src/scalar_4x64_impl.h

   1 /**********************************************************************
   2  * Copyright (c) 2013, 2014 Pieter Wuille                             *
   3  * Distributed under the MIT software license, see the accompanying   *
   4  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
   5  **********************************************************************/
   6
   7 #ifndef SECP256K1_SCALAR_REPR_IMPL_H
   8 #define SECP256K1_SCALAR_REPR_IMPL_H
   9
  10 /* Limbs of the secp256k1 order. */
  11 #define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL)
  12 #define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL)
  13 #define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL)
  14 #define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
  15
  16 /* Limbs of 2^256 minus the secp256k1 order. */
  17 #define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
  18 #define SECP256K1_N_C_1 (~SECP256K1_N_1)
  19 #define SECP256K1_N_C_2 (1)
  20
  21 /* Limbs of half the secp256k1 order. */
  22 #define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL)
  23 #define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL)
  24 #define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
  25 #define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
  26
  27 SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
  28     r->d[0] = 0;
  29     r->d[1] = 0;
  30     r->d[2] = 0;
  31     r->d[3] = 0;
  32 }
  33
  34 SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
  35     r->d[0] = v;
  36     r->d[1] = 0;
  37     r->d[2] = 0;
  38     r->d[3] = 0;
  39 }
  40
  41 SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
  42     VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
  43     return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
  44 }
  45
  46 SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
  47     VERIFY_CHECK(count < 32);
  48     VERIFY_CHECK(offset + count <= 256);
  49     if ((offset + count - 1) >> 6 == offset >> 6) {
  50         return secp256k1_scalar_get_bits(a, offset, count);
  51     } else {
  52         VERIFY_CHECK((offset >> 6) + 1 < 4);
  53         return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1);
  54     }
  55 }
  56
  57 SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
  58     int yes = 0;
  59     int no = 0;
  60     no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
  61     no |= (a->d[2] < SECP256K1_N_2);
  62     yes |= (a->d[2] > SECP256K1_N_2) & ~no;
  63     no |= (a->d[1] < SECP256K1_N_1);
  64     yes |= (a->d[1] > SECP256K1_N_1) & ~no;
  65     yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
  66     return yes;
  67 }
  68
  69 SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
  70     uint128_t t;
  71     VERIFY_CHECK(overflow <= 1);
  72     t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
  73     r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
  74     t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1;
  75     r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
  76     t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2;
  77     r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
  78     t += (uint64_t)r->d[3];
  79     r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
  80     return overflow;
  81 }
  82
  83 static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
  84     int overflow;
  85     uint128_t t = (uint128_t)a->d[0] + b->d[0];
  86     r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
  87     t += (uint128_t)a->d[1] + b->d[1];
  88     r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
  89     t += (uint128_t)a->d[2] + b->d[2];
  90     r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
  91     t += (uint128_t)a->d[3] + b->d[3];
  92     r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
  93     overflow = t + secp256k1_scalar_check_overflow(r);
  94     VERIFY_CHECK(overflow == 0 || overflow == 1);
  95     secp256k1_scalar_reduce(r, overflow);
  96     return overflow;
