-// Copyright (c) 2014 Pieter Wuille
-// Distributed under the MIT software license, see the accompanying
-// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille *
+ * Distributed under the MIT software license, see the accompanying *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
-#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
-#define _SECP256K1_SCALAR_REPR_IMPL_H_
+#ifndef SECP256K1_SCALAR_REPR_IMPL_H
+#define SECP256K1_SCALAR_REPR_IMPL_H
-typedef unsigned __int128 uint128_t;
-
-// Limbs of the secp256k1 order.
+/* Limbs of the secp256k1 order. */
#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL)
#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL)
#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL)
#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
-// Limbs of 2^256 minus the secp256k1 order.
+/* Limbs of 2^256 minus the secp256k1 order. */
#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
#define SECP256K1_N_C_1 (~SECP256K1_N_1)
#define SECP256K1_N_C_2 (1)
-// Limbs of half the secp256k1 order.
+/* Limbs of half the secp256k1 order. */
#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL)
#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL)
#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
-SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
r->d[0] = 0;
r->d[1] = 0;
r->d[2] = 0;
r->d[3] = 0;
}
-SECP256K1_INLINE static int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, int offset, int count) {
- VERIFY_CHECK((offset + count - 1) / 64 == offset / 64);
- return (a->d[offset / 64] >> (offset % 64)) & ((((uint64_t)1) << count) - 1);
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
+ r->d[0] = v;
+ r->d[1] = 0;
+ r->d[2] = 0;
+ r->d[3] = 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+ VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
+ return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+ VERIFY_CHECK(count < 32);
+ VERIFY_CHECK(offset + count <= 256);
+ if ((offset + count - 1) >> 6 == offset >> 6) {
+ return secp256k1_scalar_get_bits(a, offset, count);
+ } else {
+ VERIFY_CHECK((offset >> 6) + 1 < 4);
+ return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1);
+ }
}
-SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
int yes = 0;
int no = 0;
- no |= (a->d[3] < SECP256K1_N_3); // No need for a > check.
+ no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
no |= (a->d[2] < SECP256K1_N_2);
yes |= (a->d[2] > SECP256K1_N_2) & ~no;
no |= (a->d[1] < SECP256K1_N_1);
return yes;
}
-SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, unsigned int overflow) {
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
+ uint128_t t;
VERIFY_CHECK(overflow <= 1);
- uint128_t t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
+ t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1;
r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
return overflow;
}
-static void secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+ int overflow;
uint128_t t = (uint128_t)a->d[0] + b->d[0];
r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[1] + b->d[1];
r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
t += (uint128_t)a->d[3] + b->d[3];
r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
- secp256k1_scalar_reduce(r, t + secp256k1_scalar_check_overflow(r));
+ overflow = t + secp256k1_scalar_check_overflow(r);
+ VERIFY_CHECK(overflow == 0 || overflow == 1);
+ secp256k1_scalar_reduce(r, overflow);
+ return overflow;
}
-static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *b32, int *overflow) {
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+ uint128_t t;
+ VERIFY_CHECK(bit < 256);
+ bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 6) > 3 makes this a noop */
+ t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
+ r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+ t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
+ r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+ t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
+ r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
+ t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
+ r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
+#ifdef VERIFY
+ VERIFY_CHECK((t >> 64) == 0);
+ VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+ int over;
r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56;
r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56;
r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56;
- int over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
+ over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
if (overflow) {
*overflow = over;
}
}
-static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a) {
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3];
bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2];
bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1];
bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
}
-SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
}
-static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
r->d[0] = t & nonzero; t >>= 64;
r->d[3] = t & nonzero;
}
-SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
}
-static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
int yes = 0;
int no = 0;
no |= (a->d[3] < SECP256K1_N_H_3);
yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
- no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; // No need for a > check.
+ no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */
no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
return yes;
}
-// Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c.
