crypto/ec/curve25519.c

   1 /*
   2  * Copyright 2016-2017 The OpenSSL Project Authors. All Rights Reserved.
   3  *
   4  * Licensed under the OpenSSL license (the "License").  You may not use
   5  * this file except in compliance with the License.  You can obtain a copy
   6  * in the file LICENSE in the source distribution or at
   7  * https://www.openssl.org/source/license.html
   8  */
   9
  10 #include <string.h>
  11 #include "ec_lcl.h"
  12 #include <openssl/sha.h>
  13
  14 #if !defined(PEDANTIC) && \
  15     (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16)
  16 /*
  17  * Base 2^51 implementation.
  18  */
  19 # define BASE_2_51_IMPLEMENTED
  20
  21 typedef uint64_t fe51[5];
  22 typedef unsigned __int128 u128;
  23
  24 static const uint64_t MASK51 = 0x7ffffffffffff;
  25
  26 static uint64_t load_7(const uint8_t *in)
  27 {
  28     uint64_t result;
  29
  30     result = in[0];
  31     result |= ((uint64_t)in[1]) << 8;
  32     result |= ((uint64_t)in[2]) << 16;
  33     result |= ((uint64_t)in[3]) << 24;
  34     result |= ((uint64_t)in[4]) << 32;
  35     result |= ((uint64_t)in[5]) << 40;
  36     result |= ((uint64_t)in[6]) << 48;
  37
  38     return result;
  39 }
  40
  41 static uint64_t load_6(const uint8_t *in)
  42 {
  43     uint64_t result;
  44
  45     result = in[0];
  46     result |= ((uint64_t)in[1]) << 8;
  47     result |= ((uint64_t)in[2]) << 16;
  48     result |= ((uint64_t)in[3]) << 24;
  49     result |= ((uint64_t)in[4]) << 32;
  50     result |= ((uint64_t)in[5]) << 40;
  51
  52     return result;
  53 }
  54
  55 static void fe51_frombytes(fe51 h, const uint8_t *s)
  56 {
  57     uint64_t h0 = load_7(s);                                /* 56 bits */
  58     uint64_t h1 = load_6(s + 7) << 5;                       /* 53 bits */
  59     uint64_t h2 = load_7(s + 13) << 2;                      /* 58 bits */
  60     uint64_t h3 = load_6(s + 20) << 7;                      /* 55 bits */
  61     uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4;   /* 51 bits */
  62
  63     h1 |= h0 >> 51; h0 &= MASK51;
  64     h2 |= h1 >> 51; h1 &= MASK51;
  65     h3 |= h2 >> 51; h2 &= MASK51;
  66     h4 |= h3 >> 51; h3 &= MASK51;
  67
  68     h[0] = h0;
  69     h[1] = h1;
  70     h[2] = h2;
  71     h[3] = h3;
  72     h[4] = h4;
  73 }
  74
  75 static void fe51_tobytes(uint8_t *s, const fe51 h)
  76 {
  77     uint64_t h0 = h[0];
  78     uint64_t h1 = h[1];
  79     uint64_t h2 = h[2];
  80     uint64_t h3 = h[3];
  81     uint64_t h4 = h[4];
  82     uint64_t q;
  83
  84     /* compare to modulus */
  85     q = (h0 + 19) >> 51;
  86     q = (h1 + q) >> 51;
  87     q = (h2 + q) >> 51;
  88     q = (h3 + q) >> 51;
  89     q = (h4 + q) >> 51;
  90
  91     /* full reduce */
  92     h0 += 19 * q;
  93     h1 += h0 >> 51; h0 &= MASK51;
  94     h2 += h1 >> 51; h1 &= MASK51;
  95     h3 += h2 >> 51; h2 &= MASK51;
  96     h4 += h3 >> 51; h3 &= MASK51;
  97                     h4 &= MASK51;
  98
  99     /* smash */
 100     s[0] = h0 >> 0;
 101     s[1] = h0 >> 8;
 102     s[2] = h0 >> 16;
 103     s[3] = h0 >> 24;
 104     s[4] = h0 >> 32;
 105     s[5] = h0 >> 40;
 106     s[6] = (h0 >> 48) | ((uint32_t)h1 << 3);
 107     s[7] = h1 >> 5;
 108     s[8] = h1 >> 13;
 109     s[9] = h1 >> 21;
 110     s[10] = h1 >> 29;
 111     s[11] = h1 >> 37;
 112     s[12] = (h1 >> 45) | ((uint32_t)h2 << 6);
 113     s[13] = h2 >> 2;
 114     s[14] = h2 >> 10;
 115     s[15] = h2 >> 18;
 116     s[16] = h2 >> 26;
 117     s[17] = h2 >> 34;
 118     s[18] = h2 >> 42;
 119     s[19] = (h2 >> 50) | ((uint32_t)h3 << 1);
 120     s[20] = h3 >> 7;
 121     s[21] = h3 >> 15;
 122     s[22] = h3 >> 23;
 123     s[23] = h3 >> 31;
 124     s[24] = h3 >> 39;
 125     s[25] = (h3 >> 47) | ((uint32_t)h4 << 4);
 126     s[26] = h4 >> 4;
 127     s[27] = h4 >> 12;
 128     s[28] = h4 >> 20;
 129     s[29] = h4 >> 28;
 130     s[30] = h4 >> 36;
 131     s[31] = h4 >> 44;
 132 }
 133
 134 static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
 135 {
 136     u128 h0, h1, h2, h3, h4;
 137     uint64_t f_i, g0, g1, g2, g3, g4;
 138
 139     f_i = f[0];
 140     h0 = (u128)f_i * (g0 = g[0]);
 141     h1 = (u128)f_i * (g1 = g[1]);
 142     h2 = (u128)f_i * (g2 = g[2]);
 143     h3 = (u128)f_i * (g3 = g[3]);
 144     h4 = (u128)f_i * (g4 = g[4]);
 145
 146     f_i = f[1];
 147     h0 += (u128)f_i * (g4 *= 19);
 148     h1 += (u128)f_i * g0;
 149     h2 += (u128)f_i * g1;
 150     h3 += (u128)f_i * g2;
 151     h4 += (u128)f_i * g3;
 152
 153     f_i = f[2];
 154     h0 += (u128)f_i * (g3 *= 19);
 155     h1 += (u128)f_i * g4;
 156     h2 += (u128)f_i * g0;
 157     h3 += (u128)f_i * g1;
 158     h4 += (u128)f_i * g2;
 159
 160     f_i = f[3];
 161     h0 += (u128)f_i * (g2 *= 19);
 162     h1 += (u128)f_i * g3;
 163     h2 += (u128)f_i * g4;
 164     h3 += (u128)f_i * g0;
 165     h4 += (u128)f_i * g1;
 166
 167     f_i = f[4];
 168     h0 += (u128)f_i * (g1 *= 19);
 169     h1 += (u128)f_i * g2;
 170     h2 += (u128)f_i * g3;
 171     h3 += (u128)f_i * g4;
 172     h4 += (u128)f_i * g0;
 173
 174     /* partial [lazy] reduction */
 175     h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
 176     h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
 177
 178     h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
 179     g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
 180
 181     g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
 182     g3 += g2 >> 51; g2 &= MASK51;
 183     g1 += g0 >> 51; g0 &= MASK51;
 184
 185     h[0] = g0;
 186     h[1] = g1;
 187     h[2] = g2;
 188     h[3] = g3;
 189     h[4] = g4;
 190 }
 191
 192 static void fe51_sq(fe51 h, const fe51 f)
 193 {
 194 # if defined(OPENSSL_SMALL_FOOTPRINT)
 195     fe51_mul(h, f, f);
 196 # else
 197     /* dedicated squaring gives 16-25% overall improvement */
 198     uint64_t g0 = f[0];
 199     uint64_t g1 = f[1];
 200     uint64_t g2 = f[2];
 201     uint64_t g3 = f[3];
 202     uint64_t g4 = f[4];
 203     u128 h0, h1, h2, h3, h4;
 204
 205     h0 = (u128)g0 * g0;     g0 *= 2;
 206     h1 = (u128)g0 * g1;
 207     h2 = (u128)g0 * g2;
 208     h3 = (u128)g0 * g3;
 209     h4 = (u128)g0 * g4;
 210
 211     g0 = g4;                /* borrow g0 */
 212     h3 += (u128)g0 * (g4 *= 19);
 213
 214     h2 += (u128)g1 * g1;    g1 *= 2;
 215     h3 += (u128)g1 * g2;
 216     h4 += (u128)g1 * g3;
 217     h0 += (u128)g1 * g4;
 218
 219     g0 = g3;                /* borrow g0 */
 220     h1 += (u128)g0 * (g3 *= 19);
 221     h2 += (u128)(g0 * 2) * g4;
 222
 223     h4 += (u128)g2 * g2;    g2 *= 2;
 224     h0 += (u128)g2 * g3;
 225     h1 += (u128)g2 * g4;
 226
 227     /* partial [lazy] reduction */
 228     h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
 229     h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
 230
 231     h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
 232     g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
 233
 234     g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
 235     g3 += g2 >> 51; g2 &= MASK51;
 236     g1 += g0 >> 51; g0 &= MASK51;
 237
 238     h[0] = g0;
 239     h[1] = g1;
 240     h[2] = g2;
 241     h[3] = g3;
 242     h[4] = g4;
 243 # endif
 244 }
 245
 246 static void fe51_add(fe51 h, const fe51 f, const fe51 g)
 247 {
 248     h[0] = f[0] + g[0];
 249     h[1] = f[1] + g[1];
 250     h[2] = f[2] + g[2];
 251     h[3] = f[3] + g[3];
 252     h[4] = f[4] + g[4];
 253 }
 254
 255 static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
 256 {
 257     /*
 258      * Add 2*modulus to ensure that result remains positive
 259      * even if subtrahend is partially reduced.
 260      */
 261     h[0] = (f[0] + 0xfffffffffffda) - g[0];
 262     h[1] = (f[1] + 0xffffffffffffe) - g[1];
 263     h[2] = (f[2] + 0xffffffffffffe) - g[2];
 264     h[3] = (f[3] + 0xffffffffffffe) - g[3];
 265     h[4] = (f[4] + 0xffffffffffffe) - g[4];
 266 }
 267
 268 static void fe51_0(fe51 h)
 269 {
 270     h[0] = 0;
 271     h[1] = 0;
 272     h[2] = 0;
 273     h[3] = 0;
 274     h[4] = 0;
 275 }
 276
 277 static void fe51_1(fe51 h)
 278 {
 279     h[0] = 1;
 280     h[1] = 0;
 281     h[2] = 0;
 282     h[3] = 0;
 283     h[4] = 0;
 284 }
 285
 286 static void fe51_copy(fe51 h, const fe51 f)
 287 {
 288     h[0] = f[0];
 289     h[1] = f[1];
 290     h[2] = f[2];
 291     h[3] = f[3];
 292     h[4] = f[4];
 293 }
 294
 295 static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
 296 {
 297     int i;
 298     uint64_t mask = 0 - (uint64_t)b;
 299
 300     for (i = 0; i < 5; i++) {
 301         int64_t x = f[i] ^ g[i];
 302         x &= mask;
 303         f[i] ^= x;
 304         g[i] ^= x;
 305     }
 306 }
 307
 308 static void fe51_invert(fe51 out, const fe51 z)
 309 {
 310     fe51 t0;
 311     fe51 t1;
 312     fe51 t2;
 313     fe51 t3;
 314     int i;
 315
 316     /*
 317      * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
 318      * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
 319      */
 320
 321     /* t0 = z ** 2 */
 322     fe51_sq(t0, z);
 323
 324     /* t1 = t0 ** (2 ** 2) = z ** 8 */
 325     fe51_sq(t1, t0);
 326     fe51_sq(t1, t1);
 327
 328     /* t1 = z * t1 = z ** 9 */
 329     fe51_mul(t1, z, t1);
 330     /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
 331     fe51_mul(t0, t0, t1);
 332
 333     /* t2 = t0 ** 2 = z ** 22 */
 334     fe51_sq(t2, t0);
 335
 336     /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
 337     fe51_mul(t1, t1, t2);
 338
 339     /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
 340     fe51_sq(t2, t1);
 341     for (i = 1; i < 5; ++i)
 342         fe51_sq(t2, t2);
 343
 344     /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
 345     fe51_mul(t1, t2, t1);
 346
 347     /* Continuing similarly... */
 348
 349     /* t2 = z ** (2 ** 20 - 1) */
 350     fe51_sq(t2, t1);
 351     for (i = 1; i < 10; ++i)
 352         fe51_sq(t2, t2);
 353
 354     fe51_mul(t2, t2, t1);
 355
 356     /* t2 = z ** (2 ** 40 - 1) */
 357     fe51_sq(t3, t2);
 358     for (i = 1; i < 20; ++i)
 359         fe51_sq(t3, t3);
 360
 361     fe51_mul(t2, t3, t2);
 362
 363     /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
 364     for (i = 0; i < 10; ++i)
 365         fe51_sq(t2, t2);
 366
 367     /* t1 = z ** (2 ** 50 - 1) */
 368     fe51_mul(t1, t2, t1);
 369
 370     /* t2 = z ** (2 ** 100 - 1) */
 371     fe51_sq(t2, t1);
 372     for (i = 1; i < 50; ++i)
 373         fe51_sq(t2, t2);
 374
 375     fe51_mul(t2, t2, t1);
 376
 377     /* t2 = z ** (2 ** 200 - 1) */
 378     fe51_sq(t3, t2);
 379     for (i = 1; i < 100; ++i)
 380         fe51_sq(t3, t3);
 381
 382     fe51_mul(t2, t3, t2);
 383
 384     /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
 385     for (i = 0; i < 50; ++i)
 386         fe51_sq(t2, t2);
 387
 388     /* t1 = z ** (2 ** 250 - 1) */
 389     fe51_mul(t1, t2, t1);
 390
 391     /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
 392     for (i = 0; i < 5; ++i)
 393         fe51_sq(t1, t1);
 394
 395     /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
 396     fe51_mul(out, t1, t0);
 397 }
 398
 399 static void fe51_mul121666(fe51 h, fe51 f)
 400 {
 401     u128 h0 = f[0] * (u128)121666;
 402     u128 h1 = f[1] * (u128)121666;
 403     u128 h2 = f[2] * (u128)121666;
 404     u128 h3 = f[3] * (u128)121666;
 405     u128 h4 = f[4] * (u128)121666;
 406     uint64_t g0, g1, g2, g3, g4;
 407
 408     h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
 409     h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
 410
 411     h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
 412     g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
 413
 414     g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
 415     g3 += g2 >> 51; g2 &= MASK51;
 416     g1 += g0 >> 51; g0 &= MASK51;
 417
 418     h[0] = g0;
 419     h[1] = g1;
 420     h[2] = g2;
 421     h[3] = g3;
 422     h[4] = g4;
 423 }
 424
 425 /*
 426  * Duplicate of original x25519_scalar_mult_generic, but using
 427  * fe51_* subroutines.
 428  */
 429 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
 430                                const uint8_t point[32])
 431 {
 432     fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
 433     uint8_t e[32];
 434     unsigned swap = 0;
 435     int pos;
 436
 437     memcpy(e, scalar, 32);
 438     e[0]  &= 0xf8;
 439     e[31] &= 0x7f;
 440     e[31] |= 0x40;
 441     fe51_frombytes(x1, point);
 442     fe51_1(x2);
 443     fe51_0(z2);
 444     fe51_copy(x3, x1);
 445     fe51_1(z3);
 446
 447     for (pos = 254; pos >= 0; --pos) {
 448         unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
 449
 450         swap ^= b;
 451         fe51_cswap(x2, x3, swap);
 452         fe51_cswap(z2, z3, swap);
 453         swap = b;
 454         fe51_sub(tmp0, x3, z3);
 455         fe51_sub(tmp1, x2, z2);
 456         fe51_add(x2, x2, z2);
 457         fe51_add(z2, x3, z3);
 458         fe51_mul(z3, tmp0, x2);
 459         fe51_mul(z2, z2, tmp1);
 460         fe51_sq(tmp0, tmp1);
 461         fe51_sq(tmp1, x2);
 462         fe51_add(x3, z3, z2);
 463         fe51_sub(z2, z3, z2);
 464         fe51_mul(x2, tmp1, tmp0);
 465         fe51_sub(tmp1, tmp1, tmp0);
 466         fe51_sq(z2, z2);
 467         fe51_mul121666(z3, tmp1);
 468         fe51_sq(x3, x3);
 469         fe51_add(tmp0, tmp0, z3);
 470         fe51_mul(z3, x1, z2);
 471         fe51_mul(z2, tmp1, tmp0);
 472     }
 473     fe51_cswap(x2, x3, swap);
 474     fe51_cswap(z2, z3, swap);
 475
 476     fe51_invert(z2, z2);
 477     fe51_mul(x2, x2, z2);
 478     fe51_tobytes(out, x2);
 479
 480     OPENSSL_cleanse(e, sizeof(e));
 481 }
 482 #endif
 483
 484 /*
 485  * Reference base 2^25.5 implementation.
 486  */
 487 /*
 488  * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
 489  * 20141124 (http://bench.cr.yp.to/supercop.html).
 490  *
 491  * The field functions are shared by Ed25519 and X25519 where possible.
 492  */
 493
 494 /* fe means field element. Here the field is \Z/(2^255-19). An element t,
 495  * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
 496  * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
 497  * context.  */
 498 typedef int32_t fe[10];
 499
 500 static const int64_t kBottom25Bits = 0x1ffffffLL;
 501 static const int64_t kBottom26Bits = 0x3ffffffLL;
 502 static const int64_t kTop39Bits = 0xfffffffffe000000LL;
 503 static const int64_t kTop38Bits = 0xfffffffffc000000LL;
 504
 505 static uint64_t load_3(const uint8_t *in) {
 506   uint64_t result;
 507   result = (uint64_t)in[0];
 508   result |= ((uint64_t)in[1]) << 8;
 509   result |= ((uint64_t)in[2]) << 16;
 510   return result;
 511 }
 512
 513 static uint64_t load_4(const uint8_t *in) {
 514   uint64_t result;
 515   result = (uint64_t)in[0];
 516   result |= ((uint64_t)in[1]) << 8;
 517   result |= ((uint64_t)in[2]) << 16;
 518   result |= ((uint64_t)in[3]) << 24;
 519   return result;
 520 }
 521
 522 static void fe_frombytes(fe h, const uint8_t *s) {
 523   /* Ignores top bit of h. */
 524   int64_t h0 = load_4(s);
 525   int64_t h1 = load_3(s + 4) << 6;
 526   int64_t h2 = load_3(s + 7) << 5;
 527   int64_t h3 = load_3(s + 10) << 3;
 528   int64_t h4 = load_3(s + 13) << 2;
 529   int64_t h5 = load_4(s + 16);
 530   int64_t h6 = load_3(s + 20) << 7;
 531   int64_t h7 = load_3(s + 23) << 5;
 532   int64_t h8 = load_3(s + 26) << 4;
 533   int64_t h9 = (load_3(s + 29) & 8388607) << 2;
 534   int64_t carry0;
 535   int64_t carry1;
 536   int64_t carry2;
 537   int64_t carry3;
 538   int64_t carry4;
 539   int64_t carry5;
 540   int64_t carry6;
 541   int64_t carry7;
 542   int64_t carry8;
 543   int64_t carry9;
 544
 545   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
 546   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
 547   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
 548   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
 549   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
 550
 551   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 552   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
 553   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 554   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
 555   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
 556
 557   h[0] = (int32_t)h0;
 558   h[1] = (int32_t)h1;
 559   h[2] = (int32_t)h2;
 560   h[3] = (int32_t)h3;
 561   h[4] = (int32_t)h4;
 562   h[5] = (int32_t)h5;
 563   h[6] = (int32_t)h6;
 564   h[7] = (int32_t)h7;
 565   h[8] = (int32_t)h8;
 566   h[9] = (int32_t)h9;
 567 }
 568
 569 /* Preconditions:
 570  *  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
 571  *
 572  * Write p=2^255-19; q=floor(h/p).
 573  * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
 574  *
 575  * Proof:
 576  *   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
 577  *   Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
 578  *
 579  *   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
 580  *   Then 0<y<1.
 581  *
 582  *   Write r=h-pq.
 583  *   Have 0<=r<=p-1=2^255-20.
 584  *   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
 585  *
 586  *   Write x=r+19(2^-255)r+y.
 587  *   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
 588  *
 589  *   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
 590  *   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
 591 static void fe_tobytes(uint8_t *s, const fe h) {
 592   int32_t h0 = h[0];
 593   int32_t h1 = h[1];
 594   int32_t h2 = h[2];
 595   int32_t h3 = h[3];
 596   int32_t h4 = h[4];
 597   int32_t h5 = h[5];
 598   int32_t h6 = h[6];
 599   int32_t h7 = h[7];
 600   int32_t h8 = h[8];
 601   int32_t h9 = h[9];
 602   int32_t q;
 603
 604   q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
 605   q = (h0 + q) >> 26;
 606   q = (h1 + q) >> 25;
 607   q = (h2 + q) >> 26;
 608   q = (h3 + q) >> 25;
 609   q = (h4 + q) >> 26;
 610   q = (h5 + q) >> 25;
 611   q = (h6 + q) >> 26;
 612   q = (h7 + q) >> 25;
 613   q = (h8 + q) >> 26;
 614   q = (h9 + q) >> 25;
 615
 616   /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
 617   h0 += 19 * q;
 618   /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
 619
 620   h1 += h0 >> 26; h0 &= kBottom26Bits;
 621   h2 += h1 >> 25; h1 &= kBottom25Bits;
 622   h3 += h2 >> 26; h2 &= kBottom26Bits;
 623   h4 += h3 >> 25; h3 &= kBottom25Bits;
 624   h5 += h4 >> 26; h4 &= kBottom26Bits;
 625   h6 += h5 >> 25; h5 &= kBottom25Bits;
 626   h7 += h6 >> 26; h6 &= kBottom26Bits;
 627   h8 += h7 >> 25; h7 &= kBottom25Bits;
 628   h9 += h8 >> 26; h8 &= kBottom26Bits;
 629                   h9 &= kBottom25Bits;
 630                   /* h10 = carry9 */
 631
 632   /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
 633    * Have h0+...+2^230 h9 between 0 and 2^255-1;
 634    * evidently 2^255 h10-2^255 q = 0.
 635    * Goal: Output h0+...+2^230 h9.  */
 636
 637   s[0] = h0 >> 0;
 638   s[1] = h0 >> 8;
 639   s[2] = h0 >> 16;
 640   s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
 641   s[4] = h1 >> 6;
 642   s[5] = h1 >> 14;
 643   s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
 644   s[7] = h2 >> 5;
 645   s[8] = h2 >> 13;
 646   s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
 647   s[10] = h3 >> 3;
 648   s[11] = h3 >> 11;
 649   s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
 650   s[13] = h4 >> 2;
 651   s[14] = h4 >> 10;
 652   s[15] = h4 >> 18;
 653   s[16] = h5 >> 0;
 654   s[17] = h5 >> 8;
 655   s[18] = h5 >> 16;
 656   s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
 657   s[20] = h6 >> 7;
 658   s[21] = h6 >> 15;
 659   s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
 660   s[23] = h7 >> 5;
 661   s[24] = h7 >> 13;
 662   s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
 663   s[26] = h8 >> 4;
 664   s[27] = h8 >> 12;
 665   s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
 666   s[29] = h9 >> 2;
 667   s[30] = h9 >> 10;
 668   s[31] = h9 >> 18;
 669 }
 670
 671 /* h = f */
 672 static void fe_copy(fe h, const fe f) {
 673   memmove(h, f, sizeof(int32_t) * 10);
 674 }
 675
 676 /* h = 0 */
 677 static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
 678
 679 /* h = 1 */
 680 static void fe_1(fe h) {
 681   memset(h, 0, sizeof(int32_t) * 10);
 682   h[0] = 1;
 683 }
 684
 685 /* h = f + g
 686  * Can overlap h with f or g.
 687  *
 688  * Preconditions:
 689  *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 690  *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 691  *
 692  * Postconditions:
 693  *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
 694 static void fe_add(fe h, const fe f, const fe g) {
 695   unsigned i;
 696   for (i = 0; i < 10; i++) {
 697     h[i] = f[i] + g[i];
 698   }
 699 }
 700
 701 /* h = f - g
 702  * Can overlap h with f or g.
 703  *
 704  * Preconditions:
 705  *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 706  *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 707  *
 708  * Postconditions:
 709  *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
 710 static void fe_sub(fe h, const fe f, const fe g) {
 711   unsigned i;
 712   for (i = 0; i < 10; i++) {
 713     h[i] = f[i] - g[i];
 714   }
 715 }
 716
 717 /* h = f * g
 718  * Can overlap h with f or g.
 719  *
 720  * Preconditions:
 721  *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 722  *    |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 723  *
 724  * Postconditions:
 725  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 726  *
 727  * Notes on implementation strategy:
 728  *
 729  * Using schoolbook multiplication.
 730  * Karatsuba would save a little in some cost models.