  97 }
  98
  99 static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
 100     uint128_t t;
 101     VERIFY_CHECK(bit < 256);
 102     bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
 103     t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
 104     r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
 105     t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
 106     r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
 107     t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F));
 108     r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
 109     t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F));
 110     r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL;
 111 #ifdef VERIFY
 112     VERIFY_CHECK((t >> 64) == 0);
 113     VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
 114 #endif
 115 }
 116
 117 static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
 118     int over;
 119     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;
 120     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;
 121     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;
 122     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;
 123     over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
 124     if (overflow) {
 125         *overflow = over;
 126     }
 127 }
 128
 129 static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
 130     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];
 131     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];
 132     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];
 133     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];
 134 }
 135
 136 SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
 137     return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
 138 }
 139
 140 static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
 141     uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
 142     uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
 143     r->d[0] = t & nonzero; t >>= 64;
 144     t += (uint128_t)(~a->d[1]) + SECP256K1_N_1;
 145     r->d[1] = t & nonzero; t >>= 64;
 146     t += (uint128_t)(~a->d[2]) + SECP256K1_N_2;
 147     r->d[2] = t & nonzero; t >>= 64;
 148     t += (uint128_t)(~a->d[3]) + SECP256K1_N_3;
 149     r->d[3] = t & nonzero;
 150 }
 151
 152 SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
 153     return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
 154 }
 155
 156 static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
 157     int yes = 0;
 158     int no = 0;
 159     no |= (a->d[3] < SECP256K1_N_H_3);
 160     yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
 161     no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */
 162     no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
 163     yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
 164     yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
 165     return yes;
 166 }
 167
 168 static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
 169     /* If we are flag = 0, mask = 00...00 and this is a no-op;
 170      * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
 171     uint64_t mask = !flag - 1;
 172     uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
 173     uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
 174     r->d[0] = t & nonzero; t >>= 64;
 175     t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
 176     r->d[1] = t & nonzero; t >>= 64;
 177     t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
 178     r->d[2] = t & nonzero; t >>= 64;
 179     t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
 180     r->d[3] = t & nonzero;
 181     return 2 * (mask == 0) - 1;
 182 }
 183
 184 /* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
 185
 186 /** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
 187 #define muladd(a,b) { \
 188     uint64_t tl, th; \
 189     { \
 190         uint128_t t = (uint128_t)a * b; \
 191         th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
 192         tl = t; \
