(f, m[v + 1]) + r;
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r = z >> 15;
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d[v + 0] = z & 0x7FFF;
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z = d[v + 2] + MUL15(xu, y[v + 2])
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+ MUL15(f, m[v + 2]) + r;
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r = z >> 15;
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d[v + 1] = z & 0x7FFF;
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z = d[v + 3] + MUL15(xu, y[v + 3])
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+ MUL15(f, m[v + 3]) + r;
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r = z >> 15;
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d[v + 2] = z & 0x7FFF;
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z = d[v + 4] + MUL15(xu, y[v + 4])
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+ MUL15(f, m[v + 4]) + r;
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r = z >> 15;
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d[v + 3] = z & 0x7FFF;
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}
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for (; v < len; v ++) {
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uint32_t z;
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z = d[v + 1] + MUL15(xu, y[v + 1])
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+ MUL15(f, m[v + 1]) + r;
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r = z >> 15;
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d[v + 0] = z & 0x7FFF;
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}
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zh = dh + r;
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d[len] = zh & 0x7FFF;
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dh = zh >> 15;
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}
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/*
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* Restore the bit length (it was overwritten in the loop above).
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*/
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d[0] = m[0];
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/*
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* d[] may be greater than m[], but it is still lower than twice
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* the modulus.
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*/
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br_i15_sub(d, m, NEQ(dh, 0) | NOT(br_i15_sub(d, m, 0)));
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}
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/* see inner.h */
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void
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br_i15_to_monty(uint16_t *x, const uint16_t *m)
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{
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unsigned k;
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for (k = (m[0] + 15) >> 4; k > 0; k --) {
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br_i15_muladd_small(x, 0, m);
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}
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}
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/* see inner.h */
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void
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br_i15_modpow(uint16_t *x,
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const unsigned char *e, size_t elen,
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const uint16_t *m, uint16_t m0i, uint16_t *t1, uint16_t *t2)
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{
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size_t mlen;
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unsigned k;
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mlen = ((m[0] + 31) >> 4) * sizeof m[0];
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memcpy(t1, x, mlen);
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br_i15_to_monty(t1, m);
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br_i15_zero(x, m[0]);
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x[1] = 1;
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for (k = 0; k < ((unsigned)elen << 3); k ++) {
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uint32_t ctl;
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ctl = (e[elen - 1 - (k >> 3)] >> (k & 7)) & 1;
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br_i15_montymul(t2, x, t1, m, m0i);
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CCOPY(ctl, x, t2, mlen);
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br_i15_montymul(t2, t1, t1, m, m0i);
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memcpy(t1, t2, mlen);
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}
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}
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/* see inner.h */
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void
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br_i15_encode(void *dst, size_t len, const uint16_t *x)
|
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{
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unsigned char *buf;
|
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size_t u, xlen;
|
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uint32_t acc;
|
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int acc_len;
|
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|
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xlen = (x[0] + 15) >> 4;
|
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if (xlen == 0) {
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memset(dst, 0, len);
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return;
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}
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u = 1;
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acc = 0;
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acc_len = 0;
|
||||
buf = dst;
|
||||
while (len -- > 0) {
|
||||
if (acc_len < 8) {
|
||||
if (u <= xlen) {
|
||||
acc += (uint32_t)x[u ++] << acc_len;
|
||||
}
|
||||
acc_len += 15;
|
||||
}
|
||||
buf[len] = (unsigned char)acc;
|
||||
acc >>= 8;
|
||||
acc_len -= 8;
|
||||
}
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
uint32_t
|
||||
br_i15_decode_mod(uint16_t *x, const void *src, size_t len, const uint16_t *m)
|
||||
{
|
||||
/*
|
||||
* Two-pass algorithm: in the first pass, we determine whether the
|
||||
* value fits; in the second pass, we do the actual write.
|
||||
*
|
||||
* During the first pass, 'r' contains the comparison result so
|
||||
* far:
|
||||
* 0x00000000 value is equal to the modulus
|
||||
* 0x00000001 value is greater than the modulus
|
||||
* 0xFFFFFFFF value is lower than the modulus
|
||||
*
|
||||
* Since we iterate starting with the least significant bytes (at
|
||||
* the end of src[]), each new comparison overrides the previous
|
||||
* except when the comparison yields 0 (equal).
|
||||
*
|
||||
* During the second pass, 'r' is either 0xFFFFFFFF (value fits)
|
||||
* or 0x00000000 (value does not fit).