 731  *
 732  * Most multiplications by 2 and 19 are 32-bit precomputations;
 733  * cheaper than 64-bit postcomputations.
 734  *
 735  * There is one remaining multiplication by 19 in the carry chain;
 736  * one *19 precomputation can be merged into this,
 737  * but the resulting data flow is considerably less clean.
 738  *
 739  * There are 12 carries below.
 740  * 10 of them are 2-way parallelizable and vectorizable.
 741  * Can get away with 11 carries, but then data flow is much deeper.
 742  *
 743  * With tighter constraints on inputs can squeeze carries into int32. */
 744 static void fe_mul(fe h, const fe f, const fe g) {
 745   int32_t f0 = f[0];
 746   int32_t f1 = f[1];
 747   int32_t f2 = f[2];
 748   int32_t f3 = f[3];
 749   int32_t f4 = f[4];
 750   int32_t f5 = f[5];
 751   int32_t f6 = f[6];
 752   int32_t f7 = f[7];
 753   int32_t f8 = f[8];
 754   int32_t f9 = f[9];
 755   int32_t g0 = g[0];
 756   int32_t g1 = g[1];
 757   int32_t g2 = g[2];
 758   int32_t g3 = g[3];
 759   int32_t g4 = g[4];
 760   int32_t g5 = g[5];
 761   int32_t g6 = g[6];
 762   int32_t g7 = g[7];
 763   int32_t g8 = g[8];
 764   int32_t g9 = g[9];
 765   int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
 766   int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
 767   int32_t g3_19 = 19 * g3;
 768   int32_t g4_19 = 19 * g4;
 769   int32_t g5_19 = 19 * g5;
 770   int32_t g6_19 = 19 * g6;
 771   int32_t g7_19 = 19 * g7;
 772   int32_t g8_19 = 19 * g8;
 773   int32_t g9_19 = 19 * g9;
 774   int32_t f1_2 = 2 * f1;
 775   int32_t f3_2 = 2 * f3;
 776   int32_t f5_2 = 2 * f5;
 777   int32_t f7_2 = 2 * f7;
 778   int32_t f9_2 = 2 * f9;
 779   int64_t f0g0    = f0   * (int64_t) g0;
 780   int64_t f0g1    = f0   * (int64_t) g1;
 781   int64_t f0g2    = f0   * (int64_t) g2;
 782   int64_t f0g3    = f0   * (int64_t) g3;
 783   int64_t f0g4    = f0   * (int64_t) g4;
 784   int64_t f0g5    = f0   * (int64_t) g5;
 785   int64_t f0g6    = f0   * (int64_t) g6;
 786   int64_t f0g7    = f0   * (int64_t) g7;
 787   int64_t f0g8    = f0   * (int64_t) g8;
 788   int64_t f0g9    = f0   * (int64_t) g9;
 789   int64_t f1g0    = f1   * (int64_t) g0;
 790   int64_t f1g1_2  = f1_2 * (int64_t) g1;
 791   int64_t f1g2    = f1   * (int64_t) g2;
 792   int64_t f1g3_2  = f1_2 * (int64_t) g3;
 793   int64_t f1g4    = f1   * (int64_t) g4;
 794   int64_t f1g5_2  = f1_2 * (int64_t) g5;
 795   int64_t f1g6    = f1   * (int64_t) g6;
 796   int64_t f1g7_2  = f1_2 * (int64_t) g7;
 797   int64_t f1g8    = f1   * (int64_t) g8;
 798   int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
 799   int64_t f2g0    = f2   * (int64_t) g0;
 800   int64_t f2g1    = f2   * (int64_t) g1;
 801   int64_t f2g2    = f2   * (int64_t) g2;
 802   int64_t f2g3    = f2   * (int64_t) g3;
 803   int64_t f2g4    = f2   * (int64_t) g4;
 804   int64_t f2g5    = f2   * (int64_t) g5;
 805   int64_t f2g6    = f2   * (int64_t) g6;
 806   int64_t f2g7    = f2   * (int64_t) g7;
 807   int64_t f2g8_19 = f2   * (int64_t) g8_19;
 808   int64_t f2g9_19 = f2   * (int64_t) g9_19;
 809   int64_t f3g0    = f3   * (int64_t) g0;
 810   int64_t f3g1_2  = f3_2 * (int64_t) g1;
 811   int64_t f3g2    = f3   * (int64_t) g2;
 812   int64_t f3g3_2  = f3_2 * (int64_t) g3;
 813   int64_t f3g4    = f3   * (int64_t) g4;
 814   int64_t f3g5_2  = f3_2 * (int64_t) g5;
 815   int64_t f3g6    = f3   * (int64_t) g6;
 816   int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
 817   int64_t f3g8_19 = f3   * (int64_t) g8_19;
 818   int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
 819   int64_t f4g0    = f4   * (int64_t) g0;
 820   int64_t f4g1    = f4   * (int64_t) g1;
 821   int64_t f4g2    = f4   * (int64_t) g2;
 822   int64_t f4g3    = f4   * (int64_t) g3;
 823   int64_t f4g4    = f4   * (int64_t) g4;
 824   int64_t f4g5    = f4   * (int64_t) g5;
 825   int64_t f4g6_19 = f4   * (int64_t) g6_19;
 826   int64_t f4g7_19 = f4   * (int64_t) g7_19;
 827   int64_t f4g8_19 = f4   * (int64_t) g8_19;
 828   int64_t f4g9_19 = f4   * (int64_t) g9_19;
 829   int64_t f5g0    = f5   * (int64_t) g0;
 830   int64_t f5g1_2  = f5_2 * (int64_t) g1;
 831   int64_t f5g2    = f5   * (int64_t) g2;
 832   int64_t f5g3_2  = f5_2 * (int64_t) g3;
 833   int64_t f5g4    = f5   * (int64_t) g4;
 834   int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
 835   int64_t f5g6_19 = f5   * (int64_t) g6_19;
 836   int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
 837   int64_t f5g8_19 = f5   * (int64_t) g8_19;
 838   int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
 839   int64_t f6g0    = f6   * (int64_t) g0;
 840   int64_t f6g1    = f6   * (int64_t) g1;
 841   int64_t f6g2    = f6   * (int64_t) g2;
 842   int64_t f6g3    = f6   * (int64_t) g3;
 843   int64_t f6g4_19 = f6   * (int64_t) g4_19;
 844   int64_t f6g5_19 = f6   * (int64_t) g5_19;
 845   int64_t f6g6_19 = f6   * (int64_t) g6_19;
 846   int64_t f6g7_19 = f6   * (int64_t) g7_19;
 847   int64_t f6g8_19 = f6   * (int64_t) g8_19;
 848   int64_t f6g9_19 = f6   * (int64_t) g9_19;
 849   int64_t f7g0    = f7   * (int64_t) g0;
 850   int64_t f7g1_2  = f7_2 * (int64_t) g1;
 851   int64_t f7g2    = f7   * (int64_t) g2;
 852   int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
 853   int64_t f7g4_19 = f7   * (int64_t) g4_19;
 854   int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
 855   int64_t f7g6_19 = f7   * (int64_t) g6_19;
 856   int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
 857   int64_t f7g8_19 = f7   * (int64_t) g8_19;
 858   int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
 859   int64_t f8g0    = f8   * (int64_t) g0;
 860   int64_t f8g1    = f8   * (int64_t) g1;
 861   int64_t f8g2_19 = f8   * (int64_t) g2_19;
 862   int64_t f8g3_19 = f8   * (int64_t) g3_19;
 863   int64_t f8g4_19 = f8   * (int64_t) g4_19;
 864   int64_t f8g5_19 = f8   * (int64_t) g5_19;
 865   int64_t f8g6_19 = f8   * (int64_t) g6_19;
 866   int64_t f8g7_19 = f8   * (int64_t) g7_19;
 867   int64_t f8g8_19 = f8   * (int64_t) g8_19;
 868   int64_t f8g9_19 = f8   * (int64_t) g9_19;
 869   int64_t f9g0    = f9   * (int64_t) g0;
 870   int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
 871   int64_t f9g2_19 = f9   * (int64_t) g2_19;
 872   int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
 873   int64_t f9g4_19 = f9   * (int64_t) g4_19;
 874   int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
 875   int64_t f9g6_19 = f9   * (int64_t) g6_19;
 876   int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
 877   int64_t f9g8_19 = f9   * (int64_t) g8_19;
 878   int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
 879   int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
 880   int64_t h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
 881   int64_t h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
 882   int64_t h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
 883   int64_t h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
 884   int64_t h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
 885   int64_t h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
 886   int64_t h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
 887   int64_t h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
 888   int64_t h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
 889   int64_t carry0;
 890   int64_t carry1;
 891   int64_t carry2;
 892   int64_t carry3;
 893   int64_t carry4;
 894   int64_t carry5;
 895   int64_t carry6;
 896   int64_t carry7;
 897   int64_t carry8;
 898   int64_t carry9;
 899
 900   /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
 901    *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
 902    * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
 903    *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
 904
 905   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 906   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 907   /* |h0| <= 2^25 */
 908   /* |h4| <= 2^25 */
 909   /* |h1| <= 1.71*2^59 */
 910   /* |h5| <= 1.71*2^59 */
 911
 912   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
 913   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
 914   /* |h1| <= 2^24; from now on fits into int32 */
 915   /* |h5| <= 2^24; from now on fits into int32 */
 916   /* |h2| <= 1.41*2^60 */
 917   /* |h6| <= 1.41*2^60 */
 918
 919   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
 920   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
 921   /* |h2| <= 2^25; from now on fits into int32 unchanged */
 922   /* |h6| <= 2^25; from now on fits into int32 unchanged */
 923   /* |h3| <= 1.71*2^59 */
 924   /* |h7| <= 1.71*2^59 */
 925
 926   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
 927   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
 928   /* |h3| <= 2^24; from now on fits into int32 unchanged */
 929   /* |h7| <= 2^24; from now on fits into int32 unchanged */
 930   /* |h4| <= 1.72*2^34 */
 931   /* |h8| <= 1.41*2^60 */
 932
 933   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 934   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
 935   /* |h4| <= 2^25; from now on fits into int32 unchanged */
 936   /* |h8| <= 2^25; from now on fits into int32 unchanged */
 937   /* |h5| <= 1.01*2^24 */
 938   /* |h9| <= 1.71*2^59 */
 939
 940   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
 941   /* |h9| <= 2^24; from now on fits into int32 unchanged */
 942   /* |h0| <= 1.1*2^39 */
 943
 944   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 945   /* |h0| <= 2^25; from now on fits into int32 unchanged */
 946   /* |h1| <= 1.01*2^24 */
 947
 948   h[0] = (int32_t)h0;
 949   h[1] = (int32_t)h1;
 950   h[2] = (int32_t)h2;
 951   h[3] = (int32_t)h3;
 952   h[4] = (int32_t)h4;
 953   h[5] = (int32_t)h5;
 954   h[6] = (int32_t)h6;
 955   h[7] = (int32_t)h7;
 956   h[8] = (int32_t)h8;
 957   h[9] = (int32_t)h9;
 958 }
 959
 960 /* h = f * f
 961  * Can overlap h with f.
 962  *
 963  * Preconditions:
 964  *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 965  *
 966  * Postconditions:
 967  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 968  *
 969  * See fe_mul.c for discussion of implementation strategy. */
 970 static void fe_sq(fe h, const fe f) {
 971   int32_t f0 = f[0];
 972   int32_t f1 = f[1];
 973   int32_t f2 = f[2];
 974   int32_t f3 = f[3];
 975   int32_t f4 = f[4];
 976   int32_t f5 = f[5];
 977   int32_t f6 = f[6];
 978   int32_t f7 = f[7];
 979   int32_t f8 = f[8];
 980   int32_t f9 = f[9];
 981   int32_t f0_2 = 2 * f0;
 982   int32_t f1_2 = 2 * f1;
 983   int32_t f2_2 = 2 * f2;
 984   int32_t f3_2 = 2 * f3;
 985   int32_t f4_2 = 2 * f4;
 986   int32_t f5_2 = 2 * f5;
 987   int32_t f6_2 = 2 * f6;
 988   int32_t f7_2 = 2 * f7;
 989   int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
 990   int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
 991   int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
 992   int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
 993   int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
 994   int64_t f0f0    = f0   * (int64_t) f0;
 995   int64_t f0f1_2  = f0_2 * (int64_t) f1;
 996   int64_t f0f2_2  = f0_2 * (int64_t) f2;
 997   int64_t f0f3_2  = f0_2 * (int64_t) f3;
 998   int64_t f0f4_2  = f0_2 * (int64_t) f4;
 999   int64_t f0f5_2  = f0_2 * (int64_t) f5;
1000   int64_t f0f6_2  = f0_2 * (int64_t) f6;
1001   int64_t f0f7_2  = f0_2 * (int64_t) f7;
1002   int64_t f0f8_2  = f0_2 * (int64_t) f8;
1003   int64_t f0f9_2  = f0_2 * (int64_t) f9;
1004   int64_t f1f1_2  = f1_2 * (int64_t) f1;
1005   int64_t f1f2_2  = f1_2 * (int64_t) f2;
1006   int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
1007   int64_t f1f4_2  = f1_2 * (int64_t) f4;
1008   int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
1009   int64_t f1f6_2  = f1_2 * (int64_t) f6;
1010   int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
1011   int64_t f1f8_2  = f1_2 * (int64_t) f8;
1012   int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1013   int64_t f2f2    = f2   * (int64_t) f2;
1014   int64_t f2f3_2  = f2_2 * (int64_t) f3;
1015   int64_t f2f4_2  = f2_2 * (int64_t) f4;
1016   int64_t f2f5_2  = f2_2 * (int64_t) f5;
1017   int64_t f2f6_2  = f2_2 * (int64_t) f6;
1018   int64_t f2f7_2  = f2_2 * (int64_t) f7;
1019   int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1020   int64_t f2f9_38 = f2   * (int64_t) f9_38;
1021   int64_t f3f3_2  = f3_2 * (int64_t) f3;
1022   int64_t f3f4_2  = f3_2 * (int64_t) f4;
1023   int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
1024   int64_t f3f6_2  = f3_2 * (int64_t) f6;
1025   int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1026   int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1027   int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1028   int64_t f4f4    = f4   * (int64_t) f4;
1029   int64_t f4f5_2  = f4_2 * (int64_t) f5;
1030   int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1031   int64_t f4f7_38 = f4   * (int64_t) f7_38;
1032   int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1033   int64_t f4f9_38 = f4   * (int64_t) f9_38;
1034   int64_t f5f5_38 = f5   * (int64_t) f5_38;
1035   int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1036   int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1037   int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1038   int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1039   int64_t f6f6_19 = f6   * (int64_t) f6_19;
1040   int64_t f6f7_38 = f6   * (int64_t) f7_38;
1041   int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1042   int64_t f6f9_38 = f6   * (int64_t) f9_38;
1043   int64_t f7f7_38 = f7   * (int64_t) f7_38;
1044   int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1045   int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1046   int64_t f8f8_19 = f8   * (int64_t) f8_19;
1047   int64_t f8f9_38 = f8   * (int64_t) f9_38;
1048   int64_t f9f9_38 = f9   * (int64_t) f9_38;
1049   int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
1050   int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
1051   int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
1052   int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
1053   int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
1054   int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
1055   int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
1056   int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
1057   int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
1058   int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
1059   int64_t carry0;
1060   int64_t carry1;
1061   int64_t carry2;
1062   int64_t carry3;
1063   int64_t carry4;
1064   int64_t carry5;
1065   int64_t carry6;
1066   int64_t carry7;
1067   int64_t carry8;
1068   int64_t carry9;
1069
1070   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1071   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1072
1073   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1074   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1075
1076   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1077   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1078
1079   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1080   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1081
1082   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1083   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1084
1085   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1086
1087   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1088
1089   h[0] = (int32_t)h0;
1090   h[1] = (int32_t)h1;
1091   h[2] = (int32_t)h2;
1092   h[3] = (int32_t)h3;
1093   h[4] = (int32_t)h4;
1094   h[5] = (int32_t)h5;
1095   h[6] = (int32_t)h6;
1096   h[7] = (int32_t)h7;
1097   h[8] = (int32_t)h8;
1098   h[9] = (int32_t)h9;
1099 }
1100
1101 static void fe_invert(fe out, const fe z) {
1102   fe t0;
1103   fe t1;
1104   fe t2;
1105   fe t3;
1106   int i;
1107
1108   /*
1109    * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
1110    * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
1111    */
1112
1113   /* t0 = z ** 2 */
1114   fe_sq(t0, z);
1115
1116   /* t1 = t0 ** (2 ** 2) = z ** 8 */
1117   fe_sq(t1, t0);
1118   fe_sq(t1, t1);
1119
1120   /* t1 = z * t1 = z ** 9 */
1121   fe_mul(t1, z, t1);
1122   /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1123   fe_mul(t0, t0, t1);
1124
1125   /* t2 = t0 ** 2 = z ** 22 */
1126   fe_sq(t2, t0);
1127
1128   /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
1129   fe_mul(t1, t1, t2);
1130
1131   /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
1132   fe_sq(t2, t1);
1133   for (i = 1; i < 5; ++i) {
1134     fe_sq(t2, t2);
1135   }
1136
1137   /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
1138   fe_mul(t1, t2, t1);
1139
1140   /* Continuing similarly... */
1141
1142   /* t2 = z ** (2 ** 20 - 1) */
1143   fe_sq(t2, t1);
1144   for (i = 1; i < 10; ++i) {
1145     fe_sq(t2, t2);
1146   }
1147   fe_mul(t2, t2, t1);
1148
1149   /* t2 = z ** (2 ** 40 - 1) */
1150   fe_sq(t3, t2);
1151   for (i = 1; i < 20; ++i) {
1152     fe_sq(t3, t3);
1153   }
1154   fe_mul(t2, t3, t2);
1155
1156   /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
1157   for (i = 0; i < 10; ++i) {
1158     fe_sq(t2, t2);
1159   }
1160   /* t1 = z ** (2 ** 50 - 1) */
1161   fe_mul(t1, t2, t1);
1162
1163   /* t2 = z ** (2 ** 100 - 1) */
1164   fe_sq(t2, t1);
1165   for (i = 1; i < 50; ++i) {
1166     fe_sq(t2, t2);
1167   }
1168   fe_mul(t2, t2, t1);
1169
1170   /* t2 = z ** (2 ** 200 - 1) */
1171   fe_sq(t3, t2);
1172   for (i = 1; i < 100; ++i) {
1173     fe_sq(t3, t3);
1174   }
1175   fe_mul(t2, t3, t2);
1176
1177   /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
1178   fe_sq(t2, t2);
1179   for (i = 1; i < 50; ++i) {
1180     fe_sq(t2, t2);
1181   }
1182
1183   /* t1 = z ** (2 ** 250 - 1) */
1184   fe_mul(t1, t2, t1);
1185
1186   /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
1187   fe_sq(t1, t1);
1188   for (i = 1; i < 5; ++i) {
1189     fe_sq(t1, t1);
1190   }
1191
1192   /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
1193   fe_mul(out, t1, t0);
1194 }
1195
1196 /* h = -f
1197  *
1198  * Preconditions:
1199  *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1200  *
1201  * Postconditions:
1202  *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
1203 static void fe_neg(fe h, const fe f) {
1204   unsigned i;
1205   for (i = 0; i < 10; i++) {
1206     h[i] = -f[i];
1207   }
1208 }
1209
1210 /* Replace (f,g) with (g,g) if b == 1;
1211  * replace (f,g) with (f,g) if b == 0.
1212  *
1213  * Preconditions: b in {0,1}. */
1214 static void fe_cmov(fe f, const fe g, unsigned b) {
1215   size_t i;
1216   b = 0-b;
1217   for (i = 0; i < 10; i++) {
1218     int32_t x = f[i] ^ g[i];
1219     x &= b;
1220     f[i] ^= x;
1221   }
1222 }
1223
1224 /* return 0 if f == 0
1225  * return 1 if f != 0
1226  *
1227  * Preconditions:
1228  *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
1229 static int fe_isnonzero(const fe f) {
1230   uint8_t s[32];
1231   static const uint8_t zero[32] = {0};
1232   fe_tobytes(s, f);
1233
1234   return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1235 }
1236
1237 /* return 1 if f is in {1,3,5,...,q-2}
1238  * return 0 if f is in {0,2,4,...,q-1}
1239  *
1240  * Preconditions:
1241  *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
1242 static int fe_isnegative(const fe f) {
1243   uint8_t s[32];
1244   fe_tobytes(s, f);
1245   return s[0] & 1;
1246 }
1247
1248 /* h = 2 * f * f
1249  * Can overlap h with f.
1250  *
1251  * Preconditions:
1252  *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1253  *
1254  * Postconditions:
1255  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1256  *
1257  * See fe_mul.c for discussion of implementation strategy. */
1258 static void fe_sq2(fe h, const fe f) {
1259   int32_t f0 = f[0];
1260   int32_t f1 = f[1];
1261   int32_t f2 = f[2];
1262   int32_t f3 = f[3];
1263   int32_t f4 = f[4];
1264   int32_t f5 = f[5];
1265   int32_t f6 = f[6];
1266   int32_t f7 = f[7];
1267   int32_t f8 = f[8];
1268   int32_t f9 = f[9];
1269   int32_t f0_2 = 2 * f0;
1270   int32_t f1_2 = 2 * f1;
1271   int32_t f2_2 = 2 * f2;
1272   int32_t f3_2 = 2 * f3;
1273   int32_t f4_2 = 2 * f4;
1274   int32_t f5_2 = 2 * f5;
1275   int32_t f6_2 = 2 * f6;
1276   int32_t f7_2 = 2 * f7;
1277   int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1278   int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1279   int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1280   int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1281   int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1282   int64_t f0f0    = f0   * (int64_t) f0;
1283   int64_t f0f1_2  = f0_2 * (int64_t) f1;
1284   int64_t f0f2_2  = f0_2 * (int64_t) f2;
1285   int64_t f0f3_2  = f0_2 * (int64_t) f3;
1286   int64_t f0f4_2  = f0_2 * (int64_t) f4;
1287   int64_t f0f5_2  = f0_2 * (int64_t) f5;
1288   int64_t f0f6_2  = f0_2 * (int64_t) f6;
1289   int64_t f0f7_2  = f0_2 * (int64_t) f7;
1290   int64_t f0f8_2  = f0_2 * (int64_t) f8;
1291   int64_t f0f9_2  = f0_2 * (int64_t) f9;
1292   int64_t f1f1_2  = f1_2 * (int64_t) f1;
1293   int64_t f1f2_2  = f1_2 * (int64_t) f2;
1294   int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
1295   int64_t f1f4_2  = f1_2 * (int64_t) f4;
1296   int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
1297   int64_t f1f6_2  = f1_2 * (int64_t) f6;
1298   int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
1299   int64_t f1f8_2  = f1_2 * (int64_t) f8;
1300   int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1301   int64_t f2f2    = f2   * (int64_t) f2;
1302   int64_t f2f3_2  = f2_2 * (int64_t) f3;
1303   int64_t f2f4_2  = f2_2 * (int64_t) f4;
1304   int64_t f2f5_2  = f2_2 * (int64_t) f5;
1305   int64_t f2f6_2  = f2_2 * (int64_t) f6;
1306   int64_t f2f7_2  = f2_2 * (int64_t) f7;
1307   int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1308   int64_t f2f9_38 = f2   * (int64_t) f9_38;
1309   int64_t f3f3_2  = f3_2 * (int64_t) f3;
1310   int64_t f3f4_2  = f3_2 * (int64_t) f4;
1311   int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
1312   int64_t f3f6_2  = f3_2 * (int64_t) f6;
1313   int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1314   int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1315   int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1316   int64_t f4f4    = f4   * (int64_t) f4;
1317   int64_t f4f5_2  = f4_2 * (int64_t) f5;
1318   int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1319   int64_t f4f7_38 = f4   * (int64_t) f7_38;
1320   int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1321   int64_t f4f9_38 = f4   * (int64_t) f9_38;
1322   int64_t f5f5_38 = f5   * (int64_t) f5_38;
1323   int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1324   int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1325   int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1326   int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1327   int64_t f6f6_19 = f6   * (int64_t) f6_19;
1328   int64_t f6f7_38 = f6   * (int64_t) f7_38;
1329   int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1330   int64_t f6f9_38 = f6   * (int64_t) f9_38;
1331   int64_t f7f7_38 = f7   * (int64_t) f7_38;
1332   int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1333   int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1334   int64_t f8f8_19 = f8   * (int64_t) f8_19;
1335   int64_t f8f9_38 = f8   * (int64_t) f9_38;
1336   int64_t f9f9_38 = f9   * (int64_t) f9_38;
1337   int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
1338   int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
1339   int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
1340   int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
1341   int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
1342   int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
1343   int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
1344   int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
1345   int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
1346   int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
1347   int64_t carry0;
1348   int64_t carry1;
1349   int64_t carry2;
1350   int64_t carry3;
1351   int64_t carry4;
1352   int64_t carry5;
1353   int64_t carry6;
1354   int64_t carry7;
1355   int64_t carry8;
1356   int64_t carry9;
1357
1358   h0 += h0;
1359   h1 += h1;
1360   h2 += h2;
1361   h3 += h3;
1362   h4 += h4;
1363   h5 += h5;
1364   h6 += h6;
1365   h7 += h7;
1366   h8 += h8;
1367   h9 += h9;
1368
1369   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1370   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1371
1372   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1373   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1374
1375   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1376   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1377
1378   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1379   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1380
1381   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1382   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1383
1384   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1385
1386   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1387
1388   h[0] = (int32_t)h0;
1389   h[1] = (int32_t)h1;
1390   h[2] = (int32_t)h2;
1391   h[3] = (int32_t)h3;
1392   h[4] = (int32_t)h4;
1393   h[5] = (int32_t)h5;
1394   h[6] = (int32_t)h6;
1395   h[7] = (int32_t)h7;
1396   h[8] = (int32_t)h8;
1397   h[9] = (int32_t)h9;
1398 }
1399
1400 static void fe_pow22523(fe out, const fe z) {
1401   fe t0;
1402   fe t1;
1403   fe t2;
1404   int i;
1405
1406   fe_sq(t0, z);
1407   fe_sq(t1, t0);
1408   for (i = 1; i < 2; ++i) {
1409     fe_sq(t1, t1);
1410   }
1411   fe_mul(t1, z, t1);
1412   fe_mul(t0, t0, t1);
1413   fe_sq(t0, t0);
1414   fe_mul(t0, t1, t0);
1415   fe_sq(t1, t0);
1416   for (i = 1; i < 5; ++i) {
1417     fe_sq(t1, t1);
1418   }
1419   fe_mul(t0, t1, t0);
1420   fe_sq(t1, t0);
1421   for (i = 1; i < 10; ++i) {
1422     fe_sq(t1, t1);
1423   }
1424   fe_mul(t1, t1, t0);
1425   fe_sq(t2, t1);
1426   for (i = 1; i < 20; ++i) {
1427     fe_sq(t2, t2);
1428   }
1429   fe_mul(t1, t2, t1);
1430   fe_sq(t1, t1);
1431   for (i = 1; i < 10; ++i) {
1432     fe_sq(t1, t1);
1433   }
1434   fe_mul(t0, t1, t0);
1435   fe_sq(t1, t0);
1436   for (i = 1; i < 50; ++i) {
1437     fe_sq(t1, t1);
1438   }
1439   fe_mul(t1, t1, t0);
1440   fe_sq(t2, t1);
1441   for (i = 1; i < 100; ++i) {
1442     fe_sq(t2, t2);
1443   }
1444   fe_mul(t1, t2, t1);
1445   fe_sq(t1, t1);
1446   for (i = 1; i < 50; ++i) {
1447     fe_sq(t1, t1);
1448   }
1449   fe_mul(t0, t1, t0);
1450   fe_sq(t0, t0);
1451   for (i = 1; i < 2; ++i) {
1452     fe_sq(t0, t0);
1453   }
1454   fe_mul(out, t0, z);
1455 }
1456
1457 /* ge means group element.
