crypto/ec/curve25519.c

   1 /*
   2  * Copyright 2016 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 /* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
  11  * 20141124 (http://bench.cr.yp.to/supercop.html).
  12  *
  13  * The field functions are shared by Ed25519 and X25519 where possible. */
  14
  15 #include <string.h>
  16 #include "ec_lcl.h"
  17 #include <openssl/sha.h>
  18
  19
  20 /* fe means field element. Here the field is \Z/(2^255-19). An element t,
  21  * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
  22  * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
  23  * context.  */
  24 typedef int32_t fe[10];
  25
  26 static const int64_t kBottom25Bits = 0x1ffffffLL;
  27 static const int64_t kBottom26Bits = 0x3ffffffLL;
  28 static const int64_t kTop39Bits = 0xfffffffffe000000LL;
  29 static const int64_t kTop38Bits = 0xfffffffffc000000LL;
  30
  31 static uint64_t load_3(const uint8_t *in) {
  32   uint64_t result;
  33   result = (uint64_t)in[0];
  34   result |= ((uint64_t)in[1]) << 8;
  35   result |= ((uint64_t)in[2]) << 16;
  36   return result;
  37 }
  38
  39 static uint64_t load_4(const uint8_t *in) {
  40   uint64_t result;
  41   result = (uint64_t)in[0];
  42   result |= ((uint64_t)in[1]) << 8;
  43   result |= ((uint64_t)in[2]) << 16;
  44   result |= ((uint64_t)in[3]) << 24;
  45   return result;
  46 }
  47
  48 static void fe_frombytes(fe h, const uint8_t *s) {
  49   /* Ignores top bit of h. */
  50   int64_t h0 = load_4(s);
  51   int64_t h1 = load_3(s + 4) << 6;
  52   int64_t h2 = load_3(s + 7) << 5;
  53   int64_t h3 = load_3(s + 10) << 3;
  54   int64_t h4 = load_3(s + 13) << 2;
  55   int64_t h5 = load_4(s + 16);
  56   int64_t h6 = load_3(s + 20) << 7;
  57   int64_t h7 = load_3(s + 23) << 5;
  58   int64_t h8 = load_3(s + 26) << 4;
  59   int64_t h9 = (load_3(s + 29) & 8388607) << 2;
  60   int64_t carry0;
  61   int64_t carry1;
  62   int64_t carry2;
  63   int64_t carry3;
  64   int64_t carry4;
  65   int64_t carry5;
  66   int64_t carry6;
  67   int64_t carry7;
  68   int64_t carry8;
  69   int64_t carry9;
  70
  71   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
  72   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
  73   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
  74   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
  75   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
  76
  77   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
  78   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
  79   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
  80   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
  81   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
  82
  83   h[0] = h0;
  84   h[1] = h1;
  85   h[2] = h2;
  86   h[3] = h3;
  87   h[4] = h4;
  88   h[5] = h5;
  89   h[6] = h6;
  90   h[7] = h7;
  91   h[8] = h8;
  92   h[9] = h9;
  93 }
  94
  95 /* Preconditions:
  96  *  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
  97  *
  98  * Write p=2^255-19; q=floor(h/p).
  99  * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
 100  *
 101  * Proof:
 102  *   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
 103  *   Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
 104  *
 105  *   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
 106  *   Then 0<y<1.
 107  *
 108  *   Write r=h-pq.
 109  *   Have 0<=r<=p-1=2^255-20.
 110  *   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
 111  *
 112  *   Write x=r+19(2^-255)r+y.
 113  *   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
 114  *
 115  *   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
 116  *   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
 117 static void fe_tobytes(uint8_t *s, const fe h) {
 118   int32_t h0 = h[0];
 119   int32_t h1 = h[1];
 120   int32_t h2 = h[2];
 121   int32_t h3 = h[3];
 122   int32_t h4 = h[4];
 123   int32_t h5 = h[5];
 124   int32_t h6 = h[6];
 125   int32_t h7 = h[7];
 126   int32_t h8 = h[8];
 127   int32_t h9 = h[9];
 128   int32_t q;
 129
 130   q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
 131   q = (h0 + q) >> 26;
 132   q = (h1 + q) >> 25;
 133   q = (h2 + q) >> 26;
 134   q = (h3 + q) >> 25;
 135   q = (h4 + q) >> 26;
 136   q = (h5 + q) >> 25;
 137   q = (h6 + q) >> 26;
 138   q = (h7 + q) >> 25;
 139   q = (h8 + q) >> 26;
 140   q = (h9 + q) >> 25;
 141
 142   /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
 143   h0 += 19 * q;
 144   /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
 145
 146   h1 += h0 >> 26; h0 &= kBottom26Bits;
 147   h2 += h1 >> 25; h1 &= kBottom25Bits;
 148   h3 += h2 >> 26; h2 &= kBottom26Bits;
 149   h4 += h3 >> 25; h3 &= kBottom25Bits;
 150   h5 += h4 >> 26; h4 &= kBottom26Bits;
 151   h6 += h5 >> 25; h5 &= kBottom25Bits;
 152   h7 += h6 >> 26; h6 &= kBottom26Bits;
 153   h8 += h7 >> 25; h7 &= kBottom25Bits;
 154   h9 += h8 >> 26; h8 &= kBottom26Bits;
 155                   h9 &= kBottom25Bits;
 156                   /* h10 = carry9 */
 157
 158   /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
 159    * Have h0+...+2^230 h9 between 0 and 2^255-1;
 160    * evidently 2^255 h10-2^255 q = 0.
 161    * Goal: Output h0+...+2^230 h9.  */
 162
 163   s[0] = h0 >> 0;
 164   s[1] = h0 >> 8;
 165   s[2] = h0 >> 16;
 166   s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
 167   s[4] = h1 >> 6;
 168   s[5] = h1 >> 14;
 169   s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
 170   s[7] = h2 >> 5;
 171   s[8] = h2 >> 13;
 172   s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
 173   s[10] = h3 >> 3;
 174   s[11] = h3 >> 11;
 175   s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
 176   s[13] = h4 >> 2;
 177   s[14] = h4 >> 10;
 178   s[15] = h4 >> 18;
 179   s[16] = h5 >> 0;
 180   s[17] = h5 >> 8;
 181   s[18] = h5 >> 16;
 182   s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
 183   s[20] = h6 >> 7;
 184   s[21] = h6 >> 15;
 185   s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
 186   s[23] = h7 >> 5;
 187   s[24] = h7 >> 13;
 188   s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
 189   s[26] = h8 >> 4;
 190   s[27] = h8 >> 12;
 191   s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
 192   s[29] = h9 >> 2;
 193   s[30] = h9 >> 10;
 194   s[31] = h9 >> 18;
 195 }
 196
 197 /* h = f */
 198 static void fe_copy(fe h, const fe f) {
 199   memmove(h, f, sizeof(int32_t) * 10);
 200 }
 201
 202 /* h = 0 */
 203 static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
 204
 205 /* h = 1 */
 206 static void fe_1(fe h) {
 207   memset(h, 0, sizeof(int32_t) * 10);
 208   h[0] = 1;
 209 }
 210
 211 /* h = f + g
 212  * Can overlap h with f or g.
 213  *
 214  * Preconditions:
 215  *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 216  *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 217  *
 218  * Postconditions:
 219  *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
 220 static void fe_add(fe h, const fe f, const fe g) {
 221   unsigned i;
 222   for (i = 0; i < 10; i++) {
 223     h[i] = f[i] + g[i];
 224   }
 225 }
 226
 227 /* h = f - g
 228  * Can overlap h with f or g.
 229  *
 230  * Preconditions:
 231  *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 232  *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 233  *
 234  * Postconditions:
 235  *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
 236 static void fe_sub(fe h, const fe f, const fe g) {
 237   unsigned i;
 238   for (i = 0; i < 10; i++) {
 239     h[i] = f[i] - g[i];
 240   }
 241 }
 242
 243 /* h = f * g
 244  * Can overlap h with f or g.
 245  *
 246  * Preconditions:
 247  *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 248  *    |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 249  *
 250  * Postconditions:
 251  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 252  *
 253  * Notes on implementation strategy:
 254  *
 255  * Using schoolbook multiplication.
 256  * Karatsuba would save a little in some cost models.
 257  *
 258  * Most multiplications by 2 and 19 are 32-bit precomputations;
 259  * cheaper than 64-bit postcomputations.
 260  *
 261  * There is one remaining multiplication by 19 in the carry chain;
 262  * one *19 precomputation can be merged into this,
 263  * but the resulting data flow is considerably less clean.
 264  *
 265  * There are 12 carries below.
 266  * 10 of them are 2-way parallelizable and vectorizable.
 267  * Can get away with 11 carries, but then data flow is much deeper.
 268  *
 269  * With tighter constraints on inputs can squeeze carries into int32. */
 270 static void fe_mul(fe h, const fe f, const fe g) {
 271   int32_t f0 = f[0];
 272   int32_t f1 = f[1];
 273   int32_t f2 = f[2];
 274   int32_t f3 = f[3];
 275   int32_t f4 = f[4];
 276   int32_t f5 = f[5];
 277   int32_t f6 = f[6];
 278   int32_t f7 = f[7];
 279   int32_t f8 = f[8];
 280   int32_t f9 = f[9];
 281   int32_t g0 = g[0];
 282   int32_t g1 = g[1];
 283   int32_t g2 = g[2];
 284   int32_t g3 = g[3];
 285   int32_t g4 = g[4];
 286   int32_t g5 = g[5];
 287   int32_t g6 = g[6];
 288   int32_t g7 = g[7];
 289   int32_t g8 = g[8];
 290   int32_t g9 = g[9];
 291   int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
 292   int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
 293   int32_t g3_19 = 19 * g3;
 294   int32_t g4_19 = 19 * g4;
 295   int32_t g5_19 = 19 * g5;
 296   int32_t g6_19 = 19 * g6;
 297   int32_t g7_19 = 19 * g7;
 298   int32_t g8_19 = 19 * g8;
 299   int32_t g9_19 = 19 * g9;
 300   int32_t f1_2 = 2 * f1;
 301   int32_t f3_2 = 2 * f3;
 302   int32_t f5_2 = 2 * f5;
 303   int32_t f7_2 = 2 * f7;
 304   int32_t f9_2 = 2 * f9;
 305   int64_t f0g0    = f0   * (int64_t) g0;
 306   int64_t f0g1    = f0   * (int64_t) g1;
 307   int64_t f0g2    = f0   * (int64_t) g2;
 308   int64_t f0g3    = f0   * (int64_t) g3;
 309   int64_t f0g4    = f0   * (int64_t) g4;
 310   int64_t f0g5    = f0   * (int64_t) g5;
 311   int64_t f0g6    = f0   * (int64_t) g6;
 312   int64_t f0g7    = f0   * (int64_t) g7;
 313   int64_t f0g8    = f0   * (int64_t) g8;
 314   int64_t f0g9    = f0   * (int64_t) g9;
 315   int64_t f1g0    = f1   * (int64_t) g0;
 316   int64_t f1g1_2  = f1_2 * (int64_t) g1;
 317   int64_t f1g2    = f1   * (int64_t) g2;
 318   int64_t f1g3_2  = f1_2 * (int64_t) g3;
 319   int64_t f1g4    = f1   * (int64_t) g4;
 320   int64_t f1g5_2  = f1_2 * (int64_t) g5;
 321   int64_t f1g6    = f1   * (int64_t) g6;
 322   int64_t f1g7_2  = f1_2 * (int64_t) g7;
 323   int64_t f1g8    = f1   * (int64_t) g8;
 324   int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
 325   int64_t f2g0    = f2   * (int64_t) g0;
 326   int64_t f2g1    = f2   * (int64_t) g1;
 327   int64_t f2g2    = f2   * (int64_t) g2;
 328   int64_t f2g3    = f2   * (int64_t) g3;
 329   int64_t f2g4    = f2   * (int64_t) g4;
 330   int64_t f2g5    = f2   * (int64_t) g5;
 331   int64_t f2g6    = f2   * (int64_t) g6;
 332   int64_t f2g7    = f2   * (int64_t) g7;
 333   int64_t f2g8_19 = f2   * (int64_t) g8_19;
 334   int64_t f2g9_19 = f2   * (int64_t) g9_19;
 335   int64_t f3g0    = f3   * (int64_t) g0;
 336   int64_t f3g1_2  = f3_2 * (int64_t) g1;
 337   int64_t f3g2    = f3   * (int64_t) g2;
 338   int64_t f3g3_2  = f3_2 * (int64_t) g3;
 339   int64_t f3g4    = f3   * (int64_t) g4;
 340   int64_t f3g5_2  = f3_2 * (int64_t) g5;
 341   int64_t f3g6    = f3   * (int64_t) g6;
 342   int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
 343   int64_t f3g8_19 = f3   * (int64_t) g8_19;
 344   int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
 345   int64_t f4g0    = f4   * (int64_t) g0;
 346   int64_t f4g1    = f4   * (int64_t) g1;
 347   int64_t f4g2    = f4   * (int64_t) g2;
 348   int64_t f4g3    = f4   * (int64_t) g3;
 349   int64_t f4g4    = f4   * (int64_t) g4;
 350   int64_t f4g5    = f4   * (int64_t) g5;
 351   int64_t f4g6_19 = f4   * (int64_t) g6_19;
 352   int64_t f4g7_19 = f4   * (int64_t) g7_19;
 353   int64_t f4g8_19 = f4   * (int64_t) g8_19;
 354   int64_t f4g9_19 = f4   * (int64_t) g9_19;
 355   int64_t f5g0    = f5   * (int64_t) g0;
 356   int64_t f5g1_2  = f5_2 * (int64_t) g1;
 357   int64_t f5g2    = f5   * (int64_t) g2;
 358   int64_t f5g3_2  = f5_2 * (int64_t) g3;
 359   int64_t f5g4    = f5   * (int64_t) g4;
 360   int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
 361   int64_t f5g6_19 = f5   * (int64_t) g6_19;
 362   int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
 363   int64_t f5g8_19 = f5   * (int64_t) g8_19;
 364   int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
 365   int64_t f6g0    = f6   * (int64_t) g0;
 366   int64_t f6g1    = f6   * (int64_t) g1;
 367   int64_t f6g2    = f6   * (int64_t) g2;
 368   int64_t f6g3    = f6   * (int64_t) g3;
 369   int64_t f6g4_19 = f6   * (int64_t) g4_19;
 370   int64_t f6g5_19 = f6   * (int64_t) g5_19;
 371   int64_t f6g6_19 = f6   * (int64_t) g6_19;
 372   int64_t f6g7_19 = f6   * (int64_t) g7_19;
 373   int64_t f6g8_19 = f6   * (int64_t) g8_19;
 374   int64_t f6g9_19 = f6   * (int64_t) g9_19;
 375   int64_t f7g0    = f7   * (int64_t) g0;
 376   int64_t f7g1_2  = f7_2 * (int64_t) g1;
 377   int64_t f7g2    = f7   * (int64_t) g2;
 378   int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
 379   int64_t f7g4_19 = f7   * (int64_t) g4_19;
 380   int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
 381   int64_t f7g6_19 = f7   * (int64_t) g6_19;
 382   int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
 383   int64_t f7g8_19 = f7   * (int64_t) g8_19;
 384   int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
 385   int64_t f8g0    = f8   * (int64_t) g0;
 386   int64_t f8g1    = f8   * (int64_t) g1;
 387   int64_t f8g2_19 = f8   * (int64_t) g2_19;
 388   int64_t f8g3_19 = f8   * (int64_t) g3_19;
 389   int64_t f8g4_19 = f8   * (int64_t) g4_19;
 390   int64_t f8g5_19 = f8   * (int64_t) g5_19;
 391   int64_t f8g6_19 = f8   * (int64_t) g6_19;
 392   int64_t f8g7_19 = f8   * (int64_t) g7_19;
 393   int64_t f8g8_19 = f8   * (int64_t) g8_19;
 394   int64_t f8g9_19 = f8   * (int64_t) g9_19;
 395   int64_t f9g0    = f9   * (int64_t) g0;
 396   int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
 397   int64_t f9g2_19 = f9   * (int64_t) g2_19;
 398   int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
 399   int64_t f9g4_19 = f9   * (int64_t) g4_19;
 400   int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
 401   int64_t f9g6_19 = f9   * (int64_t) g6_19;
 402   int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
 403   int64_t f9g8_19 = f9   * (int64_t) g8_19;
 404   int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
 405   int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
 406   int64_t h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
 407   int64_t h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
 408   int64_t h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
 409   int64_t h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
 410   int64_t h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
 411   int64_t h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
 412   int64_t h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
 413   int64_t h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
 414   int64_t h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
 415   int64_t carry0;
 416   int64_t carry1;
 417   int64_t carry2;
 418   int64_t carry3;
 419   int64_t carry4;
 420   int64_t carry5;
 421   int64_t carry6;
 422   int64_t carry7;
 423   int64_t carry8;
 424   int64_t carry9;
 425
 426   /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
 427    *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
 428    * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
 429    *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
 430
 431   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 432   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 433   /* |h0| <= 2^25 */
 434   /* |h4| <= 2^25 */
 435   /* |h1| <= 1.71*2^59 */
 436   /* |h5| <= 1.71*2^59 */
 437
 438   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
 439   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
 440   /* |h1| <= 2^24; from now on fits into int32 */
 441   /* |h5| <= 2^24; from now on fits into int32 */
 442   /* |h2| <= 1.41*2^60 */
 443   /* |h6| <= 1.41*2^60 */
 444
 445   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
 446   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
 447   /* |h2| <= 2^25; from now on fits into int32 unchanged */
 448   /* |h6| <= 2^25; from now on fits into int32 unchanged */
 449   /* |h3| <= 1.71*2^59 */
 450   /* |h7| <= 1.71*2^59 */
 451
 452   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
 453   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
 454   /* |h3| <= 2^24; from now on fits into int32 unchanged */
 455   /* |h7| <= 2^24; from now on fits into int32 unchanged */
 456   /* |h4| <= 1.72*2^34 */
 457   /* |h8| <= 1.41*2^60 */
 458
 459   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 460   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
 461   /* |h4| <= 2^25; from now on fits into int32 unchanged */
 462   /* |h8| <= 2^25; from now on fits into int32 unchanged */
 463   /* |h5| <= 1.01*2^24 */
 464   /* |h9| <= 1.71*2^59 */
 465
 466   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
 467   /* |h9| <= 2^24; from now on fits into int32 unchanged */
 468   /* |h0| <= 1.1*2^39 */
 469
 470   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 471   /* |h0| <= 2^25; from now on fits into int32 unchanged */
 472   /* |h1| <= 1.01*2^24 */
 473
 474   h[0] = h0;
 475   h[1] = h1;
 476   h[2] = h2;
 477   h[3] = h3;
 478   h[4] = h4;
 479   h[5] = h5;
 480   h[6] = h6;
 481   h[7] = h7;
 482   h[8] = h8;
 483   h[9] = h9;
 484 }
 485
 486 /* h = f * f
 487  * Can overlap h with f.