 193     } \
 194     c0 += tl;                 /* overflow is handled on the next line */ \
 195     th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
 196     c1 += th;                 /* overflow is handled on the next line */ \
 197     c2 += (c1 < th) ? 1 : 0;  /* never overflows by contract (verified in the next line) */ \
 198     VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
 199 }
 200
 201 /** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
 202 #define muladd_fast(a,b) { \
 203     uint64_t tl, th; \
 204     { \
 205         uint128_t t = (uint128_t)a * b; \
 206         th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
 207         tl = t; \
 208     } \
 209     c0 += tl;                 /* overflow is handled on the next line */ \
 210     th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
 211     c1 += th;                 /* never overflows by contract (verified in the next line) */ \
 212     VERIFY_CHECK(c1 >= th); \
 213 }
 214
 215 /** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
 216 #define muladd2(a,b) { \
 217     uint64_t tl, th, th2, tl2; \
 218     { \
 219         uint128_t t = (uint128_t)a * b; \
 220         th = t >> 64;               /* at most 0xFFFFFFFFFFFFFFFE */ \
 221         tl = t; \
 222     } \
 223     th2 = th + th;                  /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \
 224     c2 += (th2 < th) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
 225     VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
 226     tl2 = tl + tl;                  /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \
 227     th2 += (tl2 < tl) ? 1 : 0;      /* at most 0xFFFFFFFFFFFFFFFF */ \
 228     c0 += tl2;                      /* overflow is handled on the next line */ \
 229     th2 += (c0 < tl2) ? 1 : 0;      /* second overflow is handled on the next line */ \
 230     c2 += (c0 < tl2) & (th2 == 0);  /* never overflows by contract (verified the next line) */ \
 231     VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
 232     c1 += th2;                      /* overflow is handled on the next line */ \
 233     c2 += (c1 < th2) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
 234     VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
 235 }
 236
 237 /** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
 238 #define sumadd(a) { \
 239     unsigned int over; \
 240     c0 += (a);                  /* overflow is handled on the next line */ \
 241     over = (c0 < (a)) ? 1 : 0; \
 242     c1 += over;                 /* overflow is handled on the next line */ \
 243     c2 += (c1 < over) ? 1 : 0;  /* never overflows by contract */ \
 244 }
 245
 246 /** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
 247 #define sumadd_fast(a) { \
 248     c0 += (a);                 /* overflow is handled on the next line */ \
 249     c1 += (c0 < (a)) ? 1 : 0;  /* never overflows by contract (verified the next line) */ \
 250     VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
 251     VERIFY_CHECK(c2 == 0); \
 252 }
 253
 254 /** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */
 255 #define extract(n) { \
 256     (n) = c0; \
 257     c0 = c1; \
 258     c1 = c2; \
 259     c2 = 0; \
 260 }
 261
 262 /** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */
 263 #define extract_fast(n) { \
 264     (n) = c0; \
 265     c0 = c1; \
 266     c1 = 0; \
 267     VERIFY_CHECK(c2 == 0); \
 268 }
 269
 270 static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) {
 271 #ifdef USE_ASM_X86_64
 272     /* Reduce 512 bits into 385. */
 273     uint64_t m0, m1, m2, m3, m4, m5, m6;
 274     uint64_t p0, p1, p2, p3, p4;
 275     uint64_t c;
 276
 277     __asm__ __volatile__(
 278     /* Preload. */
 279     "movq 32(%%rsi), %%r11\n"
 280     "movq 40(%%rsi), %%r12\n"
 281     "movq 48(%%rsi), %%r13\n"
 282     "movq 56(%%rsi), %%r14\n"
 283     /* Initialize r8,r9,r10 */
 284     "movq 0(%%rsi), %%r8\n"
 285     "xorq %%r9, %%r9\n"
 286     "xorq %%r10, %%r10\n"
 287     /* (r8,r9) += n0 * c0 */