|
||||
*
|
||||
* We must iterate over all bytes of the source, _and_ possibly
|
||||
* some extra virutal bytes (with value 0) so as to cover the
|
||||
* complete modulus as well. We also add 4 such extra bytes beyond
|
||||
* the modulus length because it then guarantees that no accumulated
|
||||
* partial word remains to be processed.
|
||||
*/
|
||||
const unsigned char *buf;
|
||||
size_t mlen, tlen;
|
||||
int pass;
|
||||
uint32_t r;
|
||||
|
||||
buf = src;
|
||||
mlen = (m[0] + 15) >> 4;
|
||||
tlen = (mlen << 1);
|
||||
if (tlen < len) {
|
||||
tlen = len;
|
||||
}
|
||||
tlen += 4;
|
||||
r = 0;
|
||||
for (pass = 0; pass < 2; pass ++) {
|
||||
size_t u, v;
|
||||
uint32_t acc;
|
||||
int acc_len;
|
||||
|
||||
v = 1;
|
||||
acc = 0;
|
||||
acc_len = 0;
|
||||
for (u = 0; u < tlen; u ++) {
|
||||
uint32_t b;
|
||||
|
||||
if (u < len) {
|
||||
b = buf[len - 1 - u];
|
||||
} else {
|
||||
b = 0;
|
||||
}
|
||||
acc |= (b << acc_len);
|
||||
acc_len += 8;
|
||||
if (acc_len >= 15) {
|
||||
uint32_t xw;
|
||||
|
||||
xw = acc & (uint32_t)0x7FFF;
|
||||
acc_len -= 15;
|
||||
acc = b >> (8 - acc_len);
|
||||
if (v <= mlen) {
|
||||
if (pass) {
|
||||
x[v] = r & xw;
|
||||
} else {
|
||||
uint32_t cc;
|
||||
|
||||
cc = (uint32_t)CMP(xw, m[v]);
|
||||
r = MUX(EQ(cc, 0), r, cc);
|
||||
}
|
||||
} else {
|
||||
if (!pass) {
|
||||
r = MUX(EQ(xw, 0), r, 1);
|
||||
}
|
||||
}
|
||||
v ++;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* When we reach this point at the end of the first pass:
|
||||
* r is either 0, 1 or -1; we want to set r to 0 if it
|
||||
* is equal to 0 or 1, and leave it to -1 otherwise.
|
||||
*
|
||||
* When we reach this point at the end of the second pass:
|
||||
* r is either 0 or -1; we want to leave that value
|
||||
* untouched. This is a subcase of the previous.
|
||||
*/
|
||||
r >>= 1;
|
||||
r |= (r << 1);
|
||||
}
|
||||
|
||||
x[0] = m[0];
|
||||
return r & (uint32_t)1;
|
||||
}
|
||||
124
src/int/i15_decmod.c
Normal file
124
src/int/i15_decmod.c
Normal file
|
|
@ -0,0 +1,124 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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 */
|
||||
uint32_t
|
||||
br_i15_decode_mod(uint16_t *x, const void *src, size_t len, const uint16_t *m)
|
||||
{
|
||||
/*
|
||||
* Two-pass algorithm: in the first pass, we determine whether the
|
||||
* value fits; in the second pass, we do the actual write.
|
||||
*
|
||||
* During the first pass, 'r' contains the comparison result so
|
||||
* far:
|
||||
* 0x00000000 value is equal to the modulus
|
||||
* 0x00000001 value is greater than the modulus
|
||||
* 0xFFFFFFFF value is lower than the modulus
|
||||
*
|
||||
* Since we iterate starting with the least significant bytes (at
|
||||
* the end of src[]), each new comparison overrides the previous
|
||||
* except when the comparison yields 0 (equal).
|
||||
*
|
||||
* During the second pass, 'r' is either 0xFFFFFFFF (value fits)
|
||||
* or 0x00000000 (value does not fit).
|
||||
*
|
||||
* We must iterate over all bytes of the source, _and_ possibly
|
||||
* some extra virutal bytes (with value 0) so as to cover the
|
||||
* complete modulus as well. We also add 4 such extra bytes beyond
|
||||
* the modulus length because it then guarantees that no accumulated
|
||||
* partial word remains to be processed.