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+ /* If we are flag = 0, mask = 00...00 and this is a no-op;
+ * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+ uint64_t mask = !flag - 1;
+ uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
+ uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+ r->d[0] = t & nonzero; t >>= 64;
+ t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+ r->d[1] = t & nonzero; t >>= 64;
+ t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+ r->d[2] = t & nonzero; t >>= 64;
+ t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+ r->d[3] = t & nonzero;
+ return 2 * (mask == 0) - 1;
+}
+
+/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd(a,b) { \
/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
#define muladd2(a,b) { \
- uint64_t tl, th; \
+ uint64_t tl, th, th2, tl2; \
{ \
uint128_t t = (uint128_t)a * b; \
th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \
tl = t; \
} \
- uint64_t th2 = th + th; /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \
+ th2 = th + th; /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \
c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \
VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
- uint64_t tl2 = tl + tl; /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \
+ tl2 = tl + tl; /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \
th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \
c0 += tl2; /* overflow is handled on the next line */ \
th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \
/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
#define sumadd(a) { \
+ unsigned int over; \
c0 += (a); /* overflow is handled on the next line */ \
- unsigned int over = (c0 < (a)) ? 1 : 0; \
+ over = (c0 < (a)) ? 1 : 0; \
c1 += over; /* overflow is handled on the next line */ \
c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \
}
VERIFY_CHECK(c2 == 0); \
}
-static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint64_t *l) {
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) {
+#ifdef USE_ASM_X86_64
+ /* Reduce 512 bits into 385. */
+ uint64_t m0, m1, m2, m3, m4, m5, m6;
+ uint64_t p0, p1, p2, p3, p4;
+ uint64_t c;
+
+ __asm__ __volatile__(
+ /* Preload. */
+ "movq 32(%%rsi), %%r11\n"
+ "movq 40(%%rsi), %%r12\n"
+ "movq 48(%%rsi), %%r13\n"
+ "movq 56(%%rsi), %%r14\n"
+ /* Initialize r8,r9,r10 */
+ "movq 0(%%rsi), %%r8\n"
+ "xorq %%r9, %%r9\n"
+ "xorq %%r10, %%r10\n"
+ /* (r8,r9) += n0 * c0 */
+ "movq %8, %%rax\n"
+ "mulq %%r11\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ /* extract m0 */
+ "movq %%r8, %q0\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r10) += l1 */
+ "addq 8(%%rsi), %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r9,r10,r8) += n1 * c0 */
+ "movq %8, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r10,r8) += n0 * c1 */
+ "movq %9, %%rax\n"
+ "mulq %%r11\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* extract m1 */
+ "movq %%r9, %q1\n"
+ "xorq %%r9, %%r9\n"
+ /* (r10,r8,r9) += l2 */
+ "addq 16(%%rsi), %%r10\n"
+ "adcq $0, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += n2 * c0 */
+ "movq %8, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += n1 * c1 */
+ "movq %9, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += n0 */
+ "addq %%r11, %%r10\n"
+ "adcq $0, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* extract m2 */
+ "movq %%r10, %q2\n"
+ "xorq %%r10, %%r10\n"
+ /* (r8,r9,r10) += l3 */
+ "addq 24(%%rsi), %%r8\n"
+ "adcq $0, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r8,r9,r10) += n3 * c0 */
+ "movq %8, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r8,r9,r10) += n2 * c1 */
+ "movq %9, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r8,r9,r10) += n1 */
+ "addq %%r12, %%r8\n"
+ "adcq $0, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* extract m3 */
+ "movq %%r8, %q3\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r10,r8) += n3 * c1 */
+ "movq %9, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r10,r8) += n2 */
+ "addq %%r13, %%r9\n"
+ "adcq $0, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* extract m4 */
+ "movq %%r9, %q4\n"
+ /* (r10,r8) += n3 */
+ "addq %%r14, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* extract m5 */
+ "movq %%r10, %q5\n"
+ /* extract m6 */
+ "movq %%r8, %q6\n"
+ : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
+ : "S"(l), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
+ : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc");
+
+ /* Reduce 385 bits into 258. */
+ __asm__ __volatile__(
+ /* Preload */
+ "movq %q9, %%r11\n"
+ "movq %q10, %%r12\n"
+ "movq %q11, %%r13\n"