 288     "movq %8, %%rax\n"
 289     "mulq %%r11\n"
 290     "addq %%rax, %%r8\n"
 291     "adcq %%rdx, %%r9\n"
 292     /* extract m0 */
 293     "movq %%r8, %q0\n"
 294     "xorq %%r8, %%r8\n"
 295     /* (r9,r10) += l1 */
 296     "addq 8(%%rsi), %%r9\n"
 297     "adcq $0, %%r10\n"
 298     /* (r9,r10,r8) += n1 * c0 */
 299     "movq %8, %%rax\n"
 300     "mulq %%r12\n"
 301     "addq %%rax, %%r9\n"
 302     "adcq %%rdx, %%r10\n"
 303     "adcq $0, %%r8\n"
 304     /* (r9,r10,r8) += n0 * c1 */
 305     "movq %9, %%rax\n"
 306     "mulq %%r11\n"
 307     "addq %%rax, %%r9\n"
 308     "adcq %%rdx, %%r10\n"
 309     "adcq $0, %%r8\n"
 310     /* extract m1 */
 311     "movq %%r9, %q1\n"
 312     "xorq %%r9, %%r9\n"
 313     /* (r10,r8,r9) += l2 */
 314     "addq 16(%%rsi), %%r10\n"
 315     "adcq $0, %%r8\n"
 316     "adcq $0, %%r9\n"
 317     /* (r10,r8,r9) += n2 * c0 */
 318     "movq %8, %%rax\n"
 319     "mulq %%r13\n"
 320     "addq %%rax, %%r10\n"
 321     "adcq %%rdx, %%r8\n"
 322     "adcq $0, %%r9\n"
 323     /* (r10,r8,r9) += n1 * c1 */
 324     "movq %9, %%rax\n"
 325     "mulq %%r12\n"
 326     "addq %%rax, %%r10\n"
 327     "adcq %%rdx, %%r8\n"
 328     "adcq $0, %%r9\n"
 329     /* (r10,r8,r9) += n0 */
 330     "addq %%r11, %%r10\n"
 331     "adcq $0, %%r8\n"
 332     "adcq $0, %%r9\n"
 333     /* extract m2 */
 334     "movq %%r10, %q2\n"
 335     "xorq %%r10, %%r10\n"
 336     /* (r8,r9,r10) += l3 */
 337     "addq 24(%%rsi), %%r8\n"
 338     "adcq $0, %%r9\n"
 339     "adcq $0, %%r10\n"
 340     /* (r8,r9,r10) += n3 * c0 */
 341     "movq %8, %%rax\n"
 342     "mulq %%r14\n"
 343     "addq %%rax, %%r8\n"
 344     "adcq %%rdx, %%r9\n"
 345     "adcq $0, %%r10\n"
 346     /* (r8,r9,r10) += n2 * c1 */
 347     "movq %9, %%rax\n"
 348     "mulq %%r13\n"
 349     "addq %%rax, %%r8\n"
 350     "adcq %%rdx, %%r9\n"
 351     "adcq $0, %%r10\n"
 352     /* (r8,r9,r10) += n1 */
 353     "addq %%r12, %%r8\n"
 354     "adcq $0, %%r9\n"
 355     "adcq $0, %%r10\n"
 356     /* extract m3 */
 357     "movq %%r8, %q3\n"
 358     "xorq %%r8, %%r8\n"
 359     /* (r9,r10,r8) += n3 * c1 */
 360     "movq %9, %%rax\n"
 361     "mulq %%r14\n"
 362     "addq %%rax, %%r9\n"
 363     "adcq %%rdx, %%r10\n"
 364     "adcq $0, %%r8\n"
 365     /* (r9,r10,r8) += n2 */
 366     "addq %%r13, %%r9\n"
 367     "adcq $0, %%r10\n"
 368     "adcq $0, %%r8\n"
 369     /* extract m4 */
 370     "movq %%r9, %q4\n"
 371     /* (r10,r8) += n3 */
 372     "addq %%r14, %%r10\n"
 373     "adcq $0, %%r8\n"
 374     /* extract m5 */
 375     "movq %%r10, %q5\n"
 376     /* extract m6 */
 377     "movq %%r8, %q6\n"
 378     : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6)
 379     : "S"(l), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
 380     : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc");
 381
 382     /* Reduce 385 bits into 258. */
 383     __asm__ __volatile__(
 384     /* Preload */
 385     "movq %q9, %%r11\n"
 386     "movq %q10, %%r12\n"
 387     "movq %q11, %%r13\n"
 388     /* Initialize (r8,r9,r10) */
 389     "movq %q5, %%r8\n"
 390     "xorq %%r9, %%r9\n"
 391     "xorq %%r10, %%r10\n"
 392     /* (r8,r9) += m4 * c0 */
 393     "movq %12, %%rax\n"
 394     "mulq %%r11\n"
 395     "addq %%rax, %%r8\n"
 396     "adcq %%rdx, %%r9\n"
 397     /* extract p0 */
 398     "movq %%r8, %q0\n"
 399     "xorq %%r8, %%r8\n"
 400     /* (r9,r10) += m1 */
 401     "addq %q6, %%r9\n"
 402     "adcq $0, %%r10\n"
 403     /* (r9,r10,r8) += m5 * c0 */
 404     "movq %12, %%rax\n"
 405     "mulq %%r12\n"
 406     "addq %%rax, %%r9\n"
 407     "adcq %%rdx, %%r10\n"
 408     "adcq $0, %%r8\n"
 409     /* (r9,r10,r8) += m4 * c1 */
 410     "movq %13, %%rax\n"
 411     "mulq %%r11\n"
 412     "addq %%rax, %%r9\n"
 413     "adcq %%rdx, %%r10\n"
 414     "adcq $0, %%r8\n"
 415     /* extract p1 */
 416     "movq %%r9, %q1\n"
 417     "xorq %%r9, %%r9\n"
 418     /* (r10,r8,r9) += m2 */
 419     "addq %q7, %%r10\n"
 420     "adcq $0, %%r8\n"
 421     "adcq $0, %%r9\n"
 422     /* (r10,r8,r9) += m6 * c0 */
 423     "movq %12, %%rax\n"