1458
1459  * Here the group is the set of pairs (x,y) of field elements (see fe.h)
1460  * satisfying -x^2 + y^2 = 1 + d x^2y^2
1461  * where d = -121665/121666.
1462  *
1463  * Representations:
1464  *   ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1465  *   ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1466  *   ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1467  *   ge_precomp (Duif): (y+x,y-x,2dxy) */
1468
1469 typedef struct {
1470   fe X;
1471   fe Y;
1472   fe Z;
1473 } ge_p2;
1474
1475 typedef struct {
1476   fe X;
1477   fe Y;
1478   fe Z;
1479   fe T;
1480 } ge_p3;
1481
1482 typedef struct {
1483   fe X;
1484   fe Y;
1485   fe Z;
1486   fe T;
1487 } ge_p1p1;
1488
1489 typedef struct {
1490   fe yplusx;
1491   fe yminusx;
1492   fe xy2d;
1493 } ge_precomp;
1494
1495 typedef struct {
1496   fe YplusX;
1497   fe YminusX;
1498   fe Z;
1499   fe T2d;
1500 } ge_cached;
1501
1502 static void ge_tobytes(uint8_t *s, const ge_p2 *h) {
1503   fe recip;
1504   fe x;
1505   fe y;
1506
1507   fe_invert(recip, h->Z);
1508   fe_mul(x, h->X, recip);
1509   fe_mul(y, h->Y, recip);
1510   fe_tobytes(s, y);
1511   s[31] ^= fe_isnegative(x) << 7;
1512 }
1513
1514 static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
1515   fe recip;
1516   fe x;
1517   fe y;
1518
1519   fe_invert(recip, h->Z);
1520   fe_mul(x, h->X, recip);
1521   fe_mul(y, h->Y, recip);
1522   fe_tobytes(s, y);
1523   s[31] ^= fe_isnegative(x) << 7;
1524 }
1525
1526 static const fe d = {-10913610, 13857413, -15372611, 6949391,   114729,
1527                      -8787816,  -6275908, -3247719,  -18696448, -12055116};
1528
1529 static const fe sqrtm1 = {-32595792, -7943725,  9377950,  3500415, 12389472,
1530                           -272473,   -25146209, -2005654, 326686,  11406482};
1531
1532 static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
1533   fe u;
1534   fe v;
1535   fe v3;
1536   fe vxx;
1537   fe check;
1538
1539   fe_frombytes(h->Y, s);
1540   fe_1(h->Z);
1541   fe_sq(u, h->Y);
1542   fe_mul(v, u, d);
1543   fe_sub(u, u, h->Z); /* u = y^2-1 */
1544   fe_add(v, v, h->Z); /* v = dy^2+1 */
1545
1546   fe_sq(v3, v);
1547   fe_mul(v3, v3, v); /* v3 = v^3 */
1548   fe_sq(h->X, v3);
1549   fe_mul(h->X, h->X, v);
1550   fe_mul(h->X, h->X, u); /* x = uv^7 */
1551
1552   fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1553   fe_mul(h->X, h->X, v3);
1554   fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1555
1556   fe_sq(vxx, h->X);
1557   fe_mul(vxx, vxx, v);
1558   fe_sub(check, vxx, u); /* vx^2-u */
1559   if (fe_isnonzero(check)) {
1560     fe_add(check, vxx, u); /* vx^2+u */
1561     if (fe_isnonzero(check)) {
1562       return -1;
1563     }
1564     fe_mul(h->X, h->X, sqrtm1);
1565   }
1566
1567   if (fe_isnegative(h->X) != (s[31] >> 7)) {
1568     fe_neg(h->X, h->X);
1569   }
1570
1571   fe_mul(h->T, h->X, h->Y);
1572   return 0;
1573 }
1574
1575 static void ge_p2_0(ge_p2 *h) {
1576   fe_0(h->X);
1577   fe_1(h->Y);
1578   fe_1(h->Z);
1579 }
1580
1581 static void ge_p3_0(ge_p3 *h) {
1582   fe_0(h->X);
1583   fe_1(h->Y);
1584   fe_1(h->Z);
1585   fe_0(h->T);
1586 }
1587
1588 static void ge_precomp_0(ge_precomp *h) {
1589   fe_1(h->yplusx);
1590   fe_1(h->yminusx);
1591   fe_0(h->xy2d);
1592 }
1593
1594 /* r = p */
1595 static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
1596   fe_copy(r->X, p->X);
1597   fe_copy(r->Y, p->Y);
1598   fe_copy(r->Z, p->Z);
1599 }
1600
1601 static const fe d2 = {-21827239, -5839606,  -30745221, 13898782, 229458,
1602                       15978800,  -12551817, -6495438,  29715968, 9444199};
1603
1604 /* r = p */
1605 static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
1606   fe_add(r->YplusX, p->Y, p->X);
1607   fe_sub(r->YminusX, p->Y, p->X);
1608   fe_copy(r->Z, p->Z);
1609   fe_mul(r->T2d, p->T, d2);
1610 }
1611
1612 /* r = p */
1613 static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
1614   fe_mul(r->X, p->X, p->T);
1615   fe_mul(r->Y, p->Y, p->Z);
1616   fe_mul(r->Z, p->Z, p->T);
1617 }
1618
1619 /* r = p */
1620 static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
1621   fe_mul(r->X, p->X, p->T);
1622   fe_mul(r->Y, p->Y, p->Z);
1623   fe_mul(r->Z, p->Z, p->T);
1624   fe_mul(r->T, p->X, p->Y);
1625 }
1626
1627 /* r = 2 * p */
1628 static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
1629   fe t0;
1630
1631   fe_sq(r->X, p->X);
1632   fe_sq(r->Z, p->Y);
1633   fe_sq2(r->T, p->Z);
1634   fe_add(r->Y, p->X, p->Y);
1635   fe_sq(t0, r->Y);
1636   fe_add(r->Y, r->Z, r->X);
1637   fe_sub(r->Z, r->Z, r->X);
1638   fe_sub(r->X, t0, r->Y);
1639   fe_sub(r->T, r->T, r->Z);
1640 }
1641
1642 /* r = 2 * p */
1643 static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
1644   ge_p2 q;
1645   ge_p3_to_p2(&q, p);
1646   ge_p2_dbl(r, &q);
1647 }
1648
1649 /* r = p + q */
1650 static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
1651   fe t0;
1652
1653   fe_add(r->X, p->Y, p->X);
1654   fe_sub(r->Y, p->Y, p->X);
1655   fe_mul(r->Z, r->X, q->yplusx);
1656   fe_mul(r->Y, r->Y, q->yminusx);
1657   fe_mul(r->T, q->xy2d, p->T);
1658   fe_add(t0, p->Z, p->Z);
1659   fe_sub(r->X, r->Z, r->Y);
1660   fe_add(r->Y, r->Z, r->Y);
1661   fe_add(r->Z, t0, r->T);
1662   fe_sub(r->T, t0, r->T);
1663 }
1664
1665 /* r = p - q */
1666 static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
1667   fe t0;
1668
1669   fe_add(r->X, p->Y, p->X);
1670   fe_sub(r->Y, p->Y, p->X);
1671   fe_mul(r->Z, r->X, q->yminusx);
1672   fe_mul(r->Y, r->Y, q->yplusx);
1673   fe_mul(r->T, q->xy2d, p->T);
1674   fe_add(t0, p->Z, p->Z);
1675   fe_sub(r->X, r->Z, r->Y);
1676   fe_add(r->Y, r->Z, r->Y);
1677   fe_sub(r->Z, t0, r->T);
1678   fe_add(r->T, t0, r->T);
1679 }
1680
1681 /* r = p + q */
1682 static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
1683   fe t0;
1684
1685   fe_add(r->X, p->Y, p->X);
1686   fe_sub(r->Y, p->Y, p->X);
1687   fe_mul(r->Z, r->X, q->YplusX);
1688   fe_mul(r->Y, r->Y, q->YminusX);
1689   fe_mul(r->T, q->T2d, p->T);
1690   fe_mul(r->X, p->Z, q->Z);
1691   fe_add(t0, r->X, r->X);
1692   fe_sub(r->X, r->Z, r->Y);
1693   fe_add(r->Y, r->Z, r->Y);
1694   fe_add(r->Z, t0, r->T);
1695   fe_sub(r->T, t0, r->T);
1696 }
1697
1698 /* r = p - q */
1699 static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
1700   fe t0;
1701
1702   fe_add(r->X, p->Y, p->X);
1703   fe_sub(r->Y, p->Y, p->X);
1704   fe_mul(r->Z, r->X, q->YminusX);
1705   fe_mul(r->Y, r->Y, q->YplusX);
1706   fe_mul(r->T, q->T2d, p->T);
1707   fe_mul(r->X, p->Z, q->Z);
1708   fe_add(t0, r->X, r->X);
1709   fe_sub(r->X, r->Z, r->Y);
1710   fe_add(r->Y, r->Z, r->Y);
1711   fe_sub(r->Z, t0, r->T);
1712   fe_add(r->T, t0, r->T);
1713 }
1714
1715 static uint8_t equal(signed char b, signed char c) {
1716   uint8_t ub = b;
1717   uint8_t uc = c;
1718   uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
1719   uint32_t y = x;      /* 0: yes; 1..255: no */
1720   y -= 1;              /* 4294967295: yes; 0..254: no */
1721   y >>= 31;            /* 1: yes; 0: no */
1722   return y;
1723 }
1724
1725 static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
1726   fe_cmov(t->yplusx, u->yplusx, b);
1727   fe_cmov(t->yminusx, u->yminusx, b);
1728   fe_cmov(t->xy2d, u->xy2d, b);
1729 }
1730
1731 /* k25519Precomp[i][j] = (j+1)*256^i*B */
1732 static const ge_precomp k25519Precomp[32][8] = {
1733     {
1734         {
1735             {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
1736              27544626, -11754271, -6079156, 2047605},
1737             {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
1738              5043384, 19500929, -15469378},
1739             {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
1740              29287919, 11864899, -24514362, -4438546},
1741         },
1742         {
1743             {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
1744              -11717903, -3814571, -358445, -10211303},
1745             {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
1746              -15616551, 11189268, -26829678, -5319081},
1747             {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
1748              -3128826, -9541118, -15472047, -4166697},
1749         },
1750         {
1751             {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
1752              27787600, -14772189, 28944400, -1550024},
1753             {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
1754              16354577, -11775962, 7689662, 11199574},
1755             {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
1756              7512774, 10017326, -17749093, -9920357},
1757         },
1758         {
1759             {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
1760              -28926210, 15006023, 3284568, -6276540},
1761             {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
1762              7464579, 9656445, 13059162, 10374397},
1763             {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
1764              -3839045, -641708, -101325},
1765         },
1766         {
1767             {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
1768              32867885, 14515107, -15438304, 10819380},
1769             {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
1770              12483688, -12668491, 5581306},
1771             {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
1772              28542350, 13850243, -23678021, -15815942},
1773         },
1774         {
1775             {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
1776              -19188627, -15224819, -9818940, -12085777},
1777             {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
1778              -15689887, 1762328, 14866737},
1779             {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
1780              -28236412, 3959421, 27914454, 4383652},
1781         },
1782         {
1783             {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
1784              5230134, -23952439, -15175766},
1785             {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
1786              20654025, 16520125, 30598449, 7715701},
1787             {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
1788              -31400660, 1370708, 29794553, -1409300},
1789         },
1790         {
1791             {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
1792              30290735, 10876454, -33154098, 2381726},
1793             {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
1794              -6236617, 3696005, -32300832, 15351955},
1795             {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
1796              -32961401, -2970515, 29551813, 10109425},
1797         },
1798     },
1799     {
1800         {
1801             {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
1802              -2378284, -1627556, 10092783, -4764171},
1803             {27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
1804              -32508754, 12005538, -17810127, 12803510},
1805             {17228999, -15661624, -1233527, 300140, -1224870, -11714777,
1806              30364213, -9038194, 18016357, 4397660},
1807         },
1808         {
1809             {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
1810              -26619106, 14544525, -17477504, 982639},
1811             {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
1812              -4120128, -21047696, 9934963},
1813             {5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
1814              -14747930, 4559895, -30123922, -10897950},
1815         },
1816         {
1817             {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
1818              24191034, 4541697, -13338309, 5500568},
1819             {12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
1820              -17430592, 12264343, 10874051, 13524335},
1821             {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
1822              5080568, -22528059, 5376628},
1823         },
1824         {
1825             {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
1826              -22321305, -9447443, 4535768, 1569007},
1827             {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
1828              -30494562, 3044290, 31848280, 12543772},
1829             {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
1830              -27377195, -2062731, 7718482, 14474653},
1831         },
1832         {
1833             {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
1834              -7236665, 24316168, -5253567},
1835             {13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
1836              33040651, -13424532, -20729456, 8321686},
1837             {21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
1838              23845965, -11874838, -9984458, 608372},
1839         },
1840         {
1841             {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
1842              1123968, -6780577, 27229399, 23887},
1843             {-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
1844              12797024, -6440308, -1633405, 16678954},
1845             {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
1846              -1508144, -4795045, -17169265, 4904953},
1847         },
1848         {
1849             {24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
1850              5169211, 16191880, 2128236, -4326833},
1851             {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
1852              -29806336, 916033, -6882542, -2986532},
1853             {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
1854              285431, 2763829, 15736322, 4143876},
1855         },
1856         {
1857             {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
1858              -14594663, 23527084, -16458268},
1859             {33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
1860              -32625340, 4087881, -15188911, -14416214},
1861             {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
1862              4357868, -4774191, -16323038},
1863         },
1864     },
1865     {
1866         {
1867             {6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
1868              23365147, -3949732, 7390890, 2759800},
1869             {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
1870              -4264057, 1244380, -12919645},
1871             {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
1872              9208236, 15886429, 16489664},
1873         },
1874         {
1875             {1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
1876              -13693198, 398369, -30606455, -712933},
1877             {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
1878              13348553, 12076947, -30836462, 5113182},
1879             {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
1880              -30341101, -7336386, 13847711, 5387222},
1881         },
1882         {
1883             {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
1884              8763061, 3617786, -19600662, 10370991},
1885             {20246567, -14369378, 22358229, -543712, 18507283, -10413996,
1886              14554437, -8746092, 32232924, 16763880},
1887             {9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
1888              11094161, 15689506, 3140038, -16510092},
1889         },
1890         {
1891             {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
1892              -27224800, 9448613, -28774454, 366295},
1893             {19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
1894              28344573, 8041113, 719605, 11671788},
1895             {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
1896              -15266516, 27000813, -10195553},
1897         },
1898         {
1899             {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
1900              5336097, 6750977, -14521026},
1901             {11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
1902              1695823, -8819122, 8169720, 16220347},
1903             {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
1904              -11144307, -2627664, -5990708, -14166033},
1905         },
1906         {
1907             {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
1908              27884329, 2847284, 2655861, 1738395},
1909             {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
1910              21651608, -3239336, -19087449, -11005278},
1911             {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
1912              5821408, 10478196, 8544890},
1913         },
1914         {
1915             {32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
1916              19270449, 12217473, 17789017, -3395995},
1917             {-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
1918              15479401, -3853233, 30460520, 1052596},
1919             {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
1920              27491595, -4612359, 3179268, -9478891},
1921         },
1922         {
1923             {31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
1924              -14756777, -16411740, 19072640, -9511060},
1925             {11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
1926              5977896, -5215017, 473099, 5040608},
1927             {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
1928              28326862, 1721092, -19558642, -3131606},
1929         },
1930     },
1931     {
1932         {
1933             {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
1934              8076149, -27868496, 11538389},
1935             {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
1936              8754525, 7446702, -5676054, 5797016},
1937             {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
1938              2014099, -9050574, -2369172, -5877341},
1939         },
1940         {
1941             {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
1942              1192730, -3714199, 15123619, 10811505},
1943             {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
1944              15776356, -28886779, -11974553},
1945             {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
1946              -20654173, -16484855, 4714547, -9600655},
1947         },
1948         {
1949             {15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
1950              24611599, -4543832, -11745876, 12340220},
1951             {12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
1952              9613953, 8241152, 15370987, 9608631},
1953             {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
1954              15866074, -28210621, -8814099},
1955         },
1956         {
1957             {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
1958              858697, 20571223, 8420556},
1959             {14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
1960              33531827, 12516406, -21574435, -12476749},
1961             {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
1962              7256740, 8791136, 15069930},
1963         },
1964         {
1965             {1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
1966              14711875, 4874229, -30663140, -2331391},
1967             {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
1968              -7912378, -33069337, 9234253},
1969             {20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
1970              31559055, -11609587, 18979186, 13396066},
1971         },
1972         {
1973             {24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
1974              -18816887, 13594782, 33514650, 7021958},
1975             {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
1976              -25948728, -3916677, -21480480, 12868082},
1977             {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
1978              -21446107, 2244500, -12455797, -8089383},
1979         },
1980         {
1981             {-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
1982              33086546, 8957937, -15233648, 5540521},
1983             {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
1984              -23710744, -1568984, -16128528, -14962807},
1985             {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
1986              892185, -11513277, -15205948},
1987         },
1988         {
1989             {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
1990              4763127, -19179614, 5867134},
1991             {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
1992              27846559, 5931263, -29749703, -16108455},
1993             {27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
1994              7283490, -15148073, -19526700, 7734629},
1995         },
1996     },
1997     {
1998         {
1999             {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
2000              7585295, -3176626, 18549497, 15302069},
2001             {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
2002              10458790, -6418461, -8872242, 8424746},
2003             {24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
2004              19206234, 7134917, -11284482, -828919},
2005         },
2006         {
2007             {11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
2008              10243738, -14685461, -5066034, 16498837},
2009             {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
2010              -14124238, 6536641, 10543906},
2011             {-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
2012              -2669190, -16625574, -27235709, 8876771},
2013         },
2014         {
2015             {-25742899, -12566864, -15649966, -846607, -33026686, -796288,
2016              -33481822, 15824474, -604426, -9039817},
2017             {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
2018              -4890037, 1657394, 3084098},
2019             {10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
2020              31280319, 14396151, -30233575, 15272409},
2021         },
2022         {
2023             {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
2024              -25173957, -12636138, -25014757, 1950504},
2025             {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
2026              -8384306, -8767532, 15341279, 8373727},
2027             {28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
2028              298136, -10232602, -2878207, 15190420},
2029         },
2030         {
2031             {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
2032              8669718, 2742393, -26033313, -6875003},
2033             {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
2034              9291594, -16247779, -12154742, 6048605},
2035             {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
2036              13934231, 5128323, 11213262, 9168384},
2037         },
2038         {
2039             {-26280513, 11007847, 19408960, -940758, -18592965, -4328580,
2040              -5088060, -11105150, 20470157, -16398701},
2041             {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
2042              -22783952, 14461608, 14042978, 5230683},
2043             {29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
2044              21556951, 3506042, -5933891, -12449708},
2045         },
2046         {
2047             {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683,
2048              -21284170, 8971513, -28539189, 15326563},
2049             {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669,
2050              -15523050, 15300988, -20514118, 9168260},
2051             {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939,
2052              -28948358, 9601605, 33087103, -9011387},
2053         },
2054         {
2055             {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461,
2056              -27444329, -15000531, -5996870, 15664672},
2057             {23294591, -16632613, -22650781, -8470978, 27844204, 11461195,
2058              13099750, -2460356, 18151676, 13417686},
2059             {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065,
2060              1661597, -12551441, 15271676, -15452665},
2061         },
2062     },
2063     {
2064         {
2065             {11433042, -13228665, 8239631, -5279517, -1985436, -725718,
2066              -18698764, 2167544, -6921301, -13440182},
2067             {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379,
2068              -9917708, -8638997, 12215110, 12028277},
2069             {14098400, 6555944, 23007258, 5757252, -15427832, -12950502,
2070              30123440, 4617780, -16900089, -655628},
2071         },
2072         {
2073             {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385,
2074              -15819999, 10154009, 23973261, -12684474},
2075             {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355,
2076              18341390, -11419951, 32013174, -10103539},
2077             {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104,
2078              21911214, 6354752, 4425632, -837822},
2079         },
2080         {
2081             {-10433389, -14612966, 22229858, -3091047, -13191166, 776729,
2082              -17415375, -12020462, 4725005, 14044970},
2083             {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390,
2084              -1411784, -19522291, -16109756},
2085             {-24864089, 12986008, -10898878, -5558584, -11312371, -148526,
2086              19541418, 8180106, 9282262, 10282508},
2087         },
2088         {
2089             {-26205082, 4428547, -8661196, -13194263, 4098402, -14165257,
2090              15522535, 8372215, 5542595, -10702683},
2091             {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360,
2092              -2781891, 6993761, -18093885, 10114655},
2093             {-20107055, -929418, 31422704, 10427861, -7110749, 6150669,
2094              -29091755, -11529146, 25953725, -106158},
2095         },
2096         {
2097             {-4234397, -8039292, -9119125, 3046000, 2101609, -12607294,
2098              19390020, 6094296, -3315279, 12831125},
2099             {-15998678, 7578152, 5310217, 14408357, -33548620, -224739,
2100              31575954, 6326196, 7381791, -2421839},
2101             {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640,
2102              6295303, 8082724, -15362489, 12339664},
2103         },
2104         {
2105             {27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414,
2106              15768922, 25091167, 14856294},
2107             {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300,
2108              -12695493, -22182473, -9012899},
2109             {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039,
2110              -27260765, 13866390, 30146206, 9142070},
2111         },
2112         {
2113             {3924129, -15307516, -13817122, -10054960, 12291820, -668366,
2114              -27702774, 9326384, -8237858, 4171294},
2115             {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944,
2116              26396185, 3731949, 345228, -5462949},
2117             {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387,
2118              2031539, -12391231, -16253183, -13582083},
2119         },
2120         {
2121             {31016211, -16722429, 26371392, -14451233, -5027349, 14854137,
2122              17477601, 3842657, 28012650, -16405420},
2123             {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560,
2124              -9189873, 16292057, -8867157, 3507940},
2125             {29439664, 3537914, 23333589, 6997794, -17555561, -11018068,
2126              -15209202, -15051267, -9164929, 6580396},
2127         },
2128     },
2129     {
2130         {
2131             {-12185861, -7679788, 16438269, 10826160, -8696817, -6235611,
2132              17860444, -9273846, -2095802, 9304567},
2133             {20714564, -4336911, 29088195, 7406487, 11426967, -5095705,
2134              14792667, -14608617, 5289421, -477127},
2135             {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462,
2136              17271490, 12349094, 26939669, -3752294},
2137         },
2138         {
2139             {-12889898, 9373458, 31595848, 16374215, 21471720, 13221525,
2140              -27283495, -12348559, -3698806, 117887},
2141             {22263325, -6560050, 3984570, -11174646, -15114008, -566785,
2142              28311253, 5358056, -23319780, 541964},
2143             {16259219, 3261970, 2309254, -15534474, -16885711, -4581916,
2144              24134070, -16705829, -13337066, -13552195},
2145         },
2146         {
2147             {9378160, -13140186, -22845982, -12745264, 28198281, -7244098,
2148              -2399684, -717351, 690426, 14876244},
2149             {24977353, -314384, -8223969, -13465086, 28432343, -1176353,
2150              -13068804, -12297348, -22380984, 6618999},
2151             {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193,
2152              8044829, -13817328, 32239829, -5652762},
2153         },
2154         {
2155             {-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647,
2156              -10350059, 32779359, 5095274},
2157             {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423,
2158              -24601656, 14506724, 21639561, -2630236},
2159             {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318,
2160              -1289502, -6863535, 17874574, 558605},
2161         },
2162         {
2163             {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700,
2164              33499487, 5080151, 2085892, 5119761},
2165             {-22205145, -2519528, -16381601, 414691, -25019550, 2170430,
2166              30634760, -8363614, -31999993, -5759884},
2167             {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256,
2168              27534430, -7192145, -22351378, 12961482},