+ /* Initialize (r8,r9,r10) */
+ "movq %q5, %%r8\n"
+ "xorq %%r9, %%r9\n"
+ "xorq %%r10, %%r10\n"
+ /* (r8,r9) += m4 * c0 */
+ "movq %12, %%rax\n"
+ "mulq %%r11\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ /* extract p0 */
+ "movq %%r8, %q0\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r10) += m1 */
+ "addq %q6, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r9,r10,r8) += m5 * c0 */
+ "movq %12, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r10,r8) += m4 * c1 */
+ "movq %13, %%rax\n"
+ "mulq %%r11\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* extract p1 */
+ "movq %%r9, %q1\n"
+ "xorq %%r9, %%r9\n"
+ /* (r10,r8,r9) += m2 */
+ "addq %q7, %%r10\n"
+ "adcq $0, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += m6 * c0 */
+ "movq %12, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += m5 * c1 */
+ "movq %13, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += m4 */
+ "addq %%r11, %%r10\n"
+ "adcq $0, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* extract p2 */
+ "movq %%r10, %q2\n"
+ /* (r8,r9) += m3 */
+ "addq %q8, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r8,r9) += m6 * c1 */
+ "movq %13, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ /* (r8,r9) += m5 */
+ "addq %%r12, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* extract p3 */
+ "movq %%r8, %q3\n"
+ /* (r9) += m6 */
+ "addq %%r13, %%r9\n"
+ /* extract p4 */
+ "movq %%r9, %q4\n"
+ : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4)
+ : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
+ : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc");
+
+ /* Reduce 258 bits into 256. */
+ __asm__ __volatile__(
+ /* Preload */
+ "movq %q5, %%r10\n"
+ /* (rax,rdx) = p4 * c0 */
+ "movq %7, %%rax\n"
+ "mulq %%r10\n"
+ /* (rax,rdx) += p0 */
+ "addq %q1, %%rax\n"
+ "adcq $0, %%rdx\n"
+ /* extract r0 */
+ "movq %%rax, 0(%q6)\n"
+ /* Move to (r8,r9) */
+ "movq %%rdx, %%r8\n"
+ "xorq %%r9, %%r9\n"
+ /* (r8,r9) += p1 */
+ "addq %q2, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r8,r9) += p4 * c1 */
+ "movq %8, %%rax\n"
+ "mulq %%r10\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ /* Extract r1 */
+ "movq %%r8, 8(%q6)\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r8) += p4 */
+ "addq %%r10, %%r9\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r8) += p2 */
+ "addq %q3, %%r9\n"
+ "adcq $0, %%r8\n"
+ /* Extract r2 */
+ "movq %%r9, 16(%q6)\n"
+ "xorq %%r9, %%r9\n"
+ /* (r8,r9) += p3 */
+ "addq %q4, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* Extract r3 */
+ "movq %%r8, 24(%q6)\n"
+ /* Extract c */
+ "movq %%r9, %q0\n"
+ : "=g"(c)
+ : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1)
+ : "rax", "rdx", "r8", "r9", "r10", "cc", "memory");
+#else
+ uint128_t c;
+ uint64_t c0, c1, c2;
uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7];
+ uint64_t m0, m1, m2, m3, m4, m5;
+ uint32_t m6;
+ uint64_t p0, p1, p2, p3;
+ uint32_t p4;
- // 160 bit accumulator.
- uint64_t c0, c1;
- uint32_t c2;
-
- // Reduce 512 bits into 385.
- // m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C.
+ /* Reduce 512 bits into 385. */
+ /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */
c0 = l[0]; c1 = 0; c2 = 0;
muladd_fast(n0, SECP256K1_N_C_0);
- uint64_t m0; extract_fast(m0);
+ extract_fast(m0);
sumadd_fast(l[1]);
muladd(n1, SECP256K1_N_C_0);
muladd(n0, SECP256K1_N_C_1);
- uint64_t m1; extract(m1);
+ extract(m1);
sumadd(l[2]);
muladd(n2, SECP256K1_N_C_0);
muladd(n1, SECP256K1_N_C_1);
sumadd(n0);
- uint64_t m2; extract(m2);
+ extract(m2);
sumadd(l[3]);
muladd(n3, SECP256K1_N_C_0);
muladd(n2, SECP256K1_N_C_1);
sumadd(n1);
- uint64_t m3; extract(m3);
+ extract(m3);
muladd(n3, SECP256K1_N_C_1);
sumadd(n2);
- uint64_t m4; extract(m4);
+ extract(m4);
sumadd_fast(n3);
- uint64_t m5; extract_fast(m5);
+ extract_fast(m5);
VERIFY_CHECK(c0 <= 1);
- uint32_t m6 = c0;
+ m6 = c0;
- // Reduce 385 bits into 258.
- // p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C.
+ /* Reduce 385 bits into 258. */
+ /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */
c0 = m0; c1 = 0; c2 = 0;
muladd_fast(m4, SECP256K1_N_C_0);
- uint64_t p0; extract_fast(p0);
+ extract_fast(p0);
sumadd_fast(m1);
muladd(m5, SECP256K1_N_C_0);
muladd(m4, SECP256K1_N_C_1);
- uint64_t p1; extract(p1);
+ extract(p1);
sumadd(m2);
muladd(m6, SECP256K1_N_C_0);
muladd(m5, SECP256K1_N_C_1);
sumadd(m4);
- uint64_t p2; extract(p2);
+ extract(p2);
sumadd_fast(m3);
muladd_fast(m6, SECP256K1_N_C_1);
sumadd_fast(m5);
- uint64_t p3; extract_fast(p3);
- uint32_t p4 = c0 + m6;
+ extract_fast(p3);
+ p4 = c0 + m6;
VERIFY_CHECK(p4 <= 2);
- // Reduce 258 bits into 256.