|
||||
*/
|
||||
const unsigned char *buf;
|
||||
size_t mlen, tlen;
|
||||
int pass;
|
||||
uint32_t r;
|
||||
|
||||
buf = src;
|
||||
mlen = (m[0] + 15) >> 4;
|
||||
tlen = (mlen << 1);
|
||||
if (tlen < len) {
|
||||
tlen = len;
|
||||
}
|
||||
tlen += 4;
|
||||
r = 0;
|
||||
for (pass = 0; pass < 2; pass ++) {
|
||||
size_t u, v;
|
||||
uint32_t acc;
|
||||
int acc_len;
|
||||
|
||||
v = 1;
|
||||
acc = 0;
|
||||
acc_len = 0;
|
||||
for (u = 0; u < tlen; u ++) {
|
||||
uint32_t b;
|
||||
|
||||
if (u < len) {
|
||||
b = buf[len - 1 - u];
|
||||
} else {
|
||||
b = 0;
|
||||
}
|
||||
acc |= (b << acc_len);
|
||||
acc_len += 8;
|
||||
if (acc_len >= 15) {
|
||||
uint32_t xw;
|
||||
|
||||
xw = acc & (uint32_t)0x7FFF;
|
||||
acc_len -= 15;
|
||||
acc = b >> (8 - acc_len);
|
||||
if (v <= mlen) {
|
||||
if (pass) {
|
||||
x[v] = r & xw;
|
||||
} else {
|
||||
uint32_t cc;
|
||||
|
||||
cc = (uint32_t)CMP(xw, m[v]);
|
||||
r = MUX(EQ(cc, 0), r, cc);
|
||||
}
|
||||
} else {
|
||||
if (!pass) {
|
||||
r = MUX(EQ(xw, 0), r, 1);
|
||||
}
|
||||
}
|
||||
v ++;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* When we reach this point at the end of the first pass:
|
||||
* r is either 0, 1 or -1; we want to set r to 0 if it
|
||||
* is equal to 0 or 1, and leave it to -1 otherwise.
|
||||
*
|
||||
* When we reach this point at the end of the second pass:
|
||||
* r is either 0 or -1; we want to leave that value
|
||||
* untouched. This is a subcase of the previous.
|
||||
*/
|
||||
r >>= 1;
|
||||
r |= (r << 1);
|
||||
}
|
||||
|
||||
x[0] = m[0];
|
||||
return r & (uint32_t)1;
|
||||
}
|
||||
56
src/int/i15_decode.c
Normal file
56
src/int/i15_decode.c
Normal file
|
|
@ -0,0 +1,56 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_decode(uint16_t *x, const void *src, size_t len)
|
||||
{
|
||||
const unsigned char *buf;
|
||||
size_t v;
|
||||
uint32_t acc;
|
||||
int acc_len;
|
||||
|
||||
buf = src;
|
||||
v = 1;
|
||||
acc = 0;
|
||||
acc_len = 0;
|
||||
while (len -- > 0) {
|
||||
uint32_t b;
|
||||
|
||||
b = buf[len];
|
||||
acc |= (b << acc_len);
|
||||
acc_len += 8;
|
||||
if (acc_len >= 15) {
|
||||
x[v ++] = acc & 0x7FFF;
|
||||
acc_len -= 15;
|
||||
acc >>= 15;
|
||||
}
|
||||
}
|
||||
if (acc_len != 0) {
|
||||
x[v ++] = acc;
|
||||
}
|
||||
x[0] = br_i15_bit_length(x + 1, v - 1);
|
||||
}
|
||||
|
|
@ -24,11 +24,6 @@
|
|||
|
||||
#include "inner.h"
|
||||
|
||||
/*
|
||||
* This file contains some additional functions for "i15" big integers.
|
||||
* These functions are needed to support RSA.
|
||||
*/
|
||||
|
||||
/* see inner.h */
|
||||
void
|
||||
br_i15_decode_reduce(uint16_t *x,
|
||||
|
|
@ -103,71 +98,3 @@ br_i15_decode_reduce(uint16_t *x,
|
|||
br_i15_muladd_small(x, acc, m);
|
||||
}
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
void
|
||||
br_i15_reduce(uint16_t *x, const uint16_t *a, const uint16_t *m)
|
||||
{
|
||||
uint32_t m_bitlen, a_bitlen;
|
||||
size_t mlen, alen, u;
|
||||
|
||||
m_bitlen = m[0];
|
||||
mlen = (m_bitlen + 15) >> 4;
|
||||
|
||||
x[0] = m_bitlen;
|
||||
if (m_bitlen == 0) {
|
||||
return;
|
||||
}
|
||||
|
||||
/*
|
||||
* If the source is shorter, then simply copy all words from a[]
|
||||
* and zero out the upper words.