2169         },
2170         {
2171             {-24492060, -9570771, 10368194, 11582341, -23397293, -2245287,
2172              16533930, 8206996, -30194652, -5159638},
2173             {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630,
2174              7031275, 7589640, 8945490},
2175             {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393,
2176              7251489, -11182180, 24099109, -14456170},
2177         },
2178         {
2179             {5019558, -7907470, 4244127, -14714356, -26933272, 6453165,
2180              -19118182, -13289025, -6231896, -10280736},
2181             {10853594, 10721687, 26480089, 5861829, -22995819, 1972175,
2182              -1866647, -10557898, -3363451, -6441124},
2183             {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661,
2184              -2008168, -13866408, 7421392},
2185         },
2186         {
2187             {8139927, -6546497, 32257646, -5890546, 30375719, 1886181,
2188              -21175108, 15441252, 28826358, -4123029},
2189             {6267086, 9695052, 7709135, -16603597, -32869068, -1886135,
2190              14795160, -7840124, 13746021, -1742048},
2191             {28584902, 7787108, -6732942, -15050729, 22846041, -7571236,
2192              -3181936, -363524, 4771362, -8419958},
2193         },
2194     },
2195     {
2196         {
2197             {24949256, 6376279, -27466481, -8174608, -18646154, -9930606,
2198              33543569, -12141695, 3569627, 11342593},
2199             {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886,
2200              4608608, 7325975, -14801071},
2201             {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312,
2202              -27400540, 10258390, -17646694, -8186692},
2203         },
2204         {
2205             {11431204, 15823007, 26570245, 14329124, 18029990, 4796082,
2206              -31446179, 15580664, 9280358, -3973687},
2207             {-160783, -10326257, -22855316, -4304997, -20861367, -13621002,
2208              -32810901, -11181622, -15545091, 4387441},
2209             {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370,
2210              -24513992, 8548137, 20617071, -7482001},
2211         },
2212         {
2213             {-938825, -3930586, -8714311, 16124718, 24603125, -6225393,
2214              -13775352, -11875822, 24345683, 10325460},
2215             {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528,
2216              16318175, -1010689, 4766743, 3552007},
2217             {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514,
2218              14481909, 10988822, -3994762},
2219         },
2220         {
2221             {15564307, -14311570, 3101243, 5684148, 30446780, -8051356,
2222              12677127, -6505343, -8295852, 13296005},
2223             {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379,
2224              31521204, 9614054, -30000824, 12074674},
2225             {4771191, -135239, 14290749, -13089852, 27992298, 14998318,
2226              -1413936, -1556716, 29832613, -16391035},
2227         },
2228         {
2229             {7064884, -7541174, -19161962, -5067537, -18891269, -2912736,
2230              25825242, 5293297, -27122660, 13101590},
2231             {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445,
2232              32512469, -5317593, -30356070, -4190957},
2233             {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044,
2234              14413974, 9515896, 19568978, 9628812},
2235         },
2236         {
2237             {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894,
2238              -6106839, -6291786, 3437740},
2239             {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290,
2240              -22961733, 70104, 7463304, 4176122},
2241             {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117,
2242              -32719404, -5322751, 24216882, 5944158},
2243         },
2244         {
2245             {8894125, 7450974, -2664149, -9765752, -28080517, -12389115,
2246              19345746, 14680796, 11632993, 5847885},
2247             {26942781, -2315317, 9129564, -4906607, 26024105, 11769399,
2248              -11518837, 6367194, -9727230, 4782140},
2249             {19916461, -4828410, -22910704, -11414391, 25606324, -5972441,
2250              33253853, 8220911, 6358847, -1873857},
2251         },
2252         {
2253             {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388,
2254              -4480480, -13538503, 1387155},
2255             {19646058, 5720633, -11416706, 12814209, 11607948, 12749789,
2256              14147075, 15156355, -21866831, 11835260},
2257             {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523,
2258              15467869, -26560550, 5052483},
2259         },
2260     },
2261     {
2262         {
2263             {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123,
2264              -12618185, 12228557, -7003677},
2265             {32944382, 14922211, -22844894, 5188528, 21913450, -8719943,
2266              4001465, 13238564, -6114803, 8653815},
2267             {22865569, -4652735, 27603668, -12545395, 14348958, 8234005,
2268              24808405, 5719875, 28483275, 2841751},
2269         },
2270         {
2271             {-16420968, -1113305, -327719, -12107856, 21886282, -15552774,
2272              -1887966, -315658, 19932058, -12739203},
2273             {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912,
2274              3999228, 13239134, -4777469, -13910208},
2275             {1382174, -11694719, 17266790, 9194690, -13324356, 9720081,
2276              20403944, 11284705, -14013818, 3093230},
2277         },
2278         {
2279             {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424,
2280              16271225, -24049421, -6691850},
2281             {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293,
2282              24123614, 15193618, -21652117, -16739389},
2283             {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484,
2284              31870908, 14690798, 17361620, 11864968},
2285         },
2286         {
2287             {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200,
2288              -12331205, -7486601, -25578460, -16240689},
2289             {14668462, -12270235, 26039039, 15305210, 25515617, 4542480,
2290              10453892, 6577524, 9145645, -6443880},
2291             {5974874, 3053895, -9433049, -10385191, -31865124, 3225009,
2292              -7972642, 3936128, -5652273, -3050304},
2293         },
2294         {
2295             {30625386, -4729400, -25555961, -12792866, -20484575, 7695099,
2296              17097188, -16303496, -27999779, 1803632},
2297             {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700,
2298              14911344, 12196514, -21405489, 7047412},
2299             {20093277, 9920966, -11138194, -5343857, 13161587, 12044805,
2300              -32856851, 4124601, -32343828, -10257566},
2301         },
2302         {
2303             {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605,
2304              4752377, -8714640, -21679658, 2288038},
2305             {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457,
2306              29457502, 14625692, -24819617, 12570232},
2307             {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109,
2308              -21159943, -3498680, -11974704, 4724943},
2309         },
2310         {
2311             {17960970, -11775534, -4140968, -9702530, -8876562, -1410617,
2312              -12907383, -8659932, -29576300, 1903856},
2313             {23134274, -14279132, -10681997, -1611936, 20684485, 15770816,
2314              -12989750, 3190296, 26955097, 14109738},
2315             {15308788, 5320727, -30113809, -14318877, 22902008, 7767164,
2316              29425325, -11277562, 31960942, 11934971},
2317         },
2318         {
2319             {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669,
2320              20638173, 4875028, 10491392, 1379718},
2321             {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801,
2322              33518459, 16176658, 21432314, 12180697},
2323             {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205,
2324              1465425, 12689540, -10301319, -13872883},
2325         },
2326     },
2327     {
2328         {
2329             {5414091, -15386041, -21007664, 9643570, 12834970, 1186149,
2330              -2622916, -1342231, 26128231, 6032912},
2331             {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156,
2332              3604025, 8316894, -25875034, -10437358},
2333             {3296484, 6223048, 24680646, -12246460, -23052020, 5903205,
2334              -8862297, -4639164, 12376617, 3188849},
2335         },
2336         {
2337             {29190488, -14659046, 27549113, -1183516, 3520066, -10697301,
2338              32049515, -7309113, -16109234, -9852307},
2339             {-14744486, -9309156, 735818, -598978, -20407687, -5057904,
2340              25246078, -15795669, 18640741, -960977},
2341             {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252,
2342              -31638386, -494430, 10530747, 1053335},
2343         },
2344         {
2345             {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384,
2346              -31462369, -2948985, 24018831, 15026644},
2347             {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631,
2348              25310643, 13003497, -2314791, -15145616},
2349             {-27419985, -603321, -8043984, -1669117, -26092265, 13987819,
2350              -27297622, 187899, -23166419, -2531735},
2351         },
2352         {
2353             {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473,
2354              9716667, 16266922, -5070217, 726099},
2355             {29370922, -6053998, 7334071, -15342259, 9385287, 2247707,
2356              -13661962, -4839461, 30007388, -15823341},
2357             {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109,
2358              730663, 9835848, 4555336},
2359         },
2360         {
2361             {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977,
2362              17693930, 544696, -11985298, 12422646},
2363             {31117226, -12215734, -13502838, 6561947, -9876867, -12757670,
2364              -5118685, -4096706, 29120153, 13924425},
2365             {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820,
2366              -9383939, -11317700, 7240931, -237388},
2367         },
2368         {
2369             {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771,
2370              1222336, 4389483, 3293637, -15551743},
2371             {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533,
2372              -24319580, 7733547, 12796905, -6335822},
2373             {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811,
2374              -28253339, 3647836, 3222231, -11160462},
2375         },
2376         {
2377             {18606113, 1693100, -25448386, -15170272, 4112353, 10045021,
2378              23603893, -2048234, -7550776, 2484985},
2379             {9255317, -3131197, -12156162, -1004256, 13098013, -9214866,
2380              16377220, -2102812, -19802075, -3034702},
2381             {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502,
2382              -31718148, 9936966, -30097688, -10618797},
2383         },
2384         {
2385             {21878590, -5001297, 4338336, 13643897, -3036865, 13160960,
2386              19708896, 5415497, -7360503, -4109293},
2387             {27736861, 10103576, 12500508, 8502413, -3413016, -9633558,
2388              10436918, -1550276, -23659143, -8132100},
2389             {19492550, -12104365, -29681976, -852630, -3208171, 12403437,
2390              30066266, 8367329, 13243957, 8709688},
2391         },
2392     },
2393     {
2394         {
2395             {12015105, 2801261, 28198131, 10151021, 24818120, -4743133,
2396              -11194191, -5645734, 5150968, 7274186},
2397             {2831366, -12492146, 1478975, 6122054, 23825128, -12733586,
2398              31097299, 6083058, 31021603, -9793610},
2399             {-2529932, -2229646, 445613, 10720828, -13849527, -11505937,
2400              -23507731, 16354465, 15067285, -14147707},
2401         },
2402         {
2403             {7840942, 14037873, -33364863, 15934016, -728213, -3642706,
2404              21403988, 1057586, -19379462, -12403220},
2405             {915865, -16469274, 15608285, -8789130, -24357026, 6060030,
2406              -17371319, 8410997, -7220461, 16527025},
2407             {32922597, -556987, 20336074, -16184568, 10903705, -5384487,
2408              16957574, 52992, 23834301, 6588044},
2409         },
2410         {
2411             {32752030, 11232950, 3381995, -8714866, 22652988, -10744103,
2412              17159699, 16689107, -20314580, -1305992},
2413             {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943,
2414              7924251, -2752281, 1976123, -7249027},
2415             {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041,
2416              -3371252, 12331345, -8237197},
2417         },
2418         {
2419             {8651614, -4477032, -16085636, -4996994, 13002507, 2950805,
2420              29054427, -5106970, 10008136, -4667901},
2421             {31486080, 15114593, -14261250, 12951354, 14369431, -7387845,
2422              16347321, -13662089, 8684155, -10532952},
2423             {19443825, 11385320, 24468943, -9659068, -23919258, 2187569,
2424              -26263207, -6086921, 31316348, 14219878},
2425         },
2426         {
2427             {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801,
2428              27146014, 6992409, 29126555, 9207390},
2429             {32382935, 1110093, 18477781, 11028262, -27411763, -7548111,
2430              -4980517, 10843782, -7957600, -14435730},
2431             {2814918, 7836403, 27519878, -7868156, -20894015, -11553689,
2432              -21494559, 8550130, 28346258, 1994730},
2433         },
2434         {
2435             {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307,
2436              -19516951, 7174894, 22628102, 8115180},
2437             {-30405132, 955511, -11133838, -15078069, -32447087, -13278079,
2438              -25651578, 3317160, -9943017, 930272},
2439             {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177,
2440              24091212, -1388970, -22765376, -10650715},
2441         },
2442         {
2443             {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053,
2444              -14839018, -16554220, -1867018, 8398970},
2445             {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670,
2446              22981545, -6291273, 18009408, -15772772},
2447             {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469,
2448              29551787, -3727419, 19288549, 1325865},
2449         },
2450         {
2451             {15100157, -15835752, -23923978, -1005098, -26450192, 15509408,
2452              12376730, -3479146, 33166107, -8042750},
2453             {20909231, 13023121, -9209752, 16251778, -5778415, -8094914,
2454              12412151, 10018715, 2213263, -13878373},
2455             {32529814, -11074689, 30361439, -16689753, -9135940, 1513226,
2456              22922121, 6382134, -5766928, 8371348},
2457         },
2458     },
2459     {
2460         {
2461             {9923462, 11271500, 12616794, 3544722, -29998368, -1721626,
2462              12891687, -8193132, -26442943, 10486144},
2463             {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726,
2464              2610596, -23921530, -11455195},
2465             {5408411, -1136691, -4969122, 10561668, 24145918, 14240566,
2466              31319731, -4235541, 19985175, -3436086},
2467         },
2468         {
2469             {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976,
2470              -17577068, 8849297, 65030, 8370684},
2471             {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277,
2472              -19442942, 6922164, 12743482, -9800518},
2473             {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717,
2474              23783145, 11038569, 18800704, 255233},
2475         },
2476         {
2477             {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847,
2478              9066957, 19258688, -14753793},
2479             {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541,
2480              -31934921, 2209390, -1524053, 2055794},
2481             {580882, 16705327, 5468415, -2683018, -30926419, -14696000,
2482              -7203346, -8994389, -30021019, 7394435},
2483         },
2484         {
2485             {23838809, 1822728, -15738443, 15242727, 8318092, -3733104,
2486              -21672180, -3492205, -4821741, 14799921},
2487             {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804,
2488              13496856, -9056018, 7402518},
2489             {2286874, -4435931, -20042458, -2008336, -13696227, 5038122,
2490              11006906, -15760352, 8205061, 1607563},
2491         },
2492         {
2493             {14414086, -8002132, 3331830, -3208217, 22249151, -5594188,
2494              18364661, -2906958, 30019587, -9029278},
2495             {-27688051, 1585953, -10775053, 931069, -29120221, -11002319,
2496              -14410829, 12029093, 9944378, 8024},
2497             {4368715, -3709630, 29874200, -15022983, -20230386, -11410704,
2498              -16114594, -999085, -8142388, 5640030},
2499         },
2500         {
2501             {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887,
2502              -16694564, 15219798, -14327783},
2503             {27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605,
2504              -1173195, -18342183, 9742717},
2505             {6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614,
2506              7406442, 12420155, 1994844},
2507         },
2508         {
2509             {14012521, -5024720, -18384453, -9578469, -26485342, -3936439,
2510              -13033478, -10909803, 24319929, -6446333},
2511             {16412690, -4507367, 10772641, 15929391, -17068788, -4658621,
2512              10555945, -10484049, -30102368, -4739048},
2513             {22397382, -7767684, -9293161, -12792868, 17166287, -9755136,
2514              -27333065, 6199366, 21880021, -12250760},
2515         },
2516         {
2517             {-4283307, 5368523, -31117018, 8163389, -30323063, 3209128,
2518              16557151, 8890729, 8840445, 4957760},
2519             {-15447727, 709327, -6919446, -10870178, -29777922, 6522332,
2520              -21720181, 12130072, -14796503, 5005757},
2521             {-2114751, -14308128, 23019042, 15765735, -25269683, 6002752,
2522              10183197, -13239326, -16395286, -2176112},
2523         },
2524     },
2525     {
2526         {
2527             {-19025756, 1632005, 13466291, -7995100, -23640451, 16573537,
2528              -32013908, -3057104, 22208662, 2000468},
2529             {3065073, -1412761, -25598674, -361432, -17683065, -5703415,
2530              -8164212, 11248527, -3691214, -7414184},
2531             {10379208, -6045554, 8877319, 1473647, -29291284, -12507580,
2532              16690915, 2553332, -3132688, 16400289},
2533         },
2534         {
2535             {15716668, 1254266, -18472690, 7446274, -8448918, 6344164,
2536              -22097271, -7285580, 26894937, 9132066},
2537             {24158887, 12938817, 11085297, -8177598, -28063478, -4457083,
2538              -30576463, 64452, -6817084, -2692882},
2539             {13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710,
2540              -3418511, -4688006, 2364226},
2541         },
2542         {
2543             {16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024,
2544              -11697457, 15445875, -7798101},
2545             {29004207, -7867081, 28661402, -640412, -12794003, -7943086,
2546              31863255, -4135540, -278050, -15759279},
2547             {-6122061, -14866665, -28614905, 14569919, -10857999, -3591829,
2548              10343412, -6976290, -29828287, -10815811},
2549         },
2550         {
2551             {27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636,
2552              15372179, 17293797, 960709},
2553             {20263915, 11434237, -5765435, 11236810, 13505955, -10857102,
2554              -16111345, 6493122, -19384511, 7639714},
2555             {-2830798, -14839232, 25403038, -8215196, -8317012, -16173699,
2556              18006287, -16043750, 29994677, -15808121},
2557         },
2558         {
2559             {9769828, 5202651, -24157398, -13631392, -28051003, -11561624,
2560              -24613141, -13860782, -31184575, 709464},
2561             {12286395, 13076066, -21775189, -1176622, -25003198, 4057652,
2562              -32018128, -8890874, 16102007, 13205847},
2563             {13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170,
2564              8525972, 10151379, 10394400},
2565         },
2566         {
2567             {4024660, -16137551, 22436262, 12276534, -9099015, -2686099,
2568              19698229, 11743039, -33302334, 8934414},
2569             {-15879800, -4525240, -8580747, -2934061, 14634845, -698278,
2570              -9449077, 3137094, -11536886, 11721158},
2571             {17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229,
2572              8835153, -9205489, -1280045},
2573         },
2574         {
2575             {-461409, -7830014, 20614118, 16688288, -7514766, -4807119,
2576              22300304, 505429, 6108462, -6183415},
2577             {-5070281, 12367917, -30663534, 3234473, 32617080, -8422642,
2578              29880583, -13483331, -26898490, -7867459},
2579             {-31975283, 5726539, 26934134, 10237677, -3173717, -605053,
2580              24199304, 3795095, 7592688, -14992079},
2581         },
2582         {
2583             {21594432, -14964228, 17466408, -4077222, 32537084, 2739898,
2584              6407723, 12018833, -28256052, 4298412},
2585             {-20650503, -11961496, -27236275, 570498, 3767144, -1717540,
2586              13891942, -1569194, 13717174, 10805743},
2587             {-14676630, -15644296, 15287174, 11927123, 24177847, -8175568,
2588              -796431, 14860609, -26938930, -5863836},
2589         },
2590     },
2591     {
2592         {
2593             {12962541, 5311799, -10060768, 11658280, 18855286, -7954201,
2594              13286263, -12808704, -4381056, 9882022},
2595             {18512079, 11319350, -20123124, 15090309, 18818594, 5271736,
2596              -22727904, 3666879, -23967430, -3299429},
2597             {-6789020, -3146043, 16192429, 13241070, 15898607, -14206114,
2598              -10084880, -6661110, -2403099, 5276065},
2599         },
2600         {
2601             {30169808, -5317648, 26306206, -11750859, 27814964, 7069267,
2602              7152851, 3684982, 1449224, 13082861},
2603             {10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382,
2604              15056736, -21016438, -8202000},
2605             {-33150110, 3261608, 22745853, 7948688, 19370557, -15177665,
2606              -26171976, 6482814, -10300080, -11060101},
2607         },
2608         {
2609             {32869458, -5408545, 25609743, 15678670, -10687769, -15471071,
2610              26112421, 2521008, -22664288, 6904815},
2611             {29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737,
2612              3841096, -29003639, -6657642},
2613             {10340844, -6630377, -18656632, -2278430, 12621151, -13339055,
2614              30878497, -11824370, -25584551, 5181966},
2615         },
2616         {
2617             {25940115, -12658025, 17324188, -10307374, -8671468, 15029094,
2618              24396252, -16450922, -2322852, -12388574},
2619             {-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390,
2620              12641087, 20603771, -6561742},
2621             {-18882287, -11673380, 24849422, 11501709, 13161720, -4768874,
2622              1925523, 11914390, 4662781, 7820689},
2623         },
2624         {
2625             {12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456,
2626              12172924, 16136752, 15264020},
2627             {-10349955, -14680563, -8211979, 2330220, -17662549, -14545780,
2628              10658213, 6671822, 19012087, 3772772},
2629             {3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732,
2630              -15762884, 20527771, 12988982},
2631         },
2632         {
2633             {-14822485, -5797269, -3707987, 12689773, -898983, -10914866,
2634              -24183046, -10564943, 3299665, -12424953},
2635             {-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197,
2636              6461331, -25583147, 8991218},
2637             {-17226263, 1816362, -1673288, -6086439, 31783888, -8175991,
2638              -32948145, 7417950, -30242287, 1507265},
2639         },
2640         {
2641             {29692663, 6829891, -10498800, 4334896, 20945975, -11906496,
2642              -28887608, 8209391, 14606362, -10647073},
2643             {-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695,
2644              9761487, 4170404, -2085325},
2645             {-11587470, 14855945, -4127778, -1531857, -26649089, 15084046,
2646              22186522, 16002000, -14276837, -8400798},
2647         },
2648         {
2649             {-4811456, 13761029, -31703877, -2483919, -3312471, 7869047,
2650              -7113572, -9620092, 13240845, 10965870},
2651             {-7742563, -8256762, -14768334, -13656260, -23232383, 12387166,
2652              4498947, 14147411, 29514390, 4302863},
2653             {-13413405, -12407859, 20757302, -13801832, 14785143, 8976368,
2654              -5061276, -2144373, 17846988, -13971927},
2655         },
2656     },
2657     {
2658         {
2659             {-2244452, -754728, -4597030, -1066309, -6247172, 1455299,
2660              -21647728, -9214789, -5222701, 12650267},
2661             {-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813,
2662              13770293, -19134326, 10958663},
2663             {22470984, 12369526, 23446014, -5441109, -21520802, -9698723,
2664              -11772496, -11574455, -25083830, 4271862},
2665         },
2666         {
2667             {-25169565, -10053642, -19909332, 15361595, -5984358, 2159192,
2668              75375, -4278529, -32526221, 8469673},
2669             {15854970, 4148314, -8893890, 7259002, 11666551, 13824734,
2670              -30531198, 2697372, 24154791, -9460943},
2671             {15446137, -15806644, 29759747, 14019369, 30811221, -9610191,
2672              -31582008, 12840104, 24913809, 9815020},
2673         },
2674         {
2675             {-4709286, -5614269, -31841498, -12288893, -14443537, 10799414,
2676              -9103676, 13438769, 18735128, 9466238},
2677             {11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821,
2678              -10896103, -22728655, 16199064},
2679             {14576810, 379472, -26786533, -8317236, -29426508, -10812974,
2680              -102766, 1876699, 30801119, 2164795},
2681         },
2682         {
2683             {15995086, 3199873, 13672555, 13712240, -19378835, -4647646,
2684              -13081610, -15496269, -13492807, 1268052},
2685             {-10290614, -3659039, -3286592, 10948818, 23037027, 3794475,
2686              -3470338, -12600221, -17055369, 3565904},
2687             {29210088, -9419337, -5919792, -4952785, 10834811, -13327726,
2688              -16512102, -10820713, -27162222, -14030531},
2689         },
2690         {
2691             {-13161890, 15508588, 16663704, -8156150, -28349942, 9019123,
2692              -29183421, -3769423, 2244111, -14001979},
2693             {-5152875, -3800936, -9306475, -6071583, 16243069, 14684434,
2694              -25673088, -16180800, 13491506, 4641841},
2695             {10813417, 643330, -19188515, -728916, 30292062, -16600078,
2696              27548447, -7721242, 14476989, -12767431},
2697         },
2698         {
2699             {10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937,
2700              -1644259, -27912810, 12651324},
2701             {-31185513, -813383, 22271204, 11835308, 10201545, 15351028,
2702              17099662, 3988035, 21721536, -3148940},
2703             {10202177, -6545839, -31373232, -9574638, -32150642, -8119683,
2704              -12906320, 3852694, 13216206, 14842320},
2705         },
2706         {
2707             {-15815640, -10601066, -6538952, -7258995, -6984659, -6581778,
2708              -31500847, 13765824, -27434397, 9900184},
2709             {14465505, -13833331, -32133984, -14738873, -27443187, 12990492,
2710              33046193, 15796406, -7051866, -8040114},
2711             {30924417, -8279620, 6359016, -12816335, 16508377, 9071735,
2712              -25488601, 15413635, 9524356, -7018878},
2713         },
2714         {
2715             {12274201, -13175547, 32627641, -1785326, 6736625, 13267305,
2716              5237659, -5109483, 15663516, 4035784},
2717             {-2951309, 8903985, 17349946, 601635, -16432815, -4612556,
2718              -13732739, -15889334, -22258478, 4659091},
2719             {-16916263, -4952973, -30393711, -15158821, 20774812, 15897498,
2720              5736189, 15026997, -2178256, -13455585},
2721         },
2722     },
2723     {
2724         {
2725             {-8858980, -2219056, 28571666, -10155518, -474467, -10105698,
2726              -3801496, 278095, 23440562, -290208},
2727             {10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275,
2728              11551483, -16571960, -7442864},
2729             {17932739, -12437276, -24039557, 10749060, 11316803, 7535897,
2730              22503767, 5561594, -3646624, 3898661},
2731         },
2732         {
2733             {7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531,
