503 lines
13 KiB
C
503 lines
13 KiB
C
/**********************************************************************
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* Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
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**********************************************************************/
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/**
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* Changelog:
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* - March 2013, Diederik Huys: original version
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* - November 2014, Pieter Wuille: updated to use Peter Dettman's parallel multiplication algorithm
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* - December 2014, Pieter Wuille: converted from YASM to GCC inline assembly
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*/
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#ifndef _SECP256K1_FIELD_INNER5X52_IMPL_H_
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#define _SECP256K1_FIELD_INNER5X52_IMPL_H_
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SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
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/**
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* Registers: rdx:rax = multiplication accumulator
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* r9:r8 = c
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* r15:rcx = d
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* r10-r14 = a0-a4
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* rbx = b
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* rdi = r
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* rsi = a / t?
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*/
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uint64_t tmp1, tmp2, tmp3;
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__asm__ __volatile__(
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"movq 0(%%rsi),%%r10\n"
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"movq 8(%%rsi),%%r11\n"
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"movq 16(%%rsi),%%r12\n"
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"movq 24(%%rsi),%%r13\n"
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"movq 32(%%rsi),%%r14\n"
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/* d += a3 * b0 */
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"movq 0(%%rbx),%%rax\n"
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"mulq %%r13\n"
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"movq %%rax,%%rcx\n"
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"movq %%rdx,%%r15\n"
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/* d += a2 * b1 */
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"movq 8(%%rbx),%%rax\n"
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"mulq %%r12\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a1 * b2 */
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"movq 16(%%rbx),%%rax\n"
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"mulq %%r11\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d = a0 * b3 */
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"movq 24(%%rbx),%%rax\n"
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"mulq %%r10\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* c = a4 * b4 */
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"movq 32(%%rbx),%%rax\n"
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"mulq %%r14\n"
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"movq %%rax,%%r8\n"
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"movq %%rdx,%%r9\n"
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/* d += (c & M) * R */
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rax\n"
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"movq $0x1000003d10,%%rdx\n"
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"mulq %%rdx\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* c >>= 52 (%%r8 only) */
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"shrdq $52,%%r9,%%r8\n"
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/* t3 (tmp1) = d & M */
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"movq %%rcx,%%rsi\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rsi\n"
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"movq %%rsi,%q1\n"
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/* d >>= 52 */
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"shrdq $52,%%r15,%%rcx\n"
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"xorq %%r15,%%r15\n"
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/* d += a4 * b0 */
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"movq 0(%%rbx),%%rax\n"
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"mulq %%r14\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a3 * b1 */
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"movq 8(%%rbx),%%rax\n"
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"mulq %%r13\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a2 * b2 */
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"movq 16(%%rbx),%%rax\n"
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"mulq %%r12\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a1 * b3 */
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"movq 24(%%rbx),%%rax\n"
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"mulq %%r11\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a0 * b4 */
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"movq 32(%%rbx),%%rax\n"
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"mulq %%r10\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += c * R */
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"movq %%r8,%%rax\n"
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"movq $0x1000003d10,%%rdx\n"
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"mulq %%rdx\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* t4 = d & M (%%rsi) */
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"movq %%rcx,%%rsi\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rsi\n"
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/* d >>= 52 */
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"shrdq $52,%%r15,%%rcx\n"
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"xorq %%r15,%%r15\n"
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/* tx = t4 >> 48 (tmp3) */
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"movq %%rsi,%%rax\n"
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"shrq $48,%%rax\n"
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"movq %%rax,%q3\n"
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/* t4 &= (M >> 4) (tmp2) */
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"movq $0xffffffffffff,%%rax\n"
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"andq %%rax,%%rsi\n"
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"movq %%rsi,%q2\n"
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/* c = a0 * b0 */
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"movq 0(%%rbx),%%rax\n"
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"mulq %%r10\n"
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"movq %%rax,%%r8\n"
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"movq %%rdx,%%r9\n"
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/* d += a4 * b1 */
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"movq 8(%%rbx),%%rax\n"
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"mulq %%r14\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a3 * b2 */
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"movq 16(%%rbx),%%rax\n"
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"mulq %%r13\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a2 * b3 */
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"movq 24(%%rbx),%%rax\n"
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"mulq %%r12\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a1 * b4 */
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"movq 32(%%rbx),%%rax\n"
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"mulq %%r11\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* u0 = d & M (%%rsi) */