|
||||
*/
|
||||
a_bitlen = a[0];
|
||||
alen = (a_bitlen + 15) >> 4;
|
||||
if (a_bitlen < m_bitlen) {
|
||||
memcpy(x + 1, a + 1, alen * sizeof *a);
|
||||
for (u = alen; u < mlen; u ++) {
|
||||
x[u + 1] = 0;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/*
|
||||
* The source length is at least equal to that of the modulus.
|
||||
* We must thus copy N-1 words, and input the remaining words
|
||||
* one by one.
|
||||
*/
|
||||
memcpy(x + 1, a + 2 + (alen - mlen), (mlen - 1) * sizeof *a);
|
||||
x[mlen] = 0;
|
||||
for (u = 1 + alen - mlen; u > 0; u --) {
|
||||
br_i15_muladd_small(x, a[u], m);
|
||||
}
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
void
|
||||
br_i15_mulacc(uint16_t *d, const uint16_t *a, const uint16_t *b)
|
||||
{
|
||||
size_t alen, blen, u;
|
||||
|
||||
alen = (a[0] + 15) >> 4;
|
||||
blen = (b[0] + 15) >> 4;
|
||||
d[0] = a[0] + b[0];
|
||||
for (u = 0; u < blen; u ++) {
|
||||
uint32_t f;
|
||||
size_t v;
|
||||
uint32_t cc;
|
||||
|
||||
f = b[1 + u];
|
||||
cc = 0;
|
||||
for (v = 0; v < alen; v ++) {
|
||||
uint32_t z;
|
||||
|
||||
z = (uint32_t)d[1 + u + v] + MUL15(f, a[1 + v]) + cc;
|
||||
cc = z >> 15;
|
||||
d[1 + u + v] = z & 0x7FFF;
|
||||
}
|
||||
d[1 + u + alen] = cc;
|
||||
}
|
||||
}
|
||||
56
src/int/i15_encode.c
Normal file
56
src/int/i15_encode.c
Normal file
|
|
@ -0,0 +1,56 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_encode(void *dst, size_t len, const uint16_t *x)
|
||||
{
|
||||
unsigned char *buf;
|
||||
size_t u, xlen;
|
||||
uint32_t acc;
|
||||
int acc_len;
|
||||
|
||||
xlen = (x[0] + 15) >> 4;
|
||||
if (xlen == 0) {
|
||||
memset(dst, 0, len);
|
||||
return;
|
||||
}
|
||||
u = 1;
|
||||
acc = 0;
|
||||
acc_len = 0;
|
||||
buf = dst;
|
||||
while (len -- > 0) {
|
||||
if (acc_len < 8) {
|
||||
if (u <= xlen) {
|
||||
acc += (uint32_t)x[u ++] << acc_len;
|
||||
}
|
||||
acc_len += 15;
|
||||
}
|
||||
buf[len] = (unsigned char)acc;
|
||||
acc >>= 8;
|
||||
acc_len -= 8;
|
||||
}
|
||||
}
|
||||
|
|
@ -24,83 +24,6 @@
|
|||
|
||||
#include "inner.h"
|
||||
|
||||
/*
|
||||
* This file contains some additional functions for "i15" big integers.
|
||||
* These functions are needed to support ECDSA.