2734              7152530, 21831162, 1245233},
2735             {26958459, -14658026, 4314586, 8346991, -5677764, 11960072,
2736              -32589295, -620035, -30402091, -16716212},
2737             {-12165896, 9166947, 33491384, 13673479, 29787085, 13096535,
2738              6280834, 14587357, -22338025, 13987525},
2739         },
2740         {
2741             {-24349909, 7778775, 21116000, 15572597, -4833266, -5357778,
2742              -4300898, -5124639, -7469781, -2858068},
2743             {9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781,
2744              6439245, -14581012, 4091397},
2745             {-8426427, 1470727, -28109679, -1596990, 3978627, -5123623,
2746              -19622683, 12092163, 29077877, -14741988},
2747         },
2748         {
2749             {5269168, -6859726, -13230211, -8020715, 25932563, 1763552,
2750              -5606110, -5505881, -20017847, 2357889},
2751             {32264008, -15407652, -5387735, -1160093, -2091322, -3946900,
2752              23104804, -12869908, 5727338, 189038},
2753             {14609123, -8954470, -6000566, -16622781, -14577387, -7743898,
2754              -26745169, 10942115, -25888931, -14884697},
2755         },
2756         {
2757             {20513500, 5557931, -15604613, 7829531, 26413943, -2019404,
2758              -21378968, 7471781, 13913677, -5137875},
2759             {-25574376, 11967826, 29233242, 12948236, -6754465, 4713227,
2760              -8940970, 14059180, 12878652, 8511905},
2761             {-25656801, 3393631, -2955415, -7075526, -2250709, 9366908,
2762              -30223418, 6812974, 5568676, -3127656},
2763         },
2764         {
2765             {11630004, 12144454, 2116339, 13606037, 27378885, 15676917,
2766              -17408753, -13504373, -14395196, 8070818},
2767             {27117696, -10007378, -31282771, -5570088, 1127282, 12772488,
2768              -29845906, 10483306, -11552749, -1028714},
2769             {10637467, -5688064, 5674781, 1072708, -26343588, -6982302,
2770              -1683975, 9177853, -27493162, 15431203},
2771         },
2772         {
2773             {20525145, 10892566, -12742472, 12779443, -29493034, 16150075,
2774              -28240519, 14943142, -15056790, -7935931},
2775             {-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767,
2776              -3239766, -3356550, 9594024},
2777             {-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683,
2778              -6492290, 13352335, -10977084},
2779         },
2780         {
2781             {-1931799, -5407458, 3304649, -12884869, 17015806, -4877091,
2782              -29783850, -7752482, -13215537, -319204},
2783             {20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742,
2784              15077870, -22750759, 14523817},
2785             {27406042, -6041657, 27423596, -4497394, 4996214, 10002360,
2786              -28842031, -4545494, -30172742, -4805667},
2787         },
2788     },
2789     {
2790         {
2791             {11374242, 12660715, 17861383, -12540833, 10935568, 1099227,
2792              -13886076, -9091740, -27727044, 11358504},
2793             {-12730809, 10311867, 1510375, 10778093, -2119455, -9145702,
2794              32676003, 11149336, -26123651, 4985768},
2795             {-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043,
2796              13794114, -19414307, -15621255},
2797         },
2798         {
2799             {6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603,
2800              6970005, -1691065, -9004790},
2801             {1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622,
2802              -5475723, -16796596, -5031438},
2803             {-22273315, -13524424, -64685, -4334223, -18605636, -10921968,
2804              -20571065, -7007978, -99853, -10237333},
2805         },
2806         {
2807             {17747465, 10039260, 19368299, -4050591, -20630635, -16041286,
2808              31992683, -15857976, -29260363, -5511971},
2809             {31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999,
2810              -3744247, 4882242, -10626905},
2811             {29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198,
2812              3272828, -5190932, -4162409},
2813         },
2814         {
2815             {12501286, 4044383, -8612957, -13392385, -32430052, 5136599,
2816              -19230378, -3529697, 330070, -3659409},
2817             {6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522,
2818              -8573892, -271295, 12071499},
2819             {-8365515, -4042521, 25133448, -4517355, -6211027, 2265927,
2820              -32769618, 1936675, -5159697, 3829363},
2821         },
2822         {
2823             {28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550,
2824              -6567787, 26333140, 14267664},
2825             {-11067219, 11871231, 27385719, -10559544, -4585914, -11189312,
2826              10004786, -8709488, -21761224, 8930324},
2827             {-21197785, -16396035, 25654216, -1725397, 12282012, 11008919,
2828              1541940, 4757911, -26491501, -16408940},
2829         },
2830         {
2831             {13537262, -7759490, -20604840, 10961927, -5922820, -13218065,
2832              -13156584, 6217254, -15943699, 13814990},
2833             {-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681,
2834              9257833, -1956526, -1776914},
2835             {-25045300, -10191966, 15366585, 15166509, -13105086, 8423556,
2836              -29171540, 12361135, -18685978, 4578290},
2837         },
2838         {
2839             {24579768, 3711570, 1342322, -11180126, -27005135, 14124956,
2840              -22544529, 14074919, 21964432, 8235257},
2841             {-6528613, -2411497, 9442966, -5925588, 12025640, -1487420,
2842              -2981514, -1669206, 13006806, 2355433},
2843             {-16304899, -13605259, -6632427, -5142349, 16974359, -10911083,
2844              27202044, 1719366, 1141648, -12796236},
2845         },
2846         {
2847             {-12863944, -13219986, -8318266, -11018091, -6810145, -4843894,
2848              13475066, -3133972, 32674895, 13715045},
2849             {11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
2850              -13265253, 16086212, -28740881, -15642093},
2851             {-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
2852              -11709148, 7791794, -27245943, 4383347},
2853         },
2854     },
2855     {
2856         {
2857             {-28970898, 5271447, -1266009, -9736989, -12455236, 16732599,
2858              -4862407, -4906449, 27193557, 6245191},
2859             {-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898,
2860              3260492, 22510453, 8577507},
2861             {-12632451, 11257346, -32692994, 13548177, -721004, 10879011,
2862              31168030, 13952092, -29571492, -3635906},
2863         },
2864         {
2865             {3877321, -9572739, 32416692, 5405324, -11004407, -13656635,
2866              3759769, 11935320, 5611860, 8164018},
2867             {-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
2868              32003002, -8832289, 5773085, -8422109},
2869             {-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
2870              12376320, 31632953, 190926},
2871         },
2872         {
2873             {-24593607, -16138885, -8423991, 13378746, 14162407, 6901328,
2874              -8288749, 4508564, -25341555, -3627528},
2875             {8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941,
2876              -14786005, -1672488, 827625},
2877             {-32720583, -16289296, -32503547, 7101210, 13354605, 2659080,
2878              -1800575, -14108036, -24878478, 1541286},
2879         },
2880         {
2881             {2901347, -1117687, 3880376, -10059388, -17620940, -3612781,
2882              -21802117, -3567481, 20456845, -1885033},
2883             {27019610, 12299467, -13658288, -1603234, -12861660, -4861471,
2884              -19540150, -5016058, 29439641, 15138866},
2885             {21536104, -6626420, -32447818, -10690208, -22408077, 5175814,
2886              -5420040, -16361163, 7779328, 109896},
2887         },
2888         {
2889             {30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390,
2890              12180118, 23177719, -554075},
2891             {26572847, 3405927, -31701700, 12890905, -19265668, 5335866,
2892              -6493768, 2378492, 4439158, -13279347},
2893             {-22716706, 3489070, -9225266, -332753, 18875722, -1140095,
2894              14819434, -12731527, -17717757, -5461437},
2895         },
2896         {
2897             {-5056483, 16566551, 15953661, 3767752, -10436499, 15627060,
2898              -820954, 2177225, 8550082, -15114165},
2899             {-18473302, 16596775, -381660, 15663611, 22860960, 15585581,
2900              -27844109, -3582739, -23260460, -8428588},
2901             {-32480551, 15707275, -8205912, -5652081, 29464558, 2713815,
2902              -22725137, 15860482, -21902570, 1494193},
2903         },
2904         {
2905             {-19562091, -14087393, -25583872, -9299552, 13127842, 759709,
2906              21923482, 16529112, 8742704, 12967017},
2907             {-28464899, 1553205, 32536856, -10473729, -24691605, -406174,
2908              -8914625, -2933896, -29903758, 15553883},
2909             {21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572,
2910              14513274, 19375923, -12647961},
2911         },
2912         {
2913             {8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818,
2914              -6222716, 2862653, 9455043},
2915             {29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124,
2916              -2990080, 15511449, 4789663},
2917             {-20679756, 7004547, 8824831, -9434977, -4045704, -3750736,
2918              -5754762, 108893, 23513200, 16652362},
2919         },
2920     },
2921     {
2922         {
2923             {-33256173, 4144782, -4476029, -6579123, 10770039, -7155542,
2924              -6650416, -12936300, -18319198, 10212860},
2925             {2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801,
2926              2600940, -9988298, -12506466},
2927             {-24645692, 13317462, -30449259, -15653928, 21365574, -10869657,
2928              11344424, 864440, -2499677, -16710063},
2929         },
2930         {
2931             {-26432803, 6148329, -17184412, -14474154, 18782929, -275997,
2932              -22561534, 211300, 2719757, 4940997},
2933             {-1323882, 3911313, -6948744, 14759765, -30027150, 7851207,
2934              21690126, 8518463, 26699843, 5276295},
2935             {-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586,
2936              149635, -15452774, 7159369},
2937         },
2938         {
2939             {9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009,
2940              8312176, 22477218, -8403385},
2941             {18155857, -16504990, 19744716, 9006923, 15154154, -10538976,
2942              24256460, -4864995, -22548173, 9334109},
2943             {2986088, -4911893, 10776628, -3473844, 10620590, -7083203,
2944              -21413845, 14253545, -22587149, 536906},
2945         },
2946         {
2947             {4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551,
2948              10589625, 10838060, -15420424},
2949             {-19342404, 867880, 9277171, -3218459, -14431572, -1986443,
2950              19295826, -15796950, 6378260, 699185},
2951             {7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039,
2952              15693155, -5045064, -13373962},
2953         },
2954         {
2955             {-7737563, -5869402, -14566319, -7406919, 11385654, 13201616,
2956              31730678, -10962840, -3918636, -9669325},
2957             {10188286, -15770834, -7336361, 13427543, 22223443, 14896287,
2958              30743455, 7116568, -21786507, 5427593},
2959             {696102, 13206899, 27047647, -10632082, 15285305, -9853179,
2960              10798490, -4578720, 19236243, 12477404},
2961         },
2962         {
2963             {-11229439, 11243796, -17054270, -8040865, -788228, -8167967,
2964              -3897669, 11180504, -23169516, 7733644},
2965             {17800790, -14036179, -27000429, -11766671, 23887827, 3149671,
2966              23466177, -10538171, 10322027, 15313801},
2967             {26246234, 11968874, 32263343, -5468728, 6830755, -13323031,
2968              -15794704, -101982, -24449242, 10890804},
2969         },
2970         {
2971             {-31365647, 10271363, -12660625, -6267268, 16690207, -13062544,
2972              -14982212, 16484931, 25180797, -5334884},
2973             {-586574, 10376444, -32586414, -11286356, 19801893, 10997610,
2974              2276632, 9482883, 316878, 13820577},
2975             {-9882808, -4510367, -2115506, 16457136, -11100081, 11674996,
2976              30756178, -7515054, 30696930, -3712849},
2977         },
2978         {
2979             {32988917, -9603412, 12499366, 7910787, -10617257, -11931514,
2980              -7342816, -9985397, -32349517, 7392473},
2981             {-8855661, 15927861, 9866406, -3649411, -2396914, -16655781,
2982              -30409476, -9134995, 25112947, -2926644},
2983             {-2504044, -436966, 25621774, -5678772, 15085042, -5479877,
2984              -24884878, -13526194, 5537438, -13914319},
2985         },
2986     },
2987     {
2988         {
2989             {-11225584, 2320285, -9584280, 10149187, -33444663, 5808648,
2990              -14876251, -1729667, 31234590, 6090599},
2991             {-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721,
2992              15878753, -6970405, -9034768},
2993             {-27757857, 247744, -15194774, -9002551, 23288161, -10011936,
2994              -23869595, 6503646, 20650474, 1804084},
2995         },
2996         {
2997             {-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995,
2998              -10329713, 27842616, -202328},
2999             {-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656,
3000              5031932, -11375082, 12714369},
3001             {20807691, -7270825, 29286141, 11421711, -27876523, -13868230,
3002              -21227475, 1035546, -19733229, 12796920},
3003         },
3004         {
3005             {12076899, -14301286, -8785001, -11848922, -25012791, 16400684,
3006              -17591495, -12899438, 3480665, -15182815},
3007             {-32361549, 5457597, 28548107, 7833186, 7303070, -11953545,
3008              -24363064, -15921875, -33374054, 2771025},
3009             {-21389266, 421932, 26597266, 6860826, 22486084, -6737172,
3010              -17137485, -4210226, -24552282, 15673397},
3011         },
3012         {
3013             {-20184622, 2338216, 19788685, -9620956, -4001265, -8740893,
3014              -20271184, 4733254, 3727144, -12934448},
3015             {6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594,
3016              7975683, 31123697, -10958981},
3017             {30069250, -11435332, 30434654, 2958439, 18399564, -976289,
3018              12296869, 9204260, -16432438, 9648165},
3019         },
3020         {
3021             {32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266,
3022              5248604, -26008332, -11377501},
3023             {17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711,
3024              15298639, 2662509, -16297073},
3025             {-1172927, -7558695, -4366770, -4287744, -21346413, -8434326,
3026              32087529, -1222777, 32247248, -14389861},
3027         },
3028         {
3029             {14312628, 1221556, 17395390, -8700143, -4945741, -8684635,
3030              -28197744, -9637817, -16027623, -13378845},
3031             {-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502,
3032              9803137, 17597934, 2346211},
3033             {18510800, 15337574, 26171504, 981392, -22241552, 7827556,
3034              -23491134, -11323352, 3059833, -11782870},
3035         },
3036         {
3037             {10141598, 6082907, 17829293, -1947643, 9830092, 13613136,
3038              -25556636, -5544586, -33502212, 3592096},
3039             {33114168, -15889352, -26525686, -13343397, 33076705, 8716171,
3040              1151462, 1521897, -982665, -6837803},
3041             {-32939165, -4255815, 23947181, -324178, -33072974, -12305637,
3042              -16637686, 3891704, 26353178, 693168},
3043         },
3044         {
3045             {30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294,
3046              -400668, 31375464, 14369965},
3047             {-14370654, -7772529, 1510301, 6434173, -18784789, -6262728,
3048              32732230, -13108839, 17901441, 16011505},
3049             {18171223, -11934626, -12500402, 15197122, -11038147, -15230035,
3050              -19172240, -16046376, 8764035, 12309598},
3051         },
3052     },
3053     {
3054         {
3055             {5975908, -5243188, -19459362, -9681747, -11541277, 14015782,
3056              -23665757, 1228319, 17544096, -10593782},
3057             {5811932, -1715293, 3442887, -2269310, -18367348, -8359541,
3058              -18044043, -15410127, -5565381, 12348900},
3059             {-31399660, 11407555, 25755363, 6891399, -3256938, 14872274,
3060              -24849353, 8141295, -10632534, -585479},
3061         },
3062         {
3063             {-12675304, 694026, -5076145, 13300344, 14015258, -14451394,
3064              -9698672, -11329050, 30944593, 1130208},
3065             {8247766, -6710942, -26562381, -7709309, -14401939, -14648910,
3066              4652152, 2488540, 23550156, -271232},
3067             {17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737,
3068              -5908146, -408818, -137719},
3069         },
3070         {
3071             {16091085, -16253926, 18599252, 7340678, 2137637, -1221657,
3072              -3364161, 14550936, 3260525, -7166271},
3073             {-4910104, -13332887, 18550887, 10864893, -16459325, -7291596,
3074              -23028869, -13204905, -12748722, 2701326},
3075             {-8574695, 16099415, 4629974, -16340524, -20786213, -6005432,
3076              -10018363, 9276971, 11329923, 1862132},
3077         },
3078         {
3079             {14763076, -15903608, -30918270, 3689867, 3511892, 10313526,
3080              -21951088, 12219231, -9037963, -940300},
3081             {8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216,
3082              -2909717, -15438168, 11595570},
3083             {15214962, 3537601, -26238722, -14058872, 4418657, -15230761,
3084              13947276, 10730794, -13489462, -4363670},
3085         },
3086         {
3087             {-2538306, 7682793, 32759013, 263109, -29984731, -7955452,
3088              -22332124, -10188635, 977108, 699994},
3089             {-12466472, 4195084, -9211532, 550904, -15565337, 12917920,
3090              19118110, -439841, -30534533, -14337913},
3091             {31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237,
3092              -10051775, 12493932, -5409317},
3093         },
3094         {
3095             {-25680606, 5260744, -19235809, -6284470, -3695942, 16566087,
3096              27218280, 2607121, 29375955, 6024730},
3097             {842132, -2794693, -4763381, -8722815, 26332018, -12405641,
3098              11831880, 6985184, -9940361, 2854096},
3099             {-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645,
3100              960770, 12121869, 16648078},
3101         },
3102         {
3103             {-15218652, 14667096, -13336229, 2013717, 30598287, -464137,
3104              -31504922, -7882064, 20237806, 2838411},
3105             {-19288047, 4453152, 15298546, -16178388, 22115043, -15972604,
3106              12544294, -13470457, 1068881, -12499905},
3107             {-9558883, -16518835, 33238498, 13506958, 30505848, -1114596,
3108              -8486907, -2630053, 12521378, 4845654},
3109         },
3110         {
3111             {-28198521, 10744108, -2958380, 10199664, 7759311, -13088600,
3112              3409348, -873400, -6482306, -12885870},
3113             {-23561822, 6230156, -20382013, 10655314, -24040585, -11621172,
3114              10477734, -1240216, -3113227, 13974498},
3115             {12966261, 15550616, -32038948, -1615346, 21025980, -629444,
3116              5642325, 7188737, 18895762, 12629579},
3117         },
3118     },
3119     {
3120         {
3121             {14741879, -14946887, 22177208, -11721237, 1279741, 8058600,
3122              11758140, 789443, 32195181, 3895677},
3123             {10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575,
3124              -3566119, -8982069, 4429647},
3125             {-2453894, 15725973, -20436342, -10410672, -5803908, -11040220,
3126              -7135870, -11642895, 18047436, -15281743},
3127         },
3128         {
3129             {-25173001, -11307165, 29759956, 11776784, -22262383, -15820455,
3130              10993114, -12850837, -17620701, -9408468},
3131             {21987233, 700364, -24505048, 14972008, -7774265, -5718395,
3132              32155026, 2581431, -29958985, 8773375},
3133             {-25568350, 454463, -13211935, 16126715, 25240068, 8594567,
3134              20656846, 12017935, -7874389, -13920155},
3135         },
3136         {
3137             {6028182, 6263078, -31011806, -11301710, -818919, 2461772,
3138              -31841174, -5468042, -1721788, -2776725},
3139             {-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845,
3140              -4166698, 28408820, 6816612},
3141             {-10358094, -8237829, 19549651, -12169222, 22082623, 16147817,
3142              20613181, 13982702, -10339570, 5067943},
3143         },
3144         {
3145             {-30505967, -3821767, 12074681, 13582412, -19877972, 2443951,
3146              -19719286, 12746132, 5331210, -10105944},
3147             {30528811, 3601899, -1957090, 4619785, -27361822, -15436388,
3148              24180793, -12570394, 27679908, -1648928},
3149             {9402404, -13957065, 32834043, 10838634, -26580150, -13237195,
3150              26653274, -8685565, 22611444, -12715406},
3151         },
3152         {
3153             {22190590, 1118029, 22736441, 15130463, -30460692, -5991321,
3154              19189625, -4648942, 4854859, 6622139},
3155             {-8310738, -2953450, -8262579, -3388049, -10401731, -271929,
3156              13424426, -3567227, 26404409, 13001963},
3157             {-31241838, -15415700, -2994250, 8939346, 11562230, -12840670,
3158              -26064365, -11621720, -15405155, 11020693},
3159         },
3160         {
3161             {1866042, -7949489, -7898649, -10301010, 12483315, 13477547,
3162              3175636, -12424163, 28761762, 1406734},
3163             {-448555, -1777666, 13018551, 3194501, -9580420, -11161737,
3164              24760585, -4347088, 25577411, -13378680},
3165             {-24290378, 4759345, -690653, -1852816, 2066747, 10693769,
3166              -29595790, 9884936, -9368926, 4745410},
3167         },
3168         {
3169             {-9141284, 6049714, -19531061, -4341411, -31260798, 9944276,
3170              -15462008, -11311852, 10931924, -11931931},
3171             {-16561513, 14112680, -8012645, 4817318, -8040464, -11414606,
3172              -22853429, 10856641, -20470770, 13434654},
3173             {22759489, -10073434, -16766264, -1871422, 13637442, -10168091,
3174              1765144, -12654326, 28445307, -5364710},
3175         },
3176         {
3177             {29875063, 12493613, 2795536, -3786330, 1710620, 15181182,
3178              -10195717, -8788675, 9074234, 1167180},
3179             {-26205683, 11014233, -9842651, -2635485, -26908120, 7532294,
3180              -18716888, -9535498, 3843903, 9367684},
3181             {-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123,
3182              8601684, -139197, 4242895},
3183         },
3184     },
3185     {
3186         {
3187             {22092954, -13191123, -2042793, -11968512, 32186753, -11517388,
3188              -6574341, 2470660, -27417366, 16625501},
3189             {-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857,
3190              2602725, -27351616, 14247413},
3191             {6314175, -10264892, -32772502, 15957557, -10157730, 168750,
3192              -8618807, 14290061, 27108877, -1180880},
3193         },
3194         {
3195             {-8586597, -7170966, 13241782, 10960156, -32991015, -13794596,
3196              33547976, -11058889, -27148451, 981874},
3197             {22833440, 9293594, -32649448, -13618667, -9136966, 14756819,
3198              -22928859, -13970780, -10479804, -16197962},
3199             {-7768587, 3326786, -28111797, 10783824, 19178761, 14905060,
3200              22680049, 13906969, -15933690, 3797899},
3201         },
3202         {
3203             {21721356, -4212746, -12206123, 9310182, -3882239, -13653110,
3204              23740224, -2709232, 20491983, -8042152},
3205             {9209270, -15135055, -13256557, -6167798, -731016, 15289673,
3206              25947805, 15286587, 30997318, -6703063},
3207             {7392032, 16618386, 23946583, -8039892, -13265164, -1533858,
3208              -14197445, -2321576, 17649998, -250080},
3209         },
3210         {
3211             {-9301088, -14193827, 30609526, -3049543, -25175069, -1283752,
3212              -15241566, -9525724, -2233253, 7662146},
3213             {-17558673, 1763594, -33114336, 15908610, -30040870, -12174295,
3214              7335080, -8472199, -3174674, 3440183},
3215             {-19889700, -5977008, -24111293, -9688870, 10799743, -16571957,
3216              40450, -4431835, 4862400, 1133},
3217         },
3218         {
3219             {-32856209, -7873957, -5422389, 14860950, -16319031, 7956142,
3220              7258061, 311861, -30594991, -7379421},
3221             {-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763,
3222              16527196, 18278453, 15405622},
3223             {-4381906, 8508652, -19898366, -3674424, -5984453, 15149970,
3224              -13313598, 843523, -21875062, 13626197},
3225         },
3226         {
3227             {2281448, -13487055, -10915418, -2609910, 1879358, 16164207,
3228              -10783882, 3953792, 13340839, 15928663},
3229             {31727126, -7179855, -18437503, -8283652, 2875793, -16390330,
3230              -25269894, -7014826, -23452306, 5964753},
3231             {4100420, -5959452, -17179337, 6017714, -18705837, 12227141,
3232              -26684835, 11344144, 2538215, -7570755},
3233         },
3234         {
3235             {-9433605, 6123113, 11159803, -2156608, 30016280, 14966241,
3236              -20474983, 1485421, -629256, -15958862},
3237             {-26804558, 4260919, 11851389, 9658551, -32017107, 16367492,
3238              -20205425, -13191288, 11659922, -11115118},
3239             {26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568,
3240              -10170080, 33100372, -1306171},
3241         },
3242         {
3243             {15121113, -5201871, -10389905, 15427821, -27509937, -15992507,
3244              21670947, 4486675, -5931810, -14466380},
3245             {16166486, -9483733, -11104130, 6023908, -31926798, -1364923,
3246              2340060, -16254968, -10735770, -10039824},
3247             {28042865, -3557089, -12126526, 12259706, -3717498, -6945899,
3248              6766453, -8689599, 18036436, 5803270},
3249         },
3250     },
3251     {
3252         {
3253             {-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391,
3254              4598332, -6159431, -14117438},
3255             {-31031306, -14256194, 17332029, -2383520, 31312682, -5967183,
3256              696309, 50292, -20095739, 11763584},
3257             {-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117,
3258              -12613632, -19773211, -10713562},
3259         },
3260         {
3261             {30464590, -11262872, -4127476, -12734478, 19835327, -7105613,
3262              -24396175, 2075773, -17020157, 992471},
3263             {18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841,
3264              8080033, -11574335, -10601610},
3265             {19598397, 10334610, 12555054, 2555664, 18821899, -10339780,
3266              21873263, 16014234, 26224780, 16452269},
3267         },
3268         {
3269             {-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804,
3270              -7618186, -20533829, 3698650},
3271             {14187449, 3448569, -10636236, -10810935, -22663880, -3433596,
3272              7268410, -10890444, 27394301, 12015369},
3273             {19695761, 16087646, 28032085, 12999827, 6817792, 11427614,
3274              20244189, -1312777, -13259127, -3402461},
3275         },
3276         {
3277             {30860103, 12735208, -1888245, -4699734, -16974906, 2256940,
3278              -8166013, 12298312, -8550524, -10393462},
3279             {-5719826, -11245325, -1910649, 15569035, 26642876, -7587760,
3280              -5789354, -15118654, -4976164, 12651793},
3281             {-2848395, 9953421, 11531313, -5282879, 26895123, -12697089,
3282              -13118820, -16517902, 9768698, -2533218},
3283         },
3284         {
3285             {-24719459, 1894651, -287698, -4704085, 15348719, -8156530,
3286              32767513, 12765450, 4940095, 10678226},
3287             {18860224, 15980149, -18987240, -1562570, -26233012, -11071856,
3288              -7843882, 13944024, -24372348, 16582019},
3289             {-15504260, 4970268, -29893044, 4175593, -20993212, -2199756,
3290              -11704054, 15444560, -11003761, 7989037},
3291         },
3292         {
3293             {31490452, 5568061, -2412803, 2182383, -32336847, 4531686,
3294              -32078269, 6200206, -19686113, -14800171},
3295             {-17308668, -15879940, -31522777, -2831, -32887382, 16375549,
3296              8680158, -16371713, 28550068, -6857132},
3297             {-28126887, -5688091, 16837845, -1820458, -6850681, 12700016,
3298              -30039981, 4364038, 1155602, 5988841},
3299         },
3300         {
3301             {21890435, -13272907, -12624011, 12154349, -7831873, 15300496,
3302              23148983, -4470481, 24618407, 8283181},
3303             {-33136107, -10512751, 9975416, 6841041, -31559793, 16356536,
3304              3070187, -7025928, 1466169, 10740210},
3305             {-1509399, -15488185, -13503385, -10655916, 32799044, 909394,
3306              -13938903, -5779719, -32164649, -15327040},
3307         },
3308         {
3309             {3960823, -14267803, -28026090, -15918051, -19404858, 13146868,
3310              15567327, 951507, -3260321, -573935},
3311             {24740841, 5052253, -30094131, 8961361, 25877428, 6165135,
3312              -24368180, 14397372, -7380369, -6144105},
3313             {-28888365, 3510803, -28103278, -1158478, -11238128, -10631454,
3314              -15441463, -14453128, -1625486, -6494814},
3315         },
3316     },
3317     {
3318         {
3319             {793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843,
3320              -4885251, -9906200, -621852},
3321             {5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374,
3322              1468826, -6171428, -15186581},
3323             {-4859255, -3779343, -2917758, -6748019, 7778750, 11688288,
3324              -30404353, -9871238, -1558923, -9863646},
3325         },
3326         {
3327             {10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958,
3328              14783338, -30581476, -15757844},
3329             {10566929, 12612572, -31944212, 11118703, -12633376, 12362879,
3330              21752402, 8822496, 24003793, 14264025},
3331             {27713862, -7355973, -11008240, 9227530, 27050101, 2504721,
3332              23886875, -13117525, 13958495, -5732453},
3333         },
3334         {
3335             {-23481610, 4867226, -27247128, 3900521, 29838369, -8212291,
3336              -31889399, -10041781, 7340521, -15410068},
3337             {4646514, -8011124, -22766023, -11532654, 23184553, 8566613,
3338              31366726, -1381061, -15066784, -10375192},
3339             {-17270517, 12723032, -16993061, 14878794, 21619651, -6197576,
3340              27584817, 3093888, -8843694, 3849921},
3341         },
3342         {
3343             {-9064912, 2103172, 25561640, -15125738, -5239824, 9582958,
3344              32477045, -9017955, 5002294, -15550259},
3345             {-12057553, -11177906, 21115585, -13365155, 8808712, -12030708,
3346              16489530, 13378448, -25845716, 12741426},
3347             {-5946367, 10645103, -30911586, 15390284, -3286982, -7118677,
3348              24306472, 15852464, 28834118, -7646072},
3349         },
3350         {
3351             {-17335748, -9107057, -24531279, 9434953, -8472084, -583362,
3352              -13090771, 455841, 20461858, 5491305},
3353             {13669248, -16095482, -12481974, -10203039, -14569770, -11893198,
3354              -24995986, 11293807, -28588204, -9421832},
3355             {28497928, 6272777, -33022994, 14470570, 8906179, -1225630,
3356              18504674, -14165166, 29867745, -8795943},
3357         },
3358         {
3359             {-16207023, 13517196, -27799630, -13697798, 24009064, -6373891,
3360              -6367600, -13175392, 22853429, -4012011},
3361             {24191378, 16712145, -13931797, 15217831, 14542237, 1646131,
3362              18603514, -11037887, 12876623, -2112447},
3363             {17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753,
3364              608397, 16031844, 3723494},
3365         },
3366         {
3367             {-28632773, 12763728, -20446446, 7577504, 33001348, -13017745,
3368              17558842, -7872890, 23896954, -4314245},
3369             {-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064,
3370              7229064, -9919646, -8826859},
3371             {28816045, 298879, -28165016, -15920938, 19000928, -1665890,
3372              -12680833, -2949325, -18051778, -2082915},
3373         },
3374         {
3375             {16000882, -344896, 3493092, -11447198, -29504595, -13159789,
3376              12577740, 16041268, -19715240, 7847707},
3377             {10151868, 10572098, 27312476, 7922682, 14825339, 4723128,
3378              -32855931, -6519018, -10020567, 3852848},
3379             {-11430470, 15697596, -21121557, -4420647, 5386314, 15063598,
3380              16514493, -15932110, 29330899, -15076224},
3381         },
3382     },
3383     {
3384         {
3385             {-25499735, -4378794, -15222908, -6901211, 16615731, 2051784,
3386              3303702, 15490, -27548796, 12314391},
3387             {15683520, -6003043, 18109120, -9980648, 15337968, -5997823,
3388              -16717435, 15921866, 16103996, -3731215},
3389             {-23169824, -10781249, 13588192, -1628807, -3798557, -1074929,
3390              -19273607, 5402699, -29815713, -9841101},
3391         },
3392         {
3393             {23190676, 2384583, -32714340, 3462154, -29903655, -1529132,
3394              -11266856, 8911517, -25205859, 2739713},
3395             {21374101, -3554250, -33524649, 9874411, 15377179, 11831242,
3396              -33529904, 6134907, 4931255, 11987849},
3397             {-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539,
3398              13861388, -30076310, 10117930},
3399         },
3400         {
3401             {-29501170, -10744872, -26163768, 13051539, -25625564, 5089643,
3402              -6325503, 6704079, 12890019, 15728940},
3403             {-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376,
3404              -10428139, 12885167, 8311031},
3405             {-17516482, 5352194, 10384213, -13811658, 7506451, 13453191,
3406              26423267, 4384730, 1888765, -5435404},
3407         },
3408         {
3409             {-25817338, -3107312, -13494599, -3182506, 30896459, -13921729,
3410              -32251644, -12707869, -19464434, -3340243},
3411             {-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245,
3412              14845197, 17151279, -9854116},
3413             {-24830458, -12733720, -15165978, 10367250, -29530908, -265356,
3414              22825805, -7087279, -16866484, 16176525},
3415         },
3416         {
3417             {-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182,
3418              -10363426, -28746253, -10197509},
3419             {-10626600, -4486402, -13320562, -5125317, 3432136, -6393229,
3420              23632037, -1940610, 32808310, 1099883},
3421             {15030977, 5768825, -27451236, -2887299, -6427378, -15361371,
3422              -15277896, -6809350, 2051441, -15225865},
3423         },
3424         {
3425             {-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398,
3426              -14154188, -22686354, 16633660},
3427             {4577086, -16752288, 13249841, -15304328, 19958763, -14537274,
3428              18559670, -10759549, 8402478, -9864273},
3429             {-28406330, -1051581, -26790155, -907698, -17212414, -11030789,
3430              9453451, -14980072, 17983010, 9967138},
3431         },
3432         {
3433             {-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990,
3434              7806337, 17507396, 3651560},
3435             {-10420457, -4118111, 14584639, 15971087, -15768321, 8861010,
3436              26556809, -5574557, -18553322, -11357135},
3437             {2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121,
3438              8459447, -5605463, -7621941},
3439         },
3440         {
3441             {-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813,
3442              -849066, 17258084, -7977739},
3443             {18164541, -10595176, -17154882, -1542417, 19237078, -9745295,
3444              23357533, -15217008, 26908270, 12150756},
3445             {-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168,
3446              -5537701, -32302074, 16215819},
3447         },
3448     },
3449     {
3450         {
3451             {-6898905, 9824394, -12304779, -4401089, -31397141, -6276835,
3452              32574489, 12532905, -7503072, -8675347},
3453             {-27343522, -16515468, -27151524, -10722951, 946346, 16291093,
3454              254968, 7168080, 21676107, -1943028},
3455             {21260961, -8424752, -16831886, -11920822, -23677961, 3968121,
3456              -3651949, -6215466, -3556191, -7913075},
3457         },
3458         {
3459             {16544754, 13250366, -16804428, 15546242, -4583003, 12757258,
3460              -2462308, -8680336, -18907032, -9662799},
3461             {-2415239, -15577728, 18312303, 4964443, -15272530, -12653564,
3462              26820651, 16690659, 25459437, -4564609},
3463             {-25144690, 11425020, 28423002, -11020557, -6144921, -15826224,
3464              9142795, -2391602, -6432418, -1644817},
3465         },
3466         {
3467             {-23104652, 6253476, 16964147, -3768872, -25113972, -12296437,
3468              -27457225, -16344658, 6335692, 7249989},
3469             {-30333227, 13979675, 7503222, -12368314, -11956721, -4621693,
3470              -30272269, 2682242, 25993170, -12478523},
3471             {4364628, 5930691, 32304656, -10044554, -8054781, 15091131,
3472              22857016, -10598955, 31820368, 15075278},
3473         },
3474         {
3475             {31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788,
3476              -9650886, -17970238, 12833045},
3477             {19073683, 14851414, -24403169, -11860168, 7625278, 11091125,
3478              -19619190, 2074449, -9413939, 14905377},
3479             {24483667, -11935567, -2518866, -11547418, -1553130, 15355506,
3480              -25282080, 9253129, 27628530, -7555480},
3481         },
3482         {
3483             {17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324,
3484              -9157582, -14110875, 15297016},
3485             {510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417,
3486              -11864220, 8683221, 2921426},
3487             {18606791, 11874196, 27155355, -5281482, -24031742, 6265446,
3488              -25178240, -1278924, 4674690, 13890525},
3489         },
3490         {
3491             {13609624, 13069022, -27372361, -13055908, 24360586, 9592974,
3492              14977157, 9835105, 4389687, 288396},
3493             {9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062,
3494              8317628, 23388070, 16052080},
3495             {12720016, 11937594, -31970060, -5028689, 26900120, 8561328,
3496              -20155687, -11632979, -14754271, -10812892},
3497         },
3498         {
3499             {15961858, 14150409, 26716931, -665832, -22794328, 13603569,
3500              11829573, 7467844, -28822128, 929275},
3501             {11038231, -11582396, -27310482, -7316562, -10498527, -16307831,
3502              -23479533, -9371869, -21393143, 2465074},
3503             {20017163, -4323226, 27915242, 1529148, 12396362, 15675764,
3504              13817261, -9658066, 2463391, -4622140},
3505         },
3506         {
3507             {-16358878, -12663911, -12065183, 4996454, -1256422, 1073572,
3508              9583558, 12851107, 4003896, 12673717},
3509             {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325,
3510              14741514, -9103726, 7903886, 2348101},
3511             {24536016, -16515207, 12715592, -3862155, 1511293, 10047386,
3512              -3842346, -7129159, -28377538, 10048127},
3513         },
3514     },
3515     {
3516         {
3517             {-12622226, -6204820, 30718825, 2591312, -10617028, 12192840,
3518              18873298, -7297090, -32297756, 15221632},
3519             {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409,
3520              -21343950, 2095755, 29769758, 6593415},
3521             {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345,
3522              -6118678, 30958054, 8292160},
3523         },
3524         {
3525             {31429822, -13959116, 29173532, 15632448, 12174511, -2760094,
3526              32808831, 3977186, 26143136, -3148876},
3527             {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633,
3528              -1674433, -3758243, -2304625},
3529             {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029,
3530              -1612713, -1535569, -16664475, 8194478},
3531         },
3532         {
3533             {27338066, -7507420, -7414224, 10140405, -19026427, -6589889,
3534              27277191, 8855376, 28572286, 3005164},
3535             {26287124, 4821776, 25476601, -4145903, -3764513, -15788984,
3536              -18008582, 1182479, -26094821, -13079595},
3537             {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192,
3538              -21876275, -13982627, 32208683, -1198248},
3539         },
3540         {
3541             {-16657702, 2817643, -10286362, 14811298, 6024667, 13349505,
3542              -27315504, -10497842, -27672585, -11539858},
3543             {15941029, -9405932, -21367050, 8062055, 31876073, -238629,
3544              -15278393, -1444429, 15397331, -4130193},
3545             {8934485, -13485467, -23286397, -13423241, -32446090, 14047986,
3546              31170398, -1441021, -27505566, 15087184},
3547         },
3548         {
3549             {-18357243, -2156491, 24524913, -16677868, 15520427, -6360776,
3550              -15502406, 11461896, 16788528, -5868942},
3551             {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433,
3552              -3770287, -10323320, 31322514, -11615635},
3553             {21426655, -5650218, -13648287, -5347537, -28812189, -4920970,
3554              -18275391, -14621414, 13040862, -12112948},
3555         },
3556         {
3557             {11293895, 12478086, -27136401, 15083750, -29307421, 14748872,
3558              14555558, -13417103, 1613711, 4896935},
3559             {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460,
3560              2825960, -4897045, -23971776, -11267415},
3561             {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618,
3562              20615400, 12405433, -23753030, -8436416},
3563         },
3564         {
3565             {-7091295, 12556208, -20191352, 9025187, -17072479, 4333801,
3566              4378436, 2432030, 23097949, -566018},
3567             {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264,
3568              10103221, -18512313, 2424778},
3569             {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
3570              1344109, -3642553, 12412659},
3571         },
3572         {
3573             {-24001791, 7690286, 14929416, -168257, -32210835, -13412986,
3574              24162697, -15326504, -3141501, 11179385},
3575             {18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
3576              -6001441, -1486897, -18684645, -11443503},
3577             {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
3578              13403813, 11052904, 5219329},
3579         },
3580     },
3581     {
3582         {
3583             {20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
3584              31186971, -3973730, 9014762, -8579056},
3585             {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
3586              -33102500, 9160280, 8473550, -3256838},
3587             {24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
3588              -7689309, -16335821, -24568481, 11788948},
3589         },
3590         {
3591             {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
3592              -20037437, 10410733, -24568470, -1458691},
3593             {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
3594              11871841, -12505194, -18513325, 8464118},
3595             {-23400612, 8348507, -14585951, -861714, -3950205, -6373419,
3596              14325289, 8628612, 33313881, -8370517},
3597         },
3598         {
3599             {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
3600              -24805667, -10236854, -8940735, -5818269},
3601             {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
3602              15989197, -12838188, 28358192, -4253904},
3603             {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
3604              -16637684, 4072016, -5351664, 5596589},
3605         },
3606         {
3607             {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
3608              29266239, 2557221, 1768301, 15373193},
3609             {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
3610              -4504991, -24660491, 3442910},
3611             {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
3612              22597931, 7176455, -18585478, 13365930},
3613         },
3614         {
3615             {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
3616              -8570186, -9689599, -3031667},
3617             {25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
3618              683793, -11823784, 15723479, -15163481},
3619             {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
3620              11879682, 5400171, 519526, -1235876},
3621         },
3622         {
3623             {22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
3624              -20353881, 7315967, 16648397, 7605640},
3625             {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
3626              23994942, -5281555, -9468848, 4763278},
3627             {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
3628              31088447, -7764523, -11356529, 728112},
3629         },
3630         {
3631             {26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
3632              -4273545, -12555558, -29365436, -5498272},
3633             {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
3634              12327945, 10750447, 10014012},
3635             {-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
3636              -27481051, -666732, 3424691, 7540221},
3637         },
3638         {
3639             {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
3640              -16317219, -9244265, 15258046},
3641             {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
3642              2711395, 1062915, -5136345},
3643             {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
3644              -6066489, 12194497, 32960380, 1459310},
3645         },
3646     },
3647     {
3648         {
3649             {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
3650              -6101885, 18638003, -11174937},
3651             {31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
3652              9012486, -7584354, -6643087, -5442636},
3653             {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
3654              9677543, -32294889, -6456008},
3655         },
3656         {
3657             {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
3658              -7839692, -7852844, -8138429},
3659             {-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
3660              -27333451, 10754588, -9431476, 5203576},
3661             {31834314, 14135496, -770007, 5159118, 20917671, -16768096,
3662              -7467973, -7337524, 31809243, 7347066},
3663         },
3664         {
3665             {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
3666              19797970, -12211255, 15192876, -2087490},
3667             {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
3668              10609330, 12694420, 33473243, -13382104},
3669             {33184999, 11180355, 15832085, -11385430, -1633671, 225884,
3670              15089336, -11023903, -6135662, 14480053},
3671         },
3672         {
3673             {31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
3674              5496208, 13685227, 27595050, 8737275},
3675             {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
3676              -31008351, -12610604, 26498114, 66511},
3677             {22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
3678              30540766, -4286747, -13327787, -7515095},
3679         },
3680         {
3681             {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
3682              8205540, 13585437, -17127465, 15115439},
3683             {23711543, -672915, 31206561, -8362711, 6164647, -9709987,
3684              -33535882, -1426096, 8236921, 16492939},
3685             {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
3686              19574902, 10071562, 6708380, -6222424},
3687         },
3688         {
3689             {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
3690              9328700, 29955601, -11678310},
3691             {3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
3692              -25892142, -12635595, -9917575, 6216608},
3693             {-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
3694              24822830, -6146567, -26767480, 7525079},
3695         },
3696         {
3697             {-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
3698              -910336, -2782495, -19386633, 11994101},
3699             {21691500, -13624626, -641331, -14367021, 3285881, -3483596,
3700              -25064666, 9718258, -7477437, 13381418},
3701             {18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
3702              23111648, -6375247, 28535282, 15779576},
3703         },
3704         {
3705             {30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
3706              -14068454, 12021730, 9955285, -16303356},
3707             {9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
3708              -18426029, 9924399, 20194861, 13380996},
3709             {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
3710              -1984914, 15707771, 26342023, 10146099},
3711         },
3712     },
3713     {
3714         {
3715             {-26016874, -219943, 21339191, -41388, 19745256, -2878700,
3716              -29637280, 2227040, 21612326, -545728},
3717             {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
3718              25764461, 12243797, -20856566, 11649658},
3719             {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
3720              6114064, 33514190, 2333242},
3721         },
3722         {
3723             {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
3724              -6679750, -12670638, 24350578, -13450001},
3725             {-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
3726              -31536088, -10406836, 8317860, 12352766},
3727             {18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
3728              -23552096, -2287550, 20712163, 6719373},
3729         },
3730         {
3731             {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
3732              -3763210, 26224235, -3297458},
3733             {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
3734              21728352, 9493610, 18620611, -16428628},
3735             {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
3736              -5269471, -9725556, -30701573, -16479657},
3737         },
3738         {
3739             {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
3740              12248509, -5240639, 13735342, 1934062},
3741             {25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
3742              -15136294, -3765346, -21277997, 5473616},
3743             {31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
3744              -7125085, 12469656, 29111212, -5451014},
3745         },
3746         {
3747             {24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
3748              24367466, 6388839, -10295587, 452383},
3749             {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
3750              -24236251, -5915248, 15766062, 8407814},
3751             {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
3752              -8917023, -4388953, -8067909, 2276718},
3753         },
3754         {
3755             {30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
3756              -23827587, 5096219, 22740376, -7303417},
3757             {2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
3758              24051124, 13742383, -15637599, 13295222},
3759             {33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
3760              -17720195, -4612972, -4451357, -14669444},
3761         },
3762         {
3763             {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
3764              -2469266, -4141880, 7770569, 9620597},
3765             {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
3766              -1694323, -33502340, -14767970},
3767             {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
3768              1220118, 30494170, -11440799},
3769         },
3770         {
3771             {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
3772              -26739026, 926050, -1684339, -13333647},
3773             {13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
3774              9021034, 9078865, 3353509, 4033511},
3775             {-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
3776              23161163, 8839127, 27485041, 7356032},
3777         },
3778     },
3779     {
3780         {
3781             {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
3782              2625015, 28431036, -16771834},
3783             {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
3784              -22545972, 14150565, 15970762, 4099461},
3785             {29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
3786              13617293, -9937143, 11465739, 8317062},
3787         },
3788         {
3789             {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
3790              14898637, 3848455, 20969334, -5157516},
3791             {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
3792              -21610826, -3649888, 11177095, 14989547},
3793             {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
3794              13515641, 2581286, -28487508, 9930240},
3795         },
3796         {
3797             {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
3798              18345767, -13403753, 16291481, -5314038},
3799             {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
3800              6957617, 4368891, 9788741},
3801             {16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
3802              -21722536, -8613148, 16250552, -11111103},
3803         },
3804         {
3805             {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
3806              10604807, -30190403, 4782747},
3807             {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
3808              -9981571, 4383045, 22546403, 437323},
3809             {31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
3810              27343084, 2786261, -30633590, -14097016},
3811         },
3812         {
3813             {-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
3814              -19690631, 2355319, -19284671, -6114373},
3815             {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
3816              18952177, 15496498, -29380133, 11754228},
3817             {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
3818              7141596, 11724556, 22761615, -10134141},
3819         },
3820         {
3821             {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
3822              -28741185, -12227393, 32851222, 11717399},
3823             {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
3824              31474879, 3483633, -1193175, -4030831},
3825             {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
3826              33142652, 6546660, -19985279, -3948376},
3827         },
3828         {
3829             {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
3830              -8537131, -12833048, -30772034, -15486313},
3831             {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
3832              -31135347, -16049879, 10928917, 3011958},
3833             {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
3834              -30831056, -12805180, 18008031, 10258577},
3835         },
3836         {
3837             {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
3838              -1853465, 1367120, 25127874, 6671743},
3839             {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
3840              21382910, 11042292, 25838796, 4642684},
3841             {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
3842              30468147, -13900640, 18423289, 4177476},
3843         },
3844     },
3845 };
3846
3847 static uint8_t negative(signed char b) {
3848   uint32_t x = b;
3849   x >>= 31; /* 1: yes; 0: no */
3850   return x;
3851 }
3852
3853 static void table_select(ge_precomp *t, int pos, signed char b) {
3854   ge_precomp minust;
3855   uint8_t bnegative = negative(b);
3856   uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
3857
3858   ge_precomp_0(t);
3859   cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
3860   cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
3861   cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
3862   cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
3863   cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
3864   cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
3865   cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
3866   cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
3867   fe_copy(minust.yplusx, t->yminusx);
3868   fe_copy(minust.yminusx, t->yplusx);
3869   fe_neg(minust.xy2d, t->xy2d);
3870   cmov(t, &minust, bnegative);
3871 }
3872
3873 /* h = a * B
3874  * where a = a[0]+256*a[1]+...+256^31 a[31]
3875  * B is the Ed25519 base point (x,4/5) with x positive.
3876  *
3877  * Preconditions:
3878  *   a[31] <= 127 */
3879 static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
3880   signed char e[64];
3881   signed char carry;
3882   ge_p1p1 r;
3883   ge_p2 s;
3884   ge_precomp t;
3885   int i;
3886
3887   for (i = 0; i < 32; ++i) {
3888     e[2 * i + 0] = (a[i] >> 0) & 15;
3889     e[2 * i + 1] = (a[i] >> 4) & 15;
3890   }
3891   /* each e[i] is between 0 and 15 */
3892   /* e[63] is between 0 and 7 */
3893
3894   carry = 0;
3895   for (i = 0; i < 63; ++i) {
3896     e[i] += carry;
3897     carry = e[i] + 8;
3898     carry >>= 4;
3899     e[i] -= carry << 4;
3900   }
3901   e[63] += carry;
3902   /* each e[i] is between -8 and 8 */
3903
3904   ge_p3_0(h);
3905   for (i = 1; i < 64; i += 2) {
3906     table_select(&t, i / 2, e[i]);
3907     ge_madd(&r, h, &t);
3908     ge_p1p1_to_p3(h, &r);
3909   }
3910
3911   ge_p3_dbl(&r, h);
3912   ge_p1p1_to_p2(&s, &r);
3913   ge_p2_dbl(&r, &s);
3914   ge_p1p1_to_p2(&s, &r);
3915   ge_p2_dbl(&r, &s);
3916   ge_p1p1_to_p2(&s, &r);
3917   ge_p2_dbl(&r, &s);
3918   ge_p1p1_to_p3(h, &r);
3919
3920   for (i = 0; i < 64; i += 2) {
3921     table_select(&t, i / 2, e[i]);
3922     ge_madd(&r, h, &t);
3923     ge_p1p1_to_p3(h, &r);
3924   }
3925
3926   OPENSSL_cleanse(e, sizeof(e));
3927 }
3928
3929 #if !defined(BASE_2_51_IMPLEMENTED)
3930 /* Replace (f,g) with (g,f) if b == 1;
3931  * replace (f,g) with (f,g) if b == 0.
3932  *
3933  * Preconditions: b in {0,1}. */
3934 static void fe_cswap(fe f, fe g, unsigned int b) {
3935   size_t i;
3936   b = 0-b;
3937   for (i = 0; i < 10; i++) {
3938     int32_t x = f[i] ^ g[i];
3939     x &= b;
3940     f[i] ^= x;
3941     g[i] ^= x;
3942   }
3943 }
3944
3945 /* h = f * 121666
3946  * Can overlap h with f.
3947  *
3948  * Preconditions:
3949  *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
3950  *
3951  * Postconditions:
3952  *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
3953 static void fe_mul121666(fe h, fe f) {
3954   int32_t f0 = f[0];
3955   int32_t f1 = f[1];
3956   int32_t f2 = f[2];
3957   int32_t f3 = f[3];
3958   int32_t f4 = f[4];
3959   int32_t f5 = f[5];
3960   int32_t f6 = f[6];
3961   int32_t f7 = f[7];
3962   int32_t f8 = f[8];
3963   int32_t f9 = f[9];
3964   int64_t h0 = f0 * (int64_t) 121666;
3965   int64_t h1 = f1 * (int64_t) 121666;
3966   int64_t h2 = f2 * (int64_t) 121666;
3967   int64_t h3 = f3 * (int64_t) 121666;
3968   int64_t h4 = f4 * (int64_t) 121666;
3969   int64_t h5 = f5 * (int64_t) 121666;
3970   int64_t h6 = f6 * (int64_t) 121666;
3971   int64_t h7 = f7 * (int64_t) 121666;
3972   int64_t h8 = f8 * (int64_t) 121666;
3973   int64_t h9 = f9 * (int64_t) 121666;
3974   int64_t carry0;
3975   int64_t carry1;
3976   int64_t carry2;
3977   int64_t carry3;
3978   int64_t carry4;
3979   int64_t carry5;
3980   int64_t carry6;
3981   int64_t carry7;
3982   int64_t carry8;
3983   int64_t carry9;
3984
3985   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
3986   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
3987   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
3988   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
3989   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
3990
3991   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
3992   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
3993   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
3994   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
3995   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
3996
3997   h[0] = (int32_t)h0;
3998   h[1] = (int32_t)h1;
3999   h[2] = (int32_t)h2;
4000   h[3] = (int32_t)h3;
4001   h[4] = (int32_t)h4;
4002   h[5] = (int32_t)h5;
4003   h[6] = (int32_t)h6;
4004   h[7] = (int32_t)h7;
4005   h[8] = (int32_t)h8;
4006   h[9] = (int32_t)h9;
4007 }
4008
4009 static void x25519_scalar_mult_generic(uint8_t out[32],
4010                                        const uint8_t scalar[32],
4011                                        const uint8_t point[32]) {
4012   fe x1, x2, z2, x3, z3, tmp0, tmp1;
4013   uint8_t e[32];
4014   unsigned swap = 0;
4015   int pos;
4016
4017   memcpy(e, scalar, 32);
4018   e[0] &= 248;
4019   e[31] &= 127;
4020   e[31] |= 64;
4021   fe_frombytes(x1, point);
4022   fe_1(x2);
4023   fe_0(z2);
4024   fe_copy(x3, x1);
4025   fe_1(z3);
4026
4027   for (pos = 254; pos >= 0; --pos) {
4028     unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4029     swap ^= b;
4030     fe_cswap(x2, x3, swap);
4031     fe_cswap(z2, z3, swap);
4032     swap = b;
4033     fe_sub(tmp0, x3, z3);
4034     fe_sub(tmp1, x2, z2);
4035     fe_add(x2, x2, z2);
4036     fe_add(z2, x3, z3);
4037     fe_mul(z3, tmp0, x2);
4038     fe_mul(z2, z2, tmp1);
4039     fe_sq(tmp0, tmp1);
4040     fe_sq(tmp1, x2);
4041     fe_add(x3, z3, z2);
4042     fe_sub(z2, z3, z2);
4043     fe_mul(x2, tmp1, tmp0);
4044     fe_sub(tmp1, tmp1, tmp0);
4045     fe_sq(z2, z2);
4046     fe_mul121666(z3, tmp1);
4047     fe_sq(x3, x3);
4048     fe_add(tmp0, tmp0, z3);
4049     fe_mul(z3, x1, z2);
4050     fe_mul(z2, tmp1, tmp0);
4051   }
4052   fe_cswap(x2, x3, swap);
4053   fe_cswap(z2, z3, swap);
4054
4055   fe_invert(z2, z2);
4056   fe_mul(x2, x2, z2);
4057   fe_tobytes(out, x2);
4058
4059   OPENSSL_cleanse(e, sizeof(e));
4060 }
4061
4062 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4063                                const uint8_t point[32]) {
4064   x25519_scalar_mult_generic(out, scalar, point);
4065 }
4066 #endif
4067
4068 static void slide(signed char *r, const uint8_t *a) {
4069   int i;
4070   int b;
4071   int k;
4072
4073   for (i = 0; i < 256; ++i) {
4074     r[i] = 1 & (a[i >> 3] >> (i & 7));
4075   }
4076
4077   for (i = 0; i < 256; ++i) {
4078     if (r[i]) {
4079       for (b = 1; b <= 6 && i + b < 256; ++b) {
4080         if (r[i + b]) {
4081           if (r[i] + (r[i + b] << b) <= 15) {
4082             r[i] += r[i + b] << b;
4083             r[i + b] = 0;
4084           } else if (r[i] - (r[i + b] << b) >= -15) {
4085             r[i] -= r[i + b] << b;
4086             for (k = i + b; k < 256; ++k) {
4087               if (!r[k]) {
4088                 r[k] = 1;
4089                 break;
4090               }
4091               r[k] = 0;
4092             }
4093           } else {
4094             break;
4095           }
4096         }
4097       }
4098     }
4099   }
4100 }
4101
4102 static const ge_precomp Bi[8] = {
4103     {
4104         {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4105          -11754271, -6079156, 2047605},
4106         {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4107          5043384, 19500929, -15469378},
4108         {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4109          11864899, -24514362, -4438546},
4110     },
4111     {
4112         {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4113          -14772189, 28944400, -1550024},
4114         {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4115          -11775962, 7689662, 11199574},
4116         {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4117          10017326, -17749093, -9920357},
4118     },
4119     {
4120         {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4121          14515107, -15438304, 10819380},
4122         {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4123          12483688, -12668491, 5581306},
4124         {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4125          13850243, -23678021, -15815942},
4126     },
4127     {
4128         {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4129          5230134, -23952439, -15175766},
4130         {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4131          16520125, 30598449, 7715701},
4132         {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4133          1370708, 29794553, -1409300},
4134     },
4135     {
4136         {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4137          -1361450, -13062696, 13821877},
4138         {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4139          -7212327, 18853322, -14220951},
4140         {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4141          -10431137, 2207753, -3209784},
4142     },
4143     {
4144         {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4145          -663000, -31111463, -16132436},
4146         {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4147          15725684, 171356, 6466918},
4148         {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4149          -14088058, -30714912, 16193877},
4150     },
4151     {
4152         {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4153          4729455, -18074513, 9256800},
4154         {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4155          9761698, -19827198, 630305},
4156         {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4157          -15960994, -2449256, -14291300},
4158     },
4159     {
4160         {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4161          15033784, 25105118, -7894876},
4162         {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4163          1573892, -2625887, 2198790, -15804619},
4164         {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4165          -16236442, -32461234, -12290683},
4166     },
4167 };
4168
4169 /* r = a * A + b * B
4170  * where a = a[0]+256*a[1]+...+256^31 a[31].
4171  * and b = b[0]+256*b[1]+...+256^31 b[31].
4172  * B is the Ed25519 base point (x,4/5) with x positive. */
4173 static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
4174                                          const ge_p3 *A, const uint8_t *b) {
4175   signed char aslide[256];
4176   signed char bslide[256];
4177   ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4178   ge_p1p1 t;
4179   ge_p3 u;
4180   ge_p3 A2;
4181   int i;
4182
4183   slide(aslide, a);
4184   slide(bslide, b);
4185
4186   ge_p3_to_cached(&Ai[0], A);
4187   ge_p3_dbl(&t, A);
4188   ge_p1p1_to_p3(&A2, &t);
4189   ge_add(&t, &A2, &Ai[0]);
4190   ge_p1p1_to_p3(&u, &t);
4191   ge_p3_to_cached(&Ai[1], &u);
4192   ge_add(&t, &A2, &Ai[1]);
4193   ge_p1p1_to_p3(&u, &t);
4194   ge_p3_to_cached(&Ai[2], &u);
4195   ge_add(&t, &A2, &Ai[2]);
4196   ge_p1p1_to_p3(&u, &t);
4197   ge_p3_to_cached(&Ai[3], &u);
4198   ge_add(&t, &A2, &Ai[3]);
4199   ge_p1p1_to_p3(&u, &t);
4200   ge_p3_to_cached(&Ai[4], &u);
4201   ge_add(&t, &A2, &Ai[4]);
4202   ge_p1p1_to_p3(&u, &t);
4203   ge_p3_to_cached(&Ai[5], &u);
4204   ge_add(&t, &A2, &Ai[5]);
4205   ge_p1p1_to_p3(&u, &t);
4206   ge_p3_to_cached(&Ai[6], &u);
4207   ge_add(&t, &A2, &Ai[6]);
4208   ge_p1p1_to_p3(&u, &t);
4209   ge_p3_to_cached(&Ai[7], &u);
4210
4211   ge_p2_0(r);
4212
4213   for (i = 255; i >= 0; --i) {
4214     if (aslide[i] || bslide[i]) {
4215       break;
4216     }
4217   }
4218
4219   for (; i >= 0; --i) {
4220     ge_p2_dbl(&t, r);
4221
4222     if (aslide[i] > 0) {
4223       ge_p1p1_to_p3(&u, &t);
4224       ge_add(&t, &u, &Ai[aslide[i] / 2]);
4225     } else if (aslide[i] < 0) {
4226       ge_p1p1_to_p3(&u, &t);
4227       ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4228     }
4229
4230     if (bslide[i] > 0) {
4231       ge_p1p1_to_p3(&u, &t);
4232       ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4233     } else if (bslide[i] < 0) {
4234       ge_p1p1_to_p3(&u, &t);
4235       ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4236     }
4237
4238     ge_p1p1_to_p2(r, &t);
4239   }
4240 }
4241
4242 /* The set of scalars is \Z/l
4243  * where l = 2^252 + 27742317777372353535851937790883648493. */
4244
4245 /* Input:
4246  *   s[0]+256*s[1]+...+256^63*s[63] = s
4247  *
4248  * Output:
4249  *   s[0]+256*s[1]+...+256^31*s[31] = s mod l
4250  *   where l = 2^252 + 27742317777372353535851937790883648493.
4251  *   Overwrites s in place. */
4252 static void x25519_sc_reduce(uint8_t *s) {
4253   int64_t s0 = 2097151 & load_3(s);
4254   int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
4255   int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
4256   int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
4257   int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
4258   int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
4259   int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
4260   int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
4261   int64_t s8 = 2097151 & load_3(s + 21);
4262   int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
4263   int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
4264   int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
4265   int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
4266   int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
4267   int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
4268   int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
4269   int64_t s16 = 2097151 & load_3(s + 42);
4270   int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
4271   int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
4272   int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
4273   int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
4274   int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
4275   int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
4276   int64_t s23 = (load_4(s + 60) >> 3);
4277   int64_t carry0;
4278   int64_t carry1;
4279   int64_t carry2;
4280   int64_t carry3;
4281   int64_t carry4;
4282   int64_t carry5;
4283   int64_t carry6;
4284   int64_t carry7;
4285   int64_t carry8;
4286   int64_t carry9;
4287   int64_t carry10;
4288   int64_t carry11;
4289   int64_t carry12;
4290   int64_t carry13;
4291   int64_t carry14;
4292   int64_t carry15;
4293   int64_t carry16;
4294
4295   s11 += s23 * 666643;
4296   s12 += s23 * 470296;
4297   s13 += s23 * 654183;
4298   s14 -= s23 * 997805;
4299   s15 += s23 * 136657;
4300   s16 -= s23 * 683901;
4301   s23 = 0;
4302
4303   s10 += s22 * 666643;
4304   s11 += s22 * 470296;
4305   s12 += s22 * 654183;
4306   s13 -= s22 * 997805;
4307   s14 += s22 * 136657;
4308   s15 -= s22 * 683901;
4309   s22 = 0;
4310
4311   s9 += s21 * 666643;
4312   s10 += s21 * 470296;
4313   s11 += s21 * 654183;
4314   s12 -= s21 * 997805;
4315   s13 += s21 * 136657;
4316   s14 -= s21 * 683901;
4317   s21 = 0;
4318
4319   s8 += s20 * 666643;
4320   s9 += s20 * 470296;
4321   s10 += s20 * 654183;
4322   s11 -= s20 * 997805;
4323   s12 += s20 * 136657;
4324   s13 -= s20 * 683901;
4325   s20 = 0;
4326
4327   s7 += s19 * 666643;
4328   s8 += s19 * 470296;
4329   s9 += s19 * 654183;
4330   s10 -= s19 * 997805;
4331   s11 += s19 * 136657;
4332   s12 -= s19 * 683901;
4333   s19 = 0;
4334
4335   s6 += s18 * 666643;
4336   s7 += s18 * 470296;
4337   s8 += s18 * 654183;
4338   s9 -= s18 * 997805;
4339   s10 += s18 * 136657;
4340   s11 -= s18 * 683901;
4341   s18 = 0;
4342
4343   carry6 = (s6 + (1 << 20)) >> 21;
4344   s7 += carry6;
4345   s6 -= carry6 * (1 << 21);
4346   carry8 = (s8 + (1 << 20)) >> 21;
4347   s9 += carry8;
4348   s8 -= carry8 * (1 << 21);
4349   carry10 = (s10 + (1 << 20)) >> 21;
4350   s11 += carry10;
4351   s10 -= carry10 * (1 << 21);
4352   carry12 = (s12 + (1 << 20)) >> 21;
4353   s13 += carry12;
4354   s12 -= carry12 * (1 << 21);
4355   carry14 = (s14 + (1 << 20)) >> 21;
4356   s15 += carry14;
4357   s14 -= carry14 * (1 << 21);
4358   carry16 = (s16 + (1 << 20)) >> 21;
4359   s17 += carry16;
4360   s16 -= carry16 * (1 << 21);
4361
4362   carry7 = (s7 + (1 << 20)) >> 21;
4363   s8 += carry7;
4364   s7 -= carry7 * (1 << 21);
4365   carry9 = (s9 + (1 << 20)) >> 21;
4366   s10 += carry9;
4367   s9 -= carry9 * (1 << 21);
4368   carry11 = (s11 + (1 << 20)) >> 21;
4369   s12 += carry11;
4370   s11 -= carry11 * (1 << 21);
4371   carry13 = (s13 + (1 << 20)) >> 21;
4372   s14 += carry13;
4373   s13 -= carry13 * (1 << 21);
4374   carry15 = (s15 + (1 << 20)) >> 21;
4375   s16 += carry15;
4376   s15 -= carry15 * (1 << 21);
4377
4378   s5 += s17 * 666643;
4379   s6 += s17 * 470296;
4380   s7 += s17 * 654183;
4381   s8 -= s17 * 997805;
4382   s9 += s17 * 136657;
4383   s10 -= s17 * 683901;
4384   s17 = 0;
4385
4386   s4 += s16 * 666643;
4387   s5 += s16 * 470296;
4388   s6 += s16 * 654183;
4389   s7 -= s16 * 997805;
4390   s8 += s16 * 136657;
4391   s9 -= s16 * 683901;
4392   s16 = 0;
4393
4394   s3 += s15 * 666643;
4395   s4 += s15 * 470296;
4396   s5 += s15 * 654183;
4397   s6 -= s15 * 997805;
4398   s7 += s15 * 136657;
4399   s8 -= s15 * 683901;
4400   s15 = 0;
4401
4402   s2 += s14 * 666643;
4403   s3 += s14 * 470296;
4404   s4 += s14 * 654183;
4405   s5 -= s14 * 997805;
4406   s6 += s14 * 136657;
4407   s7 -= s14 * 683901;
4408   s14 = 0;
4409
4410   s1 += s13 * 666643;
4411   s2 += s13 * 470296;
4412   s3 += s13 * 654183;
4413   s4 -= s13 * 997805;
4414   s5 += s13 * 136657;
4415   s6 -= s13 * 683901;
4416   s13 = 0;
4417
4418   s0 += s12 * 666643;
4419   s1 += s12 * 470296;
4420   s2 += s12 * 654183;
4421   s3 -= s12 * 997805;
4422   s4 += s12 * 136657;
4423   s5 -= s12 * 683901;
4424   s12 = 0;
4425
4426   carry0 = (s0 + (1 << 20)) >> 21;
4427   s1 += carry0;
4428   s0 -= carry0 * (1 << 21);
4429   carry2 = (s2 + (1 << 20)) >> 21;
4430   s3 += carry2;
4431   s2 -= carry2 * (1 << 21);
4432   carry4 = (s4 + (1 << 20)) >> 21;
4433   s5 += carry4;
4434   s4 -= carry4 * (1 << 21);
4435   carry6 = (s6 + (1 << 20)) >> 21;
4436   s7 += carry6;
4437   s6 -= carry6 * (1 << 21);
4438   carry8 = (s8 + (1 << 20)) >> 21;
4439   s9 += carry8;
4440   s8 -= carry8 * (1 << 21);
4441   carry10 = (s10 + (1 << 20)) >> 21;
4442   s11 += carry10;
4443   s10 -= carry10 * (1 << 21);
4444
4445   carry1 = (s1 + (1 << 20)) >> 21;
4446   s2 += carry1;
4447   s1 -= carry1 * (1 << 21);
4448   carry3 = (s3 + (1 << 20)) >> 21;
4449   s4 += carry3;
4450   s3 -= carry3 * (1 << 21);
4451   carry5 = (s5 + (1 << 20)) >> 21;
4452   s6 += carry5;
4453   s5 -= carry5 * (1 << 21);
4454   carry7 = (s7 + (1 << 20)) >> 21;
4455   s8 += carry7;
4456   s7 -= carry7 * (1 << 21);
4457   carry9 = (s9 + (1 << 20)) >> 21;
4458   s10 += carry9;
4459   s9 -= carry9 * (1 << 21);
4460   carry11 = (s11 + (1 << 20)) >> 21;
4461   s12 += carry11;
4462   s11 -= carry11 * (1 << 21);
4463
4464   s0 += s12 * 666643;
4465   s1 += s12 * 470296;
4466   s2 += s12 * 654183;
4467   s3 -= s12 * 997805;
4468   s4 += s12 * 136657;
4469   s5 -= s12 * 683901;
4470   s12 = 0;
4471
4472   carry0 = s0 >> 21;
4473   s1 += carry0;
4474   s0 -= carry0 * (1 << 21);
4475   carry1 = s1 >> 21;
4476   s2 += carry1;
4477   s1 -= carry1 * (1 << 21);
4478   carry2 = s2 >> 21;
4479   s3 += carry2;
4480   s2 -= carry2 * (1 << 21);
4481   carry3 = s3 >> 21;
4482   s4 += carry3;
4483   s3 -= carry3 * (1 << 21);
4484   carry4 = s4 >> 21;
4485   s5 += carry4;
4486   s4 -= carry4 * (1 << 21);
4487   carry5 = s5 >> 21;
4488   s6 += carry5;
4489   s5 -= carry5 * (1 << 21);
4490   carry6 = s6 >> 21;
4491   s7 += carry6;
4492   s6 -= carry6 * (1 << 21);
4493   carry7 = s7 >> 21;
4494   s8 += carry7;
4495   s7 -= carry7 * (1 << 21);
4496   carry8 = s8 >> 21;
4497   s9 += carry8;
4498   s8 -= carry8 * (1 << 21);
4499   carry9 = s9 >> 21;
4500   s10 += carry9;
4501   s9 -= carry9 * (1 << 21);
4502   carry10 = s10 >> 21;
4503   s11 += carry10;
4504   s10 -= carry10 * (1 << 21);
4505   carry11 = s11 >> 21;
4506   s12 += carry11;
4507   s11 -= carry11 * (1 << 21);
4508
4509   s0 += s12 * 666643;
4510   s1 += s12 * 470296;
4511   s2 += s12 * 654183;
4512   s3 -= s12 * 997805;
4513   s4 += s12 * 136657;
4514   s5 -= s12 * 683901;
4515   s12 = 0;
4516
4517   carry0 = s0 >> 21;
4518   s1 += carry0;
4519   s0 -= carry0 * (1 << 21);
4520   carry1 = s1 >> 21;
4521   s2 += carry1;
4522   s1 -= carry1 * (1 << 21);
4523   carry2 = s2 >> 21;
4524   s3 += carry2;
4525   s2 -= carry2 * (1 << 21);
4526   carry3 = s3 >> 21;
4527   s4 += carry3;
4528   s3 -= carry3 * (1 << 21);
4529   carry4 = s4 >> 21;
4530   s5 += carry4;
4531   s4 -= carry4 * (1 << 21);
4532   carry5 = s5 >> 21;
4533   s6 += carry5;
4534   s5 -= carry5 * (1 << 21);
4535   carry6 = s6 >> 21;
4536   s7 += carry6;
4537   s6 -= carry6 * (1 << 21);
4538   carry7 = s7 >> 21;
4539   s8 += carry7;
4540   s7 -= carry7 * (1 << 21);
4541   carry8 = s8 >> 21;
4542   s9 += carry8;
4543   s8 -= carry8 * (1 << 21);
4544   carry9 = s9 >> 21;
4545   s10 += carry9;
4546   s9 -= carry9 * (1 << 21);
4547   carry10 = s10 >> 21;
4548   s11 += carry10;
4549   s10 -= carry10 * (1 << 21);
4550
4551   s[0] = (uint8_t)(s0 >> 0);
4552   s[1] = (uint8_t)(s0 >> 8);
4553   s[2] = (uint8_t)((s0 >> 16) | (s1 << 5));
4554   s[3] = (uint8_t)(s1 >> 3);
4555   s[4] = (uint8_t)(s1 >> 11);
4556   s[5] = (uint8_t)((s1 >> 19) | (s2 << 2));
4557   s[6] = (uint8_t)(s2 >> 6);
4558   s[7] = (uint8_t)((s2 >> 14) | (s3 << 7));
4559   s[8] = (uint8_t)(s3 >> 1);
4560   s[9] = (uint8_t)(s3 >> 9);
4561   s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
4562   s[11] = (uint8_t)(s4 >> 4);
4563   s[12] = (uint8_t)(s4 >> 12);
4564   s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
4565   s[14] = (uint8_t)(s5 >> 7);
4566   s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
4567   s[16] = (uint8_t)(s6 >> 2);
4568   s[17] = (uint8_t)(s6 >> 10);
4569   s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
4570   s[19] = (uint8_t)(s7 >> 5);
4571   s[20] = (uint8_t)(s7 >> 13);
4572   s[21] = (uint8_t)(s8 >> 0);
4573   s[22] = (uint8_t)(s8 >> 8);
4574   s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
4575   s[24] = (uint8_t)(s9 >> 3);
4576   s[25] = (uint8_t)(s9 >> 11);
4577   s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
4578   s[27] = (uint8_t)(s10 >> 6);
4579   s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
4580   s[29] = (uint8_t)(s11 >> 1);
4581   s[30] = (uint8_t)(s11 >> 9);
4582   s[31] = (uint8_t)(s11 >> 17);
4583 }
4584
4585 /* Input:
4586  *   a[0]+256*a[1]+...+256^31*a[31] = a
4587  *   b[0]+256*b[1]+...+256^31*b[31] = b
4588  *   c[0]+256*c[1]+...+256^31*c[31] = c
4589  *
4590  * Output:
4591  *   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
4592  *   where l = 2^252 + 27742317777372353535851937790883648493. */
4593 static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
4594                       const uint8_t *c) {
4595   int64_t a0 = 2097151 & load_3(a);
4596   int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
4597   int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
4598   int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
4599   int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
4600   int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
4601   int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
4602   int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
4603   int64_t a8 = 2097151 & load_3(a + 21);
4604   int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
4605   int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
4606   int64_t a11 = (load_4(a + 28) >> 7);
4607   int64_t b0 = 2097151 & load_3(b);
4608   int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
4609   int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
4610   int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
4611   int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
4612   int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
4613   int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
4614   int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
4615   int64_t b8 = 2097151 & load_3(b + 21);
4616   int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
4617   int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
4618   int64_t b11 = (load_4(b + 28) >> 7);
4619   int64_t c0 = 2097151 & load_3(c);
4620   int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
4621   int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
4622   int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
4623   int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
4624   int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
4625   int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
4626   int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
4627   int64_t c8 = 2097151 & load_3(c + 21);
4628   int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
4629   int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
4630   int64_t c11 = (load_4(c + 28) >> 7);
4631   int64_t s0;
4632   int64_t s1;
4633   int64_t s2;
4634   int64_t s3;
4635   int64_t s4;
4636   int64_t s5;
4637   int64_t s6;
4638   int64_t s7;
4639   int64_t s8;
4640   int64_t s9;
4641   int64_t s10;
4642   int64_t s11;
4643   int64_t s12;
4644   int64_t s13;
4645   int64_t s14;
4646   int64_t s15;
4647   int64_t s16;
4648   int64_t s17;
4649   int64_t s18;
4650   int64_t s19;
4651   int64_t s20;
4652   int64_t s21;
4653   int64_t s22;
4654   int64_t s23;
4655   int64_t carry0;
4656   int64_t carry1;
4657   int64_t carry2;
4658   int64_t carry3;
4659   int64_t carry4;
4660   int64_t carry5;
4661   int64_t carry6;
4662   int64_t carry7;
4663   int64_t carry8;
4664   int64_t carry9;
4665   int64_t carry10;
4666   int64_t carry11;
4667   int64_t carry12;
4668   int64_t carry13;
4669   int64_t carry14;
4670   int64_t carry15;
4671   int64_t carry16;
4672   int64_t carry17;
4673   int64_t carry18;
4674   int64_t carry19;
4675   int64_t carry20;
4676   int64_t carry21;
4677   int64_t carry22;
4678
4679   s0 = c0 + a0 * b0;
4680   s1 = c1 + a0 * b1 + a1 * b0;
4681   s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
4682   s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
4683   s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
4684   s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
4685   s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
4686   s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
4687        a6 * b1 + a7 * b0;
4688   s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
4689        a6 * b2 + a7 * b1 + a8 * b0;
4690   s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
4691        a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
4692   s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
4693         a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
4694   s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
4695         a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
4696   s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
4697         a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
4698   s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
4699         a9 * b4 + a10 * b3 + a11 * b2;
4700   s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
4701         a10 * b4 + a11 * b3;
4702   s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
4703         a11 * b4;
4704   s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
4705   s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
4706   s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
4707   s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
4708   s20 = a9 * b11 + a10 * b10 + a11 * b9;
4709   s21 = a10 * b11 + a11 * b10;
4710   s22 = a11 * b11;
4711   s23 = 0;
4712
4713   carry0 = (s0 + (1 << 20)) >> 21;
4714   s1 += carry0;
4715   s0 -= carry0 * (1 << 21);
4716   carry2 = (s2 + (1 << 20)) >> 21;
4717   s3 += carry2;
4718   s2 -= carry2 * (1 << 21);
4719   carry4 = (s4 + (1 << 20)) >> 21;
4720   s5 += carry4;
4721   s4 -= carry4 * (1 << 21);
4722   carry6 = (s6 + (1 << 20)) >> 21;
4723   s7 += carry6;
4724   s6 -= carry6 * (1 << 21);
4725   carry8 = (s8 + (1 << 20)) >> 21;
4726   s9 += carry8;
4727   s8 -= carry8 * (1 << 21);
4728   carry10 = (s10 + (1 << 20)) >> 21;
4729   s11 += carry10;
4730   s10 -= carry10 * (1 << 21);
4731   carry12 = (s12 + (1 << 20)) >> 21;
4732   s13 += carry12;
4733   s12 -= carry12 * (1 << 21);
4734   carry14 = (s14 + (1 << 20)) >> 21;
4735   s15 += carry14;
4736   s14 -= carry14 * (1 << 21);
4737   carry16 = (s16 + (1 << 20)) >> 21;
4738   s17 += carry16;
4739   s16 -= carry16 * (1 << 21);
4740   carry18 = (s18 + (1 << 20)) >> 21;
4741   s19 += carry18;
4742   s18 -= carry18 * (1 << 21);
4743   carry20 = (s20 + (1 << 20)) >> 21;
4744   s21 += carry20;
4745   s20 -= carry20 * (1 << 21);
4746   carry22 = (s22 + (1 << 20)) >> 21;
4747   s23 += carry22;
4748   s22 -= carry22 * (1 << 21);
4749
4750   carry1 = (s1 + (1 << 20)) >> 21;
4751   s2 += carry1;
4752   s1 -= carry1 * (1 << 21);
4753   carry3 = (s3 + (1 << 20)) >> 21;
4754   s4 += carry3;
4755   s3 -= carry3 * (1 << 21);
4756   carry5 = (s5 + (1 << 20)) >> 21;
4757   s6 += carry5;
4758   s5 -= carry5 * (1 << 21);
4759   carry7 = (s7 + (1 << 20)) >> 21;
4760   s8 += carry7;
4761   s7 -= carry7 * (1 << 21);
4762   carry9 = (s9 + (1 << 20)) >> 21;
4763   s10 += carry9;
4764   s9 -= carry9 * (1 << 21);
4765   carry11 = (s11 + (1 << 20)) >> 21;
4766   s12 += carry11;
4767   s11 -= carry11 * (1 << 21);
4768   carry13 = (s13 + (1 << 20)) >> 21;
4769   s14 += carry13;
4770   s13 -= carry13 * (1 << 21);
4771   carry15 = (s15 + (1 << 20)) >> 21;
4772   s16 += carry15;
4773   s15 -= carry15 * (1 << 21);
4774   carry17 = (s17 + (1 << 20)) >> 21;
4775   s18 += carry17;
4776   s17 -= carry17 * (1 << 21);
4777   carry19 = (s19 + (1 << 20)) >> 21;
4778   s20 += carry19;
4779   s19 -= carry19 * (1 << 21);
4780   carry21 = (s21 + (1 << 20)) >> 21;
4781   s22 += carry21;
4782   s21 -= carry21 * (1 << 21);
4783
4784   s11 += s23 * 666643;
4785   s12 += s23 * 470296;
4786   s13 += s23 * 654183;
4787   s14 -= s23 * 997805;
4788   s15 += s23 * 136657;
4789   s16 -= s23 * 683901;
4790   s23 = 0;
4791
4792   s10 += s22 * 666643;
4793   s11 += s22 * 470296;
4794   s12 += s22 * 654183;
4795   s13 -= s22 * 997805;
4796   s14 += s22 * 136657;
4797   s15 -= s22 * 683901;
4798   s22 = 0;
4799
4800   s9 += s21 * 666643;
4801   s10 += s21 * 470296;
4802   s11 += s21 * 654183;
4803   s12 -= s21 * 997805;
4804   s13 += s21 * 136657;
4805   s14 -= s21 * 683901;
4806   s21 = 0;
4807
4808   s8 += s20 * 666643;
4809   s9 += s20 * 470296;
4810   s10 += s20 * 654183;
4811   s11 -= s20 * 997805;
4812   s12 += s20 * 136657;
4813   s13 -= s20 * 683901;
4814   s20 = 0;
4815
4816   s7 += s19 * 666643;
4817   s8 += s19 * 470296;
4818   s9 += s19 * 654183;
4819   s10 -= s19 * 997805;
4820   s11 += s19 * 136657;
4821   s12 -= s19 * 683901;
4822   s19 = 0;
4823
4824   s6 += s18 * 666643;
4825   s7 += s18 * 470296;
4826   s8 += s18 * 654183;
4827   s9 -= s18 * 997805;
4828   s10 += s18 * 136657;
4829   s11 -= s18 * 683901;
4830   s18 = 0;
4831
4832   carry6 = (s6 + (1 << 20)) >> 21;
4833   s7 += carry6;
4834   s6 -= carry6 * (1 << 21);
4835   carry8 = (s8 + (1 << 20)) >> 21;
4836   s9 += carry8;
4837   s8 -= carry8 * (1 << 21);
4838   carry10 = (s10 + (1 << 20)) >> 21;
4839   s11 += carry10;
4840   s10 -= carry10 * (1 << 21);
4841   carry12 = (s12 + (1 << 20)) >> 21;
4842   s13 += carry12;
4843   s12 -= carry12 * (1 << 21);
4844   carry14 = (s14 + (1 << 20)) >> 21;
4845   s15 += carry14;
4846   s14 -= carry14 * (1 << 21);
4847   carry16 = (s16 + (1 << 20)) >> 21;
4848   s17 += carry16;
4849   s16 -= carry16 * (1 << 21);
4850
4851   carry7 = (s7 + (1 << 20)) >> 21;
4852   s8 += carry7;
4853   s7 -= carry7 * (1 << 21);
4854   carry9 = (s9 + (1 << 20)) >> 21;
4855   s10 += carry9;
4856   s9 -= carry9 * (1 << 21);
4857   carry11 = (s11 + (1 << 20)) >> 21;
4858   s12 += carry11;
4859   s11 -= carry11 * (1 << 21);
4860   carry13 = (s13 + (1 << 20)) >> 21;
4861   s14 += carry13;
4862   s13 -= carry13 * (1 << 21);
4863   carry15 = (s15 + (1 << 20)) >> 21;
4864   s16 += carry15;
4865   s15 -= carry15 * (1 << 21);
4866
4867   s5 += s17 * 666643;
4868   s6 += s17 * 470296;
4869   s7 += s17 * 654183;
4870   s8 -= s17 * 997805;
4871   s9 += s17 * 136657;
4872   s10 -= s17 * 683901;
4873   s17 = 0;
4874
4875   s4 += s16 * 666643;
4876   s5 += s16 * 470296;
4877   s6 += s16 * 654183;
4878   s7 -= s16 * 997805;
4879   s8 += s16 * 136657;
4880   s9 -= s16 * 683901;
4881   s16 = 0;
4882
4883   s3 += s15 * 666643;
4884   s4 += s15 * 470296;
4885   s5 += s15 * 654183;
4886   s6 -= s15 * 997805;
4887   s7 += s15 * 136657;
4888   s8 -= s15 * 683901;
4889   s15 = 0;
4890
4891   s2 += s14 * 666643;
4892   s3 += s14 * 470296;
4893   s4 += s14 * 654183;
4894   s5 -= s14 * 997805;
4895   s6 += s14 * 136657;
4896   s7 -= s14 * 683901;
4897   s14 = 0;
4898
4899   s1 += s13 * 666643;
4900   s2 += s13 * 470296;
4901   s3 += s13 * 654183;
4902   s4 -= s13 * 997805;
4903   s5 += s13 * 136657;
4904   s6 -= s13 * 683901;
4905   s13 = 0;
4906
4907   s0 += s12 * 666643;
4908   s1 += s12 * 470296;
4909   s2 += s12 * 654183;
4910   s3 -= s12 * 997805;
4911   s4 += s12 * 136657;
4912   s5 -= s12 * 683901;
4913   s12 = 0;
4914
4915   carry0 = (s0 + (1 << 20)) >> 21;
4916   s1 += carry0;
4917   s0 -= carry0 * (1 << 21);
4918   carry2 = (s2 + (1 << 20)) >> 21;
4919   s3 += carry2;
4920   s2 -= carry2 * (1 << 21);
4921   carry4 = (s4 + (1 << 20)) >> 21;
4922   s5 += carry4;
4923   s4 -= carry4 * (1 << 21);
4924   carry6 = (s6 + (1 << 20)) >> 21;
4925   s7 += carry6;
4926   s6 -= carry6 * (1 << 21);
4927   carry8 = (s8 + (1 << 20)) >> 21;
4928   s9 += carry8;
4929   s8 -= carry8 * (1 << 21);
4930   carry10 = (s10 + (1 << 20)) >> 21;
4931   s11 += carry10;
4932   s10 -= carry10 * (1 << 21);
4933
4934   carry1 = (s1 + (1 << 20)) >> 21;
4935   s2 += carry1;
4936   s1 -= carry1 * (1 << 21);
4937   carry3 = (s3 + (1 << 20)) >> 21;
4938   s4 += carry3;
4939   s3 -= carry3 * (1 << 21);
4940   carry5 = (s5 + (1 << 20)) >> 21;
4941   s6 += carry5;
4942   s5 -= carry5 * (1 << 21);
4943   carry7 = (s7 + (1 << 20)) >> 21;
4944   s8 += carry7;
4945   s7 -= carry7 * (1 << 21);
4946   carry9 = (s9 + (1 << 20)) >> 21;
4947   s10 += carry9;
4948   s9 -= carry9 * (1 << 21);
4949   carry11 = (s11 + (1 << 20)) >> 21;
4950   s12 += carry11;
4951   s11 -= carry11 * (1 << 21);
4952
4953   s0 += s12 * 666643;
4954   s1 += s12 * 470296;
4955   s2 += s12 * 654183;
4956   s3 -= s12 * 997805;
4957   s4 += s12 * 136657;
4958   s5 -= s12 * 683901;
4959   s12 = 0;
4960
4961   carry0 = s0 >> 21;
4962   s1 += carry0;
4963   s0 -= carry0 * (1 << 21);
4964   carry1 = s1 >> 21;
4965   s2 += carry1;
4966   s1 -= carry1 * (1 << 21);
4967   carry2 = s2 >> 21;
4968   s3 += carry2;
4969   s2 -= carry2 * (1 << 21);
4970   carry3 = s3 >> 21;
4971   s4 += carry3;
4972   s3 -= carry3 * (1 << 21);
4973   carry4 = s4 >> 21;
4974   s5 += carry4;
4975   s4 -= carry4 * (1 << 21);
4976   carry5 = s5 >> 21;
4977   s6 += carry5;
4978   s5 -= carry5 * (1 << 21);
4979   carry6 = s6 >> 21;
4980   s7 += carry6;
4981   s6 -= carry6 * (1 << 21);
4982   carry7 = s7 >> 21;
4983   s8 += carry7;
4984   s7 -= carry7 * (1 << 21);
4985   carry8 = s8 >> 21;
4986   s9 += carry8;
4987   s8 -= carry8 * (1 << 21);
4988   carry9 = s9 >> 21;
4989   s10 += carry9;
4990   s9 -= carry9 * (1 << 21);
4991   carry10 = s10 >> 21;
4992   s11 += carry10;
4993   s10 -= carry10 * (1 << 21);
4994   carry11 = s11 >> 21;
4995   s12 += carry11;
4996   s11 -= carry11 * (1 << 21);
4997
4998   s0 += s12 * 666643;
4999   s1 += s12 * 470296;
5000   s2 += s12 * 654183;
5001   s3 -= s12 * 997805;
5002   s4 += s12 * 136657;
5003   s5 -= s12 * 683901;
5004   s12 = 0;
5005
5006   carry0 = s0 >> 21;
5007   s1 += carry0;
5008   s0 -= carry0 * (1 << 21);
5009   carry1 = s1 >> 21;
5010   s2 += carry1;
5011   s1 -= carry1 * (1 << 21);
5012   carry2 = s2 >> 21;
5013   s3 += carry2;
5014   s2 -= carry2 * (1 << 21);
5015   carry3 = s3 >> 21;
5016   s4 += carry3;
5017   s3 -= carry3 * (1 << 21);
5018   carry4 = s4 >> 21;
5019   s5 += carry4;
5020   s4 -= carry4 * (1 << 21);
5021   carry5 = s5 >> 21;
5022   s6 += carry5;
5023   s5 -= carry5 * (1 << 21);
5024   carry6 = s6 >> 21;
5025   s7 += carry6;
5026   s6 -= carry6 * (1 << 21);
5027   carry7 = s7 >> 21;
5028   s8 += carry7;
5029   s7 -= carry7 * (1 << 21);
5030   carry8 = s8 >> 21;
5031   s9 += carry8;
5032   s8 -= carry8 * (1 << 21);
5033   carry9 = s9 >> 21;
5034   s10 += carry9;
5035   s9 -= carry9 * (1 << 21);
5036   carry10 = s10 >> 21;
5037   s11 += carry10;
5038   s10 -= carry10 * (1 << 21);
5039
5040   s[0] = (uint8_t)(s0 >> 0);
5041   s[1] = (uint8_t)(s0 >> 8);
5042   s[2] = (uint8_t)((s0 >> 16) | (s1 << 5));
5043   s[3] = (uint8_t)(s1 >> 3);
5044   s[4] = (uint8_t)(s1 >> 11);
5045   s[5] = (uint8_t)((s1 >> 19) | (s2 << 2));
5046   s[6] = (uint8_t)(s2 >> 6);
5047   s[7] = (uint8_t)((s2 >> 14) | (s3 << 7));
5048   s[8] = (uint8_t)(s3 >> 1);
5049   s[9] = (uint8_t)(s3 >> 9);
5050   s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
5051   s[11] = (uint8_t)(s4 >> 4);
5052   s[12] = (uint8_t)(s4 >> 12);
5053   s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
5054   s[14] = (uint8_t)(s5 >> 7);
5055   s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
5056   s[16] = (uint8_t)(s6 >> 2);
5057   s[17] = (uint8_t)(s6 >> 10);
5058   s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
5059   s[19] = (uint8_t)(s7 >> 5);
5060   s[20] = (uint8_t)(s7 >> 13);
5061   s[21] = (uint8_t)(s8 >> 0);
5062   s[22] = (uint8_t)(s8 >> 8);
5063   s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
5064   s[24] = (uint8_t)(s9 >> 3);
5065   s[25] = (uint8_t)(s9 >> 11);
5066   s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
5067   s[27] = (uint8_t)(s10 >> 6);
5068   s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
5069   s[29] = (uint8_t)(s11 >> 1);
5070   s[30] = (uint8_t)(s11 >> 9);
5071   s[31] = (uint8_t)(s11 >> 17);
5072 }
5073
5074 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
5075                  const uint8_t public_key[32], const uint8_t private_key[32]) {
5076   uint8_t az[SHA512_DIGEST_LENGTH];
5077   uint8_t nonce[SHA512_DIGEST_LENGTH];
5078   ge_p3 R;
5079   uint8_t hram[SHA512_DIGEST_LENGTH];
5080   SHA512_CTX hash_ctx;
5081
5082   SHA512_Init(&hash_ctx);
5083   SHA512_Update(&hash_ctx, private_key, 32);
5084   SHA512_Final(az, &hash_ctx);
5085
5086   az[0] &= 248;
5087   az[31] &= 63;
5088   az[31] |= 64;
5089
5090   SHA512_Init(&hash_ctx);
5091   SHA512_Update(&hash_ctx, az + 32, 32);
5092   SHA512_Update(&hash_ctx, message, message_len);
5093   SHA512_Final(nonce, &hash_ctx);
5094
5095   x25519_sc_reduce(nonce);
5096   ge_scalarmult_base(&R, nonce);
5097   ge_p3_tobytes(out_sig, &R);
5098
5099   SHA512_Init(&hash_ctx);
5100   SHA512_Update(&hash_ctx, out_sig, 32);
5101   SHA512_Update(&hash_ctx, public_key, 32);
5102   SHA512_Update(&hash_ctx, message, message_len);
5103   SHA512_Final(hram, &hash_ctx);
5104
5105   x25519_sc_reduce(hram);
5106   sc_muladd(out_sig + 32, hram, az, nonce);
5107
5108   OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx));
5109   OPENSSL_cleanse(nonce, sizeof(nonce));
5110   OPENSSL_cleanse(az, sizeof(az));
5111
5112   return 1;
5113 }
5114
5115 int ED25519_verify(const uint8_t *message, size_t message_len,
5116                    const uint8_t signature[64], const uint8_t public_key[32]) {
5117   ge_p3 A;
5118   uint8_t rcopy[32];
5119   uint8_t scopy[32];
5120   SHA512_CTX hash_ctx;
5121   ge_p2 R;
5122   uint8_t rcheck[32];
5123   uint8_t h[SHA512_DIGEST_LENGTH];
5124
5125   if ((signature[63] & 224) != 0 ||
5126       ge_frombytes_vartime(&A, public_key) != 0) {
5127     return 0;
5128   }
5129
5130   fe_neg(A.X, A.X);
5131   fe_neg(A.T, A.T);
5132
5133   memcpy(rcopy, signature, 32);
5134   memcpy(scopy, signature + 32, 32);
5135
5136   SHA512_Init(&hash_ctx);
5137   SHA512_Update(&hash_ctx, signature, 32);
5138   SHA512_Update(&hash_ctx, public_key, 32);
5139   SHA512_Update(&hash_ctx, message, message_len);
5140   SHA512_Final(h, &hash_ctx);
5141
5142   x25519_sc_reduce(h);
5143
5144   ge_double_scalarmult_vartime(&R, h, &A, scopy);
5145
5146   ge_tobytes(rcheck, &R);
5147
5148   return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
5149 }
5150
5151 void ED25519_public_from_private(uint8_t out_public_key[32],
5152                                  const uint8_t private_key[32]) {
5153   uint8_t az[SHA512_DIGEST_LENGTH];
5154   ge_p3 A;
5155
5156   SHA512(private_key, 32, az);
5157
5158   az[0] &= 248;
5159   az[31] &= 63;
5160   az[31] |= 64;
5161
5162   ge_scalarmult_base(&A, az);
5163   ge_p3_tobytes(out_public_key, &A);
5164
5165   OPENSSL_cleanse(az, sizeof(az));
5166 }
5167
5168 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5169            const uint8_t peer_public_value[32]) {
5170   static const uint8_t kZeros[32] = {0};
5171   x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5172   /* The all-zero output results when the input is a point of small order. */
5173   return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5174 }
5175
5176 void X25519_public_from_private(uint8_t out_public_value[32],
5177                                 const uint8_t private_key[32]) {
5178   uint8_t e[32];
5179   ge_p3 A;
5180   fe zplusy, zminusy, zminusy_inv;
5181
5182   memcpy(e, private_key, 32);
5183   e[0] &= 248;
5184   e[31] &= 127;
5185   e[31] |= 64;
5186
5187   ge_scalarmult_base(&A, e);
5188
5189   /* We only need the u-coordinate of the curve25519 point. The map is
5190    * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
5191   fe_add(zplusy, A.Z, A.Y);
5192   fe_sub(zminusy, A.Z, A.Y);
5193   fe_invert(zminusy_inv, zminusy);
5194   fe_mul(zplusy, zplusy, zminusy_inv);
5195   fe_tobytes(out_public_value, zplusy);
5196
5197   OPENSSL_cleanse(e, sizeof(e));
5198 }