 424     "mulq %%r13\n"
 425     "addq %%rax, %%r10\n"
 426     "adcq %%rdx, %%r8\n"
 427     "adcq $0, %%r9\n"
 428     /* (r10,r8,r9) += m5 * c1 */
 429     "movq %13, %%rax\n"
 430     "mulq %%r12\n"
 431     "addq %%rax, %%r10\n"
 432     "adcq %%rdx, %%r8\n"
 433     "adcq $0, %%r9\n"
 434     /* (r10,r8,r9) += m4 */
 435     "addq %%r11, %%r10\n"
 436     "adcq $0, %%r8\n"
 437     "adcq $0, %%r9\n"
 438     /* extract p2 */
 439     "movq %%r10, %q2\n"
 440     /* (r8,r9) += m3 */
 441     "addq %q8, %%r8\n"
 442     "adcq $0, %%r9\n"
 443     /* (r8,r9) += m6 * c1 */
 444     "movq %13, %%rax\n"
 445     "mulq %%r13\n"
 446     "addq %%rax, %%r8\n"
 447     "adcq %%rdx, %%r9\n"
 448     /* (r8,r9) += m5 */
 449     "addq %%r12, %%r8\n"
 450     "adcq $0, %%r9\n"
 451     /* extract p3 */
 452     "movq %%r8, %q3\n"
 453     /* (r9) += m6 */
 454     "addq %%r13, %%r9\n"
 455     /* extract p4 */
 456     "movq %%r9, %q4\n"
 457     : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4)
 458     : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
 459     : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc");
 460
 461     /* Reduce 258 bits into 256. */
 462     __asm__ __volatile__(
 463     /* Preload */
 464     "movq %q5, %%r10\n"
 465     /* (rax,rdx) = p4 * c0 */
 466     "movq %7, %%rax\n"
 467     "mulq %%r10\n"
 468     /* (rax,rdx) += p0 */
 469     "addq %q1, %%rax\n"
 470     "adcq $0, %%rdx\n"
 471     /* extract r0 */
 472     "movq %%rax, 0(%q6)\n"
 473     /* Move to (r8,r9) */
 474     "movq %%rdx, %%r8\n"
 475     "xorq %%r9, %%r9\n"
 476     /* (r8,r9) += p1 */
 477     "addq %q2, %%r8\n"
 478     "adcq $0, %%r9\n"
 479     /* (r8,r9) += p4 * c1 */
 480     "movq %8, %%rax\n"
 481     "mulq %%r10\n"
 482     "addq %%rax, %%r8\n"
 483     "adcq %%rdx, %%r9\n"
 484     /* Extract r1 */
 485     "movq %%r8, 8(%q6)\n"
 486     "xorq %%r8, %%r8\n"
 487     /* (r9,r8) += p4 */
 488     "addq %%r10, %%r9\n"
 489     "adcq $0, %%r8\n"
 490     /* (r9,r8) += p2 */
 491     "addq %q3, %%r9\n"
 492     "adcq $0, %%r8\n"
 493     /* Extract r2 */
 494     "movq %%r9, 16(%q6)\n"
 495     "xorq %%r9, %%r9\n"
 496     /* (r8,r9) += p3 */
 497     "addq %q4, %%r8\n"
 498     "adcq $0, %%r9\n"
 499     /* Extract r3 */
 500     "movq %%r8, 24(%q6)\n"
 501     /* Extract c */
 502     "movq %%r9, %q0\n"
 503     : "=g"(c)
 504     : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "n"(SECP256K1_N_C_0), "n"(SECP256K1_N_C_1)
 505     : "rax", "rdx", "r8", "r9", "r10", "cc", "memory");
 506 #else
 507     uint128_t c;
 508     uint64_t c0, c1, c2;
 509     uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7];
 510     uint64_t m0, m1, m2, m3, m4, m5;
 511     uint32_t m6;
 512     uint64_t p0, p1, p2, p3;
 513     uint32_t p4;
 514
 515     /* Reduce 512 bits into 385. */
 516     /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */
 517     c0 = l[0]; c1 = 0; c2 = 0;
 518     muladd_fast(n0, SECP256K1_N_C_0);
 519     extract_fast(m0);
 520     sumadd_fast(l[1]);
 521     muladd(n1, SECP256K1_N_C_0);
 522     muladd(n0, SECP256K1_N_C_1);
 523     extract(m1);
 524     sumadd(l[2]);
 525     muladd(n2, SECP256K1_N_C_0);
 526     muladd(n1, SECP256K1_N_C_1);
 527     sumadd(n0);
 528     extract(m2);
 529     sumadd(l[3]);
 530     muladd(n3, SECP256K1_N_C_0);
 531     muladd(n2, SECP256K1_N_C_1);
 532     sumadd(n1);
 533     extract(m3);
 534     muladd(n3, SECP256K1_N_C_1);
 535     sumadd(n2);
 536     extract(m4);
 537     sumadd_fast(n3);
 538     extract_fast(m5);
 539     VERIFY_CHECK(c0 <= 1);
 540     m6 = c0;
 541
 542     /* Reduce 385 bits into 258. */
 543     /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */
 544     c0 = m0; c1 = 0; c2 = 0;
 545     muladd_fast(m4, SECP256K1_N_C_0);
 546     extract_fast(p0);
 547     sumadd_fast(m1);
 548     muladd(m5, SECP256K1_N_C_0);
 549     muladd(m4, SECP256K1_N_C_1);
 550     extract(p1);
 551     sumadd(m2);
 552     muladd(m6, SECP256K1_N_C_0);
 553     muladd(m5, SECP256K1_N_C_1);
 554     sumadd(m4);
 555     extract(p2);