|
||||
*/
|
||||
|
||||
/* see inner.h */
|
||||
void
|
||||
br_i15_rshift(uint16_t *x, int count)
|
||||
{
|
||||
size_t u, len;
|
||||
unsigned r;
|
||||
|
||||
len = (x[0] + 15) >> 4;
|
||||
if (len == 0) {
|
||||
return;
|
||||
}
|
||||
r = x[1] >> count;
|
||||
for (u = 2; u <= len; u ++) {
|
||||
unsigned w;
|
||||
|
||||
w = x[u];
|
||||
x[u - 1] = ((w << (15 - count)) | r) & 0x7FFF;
|
||||
r = w >> count;
|
||||
}
|
||||
x[len] = r;
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
uint32_t
|
||||
br_i15_bit_length(uint16_t *x, size_t xlen)
|
||||
{
|
||||
uint32_t tw, twk;
|
||||
|
||||
tw = 0;
|
||||
twk = 0;
|
||||
while (xlen -- > 0) {
|
||||
uint32_t w, c;
|
||||
|
||||
c = EQ(tw, 0);
|
||||
w = x[xlen];
|
||||
tw = MUX(c, w, tw);
|
||||
twk = MUX(c, (uint32_t)xlen, twk);
|
||||
}
|
||||
return (twk << 4) + BIT_LENGTH(tw);
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
void
|
||||
br_i15_decode(uint16_t *x, const void *src, size_t len)
|
||||
{
|
||||
const unsigned char *buf;
|
||||
size_t v;
|
||||
uint32_t acc;
|
||||
int acc_len;
|
||||
|
||||
buf = src;
|
||||
v = 1;
|
||||
acc = 0;
|
||||
acc_len = 0;
|
||||
while (len -- > 0) {
|
||||
uint32_t b;
|
||||
|
||||
b = buf[len];
|
||||
acc |= (b << acc_len);
|
||||
acc_len += 8;
|
||||
if (acc_len >= 15) {
|
||||
x[v ++] = acc & 0x7FFF;
|
||||
acc_len -= 15;
|
||||
acc >>= 15;
|
||||
}
|
||||
}
|
||||
if (acc_len != 0) {
|
||||
x[v ++] = acc;
|
||||
}
|
||||
x[0] = br_i15_bit_length(x + 1, v - 1);
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
void
|
||||
br_i15_from_monty(uint16_t *x, const uint16_t *m, uint16_t m0i)
|
||||
39
src/int/i15_iszero.c
Normal file
39
src/int/i15_iszero.c
Normal file
|
|
@ -0,0 +1,39 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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 */
|
||||
uint32_t
|
||||
br_i15_iszero(const uint16_t *x)
|
||||
{
|
||||
uint32_t z;
|
||||
size_t u;
|
||||
|
||||
z = 0;
|
||||
for (u = (x[0] + 15) >> 4; u > 0; u --) {
|
||||
z |= x[u];
|
||||
}
|
||||
return ~(z | -z) >> 31;
|
||||
}
|
||||
50
src/int/i15_modpow.c
Normal file
50
src/int/i15_modpow.c
Normal file
|
|
@ -0,0 +1,50 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_modpow(uint16_t *x,
|
||||
const unsigned char *e, size_t elen,
|
||||
const uint16_t *m, uint16_t m0i, uint16_t *t1, uint16_t *t2)
|
||||
{
|
||||
size_t mlen;
|
||||
unsigned k;
|
||||
|
||||
mlen = ((m[0] + 31) >> 4) * sizeof m[0];
|
||||
memcpy(t1, x, mlen);
|
||||
br_i15_to_monty(t1, m);
|
||||
br_i15_zero(x, m[0]);
|
||||
x[1] = 1;
|
||||
for (k = 0; k < ((unsigned)elen << 3); k ++) {
|
||||
uint32_t ctl;
|
||||
|
||||
ctl = (e[elen - 1 - (k >> 3)] >> (k & 7)) & 1;
|
||||
br_i15_montymul(t2, x, t1, m, m0i);
|
||||
CCOPY(ctl, x, t2, mlen);
|
||||
br_i15_montymul(t2, t1, t1, m, m0i);
|
||||
memcpy(t1, t2, mlen);
|
||||
}
|
||||
}
|
||||
91
src/int/i15_montmul.c
Normal file
91
src/int/i15_montmul.c
Normal file
|
|
@ -0,0 +1,91 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
|
||||
const uint16_t *m, uint16_t m0i)
|
||||
{
|
||||
size_t len, len4, u, v;
|
||||
uint32_t dh;
|
||||
|
||||
len = (m[0] + 15) >> 4;
|
||||
len4 = len & ~(size_t)3;
|
||||
br_i15_zero(d, m[0]);
|
||||
dh = 0;
|
||||
