src/field_5x52_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_FIELD_REPR_IMPL_H
   8 #define SECP256K1_FIELD_REPR_IMPL_H
   9
  10 #if defined HAVE_CONFIG_H
  11 #include "libsecp256k1-config.h"
  12 #endif
  13
  14 #include "util.h"
  15 #include "num.h"
  16 #include "field.h"
  17
  18 #if defined(USE_ASM_X86_64)
  19 #include "field_5x52_asm_impl.h"
  20 #else
  21 #include "field_5x52_int128_impl.h"
  22 #endif
  23
  24 /** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
  25  *  represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular,
  26  *  each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element
  27  *  is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations
  28  *  accept any input with magnitude at most M, and have different rules for propagating magnitude to their
  29  *  output.
  30  */
  31
  32 #ifdef VERIFY
  33 static void secp256k1_fe_verify(const secp256k1_fe *a) {
  34     const uint64_t *d = a->n;
  35     int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
  36    /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
  37     r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
  38     r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
  39     r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
  40     r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
  41     r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
  42     r &= (a->magnitude >= 0);
  43     r &= (a->magnitude <= 2048);
  44     if (a->normalized) {
  45         r &= (a->magnitude <= 1);
  46         if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
  47             r &= (d[0] < 0xFFFFEFFFFFC2FULL);
  48         }
  49     }
  50     VERIFY_CHECK(r == 1);
  51 }
  52 #endif
  53
  54 static void secp256k1_fe_normalize(secp256k1_fe *r) {
  55     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
  56
  57     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
  58     uint64_t m;
  59     uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
  60
  61     /* The first pass ensures the magnitude is 1, ... */
  62     t0 += x * 0x1000003D1ULL;
  63     t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
  64     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
  65     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
  66     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
  67
  68     /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
  69     VERIFY_CHECK(t4 >> 49 == 0);
  70
  71     /* At most a single final reduction is needed; check if the value is >= the field characteristic */
  72     x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
  73         & (t0 >= 0xFFFFEFFFFFC2FULL));
  74
  75     /* Apply the final reduction (for constant-time behaviour, we do it always) */
  76     t0 += x * 0x1000003D1ULL;
  77     t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
  78     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
  79     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
  80     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
  81
  82     /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
  83     VERIFY_CHECK(t4 >> 48 == x);
  84
  85     /* Mask off the possible multiple of 2^256 from the final reduction */
  86     t4 &= 0x0FFFFFFFFFFFFULL;
  87
  88     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
  89
  90 #ifdef VERIFY
  91     r->magnitude = 1;
  92     r->normalized = 1;
  93     secp256k1_fe_verify(r);
  94 #endif
  95 }
  96
  97 static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
  98     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
  99
 100     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
 101     uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
 102
 103     /* The first pass ensures the magnitude is 1, ... */
 104     t0 += x * 0x1000003D1ULL;
 105     t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
 106     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
 107     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
 108     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
 109
 110     /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
 111     VERIFY_CHECK(t4 >> 49 == 0);
 112
 113     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
 114
 115 #ifdef VERIFY
 116     r->magnitude = 1;