- // r[0..3] = p[0..3] + p[4] * SECP256K1_N_C.
- uint128_t c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
+ /* Reduce 258 bits into 256. */
+ /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */
+ c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p1 + (uint128_t)SECP256K1_N_C_1 * p4;
r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
c += p3;
r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
+#endif
- // Final reduction of r.
+ /* Final reduction of r. */
secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
}
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
- // 160 bit accumulator.
+static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) {
+#ifdef USE_ASM_X86_64
+ const uint64_t *pb = b->d;
+ __asm__ __volatile__(
+ /* Preload */
+ "movq 0(%%rdi), %%r15\n"
+ "movq 8(%%rdi), %%rbx\n"
+ "movq 16(%%rdi), %%rcx\n"
+ "movq 0(%%rdx), %%r11\n"
+ "movq 8(%%rdx), %%r12\n"
+ "movq 16(%%rdx), %%r13\n"
+ "movq 24(%%rdx), %%r14\n"
+ /* (rax,rdx) = a0 * b0 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r11\n"
+ /* Extract l0 */
+ "movq %%rax, 0(%%rsi)\n"
+ /* (r8,r9,r10) = (rdx) */
+ "movq %%rdx, %%r8\n"
+ "xorq %%r9, %%r9\n"
+ "xorq %%r10, %%r10\n"
+ /* (r8,r9,r10) += a0 * b1 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r8,r9,r10) += a1 * b0 */
+ "movq %%rbx, %%rax\n"
+ "mulq %%r11\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* Extract l1 */
+ "movq %%r8, 8(%%rsi)\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r10,r8) += a0 * b2 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r10,r8) += a1 * b1 */
+ "movq %%rbx, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r10,r8) += a2 * b0 */
+ "movq %%rcx, %%rax\n"
+ "mulq %%r11\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* Extract l2 */
+ "movq %%r9, 16(%%rsi)\n"
+ "xorq %%r9, %%r9\n"
+ /* (r10,r8,r9) += a0 * b3 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* Preload a3 */
+ "movq 24(%%rdi), %%r15\n"
+ /* (r10,r8,r9) += a1 * b2 */
+ "movq %%rbx, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += a2 * b1 */
+ "movq %%rcx, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += a3 * b0 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r11\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* Extract l3 */
+ "movq %%r10, 24(%%rsi)\n"
+ "xorq %%r10, %%r10\n"
+ /* (r8,r9,r10) += a1 * b3 */
+ "movq %%rbx, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r8,r9,r10) += a2 * b2 */
+ "movq %%rcx, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r8,r9,r10) += a3 * b1 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* Extract l4 */
+ "movq %%r8, 32(%%rsi)\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r10,r8) += a2 * b3 */
+ "movq %%rcx, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r10,r8) += a3 * b2 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* Extract l5 */
+ "movq %%r9, 40(%%rsi)\n"
+ /* (r10,r8) += a3 * b3 */
+ "movq %%r15, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ /* Extract l6 */
+ "movq %%r10, 48(%%rsi)\n"
+ /* Extract l7 */
+ "movq %%r8, 56(%%rsi)\n"
+ : "+d"(pb)
+ : "S"(l), "D"(a->d)
+ : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory");
+#else
+ /* 160 bit accumulator. */
uint64_t c0 = 0, c1 = 0;
uint32_t c2 = 0;
- uint64_t l[8];
-
- // l[0..7] = a[0..3] * b[0..3].
+ /* l[0..7] = a[0..3] * b[0..3]. */
muladd_fast(a->d[0], b->d[0]);
extract_fast(l[0]);
muladd(a->d[0], b->d[1]);
extract(l[5]);
muladd_fast(a->d[3], b->d[3]);
extract_fast(l[6]);
- VERIFY_CHECK(c1 <= 0);
+ VERIFY_CHECK(c1 == 0);
l[7] = c0;
-
- secp256k1_scalar_reduce_512(r, l);
+#endif
}
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
- // 160 bit accumulator.