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"movq %%rcx,%%rsi\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rsi\n"
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/* d >>= 52 */
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"shrdq $52,%%r15,%%rcx\n"
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"xorq %%r15,%%r15\n"
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/* u0 = (u0 << 4) | tx (%%rsi) */
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"shlq $4,%%rsi\n"
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"movq %q3,%%rax\n"
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"orq %%rax,%%rsi\n"
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/* c += u0 * (R >> 4) */
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"movq $0x1000003d1,%%rax\n"
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"mulq %%rsi\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* r[0] = c & M */
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"movq %%r8,%%rax\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rax\n"
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"movq %%rax,0(%%rdi)\n"
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/* c >>= 52 */
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"shrdq $52,%%r9,%%r8\n"
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"xorq %%r9,%%r9\n"
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/* c += a1 * b0 */
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"movq 0(%%rbx),%%rax\n"
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"mulq %%r11\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* c += a0 * b1 */
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"movq 8(%%rbx),%%rax\n"
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"mulq %%r10\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* d += a4 * b2 */
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"movq 16(%%rbx),%%rax\n"
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"mulq %%r14\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a3 * b3 */
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"movq 24(%%rbx),%%rax\n"
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"mulq %%r13\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a2 * b4 */
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"movq 32(%%rbx),%%rax\n"
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"mulq %%r12\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* c += (d & M) * R */
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"movq %%rcx,%%rax\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rax\n"
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"movq $0x1000003d10,%%rdx\n"
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"mulq %%rdx\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* d >>= 52 */
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"shrdq $52,%%r15,%%rcx\n"
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"xorq %%r15,%%r15\n"
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/* r[1] = c & M */
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"movq %%r8,%%rax\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rax\n"
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"movq %%rax,8(%%rdi)\n"
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/* c >>= 52 */
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"shrdq $52,%%r9,%%r8\n"
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"xorq %%r9,%%r9\n"
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/* c += a2 * b0 */
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"movq 0(%%rbx),%%rax\n"
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"mulq %%r12\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* c += a1 * b1 */
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"movq 8(%%rbx),%%rax\n"
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"mulq %%r11\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* c += a0 * b2 (last use of %%r10 = a0) */
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"movq 16(%%rbx),%%rax\n"
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"mulq %%r10\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* fetch t3 (%%r10, overwrites a0), t4 (%%rsi) */
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"movq %q2,%%rsi\n"
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"movq %q1,%%r10\n"
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/* d += a4 * b3 */
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"movq 24(%%rbx),%%rax\n"
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"mulq %%r14\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* d += a3 * b4 */
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"movq 32(%%rbx),%%rax\n"
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"mulq %%r13\n"
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"addq %%rax,%%rcx\n"
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"adcq %%rdx,%%r15\n"
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/* c += (d & M) * R */
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"movq %%rcx,%%rax\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rax\n"
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"movq $0x1000003d10,%%rdx\n"
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"mulq %%rdx\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* d >>= 52 (%%rcx only) */
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"shrdq $52,%%r15,%%rcx\n"
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/* r[2] = c & M */
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"movq %%r8,%%rax\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rax\n"
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"movq %%rax,16(%%rdi)\n"
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/* c >>= 52 */
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"shrdq $52,%%r9,%%r8\n"
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"xorq %%r9,%%r9\n"
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/* c += t3 */
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"addq %%r10,%%r8\n"
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/* c += d * R */
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"movq %%rcx,%%rax\n"
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"movq $0x1000003d10,%%rdx\n"
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"mulq %%rdx\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* r[3] = c & M */
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"movq %%r8,%%rax\n"
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"movq $0xfffffffffffff,%%rdx\n"
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"andq %%rdx,%%rax\n"
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"movq %%rax,24(%%rdi)\n"
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/* c >>= 52 (%%r8 only) */
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"shrdq $52,%%r9,%%r8\n"
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/* c += t4 (%%r8 only) */
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"addq %%rsi,%%r8\n"
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/* r[4] = c */
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"movq %%r8,32(%%rdi)\n"
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: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
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: "b"(b), "D"(r)
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: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
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);
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}
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SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
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/**
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* Registers: rdx:rax = multiplication accumulator
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* r9:r8 = c
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* rcx:rbx = d
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* r10-r14 = a0-a4
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* r15 = M (0xfffffffffffff)
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* rdi = r
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* rsi = a / t?