 117     secp256k1_fe_verify(r);
 118 #endif
 119 }
 120
 121 static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
 122     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 123
 124     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
 125     uint64_t m;
 126     uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
 127
 128     /* The first pass ensures the magnitude is 1, ... */
 129     t0 += x * 0x1000003D1ULL;
 130     t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
 131     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
 132     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
 133     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
 134
 135     /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
 136     VERIFY_CHECK(t4 >> 49 == 0);
 137
 138     /* At most a single final reduction is needed; check if the value is >= the field characteristic */
 139     x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
 140         & (t0 >= 0xFFFFEFFFFFC2FULL));
 141
 142     if (x) {
 143         t0 += 0x1000003D1ULL;
 144         t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
 145         t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
 146         t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
 147         t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
 148
 149         /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
 150         VERIFY_CHECK(t4 >> 48 == x);
 151
 152         /* Mask off the possible multiple of 2^256 from the final reduction */
 153         t4 &= 0x0FFFFFFFFFFFFULL;
 154     }
 155
 156     r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
 157
 158 #ifdef VERIFY
 159     r->magnitude = 1;
 160     r->normalized = 1;
 161     secp256k1_fe_verify(r);
 162 #endif
 163 }
 164
 165 static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
 166     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 167
 168     /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
 169     uint64_t z0, z1;
 170
 171     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
 172     uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
 173
 174     /* The first pass ensures the magnitude is 1, ... */
 175     t0 += x * 0x1000003D1ULL;
 176     t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0  = t0; z1  = t0 ^ 0x1000003D0ULL;
 177     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
 178     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
 179     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
 180                                                 z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
 181
 182     /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
 183     VERIFY_CHECK(t4 >> 49 == 0);
 184
 185     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 186 }
 187
 188 static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
 189     uint64_t t0, t1, t2, t3, t4;
 190     uint64_t z0, z1;
 191     uint64_t x;
 192
 193     t0 = r->n[0];
 194     t4 = r->n[4];
 195
 196     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
 197     x = t4 >> 48;
 198
 199     /* The first pass ensures the magnitude is 1, ... */
 200     t0 += x * 0x1000003D1ULL;
 201
 202     /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
 203     z0 = t0 & 0xFFFFFFFFFFFFFULL;
 204     z1 = z0 ^ 0x1000003D0ULL;
 205
 206     /* Fast return path should catch the majority of cases */
 207     if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
 208         return 0;
 209     }
 210
 211     t1 = r->n[1];
 212     t2 = r->n[2];
 213     t3 = r->n[3];
 214
 215     t4 &= 0x0FFFFFFFFFFFFULL;
 216
 217     t1 += (t0 >> 52);
 218     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
 219     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
 220     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
 221                                                 z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
 222
 223     /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
 224     VERIFY_CHECK(t4 >> 49 == 0);
 225
 226     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 227 }
 228
 229 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
 230     r->n[0] = a;
 231     r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
 232 #ifdef VERIFY
 233     r->magnitude = 1;