 556     sumadd_fast(m3);
 557     muladd_fast(m6, SECP256K1_N_C_1);
 558     sumadd_fast(m5);
 559     extract_fast(p3);
 560     p4 = c0 + m6;
 561     VERIFY_CHECK(p4 <= 2);
 562
 563     /* Reduce 258 bits into 256. */
 564     /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */
 565     c = p0 + (uint128_t)SECP256K1_N_C_0 * p4;
 566     r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
 567     c += p1 + (uint128_t)SECP256K1_N_C_1 * p4;
 568     r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
 569     c += p2 + (uint128_t)p4;
 570     r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
 571     c += p3;
 572     r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64;
 573 #endif
 574
 575     /* Final reduction of r. */
 576     secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
 577 }
 578
 579 static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) {
 580 #ifdef USE_ASM_X86_64
 581     const uint64_t *pb = b->d;
 582     __asm__ __volatile__(
 583     /* Preload */
 584     "movq 0(%%rdi), %%r15\n"
 585     "movq 8(%%rdi), %%rbx\n"
 586     "movq 16(%%rdi), %%rcx\n"
 587     "movq 0(%%rdx), %%r11\n"
 588     "movq 8(%%rdx), %%r12\n"
 589     "movq 16(%%rdx), %%r13\n"
 590     "movq 24(%%rdx), %%r14\n"
 591     /* (rax,rdx) = a0 * b0 */
 592     "movq %%r15, %%rax\n"
 593     "mulq %%r11\n"
 594     /* Extract l0 */
 595     "movq %%rax, 0(%%rsi)\n"
 596     /* (r8,r9,r10) = (rdx) */
 597     "movq %%rdx, %%r8\n"
 598     "xorq %%r9, %%r9\n"
 599     "xorq %%r10, %%r10\n"
 600     /* (r8,r9,r10) += a0 * b1 */
 601     "movq %%r15, %%rax\n"
 602     "mulq %%r12\n"
 603     "addq %%rax, %%r8\n"
 604     "adcq %%rdx, %%r9\n"
 605     "adcq $0, %%r10\n"
 606     /* (r8,r9,r10) += a1 * b0 */
 607     "movq %%rbx, %%rax\n"
 608     "mulq %%r11\n"
 609     "addq %%rax, %%r8\n"
 610     "adcq %%rdx, %%r9\n"
 611     "adcq $0, %%r10\n"
 612     /* Extract l1 */
 613     "movq %%r8, 8(%%rsi)\n"
 614     "xorq %%r8, %%r8\n"
 615     /* (r9,r10,r8) += a0 * b2 */
 616     "movq %%r15, %%rax\n"
 617     "mulq %%r13\n"
 618     "addq %%rax, %%r9\n"
 619     "adcq %%rdx, %%r10\n"
 620     "adcq $0, %%r8\n"
 621     /* (r9,r10,r8) += a1 * b1 */
 622     "movq %%rbx, %%rax\n"
 623     "mulq %%r12\n"
 624     "addq %%rax, %%r9\n"
 625     "adcq %%rdx, %%r10\n"
 626     "adcq $0, %%r8\n"
 627     /* (r9,r10,r8) += a2 * b0 */
 628     "movq %%rcx, %%rax\n"
 629     "mulq %%r11\n"
 630     "addq %%rax, %%r9\n"
 631     "adcq %%rdx, %%r10\n"
 632     "adcq $0, %%r8\n"
 633     /* Extract l2 */
 634     "movq %%r9, 16(%%rsi)\n"
 635     "xorq %%r9, %%r9\n"
 636     /* (r10,r8,r9) += a0 * b3 */
 637     "movq %%r15, %%rax\n"
 638     "mulq %%r14\n"
 639     "addq %%rax, %%r10\n"
 640     "adcq %%rdx, %%r8\n"
 641     "adcq $0, %%r9\n"
 642     /* Preload a3 */
 643     "movq 24(%%rdi), %%r15\n"
 644     /* (r10,r8,r9) += a1 * b2 */
 645     "movq %%rbx, %%rax\n"
 646     "mulq %%r13\n"
 647     "addq %%rax, %%r10\n"
 648     "adcq %%rdx, %%r8\n"
 649     "adcq $0, %%r9\n"
 650     /* (r10,r8,r9) += a2 * b1 */
 651     "movq %%rcx, %%rax\n"
 652     "mulq %%r12\n"
 653     "addq %%rax, %%r10\n"
 654     "adcq %%rdx, %%r8\n"
 655     "adcq $0, %%r9\n"
 656     /* (r10,r8,r9) += a3 * b0 */
 657     "movq %%r15, %%rax\n"
 658     "mulq %%r11\n"
 659     "addq %%rax, %%r10\n"
 660     "adcq %%rdx, %%r8\n"
 661     "adcq $0, %%r9\n"
 662     /* Extract l3 */
 663     "movq %%r10, 24(%%rsi)\n"
 664     "xorq %%r10, %%r10\n"
 665     /* (r8,r9,r10) += a1 * b3 */
 666     "movq %%rbx, %%rax\n"
 667     "mulq %%r14\n"
 668     "addq %%rax, %%r8\n"
 669     "adcq %%rdx, %%r9\n"
 670     "adcq $0, %%r10\n"
 671     /* (r8,r9,r10) += a2 * b2 */
 672     "movq %%rcx, %%rax\n"
 673     "mulq %%r13\n"
 674     "addq %%rax, %%r8\n"
 675     "adcq %%rdx, %%r9\n"
 676     "adcq $0, %%r10\n"
 677     /* (r8,r9,r10) += a3 * b1 */
 678     "movq %%r15, %%rax\n"
 679     "mulq %%r12\n"
 680     "addq %%rax, %%r8\n"
 681     "adcq %%rdx, %%r9\n"
 682     "adcq $0, %%r10\n"
 683     /* Extract l4 */
 684     "movq %%r8, 32(%%rsi)\n"
 685     "xorq %%r8, %%r8\n"
 686     /* (r9,r10,r8) += a2 * b3 */
 687     "movq %%rcx, %%rax\n"
 688     "mulq %%r14\n"
 689     "addq %%rax, %%r9\n"
 690     "adcq %%rdx, %%r10\n"
 691     "adcq $0, %%r8\n"
 692     /* (r9,r10,r8) += a3 * b2 */
 693     "movq %%r15, %%rax\n"
 694     "mulq %%r13\n"
 695     "addq %%rax, %%r9\n"
 696     "adcq %%rdx, %%r10\n"
 697     "adcq $0, %%r8\n"
 698     /* Extract l5 */
 699     "movq %%r9, 40(%%rsi)\n"
 700     /* (r10,r8) += a3 * b3 */
 701     "movq %%r15, %%rax\n"
 702     "mulq %%r14\n"
 703     "addq %%rax, %%r10\n"
 704     "adcq %%rdx, %%r8\n"
 705     /* Extract l6 */
 706     "movq %%r10, 48(%%rsi)\n"
 707     /* Extract l7 */
 708     "movq %%r8, 56(%%rsi)\n"
 709     : "+d"(pb)
 710     : "S"(l), "D"(a->d)
 711     : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory");
 712 #else
 713     /* 160 bit accumulator. */
 714     uint64_t c0 = 0, c1 = 0;
 715     uint32_t c2 = 0;
 716
 717     /* l[0..7] = a[0..3] * b[0..3]. */
 718     muladd_fast(a->d[0], b->d[0]);
 719     extract_fast(l[0]);
 720     muladd(a->d[0], b->d[1]);
 721     muladd(a->d[1], b->d[0]);
 722     extract(l[1]);
 723     muladd(a->d[0], b->d[2]);
 724     muladd(a->d[1], b->d[1]);
 725     muladd(a->d[2], b->d[0]);
 726     extract(l[2]);
 727     muladd(a->d[0], b->d[3]);
 728     muladd(a->d[1], b->d[2]);
 729     muladd(a->d[2], b->d[1]);
 730     muladd(a->d[3], b->d[0]);
 731     extract(l[3]);
 732     muladd(a->d[1], b->d[3]);
 733     muladd(a->d[2], b->d[2]);
 734     muladd(a->d[3], b->d[1]);
 735     extract(l[4]);
 736     muladd(a->d[2], b->d[3]);
 737     muladd(a->d[3], b->d[2]);
 738     extract(l[5]);
 739     muladd_fast(a->d[3], b->d[3]);
 740     extract_fast(l[6]);
 741     VERIFY_CHECK(c1 == 0);
 742     l[7] = c0;
 743 #endif
 744 }
 745
 746 static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) {
 747 #ifdef USE_ASM_X86_64
 748     __asm__ __volatile__(
 749     /* Preload */
 750     "movq 0(%%rdi), %%r11\n"
 751     "movq 8(%%rdi), %%r12\n"
 752     "movq 16(%%rdi), %%r13\n"
 753     "movq 24(%%rdi), %%r14\n"
 754     /* (rax,rdx) = a0 * a0 */
 755     "movq %%r11, %%rax\n"
 756     "mulq %%r11\n"
 757     /* Extract l0 */
 758     "movq %%rax, 0(%%rsi)\n"
 759     /* (r8,r9,r10) = (rdx,0) */
 760     "movq %%rdx, %%r8\n"
 761     "xorq %%r9, %%r9\n"
 762     "xorq %%r10, %%r10\n"
 763     /* (r8,r9,r10) += 2 * a0 * a1 */
 764     "movq %%r11, %%rax\n"
 765     "mulq %%r12\n"
 766     "addq %%rax, %%r8\n"
 767     "adcq %%rdx, %%r9\n"
 768     "adcq $0, %%r10\n"
 769     "addq %%rax, %%r8\n"
 770     "adcq %%rdx, %%r9\n"
 771     "adcq $0, %%r10\n"
 772     /* Extract l1 */
 773     "movq %%r8, 8(%%rsi)\n"
 774     "xorq %%r8, %%r8\n"
 775     /* (r9,r10,r8) += 2 * a0 * a2 */
 776     "movq %%r11, %%rax\n"
 777     "mulq %%r13\n"
 778     "addq %%rax, %%r9\n"
 779     "adcq %%rdx, %%r10\n"
 780     "adcq $0, %%r8\n"
 781     "addq %%rax, %%r9\n"
 782     "adcq %%rdx, %%r10\n"
 783     "adcq $0, %%r8\n"
 784     /* (r9,r10,r8) += a1 * a1 */
 785     "movq %%r12, %%rax\n"
 786     "mulq %%r12\n"
 787     "addq %%rax, %%r9\n"
 788     "adcq %%rdx, %%r10\n"
 789     "adcq $0, %%r8\n"
 790     /* Extract l2 */
 791     "movq %%r9, 16(%%rsi)\n"
 792     "xorq %%r9, %%r9\n"
 793     /* (r10,r8,r9) += 2 * a0 * a3 */
 794     "movq %%r11, %%rax\n"
 795     "mulq %%r14\n"
 796     "addq %%rax, %%r10\n"
 797     "adcq %%rdx, %%r8\n"
 798     "adcq $0, %%r9\n"
 799     "addq %%rax, %%r10\n"
 800     "adcq %%rdx, %%r8\n"
 801     "adcq $0, %%r9\n"
 802     /* (r10,r8,r9) += 2 * a1 * a2 */
 803     "movq %%r12, %%rax\n"
 804     "mulq %%r13\n"
 805     "addq %%rax, %%r10\n"
 806     "adcq %%rdx, %%r8\n"
 807     "adcq $0, %%r9\n"
 808     "addq %%rax, %%r10\n"
 809     "adcq %%rdx, %%r8\n"
 810     "adcq $0, %%r9\n"
 811     /* Extract l3 */
 812     "movq %%r10, 24(%%rsi)\n"
 813     "xorq %%r10, %%r10\n"
 814     /* (r8,r9,r10) += 2 * a1 * a3 */
 815     "movq %%r12, %%rax\n"
 816     "mulq %%r14\n"
 817     "addq %%rax, %%r8\n"
 818     "adcq %%rdx, %%r9\n"
 819     "adcq $0, %%r10\n"
 820     "addq %%rax, %%r8\n"
 821     "adcq %%rdx, %%r9\n"
 822     "adcq $0, %%r10\n"
 823     /* (r8,r9,r10) += a2 * a2 */
 824     "movq %%r13, %%rax\n"
 825     "mulq %%r13\n"
 826     "addq %%rax, %%r8\n"
 827     "adcq %%rdx, %%r9\n"
 828     "adcq $0, %%r10\n"
 829     /* Extract l4 */
 830     "movq %%r8, 32(%%rsi)\n"
 831     "xorq %%r8, %%r8\n"
 832     /* (r9,r10,r8) += 2 * a2 * a3 */
 833     "movq %%r13, %%rax\n"
 834     "mulq %%r14\n"
 835     "addq %%rax, %%r9\n"
 836     "adcq %%rdx, %%r10\n"
 837     "adcq $0, %%r8\n"
 838     "addq %%rax, %%r9\n"
 839     "adcq %%rdx, %%r10\n"
 840     "adcq $0, %%r8\n"
 841     /* Extract l5 */
 842     "movq %%r9, 40(%%rsi)\n"
 843     /* (r10,r8) += a3 * a3 */
 844     "movq %%r14, %%rax\n"
 845     "mulq %%r14\n"
 846     "addq %%rax, %%r10\n"
 847     "adcq %%rdx, %%r8\n"
 848     /* Extract l6 */
 849     "movq %%r10, 48(%%rsi)\n"
 850     /* Extract l7 */
 851     "movq %%r8, 56(%%rsi)\n"
 852     :
 853     : "S"(l), "D"(a->d)
 854     : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc", "memory");
 855 #else
 856     /* 160 bit accumulator. */
 857     uint64_t c0 = 0, c1 = 0;
 858     uint32_t c2 = 0;
 859
 860     /* l[0..7] = a[0..3] * b[0..3]. */
 861     muladd_fast(a->d[0], a->d[0]);
 862     extract_fast(l[0]);
 863     muladd2(a->d[0], a->d[1]);
 864     extract(l[1]);
 865     muladd2(a->d[0], a->d[2]);
 866     muladd(a->d[1], a->d[1]);
 867     extract(l[2]);
 868     muladd2(a->d[0], a->d[3]);
 869     muladd2(a->d[1], a->d[2]);
 870     extract(l[3]);
 871     muladd2(a->d[1], a->d[3]);
 872     muladd(a->d[2], a->d[2]);
 873     extract(l[4]);
 874     muladd2(a->d[2], a->d[3]);
 875     extract(l[5]);
 876     muladd_fast(a->d[3], a->d[3]);
 877     extract_fast(l[6]);
 878     VERIFY_CHECK(c1 == 0);
 879     l[7] = c0;
 880 #endif
 881 }
 882
 883 #undef sumadd
 884 #undef sumadd_fast
 885 #undef muladd
 886 #undef muladd_fast
 887 #undef muladd2
 888 #undef extract
 889 #undef extract_fast
 890
 891 static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
 892     uint64_t l[8];
 893     secp256k1_scalar_mul_512(l, a, b);
 894     secp256k1_scalar_reduce_512(r, l);
 895 }
 896
 897 static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
 898     int ret;
 899     VERIFY_CHECK(n > 0);
 900     VERIFY_CHECK(n < 16);
 901     ret = r->d[0] & ((1 << n) - 1);
 902     r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n));
 903     r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n));
 904     r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n));
 905     r->d[3] = (r->d[3] >> n);
 906     return ret;
 907 }
 908
 909 static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
 910     uint64_t l[8];
 911     secp256k1_scalar_sqr_512(l, a);
 912     secp256k1_scalar_reduce_512(r, l);
 913 }
 914
 915 #ifdef USE_ENDOMORPHISM
 916 static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
 917     r1->d[0] = a->d[0];
 918     r1->d[1] = a->d[1];
 919     r1->d[2] = 0;
 920     r1->d[3] = 0;
 921     r2->d[0] = a->d[2];
 922     r2->d[1] = a->d[3];
 923     r2->d[2] = 0;
 924     r2->d[3] = 0;
 925 }
 926 #endif
 927
 928 SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
 929     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;
 930 }
 931
 932 SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
 933     uint64_t l[8];
 934     unsigned int shiftlimbs;
 935     unsigned int shiftlow;
 936     unsigned int shifthigh;
 937     VERIFY_CHECK(shift >= 256);
 938     secp256k1_scalar_mul_512(l, a, b);
 939     shiftlimbs = shift >> 6;
 940     shiftlow = shift & 0x3F;
 941     shifthigh = 64 - shiftlow;
 942     r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
 943     r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
 944     r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
 945     r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
 946     secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1);
 947 }
 948
 949 #endif /* SECP256K1_SCALAR_REPR_IMPL_H */