for (u = 0; u < len; u ++) {
|
||||
uint32_t f, xu, r, zh;
|
||||
|
||||
xu = x[u + 1];
|
||||
f = MUL15((d[1] + MUL15(x[u + 1], y[1])) & 0x7FFF, m0i)
|
||||
& 0x7FFF;
|
||||
|
||||
r = 0;
|
||||
for (v = 0; v < len4; v += 4) {
|
||||
uint32_t z;
|
||||
|
||||
z = d[v + 1] + MUL15(xu, y[v + 1])
|
||||
+ MUL15(f, m[v + 1]) + r;
|
||||
r = z >> 15;
|
||||
d[v + 0] = z & 0x7FFF;
|
||||
z = d[v + 2] + MUL15(xu, y[v + 2])
|
||||
+ MUL15(f, m[v + 2]) + r;
|
||||
r = z >> 15;
|
||||
d[v + 1] = z & 0x7FFF;
|
||||
z = d[v + 3] + MUL15(xu, y[v + 3])
|
||||
+ MUL15(f, m[v + 3]) + r;
|
||||
r = z >> 15;
|
||||
d[v + 2] = z & 0x7FFF;
|
||||
z = d[v + 4] + MUL15(xu, y[v + 4])
|
||||
+ MUL15(f, m[v + 4]) + r;
|
||||
r = z >> 15;
|
||||
d[v + 3] = z & 0x7FFF;
|
||||
}
|
||||
for (; v < len; v ++) {
|
||||
uint32_t z;
|
||||
|
||||
z = d[v + 1] + MUL15(xu, y[v + 1])
|
||||
+ MUL15(f, m[v + 1]) + r;
|
||||
r = z >> 15;
|
||||
d[v + 0] = z & 0x7FFF;
|
||||
}
|
||||
|
||||
zh = dh + r;
|
||||
d[len] = zh & 0x7FFF;
|
||||
dh = zh >> 15;
|
||||
}
|
||||
|
||||
/*
|
||||
* Restore the bit length (it was overwritten in the loop above).
|
||||
*/
|
||||
d[0] = m[0];
|
||||
|
||||
/*
|
||||
* d[] may be greater than m[], but it is still lower than twice
|
||||
* the modulus.
|
||||
*/
|
||||
br_i15_sub(d, m, NEQ(dh, 0) | NOT(br_i15_sub(d, m, 0)));
|
||||
}
|
||||
52
src/int/i15_mulacc.c
Normal file
52
src/int/i15_mulacc.c
Normal file
|
|
@ -0,0 +1,52 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_mulacc(uint16_t *d, const uint16_t *a, const uint16_t *b)
|
||||
{
|
||||
size_t alen, blen, u;
|
||||
|
||||
alen = (a[0] + 15) >> 4;
|
||||
blen = (b[0] + 15) >> 4;
|
||||
d[0] = a[0] + b[0];
|
||||
for (u = 0; u < blen; u ++) {
|
||||
uint32_t f;
|
||||
size_t v;
|
||||
uint32_t cc;
|
||||
|
||||
f = b[1 + u];
|
||||
cc = 0;
|
||||
for (v = 0; v < alen; v ++) {
|
||||
uint32_t z;
|
||||
|
||||
z = (uint32_t)d[1 + u + v] + MUL15(f, a[1 + v]) + cc;
|
||||
cc = z >> 15;
|
||||
d[1 + u + v] = z & 0x7FFF;
|
||||
}
|
||||
d[1 + u + alen] = cc;
|
||||
}
|
||||
}
|
||||
173
src/int/i15_muladd.c
Normal file
173
src/int/i15_muladd.c
Normal file
|
|
@ -0,0 +1,173 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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"
|
||||
|
||||
/*
|
||||
* Constant-time division. The divisor must not be larger than 16 bits,
|
||||
* and the quotient must fit on 17 bits.
|
||||
*/
|
||||
static uint32_t
|
||||
divrem16(uint32_t x, uint32_t d, uint32_t *r)
|
||||
{
|
||||
int i;
|
||||
uint32_t q;
|
||||
|
||||
q = 0;
|
||||
d <<= 16;
|
||||
for (i = 16; i >= 0; i --) {
|
||||
uint32_t ctl;
|
||||
|
||||
ctl = LE(d, x);
|
||||
q |= ctl << i;
|
||||
x -= (-ctl) & d;
|
||||
d >>= 1;
|
||||
}
|
||||
if (r != NULL) {
|
||||
*r = x;
|
||||
}
|
||||
return q;
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
void
|
||||
br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m)
|
||||
{
|
||||
/*
|
||||
* Constant-time: we accept to leak the exact bit length of the
|
||||
* modulus m.
|
||||
*/
|
||||
unsigned m_bitlen, mblr;
|
||||
size_t u, mlen;
|
||||
uint32_t hi, a0, a, b, q;
|
||||
uint32_t cc, tb, over, under;
|
||||
|
||||
/*
|
||||
* Simple case: the modulus fits on one word.