 234     r->normalized = 1;
 235     secp256k1_fe_verify(r);
 236 #endif
 237 }
 238
 239 SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
 240     const uint64_t *t = a->n;
 241 #ifdef VERIFY
 242     VERIFY_CHECK(a->normalized);
 243     secp256k1_fe_verify(a);
 244 #endif
 245     return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
 246 }
 247
 248 SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
 249 #ifdef VERIFY
 250     VERIFY_CHECK(a->normalized);
 251     secp256k1_fe_verify(a);
 252 #endif
 253     return a->n[0] & 1;
 254 }
 255
 256 SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
 257     int i;
 258 #ifdef VERIFY
 259     a->magnitude = 0;
 260     a->normalized = 1;
 261 #endif
 262     for (i=0; i<5; i++) {
 263         a->n[i] = 0;
 264     }
 265 }
 266
 267 static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
 268     int i;
 269 #ifdef VERIFY
 270     VERIFY_CHECK(a->normalized);
 271     VERIFY_CHECK(b->normalized);
 272     secp256k1_fe_verify(a);
 273     secp256k1_fe_verify(b);
 274 #endif
 275     for (i = 4; i >= 0; i--) {
 276         if (a->n[i] > b->n[i]) {
 277             return 1;
 278         }
 279         if (a->n[i] < b->n[i]) {
 280             return -1;
 281         }
 282     }
 283     return 0;
 284 }
 285
 286 static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
 287     r->n[0] = (uint64_t)a[31]
 288             | ((uint64_t)a[30] << 8)
 289             | ((uint64_t)a[29] << 16)
 290             | ((uint64_t)a[28] << 24)
 291             | ((uint64_t)a[27] << 32)
 292             | ((uint64_t)a[26] << 40)
 293             | ((uint64_t)(a[25] & 0xF)  << 48);
 294     r->n[1] = (uint64_t)((a[25] >> 4) & 0xF)
 295             | ((uint64_t)a[24] << 4)
 296             | ((uint64_t)a[23] << 12)
 297             | ((uint64_t)a[22] << 20)
 298             | ((uint64_t)a[21] << 28)
 299             | ((uint64_t)a[20] << 36)
 300             | ((uint64_t)a[19] << 44);
 301     r->n[2] = (uint64_t)a[18]
 302             | ((uint64_t)a[17] << 8)
 303             | ((uint64_t)a[16] << 16)
 304             | ((uint64_t)a[15] << 24)
 305             | ((uint64_t)a[14] << 32)
 306             | ((uint64_t)a[13] << 40)
 307             | ((uint64_t)(a[12] & 0xF) << 48);
 308     r->n[3] = (uint64_t)((a[12] >> 4) & 0xF)
 309             | ((uint64_t)a[11] << 4)
 310             | ((uint64_t)a[10] << 12)
 311             | ((uint64_t)a[9]  << 20)
 312             | ((uint64_t)a[8]  << 28)
 313             | ((uint64_t)a[7]  << 36)
 314             | ((uint64_t)a[6]  << 44);
 315     r->n[4] = (uint64_t)a[5]
 316             | ((uint64_t)a[4] << 8)
 317             | ((uint64_t)a[3] << 16)
 318             | ((uint64_t)a[2] << 24)
 319             | ((uint64_t)a[1] << 32)
 320             | ((uint64_t)a[0] << 40);
 321     if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) {
 322         return 0;
 323     }
 324 #ifdef VERIFY
 325     r->magnitude = 1;
 326     r->normalized = 1;
 327     secp256k1_fe_verify(r);
 328 #endif
 329     return 1;
 330 }
 331
 332 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
 333 static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
 334 #ifdef VERIFY
 335     VERIFY_CHECK(a->normalized);
 336     secp256k1_fe_verify(a);
 337 #endif
 338     r[0] = (a->n[4] >> 40) & 0xFF;
 339     r[1] = (a->n[4] >> 32) & 0xFF;
 340     r[2] = (a->n[4] >> 24) & 0xFF;
 341     r[3] = (a->n[4] >> 16) & 0xFF;
 342     r[4] = (a->n[4] >> 8) & 0xFF;
 343     r[5] = a->n[4] & 0xFF;
 344     r[6] = (a->n[3] >> 44) & 0xFF;
 345     r[7] = (a->n[3] >> 36) & 0xFF;
 346     r[8] = (a->n[3] >> 28) & 0xFF;
 347     r[9] = (a->n[3] >> 20) & 0xFF;
 348     r[10] = (a->n[3] >> 12) & 0xFF;
 349     r[11] = (a->n[3] >> 4) & 0xFF;
 350     r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4);
 351     r[13] = (a->n[2] >> 40) & 0xFF;
 352     r[14] = (a->n[2] >> 32) & 0xFF;
 353     r[15] = (a->n[2] >> 24) & 0xFF;
 354     r[16] = (a->n[2] >> 16) & 0xFF;
 355     r[17] = (a->n[2] >> 8) & 0xFF;
 356     r[18] = a->n[2] & 0xFF;
 357     r[19] = (a->n[1] >> 44) & 0xFF;
 358     r[20] = (a->n[1] >> 36) & 0xFF;
 359     r[21] = (a->n[1] >> 28) & 0xFF;
 360     r[22] = (a->n[1] >> 20) & 0xFF;
 361     r[23] = (a->n[1] >> 12) & 0xFF;
 362     r[24] = (a->n[1] >> 4) & 0xFF;
 363     r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4);