+static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) {
+#ifdef USE_ASM_X86_64
+ __asm__ __volatile__(
+ /* Preload */
+ "movq 0(%%rdi), %%r11\n"
+ "movq 8(%%rdi), %%r12\n"
+ "movq 16(%%rdi), %%r13\n"
+ "movq 24(%%rdi), %%r14\n"
+ /* (rax,rdx) = a0 * a0 */
+ "movq %%r11, %%rax\n"
+ "mulq %%r11\n"
+ /* Extract l0 */
+ "movq %%rax, 0(%%rsi)\n"
+ /* (r8,r9,r10) = (rdx,0) */
+ "movq %%rdx, %%r8\n"
+ "xorq %%r9, %%r9\n"
+ "xorq %%r10, %%r10\n"
+ /* (r8,r9,r10) += 2 * a0 * a1 */
+ "movq %%r11, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* Extract l1 */
+ "movq %%r8, 8(%%rsi)\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r10,r8) += 2 * a0 * a2 */
+ "movq %%r11, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* (r9,r10,r8) += a1 * a1 */
+ "movq %%r12, %%rax\n"
+ "mulq %%r12\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* Extract l2 */
+ "movq %%r9, 16(%%rsi)\n"
+ "xorq %%r9, %%r9\n"
+ /* (r10,r8,r9) += 2 * a0 * a3 */
+ "movq %%r11, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* (r10,r8,r9) += 2 * a1 * a2 */
+ "movq %%r12, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ "adcq $0, %%r9\n"
+ /* Extract l3 */
+ "movq %%r10, 24(%%rsi)\n"
+ "xorq %%r10, %%r10\n"
+ /* (r8,r9,r10) += 2 * a1 * a3 */
+ "movq %%r12, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* (r8,r9,r10) += a2 * a2 */
+ "movq %%r13, %%rax\n"
+ "mulq %%r13\n"
+ "addq %%rax, %%r8\n"
+ "adcq %%rdx, %%r9\n"
+ "adcq $0, %%r10\n"
+ /* Extract l4 */
+ "movq %%r8, 32(%%rsi)\n"
+ "xorq %%r8, %%r8\n"
+ /* (r9,r10,r8) += 2 * a2 * a3 */
+ "movq %%r13, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ "addq %%rax, %%r9\n"
+ "adcq %%rdx, %%r10\n"
+ "adcq $0, %%r8\n"
+ /* Extract l5 */
+ "movq %%r9, 40(%%rsi)\n"
+ /* (r10,r8) += a3 * a3 */
+ "movq %%r14, %%rax\n"
+ "mulq %%r14\n"
+ "addq %%rax, %%r10\n"
+ "adcq %%rdx, %%r8\n"
+ /* Extract l6 */
+ "movq %%r10, 48(%%rsi)\n"
+ /* Extract l7 */
+ "movq %%r8, 56(%%rsi)\n"
+ :
+ : "S"(l), "D"(a->d)
+ : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc", "memory");
+#else
+ /* 160 bit accumulator. */
uint64_t c0 = 0, c1 = 0;
uint32_t c2 = 0;
- uint64_t l[8];
-
- // l[0..7] = a[0..3] * b[0..3].
+ /* l[0..7] = a[0..3] * b[0..3]. */
muladd_fast(a->d[0], a->d[0]);
extract_fast(l[0]);
muladd2(a->d[0], a->d[1]);
extract_fast(l[6]);
VERIFY_CHECK(c1 == 0);
l[7] = c0;
-
- secp256k1_scalar_reduce_512(r, l);
+#endif
}
#undef sumadd
#undef extract
#undef extract_fast
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+ uint64_t l[8];
+ secp256k1_scalar_mul_512(l, a, b);
+ secp256k1_scalar_reduce_512(r, l);
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+ int ret;
+ VERIFY_CHECK(n > 0);
+ VERIFY_CHECK(n < 16);
+ ret = r->d[0] & ((1 << n) - 1);
+ r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n));
+ r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n));
+ r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n));
+ r->d[3] = (r->d[3] >> n);
+ return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+ uint64_t l[8];
+ secp256k1_scalar_sqr_512(l, a);
+ secp256k1_scalar_reduce_512(r, l);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+ r1->d[0] = a->d[0];
+ r1->d[1] = a->d[1];
+ r1->d[2] = 0;
+ r1->d[3] = 0;
+ r2->d[0] = a->d[2];
+ r2->d[1] = a->d[3];
+ r2->d[2] = 0;
+ r2->d[3] = 0;
+}
#endif
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+ return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
+ uint64_t l[8];
+ unsigned int shiftlimbs;
+ unsigned int shiftlow;
+ unsigned int shifthigh;
+ VERIFY_CHECK(shift >= 256);
+ secp256k1_scalar_mul_512(l, a, b);
+ shiftlimbs = shift >> 6;
+ shiftlow = shift & 0x3F;
+ shifthigh = 64 - shiftlow;
+ r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
+ r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
+ r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
+ r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
+ secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1);
+}
+
+#endif /* SECP256K1_SCALAR_REPR_IMPL_H */
projects / secp256k1.git / blobdiff