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*/
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uint64_t tmp1, tmp2, tmp3;
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__asm__ __volatile__(
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"movq 0(%%rsi),%%r10\n"
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"movq 8(%%rsi),%%r11\n"
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"movq 16(%%rsi),%%r12\n"
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"movq 24(%%rsi),%%r13\n"
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"movq 32(%%rsi),%%r14\n"
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"movq $0xfffffffffffff,%%r15\n"
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/* d = (a0*2) * a3 */
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"leaq (%%r10,%%r10,1),%%rax\n"
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"mulq %%r13\n"
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"movq %%rax,%%rbx\n"
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"movq %%rdx,%%rcx\n"
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/* d += (a1*2) * a2 */
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"leaq (%%r11,%%r11,1),%%rax\n"
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"mulq %%r12\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* c = a4 * a4 */
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"movq %%r14,%%rax\n"
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"mulq %%r14\n"
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"movq %%rax,%%r8\n"
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"movq %%rdx,%%r9\n"
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/* d += (c & M) * R */
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"andq %%r15,%%rax\n"
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"movq $0x1000003d10,%%rdx\n"
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"mulq %%rdx\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* c >>= 52 (%%r8 only) */
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"shrdq $52,%%r9,%%r8\n"
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/* t3 (tmp1) = d & M */
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"movq %%rbx,%%rsi\n"
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"andq %%r15,%%rsi\n"
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"movq %%rsi,%q1\n"
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/* d >>= 52 */
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"shrdq $52,%%rcx,%%rbx\n"
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"xorq %%rcx,%%rcx\n"
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/* a4 *= 2 */
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"addq %%r14,%%r14\n"
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/* d += a0 * a4 */
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"movq %%r10,%%rax\n"
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"mulq %%r14\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* d+= (a1*2) * a3 */
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"leaq (%%r11,%%r11,1),%%rax\n"
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"mulq %%r13\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* d += a2 * a2 */
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"movq %%r12,%%rax\n"
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"mulq %%r12\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* d += c * R */
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"movq %%r8,%%rax\n"
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"movq $0x1000003d10,%%rdx\n"
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"mulq %%rdx\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* t4 = d & M (%%rsi) */
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"movq %%rbx,%%rsi\n"
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"andq %%r15,%%rsi\n"
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/* d >>= 52 */
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"shrdq $52,%%rcx,%%rbx\n"
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"xorq %%rcx,%%rcx\n"
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/* tx = t4 >> 48 (tmp3) */
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"movq %%rsi,%%rax\n"
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"shrq $48,%%rax\n"
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"movq %%rax,%q3\n"
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/* t4 &= (M >> 4) (tmp2) */
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"movq $0xffffffffffff,%%rax\n"
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"andq %%rax,%%rsi\n"
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"movq %%rsi,%q2\n"
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/* c = a0 * a0 */