 364     r[26] = (a->n[0] >> 40) & 0xFF;
 365     r[27] = (a->n[0] >> 32) & 0xFF;
 366     r[28] = (a->n[0] >> 24) & 0xFF;
 367     r[29] = (a->n[0] >> 16) & 0xFF;
 368     r[30] = (a->n[0] >> 8) & 0xFF;
 369     r[31] = a->n[0] & 0xFF;
 370 }
 371
 372 SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
 373 #ifdef VERIFY
 374     VERIFY_CHECK(a->magnitude <= m);
 375     secp256k1_fe_verify(a);
 376 #endif
 377     r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
 378     r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
 379     r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
 380     r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
 381     r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
 382 #ifdef VERIFY
 383     r->magnitude = m + 1;
 384     r->normalized = 0;
 385     secp256k1_fe_verify(r);
 386 #endif
 387 }
 388
 389 SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
 390     r->n[0] *= a;
 391     r->n[1] *= a;
 392     r->n[2] *= a;
 393     r->n[3] *= a;
 394     r->n[4] *= a;
 395 #ifdef VERIFY
 396     r->magnitude *= a;
 397     r->normalized = 0;
 398     secp256k1_fe_verify(r);
 399 #endif
 400 }
 401
 402 SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
 403 #ifdef VERIFY
 404     secp256k1_fe_verify(a);
 405 #endif
 406     r->n[0] += a->n[0];
 407     r->n[1] += a->n[1];
 408     r->n[2] += a->n[2];
 409     r->n[3] += a->n[3];
 410     r->n[4] += a->n[4];
 411 #ifdef VERIFY
 412     r->magnitude += a->magnitude;
 413     r->normalized = 0;
 414     secp256k1_fe_verify(r);
 415 #endif
 416 }
 417
 418 static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
 419 #ifdef VERIFY
 420     VERIFY_CHECK(a->magnitude <= 8);
 421     VERIFY_CHECK(b->magnitude <= 8);
 422     secp256k1_fe_verify(a);
 423     secp256k1_fe_verify(b);
 424     VERIFY_CHECK(r != b);
 425 #endif
 426     secp256k1_fe_mul_inner(r->n, a->n, b->n);
 427 #ifdef VERIFY
 428     r->magnitude = 1;
 429     r->normalized = 0;
 430     secp256k1_fe_verify(r);
 431 #endif
 432 }
 433
 434 static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
 435 #ifdef VERIFY
 436     VERIFY_CHECK(a->magnitude <= 8);
 437     secp256k1_fe_verify(a);
 438 #endif
 439     secp256k1_fe_sqr_inner(r->n, a->n);
 440 #ifdef VERIFY
 441     r->magnitude = 1;
 442     r->normalized = 0;
 443     secp256k1_fe_verify(r);
 444 #endif
 445 }
 446
 447 static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
 448     uint64_t mask0, mask1;
 449     mask0 = flag + ~((uint64_t)0);
 450     mask1 = ~mask0;
 451     r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
 452     r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
 453     r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
 454     r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
 455     r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
 456 #ifdef VERIFY
 457     if (a->magnitude > r->magnitude) {
 458         r->magnitude = a->magnitude;
 459     }
 460     r->normalized &= a->normalized;
 461 #endif
 462 }
 463
 464 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
 465     uint64_t mask0, mask1;
 466     mask0 = flag + ~((uint64_t)0);
 467     mask1 = ~mask0;
 468     r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
 469     r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
 470     r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
 471     r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
 472 }
 473
 474 static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
 475 #ifdef VERIFY
 476     VERIFY_CHECK(a->normalized);
 477 #endif
 478     r->n[0] = a->n[0] | a->n[1] << 52;
 479     r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
 480     r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
 481     r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
 482 }
 483
 484 static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
 485     r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
 486     r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
 487     r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
 488     r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
 489     r->n[4] = a->n[3] >> 16;
 490 #ifdef VERIFY
 491     r->magnitude = 1;
 492     r->normalized = 1;
 493 #endif
 494 }
 495
 496 #endif /* SECP256K1_FIELD_REPR_IMPL_H */