|
||||
*/
|
||||
m_bitlen = m[0];
|
||||
if (m_bitlen == 0) {
|
||||
return;
|
||||
}
|
||||
if (m_bitlen <= 15) {
|
||||
uint32_t rem;
|
||||
|
||||
divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem);
|
||||
x[1] = rem;
|
||||
return;
|
||||
}
|
||||
mlen = (m_bitlen + 15) >> 4;
|
||||
mblr = m_bitlen & 15;
|
||||
|
||||
/*
|
||||
* Principle: we estimate the quotient (x*2^15+z)/m by
|
||||
* doing a 30/15 division with the high words.
|
||||
*
|
||||
* Let:
|
||||
* w = 2^15
|
||||
* a = (w*a0 + a1) * w^N + a2
|
||||
* b = b0 * w^N + b2
|
||||
* such that:
|
||||
* 0 <= a0 < w
|
||||
* 0 <= a1 < w
|
||||
* 0 <= a2 < w^N
|
||||
* w/2 <= b0 < w
|
||||
* 0 <= b2 < w^N
|
||||
* a < w*b
|
||||
* I.e. the two top words of a are a0:a1, the top word of b is
|
||||
* b0, we ensured that b0 is "full" (high bit set), and a is
|
||||
* such that the quotient q = a/b fits on one word (0 <= q < w).
|
||||
*
|
||||
* If a = b*q + r (with 0 <= r < q), then we can estimate q by
|
||||
* using a division on the top words:
|
||||
* a0*w + a1 = b0*u + v (with 0 <= v < b0)
|
||||
* Then the following holds:
|
||||
* 0 <= u <= w
|
||||
* u-2 <= q <= u
|
||||
*/
|
||||
hi = x[mlen];
|
||||
if (mblr == 0) {
|
||||
a0 = x[mlen];
|
||||
memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
|
||||
x[1] = z;
|
||||
a = (a0 << 15) + x[mlen];
|
||||
b = m[mlen];
|
||||
} else {
|
||||
a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr);
|
||||
memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
|
||||
x[1] = z;
|
||||
a = (a0 << 15) | (((x[mlen] << (15 - mblr))
|
||||
| (x[mlen - 1] >> mblr)) & 0x7FFF);
|
||||
b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr);
|
||||
}
|
||||
q = divrem16(a, b, NULL);
|
||||
|
||||
/*
|
||||
* We computed an estimate for q, but the real one may be q,
|
||||
* q-1 or q-2; moreover, the division may have returned a value
|
||||
* 8000 or even 8001 if the two high words were identical, and
|
||||
* we want to avoid values beyond 7FFF. We thus adjust q so
|
||||
* that the "true" multiplier will be q+1, q or q-1, and q is
|
||||
* in the 0000..7FFF range.
|
||||
*/
|
||||
q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31));
|
||||
|
||||
/*
|
||||
* We subtract q*m from x (x has an extra high word of value 'hi').
|
||||
* Since q may be off by 1 (in either direction), we may have to
|
||||
* add or subtract m afterwards.
|
||||
*
|
||||
* The 'tb' flag will be true (1) at the end of the loop if the
|
||||
* result is greater than or equal to the modulus (not counting
|
||||
* 'hi' or the carry).
|
||||
*/
|
||||
cc = 0;
|
||||
tb = 1;
|
||||
for (u = 1; u <= mlen; u ++) {
|
||||
uint32_t mw, zl, xw, nxw;
|
||||
|
||||
mw = m[u];
|
||||
zl = MUL15(mw, q) + cc;
|
||||
cc = zl >> 15;
|
||||
zl &= 0x7FFF;
|
||||
xw = x[u];
|
||||
nxw = xw - zl;
|
||||
cc += nxw >> 31;
|
||||
nxw &= 0x7FFF;
|
||||
x[u] = nxw;
|
||||
tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
|
||||
}
|
||||
|
||||
/*
|
||||
* If we underestimated q, then either cc < hi (one extra bit
|
||||
* beyond the top array word), or cc == hi and tb is true (no
|
||||
* extra bit, but the result is not lower than the modulus).
|
||||
*
|
||||
* If we overestimated q, then cc > hi.