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"movq %%r10,%%rax\n"
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"mulq %%r10\n"
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"movq %%rax,%%r8\n"
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"movq %%rdx,%%r9\n"
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/* d += a1 * a4 */
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"movq %%r11,%%rax\n"
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"mulq %%r14\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* d += (a2*2) * a3 */
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"leaq (%%r12,%%r12,1),%%rax\n"
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"mulq %%r13\n"
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"addq %%rax,%%rbx\n"
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"adcq %%rdx,%%rcx\n"
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/* u0 = d & M (%%rsi) */
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"movq %%rbx,%%rsi\n"
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"andq %%r15,%%rsi\n"
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/* d >>= 52 */
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"shrdq $52,%%rcx,%%rbx\n"
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"xorq %%rcx,%%rcx\n"
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/* u0 = (u0 << 4) | tx (%%rsi) */
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"shlq $4,%%rsi\n"
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"movq %q3,%%rax\n"
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"orq %%rax,%%rsi\n"
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/* c += u0 * (R >> 4) */
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"movq $0x1000003d1,%%rax\n"
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"mulq %%rsi\n"
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"addq %%rax,%%r8\n"
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"adcq %%rdx,%%r9\n"
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/* r[0] = c & M */
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"movq %%r8,%%rax\n"
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"andq %%r15,%%rax\n"
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"movq %%rax,0(%%rdi)\n"
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/* c >>= 52 */
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"shrdq $52,%%r9,%%r8\n"
|
|
"xorq %%r9,%%r9\n"
|
|
/* a0 *= 2 */
|
|
"addq %%r10,%%r10\n"
|
|
/* c += a0 * a1 */
|
|
"movq %%r10,%%rax\n"
|
|
"mulq %%r11\n"
|
|
"addq %%rax,%%r8\n"
|
|
"adcq %%rdx,%%r9\n"
|
|
/* d += a2 * a4 */
|
|
"movq %%r12,%%rax\n"
|
|
"mulq %%r14\n"
|
|
"addq %%rax,%%rbx\n"
|
|
"adcq %%rdx,%%rcx\n"
|
|
/* d += a3 * a3 */
|
|
"movq %%r13,%%rax\n"
|
|
"mulq %%r13\n"
|
|
"addq %%rax,%%rbx\n"
|
|
"adcq %%rdx,%%rcx\n"
|
|
/* c += (d & M) * R */
|
|
"movq %%rbx,%%rax\n"
|
|
"andq %%r15,%%rax\n"
|
|
"movq $0x1000003d10,%%rdx\n"
|
|
"mulq %%rdx\n"
|
|
"addq %%rax,%%r8\n"
|
|
"adcq %%rdx,%%r9\n"
|
|
/* d >>= 52 */
|
|
"shrdq $52,%%rcx,%%rbx\n"
|
|
"xorq %%rcx,%%rcx\n"
|
|
/* r[1] = c & M */
|
|
"movq %%r8,%%rax\n"
|
|
"andq %%r15,%%rax\n"
|
|
"movq %%rax,8(%%rdi)\n"
|
|
/* c >>= 52 */
|
|
"shrdq $52,%%r9,%%r8\n"
|
|
"xorq %%r9,%%r9\n"
|
|
/* c += a0 * a2 (last use of %%r10) */
|
|
"movq %%r10,%%rax\n"
|
|
"mulq %%r12\n"
|
|
"addq %%rax,%%r8\n"
|
|
"adcq %%rdx,%%r9\n"
|
|
/* fetch t3 (%%r10, overwrites a0),t4 (%%rsi) */
|
|
"movq %q2,%%rsi\n"
|
|
"movq %q1,%%r10\n"
|
|
/* c += a1 * a1 */
|
|
"movq %%r11,%%rax\n"
|
|
"mulq %%r11\n"
|
|
"addq %%rax,%%r8\n"
|
|
"adcq %%rdx,%%r9\n"
|
|
/* d += a3 * a4 */
|
|
"movq %%r13,%%rax\n"
|
|
"mulq %%r14\n"
|
|
"addq %%rax,%%rbx\n"
|
|
"adcq %%rdx,%%rcx\n"
|
|
/* c += (d & M) * R */
|
|
"movq %%rbx,%%rax\n"
|
|
"andq %%r15,%%rax\n"
|
|
"movq $0x1000003d10,%%rdx\n"
|
|
"mulq %%rdx\n"
|
|
"addq %%rax,%%r8\n"
|
|
"adcq %%rdx,%%r9\n"
|
|
/* d >>= 52 (%%rbx only) */
|
|
"shrdq $52,%%rcx,%%rbx\n"
|
|
/* r[2] = c & M */
|
|
"movq %%r8,%%rax\n"
|
|
"andq %%r15,%%rax\n"
|
|
"movq %%rax,16(%%rdi)\n"
|
|
/* c >>= 52 */
|
|
"shrdq $52,%%r9,%%r8\n"
|
|
"xorq %%r9,%%r9\n"
|
|
/* c += t3 */
|
|
"addq %%r10,%%r8\n"
|
|
/* c += d * R */
|
|
"movq %%rbx,%%rax\n"
|
|
"movq $0x1000003d10,%%rdx\n"
|
|
"mulq %%rdx\n"
|
|
"addq %%rax,%%r8\n"
|
|
"adcq %%rdx,%%r9\n"
|
|
/* r[3] = c & M */
|
|
"movq %%r8,%%rax\n"
|
|
"andq %%r15,%%rax\n"
|
|
"movq %%rax,24(%%rdi)\n"
|
|
/* c >>= 52 (%%r8 only) */
|
|
"shrdq $52,%%r9,%%r8\n"
|
|
/* c += t4 (%%r8 only) */
|
|
"addq %%rsi,%%r8\n"
|
|
/* r[4] = c */
|
|
"movq %%r8,32(%%rdi)\n"
|
|
: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3)
|
|
: "D"(r)
|
|
: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory"
|
|
);
|
|
}
|
|
|
|
#endif
|