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- /*-
- * Copyright (c) 2014 The FreeBSD Foundation
- * All rights reserved.
- *
- * This software was developed by John-Mark Gurney under
- * the sponsorship of the FreeBSD Foundation and
- * Rubicon Communications, LLC (Netgate).
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- *
- * $FreeBSD$
- *
- */
- #include "gfmult.h"
- #define REV_POLY_REDUCT 0xe1 /* 0x87 bit reversed */
- /* reverse the bits of a nibble */
- static const uint8_t nib_rev[] = {
- 0x0, 0x8, 0x4, 0xc, 0x2, 0xa, 0x6, 0xe,
- 0x1, 0x9, 0x5, 0xd, 0x3, 0xb, 0x7, 0xf,
- };
- /* calculate v * 2 */
- static inline struct gf128
- gf128_mulalpha(struct gf128 v)
- {
- uint64_t mask;
- mask = !!(v.v[1] & 1);
- mask = ~(mask - 1);
- v.v[1] = (v.v[1] >> 1) | ((v.v[0] & 1) << 63);
- v.v[0] = (v.v[0] >> 1) ^ ((mask & REV_POLY_REDUCT) << 56);
- return v;
- }
- /*
- * Generate a table for 0-16 * h. Store the results in the table w/ indexes
- * bit reversed, and the words striped across the values.
- */
- void
- gf128_genmultable(struct gf128 h, struct gf128table *t)
- {
- struct gf128 tbl[16];
- int i;
- tbl[0] = MAKE_GF128(0, 0);
- tbl[1] = h;
- for (i = 2; i < 16; i += 2) {
- tbl[i] = gf128_mulalpha(tbl[i / 2]);
- tbl[i + 1] = gf128_add(tbl[i], h);
- }
- for (i = 0; i < 16; i++) {
- t->a[nib_rev[i]] = tbl[i].v[0] >> 32;
- t->b[nib_rev[i]] = tbl[i].v[0];
- t->c[nib_rev[i]] = tbl[i].v[1] >> 32;
- t->d[nib_rev[i]] = tbl[i].v[1];
- }
- }
- /*
- * Generate tables containing h, h^2, h^3 and h^4, starting at 0.
- */
- void
- gf128_genmultable4(struct gf128 h, struct gf128table4 *t)
- {
- struct gf128 h2, h3, h4;
- gf128_genmultable(h, &t->tbls[0]);
- h2 = gf128_mul(h, &t->tbls[0]);
- gf128_genmultable(h2, &t->tbls[1]);
- h3 = gf128_mul(h, &t->tbls[1]);
- gf128_genmultable(h3, &t->tbls[2]);
- h4 = gf128_mul(h2, &t->tbls[1]);
- gf128_genmultable(h4, &t->tbls[3]);
- }
- /*
- * Read a row from the table.
- */
- static inline struct gf128
- readrow(struct gf128table *tbl, unsigned bits)
- {
- struct gf128 r;
- bits = bits % 16;
- r.v[0] = ((uint64_t)tbl->a[bits] << 32) | tbl->b[bits];
- r.v[1] = ((uint64_t)tbl->c[bits] << 32) | tbl->d[bits];
- return r;
- }
- /*
- * These are the reduction values. Since we are dealing with bit reversed
- * version, the values need to be bit reversed, AND the indexes are also
- * bit reversed to make lookups quicker.
- */
- static uint16_t reduction[] = {
- 0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0,
- 0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0,
- };
- /*
- * Calculate:
- * (x*2^4 + word[3,0]*h) *
- * 2^4 + word[7,4]*h) *
- * ...
- * 2^4 + word[63,60]*h
- */
- static struct gf128
- gfmultword(uint64_t word, struct gf128 x, struct gf128table *tbl)
- {
- struct gf128 row;
- unsigned bits;
- unsigned redbits;
- int i;
- for (i = 0; i < 64; i += 4) {
- bits = word % 16;
- /* fetch row */
- row = readrow(tbl, bits);
- /* x * 2^4 */
- redbits = x.v[1] % 16;
- x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
- x.v[0] >>= 4;
- x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
- word >>= 4;
- x = gf128_add(x, row);
- }
- return x;
- }
- /*
- * Calculate
- * (x*2^4 + worda[3,0]*h^4+wordb[3,0]*h^3+...+wordd[3,0]*h) *
- * ...
- * 2^4 + worda[63,60]*h^4+ ... + wordd[63,60]*h
- *
- * Passing/returning struct is .5% faster than passing in via pointer on
- * amd64.
- */
- static struct gf128
- gfmultword4(uint64_t worda, uint64_t wordb, uint64_t wordc, uint64_t wordd,
- struct gf128 x, struct gf128table4 *tbl)
- {
- struct gf128 rowa, rowb, rowc, rowd;
- unsigned bitsa, bitsb, bitsc, bitsd;
- unsigned redbits;
- int i;
- /*
- * XXX - nibble reverse words to save a shift? probably not as
- * nibble reverse would take 20 ops (5 * 4) verse 16
- */
- for (i = 0; i < 64; i += 4) {
- bitsa = worda % 16;
- bitsb = wordb % 16;
- bitsc = wordc % 16;
- bitsd = wordd % 16;
- /* fetch row */
- rowa = readrow(&tbl->tbls[3], bitsa);
- rowb = readrow(&tbl->tbls[2], bitsb);
- rowc = readrow(&tbl->tbls[1], bitsc);
- rowd = readrow(&tbl->tbls[0], bitsd);
- /* x * 2^4 */
- redbits = x.v[1] % 16;
- x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
- x.v[0] >>= 4;
- x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
- worda >>= 4;
- wordb >>= 4;
- wordc >>= 4;
- wordd >>= 4;
- x = gf128_add(x, gf128_add(rowa, gf128_add(rowb,
- gf128_add(rowc, rowd))));
- }
- return x;
- }
- struct gf128
- gf128_mul(struct gf128 v, struct gf128table *tbl)
- {
- struct gf128 ret;
- ret = MAKE_GF128(0, 0);
- ret = gfmultword(v.v[1], ret, tbl);
- ret = gfmultword(v.v[0], ret, tbl);
- return ret;
- }
- /*
- * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
- * (((a*h+b)*h+c)*h+d)*h
- */
- struct gf128
- gf128_mul4(struct gf128 a, struct gf128 b, struct gf128 c, struct gf128 d,
- struct gf128table4 *tbl)
- {
- struct gf128 tmp;
- tmp = MAKE_GF128(0, 0);
- tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
- tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);
- return tmp;
- }
- /*
- * a = data[0..15] + r
- * b = data[16..31]
- * c = data[32..47]
- * d = data[48..63]
- *
- * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
- * (((a*h+b)*h+c)*h+d)*h
- */
- struct gf128
- gf128_mul4b(struct gf128 r, const uint8_t *v, struct gf128table4 *tbl)
- {
- struct gf128 a, b, c, d;
- struct gf128 tmp;
- tmp = MAKE_GF128(0, 0);
- a = gf128_add(r, gf128_read(&v[0*16]));
- b = gf128_read(&v[1*16]);
- c = gf128_read(&v[2*16]);
- d = gf128_read(&v[3*16]);
- tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
- tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);
- return tmp;
- }
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