 488  *
 489  * Preconditions:
 490  *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 491  *
 492  * Postconditions:
 493  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 494  *
 495  * See fe_mul.c for discussion of implementation strategy. */
 496 static void fe_sq(fe h, const fe f) {
 497   int32_t f0 = f[0];
 498   int32_t f1 = f[1];
 499   int32_t f2 = f[2];
 500   int32_t f3 = f[3];
 501   int32_t f4 = f[4];
 502   int32_t f5 = f[5];
 503   int32_t f6 = f[6];
 504   int32_t f7 = f[7];
 505   int32_t f8 = f[8];
 506   int32_t f9 = f[9];
 507   int32_t f0_2 = 2 * f0;
 508   int32_t f1_2 = 2 * f1;
 509   int32_t f2_2 = 2 * f2;
 510   int32_t f3_2 = 2 * f3;
 511   int32_t f4_2 = 2 * f4;
 512   int32_t f5_2 = 2 * f5;
 513   int32_t f6_2 = 2 * f6;
 514   int32_t f7_2 = 2 * f7;
 515   int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
 516   int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
 517   int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
 518   int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
 519   int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
 520   int64_t f0f0    = f0   * (int64_t) f0;
 521   int64_t f0f1_2  = f0_2 * (int64_t) f1;
 522   int64_t f0f2_2  = f0_2 * (int64_t) f2;
 523   int64_t f0f3_2  = f0_2 * (int64_t) f3;
 524   int64_t f0f4_2  = f0_2 * (int64_t) f4;
 525   int64_t f0f5_2  = f0_2 * (int64_t) f5;
 526   int64_t f0f6_2  = f0_2 * (int64_t) f6;
 527   int64_t f0f7_2  = f0_2 * (int64_t) f7;
 528   int64_t f0f8_2  = f0_2 * (int64_t) f8;
 529   int64_t f0f9_2  = f0_2 * (int64_t) f9;
 530   int64_t f1f1_2  = f1_2 * (int64_t) f1;
 531   int64_t f1f2_2  = f1_2 * (int64_t) f2;
 532   int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
 533   int64_t f1f4_2  = f1_2 * (int64_t) f4;
 534   int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
 535   int64_t f1f6_2  = f1_2 * (int64_t) f6;
 536   int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
 537   int64_t f1f8_2  = f1_2 * (int64_t) f8;
 538   int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
 539   int64_t f2f2    = f2   * (int64_t) f2;
 540   int64_t f2f3_2  = f2_2 * (int64_t) f3;
 541   int64_t f2f4_2  = f2_2 * (int64_t) f4;
 542   int64_t f2f5_2  = f2_2 * (int64_t) f5;
 543   int64_t f2f6_2  = f2_2 * (int64_t) f6;
 544   int64_t f2f7_2  = f2_2 * (int64_t) f7;
 545   int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
 546   int64_t f2f9_38 = f2   * (int64_t) f9_38;
 547   int64_t f3f3_2  = f3_2 * (int64_t) f3;
 548   int64_t f3f4_2  = f3_2 * (int64_t) f4;
 549   int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
 550   int64_t f3f6_2  = f3_2 * (int64_t) f6;
 551   int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
 552   int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
 553   int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
 554   int64_t f4f4    = f4   * (int64_t) f4;
 555   int64_t f4f5_2  = f4_2 * (int64_t) f5;
 556   int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
 557   int64_t f4f7_38 = f4   * (int64_t) f7_38;
 558   int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
 559   int64_t f4f9_38 = f4   * (int64_t) f9_38;
 560   int64_t f5f5_38 = f5   * (int64_t) f5_38;
 561   int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
 562   int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
 563   int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
 564   int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
 565   int64_t f6f6_19 = f6   * (int64_t) f6_19;
 566   int64_t f6f7_38 = f6   * (int64_t) f7_38;
 567   int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
 568   int64_t f6f9_38 = f6   * (int64_t) f9_38;
 569   int64_t f7f7_38 = f7   * (int64_t) f7_38;
 570   int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
 571   int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
 572   int64_t f8f8_19 = f8   * (int64_t) f8_19;
 573   int64_t f8f9_38 = f8   * (int64_t) f9_38;
 574   int64_t f9f9_38 = f9   * (int64_t) f9_38;
 575   int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
 576   int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
 577   int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
 578   int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
 579   int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
 580   int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
 581   int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
 582   int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
 583   int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
 584   int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
 585   int64_t carry0;
 586   int64_t carry1;
 587   int64_t carry2;
 588   int64_t carry3;
 589   int64_t carry4;
 590   int64_t carry5;
 591   int64_t carry6;
 592   int64_t carry7;
 593   int64_t carry8;
 594   int64_t carry9;
 595
 596   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 597   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 598
 599   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
 600   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
 601
 602   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
 603   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
 604
 605   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
 606   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
 607
 608   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 609   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
 610
 611   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
 612
 613   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 614
 615   h[0] = h0;
 616   h[1] = h1;
 617   h[2] = h2;
 618   h[3] = h3;
 619   h[4] = h4;
 620   h[5] = h5;
 621   h[6] = h6;
 622   h[7] = h7;
 623   h[8] = h8;
 624   h[9] = h9;
 625 }
 626
 627 static void fe_invert(fe out, const fe z) {
 628   fe t0;
 629   fe t1;
 630   fe t2;
 631   fe t3;
 632   int i;
 633
 634   /*
 635    * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
 636    * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
 637    */
 638
 639   /* t0 = z ** 2 */
 640   fe_sq(t0, z);
 641
 642   /* t1 = t0 ** (2 ** 2) = z ** 8 */
 643   fe_sq(t1, t0);
 644   fe_sq(t1, t1);
 645
 646   /* t1 = z * t1 = z ** 9 */
 647   fe_mul(t1, z, t1);
 648   /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
 649   fe_mul(t0, t0, t1);
 650
 651   /* t2 = t0 ** 2 = z ** 22 */
 652   fe_sq(t2, t0);
 653
 654   /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
 655   fe_mul(t1, t1, t2);
 656
 657   /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
 658   fe_sq(t2, t1);
 659   for (i = 1; i < 5; ++i) {
 660     fe_sq(t2, t2);
 661   }
 662
 663   /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
 664   fe_mul(t1, t2, t1);
 665
 666   /* Continuing similarly... */
 667
 668   /* t2 = z ** (2 ** 20 - 1) */
 669   fe_sq(t2, t1);
 670   for (i = 1; i < 10; ++i) {
 671     fe_sq(t2, t2);
 672   }
 673   fe_mul(t2, t2, t1);
 674
 675   /* t2 = z ** (2 ** 40 - 1) */
 676   fe_sq(t3, t2);
 677   for (i = 1; i < 20; ++i) {
 678     fe_sq(t3, t3);
 679   }
 680   fe_mul(t2, t3, t2);
 681
 682   /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
 683   for (i = 0; i < 10; ++i) {
 684     fe_sq(t2, t2);
 685   }
 686   /* t1 = z ** (2 ** 50 - 1) */
 687   fe_mul(t1, t2, t1);
 688
 689   /* t2 = z ** (2 ** 100 - 1) */
 690   fe_sq(t2, t1);
 691   for (i = 1; i < 50; ++i) {
 692     fe_sq(t2, t2);
 693   }
 694   fe_mul(t2, t2, t1);
 695
 696   /* t2 = z ** (2 ** 200 - 1) */
 697   fe_sq(t3, t2);
 698   for (i = 1; i < 100; ++i) {
 699     fe_sq(t3, t3);
 700   }
 701   fe_mul(t2, t3, t2);
 702
 703   /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
 704   fe_sq(t2, t2);
 705   for (i = 1; i < 50; ++i) {
 706     fe_sq(t2, t2);
 707   }
 708
 709   /* t1 = z ** (2 ** 250 - 1) */
 710   fe_mul(t1, t2, t1);
 711
 712   /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
 713   fe_sq(t1, t1);
 714   for (i = 1; i < 5; ++i) {
 715     fe_sq(t1, t1);
 716   }
 717
 718   /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
 719   fe_mul(out, t1, t0);
 720 }
 721
 722 /* h = -f
 723  *
 724  * Preconditions:
 725  *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
 726  *
 727  * Postconditions:
 728  *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
 729 static void fe_neg(fe h, const fe f) {
 730   unsigned i;
 731   for (i = 0; i < 10; i++) {
 732     h[i] = -f[i];
 733   }
 734 }
 735
 736 /* Replace (f,g) with (g,g) if b == 1;
 737  * replace (f,g) with (f,g) if b == 0.
 738  *
 739  * Preconditions: b in {0,1}. */
 740 static void fe_cmov(fe f, const fe g, unsigned b) {
 741   size_t i;
 742   b = 0-b;
 743   for (i = 0; i < 10; i++) {
 744     int32_t x = f[i] ^ g[i];
 745     x &= b;
 746     f[i] ^= x;
 747   }
 748 }
 749
 750 /* return 0 if f == 0
 751  * return 1 if f != 0
 752  *
 753  * Preconditions:
 754  *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
 755 static int fe_isnonzero(const fe f) {
 756   uint8_t s[32];
 757   static const uint8_t zero[32] = {0};
 758   fe_tobytes(s, f);
 759
 760   return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
 761 }
 762
 763 /* return 1 if f is in {1,3,5,...,q-2}
 764  * return 0 if f is in {0,2,4,...,q-1}
 765  *
 766  * Preconditions:
 767  *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
 768 static int fe_isnegative(const fe f) {
 769   uint8_t s[32];
 770   fe_tobytes(s, f);
 771   return s[0] & 1;
 772 }
 773
 774 /* h = 2 * f * f
 775  * Can overlap h with f.
 776  *
 777  * Preconditions:
 778  *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
 779  *
 780  * Postconditions:
 781  *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
 782  *
 783  * See fe_mul.c for discussion of implementation strategy. */
 784 static void fe_sq2(fe h, const fe f) {
 785   int32_t f0 = f[0];
 786   int32_t f1 = f[1];
 787   int32_t f2 = f[2];
 788   int32_t f3 = f[3];
 789   int32_t f4 = f[4];
 790   int32_t f5 = f[5];
 791   int32_t f6 = f[6];
 792   int32_t f7 = f[7];
 793   int32_t f8 = f[8];
 794   int32_t f9 = f[9];
 795   int32_t f0_2 = 2 * f0;
 796   int32_t f1_2 = 2 * f1;
 797   int32_t f2_2 = 2 * f2;
 798   int32_t f3_2 = 2 * f3;
 799   int32_t f4_2 = 2 * f4;
 800   int32_t f5_2 = 2 * f5;
 801   int32_t f6_2 = 2 * f6;
 802   int32_t f7_2 = 2 * f7;
 803   int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
 804   int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
 805   int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
 806   int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
 807   int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
 808   int64_t f0f0    = f0   * (int64_t) f0;
 809   int64_t f0f1_2  = f0_2 * (int64_t) f1;
 810   int64_t f0f2_2  = f0_2 * (int64_t) f2;
 811   int64_t f0f3_2  = f0_2 * (int64_t) f3;
 812   int64_t f0f4_2  = f0_2 * (int64_t) f4;
 813   int64_t f0f5_2  = f0_2 * (int64_t) f5;
 814   int64_t f0f6_2  = f0_2 * (int64_t) f6;
 815   int64_t f0f7_2  = f0_2 * (int64_t) f7;
 816   int64_t f0f8_2  = f0_2 * (int64_t) f8;
 817   int64_t f0f9_2  = f0_2 * (int64_t) f9;
 818   int64_t f1f1_2  = f1_2 * (int64_t) f1;
 819   int64_t f1f2_2  = f1_2 * (int64_t) f2;
 820   int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
 821   int64_t f1f4_2  = f1_2 * (int64_t) f4;
 822   int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
 823   int64_t f1f6_2  = f1_2 * (int64_t) f6;
 824   int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
 825   int64_t f1f8_2  = f1_2 * (int64_t) f8;
 826   int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
 827   int64_t f2f2    = f2   * (int64_t) f2;
 828   int64_t f2f3_2  = f2_2 * (int64_t) f3;
 829   int64_t f2f4_2  = f2_2 * (int64_t) f4;
 830   int64_t f2f5_2  = f2_2 * (int64_t) f5;
 831   int64_t f2f6_2  = f2_2 * (int64_t) f6;
 832   int64_t f2f7_2  = f2_2 * (int64_t) f7;
 833   int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
 834   int64_t f2f9_38 = f2   * (int64_t) f9_38;
 835   int64_t f3f3_2  = f3_2 * (int64_t) f3;
 836   int64_t f3f4_2  = f3_2 * (int64_t) f4;
 837   int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
 838   int64_t f3f6_2  = f3_2 * (int64_t) f6;
 839   int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
 840   int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
 841   int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
 842   int64_t f4f4    = f4   * (int64_t) f4;
 843   int64_t f4f5_2  = f4_2 * (int64_t) f5;
 844   int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
 845   int64_t f4f7_38 = f4   * (int64_t) f7_38;
 846   int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
 847   int64_t f4f9_38 = f4   * (int64_t) f9_38;
 848   int64_t f5f5_38 = f5   * (int64_t) f5_38;
 849   int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
 850   int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
 851   int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
 852   int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
 853   int64_t f6f6_19 = f6   * (int64_t) f6_19;
 854   int64_t f6f7_38 = f6   * (int64_t) f7_38;
 855   int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
 856   int64_t f6f9_38 = f6   * (int64_t) f9_38;
 857   int64_t f7f7_38 = f7   * (int64_t) f7_38;
 858   int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
 859   int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
 860   int64_t f8f8_19 = f8   * (int64_t) f8_19;
 861   int64_t f8f9_38 = f8   * (int64_t) f9_38;
 862   int64_t f9f9_38 = f9   * (int64_t) f9_38;
 863   int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
 864   int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
 865   int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
 866   int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
 867   int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
 868   int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
 869   int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
 870   int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
 871   int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
 872   int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
 873   int64_t carry0;
 874   int64_t carry1;
 875   int64_t carry2;
 876   int64_t carry3;
 877   int64_t carry4;
 878   int64_t carry5;
 879   int64_t carry6;
 880   int64_t carry7;
 881   int64_t carry8;
 882   int64_t carry9;
 883
 884   h0 += h0;
 885   h1 += h1;
 886   h2 += h2;
 887   h3 += h3;
 888   h4 += h4;
 889   h5 += h5;
 890   h6 += h6;
 891   h7 += h7;
 892   h8 += h8;
 893   h9 += h9;
 894
 895   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 896   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 897
 898   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
 899   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
 900
 901   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
 902   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
 903
 904   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
 905   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
 906
 907   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
 908   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
 909
 910   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
 911
 912   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
 913
 914   h[0] = h0;
 915   h[1] = h1;
 916   h[2] = h2;
 917   h[3] = h3;
 918   h[4] = h4;
 919   h[5] = h5;
 920   h[6] = h6;
 921   h[7] = h7;
 922   h[8] = h8;
 923   h[9] = h9;
 924 }
 925
 926 static void fe_pow22523(fe out, const fe z) {
 927   fe t0;
 928   fe t1;
 929   fe t2;
 930   int i;
 931
 932   fe_sq(t0, z);
 933   fe_sq(t1, t0);
 934   for (i = 1; i < 2; ++i) {
 935     fe_sq(t1, t1);
 936   }
 937   fe_mul(t1, z, t1);
 938   fe_mul(t0, t0, t1);
 939   fe_sq(t0, t0);
 940   fe_mul(t0, t1, t0);
 941   fe_sq(t1, t0);
 942   for (i = 1; i < 5; ++i) {
 943     fe_sq(t1, t1);
 944   }
 945   fe_mul(t0, t1, t0);
 946   fe_sq(t1, t0);
 947   for (i = 1; i < 10; ++i) {
 948     fe_sq(t1, t1);
 949   }
 950   fe_mul(t1, t1, t0);
 951   fe_sq(t2, t1);
 952   for (i = 1; i < 20; ++i) {
 953     fe_sq(t2, t2);
 954   }
 955   fe_mul(t1, t2, t1);
 956   fe_sq(t1, t1);
 957   for (i = 1; i < 10; ++i) {
 958     fe_sq(t1, t1);
 959   }
 960   fe_mul(t0, t1, t0);
 961   fe_sq(t1, t0);
 962   for (i = 1; i < 50; ++i) {
 963     fe_sq(t1, t1);
 964   }
 965   fe_mul(t1, t1, t0);
 966   fe_sq(t2, t1);
 967   for (i = 1; i < 100; ++i) {
 968     fe_sq(t2, t2);
 969   }
 970   fe_mul(t1, t2, t1);
 971   fe_sq(t1, t1);
 972   for (i = 1; i < 50; ++i) {
 973     fe_sq(t1, t1);
 974   }
 975   fe_mul(t0, t1, t0);
 976   fe_sq(t0, t0);
 977   for (i = 1; i < 2; ++i) {
 978     fe_sq(t0, t0);
 979   }
 980   fe_mul(out, t0, z);
 981 }
 982
 983 /* ge means group element.
 984
 985  * Here the group is the set of pairs (x,y) of field elements (see fe.h)
 986  * satisfying -x^2 + y^2 = 1 + d x^2y^2
 987  * where d = -121665/121666.
 988  *
 989  * Representations:
 990  *   ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
 991  *   ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
 992  *   ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
 993  *   ge_precomp (Duif): (y+x,y-x,2dxy) */
 994
 995 typedef struct {
 996   fe X;
 997   fe Y;
 998   fe Z;
 999 } ge_p2;
1000
1001 typedef struct {
1002   fe X;
1003   fe Y;
1004   fe Z;
1005   fe T;
1006 } ge_p3;
1007
1008 typedef struct {
1009   fe X;
1010   fe Y;
1011   fe Z;
1012   fe T;
1013 } ge_p1p1;
1014
1015 typedef struct {
1016   fe yplusx;
1017   fe yminusx;
1018   fe xy2d;
1019 } ge_precomp;
1020
1021 typedef struct {
1022   fe YplusX;
1023   fe YminusX;
1024   fe Z;
1025   fe T2d;
1026 } ge_cached;
1027
1028 static void ge_tobytes(uint8_t *s, const ge_p2 *h) {
1029   fe recip;
1030   fe x;
1031   fe y;
1032
1033   fe_invert(recip, h->Z);
1034   fe_mul(x, h->X, recip);
1035   fe_mul(y, h->Y, recip);
1036   fe_tobytes(s, y);
1037   s[31] ^= fe_isnegative(x) << 7;
1038 }
1039
1040 static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
1041   fe recip;
1042   fe x;
1043   fe y;
1044
1045   fe_invert(recip, h->Z);
1046   fe_mul(x, h->X, recip);
1047   fe_mul(y, h->Y, recip);
1048   fe_tobytes(s, y);
1049   s[31] ^= fe_isnegative(x) << 7;
1050 }
1051
1052 static const fe d = {-10913610, 13857413, -15372611, 6949391,   114729,
1053                      -8787816,  -6275908, -3247719,  -18696448, -12055116};
1054
1055 static const fe sqrtm1 = {-32595792, -7943725,  9377950,  3500415, 12389472,
1056                           -272473,   -25146209, -2005654, 326686,  11406482};
1057
1058 static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
1059   fe u;
1060   fe v;
1061   fe v3;
1062   fe vxx;
1063   fe check;
1064
1065   fe_frombytes(h->Y, s);
1066   fe_1(h->Z);
1067   fe_sq(u, h->Y);
1068   fe_mul(v, u, d);
1069   fe_sub(u, u, h->Z); /* u = y^2-1 */
1070   fe_add(v, v, h->Z); /* v = dy^2+1 */
1071
1072   fe_sq(v3, v);
1073   fe_mul(v3, v3, v); /* v3 = v^3 */
1074   fe_sq(h->X, v3);
1075   fe_mul(h->X, h->X, v);
1076   fe_mul(h->X, h->X, u); /* x = uv^7 */
1077
1078   fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1079   fe_mul(h->X, h->X, v3);
1080   fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1081
1082   fe_sq(vxx, h->X);
1083   fe_mul(vxx, vxx, v);
1084   fe_sub(check, vxx, u); /* vx^2-u */
1085   if (fe_isnonzero(check)) {
1086     fe_add(check, vxx, u); /* vx^2+u */
1087     if (fe_isnonzero(check)) {
1088       return -1;
1089     }
1090     fe_mul(h->X, h->X, sqrtm1);
1091   }
1092
1093   if (fe_isnegative(h->X) != (s[31] >> 7)) {
1094     fe_neg(h->X, h->X);
1095   }
1096
1097   fe_mul(h->T, h->X, h->Y);
1098   return 0;
1099 }
1100
1101 static void ge_p2_0(ge_p2 *h) {
1102   fe_0(h->X);
1103   fe_1(h->Y);
1104   fe_1(h->Z);
1105 }
1106
1107 static void ge_p3_0(ge_p3 *h) {
1108   fe_0(h->X);
1109   fe_1(h->Y);
1110   fe_1(h->Z);
1111   fe_0(h->T);
1112 }
1113
1114 static void ge_precomp_0(ge_precomp *h) {
1115   fe_1(h->yplusx);
1116   fe_1(h->yminusx);
1117   fe_0(h->xy2d);
1118 }
1119
1120 /* r = p */
1121 static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
1122   fe_copy(r->X, p->X);
1123   fe_copy(r->Y, p->Y);
1124   fe_copy(r->Z, p->Z);
1125 }
1126
1127 static const fe d2 = {-21827239, -5839606,  -30745221, 13898782, 229458,
1128                       15978800,  -12551817, -6495438,  29715968, 9444199};
1129
1130 /* r = p */
1131 static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
1132   fe_add(r->YplusX, p->Y, p->X);
1133   fe_sub(r->YminusX, p->Y, p->X);
1134   fe_copy(r->Z, p->Z);
1135   fe_mul(r->T2d, p->T, d2);
1136 }
1137
1138 /* r = p */
1139 static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
1140   fe_mul(r->X, p->X, p->T);
1141   fe_mul(r->Y, p->Y, p->Z);
1142   fe_mul(r->Z, p->Z, p->T);
1143 }
1144
1145 /* r = p */
1146 static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
1147   fe_mul(r->X, p->X, p->T);
1148   fe_mul(r->Y, p->Y, p->Z);
1149   fe_mul(r->Z, p->Z, p->T);
1150   fe_mul(r->T, p->X, p->Y);
1151 }
1152
1153 /* r = 2 * p */
1154 static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
1155   fe t0;
1156
1157   fe_sq(r->X, p->X);
1158   fe_sq(r->Z, p->Y);
1159   fe_sq2(r->T, p->Z);
1160   fe_add(r->Y, p->X, p->Y);
1161   fe_sq(t0, r->Y);
1162   fe_add(r->Y, r->Z, r->X);
1163   fe_sub(r->Z, r->Z, r->X);
1164   fe_sub(r->X, t0, r->Y);
1165   fe_sub(r->T, r->T, r->Z);
1166 }
1167
1168 /* r = 2 * p */
1169 static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
1170   ge_p2 q;
1171   ge_p3_to_p2(&q, p);
1172   ge_p2_dbl(r, &q);
1173 }
1174
1175 /* r = p + q */
1176 static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
1177   fe t0;
1178
1179   fe_add(r->X, p->Y, p->X);
1180   fe_sub(r->Y, p->Y, p->X);
1181   fe_mul(r->Z, r->X, q->yplusx);
1182   fe_mul(r->Y, r->Y, q->yminusx);
1183   fe_mul(r->T, q->xy2d, p->T);
1184   fe_add(t0, p->Z, p->Z);
1185   fe_sub(r->X, r->Z, r->Y);
1186   fe_add(r->Y, r->Z, r->Y);
1187   fe_add(r->Z, t0, r->T);
1188   fe_sub(r->T, t0, r->T);
1189 }
1190
1191 /* r = p - q */
1192 static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
1193   fe t0;
1194
1195   fe_add(r->X, p->Y, p->X);
1196   fe_sub(r->Y, p->Y, p->X);
1197   fe_mul(r->Z, r->X, q->yminusx);
1198   fe_mul(r->Y, r->Y, q->yplusx);
1199   fe_mul(r->T, q->xy2d, p->T);
1200   fe_add(t0, p->Z, p->Z);
1201   fe_sub(r->X, r->Z, r->Y);
1202   fe_add(r->Y, r->Z, r->Y);
1203   fe_sub(r->Z, t0, r->T);
1204   fe_add(r->T, t0, r->T);
1205 }
1206
1207 /* r = p + q */
1208 static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
1209   fe t0;
1210
1211   fe_add(r->X, p->Y, p->X);
1212   fe_sub(r->Y, p->Y, p->X);
1213   fe_mul(r->Z, r->X, q->YplusX);
1214   fe_mul(r->Y, r->Y, q->YminusX);
1215   fe_mul(r->T, q->T2d, p->T);
1216   fe_mul(r->X, p->Z, q->Z);
1217   fe_add(t0, r->X, r->X);
1218   fe_sub(r->X, r->Z, r->Y);
1219   fe_add(r->Y, r->Z, r->Y);
1220   fe_add(r->Z, t0, r->T);
1221   fe_sub(r->T, t0, r->T);
1222 }
1223
1224 /* r = p - q */
1225 static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
1226   fe t0;
1227
1228   fe_add(r->X, p->Y, p->X);
1229   fe_sub(r->Y, p->Y, p->X);
1230   fe_mul(r->Z, r->X, q->YminusX);
1231   fe_mul(r->Y, r->Y, q->YplusX);
1232   fe_mul(r->T, q->T2d, p->T);
1233   fe_mul(r->X, p->Z, q->Z);
1234   fe_add(t0, r->X, r->X);
1235   fe_sub(r->X, r->Z, r->Y);
1236   fe_add(r->Y, r->Z, r->Y);
1237   fe_sub(r->Z, t0, r->T);
1238   fe_add(r->T, t0, r->T);
1239 }
1240
1241 static uint8_t equal(signed char b, signed char c) {
1242   uint8_t ub = b;
1243   uint8_t uc = c;
1244   uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
1245   uint32_t y = x;      /* 0: yes; 1..255: no */
1246   y -= 1;              /* 4294967295: yes; 0..254: no */
1247   y >>= 31;            /* 1: yes; 0: no */
1248   return y;
1249 }
1250
1251 static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
1252   fe_cmov(t->yplusx, u->yplusx, b);
1253   fe_cmov(t->yminusx, u->yminusx, b);
1254   fe_cmov(t->xy2d, u->xy2d, b);
1255 }
1256
1257 /* k25519Precomp[i][j] = (j+1)*256^i*B */
1258 static const ge_precomp k25519Precomp[32][8] = {
1259     {
1260         {
1261             {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
1262              27544626, -11754271, -6079156, 2047605},
1263             {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
1264              5043384, 19500929, -15469378},
1265             {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
1266              29287919, 11864899, -24514362, -4438546},
1267         },
1268         {
1269             {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
1270              -11717903, -3814571, -358445, -10211303},
1271             {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
1272              -15616551, 11189268, -26829678, -5319081},
1273             {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
1274              -3128826, -9541118, -15472047, -4166697},
1275         },
1276         {
1277             {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
1278              27787600, -14772189, 28944400, -1550024},
1279             {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
1280              16354577, -11775962, 7689662, 11199574},
1281             {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
1282              7512774, 10017326, -17749093, -9920357},
1283         },
1284         {
1285             {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
1286              -28926210, 15006023, 3284568, -6276540},
1287             {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
1288              7464579, 9656445, 13059162, 10374397},
1289             {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
1290              -3839045, -641708, -101325},
1291         },
1292         {
1293             {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
1294              32867885, 14515107, -15438304, 10819380},
1295             {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
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1297             {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
1298              28542350, 13850243, -23678021, -15815942},
1299         },
1300         {
1301             {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
1302              -19188627, -15224819, -9818940, -12085777},
1303             {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
1304              -15689887, 1762328, 14866737},
1305             {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
1306              -28236412, 3959421, 27914454, 4383652},
1307         },
1308         {
1309             {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
1310              5230134, -23952439, -15175766},
1311             {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
1312              20654025, 16520125, 30598449, 7715701},
1313             {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
1314              -31400660, 1370708, 29794553, -1409300},
1315         },
1316         {
1317             {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
1318              30290735, 10876454, -33154098, 2381726},
1319             {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
1320              -6236617, 3696005, -32300832, 15351955},
1321             {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
1322              -32961401, -2970515, 29551813, 10109425},
1323         },
1324     },
1325     {
1326         {
1327             {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
1328              -2378284, -1627556, 10092783, -4764171},
1329             {27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
1330              -32508754, 12005538, -17810127, 12803510},
1331             {17228999, -15661624, -1233527, 300140, -1224870, -11714777,
1332              30364213, -9038194, 18016357, 4397660},
1333         },
1334         {
1335             {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
1336              -26619106, 14544525, -17477504, 982639},
1337             {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
1338              -4120128, -21047696, 9934963},
1339             {5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
1340              -14747930, 4559895, -30123922, -10897950},
1341         },
1342         {
1343             {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
1344              24191034, 4541697, -13338309, 5500568},
1345             {12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
1346              -17430592, 12264343, 10874051, 13524335},
1347             {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
1348              5080568, -22528059, 5376628},
1349         },
1350         {
1351             {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
1352              -22321305, -9447443, 4535768, 1569007},
1353             {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
1354              -30494562, 3044290, 31848280, 12543772},
1355             {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
1356              -27377195, -2062731, 7718482, 14474653},
1357         },
1358         {
1359             {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
1360              -7236665, 24316168, -5253567},
1361             {13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
1362              33040651, -13424532, -20729456, 8321686},
1363             {21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
1364              23845965, -11874838, -9984458, 608372},
1365         },
1366         {
1367             {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
1368              1123968, -6780577, 27229399, 23887},
1369             {-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
1370              12797024, -6440308, -1633405, 16678954},
1371             {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
1372              -1508144, -4795045, -17169265, 4904953},
1373         },
1374         {
1375             {24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
1376              5169211, 16191880, 2128236, -4326833},
1377             {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
1378              -29806336, 916033, -6882542, -2986532},
1379             {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
1380              285431, 2763829, 15736322, 4143876},
1381         },
1382         {
1383             {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
1384              -14594663, 23527084, -16458268},
1385             {33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
1386              -32625340, 4087881, -15188911, -14416214},
1387             {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
1388              4357868, -4774191, -16323038},
1389         },
1390     },
1391     {
1392         {
1393             {6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
1394              23365147, -3949732, 7390890, 2759800},
1395             {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
1396              -4264057, 1244380, -12919645},
1397             {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
1398              9208236, 15886429, 16489664},
1399         },
1400         {
1401             {1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
1402              -13693198, 398369, -30606455, -712933},
1403             {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
1404              13348553, 12076947, -30836462, 5113182},
1405             {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
1406              -30341101, -7336386, 13847711, 5387222},
1407         },
1408         {
1409             {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
1410              8763061, 3617786, -19600662, 10370991},
1411             {20246567, -14369378, 22358229, -543712, 18507283, -10413996,
1412              14554437, -8746092, 32232924, 16763880},
1413             {9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
1414              11094161, 15689506, 3140038, -16510092},
1415         },
1416         {
1417             {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
1418              -27224800, 9448613, -28774454, 366295},
1419             {19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
1420              28344573, 8041113, 719605, 11671788},
1421             {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
1422              -15266516, 27000813, -10195553},
1423         },
1424         {
1425             {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
1426              5336097, 6750977, -14521026},
1427             {11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
1428              1695823, -8819122, 8169720, 16220347},
1429             {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
1430              -11144307, -2627664, -5990708, -14166033},
1431         },
1432         {
1433             {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
1434              27884329, 2847284, 2655861, 1738395},
1435             {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
1436              21651608, -3239336, -19087449, -11005278},
1437             {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
1438              5821408, 10478196, 8544890},
1439         },
1440         {
1441             {32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
1442              19270449, 12217473, 17789017, -3395995},
1443             {-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
1444              15479401, -3853233, 30460520, 1052596},
1445             {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
1446              27491595, -4612359, 3179268, -9478891},
1447         },
1448         {
1449             {31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
1450              -14756777, -16411740, 19072640, -9511060},
1451             {11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
1452              5977896, -5215017, 473099, 5040608},
1453             {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
1454              28326862, 1721092, -19558642, -3131606},
1455         },
1456     },
1457     {
1458         {
1459             {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
1460              8076149, -27868496, 11538389},
1461             {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
1462              8754525, 7446702, -5676054, 5797016},
1463             {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
1464              2014099, -9050574, -2369172, -5877341},
1465         },
1466         {
1467             {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
1468              1192730, -3714199, 15123619, 10811505},
1469             {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
1470              15776356, -28886779, -11974553},
1471             {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
1472              -20654173, -16484855, 4714547, -9600655},
1473         },
1474         {
1475             {15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
1476              24611599, -4543832, -11745876, 12340220},
1477             {12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
1478              9613953, 8241152, 15370987, 9608631},
1479             {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
1480              15866074, -28210621, -8814099},
1481         },
1482         {
1483             {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
1484              858697, 20571223, 8420556},
1485             {14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
1486              33531827, 12516406, -21574435, -12476749},
1487             {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
1488              7256740, 8791136, 15069930},
1489         },
1490         {
1491             {1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
1492              14711875, 4874229, -30663140, -2331391},
1493             {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
1494              -7912378, -33069337, 9234253},
1495             {20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
1496              31559055, -11609587, 18979186, 13396066},
1497         },
1498         {
1499             {24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
1500              -18816887, 13594782, 33514650, 7021958},
1501             {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
1502              -25948728, -3916677, -21480480, 12868082},
1503             {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
1504              -21446107, 2244500, -12455797, -8089383},
1505         },
1506         {
1507             {-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
1508              33086546, 8957937, -15233648, 5540521},
1509             {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
1510              -23710744, -1568984, -16128528, -14962807},
1511             {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
1512              892185, -11513277, -15205948},
1513         },
1514         {
1515             {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
1516              4763127, -19179614, 5867134},
1517             {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
1518              27846559, 5931263, -29749703, -16108455},
1519             {27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
1520              7283490, -15148073, -19526700, 7734629},
1521         },
1522     },
1523     {
1524         {
1525             {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
1526              7585295, -3176626, 18549497, 15302069},
1527             {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
1528              10458790, -6418461, -8872242, 8424746},
1529             {24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
1530              19206234, 7134917, -11284482, -828919},
1531         },
1532         {
1533             {11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
1534              10243738, -14685461, -5066034, 16498837},
1535             {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
1536              -14124238, 6536641, 10543906},
1537             {-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
1538              -2669190, -16625574, -27235709, 8876771},
1539         },
1540         {
1541             {-25742899, -12566864, -15649966, -846607, -33026686, -796288,
1542              -33481822, 15824474, -604426, -9039817},
1543             {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
1544              -4890037, 1657394, 3084098},
1545             {10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
1546              31280319, 14396151, -30233575, 15272409},
1547         },
1548         {
1549             {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
1550              -25173957, -12636138, -25014757, 1950504},
1551             {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
1552              -8384306, -8767532, 15341279, 8373727},
1553             {28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
1554              298136, -10232602, -2878207, 15190420},
1555         },
1556         {
1557             {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
1558              8669718, 2742393, -26033313, -6875003},
1559             {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
1560              9291594, -16247779, -12154742, 6048605},
1561             {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
1562              13934231, 5128323, 11213262, 9168384},
1563         },
1564         {
1565             {-26280513, 11007847, 19408960, -940758, -18592965, -4328580,
1566              -5088060, -11105150, 20470157, -16398701},
1567             {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
1568              -22783952, 14461608, 14042978, 5230683},
1569             {29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
1570              21556951, 3506042, -5933891, -12449708},
1571         },
1572         {
1573             {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683,
1574              -21284170, 8971513, -28539189, 15326563},
1575             {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669,
1576              -15523050, 15300988, -20514118, 9168260},
1577             {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939,
1578              -28948358, 9601605, 33087103, -9011387},
1579         },
1580         {
1581             {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461,
1582              -27444329, -15000531, -5996870, 15664672},
1583             {23294591, -16632613, -22650781, -8470978, 27844204, 11461195,
1584              13099750, -2460356, 18151676, 13417686},
1585             {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065,
1586              1661597, -12551441, 15271676, -15452665},
1587         },
1588     },
1589     {
1590         {
1591             {11433042, -13228665, 8239631, -5279517, -1985436, -725718,
1592              -18698764, 2167544, -6921301, -13440182},
1593             {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379,
1594              -9917708, -8638997, 12215110, 12028277},
1595             {14098400, 6555944, 23007258, 5757252, -15427832, -12950502,
1596              30123440, 4617780, -16900089, -655628},
1597         },
1598         {
1599             {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385,
1600              -15819999, 10154009, 23973261, -12684474},
1601             {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355,
1602              18341390, -11419951, 32013174, -10103539},
1603             {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104,
1604              21911214, 6354752, 4425632, -837822},
1605         },
1606         {
1607             {-10433389, -14612966, 22229858, -3091047, -13191166, 776729,
1608              -17415375, -12020462, 4725005, 14044970},
1609             {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390,
1610              -1411784, -19522291, -16109756},
1611             {-24864089, 12986008, -10898878, -5558584, -11312371, -148526,
1612              19541418, 8180106, 9282262, 10282508},
1613         },
1614         {
1615             {-26205082, 4428547, -8661196, -13194263, 4098402, -14165257,
1616              15522535, 8372215, 5542595, -10702683},
1617             {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360,
1618              -2781891, 6993761, -18093885, 10114655},
1619             {-20107055, -929418, 31422704, 10427861, -7110749, 6150669,
1620              -29091755, -11529146, 25953725, -106158},
1621         },
1622         {
1623             {-4234397, -8039292, -9119125, 3046000, 2101609, -12607294,
1624              19390020, 6094296, -3315279, 12831125},
1625             {-15998678, 7578152, 5310217, 14408357, -33548620, -224739,
1626              31575954, 6326196, 7381791, -2421839},
1627             {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640,
1628              6295303, 8082724, -15362489, 12339664},
1629         },
1630         {
1631             {27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414,
1632              15768922, 25091167, 14856294},
1633             {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300,
1634              -12695493, -22182473, -9012899},
1635             {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039,
1636              -27260765, 13866390, 30146206, 9142070},
1637         },
1638         {
1639             {3924129, -15307516, -13817122, -10054960, 12291820, -668366,
1640              -27702774, 9326384, -8237858, 4171294},
1641             {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944,
1642              26396185, 3731949, 345228, -5462949},
1643             {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387,
1644              2031539, -12391231, -16253183, -13582083},
1645         },
1646         {
1647             {31016211, -16722429, 26371392, -14451233, -5027349, 14854137,
1648              17477601, 3842657, 28012650, -16405420},
1649             {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560,
1650              -9189873, 16292057, -8867157, 3507940},
1651             {29439664, 3537914, 23333589, 6997794, -17555561, -11018068,
1652              -15209202, -15051267, -9164929, 6580396},
1653         },
1654     },
1655     {
1656         {
1657             {-12185861, -7679788, 16438269, 10826160, -8696817, -6235611,
1658              17860444, -9273846, -2095802, 9304567},
1659             {20714564, -4336911, 29088195, 7406487, 11426967, -5095705,
1660              14792667, -14608617, 5289421, -477127},
1661             {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462,
1662              17271490, 12349094, 26939669, -3752294},
1663         },
1664         {
1665             {-12889898, 9373458, 31595848, 16374215, 21471720, 13221525,
1666              -27283495, -12348559, -3698806, 117887},
1667             {22263325, -6560050, 3984570, -11174646, -15114008, -566785,
1668              28311253, 5358056, -23319780, 541964},
1669             {16259219, 3261970, 2309254, -15534474, -16885711, -4581916,
1670              24134070, -16705829, -13337066, -13552195},
1671         },
1672         {
1673             {9378160, -13140186, -22845982, -12745264, 28198281, -7244098,
1674              -2399684, -717351, 690426, 14876244},
1675             {24977353, -314384, -8223969, -13465086, 28432343, -1176353,
1676              -13068804, -12297348, -22380984, 6618999},
1677             {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193,
1678              8044829, -13817328, 32239829, -5652762},
1679         },
1680         {
1681             {-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647,
1682              -10350059, 32779359, 5095274},
1683             {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423,
1684              -24601656, 14506724, 21639561, -2630236},
1685             {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318,
1686              -1289502, -6863535, 17874574, 558605},
1687         },
1688         {
1689             {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700,
1690              33499487, 5080151, 2085892, 5119761},
1691             {-22205145, -2519528, -16381601, 414691, -25019550, 2170430,
1692              30634760, -8363614, -31999993, -5759884},
1693             {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256,
1694              27534430, -7192145, -22351378, 12961482},
1695         },
1696         {
1697             {-24492060, -9570771, 10368194, 11582341, -23397293, -2245287,
1698              16533930, 8206996, -30194652, -5159638},
1699             {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630,
1700              7031275, 7589640, 8945490},
1701             {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393,
1702              7251489, -11182180, 24099109, -14456170},
1703         },
1704         {
1705             {5019558, -7907470, 4244127, -14714356, -26933272, 6453165,
1706              -19118182, -13289025, -6231896, -10280736},
1707             {10853594, 10721687, 26480089, 5861829, -22995819, 1972175,
1708              -1866647, -10557898, -3363451, -6441124},
1709             {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661,
1710              -2008168, -13866408, 7421392},
1711         },
1712         {
1713             {8139927, -6546497, 32257646, -5890546, 30375719, 1886181,
1714              -21175108, 15441252, 28826358, -4123029},
1715             {6267086, 9695052, 7709135, -16603597, -32869068, -1886135,
1716              14795160, -7840124, 13746021, -1742048},
1717             {28584902, 7787108, -6732942, -15050729, 22846041, -7571236,
1718              -3181936, -363524, 4771362, -8419958},
1719         },
1720     },
1721     {
1722         {
1723             {24949256, 6376279, -27466481, -8174608, -18646154, -9930606,
1724              33543569, -12141695, 3569627, 11342593},
1725             {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886,
1726              4608608, 7325975, -14801071},
1727             {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312,
1728              -27400540, 10258390, -17646694, -8186692},
1729         },
1730         {
1731             {11431204, 15823007, 26570245, 14329124, 18029990, 4796082,
1732              -31446179, 15580664, 9280358, -3973687},
1733             {-160783, -10326257, -22855316, -4304997, -20861367, -13621002,
1734              -32810901, -11181622, -15545091, 4387441},
1735             {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370,
1736              -24513992, 8548137, 20617071, -7482001},
1737         },
1738         {
1739             {-938825, -3930586, -8714311, 16124718, 24603125, -6225393,
1740              -13775352, -11875822, 24345683, 10325460},
1741             {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528,
1742              16318175, -1010689, 4766743, 3552007},
1743             {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514,
1744              14481909, 10988822, -3994762},
1745         },
1746         {
1747             {15564307, -14311570, 3101243, 5684148, 30446780, -8051356,
1748              12677127, -6505343, -8295852, 13296005},
1749             {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379,
1750              31521204, 9614054, -30000824, 12074674},
1751             {4771191, -135239, 14290749, -13089852, 27992298, 14998318,
1752              -1413936, -1556716, 29832613, -16391035},
1753         },
1754         {
1755             {7064884, -7541174, -19161962, -5067537, -18891269, -2912736,
1756              25825242, 5293297, -27122660, 13101590},
1757             {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445,
1758              32512469, -5317593, -30356070, -4190957},
1759             {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044,
1760              14413974, 9515896, 19568978, 9628812},
1761         },
1762         {
1763             {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894,
1764              -6106839, -6291786, 3437740},
1765             {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290,
1766              -22961733, 70104, 7463304, 4176122},
1767             {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117,
1768              -32719404, -5322751, 24216882, 5944158},
1769         },
1770         {
1771             {8894125, 7450974, -2664149, -9765752, -28080517, -12389115,
1772              19345746, 14680796, 11632993, 5847885},
1773             {26942781, -2315317, 9129564, -4906607, 26024105, 11769399,
1774              -11518837, 6367194, -9727230, 4782140},
1775             {19916461, -4828410, -22910704, -11414391, 25606324, -5972441,
1776              33253853, 8220911, 6358847, -1873857},
1777         },
1778         {
1779             {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388,
1780              -4480480, -13538503, 1387155},
1781             {19646058, 5720633, -11416706, 12814209, 11607948, 12749789,
1782              14147075, 15156355, -21866831, 11835260},
1783             {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523,
1784              15467869, -26560550, 5052483},
1785         },
1786     },
1787     {
1788         {
1789             {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123,
1790              -12618185, 12228557, -7003677},
1791             {32944382, 14922211, -22844894, 5188528, 21913450, -8719943,
1792              4001465, 13238564, -6114803, 8653815},
1793             {22865569, -4652735, 27603668, -12545395, 14348958, 8234005,
1794              24808405, 5719875, 28483275, 2841751},
1795         },
1796         {
1797             {-16420968, -1113305, -327719, -12107856, 21886282, -15552774,
1798              -1887966, -315658, 19932058, -12739203},
1799             {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912,
1800              3999228, 13239134, -4777469, -13910208},
1801             {1382174, -11694719, 17266790, 9194690, -13324356, 9720081,
1802              20403944, 11284705, -14013818, 3093230},
1803         },
1804         {
1805             {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424,
1806              16271225, -24049421, -6691850},
1807             {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293,
1808              24123614, 15193618, -21652117, -16739389},
1809             {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484,
1810              31870908, 14690798, 17361620, 11864968},
1811         },
1812         {
1813             {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200,
1814              -12331205, -7486601, -25578460, -16240689},
1815             {14668462, -12270235, 26039039, 15305210, 25515617, 4542480,
1816              10453892, 6577524, 9145645, -6443880},
1817             {5974874, 3053895, -9433049, -10385191, -31865124, 3225009,
1818              -7972642, 3936128, -5652273, -3050304},
1819         },
1820         {
1821             {30625386, -4729400, -25555961, -12792866, -20484575, 7695099,
1822              17097188, -16303496, -27999779, 1803632},
1823             {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700,
1824              14911344, 12196514, -21405489, 7047412},
1825             {20093277, 9920966, -11138194, -5343857, 13161587, 12044805,
1826              -32856851, 4124601, -32343828, -10257566},
1827         },
1828         {
1829             {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605,
1830              4752377, -8714640, -21679658, 2288038},
1831             {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457,
1832              29457502, 14625692, -24819617, 12570232},
1833             {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109,
1834              -21159943, -3498680, -11974704, 4724943},
1835         },
1836         {
1837             {17960970, -11775534, -4140968, -9702530, -8876562, -1410617,
1838              -12907383, -8659932, -29576300, 1903856},
1839             {23134274, -14279132, -10681997, -1611936, 20684485, 15770816,
1840              -12989750, 3190296, 26955097, 14109738},
1841             {15308788, 5320727, -30113809, -14318877, 22902008, 7767164,
1842              29425325, -11277562, 31960942, 11934971},
1843         },
1844         {
1845             {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669,
1846              20638173, 4875028, 10491392, 1379718},
1847             {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801,
1848              33518459, 16176658, 21432314, 12180697},
1849             {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205,
1850              1465425, 12689540, -10301319, -13872883},
1851         },
1852     },
1853     {
1854         {
1855             {5414091, -15386041, -21007664, 9643570, 12834970, 1186149,
1856              -2622916, -1342231, 26128231, 6032912},
1857             {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156,
1858              3604025, 8316894, -25875034, -10437358},
1859             {3296484, 6223048, 24680646, -12246460, -23052020, 5903205,
1860              -8862297, -4639164, 12376617, 3188849},
1861         },
1862         {
1863             {29190488, -14659046, 27549113, -1183516, 3520066, -10697301,
1864              32049515, -7309113, -16109234, -9852307},
1865             {-14744486, -9309156, 735818, -598978, -20407687, -5057904,
1866              25246078, -15795669, 18640741, -960977},
1867             {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252,
1868              -31638386, -494430, 10530747, 1053335},
1869         },
1870         {
1871             {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384,
1872              -31462369, -2948985, 24018831, 15026644},
1873             {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631,
1874              25310643, 13003497, -2314791, -15145616},
1875             {-27419985, -603321, -8043984, -1669117, -26092265, 13987819,
1876              -27297622, 187899, -23166419, -2531735},
1877         },
1878         {
1879             {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473,
1880              9716667, 16266922, -5070217, 726099},
1881             {29370922, -6053998, 7334071, -15342259, 9385287, 2247707,
1882              -13661962, -4839461, 30007388, -15823341},
1883             {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109,
1884              730663, 9835848, 4555336},
1885         },
1886         {
1887             {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977,
1888              17693930, 544696, -11985298, 12422646},
1889             {31117226, -12215734, -13502838, 6561947, -9876867, -12757670,
1890              -5118685, -4096706, 29120153, 13924425},
1891             {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820,
1892              -9383939, -11317700, 7240931, -237388},
1893         },
1894         {
1895             {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771,
1896              1222336, 4389483, 3293637, -15551743},
1897             {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533,
1898              -24319580, 7733547, 12796905, -6335822},
1899             {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811,
1900              -28253339, 3647836, 3222231, -11160462},
1901         },
1902         {
1903             {18606113, 1693100, -25448386, -15170272, 4112353, 10045021,
1904              23603893, -2048234, -7550776, 2484985},
1905             {9255317, -3131197, -12156162, -1004256, 13098013, -9214866,
1906              16377220, -2102812, -19802075, -3034702},
1907             {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502,
1908              -31718148, 9936966, -30097688, -10618797},
1909         },
1910         {
1911             {21878590, -5001297, 4338336, 13643897, -3036865, 13160960,
1912              19708896, 5415497, -7360503, -4109293},
1913             {27736861, 10103576, 12500508, 8502413, -3413016, -9633558,
1914              10436918, -1550276, -23659143, -8132100},
1915             {19492550, -12104365, -29681976, -852630, -3208171, 12403437,
1916              30066266, 8367329, 13243957, 8709688},
1917         },
1918     },
1919     {
1920         {
1921             {12015105, 2801261, 28198131, 10151021, 24818120, -4743133,
1922              -11194191, -5645734, 5150968, 7274186},
1923             {2831366, -12492146, 1478975, 6122054, 23825128, -12733586,
1924              31097299, 6083058, 31021603, -9793610},
1925             {-2529932, -2229646, 445613, 10720828, -13849527, -11505937,
1926              -23507731, 16354465, 15067285, -14147707},
1927         },
1928         {
1929             {7840942, 14037873, -33364863, 15934016, -728213, -3642706,
1930              21403988, 1057586, -19379462, -12403220},
1931             {915865, -16469274, 15608285, -8789130, -24357026, 6060030,
1932              -17371319, 8410997, -7220461, 16527025},
1933             {32922597, -556987, 20336074, -16184568, 10903705, -5384487,
1934              16957574, 52992, 23834301, 6588044},
1935         },
1936         {
1937             {32752030, 11232950, 3381995, -8714866, 22652988, -10744103,
1938              17159699, 16689107, -20314580, -1305992},
1939             {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943,
1940              7924251, -2752281, 1976123, -7249027},
1941             {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041,
1942              -3371252, 12331345, -8237197},
1943         },
1944         {
1945             {8651614, -4477032, -16085636, -4996994, 13002507, 2950805,
1946              29054427, -5106970, 10008136, -4667901},
1947             {31486080, 15114593, -14261250, 12951354, 14369431, -7387845,
1948              16347321, -13662089, 8684155, -10532952},
1949             {19443825, 11385320, 24468943, -9659068, -23919258, 2187569,
1950              -26263207, -6086921, 31316348, 14219878},
1951         },
1952         {
1953             {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801,
1954              27146014, 6992409, 29126555, 9207390},
1955             {32382935, 1110093, 18477781, 11028262, -27411763, -7548111,
1956              -4980517, 10843782, -7957600, -14435730},
1957             {2814918, 7836403, 27519878, -7868156, -20894015, -11553689,
1958              -21494559, 8550130, 28346258, 1994730},
1959         },
1960         {
1961             {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307,
1962              -19516951, 7174894, 22628102, 8115180},
1963             {-30405132, 955511, -11133838, -15078069, -32447087, -13278079,
1964              -25651578, 3317160, -9943017, 930272},
1965             {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177,
1966              24091212, -1388970, -22765376, -10650715},
1967         },
1968         {
1969             {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053,
1970              -14839018, -16554220, -1867018, 8398970},
1971             {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670,
1972              22981545, -6291273, 18009408, -15772772},
1973             {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469,
1974              29551787, -3727419, 19288549, 1325865},
1975         },
1976         {
1977             {15100157, -15835752, -23923978, -1005098, -26450192, 15509408,
1978              12376730, -3479146, 33166107, -8042750},
1979             {20909231, 13023121, -9209752, 16251778, -5778415, -8094914,
1980              12412151, 10018715, 2213263, -13878373},
1981             {32529814, -11074689, 30361439, -16689753, -9135940, 1513226,
1982              22922121, 6382134, -5766928, 8371348},
1983         },
1984     },
1985     {
1986         {
1987             {9923462, 11271500, 12616794, 3544722, -29998368, -1721626,
1988              12891687, -8193132, -26442943, 10486144},
1989             {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726,
1990              2610596, -23921530, -11455195},
1991             {5408411, -1136691, -4969122, 10561668, 24145918, 14240566,
1992              31319731, -4235541, 19985175, -3436086},
1993         },
1994         {
1995             {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976,
1996              -17577068, 8849297, 65030, 8370684},
1997             {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277,
1998              -19442942, 6922164, 12743482, -9800518},
1999             {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717,
2000              23783145, 11038569, 18800704, 255233},
2001         },
2002         {
2003             {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847,
2004              9066957, 19258688, -14753793},
2005             {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541,
2006              -31934921, 2209390, -1524053, 2055794},
2007             {580882, 16705327, 5468415, -2683018, -30926419, -14696000,
2008              -7203346, -8994389, -30021019, 7394435},
2009         },
2010         {
2011             {23838809, 1822728, -15738443, 15242727, 8318092, -3733104,
2012              -21672180, -3492205, -4821741, 14799921},
2013             {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804,
2014              13496856, -9056018, 7402518},
2015             {2286874, -4435931, -20042458, -2008336, -13696227, 5038122,
2016              11006906, -15760352, 8205061, 1607563},
2017         },
2018         {
2019             {14414086, -8002132, 3331830, -3208217, 22249151, -5594188,
2020              18364661, -2906958, 30019587, -9029278},
2021             {-27688051, 1585953, -10775053, 931069, -29120221, -11002319,
2022              -14410829, 12029093, 9944378, 8024},
2023             {4368715, -3709630, 29874200, -15022983, -20230386, -11410704,
2024              -16114594, -999085, -8142388, 5640030},
2025         },
2026         {
2027             {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887,
2028              -16694564, 15219798, -14327783},
2029             {27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605,
2030              -1173195, -18342183, 9742717},
2031             {6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614,
2032              7406442, 12420155, 1994844},
2033         },
2034         {
2035             {14012521, -5024720, -18384453, -9578469, -26485342, -3936439,
2036              -13033478, -10909803, 24319929, -6446333},
2037             {16412690, -4507367, 10772641, 15929391, -17068788, -4658621,
2038              10555945, -10484049, -30102368, -4739048},
2039             {22397382, -7767684, -9293161, -12792868, 17166287, -9755136,
2040              -27333065, 6199366, 21880021, -12250760},
2041         },
2042         {
2043             {-4283307, 5368523, -31117018, 8163389, -30323063, 3209128,
2044              16557151, 8890729, 8840445, 4957760},
2045             {-15447727, 709327, -6919446, -10870178, -29777922, 6522332,
2046              -21720181, 12130072, -14796503, 5005757},
2047             {-2114751, -14308128, 23019042, 15765735, -25269683, 6002752,
2048              10183197, -13239326, -16395286, -2176112},
2049         },
2050     },
2051     {
2052         {
2053             {-19025756, 1632005, 13466291, -7995100, -23640451, 16573537,
2054              -32013908, -3057104, 22208662, 2000468},
2055             {3065073, -1412761, -25598674, -361432, -17683065, -5703415,
2056              -8164212, 11248527, -3691214, -7414184},
2057             {10379208, -6045554, 8877319, 1473647, -29291284, -12507580,
2058              16690915, 2553332, -3132688, 16400289},
2059         },
2060         {
2061             {15716668, 1254266, -18472690, 7446274, -8448918, 6344164,
2062              -22097271, -7285580, 26894937, 9132066},
2063             {24158887, 12938817, 11085297, -8177598, -28063478, -4457083,
2064              -30576463, 64452, -6817084, -2692882},
2065             {13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710,
2066              -3418511, -4688006, 2364226},
2067         },
2068         {
2069             {16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024,
2070              -11697457, 15445875, -7798101},
2071             {29004207, -7867081, 28661402, -640412, -12794003, -7943086,
2072              31863255, -4135540, -278050, -15759279},
2073             {-6122061, -14866665, -28614905, 14569919, -10857999, -3591829,
2074              10343412, -6976290, -29828287, -10815811},
2075         },
2076         {
2077             {27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636,
2078              15372179, 17293797, 960709},
2079             {20263915, 11434237, -5765435, 11236810, 13505955, -10857102,
2080              -16111345, 6493122, -19384511, 7639714},
2081             {-2830798, -14839232, 25403038, -8215196, -8317012, -16173699,
2082              18006287, -16043750, 29994677, -15808121},
2083         },
2084         {
2085             {9769828, 5202651, -24157398, -13631392, -28051003, -11561624,
2086              -24613141, -13860782, -31184575, 709464},
2087             {12286395, 13076066, -21775189, -1176622, -25003198, 4057652,
2088              -32018128, -8890874, 16102007, 13205847},
2089             {13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170,
2090              8525972, 10151379, 10394400},
2091         },
2092         {
2093             {4024660, -16137551, 22436262, 12276534, -9099015, -2686099,
2094              19698229, 11743039, -33302334, 8934414},
2095             {-15879800, -4525240, -8580747, -2934061, 14634845, -698278,
2096              -9449077, 3137094, -11536886, 11721158},
2097             {17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229,
2098              8835153, -9205489, -1280045},
2099         },
2100         {
2101             {-461409, -7830014, 20614118, 16688288, -7514766, -4807119,
2102              22300304, 505429, 6108462, -6183415},
2103             {-5070281, 12367917, -30663534, 3234473, 32617080, -8422642,
2104              29880583, -13483331, -26898490, -7867459},
2105             {-31975283, 5726539, 26934134, 10237677, -3173717, -605053,
2106              24199304, 3795095, 7592688, -14992079},
2107         },
2108         {
2109             {21594432, -14964228, 17466408, -4077222, 32537084, 2739898,
2110              6407723, 12018833, -28256052, 4298412},
2111             {-20650503, -11961496, -27236275, 570498, 3767144, -1717540,
2112              13891942, -1569194, 13717174, 10805743},
2113             {-14676630, -15644296, 15287174, 11927123, 24177847, -8175568,
2114              -796431, 14860609, -26938930, -5863836},
2115         },
2116     },
2117     {
2118         {
2119             {12962541, 5311799, -10060768, 11658280, 18855286, -7954201,
2120              13286263, -12808704, -4381056, 9882022},
2121             {18512079, 11319350, -20123124, 15090309, 18818594, 5271736,
2122              -22727904, 3666879, -23967430, -3299429},
2123             {-6789020, -3146043, 16192429, 13241070, 15898607, -14206114,
2124              -10084880, -6661110, -2403099, 5276065},
2125         },
2126         {
2127             {30169808, -5317648, 26306206, -11750859, 27814964, 7069267,
2128              7152851, 3684982, 1449224, 13082861},
2129             {10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382,
2130              15056736, -21016438, -8202000},
2131             {-33150110, 3261608, 22745853, 7948688, 19370557, -15177665,
2132              -26171976, 6482814, -10300080, -11060101},
2133         },
2134         {
2135             {32869458, -5408545, 25609743, 15678670, -10687769, -15471071,
2136              26112421, 2521008, -22664288, 6904815},
2137             {29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737,
2138              3841096, -29003639, -6657642},
2139             {10340844, -6630377, -18656632, -2278430, 12621151, -13339055,
2140              30878497, -11824370, -25584551, 5181966},
2141         },
2142         {
2143             {25940115, -12658025, 17324188, -10307374, -8671468, 15029094,
2144              24396252, -16450922, -2322852, -12388574},
2145             {-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390,
2146              12641087, 20603771, -6561742},
2147             {-18882287, -11673380, 24849422, 11501709, 13161720, -4768874,
2148              1925523, 11914390, 4662781, 7820689},
2149         },
2150         {
2151             {12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456,
2152              12172924, 16136752, 15264020},
2153             {-10349955, -14680563, -8211979, 2330220, -17662549, -14545780,
2154              10658213, 6671822, 19012087, 3772772},
2155             {3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732,
2156              -15762884, 20527771, 12988982},
2157         },
2158         {
2159             {-14822485, -5797269, -3707987, 12689773, -898983, -10914866,
2160              -24183046, -10564943, 3299665, -12424953},
2161             {-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197,
2162              6461331, -25583147, 8991218},
2163             {-17226263, 1816362, -1673288, -6086439, 31783888, -8175991,
2164              -32948145, 7417950, -30242287, 1507265},
2165         },
2166         {
2167             {29692663, 6829891, -10498800, 4334896, 20945975, -11906496,
2168              -28887608, 8209391, 14606362, -10647073},
2169             {-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695,
2170              9761487, 4170404, -2085325},
2171             {-11587470, 14855945, -4127778, -1531857, -26649089, 15084046,
2172              22186522, 16002000, -14276837, -8400798},
2173         },
2174         {
2175             {-4811456, 13761029, -31703877, -2483919, -3312471, 7869047,
2176              -7113572, -9620092, 13240845, 10965870},
2177             {-7742563, -8256762, -14768334, -13656260, -23232383, 12387166,
2178              4498947, 14147411, 29514390, 4302863},
2179             {-13413405, -12407859, 20757302, -13801832, 14785143, 8976368,
2180              -5061276, -2144373, 17846988, -13971927},
2181         },
2182     },
2183     {
2184         {
2185             {-2244452, -754728, -4597030, -1066309, -6247172, 1455299,
2186              -21647728, -9214789, -5222701, 12650267},
2187             {-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813,
2188              13770293, -19134326, 10958663},
2189             {22470984, 12369526, 23446014, -5441109, -21520802, -9698723,
2190              -11772496, -11574455, -25083830, 4271862},
2191         },
2192         {
2193             {-25169565, -10053642, -19909332, 15361595, -5984358, 2159192,
2194              75375, -4278529, -32526221, 8469673},
2195             {15854970, 4148314, -8893890, 7259002, 11666551, 13824734,
2196              -30531198, 2697372, 24154791, -9460943},
2197             {15446137, -15806644, 29759747, 14019369, 30811221, -9610191,
2198              -31582008, 12840104, 24913809, 9815020},
2199         },
2200         {
2201             {-4709286, -5614269, -31841498, -12288893, -14443537, 10799414,
2202              -9103676, 13438769, 18735128, 9466238},
2203             {11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821,
2204              -10896103, -22728655, 16199064},
2205             {14576810, 379472, -26786533, -8317236, -29426508, -10812974,
2206              -102766, 1876699, 30801119, 2164795},
2207         },
2208         {
2209             {15995086, 3199873, 13672555, 13712240, -19378835, -4647646,
2210              -13081610, -15496269, -13492807, 1268052},
2211             {-10290614, -3659039, -3286592, 10948818, 23037027, 3794475,
2212              -3470338, -12600221, -17055369, 3565904},
2213             {29210088, -9419337, -5919792, -4952785, 10834811, -13327726,
2214              -16512102, -10820713, -27162222, -14030531},
2215         },
2216         {
2217             {-13161890, 15508588, 16663704, -8156150, -28349942, 9019123,
2218              -29183421, -3769423, 2244111, -14001979},
2219             {-5152875, -3800936, -9306475, -6071583, 16243069, 14684434,
2220              -25673088, -16180800, 13491506, 4641841},
2221             {10813417, 643330, -19188515, -728916, 30292062, -16600078,
2222              27548447, -7721242, 14476989, -12767431},
2223         },
2224         {
2225             {10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937,
2226              -1644259, -27912810, 12651324},
2227             {-31185513, -813383, 22271204, 11835308, 10201545, 15351028,
2228              17099662, 3988035, 21721536, -3148940},
2229             {10202177, -6545839, -31373232, -9574638, -32150642, -8119683,
2230              -12906320, 3852694, 13216206, 14842320},
2231         },
2232         {
2233             {-15815640, -10601066, -6538952, -7258995, -6984659, -6581778,
2234              -31500847, 13765824, -27434397, 9900184},
2235             {14465505, -13833331, -32133984, -14738873, -27443187, 12990492,
2236              33046193, 15796406, -7051866, -8040114},
2237             {30924417, -8279620, 6359016, -12816335, 16508377, 9071735,
2238              -25488601, 15413635, 9524356, -7018878},
2239         },
2240         {
2241             {12274201, -13175547, 32627641, -1785326, 6736625, 13267305,
2242              5237659, -5109483, 15663516, 4035784},
2243             {-2951309, 8903985, 17349946, 601635, -16432815, -4612556,
2244              -13732739, -15889334, -22258478, 4659091},
2245             {-16916263, -4952973, -30393711, -15158821, 20774812, 15897498,
2246              5736189, 15026997, -2178256, -13455585},
2247         },
2248     },
2249     {
2250         {
2251             {-8858980, -2219056, 28571666, -10155518, -474467, -10105698,
2252              -3801496, 278095, 23440562, -290208},
2253             {10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275,
2254              11551483, -16571960, -7442864},
2255             {17932739, -12437276, -24039557, 10749060, 11316803, 7535897,
2256              22503767, 5561594, -3646624, 3898661},
2257         },
2258         {
2259             {7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531,
2260              7152530, 21831162, 1245233},
2261             {26958459, -14658026, 4314586, 8346991, -5677764, 11960072,
2262              -32589295, -620035, -30402091, -16716212},
2263             {-12165896, 9166947, 33491384, 13673479, 29787085, 13096535,
2264              6280834, 14587357, -22338025, 13987525},
2265         },
2266         {
2267             {-24349909, 7778775, 21116000, 15572597, -4833266, -5357778,
2268              -4300898, -5124639, -7469781, -2858068},
2269             {9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781,
2270              6439245, -14581012, 4091397},
2271             {-8426427, 1470727, -28109679, -1596990, 3978627, -5123623,
2272              -19622683, 12092163, 29077877, -14741988},
2273         },
2274         {
2275             {5269168, -6859726, -13230211, -8020715, 25932563, 1763552,
2276              -5606110, -5505881, -20017847, 2357889},
2277             {32264008, -15407652, -5387735, -1160093, -2091322, -3946900,
2278              23104804, -12869908, 5727338, 189038},
2279             {14609123, -8954470, -6000566, -16622781, -14577387, -7743898,
2280              -26745169, 10942115, -25888931, -14884697},
2281         },
2282         {
2283             {20513500, 5557931, -15604613, 7829531, 26413943, -2019404,
2284              -21378968, 7471781, 13913677, -5137875},
2285             {-25574376, 11967826, 29233242, 12948236, -6754465, 4713227,
2286              -8940970, 14059180, 12878652, 8511905},
2287             {-25656801, 3393631, -2955415, -7075526, -2250709, 9366908,
2288              -30223418, 6812974, 5568676, -3127656},
2289         },
2290         {
2291             {11630004, 12144454, 2116339, 13606037, 27378885, 15676917,
2292              -17408753, -13504373, -14395196, 8070818},
2293             {27117696, -10007378, -31282771, -5570088, 1127282, 12772488,
2294              -29845906, 10483306, -11552749, -1028714},
2295             {10637467, -5688064, 5674781, 1072708, -26343588, -6982302,
2296              -1683975, 9177853, -27493162, 15431203},
2297         },
2298         {
2299             {20525145, 10892566, -12742472, 12779443, -29493034, 16150075,
2300              -28240519, 14943142, -15056790, -7935931},
2301             {-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767,
2302              -3239766, -3356550, 9594024},
2303             {-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683,
2304              -6492290, 13352335, -10977084},
2305         },
2306         {
2307             {-1931799, -5407458, 3304649, -12884869, 17015806, -4877091,
2308              -29783850, -7752482, -13215537, -319204},
2309             {20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742,
2310              15077870, -22750759, 14523817},
2311             {27406042, -6041657, 27423596, -4497394, 4996214, 10002360,
2312              -28842031, -4545494, -30172742, -4805667},
2313         },
2314     },
2315     {
2316         {
2317             {11374242, 12660715, 17861383, -12540833, 10935568, 1099227,
2318              -13886076, -9091740, -27727044, 11358504},
2319             {-12730809, 10311867, 1510375, 10778093, -2119455, -9145702,
2320              32676003, 11149336, -26123651, 4985768},
2321             {-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043,
2322              13794114, -19414307, -15621255},
2323         },
2324         {
2325             {6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603,
2326              6970005, -1691065, -9004790},
2327             {1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622,
2328              -5475723, -16796596, -5031438},
2329             {-22273315, -13524424, -64685, -4334223, -18605636, -10921968,
2330              -20571065, -7007978, -99853, -10237333},
2331         },
2332         {
2333             {17747465, 10039260, 19368299, -4050591, -20630635, -16041286,
2334              31992683, -15857976, -29260363, -5511971},
2335             {31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999,
2336              -3744247, 4882242, -10626905},
2337             {29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198,
2338              3272828, -5190932, -4162409},
2339         },
2340         {
2341             {12501286, 4044383, -8612957, -13392385, -32430052, 5136599,
2342              -19230378, -3529697, 330070, -3659409},
2343             {6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522,
2344              -8573892, -271295, 12071499},
2345             {-8365515, -4042521, 25133448, -4517355, -6211027, 2265927,
2346              -32769618, 1936675, -5159697, 3829363},
2347         },
2348         {
2349             {28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550,
2350              -6567787, 26333140, 14267664},
2351             {-11067219, 11871231, 27385719, -10559544, -4585914, -11189312,
2352              10004786, -8709488, -21761224, 8930324},
2353             {-21197785, -16396035, 25654216, -1725397, 12282012, 11008919,
2354              1541940, 4757911, -26491501, -16408940},
2355         },
2356         {
2357             {13537262, -7759490, -20604840, 10961927, -5922820, -13218065,
2358              -13156584, 6217254, -15943699, 13814990},
2359             {-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681,
2360              9257833, -1956526, -1776914},
2361             {-25045300, -10191966, 15366585, 15166509, -13105086, 8423556,
2362              -29171540, 12361135, -18685978, 4578290},
2363         },
2364         {
2365             {24579768, 3711570, 1342322, -11180126, -27005135, 14124956,
2366              -22544529, 14074919, 21964432, 8235257},
2367             {-6528613, -2411497, 9442966, -5925588, 12025640, -1487420,
2368              -2981514, -1669206, 13006806, 2355433},
2369             {-16304899, -13605259, -6632427, -5142349, 16974359, -10911083,
2370              27202044, 1719366, 1141648, -12796236},
2371         },
2372         {
2373             {-12863944, -13219986, -8318266, -11018091, -6810145, -4843894,
2374              13475066, -3133972, 32674895, 13715045},
2375             {11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
2376              -13265253, 16086212, -28740881, -15642093},
2377             {-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
2378              -11709148, 7791794, -27245943, 4383347},
2379         },
2380     },
2381     {
2382         {
2383             {-28970898, 5271447, -1266009, -9736989, -12455236, 16732599,
2384              -4862407, -4906449, 27193557, 6245191},
2385             {-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898,
2386              3260492, 22510453, 8577507},
2387             {-12632451, 11257346, -32692994, 13548177, -721004, 10879011,
2388              31168030, 13952092, -29571492, -3635906},
2389         },
2390         {
2391             {3877321, -9572739, 32416692, 5405324, -11004407, -13656635,
2392              3759769, 11935320, 5611860, 8164018},
2393             {-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
2394              32003002, -8832289, 5773085, -8422109},
2395             {-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
2396              12376320, 31632953, 190926},
2397         },
2398         {
2399             {-24593607, -16138885, -8423991, 13378746, 14162407, 6901328,
2400              -8288749, 4508564, -25341555, -3627528},
2401             {8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941,
2402              -14786005, -1672488, 827625},
2403             {-32720583, -16289296, -32503547, 7101210, 13354605, 2659080,
2404              -1800575, -14108036, -24878478, 1541286},
2405         },
2406         {
2407             {2901347, -1117687, 3880376, -10059388, -17620940, -3612781,
2408              -21802117, -3567481, 20456845, -1885033},
2409             {27019610, 12299467, -13658288, -1603234, -12861660, -4861471,
2410              -19540150, -5016058, 29439641, 15138866},
2411             {21536104, -6626420, -32447818, -10690208, -22408077, 5175814,
2412              -5420040, -16361163, 7779328, 109896},
2413         },
2414         {
2415             {30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390,
2416              12180118, 23177719, -554075},
2417             {26572847, 3405927, -31701700, 12890905, -19265668, 5335866,
2418              -6493768, 2378492, 4439158, -13279347},
2419             {-22716706, 3489070, -9225266, -332753, 18875722, -1140095,
2420              14819434, -12731527, -17717757, -5461437},
2421         },
2422         {
2423             {-5056483, 16566551, 15953661, 3767752, -10436499, 15627060,
2424              -820954, 2177225, 8550082, -15114165},
2425             {-18473302, 16596775, -381660, 15663611, 22860960, 15585581,
2426              -27844109, -3582739, -23260460, -8428588},
2427             {-32480551, 15707275, -8205912, -5652081, 29464558, 2713815,
2428              -22725137, 15860482, -21902570, 1494193},
2429         },
2430         {
2431             {-19562091, -14087393, -25583872, -9299552, 13127842, 759709,
2432              21923482, 16529112, 8742704, 12967017},
2433             {-28464899, 1553205, 32536856, -10473729, -24691605, -406174,
2434              -8914625, -2933896, -29903758, 15553883},
2435             {21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572,
2436              14513274, 19375923, -12647961},
2437         },
2438         {
2439             {8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818,
2440              -6222716, 2862653, 9455043},
2441             {29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124,
2442              -2990080, 15511449, 4789663},
2443             {-20679756, 7004547, 8824831, -9434977, -4045704, -3750736,
2444              -5754762, 108893, 23513200, 16652362},
2445         },
2446     },
2447     {
2448         {
2449             {-33256173, 4144782, -4476029, -6579123, 10770039, -7155542,
2450              -6650416, -12936300, -18319198, 10212860},
2451             {2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801,
2452              2600940, -9988298, -12506466},
2453             {-24645692, 13317462, -30449259, -15653928, 21365574, -10869657,
2454              11344424, 864440, -2499677, -16710063},
2455         },
2456         {
2457             {-26432803, 6148329, -17184412, -14474154, 18782929, -275997,
2458              -22561534, 211300, 2719757, 4940997},
2459             {-1323882, 3911313, -6948744, 14759765, -30027150, 7851207,
2460              21690126, 8518463, 26699843, 5276295},
2461             {-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586,
2462              149635, -15452774, 7159369},
2463         },
2464         {
2465             {9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009,
2466              8312176, 22477218, -8403385},
2467             {18155857, -16504990, 19744716, 9006923, 15154154, -10538976,
2468              24256460, -4864995, -22548173, 9334109},
2469             {2986088, -4911893, 10776628, -3473844, 10620590, -7083203,
2470              -21413845, 14253545, -22587149, 536906},
2471         },
2472         {
2473             {4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551,
2474              10589625, 10838060, -15420424},
2475             {-19342404, 867880, 9277171, -3218459, -14431572, -1986443,
2476              19295826, -15796950, 6378260, 699185},
2477             {7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039,
2478              15693155, -5045064, -13373962},
2479         },
2480         {
2481             {-7737563, -5869402, -14566319, -7406919, 11385654, 13201616,
2482              31730678, -10962840, -3918636, -9669325},
2483             {10188286, -15770834, -7336361, 13427543, 22223443, 14896287,
2484              30743455, 7116568, -21786507, 5427593},
2485             {696102, 13206899, 27047647, -10632082, 15285305, -9853179,
2486              10798490, -4578720, 19236243, 12477404},
2487         },
2488         {
2489             {-11229439, 11243796, -17054270, -8040865, -788228, -8167967,
2490              -3897669, 11180504, -23169516, 7733644},
2491             {17800790, -14036179, -27000429, -11766671, 23887827, 3149671,
2492              23466177, -10538171, 10322027, 15313801},
2493             {26246234, 11968874, 32263343, -5468728, 6830755, -13323031,
2494              -15794704, -101982, -24449242, 10890804},
2495         },
2496         {
2497             {-31365647, 10271363, -12660625, -6267268, 16690207, -13062544,
2498              -14982212, 16484931, 25180797, -5334884},
2499             {-586574, 10376444, -32586414, -11286356, 19801893, 10997610,
2500              2276632, 9482883, 316878, 13820577},
2501             {-9882808, -4510367, -2115506, 16457136, -11100081, 11674996,
2502              30756178, -7515054, 30696930, -3712849},
2503         },
2504         {
2505             {32988917, -9603412, 12499366, 7910787, -10617257, -11931514,
2506              -7342816, -9985397, -32349517, 7392473},
2507             {-8855661, 15927861, 9866406, -3649411, -2396914, -16655781,
2508              -30409476, -9134995, 25112947, -2926644},
2509             {-2504044, -436966, 25621774, -5678772, 15085042, -5479877,
2510              -24884878, -13526194, 5537438, -13914319},
2511         },
2512     },
2513     {
2514         {
2515             {-11225584, 2320285, -9584280, 10149187, -33444663, 5808648,
2516              -14876251, -1729667, 31234590, 6090599},
2517             {-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721,
2518              15878753, -6970405, -9034768},
2519             {-27757857, 247744, -15194774, -9002551, 23288161, -10011936,
2520              -23869595, 6503646, 20650474, 1804084},
2521         },
2522         {
2523             {-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995,
2524              -10329713, 27842616, -202328},
2525             {-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656,
2526              5031932, -11375082, 12714369},
2527             {20807691, -7270825, 29286141, 11421711, -27876523, -13868230,
2528              -21227475, 1035546, -19733229, 12796920},
2529         },
2530         {
2531             {12076899, -14301286, -8785001, -11848922, -25012791, 16400684,
2532              -17591495, -12899438, 3480665, -15182815},
2533             {-32361549, 5457597, 28548107, 7833186, 7303070, -11953545,
2534              -24363064, -15921875, -33374054, 2771025},
2535             {-21389266, 421932, 26597266, 6860826, 22486084, -6737172,
2536              -17137485, -4210226, -24552282, 15673397},
2537         },
2538         {
2539             {-20184622, 2338216, 19788685, -9620956, -4001265, -8740893,
2540              -20271184, 4733254, 3727144, -12934448},
2541             {6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594,
2542              7975683, 31123697, -10958981},
2543             {30069250, -11435332, 30434654, 2958439, 18399564, -976289,
2544              12296869, 9204260, -16432438, 9648165},
2545         },
2546         {
2547             {32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266,
2548              5248604, -26008332, -11377501},
2549             {17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711,
2550              15298639, 2662509, -16297073},
2551             {-1172927, -7558695, -4366770, -4287744, -21346413, -8434326,
2552              32087529, -1222777, 32247248, -14389861},
2553         },
2554         {
2555             {14312628, 1221556, 17395390, -8700143, -4945741, -8684635,
2556              -28197744, -9637817, -16027623, -13378845},
2557             {-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502,
2558              9803137, 17597934, 2346211},
2559             {18510800, 15337574, 26171504, 981392, -22241552, 7827556,
2560              -23491134, -11323352, 3059833, -11782870},
2561         },
2562         {
2563             {10141598, 6082907, 17829293, -1947643, 9830092, 13613136,
2564              -25556636, -5544586, -33502212, 3592096},
2565             {33114168, -15889352, -26525686, -13343397, 33076705, 8716171,
2566              1151462, 1521897, -982665, -6837803},
2567             {-32939165, -4255815, 23947181, -324178, -33072974, -12305637,
2568              -16637686, 3891704, 26353178, 693168},
2569         },
2570         {
2571             {30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294,
2572              -400668, 31375464, 14369965},
2573             {-14370654, -7772529, 1510301, 6434173, -18784789, -6262728,
2574              32732230, -13108839, 17901441, 16011505},
2575             {18171223, -11934626, -12500402, 15197122, -11038147, -15230035,
2576              -19172240, -16046376, 8764035, 12309598},
2577         },
2578     },
2579     {
2580         {
2581             {5975908, -5243188, -19459362, -9681747, -11541277, 14015782,
2582              -23665757, 1228319, 17544096, -10593782},
2583             {5811932, -1715293, 3442887, -2269310, -18367348, -8359541,
2584              -18044043, -15410127, -5565381, 12348900},
2585             {-31399660, 11407555, 25755363, 6891399, -3256938, 14872274,
2586              -24849353, 8141295, -10632534, -585479},
2587         },
2588         {
2589             {-12675304, 694026, -5076145, 13300344, 14015258, -14451394,
2590              -9698672, -11329050, 30944593, 1130208},
2591             {8247766, -6710942, -26562381, -7709309, -14401939, -14648910,
2592              4652152, 2488540, 23550156, -271232},
2593             {17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737,
2594              -5908146, -408818, -137719},
2595         },
2596         {
2597             {16091085, -16253926, 18599252, 7340678, 2137637, -1221657,
2598              -3364161, 14550936, 3260525, -7166271},
2599             {-4910104, -13332887, 18550887, 10864893, -16459325, -7291596,
2600              -23028869, -13204905, -12748722, 2701326},
2601             {-8574695, 16099415, 4629974, -16340524, -20786213, -6005432,
2602              -10018363, 9276971, 11329923, 1862132},
2603         },
2604         {
2605             {14763076, -15903608, -30918270, 3689867, 3511892, 10313526,
2606              -21951088, 12219231, -9037963, -940300},
2607             {8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216,
2608              -2909717, -15438168, 11595570},
2609             {15214962, 3537601, -26238722, -14058872, 4418657, -15230761,
2610              13947276, 10730794, -13489462, -4363670},
2611         },
2612         {
2613             {-2538306, 7682793, 32759013, 263109, -29984731, -7955452,
2614              -22332124, -10188635, 977108, 699994},
2615             {-12466472, 4195084, -9211532, 550904, -15565337, 12917920,
2616              19118110, -439841, -30534533, -14337913},
2617             {31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237,
2618              -10051775, 12493932, -5409317},
2619         },
2620         {
2621             {-25680606, 5260744, -19235809, -6284470, -3695942, 16566087,
2622              27218280, 2607121, 29375955, 6024730},
2623             {842132, -2794693, -4763381, -8722815, 26332018, -12405641,
2624              11831880, 6985184, -9940361, 2854096},
2625             {-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645,
2626              960770, 12121869, 16648078},
2627         },
2628         {
2629             {-15218652, 14667096, -13336229, 2013717, 30598287, -464137,
2630              -31504922, -7882064, 20237806, 2838411},
2631             {-19288047, 4453152, 15298546, -16178388, 22115043, -15972604,
2632              12544294, -13470457, 1068881, -12499905},
2633             {-9558883, -16518835, 33238498, 13506958, 30505848, -1114596,
2634              -8486907, -2630053, 12521378, 4845654},
2635         },
2636         {
2637             {-28198521, 10744108, -2958380, 10199664, 7759311, -13088600,
2638              3409348, -873400, -6482306, -12885870},
2639             {-23561822, 6230156, -20382013, 10655314, -24040585, -11621172,
2640              10477734, -1240216, -3113227, 13974498},
2641             {12966261, 15550616, -32038948, -1615346, 21025980, -629444,
2642              5642325, 7188737, 18895762, 12629579},
2643         },
2644     },
2645     {
2646         {
2647             {14741879, -14946887, 22177208, -11721237, 1279741, 8058600,
2648              11758140, 789443, 32195181, 3895677},
2649             {10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575,
2650              -3566119, -8982069, 4429647},
2651             {-2453894, 15725973, -20436342, -10410672, -5803908, -11040220,
2652              -7135870, -11642895, 18047436, -15281743},
2653         },
2654         {
2655             {-25173001, -11307165, 29759956, 11776784, -22262383, -15820455,
2656              10993114, -12850837, -17620701, -9408468},
2657             {21987233, 700364, -24505048, 14972008, -7774265, -5718395,
2658              32155026, 2581431, -29958985, 8773375},
2659             {-25568350, 454463, -13211935, 16126715, 25240068, 8594567,
2660              20656846, 12017935, -7874389, -13920155},
2661         },
2662         {
2663             {6028182, 6263078, -31011806, -11301710, -818919, 2461772,
2664              -31841174, -5468042, -1721788, -2776725},
2665             {-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845,
2666              -4166698, 28408820, 6816612},
2667             {-10358094, -8237829, 19549651, -12169222, 22082623, 16147817,
2668              20613181, 13982702, -10339570, 5067943},
2669         },
2670         {
2671             {-30505967, -3821767, 12074681, 13582412, -19877972, 2443951,
2672              -19719286, 12746132, 5331210, -10105944},
2673             {30528811, 3601899, -1957090, 4619785, -27361822, -15436388,
2674              24180793, -12570394, 27679908, -1648928},
2675             {9402404, -13957065, 32834043, 10838634, -26580150, -13237195,
2676              26653274, -8685565, 22611444, -12715406},
2677         },
2678         {
2679             {22190590, 1118029, 22736441, 15130463, -30460692, -5991321,
2680              19189625, -4648942, 4854859, 6622139},
2681             {-8310738, -2953450, -8262579, -3388049, -10401731, -271929,
2682              13424426, -3567227, 26404409, 13001963},
2683             {-31241838, -15415700, -2994250, 8939346, 11562230, -12840670,
2684              -26064365, -11621720, -15405155, 11020693},
2685         },
2686         {
2687             {1866042, -7949489, -7898649, -10301010, 12483315, 13477547,
2688              3175636, -12424163, 28761762, 1406734},
2689             {-448555, -1777666, 13018551, 3194501, -9580420, -11161737,
2690              24760585, -4347088, 25577411, -13378680},
2691             {-24290378, 4759345, -690653, -1852816, 2066747, 10693769,
2692              -29595790, 9884936, -9368926, 4745410},
2693         },
2694         {
2695             {-9141284, 6049714, -19531061, -4341411, -31260798, 9944276,
2696              -15462008, -11311852, 10931924, -11931931},
2697             {-16561513, 14112680, -8012645, 4817318, -8040464, -11414606,
2698              -22853429, 10856641, -20470770, 13434654},
2699             {22759489, -10073434, -16766264, -1871422, 13637442, -10168091,
2700              1765144, -12654326, 28445307, -5364710},
2701         },
2702         {
2703             {29875063, 12493613, 2795536, -3786330, 1710620, 15181182,
2704              -10195717, -8788675, 9074234, 1167180},
2705             {-26205683, 11014233, -9842651, -2635485, -26908120, 7532294,
2706              -18716888, -9535498, 3843903, 9367684},
2707             {-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123,
2708              8601684, -139197, 4242895},
2709         },
2710     },
2711     {
2712         {
2713             {22092954, -13191123, -2042793, -11968512, 32186753, -11517388,
2714              -6574341, 2470660, -27417366, 16625501},
2715             {-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857,
2716              2602725, -27351616, 14247413},
2717             {6314175, -10264892, -32772502, 15957557, -10157730, 168750,
2718              -8618807, 14290061, 27108877, -1180880},
2719         },
2720         {
2721             {-8586597, -7170966, 13241782, 10960156, -32991015, -13794596,
2722              33547976, -11058889, -27148451, 981874},
2723             {22833440, 9293594, -32649448, -13618667, -9136966, 14756819,
2724              -22928859, -13970780, -10479804, -16197962},
2725             {-7768587, 3326786, -28111797, 10783824, 19178761, 14905060,
2726              22680049, 13906969, -15933690, 3797899},
2727         },
2728         {
2729             {21721356, -4212746, -12206123, 9310182, -3882239, -13653110,
2730              23740224, -2709232, 20491983, -8042152},
2731             {9209270, -15135055, -13256557, -6167798, -731016, 15289673,
2732              25947805, 15286587, 30997318, -6703063},
2733             {7392032, 16618386, 23946583, -8039892, -13265164, -1533858,
2734              -14197445, -2321576, 17649998, -250080},
2735         },
2736         {
2737             {-9301088, -14193827, 30609526, -3049543, -25175069, -1283752,
2738              -15241566, -9525724, -2233253, 7662146},
2739             {-17558673, 1763594, -33114336, 15908610, -30040870, -12174295,
2740              7335080, -8472199, -3174674, 3440183},
2741             {-19889700, -5977008, -24111293, -9688870, 10799743, -16571957,
2742              40450, -4431835, 4862400, 1133},
2743         },
2744         {
2745             {-32856209, -7873957, -5422389, 14860950, -16319031, 7956142,
2746              7258061, 311861, -30594991, -7379421},
2747             {-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763,
2748              16527196, 18278453, 15405622},
2749             {-4381906, 8508652, -19898366, -3674424, -5984453, 15149970,
2750              -13313598, 843523, -21875062, 13626197},
2751         },
2752         {
2753             {2281448, -13487055, -10915418, -2609910, 1879358, 16164207,
2754              -10783882, 3953792, 13340839, 15928663},
2755             {31727126, -7179855, -18437503, -8283652, 2875793, -16390330,
2756              -25269894, -7014826, -23452306, 5964753},
2757             {4100420, -5959452, -17179337, 6017714, -18705837, 12227141,
2758              -26684835, 11344144, 2538215, -7570755},
2759         },
2760         {
2761             {-9433605, 6123113, 11159803, -2156608, 30016280, 14966241,
2762              -20474983, 1485421, -629256, -15958862},
2763             {-26804558, 4260919, 11851389, 9658551, -32017107, 16367492,
2764              -20205425, -13191288, 11659922, -11115118},
2765             {26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568,
2766              -10170080, 33100372, -1306171},
2767         },
2768         {
2769             {15121113, -5201871, -10389905, 15427821, -27509937, -15992507,
2770              21670947, 4486675, -5931810, -14466380},
2771             {16166486, -9483733, -11104130, 6023908, -31926798, -1364923,
2772              2340060, -16254968, -10735770, -10039824},
2773             {28042865, -3557089, -12126526, 12259706, -3717498, -6945899,
2774              6766453, -8689599, 18036436, 5803270},
2775         },
2776     },
2777     {
2778         {
2779             {-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391,
2780              4598332, -6159431, -14117438},
2781             {-31031306, -14256194, 17332029, -2383520, 31312682, -5967183,
2782              696309, 50292, -20095739, 11763584},
2783             {-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117,
2784              -12613632, -19773211, -10713562},
2785         },
2786         {
2787             {30464590, -11262872, -4127476, -12734478, 19835327, -7105613,
2788              -24396175, 2075773, -17020157, 992471},
2789             {18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841,
2790              8080033, -11574335, -10601610},
2791             {19598397, 10334610, 12555054, 2555664, 18821899, -10339780,
2792              21873263, 16014234, 26224780, 16452269},
2793         },
2794         {
2795             {-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804,
2796              -7618186, -20533829, 3698650},
2797             {14187449, 3448569, -10636236, -10810935, -22663880, -3433596,
2798              7268410, -10890444, 27394301, 12015369},
2799             {19695761, 16087646, 28032085, 12999827, 6817792, 11427614,
2800              20244189, -1312777, -13259127, -3402461},
2801         },
2802         {
2803             {30860103, 12735208, -1888245, -4699734, -16974906, 2256940,
2804              -8166013, 12298312, -8550524, -10393462},
2805             {-5719826, -11245325, -1910649, 15569035, 26642876, -7587760,
2806              -5789354, -15118654, -4976164, 12651793},
2807             {-2848395, 9953421, 11531313, -5282879, 26895123, -12697089,
2808              -13118820, -16517902, 9768698, -2533218},
2809         },
2810         {
2811             {-24719459, 1894651, -287698, -4704085, 15348719, -8156530,
2812              32767513, 12765450, 4940095, 10678226},
2813             {18860224, 15980149, -18987240, -1562570, -26233012, -11071856,
2814              -7843882, 13944024, -24372348, 16582019},
2815             {-15504260, 4970268, -29893044, 4175593, -20993212, -2199756,
2816              -11704054, 15444560, -11003761, 7989037},
2817         },
2818         {
2819             {31490452, 5568061, -2412803, 2182383, -32336847, 4531686,
2820              -32078269, 6200206, -19686113, -14800171},
2821             {-17308668, -15879940, -31522777, -2831, -32887382, 16375549,
2822              8680158, -16371713, 28550068, -6857132},
2823             {-28126887, -5688091, 16837845, -1820458, -6850681, 12700016,
2824              -30039981, 4364038, 1155602, 5988841},
2825         },
2826         {
2827             {21890435, -13272907, -12624011, 12154349, -7831873, 15300496,
2828              23148983, -4470481, 24618407, 8283181},
2829             {-33136107, -10512751, 9975416, 6841041, -31559793, 16356536,
2830              3070187, -7025928, 1466169, 10740210},
2831             {-1509399, -15488185, -13503385, -10655916, 32799044, 909394,
2832              -13938903, -5779719, -32164649, -15327040},
2833         },
2834         {
2835             {3960823, -14267803, -28026090, -15918051, -19404858, 13146868,
2836              15567327, 951507, -3260321, -573935},
2837             {24740841, 5052253, -30094131, 8961361, 25877428, 6165135,
2838              -24368180, 14397372, -7380369, -6144105},
2839             {-28888365, 3510803, -28103278, -1158478, -11238128, -10631454,
2840              -15441463, -14453128, -1625486, -6494814},
2841         },
2842     },
2843     {
2844         {
2845             {793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843,
2846              -4885251, -9906200, -621852},
2847             {5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374,
2848              1468826, -6171428, -15186581},
2849             {-4859255, -3779343, -2917758, -6748019, 7778750, 11688288,
2850              -30404353, -9871238, -1558923, -9863646},
2851         },
2852         {
2853             {10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958,
2854              14783338, -30581476, -15757844},
2855             {10566929, 12612572, -31944212, 11118703, -12633376, 12362879,
2856              21752402, 8822496, 24003793, 14264025},
2857             {27713862, -7355973, -11008240, 9227530, 27050101, 2504721,
2858              23886875, -13117525, 13958495, -5732453},
2859         },
2860         {
2861             {-23481610, 4867226, -27247128, 3900521, 29838369, -8212291,
2862              -31889399, -10041781, 7340521, -15410068},
2863             {4646514, -8011124, -22766023, -11532654, 23184553, 8566613,
2864              31366726, -1381061, -15066784, -10375192},
2865             {-17270517, 12723032, -16993061, 14878794, 21619651, -6197576,
2866              27584817, 3093888, -8843694, 3849921},
2867         },
2868         {
2869             {-9064912, 2103172, 25561640, -15125738, -5239824, 9582958,
2870              32477045, -9017955, 5002294, -15550259},
2871             {-12057553, -11177906, 21115585, -13365155, 8808712, -12030708,
2872              16489530, 13378448, -25845716, 12741426},
2873             {-5946367, 10645103, -30911586, 15390284, -3286982, -7118677,
2874              24306472, 15852464, 28834118, -7646072},
2875         },
2876         {
2877             {-17335748, -9107057, -24531279, 9434953, -8472084, -583362,
2878              -13090771, 455841, 20461858, 5491305},
2879             {13669248, -16095482, -12481974, -10203039, -14569770, -11893198,
2880              -24995986, 11293807, -28588204, -9421832},
2881             {28497928, 6272777, -33022994, 14470570, 8906179, -1225630,
2882              18504674, -14165166, 29867745, -8795943},
2883         },
2884         {
2885             {-16207023, 13517196, -27799630, -13697798, 24009064, -6373891,
2886              -6367600, -13175392, 22853429, -4012011},
2887             {24191378, 16712145, -13931797, 15217831, 14542237, 1646131,
2888              18603514, -11037887, 12876623, -2112447},
2889             {17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753,
2890              608397, 16031844, 3723494},
2891         },
2892         {
2893             {-28632773, 12763728, -20446446, 7577504, 33001348, -13017745,
2894              17558842, -7872890, 23896954, -4314245},
2895             {-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064,
2896              7229064, -9919646, -8826859},
2897             {28816045, 298879, -28165016, -15920938, 19000928, -1665890,
2898              -12680833, -2949325, -18051778, -2082915},
2899         },
2900         {
2901             {16000882, -344896, 3493092, -11447198, -29504595, -13159789,
2902              12577740, 16041268, -19715240, 7847707},
2903             {10151868, 10572098, 27312476, 7922682, 14825339, 4723128,
2904              -32855931, -6519018, -10020567, 3852848},
2905             {-11430470, 15697596, -21121557, -4420647, 5386314, 15063598,
2906              16514493, -15932110, 29330899, -15076224},
2907         },
2908     },
2909     {
2910         {
2911             {-25499735, -4378794, -15222908, -6901211, 16615731, 2051784,
2912              3303702, 15490, -27548796, 12314391},
2913             {15683520, -6003043, 18109120, -9980648, 15337968, -5997823,
2914              -16717435, 15921866, 16103996, -3731215},
2915             {-23169824, -10781249, 13588192, -1628807, -3798557, -1074929,
2916              -19273607, 5402699, -29815713, -9841101},
2917         },
2918         {
2919             {23190676, 2384583, -32714340, 3462154, -29903655, -1529132,
2920              -11266856, 8911517, -25205859, 2739713},
2921             {21374101, -3554250, -33524649, 9874411, 15377179, 11831242,
2922              -33529904, 6134907, 4931255, 11987849},
2923             {-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539,
2924              13861388, -30076310, 10117930},
2925         },
2926         {
2927             {-29501170, -10744872, -26163768, 13051539, -25625564, 5089643,
2928              -6325503, 6704079, 12890019, 15728940},
2929             {-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376,
2930              -10428139, 12885167, 8311031},
2931             {-17516482, 5352194, 10384213, -13811658, 7506451, 13453191,
2932              26423267, 4384730, 1888765, -5435404},
2933         },
2934         {
2935             {-25817338, -3107312, -13494599, -3182506, 30896459, -13921729,
2936              -32251644, -12707869, -19464434, -3340243},
2937             {-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245,
2938              14845197, 17151279, -9854116},
2939             {-24830458, -12733720, -15165978, 10367250, -29530908, -265356,
2940              22825805, -7087279, -16866484, 16176525},
2941         },
2942         {
2943             {-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182,
2944              -10363426, -28746253, -10197509},
2945             {-10626600, -4486402, -13320562, -5125317, 3432136, -6393229,
2946              23632037, -1940610, 32808310, 1099883},
2947             {15030977, 5768825, -27451236, -2887299, -6427378, -15361371,
2948              -15277896, -6809350, 2051441, -15225865},
2949         },
2950         {
2951             {-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398,
2952              -14154188, -22686354, 16633660},
2953             {4577086, -16752288, 13249841, -15304328, 19958763, -14537274,
2954              18559670, -10759549, 8402478, -9864273},
2955             {-28406330, -1051581, -26790155, -907698, -17212414, -11030789,
2956              9453451, -14980072, 17983010, 9967138},
2957         },
2958         {
2959             {-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990,
2960              7806337, 17507396, 3651560},
2961             {-10420457, -4118111, 14584639, 15971087, -15768321, 8861010,
2962              26556809, -5574557, -18553322, -11357135},
2963             {2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121,
2964              8459447, -5605463, -7621941},
2965         },
2966         {
2967             {-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813,
2968              -849066, 17258084, -7977739},
2969             {18164541, -10595176, -17154882, -1542417, 19237078, -9745295,
2970              23357533, -15217008, 26908270, 12150756},
2971             {-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168,
2972              -5537701, -32302074, 16215819},
2973         },
2974     },
2975     {
2976         {
2977             {-6898905, 9824394, -12304779, -4401089, -31397141, -6276835,
2978              32574489, 12532905, -7503072, -8675347},
2979             {-27343522, -16515468, -27151524, -10722951, 946346, 16291093,
2980              254968, 7168080, 21676107, -1943028},
2981             {21260961, -8424752, -16831886, -11920822, -23677961, 3968121,
2982              -3651949, -6215466, -3556191, -7913075},
2983         },
2984         {
2985             {16544754, 13250366, -16804428, 15546242, -4583003, 12757258,
2986              -2462308, -8680336, -18907032, -9662799},
2987             {-2415239, -15577728, 18312303, 4964443, -15272530, -12653564,
2988              26820651, 16690659, 25459437, -4564609},
2989             {-25144690, 11425020, 28423002, -11020557, -6144921, -15826224,
2990              9142795, -2391602, -6432418, -1644817},
2991         },
2992         {
2993             {-23104652, 6253476, 16964147, -3768872, -25113972, -12296437,
2994              -27457225, -16344658, 6335692, 7249989},
2995             {-30333227, 13979675, 7503222, -12368314, -11956721, -4621693,
2996              -30272269, 2682242, 25993170, -12478523},
2997             {4364628, 5930691, 32304656, -10044554, -8054781, 15091131,
2998              22857016, -10598955, 31820368, 15075278},
2999         },
3000         {
3001             {31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788,
3002              -9650886, -17970238, 12833045},
3003             {19073683, 14851414, -24403169, -11860168, 7625278, 11091125,
3004              -19619190, 2074449, -9413939, 14905377},
3005             {24483667, -11935567, -2518866, -11547418, -1553130, 15355506,
3006              -25282080, 9253129, 27628530, -7555480},
3007         },
3008         {
3009             {17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324,
3010              -9157582, -14110875, 15297016},
3011             {510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417,
3012              -11864220, 8683221, 2921426},
3013             {18606791, 11874196, 27155355, -5281482, -24031742, 6265446,
3014              -25178240, -1278924, 4674690, 13890525},
3015         },
3016         {
3017             {13609624, 13069022, -27372361, -13055908, 24360586, 9592974,
3018              14977157, 9835105, 4389687, 288396},
3019             {9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062,
3020              8317628, 23388070, 16052080},
3021             {12720016, 11937594, -31970060, -5028689, 26900120, 8561328,
3022              -20155687, -11632979, -14754271, -10812892},
3023         },
3024         {
3025             {15961858, 14150409, 26716931, -665832, -22794328, 13603569,
3026              11829573, 7467844, -28822128, 929275},
3027             {11038231, -11582396, -27310482, -7316562, -10498527, -16307831,
3028              -23479533, -9371869, -21393143, 2465074},
3029             {20017163, -4323226, 27915242, 1529148, 12396362, 15675764,
3030              13817261, -9658066, 2463391, -4622140},
3031         },
3032         {
3033             {-16358878, -12663911, -12065183, 4996454, -1256422, 1073572,
3034              9583558, 12851107, 4003896, 12673717},
3035             {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325,
3036              14741514, -9103726, 7903886, 2348101},
3037             {24536016, -16515207, 12715592, -3862155, 1511293, 10047386,
3038              -3842346, -7129159, -28377538, 10048127},
3039         },
3040     },
3041     {
3042         {
3043             {-12622226, -6204820, 30718825, 2591312, -10617028, 12192840,
3044              18873298, -7297090, -32297756, 15221632},
3045             {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409,
3046              -21343950, 2095755, 29769758, 6593415},
3047             {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345,
3048              -6118678, 30958054, 8292160},
3049         },
3050         {
3051             {31429822, -13959116, 29173532, 15632448, 12174511, -2760094,
3052              32808831, 3977186, 26143136, -3148876},
3053             {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633,
3054              -1674433, -3758243, -2304625},
3055             {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029,
3056              -1612713, -1535569, -16664475, 8194478},
3057         },
3058         {
3059             {27338066, -7507420, -7414224, 10140405, -19026427, -6589889,
3060              27277191, 8855376, 28572286, 3005164},
3061             {26287124, 4821776, 25476601, -4145903, -3764513, -15788984,
3062              -18008582, 1182479, -26094821, -13079595},
3063             {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192,
3064              -21876275, -13982627, 32208683, -1198248},
3065         },
3066         {
3067             {-16657702, 2817643, -10286362, 14811298, 6024667, 13349505,
3068              -27315504, -10497842, -27672585, -11539858},
3069             {15941029, -9405932, -21367050, 8062055, 31876073, -238629,
3070              -15278393, -1444429, 15397331, -4130193},
3071             {8934485, -13485467, -23286397, -13423241, -32446090, 14047986,
3072              31170398, -1441021, -27505566, 15087184},
3073         },
3074         {
3075             {-18357243, -2156491, 24524913, -16677868, 15520427, -6360776,
3076              -15502406, 11461896, 16788528, -5868942},
3077             {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433,
3078              -3770287, -10323320, 31322514, -11615635},
3079             {21426655, -5650218, -13648287, -5347537, -28812189, -4920970,
3080              -18275391, -14621414, 13040862, -12112948},
3081         },
3082         {
3083             {11293895, 12478086, -27136401, 15083750, -29307421, 14748872,
3084              14555558, -13417103, 1613711, 4896935},
3085             {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460,
3086              2825960, -4897045, -23971776, -11267415},
3087             {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618,
3088              20615400, 12405433, -23753030, -8436416},
3089         },
3090         {
3091             {-7091295, 12556208, -20191352, 9025187, -17072479, 4333801,
3092              4378436, 2432030, 23097949, -566018},
3093             {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264,
3094              10103221, -18512313, 2424778},
3095             {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
3096              1344109, -3642553, 12412659},
3097         },
3098         {
3099             {-24001791, 7690286, 14929416, -168257, -32210835, -13412986,
3100              24162697, -15326504, -3141501, 11179385},
3101             {18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
3102              -6001441, -1486897, -18684645, -11443503},
3103             {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
3104              13403813, 11052904, 5219329},
3105         },
3106     },
3107     {
3108         {
3109             {20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
3110              31186971, -3973730, 9014762, -8579056},
3111             {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
3112              -33102500, 9160280, 8473550, -3256838},
3113             {24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
3114              -7689309, -16335821, -24568481, 11788948},
3115         },
3116         {
3117             {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
3118              -20037437, 10410733, -24568470, -1458691},
3119             {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
3120              11871841, -12505194, -18513325, 8464118},
3121             {-23400612, 8348507, -14585951, -861714, -3950205, -6373419,
3122              14325289, 8628612, 33313881, -8370517},
3123         },
3124         {
3125             {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
3126              -24805667, -10236854, -8940735, -5818269},
3127             {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
3128              15989197, -12838188, 28358192, -4253904},
3129             {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
3130              -16637684, 4072016, -5351664, 5596589},
3131         },
3132         {
3133             {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
3134              29266239, 2557221, 1768301, 15373193},
3135             {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
3136              -4504991, -24660491, 3442910},
3137             {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
3138              22597931, 7176455, -18585478, 13365930},
3139         },
3140         {
3141             {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
3142              -8570186, -9689599, -3031667},
3143             {25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
3144              683793, -11823784, 15723479, -15163481},
3145             {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
3146              11879682, 5400171, 519526, -1235876},
3147         },
3148         {
3149             {22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
3150              -20353881, 7315967, 16648397, 7605640},
3151             {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
3152              23994942, -5281555, -9468848, 4763278},
3153             {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
3154              31088447, -7764523, -11356529, 728112},
3155         },
3156         {
3157             {26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
3158              -4273545, -12555558, -29365436, -5498272},
3159             {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
3160              12327945, 10750447, 10014012},
3161             {-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
3162              -27481051, -666732, 3424691, 7540221},
3163         },
3164         {
3165             {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
3166              -16317219, -9244265, 15258046},
3167             {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
3168              2711395, 1062915, -5136345},
3169             {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
3170              -6066489, 12194497, 32960380, 1459310},
3171         },
3172     },
3173     {
3174         {
3175             {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
3176              -6101885, 18638003, -11174937},
3177             {31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
3178              9012486, -7584354, -6643087, -5442636},
3179             {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
3180              9677543, -32294889, -6456008},
3181         },
3182         {
3183             {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
3184              -7839692, -7852844, -8138429},
3185             {-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
3186              -27333451, 10754588, -9431476, 5203576},
3187             {31834314, 14135496, -770007, 5159118, 20917671, -16768096,
3188              -7467973, -7337524, 31809243, 7347066},
3189         },
3190         {
3191             {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
3192              19797970, -12211255, 15192876, -2087490},
3193             {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
3194              10609330, 12694420, 33473243, -13382104},
3195             {33184999, 11180355, 15832085, -11385430, -1633671, 225884,
3196              15089336, -11023903, -6135662, 14480053},
3197         },
3198         {
3199             {31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
3200              5496208, 13685227, 27595050, 8737275},
3201             {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
3202              -31008351, -12610604, 26498114, 66511},
3203             {22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
3204              30540766, -4286747, -13327787, -7515095},
3205         },
3206         {
3207             {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
3208              8205540, 13585437, -17127465, 15115439},
3209             {23711543, -672915, 31206561, -8362711, 6164647, -9709987,
3210              -33535882, -1426096, 8236921, 16492939},
3211             {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
3212              19574902, 10071562, 6708380, -6222424},
3213         },
3214         {
3215             {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
3216              9328700, 29955601, -11678310},
3217             {3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
3218              -25892142, -12635595, -9917575, 6216608},
3219             {-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
3220              24822830, -6146567, -26767480, 7525079},
3221         },
3222         {
3223             {-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
3224              -910336, -2782495, -19386633, 11994101},
3225             {21691500, -13624626, -641331, -14367021, 3285881, -3483596,
3226              -25064666, 9718258, -7477437, 13381418},
3227             {18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
3228              23111648, -6375247, 28535282, 15779576},
3229         },
3230         {
3231             {30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
3232              -14068454, 12021730, 9955285, -16303356},
3233             {9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
3234              -18426029, 9924399, 20194861, 13380996},
3235             {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
3236              -1984914, 15707771, 26342023, 10146099},
3237         },
3238     },
3239     {
3240         {
3241             {-26016874, -219943, 21339191, -41388, 19745256, -2878700,
3242              -29637280, 2227040, 21612326, -545728},
3243             {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
3244              25764461, 12243797, -20856566, 11649658},
3245             {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
3246              6114064, 33514190, 2333242},
3247         },
3248         {
3249             {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
3250              -6679750, -12670638, 24350578, -13450001},
3251             {-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
3252              -31536088, -10406836, 8317860, 12352766},
3253             {18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
3254              -23552096, -2287550, 20712163, 6719373},
3255         },
3256         {
3257             {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
3258              -3763210, 26224235, -3297458},
3259             {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
3260              21728352, 9493610, 18620611, -16428628},
3261             {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
3262              -5269471, -9725556, -30701573, -16479657},
3263         },
3264         {
3265             {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
3266              12248509, -5240639, 13735342, 1934062},
3267             {25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
3268              -15136294, -3765346, -21277997, 5473616},
3269             {31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
3270              -7125085, 12469656, 29111212, -5451014},
3271         },
3272         {
3273             {24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
3274              24367466, 6388839, -10295587, 452383},
3275             {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
3276              -24236251, -5915248, 15766062, 8407814},
3277             {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
3278              -8917023, -4388953, -8067909, 2276718},
3279         },
3280         {
3281             {30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
3282              -23827587, 5096219, 22740376, -7303417},
3283             {2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
3284              24051124, 13742383, -15637599, 13295222},
3285             {33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
3286              -17720195, -4612972, -4451357, -14669444},
3287         },
3288         {
3289             {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
3290              -2469266, -4141880, 7770569, 9620597},
3291             {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
3292              -1694323, -33502340, -14767970},
3293             {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
3294              1220118, 30494170, -11440799},
3295         },
3296         {
3297             {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
3298              -26739026, 926050, -1684339, -13333647},
3299             {13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
3300              9021034, 9078865, 3353509, 4033511},
3301             {-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
3302              23161163, 8839127, 27485041, 7356032},
3303         },
3304     },
3305     {
3306         {
3307             {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
3308              2625015, 28431036, -16771834},
3309             {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
3310              -22545972, 14150565, 15970762, 4099461},
3311             {29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
3312              13617293, -9937143, 11465739, 8317062},
3313         },
3314         {
3315             {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
3316              14898637, 3848455, 20969334, -5157516},
3317             {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
3318              -21610826, -3649888, 11177095, 14989547},
3319             {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
3320              13515641, 2581286, -28487508, 9930240},
3321         },
3322         {
3323             {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
3324              18345767, -13403753, 16291481, -5314038},
3325             {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
3326              6957617, 4368891, 9788741},
3327             {16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
3328              -21722536, -8613148, 16250552, -11111103},
3329         },
3330         {
3331             {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
3332              10604807, -30190403, 4782747},
3333             {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
3334              -9981571, 4383045, 22546403, 437323},
3335             {31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
3336              27343084, 2786261, -30633590, -14097016},
3337         },
3338         {
3339             {-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
3340              -19690631, 2355319, -19284671, -6114373},
3341             {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
3342              18952177, 15496498, -29380133, 11754228},
3343             {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
3344              7141596, 11724556, 22761615, -10134141},
3345         },
3346         {
3347             {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
3348              -28741185, -12227393, 32851222, 11717399},
3349             {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
3350              31474879, 3483633, -1193175, -4030831},
3351             {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
3352              33142652, 6546660, -19985279, -3948376},
3353         },
3354         {
3355             {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
3356              -8537131, -12833048, -30772034, -15486313},
3357             {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
3358              -31135347, -16049879, 10928917, 3011958},
3359             {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
3360              -30831056, -12805180, 18008031, 10258577},
3361         },
3362         {
3363             {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
3364              -1853465, 1367120, 25127874, 6671743},
3365             {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
3366              21382910, 11042292, 25838796, 4642684},
3367             {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
3368              30468147, -13900640, 18423289, 4177476},
3369         },
3370     },
3371 };
3372
3373 static uint8_t negative(signed char b) {
3374   uint32_t x = b;
3375   x >>= 31; /* 1: yes; 0: no */
3376   return x;
3377 }
3378
3379 static void table_select(ge_precomp *t, int pos, signed char b) {
3380   ge_precomp minust;
3381   uint8_t bnegative = negative(b);
3382   uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
3383
3384   ge_precomp_0(t);
3385   cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
3386   cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
3387   cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
3388   cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
3389   cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
3390   cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
3391   cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
3392   cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
3393   fe_copy(minust.yplusx, t->yminusx);
3394   fe_copy(minust.yminusx, t->yplusx);
3395   fe_neg(minust.xy2d, t->xy2d);
3396   cmov(t, &minust, bnegative);
3397 }
3398
3399 /* h = a * B
3400  * where a = a[0]+256*a[1]+...+256^31 a[31]
3401  * B is the Ed25519 base point (x,4/5) with x positive.
3402  *
3403  * Preconditions:
3404  *   a[31] <= 127 */
3405 static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
3406   signed char e[64];
3407   signed char carry;
3408   ge_p1p1 r;
3409   ge_p2 s;
3410   ge_precomp t;
3411   int i;
3412
3413   for (i = 0; i < 32; ++i) {
3414     e[2 * i + 0] = (a[i] >> 0) & 15;
3415     e[2 * i + 1] = (a[i] >> 4) & 15;
3416   }
3417   /* each e[i] is between 0 and 15 */
3418   /* e[63] is between 0 and 7 */
3419
3420   carry = 0;
3421   for (i = 0; i < 63; ++i) {
3422     e[i] += carry;
3423     carry = e[i] + 8;
3424     carry >>= 4;
3425     e[i] -= carry << 4;
3426   }
3427   e[63] += carry;
3428   /* each e[i] is between -8 and 8 */
3429
3430   ge_p3_0(h);
3431   for (i = 1; i < 64; i += 2) {
3432     table_select(&t, i / 2, e[i]);
3433     ge_madd(&r, h, &t);
3434     ge_p1p1_to_p3(h, &r);
3435   }
3436
3437   ge_p3_dbl(&r, h);
3438   ge_p1p1_to_p2(&s, &r);
3439   ge_p2_dbl(&r, &s);
3440   ge_p1p1_to_p2(&s, &r);
3441   ge_p2_dbl(&r, &s);
3442   ge_p1p1_to_p2(&s, &r);
3443   ge_p2_dbl(&r, &s);
3444   ge_p1p1_to_p3(h, &r);
3445
3446   for (i = 0; i < 64; i += 2) {
3447     table_select(&t, i / 2, e[i]);
3448     ge_madd(&r, h, &t);
3449     ge_p1p1_to_p3(h, &r);
3450   }
3451 }
3452
3453 /* Replace (f,g) with (g,f) if b == 1;
3454  * replace (f,g) with (f,g) if b == 0.
3455  *
3456  * Preconditions: b in {0,1}. */
3457 static void fe_cswap(fe f, fe g, unsigned int b) {
3458   size_t i;
3459   b = 0-b;
3460   for (i = 0; i < 10; i++) {
3461     int32_t x = f[i] ^ g[i];
3462     x &= b;
3463     f[i] ^= x;
3464     g[i] ^= x;
3465   }
3466 }
3467
3468 /* h = f * 121666
3469  * Can overlap h with f.
3470  *
3471  * Preconditions:
3472  *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
3473  *
3474  * Postconditions:
3475  *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
3476 static void fe_mul121666(fe h, fe f) {
3477   int32_t f0 = f[0];
3478   int32_t f1 = f[1];
3479   int32_t f2 = f[2];
3480   int32_t f3 = f[3];
3481   int32_t f4 = f[4];
3482   int32_t f5 = f[5];
3483   int32_t f6 = f[6];
3484   int32_t f7 = f[7];
3485   int32_t f8 = f[8];
3486   int32_t f9 = f[9];
3487   int64_t h0 = f0 * (int64_t) 121666;
3488   int64_t h1 = f1 * (int64_t) 121666;
3489   int64_t h2 = f2 * (int64_t) 121666;
3490   int64_t h3 = f3 * (int64_t) 121666;
3491   int64_t h4 = f4 * (int64_t) 121666;
3492   int64_t h5 = f5 * (int64_t) 121666;
3493   int64_t h6 = f6 * (int64_t) 121666;
3494   int64_t h7 = f7 * (int64_t) 121666;
3495   int64_t h8 = f8 * (int64_t) 121666;
3496   int64_t h9 = f9 * (int64_t) 121666;
3497   int64_t carry0;
3498   int64_t carry1;
3499   int64_t carry2;
3500   int64_t carry3;
3501   int64_t carry4;
3502   int64_t carry5;
3503   int64_t carry6;
3504   int64_t carry7;
3505   int64_t carry8;
3506   int64_t carry9;
3507
3508   carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
3509   carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
3510   carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
3511   carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
3512   carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
3513
3514   carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
3515   carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
3516   carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
3517   carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
3518   carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
3519
3520   h[0] = h0;
3521   h[1] = h1;
3522   h[2] = h2;
3523   h[3] = h3;
3524   h[4] = h4;
3525   h[5] = h5;
3526   h[6] = h6;
3527   h[7] = h7;
3528   h[8] = h8;
3529   h[9] = h9;
3530 }
3531
3532 static void x25519_scalar_mult_generic(uint8_t out[32],
3533                                        const uint8_t scalar[32],
3534                                        const uint8_t point[32]) {
3535   fe x1, x2, z2, x3, z3, tmp0, tmp1;
3536   uint8_t e[32];
3537   unsigned swap = 0;
3538   int pos;
3539
3540   memcpy(e, scalar, 32);
3541   e[0] &= 248;
3542   e[31] &= 127;
3543   e[31] |= 64;
3544   fe_frombytes(x1, point);
3545   fe_1(x2);
3546   fe_0(z2);
3547   fe_copy(x3, x1);
3548   fe_1(z3);
3549
3550   for (pos = 254; pos >= 0; --pos) {
3551     unsigned b = 1 & (e[pos / 8] >> (pos & 7));
3552     swap ^= b;
3553     fe_cswap(x2, x3, swap);
3554     fe_cswap(z2, z3, swap);
3555     swap = b;
3556     fe_sub(tmp0, x3, z3);
3557     fe_sub(tmp1, x2, z2);
3558     fe_add(x2, x2, z2);
3559     fe_add(z2, x3, z3);
3560     fe_mul(z3, tmp0, x2);
3561     fe_mul(z2, z2, tmp1);
3562     fe_sq(tmp0, tmp1);
3563     fe_sq(tmp1, x2);
3564     fe_add(x3, z3, z2);
3565     fe_sub(z2, z3, z2);
3566     fe_mul(x2, tmp1, tmp0);
3567     fe_sub(tmp1, tmp1, tmp0);
3568     fe_sq(z2, z2);
3569     fe_mul121666(z3, tmp1);
3570     fe_sq(x3, x3);
3571     fe_add(tmp0, tmp0, z3);
3572     fe_mul(z3, x1, z2);
3573     fe_mul(z2, tmp1, tmp0);
3574   }
3575   fe_cswap(x2, x3, swap);
3576   fe_cswap(z2, z3, swap);
3577
3578   fe_invert(z2, z2);
3579   fe_mul(x2, x2, z2);
3580   fe_tobytes(out, x2);
3581 }
3582
3583 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
3584                                const uint8_t point[32]) {
3585   x25519_scalar_mult_generic(out, scalar, point);
3586 }
3587
3588 static void slide(signed char *r, const uint8_t *a) {
3589   int i;
3590   int b;
3591   int k;
3592
3593   for (i = 0; i < 256; ++i) {
3594     r[i] = 1 & (a[i >> 3] >> (i & 7));
3595   }
3596
3597   for (i = 0; i < 256; ++i) {
3598     if (r[i]) {
3599       for (b = 1; b <= 6 && i + b < 256; ++b) {
3600         if (r[i + b]) {
3601           if (r[i] + (r[i + b] << b) <= 15) {
3602             r[i] += r[i + b] << b;
3603             r[i + b] = 0;
3604           } else if (r[i] - (r[i + b] << b) >= -15) {
3605             r[i] -= r[i + b] << b;
3606             for (k = i + b; k < 256; ++k) {
3607               if (!r[k]) {
3608                 r[k] = 1;
3609                 break;
3610               }
3611               r[k] = 0;
3612             }
3613           } else {
3614             break;
3615           }
3616         }
3617       }
3618     }
3619   }
3620 }
3621
3622 static const ge_precomp Bi[8] = {
3623     {
3624         {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
3625          -11754271, -6079156, 2047605},
3626         {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
3627          5043384, 19500929, -15469378},
3628         {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
3629          11864899, -24514362, -4438546},
3630     },
3631     {
3632         {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
3633          -14772189, 28944400, -1550024},
3634         {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
3635          -11775962, 7689662, 11199574},
3636         {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
3637          10017326, -17749093, -9920357},
3638     },
3639     {
3640         {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
3641          14515107, -15438304, 10819380},
3642         {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
3643          12483688, -12668491, 5581306},
3644         {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
3645          13850243, -23678021, -15815942},
3646     },
3647     {
3648         {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
3649          5230134, -23952439, -15175766},
3650         {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
3651          16520125, 30598449, 7715701},
3652         {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
3653          1370708, 29794553, -1409300},
3654     },
3655     {
3656         {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
3657          -1361450, -13062696, 13821877},
3658         {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
3659          -7212327, 18853322, -14220951},
3660         {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
3661          -10431137, 2207753, -3209784},
3662     },
3663     {
3664         {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
3665          -663000, -31111463, -16132436},
3666         {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
3667          15725684, 171356, 6466918},
3668         {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
3669          -14088058, -30714912, 16193877},
3670     },
3671     {
3672         {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
3673          4729455, -18074513, 9256800},
3674         {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
3675          9761698, -19827198, 630305},
3676         {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
3677          -15960994, -2449256, -14291300},
3678     },
3679     {
3680         {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
3681          15033784, 25105118, -7894876},
3682         {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
3683          1573892, -2625887, 2198790, -15804619},
3684         {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
3685          -16236442, -32461234, -12290683},
3686     },
3687 };
3688
3689 /* r = a * A + b * B
3690  * where a = a[0]+256*a[1]+...+256^31 a[31].
3691  * and b = b[0]+256*b[1]+...+256^31 b[31].
3692  * B is the Ed25519 base point (x,4/5) with x positive. */
3693 static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
3694                                          const ge_p3 *A, const uint8_t *b) {
3695   signed char aslide[256];
3696   signed char bslide[256];
3697   ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
3698   ge_p1p1 t;
3699   ge_p3 u;
3700   ge_p3 A2;
3701   int i;
3702
3703   slide(aslide, a);
3704   slide(bslide, b);
3705
3706   ge_p3_to_cached(&Ai[0], A);
3707   ge_p3_dbl(&t, A);
3708   ge_p1p1_to_p3(&A2, &t);
3709   ge_add(&t, &A2, &Ai[0]);
3710   ge_p1p1_to_p3(&u, &t);
3711   ge_p3_to_cached(&Ai[1], &u);
3712   ge_add(&t, &A2, &Ai[1]);
3713   ge_p1p1_to_p3(&u, &t);
3714   ge_p3_to_cached(&Ai[2], &u);
3715   ge_add(&t, &A2, &Ai[2]);
3716   ge_p1p1_to_p3(&u, &t);
3717   ge_p3_to_cached(&Ai[3], &u);
3718   ge_add(&t, &A2, &Ai[3]);
3719   ge_p1p1_to_p3(&u, &t);
3720   ge_p3_to_cached(&Ai[4], &u);
3721   ge_add(&t, &A2, &Ai[4]);
3722   ge_p1p1_to_p3(&u, &t);
3723   ge_p3_to_cached(&Ai[5], &u);
3724   ge_add(&t, &A2, &Ai[5]);
3725   ge_p1p1_to_p3(&u, &t);
3726   ge_p3_to_cached(&Ai[6], &u);
3727   ge_add(&t, &A2, &Ai[6]);
3728   ge_p1p1_to_p3(&u, &t);
3729   ge_p3_to_cached(&Ai[7], &u);
3730
3731   ge_p2_0(r);
3732
3733   for (i = 255; i >= 0; --i) {
3734     if (aslide[i] || bslide[i]) {
3735       break;
3736     }
3737   }
3738
3739   for (; i >= 0; --i) {
3740     ge_p2_dbl(&t, r);
3741
3742     if (aslide[i] > 0) {
3743       ge_p1p1_to_p3(&u, &t);
3744       ge_add(&t, &u, &Ai[aslide[i] / 2]);
3745     } else if (aslide[i] < 0) {
3746       ge_p1p1_to_p3(&u, &t);
3747       ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
3748     }
3749
3750     if (bslide[i] > 0) {
3751       ge_p1p1_to_p3(&u, &t);
3752       ge_madd(&t, &u, &Bi[bslide[i] / 2]);
3753     } else if (bslide[i] < 0) {
3754       ge_p1p1_to_p3(&u, &t);
3755       ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
3756     }
3757
3758     ge_p1p1_to_p2(r, &t);
3759   }
3760 }
3761
3762 /* The set of scalars is \Z/l
3763  * where l = 2^252 + 27742317777372353535851937790883648493. */
3764
3765 /* Input:
3766  *   s[0]+256*s[1]+...+256^63*s[63] = s
3767  *
3768  * Output:
3769  *   s[0]+256*s[1]+...+256^31*s[31] = s mod l
3770  *   where l = 2^252 + 27742317777372353535851937790883648493.
3771  *   Overwrites s in place. */
3772 static void x25519_sc_reduce(uint8_t *s) {
3773   int64_t s0 = 2097151 & load_3(s);
3774   int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
3775   int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
3776   int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
3777   int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
3778   int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
3779   int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
3780   int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
3781   int64_t s8 = 2097151 & load_3(s + 21);
3782   int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
3783   int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
3784   int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
3785   int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
3786   int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
3787   int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
3788   int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
3789   int64_t s16 = 2097151 & load_3(s + 42);
3790   int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
3791   int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
3792   int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
3793   int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
3794   int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
3795   int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
3796   int64_t s23 = (load_4(s + 60) >> 3);
3797   int64_t carry0;
3798   int64_t carry1;
3799   int64_t carry2;
3800   int64_t carry3;
3801   int64_t carry4;
3802   int64_t carry5;
3803   int64_t carry6;
3804   int64_t carry7;
3805   int64_t carry8;
3806   int64_t carry9;
3807   int64_t carry10;
3808   int64_t carry11;
3809   int64_t carry12;
3810   int64_t carry13;
3811   int64_t carry14;
3812   int64_t carry15;
3813   int64_t carry16;
3814
3815   s11 += s23 * 666643;
3816   s12 += s23 * 470296;
3817   s13 += s23 * 654183;
3818   s14 -= s23 * 997805;
3819   s15 += s23 * 136657;
3820   s16 -= s23 * 683901;
3821   s23 = 0;
3822
3823   s10 += s22 * 666643;
3824   s11 += s22 * 470296;
3825   s12 += s22 * 654183;
3826   s13 -= s22 * 997805;
3827   s14 += s22 * 136657;
3828   s15 -= s22 * 683901;
3829   s22 = 0;
3830
3831   s9 += s21 * 666643;
3832   s10 += s21 * 470296;
3833   s11 += s21 * 654183;
3834   s12 -= s21 * 997805;
3835   s13 += s21 * 136657;
3836   s14 -= s21 * 683901;
3837   s21 = 0;
3838
3839   s8 += s20 * 666643;
3840   s9 += s20 * 470296;
3841   s10 += s20 * 654183;
3842   s11 -= s20 * 997805;
3843   s12 += s20 * 136657;
3844   s13 -= s20 * 683901;
3845   s20 = 0;
3846
3847   s7 += s19 * 666643;
3848   s8 += s19 * 470296;
3849   s9 += s19 * 654183;
3850   s10 -= s19 * 997805;
3851   s11 += s19 * 136657;
3852   s12 -= s19 * 683901;
3853   s19 = 0;
3854
3855   s6 += s18 * 666643;
3856   s7 += s18 * 470296;
3857   s8 += s18 * 654183;
3858   s9 -= s18 * 997805;
3859   s10 += s18 * 136657;
3860   s11 -= s18 * 683901;
3861   s18 = 0;
3862
3863   carry6 = (s6 + (1 << 20)) >> 21;
3864   s7 += carry6;
3865   s6 -= carry6 << 21;
3866   carry8 = (s8 + (1 << 20)) >> 21;
3867   s9 += carry8;
3868   s8 -= carry8 << 21;
3869   carry10 = (s10 + (1 << 20)) >> 21;
3870   s11 += carry10;
3871   s10 -= carry10 << 21;
3872   carry12 = (s12 + (1 << 20)) >> 21;
3873   s13 += carry12;
3874   s12 -= carry12 << 21;
3875   carry14 = (s14 + (1 << 20)) >> 21;
3876   s15 += carry14;
3877   s14 -= carry14 << 21;
3878   carry16 = (s16 + (1 << 20)) >> 21;
3879   s17 += carry16;
3880   s16 -= carry16 << 21;
3881
3882   carry7 = (s7 + (1 << 20)) >> 21;
3883   s8 += carry7;
3884   s7 -= carry7 << 21;
3885   carry9 = (s9 + (1 << 20)) >> 21;
3886   s10 += carry9;
3887   s9 -= carry9 << 21;
3888   carry11 = (s11 + (1 << 20)) >> 21;
3889   s12 += carry11;
3890   s11 -= carry11 << 21;
3891   carry13 = (s13 + (1 << 20)) >> 21;
3892   s14 += carry13;
3893   s13 -= carry13 << 21;
3894   carry15 = (s15 + (1 << 20)) >> 21;
3895   s16 += carry15;
3896   s15 -= carry15 << 21;
3897
3898   s5 += s17 * 666643;
3899   s6 += s17 * 470296;
3900   s7 += s17 * 654183;
3901   s8 -= s17 * 997805;
3902   s9 += s17 * 136657;
3903   s10 -= s17 * 683901;
3904   s17 = 0;
3905
3906   s4 += s16 * 666643;
3907   s5 += s16 * 470296;
3908   s6 += s16 * 654183;
3909   s7 -= s16 * 997805;
3910   s8 += s16 * 136657;
3911   s9 -= s16 * 683901;
3912   s16 = 0;
3913
3914   s3 += s15 * 666643;
3915   s4 += s15 * 470296;
3916   s5 += s15 * 654183;
3917   s6 -= s15 * 997805;
3918   s7 += s15 * 136657;
3919   s8 -= s15 * 683901;
3920   s15 = 0;
3921
3922   s2 += s14 * 666643;
3923   s3 += s14 * 470296;
3924   s4 += s14 * 654183;
3925   s5 -= s14 * 997805;
3926   s6 += s14 * 136657;
3927   s7 -= s14 * 683901;
3928   s14 = 0;
3929
3930   s1 += s13 * 666643;
3931   s2 += s13 * 470296;
3932   s3 += s13 * 654183;
3933   s4 -= s13 * 997805;
3934   s5 += s13 * 136657;
3935   s6 -= s13 * 683901;
3936   s13 = 0;
3937
3938   s0 += s12 * 666643;
3939   s1 += s12 * 470296;
3940   s2 += s12 * 654183;
3941   s3 -= s12 * 997805;
3942   s4 += s12 * 136657;
3943   s5 -= s12 * 683901;
3944   s12 = 0;
3945
3946   carry0 = (s0 + (1 << 20)) >> 21;
3947   s1 += carry0;
3948   s0 -= carry0 << 21;
3949   carry2 = (s2 + (1 << 20)) >> 21;
3950   s3 += carry2;
3951   s2 -= carry2 << 21;
3952   carry4 = (s4 + (1 << 20)) >> 21;
3953   s5 += carry4;
3954   s4 -= carry4 << 21;
3955   carry6 = (s6 + (1 << 20)) >> 21;
3956   s7 += carry6;
3957   s6 -= carry6 << 21;
3958   carry8 = (s8 + (1 << 20)) >> 21;
3959   s9 += carry8;
3960   s8 -= carry8 << 21;
3961   carry10 = (s10 + (1 << 20)) >> 21;
3962   s11 += carry10;
3963   s10 -= carry10 << 21;
3964
3965   carry1 = (s1 + (1 << 20)) >> 21;
3966   s2 += carry1;
3967   s1 -= carry1 << 21;
3968   carry3 = (s3 + (1 << 20)) >> 21;
3969   s4 += carry3;
3970   s3 -= carry3 << 21;
3971   carry5 = (s5 + (1 << 20)) >> 21;
3972   s6 += carry5;
3973   s5 -= carry5 << 21;
3974   carry7 = (s7 + (1 << 20)) >> 21;
3975   s8 += carry7;
3976   s7 -= carry7 << 21;
3977   carry9 = (s9 + (1 << 20)) >> 21;
3978   s10 += carry9;
3979   s9 -= carry9 << 21;
3980   carry11 = (s11 + (1 << 20)) >> 21;
3981   s12 += carry11;
3982   s11 -= carry11 << 21;
3983
3984   s0 += s12 * 666643;
3985   s1 += s12 * 470296;
3986   s2 += s12 * 654183;
3987   s3 -= s12 * 997805;
3988   s4 += s12 * 136657;
3989   s5 -= s12 * 683901;
3990   s12 = 0;
3991
3992   carry0 = s0 >> 21;
3993   s1 += carry0;
3994   s0 -= carry0 << 21;
3995   carry1 = s1 >> 21;
3996   s2 += carry1;
3997   s1 -= carry1 << 21;
3998   carry2 = s2 >> 21;
3999   s3 += carry2;
4000   s2 -= carry2 << 21;
4001   carry3 = s3 >> 21;
4002   s4 += carry3;
4003   s3 -= carry3 << 21;
4004   carry4 = s4 >> 21;
4005   s5 += carry4;
4006   s4 -= carry4 << 21;
4007   carry5 = s5 >> 21;
4008   s6 += carry5;
4009   s5 -= carry5 << 21;
4010   carry6 = s6 >> 21;
4011   s7 += carry6;
4012   s6 -= carry6 << 21;
4013   carry7 = s7 >> 21;
4014   s8 += carry7;
4015   s7 -= carry7 << 21;
4016   carry8 = s8 >> 21;
4017   s9 += carry8;
4018   s8 -= carry8 << 21;
4019   carry9 = s9 >> 21;
4020   s10 += carry9;
4021   s9 -= carry9 << 21;
4022   carry10 = s10 >> 21;
4023   s11 += carry10;
4024   s10 -= carry10 << 21;
4025   carry11 = s11 >> 21;
4026   s12 += carry11;
4027   s11 -= carry11 << 21;
4028
4029   s0 += s12 * 666643;
4030   s1 += s12 * 470296;
4031   s2 += s12 * 654183;
4032   s3 -= s12 * 997805;
4033   s4 += s12 * 136657;
4034   s5 -= s12 * 683901;
4035   s12 = 0;
4036
4037   carry0 = s0 >> 21;
4038   s1 += carry0;
4039   s0 -= carry0 << 21;
4040   carry1 = s1 >> 21;
4041   s2 += carry1;
4042   s1 -= carry1 << 21;
4043   carry2 = s2 >> 21;
4044   s3 += carry2;
4045   s2 -= carry2 << 21;
4046   carry3 = s3 >> 21;
4047   s4 += carry3;
4048   s3 -= carry3 << 21;
4049   carry4 = s4 >> 21;
4050   s5 += carry4;
4051   s4 -= carry4 << 21;
4052   carry5 = s5 >> 21;
4053   s6 += carry5;
4054   s5 -= carry5 << 21;
4055   carry6 = s6 >> 21;
4056   s7 += carry6;
4057   s6 -= carry6 << 21;
4058   carry7 = s7 >> 21;
4059   s8 += carry7;
4060   s7 -= carry7 << 21;
4061   carry8 = s8 >> 21;
4062   s9 += carry8;
4063   s8 -= carry8 << 21;
4064   carry9 = s9 >> 21;
4065   s10 += carry9;
4066   s9 -= carry9 << 21;
4067   carry10 = s10 >> 21;
4068   s11 += carry10;
4069   s10 -= carry10 << 21;
4070
4071   s[0] = s0 >> 0;
4072   s[1] = s0 >> 8;
4073   s[2] = (s0 >> 16) | (s1 << 5);
4074   s[3] = s1 >> 3;
4075   s[4] = s1 >> 11;
4076   s[5] = (s1 >> 19) | (s2 << 2);
4077   s[6] = s2 >> 6;
4078   s[7] = (s2 >> 14) | (s3 << 7);
4079   s[8] = s3 >> 1;
4080   s[9] = s3 >> 9;
4081   s[10] = (s3 >> 17) | (s4 << 4);
4082   s[11] = s4 >> 4;
4083   s[12] = s4 >> 12;
4084   s[13] = (s4 >> 20) | (s5 << 1);
4085   s[14] = s5 >> 7;
4086   s[15] = (s5 >> 15) | (s6 << 6);
4087   s[16] = s6 >> 2;
4088   s[17] = s6 >> 10;
4089   s[18] = (s6 >> 18) | (s7 << 3);
4090   s[19] = s7 >> 5;
4091   s[20] = s7 >> 13;
4092   s[21] = s8 >> 0;
4093   s[22] = s8 >> 8;
4094   s[23] = (s8 >> 16) | (s9 << 5);
4095   s[24] = s9 >> 3;
4096   s[25] = s9 >> 11;
4097   s[26] = (s9 >> 19) | (s10 << 2);
4098   s[27] = s10 >> 6;
4099   s[28] = (s10 >> 14) | (s11 << 7);
4100   s[29] = s11 >> 1;
4101   s[30] = s11 >> 9;
4102   s[31] = s11 >> 17;
4103 }
4104
4105 /* Input:
4106  *   a[0]+256*a[1]+...+256^31*a[31] = a
4107  *   b[0]+256*b[1]+...+256^31*b[31] = b
4108  *   c[0]+256*c[1]+...+256^31*c[31] = c
4109  *
4110  * Output:
4111  *   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
4112  *   where l = 2^252 + 27742317777372353535851937790883648493. */
4113 static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
4114                       const uint8_t *c) {
4115   int64_t a0 = 2097151 & load_3(a);
4116   int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
4117   int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
4118   int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
4119   int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
4120   int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
4121   int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
4122   int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
4123   int64_t a8 = 2097151 & load_3(a + 21);
4124   int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
4125   int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
4126   int64_t a11 = (load_4(a + 28) >> 7);
4127   int64_t b0 = 2097151 & load_3(b);
4128   int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
4129   int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
4130   int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
4131   int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
4132   int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
4133   int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
4134   int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
4135   int64_t b8 = 2097151 & load_3(b + 21);
4136   int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
4137   int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
4138   int64_t b11 = (load_4(b + 28) >> 7);
4139   int64_t c0 = 2097151 & load_3(c);
4140   int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
4141   int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
4142   int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
4143   int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
4144   int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
4145   int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
4146   int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
4147   int64_t c8 = 2097151 & load_3(c + 21);
4148   int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
4149   int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
4150   int64_t c11 = (load_4(c + 28) >> 7);
4151   int64_t s0;
4152   int64_t s1;
4153   int64_t s2;
4154   int64_t s3;
4155   int64_t s4;
4156   int64_t s5;
4157   int64_t s6;
4158   int64_t s7;
4159   int64_t s8;
4160   int64_t s9;
4161   int64_t s10;
4162   int64_t s11;
4163   int64_t s12;
4164   int64_t s13;
4165   int64_t s14;
4166   int64_t s15;
4167   int64_t s16;
4168   int64_t s17;
4169   int64_t s18;
4170   int64_t s19;
4171   int64_t s20;
4172   int64_t s21;
4173   int64_t s22;
4174   int64_t s23;
4175   int64_t carry0;
4176   int64_t carry1;
4177   int64_t carry2;
4178   int64_t carry3;
4179   int64_t carry4;
4180   int64_t carry5;
4181   int64_t carry6;
4182   int64_t carry7;
4183   int64_t carry8;
4184   int64_t carry9;
4185   int64_t carry10;
4186   int64_t carry11;
4187   int64_t carry12;
4188   int64_t carry13;
4189   int64_t carry14;
4190   int64_t carry15;
4191   int64_t carry16;
4192   int64_t carry17;
4193   int64_t carry18;
4194   int64_t carry19;
4195   int64_t carry20;
4196   int64_t carry21;
4197   int64_t carry22;
4198
4199   s0 = c0 + a0 * b0;
4200   s1 = c1 + a0 * b1 + a1 * b0;
4201   s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
4202   s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
4203   s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
4204   s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
4205   s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
4206   s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
4207        a6 * b1 + a7 * b0;
4208   s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
4209        a6 * b2 + a7 * b1 + a8 * b0;
4210   s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
4211        a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
4212   s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
4213         a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
4214   s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
4215         a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
4216   s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
4217         a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
4218   s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
4219         a9 * b4 + a10 * b3 + a11 * b2;
4220   s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
4221         a10 * b4 + a11 * b3;
4222   s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
4223         a11 * b4;
4224   s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
4225   s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
4226   s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
4227   s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
4228   s20 = a9 * b11 + a10 * b10 + a11 * b9;
4229   s21 = a10 * b11 + a11 * b10;
4230   s22 = a11 * b11;
4231   s23 = 0;
4232
4233   carry0 = (s0 + (1 << 20)) >> 21;
4234   s1 += carry0;
4235   s0 -= carry0 << 21;
4236   carry2 = (s2 + (1 << 20)) >> 21;
4237   s3 += carry2;
4238   s2 -= carry2 << 21;
4239   carry4 = (s4 + (1 << 20)) >> 21;
4240   s5 += carry4;
4241   s4 -= carry4 << 21;
4242   carry6 = (s6 + (1 << 20)) >> 21;
4243   s7 += carry6;
4244   s6 -= carry6 << 21;
4245   carry8 = (s8 + (1 << 20)) >> 21;
4246   s9 += carry8;
4247   s8 -= carry8 << 21;
4248   carry10 = (s10 + (1 << 20)) >> 21;
4249   s11 += carry10;
4250   s10 -= carry10 << 21;
4251   carry12 = (s12 + (1 << 20)) >> 21;
4252   s13 += carry12;
4253   s12 -= carry12 << 21;
4254   carry14 = (s14 + (1 << 20)) >> 21;
4255   s15 += carry14;
4256   s14 -= carry14 << 21;
4257   carry16 = (s16 + (1 << 20)) >> 21;
4258   s17 += carry16;
4259   s16 -= carry16 << 21;
4260   carry18 = (s18 + (1 << 20)) >> 21;
4261   s19 += carry18;
4262   s18 -= carry18 << 21;
4263   carry20 = (s20 + (1 << 20)) >> 21;
4264   s21 += carry20;
4265   s20 -= carry20 << 21;
4266   carry22 = (s22 + (1 << 20)) >> 21;
4267   s23 += carry22;
4268   s22 -= carry22 << 21;
4269
4270   carry1 = (s1 + (1 << 20)) >> 21;
4271   s2 += carry1;
4272   s1 -= carry1 << 21;
4273   carry3 = (s3 + (1 << 20)) >> 21;
4274   s4 += carry3;
4275   s3 -= carry3 << 21;
4276   carry5 = (s5 + (1 << 20)) >> 21;
4277   s6 += carry5;
4278   s5 -= carry5 << 21;
4279   carry7 = (s7 + (1 << 20)) >> 21;
4280   s8 += carry7;
4281   s7 -= carry7 << 21;
4282   carry9 = (s9 + (1 << 20)) >> 21;
4283   s10 += carry9;
4284   s9 -= carry9 << 21;
4285   carry11 = (s11 + (1 << 20)) >> 21;
4286   s12 += carry11;
4287   s11 -= carry11 << 21;
4288   carry13 = (s13 + (1 << 20)) >> 21;
4289   s14 += carry13;
4290   s13 -= carry13 << 21;
4291   carry15 = (s15 + (1 << 20)) >> 21;
4292   s16 += carry15;
4293   s15 -= carry15 << 21;
4294   carry17 = (s17 + (1 << 20)) >> 21;
4295   s18 += carry17;
4296   s17 -= carry17 << 21;
4297   carry19 = (s19 + (1 << 20)) >> 21;
4298   s20 += carry19;
4299   s19 -= carry19 << 21;
4300   carry21 = (s21 + (1 << 20)) >> 21;
4301   s22 += carry21;
4302   s21 -= carry21 << 21;
4303
4304   s11 += s23 * 666643;
4305   s12 += s23 * 470296;
4306   s13 += s23 * 654183;
4307   s14 -= s23 * 997805;
4308   s15 += s23 * 136657;
4309   s16 -= s23 * 683901;
4310   s23 = 0;
4311
4312   s10 += s22 * 666643;
4313   s11 += s22 * 470296;
4314   s12 += s22 * 654183;
4315   s13 -= s22 * 997805;
4316   s14 += s22 * 136657;
4317   s15 -= s22 * 683901;
4318   s22 = 0;
4319
4320   s9 += s21 * 666643;
4321   s10 += s21 * 470296;
4322   s11 += s21 * 654183;
4323   s12 -= s21 * 997805;
4324   s13 += s21 * 136657;
4325   s14 -= s21 * 683901;
4326   s21 = 0;
4327
4328   s8 += s20 * 666643;
4329   s9 += s20 * 470296;
4330   s10 += s20 * 654183;
4331   s11 -= s20 * 997805;
4332   s12 += s20 * 136657;
4333   s13 -= s20 * 683901;
4334   s20 = 0;
4335
4336   s7 += s19 * 666643;
4337   s8 += s19 * 470296;
4338   s9 += s19 * 654183;
4339   s10 -= s19 * 997805;
4340   s11 += s19 * 136657;
4341   s12 -= s19 * 683901;
4342   s19 = 0;
4343
4344   s6 += s18 * 666643;
4345   s7 += s18 * 470296;
4346   s8 += s18 * 654183;
4347   s9 -= s18 * 997805;
4348   s10 += s18 * 136657;
4349   s11 -= s18 * 683901;
4350   s18 = 0;
4351
4352   carry6 = (s6 + (1 << 20)) >> 21;
4353   s7 += carry6;
4354   s6 -= carry6 << 21;
4355   carry8 = (s8 + (1 << 20)) >> 21;
4356   s9 += carry8;
4357   s8 -= carry8 << 21;
4358   carry10 = (s10 + (1 << 20)) >> 21;
4359   s11 += carry10;
4360   s10 -= carry10 << 21;
4361   carry12 = (s12 + (1 << 20)) >> 21;
4362   s13 += carry12;
4363   s12 -= carry12 << 21;
4364   carry14 = (s14 + (1 << 20)) >> 21;
4365   s15 += carry14;
4366   s14 -= carry14 << 21;
4367   carry16 = (s16 + (1 << 20)) >> 21;
4368   s17 += carry16;
4369   s16 -= carry16 << 21;
4370
4371   carry7 = (s7 + (1 << 20)) >> 21;
4372   s8 += carry7;
4373   s7 -= carry7 << 21;
4374   carry9 = (s9 + (1 << 20)) >> 21;
4375   s10 += carry9;
4376   s9 -= carry9 << 21;
4377   carry11 = (s11 + (1 << 20)) >> 21;
4378   s12 += carry11;
4379   s11 -= carry11 << 21;
4380   carry13 = (s13 + (1 << 20)) >> 21;
4381   s14 += carry13;
4382   s13 -= carry13 << 21;
4383   carry15 = (s15 + (1 << 20)) >> 21;
4384   s16 += carry15;
4385   s15 -= carry15 << 21;
4386
4387   s5 += s17 * 666643;
4388   s6 += s17 * 470296;
4389   s7 += s17 * 654183;
4390   s8 -= s17 * 997805;
4391   s9 += s17 * 136657;
4392   s10 -= s17 * 683901;
4393   s17 = 0;
4394
4395   s4 += s16 * 666643;
4396   s5 += s16 * 470296;
4397   s6 += s16 * 654183;
4398   s7 -= s16 * 997805;
4399   s8 += s16 * 136657;
4400   s9 -= s16 * 683901;
4401   s16 = 0;
4402
4403   s3 += s15 * 666643;
4404   s4 += s15 * 470296;
4405   s5 += s15 * 654183;
4406   s6 -= s15 * 997805;
4407   s7 += s15 * 136657;
4408   s8 -= s15 * 683901;
4409   s15 = 0;
4410
4411   s2 += s14 * 666643;
4412   s3 += s14 * 470296;
4413   s4 += s14 * 654183;
4414   s5 -= s14 * 997805;
4415   s6 += s14 * 136657;
4416   s7 -= s14 * 683901;
4417   s14 = 0;
4418
4419   s1 += s13 * 666643;
4420   s2 += s13 * 470296;
4421   s3 += s13 * 654183;
4422   s4 -= s13 * 997805;
4423   s5 += s13 * 136657;
4424   s6 -= s13 * 683901;
4425   s13 = 0;
4426
4427   s0 += s12 * 666643;
4428   s1 += s12 * 470296;
4429   s2 += s12 * 654183;
4430   s3 -= s12 * 997805;
4431   s4 += s12 * 136657;
4432   s5 -= s12 * 683901;
4433   s12 = 0;
4434
4435   carry0 = (s0 + (1 << 20)) >> 21;
4436   s1 += carry0;
4437   s0 -= carry0 << 21;
4438   carry2 = (s2 + (1 << 20)) >> 21;
4439   s3 += carry2;
4440   s2 -= carry2 << 21;
4441   carry4 = (s4 + (1 << 20)) >> 21;
4442   s5 += carry4;
4443   s4 -= carry4 << 21;
4444   carry6 = (s6 + (1 << 20)) >> 21;
4445   s7 += carry6;
4446   s6 -= carry6 << 21;
4447   carry8 = (s8 + (1 << 20)) >> 21;
4448   s9 += carry8;
4449   s8 -= carry8 << 21;
4450   carry10 = (s10 + (1 << 20)) >> 21;
4451   s11 += carry10;
4452   s10 -= carry10 << 21;
4453
4454   carry1 = (s1 + (1 << 20)) >> 21;
4455   s2 += carry1;
4456   s1 -= carry1 << 21;
4457   carry3 = (s3 + (1 << 20)) >> 21;
4458   s4 += carry3;
4459   s3 -= carry3 << 21;
4460   carry5 = (s5 + (1 << 20)) >> 21;
4461   s6 += carry5;
4462   s5 -= carry5 << 21;
4463   carry7 = (s7 + (1 << 20)) >> 21;
4464   s8 += carry7;
4465   s7 -= carry7 << 21;
4466   carry9 = (s9 + (1 << 20)) >> 21;
4467   s10 += carry9;
4468   s9 -= carry9 << 21;
4469   carry11 = (s11 + (1 << 20)) >> 21;
4470   s12 += carry11;
4471   s11 -= carry11 << 21;
4472
4473   s0 += s12 * 666643;
4474   s1 += s12 * 470296;
4475   s2 += s12 * 654183;
4476   s3 -= s12 * 997805;
4477   s4 += s12 * 136657;
4478   s5 -= s12 * 683901;
4479   s12 = 0;
4480
4481   carry0 = s0 >> 21;
4482   s1 += carry0;
4483   s0 -= carry0 << 21;
4484   carry1 = s1 >> 21;
4485   s2 += carry1;
4486   s1 -= carry1 << 21;
4487   carry2 = s2 >> 21;
4488   s3 += carry2;
4489   s2 -= carry2 << 21;
4490   carry3 = s3 >> 21;
4491   s4 += carry3;
4492   s3 -= carry3 << 21;
4493   carry4 = s4 >> 21;
4494   s5 += carry4;
4495   s4 -= carry4 << 21;
4496   carry5 = s5 >> 21;
4497   s6 += carry5;
4498   s5 -= carry5 << 21;
4499   carry6 = s6 >> 21;
4500   s7 += carry6;
4501   s6 -= carry6 << 21;
4502   carry7 = s7 >> 21;
4503   s8 += carry7;
4504   s7 -= carry7 << 21;
4505   carry8 = s8 >> 21;
4506   s9 += carry8;
4507   s8 -= carry8 << 21;
4508   carry9 = s9 >> 21;
4509   s10 += carry9;
4510   s9 -= carry9 << 21;
4511   carry10 = s10 >> 21;
4512   s11 += carry10;
4513   s10 -= carry10 << 21;
4514   carry11 = s11 >> 21;
4515   s12 += carry11;
4516   s11 -= carry11 << 21;
4517
4518   s0 += s12 * 666643;
4519   s1 += s12 * 470296;
4520   s2 += s12 * 654183;
4521   s3 -= s12 * 997805;
4522   s4 += s12 * 136657;
4523   s5 -= s12 * 683901;
4524   s12 = 0;
4525
4526   carry0 = s0 >> 21;
4527   s1 += carry0;
4528   s0 -= carry0 << 21;
4529   carry1 = s1 >> 21;
4530   s2 += carry1;
4531   s1 -= carry1 << 21;
4532   carry2 = s2 >> 21;
4533   s3 += carry2;
4534   s2 -= carry2 << 21;
4535   carry3 = s3 >> 21;
4536   s4 += carry3;
4537   s3 -= carry3 << 21;
4538   carry4 = s4 >> 21;
4539   s5 += carry4;
4540   s4 -= carry4 << 21;
4541   carry5 = s5 >> 21;
4542   s6 += carry5;
4543   s5 -= carry5 << 21;
4544   carry6 = s6 >> 21;
4545   s7 += carry6;
4546   s6 -= carry6 << 21;
4547   carry7 = s7 >> 21;
4548   s8 += carry7;
4549   s7 -= carry7 << 21;
4550   carry8 = s8 >> 21;
4551   s9 += carry8;
4552   s8 -= carry8 << 21;
4553   carry9 = s9 >> 21;
4554   s10 += carry9;
4555   s9 -= carry9 << 21;
4556   carry10 = s10 >> 21;
4557   s11 += carry10;
4558   s10 -= carry10 << 21;
4559
4560   s[0] = s0 >> 0;
4561   s[1] = s0 >> 8;
4562   s[2] = (s0 >> 16) | (s1 << 5);
4563   s[3] = s1 >> 3;
4564   s[4] = s1 >> 11;
4565   s[5] = (s1 >> 19) | (s2 << 2);
4566   s[6] = s2 >> 6;
4567   s[7] = (s2 >> 14) | (s3 << 7);
4568   s[8] = s3 >> 1;
4569   s[9] = s3 >> 9;
4570   s[10] = (s3 >> 17) | (s4 << 4);
4571   s[11] = s4 >> 4;
4572   s[12] = s4 >> 12;
4573   s[13] = (s4 >> 20) | (s5 << 1);
4574   s[14] = s5 >> 7;
4575   s[15] = (s5 >> 15) | (s6 << 6);
4576   s[16] = s6 >> 2;
4577   s[17] = s6 >> 10;
4578   s[18] = (s6 >> 18) | (s7 << 3);
4579   s[19] = s7 >> 5;
4580   s[20] = s7 >> 13;
4581   s[21] = s8 >> 0;
4582   s[22] = s8 >> 8;
4583   s[23] = (s8 >> 16) | (s9 << 5);
4584   s[24] = s9 >> 3;
4585   s[25] = s9 >> 11;
4586   s[26] = (s9 >> 19) | (s10 << 2);
4587   s[27] = s10 >> 6;
4588   s[28] = (s10 >> 14) | (s11 << 7);
4589   s[29] = s11 >> 1;
4590   s[30] = s11 >> 9;
4591   s[31] = s11 >> 17;
4592 }
4593 #if 0
4594 void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
4595   uint8_t seed[32];
4596   RAND_bytes(seed, 32);
4597   ED25519_keypair_from_seed(out_public_key, out_private_key, seed);
4598 }
4599 #endif
4600 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
4601                  const uint8_t private_key[64]) {
4602   uint8_t az[SHA512_DIGEST_LENGTH];
4603   uint8_t nonce[SHA512_DIGEST_LENGTH];
4604   ge_p3 R;
4605   uint8_t hram[SHA512_DIGEST_LENGTH];
4606   SHA512_CTX hash_ctx;
4607
4608   SHA512(private_key, 32, az);
4609
4610   az[0] &= 248;
4611   az[31] &= 63;
4612   az[31] |= 64;
4613
4614   SHA512_Init(&hash_ctx);
4615   SHA512_Update(&hash_ctx, az + 32, 32);
4616   SHA512_Update(&hash_ctx, message, message_len);
4617   SHA512_Final(nonce, &hash_ctx);
4618
4619   x25519_sc_reduce(nonce);
4620   ge_scalarmult_base(&R, nonce);
4621   ge_p3_tobytes(out_sig, &R);
4622
4623   SHA512_Init(&hash_ctx);
4624   SHA512_Update(&hash_ctx, out_sig, 32);
4625   SHA512_Update(&hash_ctx, private_key + 32, 32);
4626   SHA512_Update(&hash_ctx, message, message_len);
4627   SHA512_Final(hram, &hash_ctx);
4628
4629   x25519_sc_reduce(hram);
4630   sc_muladd(out_sig + 32, hram, az, nonce);
4631
4632   return 1;
4633 }
4634
4635 int ED25519_verify(const uint8_t *message, size_t message_len,
4636                    const uint8_t signature[64], const uint8_t public_key[32]) {
4637   ge_p3 A;
4638   uint8_t pkcopy[32];
4639   uint8_t rcopy[32];
4640   uint8_t scopy[32];
4641   SHA512_CTX hash_ctx;
4642   ge_p2 R;
4643   uint8_t rcheck[32];
4644   uint8_t h[SHA512_DIGEST_LENGTH];
4645
4646   if ((signature[63] & 224) != 0 ||
4647       ge_frombytes_vartime(&A, public_key) != 0) {
4648     return 0;
4649   }
4650
4651   fe_neg(A.X, A.X);
4652   fe_neg(A.T, A.T);
4653
4654   memcpy(pkcopy, public_key, 32);
4655   memcpy(rcopy, signature, 32);
4656   memcpy(scopy, signature + 32, 32);
4657
4658   SHA512_Init(&hash_ctx);
4659   SHA512_Update(&hash_ctx, signature, 32);
4660   SHA512_Update(&hash_ctx, public_key, 32);
4661   SHA512_Update(&hash_ctx, message, message_len);
4662   SHA512_Final(h, &hash_ctx);
4663
4664   x25519_sc_reduce(h);
4665
4666   ge_double_scalarmult_vartime(&R, h, &A, scopy);
4667
4668   ge_tobytes(rcheck, &R);
4669
4670   return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
4671 }
4672
4673 void ED25519_keypair_from_seed(uint8_t out_public_key[32],
4674                                uint8_t out_private_key[64],
4675                                const uint8_t seed[32]) {
4676   uint8_t az[SHA512_DIGEST_LENGTH];
4677   ge_p3 A;
4678
4679   SHA512(seed, 32, az);
4680
4681   az[0] &= 248;
4682   az[31] &= 63;
4683   az[31] |= 64;
4684
4685   ge_scalarmult_base(&A, az);
4686   ge_p3_tobytes(out_public_key, &A);
4687
4688   memcpy(out_private_key, seed, 32);
4689   memcpy(out_private_key + 32, out_public_key, 32);
4690 }
4691
4692 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
4693            const uint8_t peer_public_value[32]) {
4694   static const uint8_t kZeros[32] = {0};
4695   x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
4696   /* The all-zero output results when the input is a point of small order. */
4697   return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
4698 }
4699
4700 void X25519_public_from_private(uint8_t out_public_value[32],
4701                                 const uint8_t private_key[32]) {
4702   uint8_t e[32];
4703   ge_p3 A;
4704   fe zplusy, zminusy, zminusy_inv;
4705
4706   memcpy(e, private_key, 32);
4707   e[0] &= 248;
4708   e[31] &= 127;
4709   e[31] |= 64;
4710
4711   ge_scalarmult_base(&A, e);
4712
4713   /* We only need the u-coordinate of the curve25519 point. The map is
4714    * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */
4715   fe_add(zplusy, A.Z, A.Y);
4716   fe_sub(zminusy, A.Z, A.Y);
4717   fe_invert(zminusy_inv, zminusy);
4718   fe_mul(zplusy, zplusy, zminusy_inv);
4719   fe_tobytes(out_public_value, zplusy);
4720 }