|
||||
*/
|
||||
over = GT(cc, hi);
|
||||
under = ~over & (tb | LT(cc, hi));
|
||||
br_i15_add(x, m, over);
|
||||
br_i15_sub(x, m, under);
|
||||
}
|
||||
38
src/int/i15_ninv15.c
Normal file
38
src/int/i15_ninv15.c
Normal file
|
|
@ -0,0 +1,38 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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 */
|
||||
uint16_t
|
||||
br_i15_ninv15(uint16_t x)
|
||||
{
|
||||
uint32_t y;
|
||||
|
||||
y = 2 - x;
|
||||
y = MUL15(y, 2 - MUL15(x, y));
|
||||
y = MUL15(y, 2 - MUL15(x, y));
|
||||
y = MUL15(y, 2 - MUL15(x, y));
|
||||
return MUX(x & 1, -y, 0) & 0x7FFF;
|
||||
}
|
||||
66
src/int/i15_reduce.c
Normal file
66
src/int/i15_reduce.c
Normal file
|
|
@ -0,0 +1,66 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_reduce(uint16_t *x, const uint16_t *a, const uint16_t *m)
|
||||
{
|
||||
uint32_t m_bitlen, a_bitlen;
|
||||
size_t mlen, alen, u;
|
||||
|
||||
m_bitlen = m[0];
|
||||
mlen = (m_bitlen + 15) >> 4;
|
||||
|
||||
x[0] = m_bitlen;
|
||||
if (m_bitlen == 0) {
|
||||
return;
|
||||
}
|
||||
|
||||
/*
|
||||
* If the source is shorter, then simply copy all words from a[]
|
||||
* and zero out the upper words.
|
||||
*/
|
||||
a_bitlen = a[0];
|
||||
alen = (a_bitlen + 15) >> 4;
|
||||
if (a_bitlen < m_bitlen) {
|
||||
memcpy(x + 1, a + 1, alen * sizeof *a);
|
||||
for (u = alen; u < mlen; u ++) {
|
||||
x[u + 1] = 0;
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/*
|
||||
* The source length is at least equal to that of the modulus.
|
||||
* We must thus copy N-1 words, and input the remaining words
|
||||
* one by one.
|
||||
*/
|
||||
memcpy(x + 1, a + 2 + (alen - mlen), (mlen - 1) * sizeof *a);
|
||||
x[mlen] = 0;
|
||||
for (u = 1 + alen - mlen; u > 0; u --) {
|
||||
br_i15_muladd_small(x, a[u], m);
|
||||
}
|
||||
}
|
||||
47
src/int/i15_rshift.c
Normal file
47
src/int/i15_rshift.c
Normal file
|
|
@ -0,0 +1,47 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_rshift(uint16_t *x, int count)
|
||||
{
|
||||
size_t u, len;
|
||||
unsigned r;
|
||||
|
||||
len = (x[0] + 15) >> 4;
|
||||
if (len == 0) {
|
||||
return;
|
||||
}
|
||||
r = x[1] >> count;
|
||||
for (u = 2; u <= len; u ++) {
|
||||
unsigned w;
|
||||
|
||||
w = x[u];
|
||||
x[u - 1] = ((w << (15 - count)) | r) & 0x7FFF;
|
||||
r = w >> count;
|
||||
}
|
||||
x[len] = r;
|
||||
}
|
||||
46
src/int/i15_sub.c
Normal file
46
src/int/i15_sub.c
Normal file
|
|
@ -0,0 +1,46 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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 */
|
||||
uint32_t
|
||||
br_i15_sub(uint16_t *a, const uint16_t *b, uint32_t ctl)
|
||||
{
|
||||
uint32_t cc;
|
||||
size_t u, m;
|
||||
|
||||
cc = 0;
|
||||
m = (a[0] + 31) >> 4;
|
||||
for (u = 1; u < m; u ++) {
|
||||
uint32_t aw, bw, naw;
|
||||
|
||||
aw = a[u];
|
||||
bw = b[u];
|
||||
naw = aw - bw - cc;
|
||||
cc = naw >> 31;
|
||||
a[u] = MUX(ctl, naw & 0x7FFF, aw);
|
||||
}
|
||||
return cc;
|
||||
}
|
||||
36
src/int/i15_tmont.c
Normal file
36
src/int/i15_tmont.c
Normal file
|
|
@ -0,0 +1,36 @@
|
|||
/*
|
||||
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* 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_i15_to_monty(uint16_t *x, const uint16_t *m)
|
||||
{
|
||||
unsigned k;
|
||||
|
||||
for (k = (m[0] + 15) >> 4; k > 0; k --) {
|
||||
br_i15_muladd_small(x, 0, m);
|
||||
}
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue