1/*
2 * Copyright 2016-2019 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the OpenSSL license (the "License").  You may not use
5 * this file except in compliance with the License.  You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10#include <string.h>
11#include "ec_local.h"
12#include <openssl/sha.h>
13
14#if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \
15                            defined(_M_AMD64) || defined(_M_X64))
16
17# define BASE_2_64_IMPLEMENTED
18
19typedef uint64_t fe64[4];
20
21int x25519_fe64_eligible(void);
22
23/*
24 * Following subroutines perform corresponding operations modulo
25 * 2^256-38, i.e. double the curve modulus. However, inputs and
26 * outputs are permitted to be partially reduced, i.e. to remain
27 * in [0..2^256) range. It's all tied up in final fe64_tobytes
28 * that performs full reduction modulo 2^255-19.
29 *
30 * There are no reference C implementations for these.
31 */
32void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
33void x25519_fe64_sqr(fe64 h, const fe64 f);
34void x25519_fe64_mul121666(fe64 h, fe64 f);
35void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
36void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
37void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
38# define fe64_mul x25519_fe64_mul
39# define fe64_sqr x25519_fe64_sqr
40# define fe64_mul121666 x25519_fe64_mul121666
41# define fe64_add x25519_fe64_add
42# define fe64_sub x25519_fe64_sub
43# define fe64_tobytes x25519_fe64_tobytes
44
45static uint64_t load_8(const uint8_t *in)
46{
47    uint64_t result;
48
49    result = in[0];
50    result |= ((uint64_t)in[1]) << 8;
51    result |= ((uint64_t)in[2]) << 16;
52    result |= ((uint64_t)in[3]) << 24;
53    result |= ((uint64_t)in[4]) << 32;
54    result |= ((uint64_t)in[5]) << 40;
55    result |= ((uint64_t)in[6]) << 48;
56    result |= ((uint64_t)in[7]) << 56;
57
58    return result;
59}
60
61static void fe64_frombytes(fe64 h, const uint8_t *s)
62{
63    h[0] = load_8(s);
64    h[1] = load_8(s + 8);
65    h[2] = load_8(s + 16);
66    h[3] = load_8(s + 24) & 0x7fffffffffffffff;
67}
68
69static void fe64_0(fe64 h)
70{
71    h[0] = 0;
72    h[1] = 0;
73    h[2] = 0;
74    h[3] = 0;
75}
76
77static void fe64_1(fe64 h)
78{
79    h[0] = 1;
80    h[1] = 0;
81    h[2] = 0;
82    h[3] = 0;
83}
84
85static void fe64_copy(fe64 h, const fe64 f)
86{
87    h[0] = f[0];
88    h[1] = f[1];
89    h[2] = f[2];
90    h[3] = f[3];
91}
92
93static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
94{
95    int i;
96    uint64_t mask = 0 - (uint64_t)b;
97
98    for (i = 0; i < 4; i++) {
99        uint64_t x = f[i] ^ g[i];
100        x &= mask;
101        f[i] ^= x;
102        g[i] ^= x;
103    }
104}
105
106static void fe64_invert(fe64 out, const fe64 z)
107{
108    fe64 t0;
109    fe64 t1;
110    fe64 t2;
111    fe64 t3;
112    int i;
113
114    /*
115     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
116     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
117     */
118
119    /* t0 = z ** 2 */
120    fe64_sqr(t0, z);
121
122    /* t1 = t0 ** (2 ** 2) = z ** 8 */
123    fe64_sqr(t1, t0);
124    fe64_sqr(t1, t1);
125
126    /* t1 = z * t1 = z ** 9 */
127    fe64_mul(t1, z, t1);
128    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
129    fe64_mul(t0, t0, t1);
130
131    /* t2 = t0 ** 2 = z ** 22 */
132    fe64_sqr(t2, t0);
133
134    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
135    fe64_mul(t1, t1, t2);
136
137    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
138    fe64_sqr(t2, t1);
139    for (i = 1; i < 5; ++i)
140        fe64_sqr(t2, t2);
141
142    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
143    fe64_mul(t1, t2, t1);
144
145    /* Continuing similarly... */
146
147    /* t2 = z ** (2 ** 20 - 1) */
148    fe64_sqr(t2, t1);
149    for (i = 1; i < 10; ++i)
150        fe64_sqr(t2, t2);
151
152    fe64_mul(t2, t2, t1);
153
154    /* t2 = z ** (2 ** 40 - 1) */
155    fe64_sqr(t3, t2);
156    for (i = 1; i < 20; ++i)
157        fe64_sqr(t3, t3);
158
159    fe64_mul(t2, t3, t2);
160
161    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
162    for (i = 0; i < 10; ++i)
163        fe64_sqr(t2, t2);
164
165    /* t1 = z ** (2 ** 50 - 1) */
166    fe64_mul(t1, t2, t1);
167
168    /* t2 = z ** (2 ** 100 - 1) */
169    fe64_sqr(t2, t1);
170    for (i = 1; i < 50; ++i)
171        fe64_sqr(t2, t2);
172
173    fe64_mul(t2, t2, t1);
174
175    /* t2 = z ** (2 ** 200 - 1) */
176    fe64_sqr(t3, t2);
177    for (i = 1; i < 100; ++i)
178        fe64_sqr(t3, t3);
179
180    fe64_mul(t2, t3, t2);
181
182    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
183    for (i = 0; i < 50; ++i)
184        fe64_sqr(t2, t2);
185
186    /* t1 = z ** (2 ** 250 - 1) */
187    fe64_mul(t1, t2, t1);
188
189    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
190    for (i = 0; i < 5; ++i)
191        fe64_sqr(t1, t1);
192
193    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
194    fe64_mul(out, t1, t0);
195}
196
197/*
198 * Duplicate of original x25519_scalar_mult_generic, but using
199 * fe64_* subroutines.
200 */
201static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
202                               const uint8_t point[32])
203{
204    fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
205    uint8_t e[32];
206    unsigned swap = 0;
207    int pos;
208
209    memcpy(e, scalar, 32);
210    e[0]  &= 0xf8;
211    e[31] &= 0x7f;
212    e[31] |= 0x40;
213    fe64_frombytes(x1, point);
214    fe64_1(x2);
215    fe64_0(z2);
216    fe64_copy(x3, x1);
217    fe64_1(z3);
218
219    for (pos = 254; pos >= 0; --pos) {
220        unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
221
222        swap ^= b;
223        fe64_cswap(x2, x3, swap);
224        fe64_cswap(z2, z3, swap);
225        swap = b;
226        fe64_sub(tmp0, x3, z3);
227        fe64_sub(tmp1, x2, z2);
228        fe64_add(x2, x2, z2);
229        fe64_add(z2, x3, z3);
230        fe64_mul(z3, x2, tmp0);
231        fe64_mul(z2, z2, tmp1);
232        fe64_sqr(tmp0, tmp1);
233        fe64_sqr(tmp1, x2);
234        fe64_add(x3, z3, z2);
235        fe64_sub(z2, z3, z2);
236        fe64_mul(x2, tmp1, tmp0);
237        fe64_sub(tmp1, tmp1, tmp0);
238        fe64_sqr(z2, z2);
239        fe64_mul121666(z3, tmp1);
240        fe64_sqr(x3, x3);
241        fe64_add(tmp0, tmp0, z3);
242        fe64_mul(z3, x1, z2);
243        fe64_mul(z2, tmp1, tmp0);
244    }
245
246    fe64_invert(z2, z2);
247    fe64_mul(x2, x2, z2);
248    fe64_tobytes(out, x2);
249
250    OPENSSL_cleanse(e, sizeof(e));
251}
252#endif
253
254#if defined(X25519_ASM) \
255    || ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \
256         && !defined(__sparc__) \
257         && (!defined(__SIZEOF_LONG__) || (__SIZEOF_LONG__ == 8)) \
258         && !(defined(__ANDROID__) && !defined(__clang__)) )
259/*
260 * Base 2^51 implementation. It's virtually no different from reference
261 * base 2^25.5 implementation in respect to lax boundary conditions for
262 * intermediate values and even individual limbs. So that whatever you
263 * know about the reference, applies even here...
264 */
265# define BASE_2_51_IMPLEMENTED
266
267typedef uint64_t fe51[5];
268
269static const uint64_t MASK51 = 0x7ffffffffffff;
270
271static uint64_t load_7(const uint8_t *in)
272{
273    uint64_t result;
274
275    result = in[0];
276    result |= ((uint64_t)in[1]) << 8;
277    result |= ((uint64_t)in[2]) << 16;
278    result |= ((uint64_t)in[3]) << 24;
279    result |= ((uint64_t)in[4]) << 32;
280    result |= ((uint64_t)in[5]) << 40;
281    result |= ((uint64_t)in[6]) << 48;
282
283    return result;
284}
285
286static uint64_t load_6(const uint8_t *in)
287{
288    uint64_t result;
289
290    result = in[0];
291    result |= ((uint64_t)in[1]) << 8;
292    result |= ((uint64_t)in[2]) << 16;
293    result |= ((uint64_t)in[3]) << 24;
294    result |= ((uint64_t)in[4]) << 32;
295    result |= ((uint64_t)in[5]) << 40;
296
297    return result;
298}
299
300static void fe51_frombytes(fe51 h, const uint8_t *s)
301{
302    uint64_t h0 = load_7(s);                                /* 56 bits */
303    uint64_t h1 = load_6(s + 7) << 5;                       /* 53 bits */
304    uint64_t h2 = load_7(s + 13) << 2;                      /* 58 bits */
305    uint64_t h3 = load_6(s + 20) << 7;                      /* 55 bits */
306    uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4;   /* 51 bits */
307
308    h1 |= h0 >> 51; h0 &= MASK51;
309    h2 |= h1 >> 51; h1 &= MASK51;
310    h3 |= h2 >> 51; h2 &= MASK51;
311    h4 |= h3 >> 51; h3 &= MASK51;
312
313    h[0] = h0;
314    h[1] = h1;
315    h[2] = h2;
316    h[3] = h3;
317    h[4] = h4;
318}
319
320static void fe51_tobytes(uint8_t *s, const fe51 h)
321{
322    uint64_t h0 = h[0];
323    uint64_t h1 = h[1];
324    uint64_t h2 = h[2];
325    uint64_t h3 = h[3];
326    uint64_t h4 = h[4];
327    uint64_t q;
328
329    /* compare to modulus */
330    q = (h0 + 19) >> 51;
331    q = (h1 + q) >> 51;
332    q = (h2 + q) >> 51;
333    q = (h3 + q) >> 51;
334    q = (h4 + q) >> 51;
335
336    /* full reduce */
337    h0 += 19 * q;
338    h1 += h0 >> 51; h0 &= MASK51;
339    h2 += h1 >> 51; h1 &= MASK51;
340    h3 += h2 >> 51; h2 &= MASK51;
341    h4 += h3 >> 51; h3 &= MASK51;
342                    h4 &= MASK51;
343
344    /* smash */
345    s[0] = (uint8_t)(h0 >> 0);
346    s[1] = (uint8_t)(h0 >> 8);
347    s[2] = (uint8_t)(h0 >> 16);
348    s[3] = (uint8_t)(h0 >> 24);
349    s[4] = (uint8_t)(h0 >> 32);
350    s[5] = (uint8_t)(h0 >> 40);
351    s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3));
352    s[7] = (uint8_t)(h1 >> 5);
353    s[8] = (uint8_t)(h1 >> 13);
354    s[9] = (uint8_t)(h1 >> 21);
355    s[10] = (uint8_t)(h1 >> 29);
356    s[11] = (uint8_t)(h1 >> 37);
357    s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6));
358    s[13] = (uint8_t)(h2 >> 2);
359    s[14] = (uint8_t)(h2 >> 10);
360    s[15] = (uint8_t)(h2 >> 18);
361    s[16] = (uint8_t)(h2 >> 26);
362    s[17] = (uint8_t)(h2 >> 34);
363    s[18] = (uint8_t)(h2 >> 42);
364    s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1));
365    s[20] = (uint8_t)(h3 >> 7);
366    s[21] = (uint8_t)(h3 >> 15);
367    s[22] = (uint8_t)(h3 >> 23);
368    s[23] = (uint8_t)(h3 >> 31);
369    s[24] = (uint8_t)(h3 >> 39);
370    s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4));
371    s[26] = (uint8_t)(h4 >> 4);
372    s[27] = (uint8_t)(h4 >> 12);
373    s[28] = (uint8_t)(h4 >> 20);
374    s[29] = (uint8_t)(h4 >> 28);
375    s[30] = (uint8_t)(h4 >> 36);
376    s[31] = (uint8_t)(h4 >> 44);
377}
378
379# if defined(X25519_ASM)
380void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
381void x25519_fe51_sqr(fe51 h, const fe51 f);
382void x25519_fe51_mul121666(fe51 h, fe51 f);
383#  define fe51_mul x25519_fe51_mul
384#  define fe51_sq  x25519_fe51_sqr
385#  define fe51_mul121666 x25519_fe51_mul121666
386# else
387
388typedef __uint128_t u128;
389
390static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
391{
392    u128 h0, h1, h2, h3, h4;
393    uint64_t f_i, g0, g1, g2, g3, g4;
394
395    f_i = f[0];
396    h0 = (u128)f_i * (g0 = g[0]);
397    h1 = (u128)f_i * (g1 = g[1]);
398    h2 = (u128)f_i * (g2 = g[2]);
399    h3 = (u128)f_i * (g3 = g[3]);
400    h4 = (u128)f_i * (g4 = g[4]);
401
402    f_i = f[1];
403    h0 += (u128)f_i * (g4 *= 19);
404    h1 += (u128)f_i * g0;
405    h2 += (u128)f_i * g1;
406    h3 += (u128)f_i * g2;
407    h4 += (u128)f_i * g3;
408
409    f_i = f[2];
410    h0 += (u128)f_i * (g3 *= 19);
411    h1 += (u128)f_i * g4;
412    h2 += (u128)f_i * g0;
413    h3 += (u128)f_i * g1;
414    h4 += (u128)f_i * g2;
415
416    f_i = f[3];
417    h0 += (u128)f_i * (g2 *= 19);
418    h1 += (u128)f_i * g3;
419    h2 += (u128)f_i * g4;
420    h3 += (u128)f_i * g0;
421    h4 += (u128)f_i * g1;
422
423    f_i = f[4];
424    h0 += (u128)f_i * (g1 *= 19);
425    h1 += (u128)f_i * g2;
426    h2 += (u128)f_i * g3;
427    h3 += (u128)f_i * g4;
428    h4 += (u128)f_i * g0;
429
430    /* partial [lazy] reduction */
431    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
432    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
433
434    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
435    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
436
437    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
438    g3 += g2 >> 51; g2 &= MASK51;
439    g1 += g0 >> 51; g0 &= MASK51;
440
441    h[0] = g0;
442    h[1] = g1;
443    h[2] = g2;
444    h[3] = g3;
445    h[4] = g4;
446}
447
448static void fe51_sq(fe51 h, const fe51 f)
449{
450#  if defined(OPENSSL_SMALL_FOOTPRINT)
451    fe51_mul(h, f, f);
452#  else
453    /* dedicated squaring gives 16-25% overall improvement */
454    uint64_t g0 = f[0];
455    uint64_t g1 = f[1];
456    uint64_t g2 = f[2];
457    uint64_t g3 = f[3];
458    uint64_t g4 = f[4];
459    u128 h0, h1, h2, h3, h4;
460
461    h0 = (u128)g0 * g0;     g0 *= 2;
462    h1 = (u128)g0 * g1;
463    h2 = (u128)g0 * g2;
464    h3 = (u128)g0 * g3;
465    h4 = (u128)g0 * g4;
466
467    g0 = g4;                /* borrow g0 */
468    h3 += (u128)g0 * (g4 *= 19);
469
470    h2 += (u128)g1 * g1;    g1 *= 2;
471    h3 += (u128)g1 * g2;
472    h4 += (u128)g1 * g3;
473    h0 += (u128)g1 * g4;
474
475    g0 = g3;                /* borrow g0 */
476    h1 += (u128)g0 * (g3 *= 19);
477    h2 += (u128)(g0 * 2) * g4;
478
479    h4 += (u128)g2 * g2;    g2 *= 2;
480    h0 += (u128)g2 * g3;
481    h1 += (u128)g2 * g4;
482
483    /* partial [lazy] reduction */
484    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
485    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
486
487    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
488    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
489
490    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
491    g3 += g2 >> 51; g2 &= MASK51;
492    g1 += g0 >> 51; g0 &= MASK51;
493
494    h[0] = g0;
495    h[1] = g1;
496    h[2] = g2;
497    h[3] = g3;
498    h[4] = g4;
499#  endif
500}
501
502static void fe51_mul121666(fe51 h, fe51 f)
503{
504    u128 h0 = f[0] * (u128)121666;
505    u128 h1 = f[1] * (u128)121666;
506    u128 h2 = f[2] * (u128)121666;
507    u128 h3 = f[3] * (u128)121666;
508    u128 h4 = f[4] * (u128)121666;
509    uint64_t g0, g1, g2, g3, g4;
510
511    h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
512    h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
513
514    h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
515    g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
516
517    g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
518    g3 += g2 >> 51; g2 &= MASK51;
519    g1 += g0 >> 51; g0 &= MASK51;
520
521    h[0] = g0;
522    h[1] = g1;
523    h[2] = g2;
524    h[3] = g3;
525    h[4] = g4;
526}
527# endif
528
529static void fe51_add(fe51 h, const fe51 f, const fe51 g)
530{
531    h[0] = f[0] + g[0];
532    h[1] = f[1] + g[1];
533    h[2] = f[2] + g[2];
534    h[3] = f[3] + g[3];
535    h[4] = f[4] + g[4];
536}
537
538static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
539{
540    /*
541     * Add 2*modulus to ensure that result remains positive
542     * even if subtrahend is partially reduced.
543     */
544    h[0] = (f[0] + 0xfffffffffffda) - g[0];
545    h[1] = (f[1] + 0xffffffffffffe) - g[1];
546    h[2] = (f[2] + 0xffffffffffffe) - g[2];
547    h[3] = (f[3] + 0xffffffffffffe) - g[3];
548    h[4] = (f[4] + 0xffffffffffffe) - g[4];
549}
550
551static void fe51_0(fe51 h)
552{
553    h[0] = 0;
554    h[1] = 0;
555    h[2] = 0;
556    h[3] = 0;
557    h[4] = 0;
558}
559
560static void fe51_1(fe51 h)
561{
562    h[0] = 1;
563    h[1] = 0;
564    h[2] = 0;
565    h[3] = 0;
566    h[4] = 0;
567}
568
569static void fe51_copy(fe51 h, const fe51 f)
570{
571    h[0] = f[0];
572    h[1] = f[1];
573    h[2] = f[2];
574    h[3] = f[3];
575    h[4] = f[4];
576}
577
578static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
579{
580    int i;
581    uint64_t mask = 0 - (uint64_t)b;
582
583    for (i = 0; i < 5; i++) {
584        int64_t x = f[i] ^ g[i];
585        x &= mask;
586        f[i] ^= x;
587        g[i] ^= x;
588    }
589}
590
591static void fe51_invert(fe51 out, const fe51 z)
592{
593    fe51 t0;
594    fe51 t1;
595    fe51 t2;
596    fe51 t3;
597    int i;
598
599    /*
600     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
601     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
602     */
603
604    /* t0 = z ** 2 */
605    fe51_sq(t0, z);
606
607    /* t1 = t0 ** (2 ** 2) = z ** 8 */
608    fe51_sq(t1, t0);
609    fe51_sq(t1, t1);
610
611    /* t1 = z * t1 = z ** 9 */
612    fe51_mul(t1, z, t1);
613    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
614    fe51_mul(t0, t0, t1);
615
616    /* t2 = t0 ** 2 = z ** 22 */
617    fe51_sq(t2, t0);
618
619    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
620    fe51_mul(t1, t1, t2);
621
622    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
623    fe51_sq(t2, t1);
624    for (i = 1; i < 5; ++i)
625        fe51_sq(t2, t2);
626
627    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
628    fe51_mul(t1, t2, t1);
629
630    /* Continuing similarly... */
631
632    /* t2 = z ** (2 ** 20 - 1) */
633    fe51_sq(t2, t1);
634    for (i = 1; i < 10; ++i)
635        fe51_sq(t2, t2);
636
637    fe51_mul(t2, t2, t1);
638
639    /* t2 = z ** (2 ** 40 - 1) */
640    fe51_sq(t3, t2);
641    for (i = 1; i < 20; ++i)
642        fe51_sq(t3, t3);
643
644    fe51_mul(t2, t3, t2);
645
646    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
647    for (i = 0; i < 10; ++i)
648        fe51_sq(t2, t2);
649
650    /* t1 = z ** (2 ** 50 - 1) */
651    fe51_mul(t1, t2, t1);
652
653    /* t2 = z ** (2 ** 100 - 1) */
654    fe51_sq(t2, t1);
655    for (i = 1; i < 50; ++i)
656        fe51_sq(t2, t2);
657
658    fe51_mul(t2, t2, t1);
659
660    /* t2 = z ** (2 ** 200 - 1) */
661    fe51_sq(t3, t2);
662    for (i = 1; i < 100; ++i)
663        fe51_sq(t3, t3);
664
665    fe51_mul(t2, t3, t2);
666
667    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
668    for (i = 0; i < 50; ++i)
669        fe51_sq(t2, t2);
670
671    /* t1 = z ** (2 ** 250 - 1) */
672    fe51_mul(t1, t2, t1);
673
674    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
675    for (i = 0; i < 5; ++i)
676        fe51_sq(t1, t1);
677
678    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
679    fe51_mul(out, t1, t0);
680}
681
682/*
683 * Duplicate of original x25519_scalar_mult_generic, but using
684 * fe51_* subroutines.
685 */
686static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
687                               const uint8_t point[32])
688{
689    fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
690    uint8_t e[32];
691    unsigned swap = 0;
692    int pos;
693
694# ifdef BASE_2_64_IMPLEMENTED
695    if (x25519_fe64_eligible()) {
696        x25519_scalar_mulx(out, scalar, point);
697        return;
698    }
699# endif
700
701    memcpy(e, scalar, 32);
702    e[0]  &= 0xf8;
703    e[31] &= 0x7f;
704    e[31] |= 0x40;
705    fe51_frombytes(x1, point);
706    fe51_1(x2);
707    fe51_0(z2);
708    fe51_copy(x3, x1);
709    fe51_1(z3);
710
711    for (pos = 254; pos >= 0; --pos) {
712        unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
713
714        swap ^= b;
715        fe51_cswap(x2, x3, swap);
716        fe51_cswap(z2, z3, swap);
717        swap = b;
718        fe51_sub(tmp0, x3, z3);
719        fe51_sub(tmp1, x2, z2);
720        fe51_add(x2, x2, z2);
721        fe51_add(z2, x3, z3);
722        fe51_mul(z3, tmp0, x2);
723        fe51_mul(z2, z2, tmp1);
724        fe51_sq(tmp0, tmp1);
725        fe51_sq(tmp1, x2);
726        fe51_add(x3, z3, z2);
727        fe51_sub(z2, z3, z2);
728        fe51_mul(x2, tmp1, tmp0);
729        fe51_sub(tmp1, tmp1, tmp0);
730        fe51_sq(z2, z2);
731        fe51_mul121666(z3, tmp1);
732        fe51_sq(x3, x3);
733        fe51_add(tmp0, tmp0, z3);
734        fe51_mul(z3, x1, z2);
735        fe51_mul(z2, tmp1, tmp0);
736    }
737
738    fe51_invert(z2, z2);
739    fe51_mul(x2, x2, z2);
740    fe51_tobytes(out, x2);
741
742    OPENSSL_cleanse(e, sizeof(e));
743}
744#endif
745
746/*
747 * Reference base 2^25.5 implementation.
748 *
749 * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
750 * 20141124 (http://bench.cr.yp.to/supercop.html).
751 *
752 * The field functions are shared by Ed25519 and X25519 where possible.
753 */
754
755/*
756 * fe means field element. Here the field is \Z/(2^255-19). An element t,
757 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
758 * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
759 * context.
760 */
761typedef int32_t fe[10];
762
763static const int64_t kBottom21Bits =  0x1fffffLL;
764static const int64_t kBottom25Bits = 0x1ffffffLL;
765static const int64_t kBottom26Bits = 0x3ffffffLL;
766static const int64_t kTop39Bits = 0xfffffffffe000000LL;
767static const int64_t kTop38Bits = 0xfffffffffc000000LL;
768
769static uint64_t load_3(const uint8_t *in)
770{
771    uint64_t result;
772
773    result  = ((uint64_t)in[0]);
774    result |= ((uint64_t)in[1]) << 8;
775    result |= ((uint64_t)in[2]) << 16;
776    return result;
777}
778
779static uint64_t load_4(const uint8_t *in)
780{
781    uint64_t result;
782
783    result  = ((uint64_t)in[0]);
784    result |= ((uint64_t)in[1]) << 8;
785    result |= ((uint64_t)in[2]) << 16;
786    result |= ((uint64_t)in[3]) << 24;
787    return result;
788}
789
790static void fe_frombytes(fe h, const uint8_t *s)
791{
792    /* Ignores top bit of h. */
793    int64_t h0 =  load_4(s);
794    int64_t h1 =  load_3(s +  4) << 6;
795    int64_t h2 =  load_3(s +  7) << 5;
796    int64_t h3 =  load_3(s + 10) << 3;
797    int64_t h4 =  load_3(s + 13) << 2;
798    int64_t h5 =  load_4(s + 16);
799    int64_t h6 =  load_3(s + 20) << 7;
800    int64_t h7 =  load_3(s + 23) << 5;
801    int64_t h8 =  load_3(s + 26) << 4;
802    int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
803    int64_t carry0;
804    int64_t carry1;
805    int64_t carry2;
806    int64_t carry3;
807    int64_t carry4;
808    int64_t carry5;
809    int64_t carry6;
810    int64_t carry7;
811    int64_t carry8;
812    int64_t carry9;
813
814    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
815    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
816    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
817    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
818    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
819
820    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
821    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
822    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
823    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
824    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
825
826    h[0] = (int32_t)h0;
827    h[1] = (int32_t)h1;
828    h[2] = (int32_t)h2;
829    h[3] = (int32_t)h3;
830    h[4] = (int32_t)h4;
831    h[5] = (int32_t)h5;
832    h[6] = (int32_t)h6;
833    h[7] = (int32_t)h7;
834    h[8] = (int32_t)h8;
835    h[9] = (int32_t)h9;
836}
837
838/*
839 * Preconditions:
840 *   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
841 *
842 * Write p=2^255-19; q=floor(h/p).
843 * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
844 *
845 * Proof:
846 *   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
847 *   Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
848 *
849 *   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
850 *   Then 0<y<1.
851 *
852 *   Write r=h-pq.
853 *   Have 0<=r<=p-1=2^255-20.
854 *   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
855 *
856 *   Write x=r+19(2^-255)r+y.
857 *   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
858 *
859 *   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
860 *   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
861 */
862static void fe_tobytes(uint8_t *s, const fe h)
863{
864    int32_t h0 = h[0];
865    int32_t h1 = h[1];
866    int32_t h2 = h[2];
867    int32_t h3 = h[3];
868    int32_t h4 = h[4];
869    int32_t h5 = h[5];
870    int32_t h6 = h[6];
871    int32_t h7 = h[7];
872    int32_t h8 = h[8];
873    int32_t h9 = h[9];
874    int32_t q;
875
876    q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
877    q = (h0 + q) >> 26;
878    q = (h1 + q) >> 25;
879    q = (h2 + q) >> 26;
880    q = (h3 + q) >> 25;
881    q = (h4 + q) >> 26;
882    q = (h5 + q) >> 25;
883    q = (h6 + q) >> 26;
884    q = (h7 + q) >> 25;
885    q = (h8 + q) >> 26;
886    q = (h9 + q) >> 25;
887
888    /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
889    h0 += 19 * q;
890    /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
891
892    h1 += h0 >> 26; h0 &= kBottom26Bits;
893    h2 += h1 >> 25; h1 &= kBottom25Bits;
894    h3 += h2 >> 26; h2 &= kBottom26Bits;
895    h4 += h3 >> 25; h3 &= kBottom25Bits;
896    h5 += h4 >> 26; h4 &= kBottom26Bits;
897    h6 += h5 >> 25; h5 &= kBottom25Bits;
898    h7 += h6 >> 26; h6 &= kBottom26Bits;
899    h8 += h7 >> 25; h7 &= kBottom25Bits;
900    h9 += h8 >> 26; h8 &= kBottom26Bits;
901                    h9 &= kBottom25Bits;
902    /* h10 = carry9 */
903
904    /*
905     * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
906     * Have h0+...+2^230 h9 between 0 and 2^255-1;
907     * evidently 2^255 h10-2^255 q = 0.
908     * Goal: Output h0+...+2^230 h9.
909     */
910    s[ 0] = (uint8_t) (h0 >>  0);
911    s[ 1] = (uint8_t) (h0 >>  8);
912    s[ 2] = (uint8_t) (h0 >> 16);
913    s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2));
914    s[ 4] = (uint8_t) (h1 >>  6);
915    s[ 5] = (uint8_t) (h1 >> 14);
916    s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3));
917    s[ 7] = (uint8_t) (h2 >>  5);
918    s[ 8] = (uint8_t) (h2 >> 13);
919    s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5));
920    s[10] = (uint8_t) (h3 >>  3);
921    s[11] = (uint8_t) (h3 >> 11);
922    s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6));
923    s[13] = (uint8_t) (h4 >>  2);
924    s[14] = (uint8_t) (h4 >> 10);
925    s[15] = (uint8_t) (h4 >> 18);
926    s[16] = (uint8_t) (h5 >>  0);
927    s[17] = (uint8_t) (h5 >>  8);
928    s[18] = (uint8_t) (h5 >> 16);
929    s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1));
930    s[20] = (uint8_t) (h6 >>  7);
931    s[21] = (uint8_t) (h6 >> 15);
932    s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3));
933    s[23] = (uint8_t) (h7 >>  5);
934    s[24] = (uint8_t) (h7 >> 13);
935    s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4));
936    s[26] = (uint8_t) (h8 >>  4);
937    s[27] = (uint8_t) (h8 >> 12);
938    s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6));
939    s[29] = (uint8_t) (h9 >>  2);
940    s[30] = (uint8_t) (h9 >> 10);
941    s[31] = (uint8_t) (h9 >> 18);
942}
943
944/* h = f */
945static void fe_copy(fe h, const fe f)
946{
947    memmove(h, f, sizeof(int32_t) * 10);
948}
949
950/* h = 0 */
951static void fe_0(fe h)
952{
953    memset(h, 0, sizeof(int32_t) * 10);
954}
955
956/* h = 1 */
957static void fe_1(fe h)
958{
959    memset(h, 0, sizeof(int32_t) * 10);
960    h[0] = 1;
961}
962
963/*
964 * h = f + g
965 *
966 * Can overlap h with f or g.
967 *
968 * Preconditions:
969 *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
970 *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
971 *
972 * Postconditions:
973 *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
974 */
975static void fe_add(fe h, const fe f, const fe g)
976{
977    unsigned i;
978
979    for (i = 0; i < 10; i++) {
980        h[i] = f[i] + g[i];
981    }
982}
983
984/*
985 * h = f - g
986 *
987 * Can overlap h with f or g.
988 *
989 * Preconditions:
990 *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
991 *    |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
992 *
993 * Postconditions:
994 *    |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
995 */
996static void fe_sub(fe h, const fe f, const fe g)
997{
998    unsigned i;
999
1000    for (i = 0; i < 10; i++) {
1001        h[i] = f[i] - g[i];
1002    }
1003}
1004
1005/*
1006 * h = f * g
1007 *
1008 * Can overlap h with f or g.
1009 *
1010 * Preconditions:
1011 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1012 *    |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1013 *
1014 * Postconditions:
1015 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1016 *
1017 * Notes on implementation strategy:
1018 *
1019 * Using schoolbook multiplication.
1020 * Karatsuba would save a little in some cost models.
1021 *
1022 * Most multiplications by 2 and 19 are 32-bit precomputations;
1023 * cheaper than 64-bit postcomputations.
1024 *
1025 * There is one remaining multiplication by 19 in the carry chain;
1026 * one *19 precomputation can be merged into this,
1027 * but the resulting data flow is considerably less clean.
1028 *
1029 * There are 12 carries below.
1030 * 10 of them are 2-way parallelizable and vectorizable.
1031 * Can get away with 11 carries, but then data flow is much deeper.
1032 *
1033 * With tighter constraints on inputs can squeeze carries into int32.
1034 */
1035static void fe_mul(fe h, const fe f, const fe g)
1036{
1037    int32_t f0 = f[0];
1038    int32_t f1 = f[1];
1039    int32_t f2 = f[2];
1040    int32_t f3 = f[3];
1041    int32_t f4 = f[4];
1042    int32_t f5 = f[5];
1043    int32_t f6 = f[6];
1044    int32_t f7 = f[7];
1045    int32_t f8 = f[8];
1046    int32_t f9 = f[9];
1047    int32_t g0 = g[0];
1048    int32_t g1 = g[1];
1049    int32_t g2 = g[2];
1050    int32_t g3 = g[3];
1051    int32_t g4 = g[4];
1052    int32_t g5 = g[5];
1053    int32_t g6 = g[6];
1054    int32_t g7 = g[7];
1055    int32_t g8 = g[8];
1056    int32_t g9 = g[9];
1057    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
1058    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
1059    int32_t g3_19 = 19 * g3;
1060    int32_t g4_19 = 19 * g4;
1061    int32_t g5_19 = 19 * g5;
1062    int32_t g6_19 = 19 * g6;
1063    int32_t g7_19 = 19 * g7;
1064    int32_t g8_19 = 19 * g8;
1065    int32_t g9_19 = 19 * g9;
1066    int32_t f1_2 = 2 * f1;
1067    int32_t f3_2 = 2 * f3;
1068    int32_t f5_2 = 2 * f5;
1069    int32_t f7_2 = 2 * f7;
1070    int32_t f9_2 = 2 * f9;
1071    int64_t f0g0    = f0   * (int64_t) g0;
1072    int64_t f0g1    = f0   * (int64_t) g1;
1073    int64_t f0g2    = f0   * (int64_t) g2;
1074    int64_t f0g3    = f0   * (int64_t) g3;
1075    int64_t f0g4    = f0   * (int64_t) g4;
1076    int64_t f0g5    = f0   * (int64_t) g5;
1077    int64_t f0g6    = f0   * (int64_t) g6;
1078    int64_t f0g7    = f0   * (int64_t) g7;
1079    int64_t f0g8    = f0   * (int64_t) g8;
1080    int64_t f0g9    = f0   * (int64_t) g9;
1081    int64_t f1g0    = f1   * (int64_t) g0;
1082    int64_t f1g1_2  = f1_2 * (int64_t) g1;
1083    int64_t f1g2    = f1   * (int64_t) g2;
1084    int64_t f1g3_2  = f1_2 * (int64_t) g3;
1085    int64_t f1g4    = f1   * (int64_t) g4;
1086    int64_t f1g5_2  = f1_2 * (int64_t) g5;
1087    int64_t f1g6    = f1   * (int64_t) g6;
1088    int64_t f1g7_2  = f1_2 * (int64_t) g7;
1089    int64_t f1g8    = f1   * (int64_t) g8;
1090    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1091    int64_t f2g0    = f2   * (int64_t) g0;
1092    int64_t f2g1    = f2   * (int64_t) g1;
1093    int64_t f2g2    = f2   * (int64_t) g2;
1094    int64_t f2g3    = f2   * (int64_t) g3;
1095    int64_t f2g4    = f2   * (int64_t) g4;
1096    int64_t f2g5    = f2   * (int64_t) g5;
1097    int64_t f2g6    = f2   * (int64_t) g6;
1098    int64_t f2g7    = f2   * (int64_t) g7;
1099    int64_t f2g8_19 = f2   * (int64_t) g8_19;
1100    int64_t f2g9_19 = f2   * (int64_t) g9_19;
1101    int64_t f3g0    = f3   * (int64_t) g0;
1102    int64_t f3g1_2  = f3_2 * (int64_t) g1;
1103    int64_t f3g2    = f3   * (int64_t) g2;
1104    int64_t f3g3_2  = f3_2 * (int64_t) g3;
1105    int64_t f3g4    = f3   * (int64_t) g4;
1106    int64_t f3g5_2  = f3_2 * (int64_t) g5;
1107    int64_t f3g6    = f3   * (int64_t) g6;
1108    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1109    int64_t f3g8_19 = f3   * (int64_t) g8_19;
1110    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1111    int64_t f4g0    = f4   * (int64_t) g0;
1112    int64_t f4g1    = f4   * (int64_t) g1;
1113    int64_t f4g2    = f4   * (int64_t) g2;
1114    int64_t f4g3    = f4   * (int64_t) g3;
1115    int64_t f4g4    = f4   * (int64_t) g4;
1116    int64_t f4g5    = f4   * (int64_t) g5;
1117    int64_t f4g6_19 = f4   * (int64_t) g6_19;
1118    int64_t f4g7_19 = f4   * (int64_t) g7_19;
1119    int64_t f4g8_19 = f4   * (int64_t) g8_19;
1120    int64_t f4g9_19 = f4   * (int64_t) g9_19;
1121    int64_t f5g0    = f5   * (int64_t) g0;
1122    int64_t f5g1_2  = f5_2 * (int64_t) g1;
1123    int64_t f5g2    = f5   * (int64_t) g2;
1124    int64_t f5g3_2  = f5_2 * (int64_t) g3;
1125    int64_t f5g4    = f5   * (int64_t) g4;
1126    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1127    int64_t f5g6_19 = f5   * (int64_t) g6_19;
1128    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1129    int64_t f5g8_19 = f5   * (int64_t) g8_19;
1130    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1131    int64_t f6g0    = f6   * (int64_t) g0;
1132    int64_t f6g1    = f6   * (int64_t) g1;
1133    int64_t f6g2    = f6   * (int64_t) g2;
1134    int64_t f6g3    = f6   * (int64_t) g3;
1135    int64_t f6g4_19 = f6   * (int64_t) g4_19;
1136    int64_t f6g5_19 = f6   * (int64_t) g5_19;
1137    int64_t f6g6_19 = f6   * (int64_t) g6_19;
1138    int64_t f6g7_19 = f6   * (int64_t) g7_19;
1139    int64_t f6g8_19 = f6   * (int64_t) g8_19;
1140    int64_t f6g9_19 = f6   * (int64_t) g9_19;
1141    int64_t f7g0    = f7   * (int64_t) g0;
1142    int64_t f7g1_2  = f7_2 * (int64_t) g1;
1143    int64_t f7g2    = f7   * (int64_t) g2;
1144    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1145    int64_t f7g4_19 = f7   * (int64_t) g4_19;
1146    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1147    int64_t f7g6_19 = f7   * (int64_t) g6_19;
1148    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1149    int64_t f7g8_19 = f7   * (int64_t) g8_19;
1150    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1151    int64_t f8g0    = f8   * (int64_t) g0;
1152    int64_t f8g1    = f8   * (int64_t) g1;
1153    int64_t f8g2_19 = f8   * (int64_t) g2_19;
1154    int64_t f8g3_19 = f8   * (int64_t) g3_19;
1155    int64_t f8g4_19 = f8   * (int64_t) g4_19;
1156    int64_t f8g5_19 = f8   * (int64_t) g5_19;
1157    int64_t f8g6_19 = f8   * (int64_t) g6_19;
1158    int64_t f8g7_19 = f8   * (int64_t) g7_19;
1159    int64_t f8g8_19 = f8   * (int64_t) g8_19;
1160    int64_t f8g9_19 = f8   * (int64_t) g9_19;
1161    int64_t f9g0    = f9   * (int64_t) g0;
1162    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1163    int64_t f9g2_19 = f9   * (int64_t) g2_19;
1164    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1165    int64_t f9g4_19 = f9   * (int64_t) g4_19;
1166    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1167    int64_t f9g6_19 = f9   * (int64_t) g6_19;
1168    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1169    int64_t f9g8_19 = f9   * (int64_t) g8_19;
1170    int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1171    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1172    int64_t h1 = f0g1 + f1g0    + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1173    int64_t h2 = f0g2 + f1g1_2  + f2g0    + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1174    int64_t h3 = f0g3 + f1g2    + f2g1    + f3g0    + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1175    int64_t h4 = f0g4 + f1g3_2  + f2g2    + f3g1_2  + f4g0    + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1176    int64_t h5 = f0g5 + f1g4    + f2g3    + f3g2    + f4g1    + f5g0    + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1177    int64_t h6 = f0g6 + f1g5_2  + f2g4    + f3g3_2  + f4g2    + f5g1_2  + f6g0    + f7g9_38 + f8g8_19 + f9g7_38;
1178    int64_t h7 = f0g7 + f1g6    + f2g5    + f3g4    + f4g3    + f5g2    + f6g1    + f7g0    + f8g9_19 + f9g8_19;
1179    int64_t h8 = f0g8 + f1g7_2  + f2g6    + f3g5_2  + f4g4    + f5g3_2  + f6g2    + f7g1_2  + f8g0    + f9g9_38;
1180    int64_t h9 = f0g9 + f1g8    + f2g7    + f3g6    + f4g5    + f5g4    + f6g3    + f7g2    + f8g1    + f9g0   ;
1181    int64_t carry0;
1182    int64_t carry1;
1183    int64_t carry2;
1184    int64_t carry3;
1185    int64_t carry4;
1186    int64_t carry5;
1187    int64_t carry6;
1188    int64_t carry7;
1189    int64_t carry8;
1190    int64_t carry9;
1191
1192    /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
1193     *   i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1194     * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
1195     *   i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
1196
1197    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1198    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1199    /* |h0| <= 2^25 */
1200    /* |h4| <= 2^25 */
1201    /* |h1| <= 1.71*2^59 */
1202    /* |h5| <= 1.71*2^59 */
1203
1204    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1205    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1206    /* |h1| <= 2^24; from now on fits into int32 */
1207    /* |h5| <= 2^24; from now on fits into int32 */
1208    /* |h2| <= 1.41*2^60 */
1209    /* |h6| <= 1.41*2^60 */
1210
1211    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1212    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1213    /* |h2| <= 2^25; from now on fits into int32 unchanged */
1214    /* |h6| <= 2^25; from now on fits into int32 unchanged */
1215    /* |h3| <= 1.71*2^59 */
1216    /* |h7| <= 1.71*2^59 */
1217
1218    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1219    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1220    /* |h3| <= 2^24; from now on fits into int32 unchanged */
1221    /* |h7| <= 2^24; from now on fits into int32 unchanged */
1222    /* |h4| <= 1.72*2^34 */
1223    /* |h8| <= 1.41*2^60 */
1224
1225    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1226    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1227    /* |h4| <= 2^25; from now on fits into int32 unchanged */
1228    /* |h8| <= 2^25; from now on fits into int32 unchanged */
1229    /* |h5| <= 1.01*2^24 */
1230    /* |h9| <= 1.71*2^59 */
1231
1232    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1233    /* |h9| <= 2^24; from now on fits into int32 unchanged */
1234    /* |h0| <= 1.1*2^39 */
1235
1236    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1237    /* |h0| <= 2^25; from now on fits into int32 unchanged */
1238    /* |h1| <= 1.01*2^24 */
1239
1240    h[0] = (int32_t)h0;
1241    h[1] = (int32_t)h1;
1242    h[2] = (int32_t)h2;
1243    h[3] = (int32_t)h3;
1244    h[4] = (int32_t)h4;
1245    h[5] = (int32_t)h5;
1246    h[6] = (int32_t)h6;
1247    h[7] = (int32_t)h7;
1248    h[8] = (int32_t)h8;
1249    h[9] = (int32_t)h9;
1250}
1251
1252/*
1253 * h = f * f
1254 *
1255 * Can overlap h with f.
1256 *
1257 * Preconditions:
1258 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1259 *
1260 * Postconditions:
1261 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1262 *
1263 * See fe_mul.c for discussion of implementation strategy.
1264 */
1265static void fe_sq(fe h, const fe f)
1266{
1267    int32_t f0 = f[0];
1268    int32_t f1 = f[1];
1269    int32_t f2 = f[2];
1270    int32_t f3 = f[3];
1271    int32_t f4 = f[4];
1272    int32_t f5 = f[5];
1273    int32_t f6 = f[6];
1274    int32_t f7 = f[7];
1275    int32_t f8 = f[8];
1276    int32_t f9 = f[9];
1277    int32_t f0_2 = 2 * f0;
1278    int32_t f1_2 = 2 * f1;
1279    int32_t f2_2 = 2 * f2;
1280    int32_t f3_2 = 2 * f3;
1281    int32_t f4_2 = 2 * f4;
1282    int32_t f5_2 = 2 * f5;
1283    int32_t f6_2 = 2 * f6;
1284    int32_t f7_2 = 2 * f7;
1285    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1286    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1287    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1288    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1289    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1290    int64_t f0f0    = f0   * (int64_t) f0;
1291    int64_t f0f1_2  = f0_2 * (int64_t) f1;
1292    int64_t f0f2_2  = f0_2 * (int64_t) f2;
1293    int64_t f0f3_2  = f0_2 * (int64_t) f3;
1294    int64_t f0f4_2  = f0_2 * (int64_t) f4;
1295    int64_t f0f5_2  = f0_2 * (int64_t) f5;
1296    int64_t f0f6_2  = f0_2 * (int64_t) f6;
1297    int64_t f0f7_2  = f0_2 * (int64_t) f7;
1298    int64_t f0f8_2  = f0_2 * (int64_t) f8;
1299    int64_t f0f9_2  = f0_2 * (int64_t) f9;
1300    int64_t f1f1_2  = f1_2 * (int64_t) f1;
1301    int64_t f1f2_2  = f1_2 * (int64_t) f2;
1302    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
1303    int64_t f1f4_2  = f1_2 * (int64_t) f4;
1304    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
1305    int64_t f1f6_2  = f1_2 * (int64_t) f6;
1306    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
1307    int64_t f1f8_2  = f1_2 * (int64_t) f8;
1308    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1309    int64_t f2f2    = f2   * (int64_t) f2;
1310    int64_t f2f3_2  = f2_2 * (int64_t) f3;
1311    int64_t f2f4_2  = f2_2 * (int64_t) f4;
1312    int64_t f2f5_2  = f2_2 * (int64_t) f5;
1313    int64_t f2f6_2  = f2_2 * (int64_t) f6;
1314    int64_t f2f7_2  = f2_2 * (int64_t) f7;
1315    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1316    int64_t f2f9_38 = f2   * (int64_t) f9_38;
1317    int64_t f3f3_2  = f3_2 * (int64_t) f3;
1318    int64_t f3f4_2  = f3_2 * (int64_t) f4;
1319    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
1320    int64_t f3f6_2  = f3_2 * (int64_t) f6;
1321    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1322    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1323    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1324    int64_t f4f4    = f4   * (int64_t) f4;
1325    int64_t f4f5_2  = f4_2 * (int64_t) f5;
1326    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1327    int64_t f4f7_38 = f4   * (int64_t) f7_38;
1328    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1329    int64_t f4f9_38 = f4   * (int64_t) f9_38;
1330    int64_t f5f5_38 = f5   * (int64_t) f5_38;
1331    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1332    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1333    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1334    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1335    int64_t f6f6_19 = f6   * (int64_t) f6_19;
1336    int64_t f6f7_38 = f6   * (int64_t) f7_38;
1337    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1338    int64_t f6f9_38 = f6   * (int64_t) f9_38;
1339    int64_t f7f7_38 = f7   * (int64_t) f7_38;
1340    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1341    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1342    int64_t f8f8_19 = f8   * (int64_t) f8_19;
1343    int64_t f8f9_38 = f8   * (int64_t) f9_38;
1344    int64_t f9f9_38 = f9   * (int64_t) f9_38;
1345    int64_t h0 = f0f0   + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1346    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1347    int64_t h2 = f0f2_2 + f1f1_2  + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1348    int64_t h3 = f0f3_2 + f1f2_2  + f4f9_38 + f5f8_38 + f6f7_38;
1349    int64_t h4 = f0f4_2 + f1f3_4  + f2f2    + f5f9_76 + f6f8_38 + f7f7_38;
1350    int64_t h5 = f0f5_2 + f1f4_2  + f2f3_2  + f6f9_38 + f7f8_38;
1351    int64_t h6 = f0f6_2 + f1f5_4  + f2f4_2  + f3f3_2  + f7f9_76 + f8f8_19;
1352    int64_t h7 = f0f7_2 + f1f6_2  + f2f5_2  + f3f4_2  + f8f9_38;
1353    int64_t h8 = f0f8_2 + f1f7_4  + f2f6_2  + f3f5_4  + f4f4    + f9f9_38;
1354    int64_t h9 = f0f9_2 + f1f8_2  + f2f7_2  + f3f6_2  + f4f5_2;
1355    int64_t carry0;
1356    int64_t carry1;
1357    int64_t carry2;
1358    int64_t carry3;
1359    int64_t carry4;
1360    int64_t carry5;
1361    int64_t carry6;
1362    int64_t carry7;
1363    int64_t carry8;
1364    int64_t carry9;
1365
1366    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1367    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1368
1369    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1370    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1371
1372    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1373    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1374
1375    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1376    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1377
1378    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1379    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1380
1381    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1382
1383    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1384
1385    h[0] = (int32_t)h0;
1386    h[1] = (int32_t)h1;
1387    h[2] = (int32_t)h2;
1388    h[3] = (int32_t)h3;
1389    h[4] = (int32_t)h4;
1390    h[5] = (int32_t)h5;
1391    h[6] = (int32_t)h6;
1392    h[7] = (int32_t)h7;
1393    h[8] = (int32_t)h8;
1394    h[9] = (int32_t)h9;
1395}
1396
1397static void fe_invert(fe out, const fe z)
1398{
1399    fe t0;
1400    fe t1;
1401    fe t2;
1402    fe t3;
1403    int i;
1404
1405    /*
1406     * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
1407     * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
1408     */
1409
1410    /* t0 = z ** 2 */
1411    fe_sq(t0, z);
1412
1413    /* t1 = t0 ** (2 ** 2) = z ** 8 */
1414    fe_sq(t1, t0);
1415    fe_sq(t1, t1);
1416
1417    /* t1 = z * t1 = z ** 9 */
1418    fe_mul(t1, z, t1);
1419    /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1420    fe_mul(t0, t0, t1);
1421
1422    /* t2 = t0 ** 2 = z ** 22 */
1423    fe_sq(t2, t0);
1424
1425    /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
1426    fe_mul(t1, t1, t2);
1427
1428    /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
1429    fe_sq(t2, t1);
1430    for (i = 1; i < 5; ++i) {
1431        fe_sq(t2, t2);
1432    }
1433
1434    /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
1435    fe_mul(t1, t2, t1);
1436
1437    /* Continuing similarly... */
1438
1439    /* t2 = z ** (2 ** 20 - 1) */
1440    fe_sq(t2, t1);
1441    for (i = 1; i < 10; ++i) {
1442        fe_sq(t2, t2);
1443    }
1444    fe_mul(t2, t2, t1);
1445
1446    /* t2 = z ** (2 ** 40 - 1) */
1447    fe_sq(t3, t2);
1448    for (i = 1; i < 20; ++i) {
1449        fe_sq(t3, t3);
1450    }
1451    fe_mul(t2, t3, t2);
1452
1453    /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
1454    for (i = 0; i < 10; ++i) {
1455        fe_sq(t2, t2);
1456    }
1457    /* t1 = z ** (2 ** 50 - 1) */
1458    fe_mul(t1, t2, t1);
1459
1460    /* t2 = z ** (2 ** 100 - 1) */
1461    fe_sq(t2, t1);
1462    for (i = 1; i < 50; ++i) {
1463        fe_sq(t2, t2);
1464    }
1465    fe_mul(t2, t2, t1);
1466
1467    /* t2 = z ** (2 ** 200 - 1) */
1468    fe_sq(t3, t2);
1469    for (i = 1; i < 100; ++i) {
1470        fe_sq(t3, t3);
1471    }
1472    fe_mul(t2, t3, t2);
1473
1474    /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
1475    fe_sq(t2, t2);
1476    for (i = 1; i < 50; ++i) {
1477        fe_sq(t2, t2);
1478    }
1479
1480    /* t1 = z ** (2 ** 250 - 1) */
1481    fe_mul(t1, t2, t1);
1482
1483    /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
1484    fe_sq(t1, t1);
1485    for (i = 1; i < 5; ++i) {
1486        fe_sq(t1, t1);
1487    }
1488
1489    /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
1490    fe_mul(out, t1, t0);
1491}
1492
1493/*
1494 * h = -f
1495 *
1496 * Preconditions:
1497 *    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1498 *
1499 * Postconditions:
1500 *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1501 */
1502static void fe_neg(fe h, const fe f)
1503{
1504    unsigned i;
1505
1506    for (i = 0; i < 10; i++) {
1507        h[i] = -f[i];
1508    }
1509}
1510
1511/*
1512 * Replace (f,g) with (g,g) if b == 1;
1513 * replace (f,g) with (f,g) if b == 0.
1514 *
1515 * Preconditions: b in {0,1}.
1516 */
1517static void fe_cmov(fe f, const fe g, unsigned b)
1518{
1519    size_t i;
1520
1521    b = 0-b;
1522    for (i = 0; i < 10; i++) {
1523        int32_t x = f[i] ^ g[i];
1524        x &= b;
1525        f[i] ^= x;
1526    }
1527}
1528
1529/*
1530 * return 0 if f == 0
1531 * return 1 if f != 0
1532 *
1533 * Preconditions:
1534 *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1535 */
1536static int fe_isnonzero(const fe f)
1537{
1538    uint8_t s[32];
1539    static const uint8_t zero[32] = {0};
1540
1541    fe_tobytes(s, f);
1542
1543    return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1544}
1545
1546/*
1547 * return 1 if f is in {1,3,5,...,q-2}
1548 * return 0 if f is in {0,2,4,...,q-1}
1549 *
1550 * Preconditions:
1551 *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1552 */
1553static int fe_isnegative(const fe f)
1554{
1555    uint8_t s[32];
1556
1557    fe_tobytes(s, f);
1558    return s[0] & 1;
1559}
1560
1561/*
1562 * h = 2 * f * f
1563 *
1564 * Can overlap h with f.
1565 *
1566 * Preconditions:
1567 *    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1568 *
1569 * Postconditions:
1570 *    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1571 *
1572 * See fe_mul.c for discussion of implementation strategy.
1573 */
1574static void fe_sq2(fe h, const fe f)
1575{
1576    int32_t f0 = f[0];
1577    int32_t f1 = f[1];
1578    int32_t f2 = f[2];
1579    int32_t f3 = f[3];
1580    int32_t f4 = f[4];
1581    int32_t f5 = f[5];
1582    int32_t f6 = f[6];
1583    int32_t f7 = f[7];
1584    int32_t f8 = f[8];
1585    int32_t f9 = f[9];
1586    int32_t f0_2 = 2 * f0;
1587    int32_t f1_2 = 2 * f1;
1588    int32_t f2_2 = 2 * f2;
1589    int32_t f3_2 = 2 * f3;
1590    int32_t f4_2 = 2 * f4;
1591    int32_t f5_2 = 2 * f5;
1592    int32_t f6_2 = 2 * f6;
1593    int32_t f7_2 = 2 * f7;
1594    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1595    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1596    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1597    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1598    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1599    int64_t f0f0    = f0   * (int64_t) f0;
1600    int64_t f0f1_2  = f0_2 * (int64_t) f1;
1601    int64_t f0f2_2  = f0_2 * (int64_t) f2;
1602    int64_t f0f3_2  = f0_2 * (int64_t) f3;
1603    int64_t f0f4_2  = f0_2 * (int64_t) f4;
1604    int64_t f0f5_2  = f0_2 * (int64_t) f5;
1605    int64_t f0f6_2  = f0_2 * (int64_t) f6;
1606    int64_t f0f7_2  = f0_2 * (int64_t) f7;
1607    int64_t f0f8_2  = f0_2 * (int64_t) f8;
1608    int64_t f0f9_2  = f0_2 * (int64_t) f9;
1609    int64_t f1f1_2  = f1_2 * (int64_t) f1;
1610    int64_t f1f2_2  = f1_2 * (int64_t) f2;
1611    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
1612    int64_t f1f4_2  = f1_2 * (int64_t) f4;
1613    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
1614    int64_t f1f6_2  = f1_2 * (int64_t) f6;
1615    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
1616    int64_t f1f8_2  = f1_2 * (int64_t) f8;
1617    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1618    int64_t f2f2    = f2   * (int64_t) f2;
1619    int64_t f2f3_2  = f2_2 * (int64_t) f3;
1620    int64_t f2f4_2  = f2_2 * (int64_t) f4;
1621    int64_t f2f5_2  = f2_2 * (int64_t) f5;
1622    int64_t f2f6_2  = f2_2 * (int64_t) f6;
1623    int64_t f2f7_2  = f2_2 * (int64_t) f7;
1624    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1625    int64_t f2f9_38 = f2   * (int64_t) f9_38;
1626    int64_t f3f3_2  = f3_2 * (int64_t) f3;
1627    int64_t f3f4_2  = f3_2 * (int64_t) f4;
1628    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
1629    int64_t f3f6_2  = f3_2 * (int64_t) f6;
1630    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1631    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1632    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1633    int64_t f4f4    = f4   * (int64_t) f4;
1634    int64_t f4f5_2  = f4_2 * (int64_t) f5;
1635    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1636    int64_t f4f7_38 = f4   * (int64_t) f7_38;
1637    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1638    int64_t f4f9_38 = f4   * (int64_t) f9_38;
1639    int64_t f5f5_38 = f5   * (int64_t) f5_38;
1640    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1641    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1642    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1643    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1644    int64_t f6f6_19 = f6   * (int64_t) f6_19;
1645    int64_t f6f7_38 = f6   * (int64_t) f7_38;
1646    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1647    int64_t f6f9_38 = f6   * (int64_t) f9_38;
1648    int64_t f7f7_38 = f7   * (int64_t) f7_38;
1649    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1650    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1651    int64_t f8f8_19 = f8   * (int64_t) f8_19;
1652    int64_t f8f9_38 = f8   * (int64_t) f9_38;
1653    int64_t f9f9_38 = f9   * (int64_t) f9_38;
1654    int64_t h0 = f0f0   + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1655    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1656    int64_t h2 = f0f2_2 + f1f1_2  + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1657    int64_t h3 = f0f3_2 + f1f2_2  + f4f9_38 + f5f8_38 + f6f7_38;
1658    int64_t h4 = f0f4_2 + f1f3_4  + f2f2    + f5f9_76 + f6f8_38 + f7f7_38;
1659    int64_t h5 = f0f5_2 + f1f4_2  + f2f3_2  + f6f9_38 + f7f8_38;
1660    int64_t h6 = f0f6_2 + f1f5_4  + f2f4_2  + f3f3_2  + f7f9_76 + f8f8_19;
1661    int64_t h7 = f0f7_2 + f1f6_2  + f2f5_2  + f3f4_2  + f8f9_38;
1662    int64_t h8 = f0f8_2 + f1f7_4  + f2f6_2  + f3f5_4  + f4f4    + f9f9_38;
1663    int64_t h9 = f0f9_2 + f1f8_2  + f2f7_2  + f3f6_2  + f4f5_2;
1664    int64_t carry0;
1665    int64_t carry1;
1666    int64_t carry2;
1667    int64_t carry3;
1668    int64_t carry4;
1669    int64_t carry5;
1670    int64_t carry6;
1671    int64_t carry7;
1672    int64_t carry8;
1673    int64_t carry9;
1674
1675    h0 += h0;
1676    h1 += h1;
1677    h2 += h2;
1678    h3 += h3;
1679    h4 += h4;
1680    h5 += h5;
1681    h6 += h6;
1682    h7 += h7;
1683    h8 += h8;
1684    h9 += h9;
1685
1686    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1687    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1688
1689    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1690    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1691
1692    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1693    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1694
1695    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1696    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1697
1698    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1699    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1700
1701    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1702
1703    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1704
1705    h[0] = (int32_t)h0;
1706    h[1] = (int32_t)h1;
1707    h[2] = (int32_t)h2;
1708    h[3] = (int32_t)h3;
1709    h[4] = (int32_t)h4;
1710    h[5] = (int32_t)h5;
1711    h[6] = (int32_t)h6;
1712    h[7] = (int32_t)h7;
1713    h[8] = (int32_t)h8;
1714    h[9] = (int32_t)h9;
1715}
1716
1717static void fe_pow22523(fe out, const fe z)
1718{
1719    fe t0;
1720    fe t1;
1721    fe t2;
1722    int i;
1723
1724    fe_sq(t0, z);
1725    fe_sq(t1, t0);
1726    for (i = 1; i < 2; ++i) {
1727        fe_sq(t1, t1);
1728    }
1729    fe_mul(t1, z, t1);
1730    fe_mul(t0, t0, t1);
1731    fe_sq(t0, t0);
1732    fe_mul(t0, t1, t0);
1733    fe_sq(t1, t0);
1734    for (i = 1; i < 5; ++i) {
1735        fe_sq(t1, t1);
1736    }
1737    fe_mul(t0, t1, t0);
1738    fe_sq(t1, t0);
1739    for (i = 1; i < 10; ++i) {
1740        fe_sq(t1, t1);
1741    }
1742    fe_mul(t1, t1, t0);
1743    fe_sq(t2, t1);
1744    for (i = 1; i < 20; ++i) {
1745        fe_sq(t2, t2);
1746    }
1747    fe_mul(t1, t2, t1);
1748    fe_sq(t1, t1);
1749    for (i = 1; i < 10; ++i) {
1750        fe_sq(t1, t1);
1751    }
1752    fe_mul(t0, t1, t0);
1753    fe_sq(t1, t0);
1754    for (i = 1; i < 50; ++i) {
1755        fe_sq(t1, t1);
1756    }
1757    fe_mul(t1, t1, t0);
1758    fe_sq(t2, t1);
1759    for (i = 1; i < 100; ++i) {
1760        fe_sq(t2, t2);
1761    }
1762    fe_mul(t1, t2, t1);
1763    fe_sq(t1, t1);
1764    for (i = 1; i < 50; ++i) {
1765        fe_sq(t1, t1);
1766    }
1767    fe_mul(t0, t1, t0);
1768    fe_sq(t0, t0);
1769    for (i = 1; i < 2; ++i) {
1770        fe_sq(t0, t0);
1771    }
1772    fe_mul(out, t0, z);
1773}
1774
1775/*
1776 * ge means group element.
1777 *
1778 * Here the group is the set of pairs (x,y) of field elements (see fe.h)
1779 * satisfying -x^2 + y^2 = 1 + d x^2y^2
1780 * where d = -121665/121666.
1781 *
1782 * Representations:
1783 *   ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1784 *   ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1785 *   ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1786 *   ge_precomp (Duif): (y+x,y-x,2dxy)
1787 */
1788typedef struct {
1789    fe X;
1790    fe Y;
1791    fe Z;
1792} ge_p2;
1793
1794typedef struct {
1795    fe X;
1796    fe Y;
1797    fe Z;
1798    fe T;
1799} ge_p3;
1800
1801typedef struct {
1802    fe X;
1803    fe Y;
1804    fe Z;
1805    fe T;
1806} ge_p1p1;
1807
1808typedef struct {
1809    fe yplusx;
1810    fe yminusx;
1811    fe xy2d;
1812} ge_precomp;
1813
1814typedef struct {
1815    fe YplusX;
1816    fe YminusX;
1817    fe Z;
1818    fe T2d;
1819} ge_cached;
1820
1821static void ge_tobytes(uint8_t *s, const ge_p2 *h)
1822{
1823    fe recip;
1824    fe x;
1825    fe y;
1826
1827    fe_invert(recip, h->Z);
1828    fe_mul(x, h->X, recip);
1829    fe_mul(y, h->Y, recip);
1830    fe_tobytes(s, y);
1831    s[31] ^= fe_isnegative(x) << 7;
1832}
1833
1834static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h)
1835{
1836    fe recip;
1837    fe x;
1838    fe y;
1839
1840    fe_invert(recip, h->Z);
1841    fe_mul(x, h->X, recip);
1842    fe_mul(y, h->Y, recip);
1843    fe_tobytes(s, y);
1844    s[31] ^= fe_isnegative(x) << 7;
1845}
1846
1847static const fe d = {
1848    -10913610, 13857413, -15372611, 6949391,   114729,
1849    -8787816,  -6275908, -3247719,  -18696448, -12055116
1850};
1851
1852static const fe sqrtm1 = {
1853    -32595792, -7943725,  9377950,  3500415, 12389472,
1854    -272473,   -25146209, -2005654, 326686,  11406482
1855};
1856
1857static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s)
1858{
1859    fe u;
1860    fe v;
1861    fe v3;
1862    fe vxx;
1863    fe check;
1864
1865    fe_frombytes(h->Y, s);
1866    fe_1(h->Z);
1867    fe_sq(u, h->Y);
1868    fe_mul(v, u, d);
1869    fe_sub(u, u, h->Z); /* u = y^2-1 */
1870    fe_add(v, v, h->Z); /* v = dy^2+1 */
1871
1872    fe_sq(v3, v);
1873    fe_mul(v3, v3, v); /* v3 = v^3 */
1874    fe_sq(h->X, v3);
1875    fe_mul(h->X, h->X, v);
1876    fe_mul(h->X, h->X, u); /* x = uv^7 */
1877
1878    fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1879    fe_mul(h->X, h->X, v3);
1880    fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1881
1882    fe_sq(vxx, h->X);
1883    fe_mul(vxx, vxx, v);
1884    fe_sub(check, vxx, u); /* vx^2-u */
1885    if (fe_isnonzero(check)) {
1886        fe_add(check, vxx, u); /* vx^2+u */
1887        if (fe_isnonzero(check)) {
1888            return -1;
1889        }
1890        fe_mul(h->X, h->X, sqrtm1);
1891    }
1892
1893    if (fe_isnegative(h->X) != (s[31] >> 7)) {
1894        fe_neg(h->X, h->X);
1895    }
1896
1897    fe_mul(h->T, h->X, h->Y);
1898    return 0;
1899}
1900
1901static void ge_p2_0(ge_p2 *h)
1902{
1903    fe_0(h->X);
1904    fe_1(h->Y);
1905    fe_1(h->Z);
1906}
1907
1908static void ge_p3_0(ge_p3 *h)
1909{
1910    fe_0(h->X);
1911    fe_1(h->Y);
1912    fe_1(h->Z);
1913    fe_0(h->T);
1914}
1915
1916static void ge_precomp_0(ge_precomp *h)
1917{
1918    fe_1(h->yplusx);
1919    fe_1(h->yminusx);
1920    fe_0(h->xy2d);
1921}
1922
1923/* r = p */
1924static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
1925{
1926    fe_copy(r->X, p->X);
1927    fe_copy(r->Y, p->Y);
1928    fe_copy(r->Z, p->Z);
1929}
1930
1931static const fe d2 = {
1932    -21827239, -5839606,  -30745221, 13898782, 229458,
1933    15978800,  -12551817, -6495438,  29715968, 9444199
1934};
1935
1936/* r = p */
1937static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
1938{
1939    fe_add(r->YplusX, p->Y, p->X);
1940    fe_sub(r->YminusX, p->Y, p->X);
1941    fe_copy(r->Z, p->Z);
1942    fe_mul(r->T2d, p->T, d2);
1943}
1944
1945/* r = p */
1946static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
1947{
1948    fe_mul(r->X, p->X, p->T);
1949    fe_mul(r->Y, p->Y, p->Z);
1950    fe_mul(r->Z, p->Z, p->T);
1951}
1952
1953/* r = p */
1954static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
1955{
1956    fe_mul(r->X, p->X, p->T);
1957    fe_mul(r->Y, p->Y, p->Z);
1958    fe_mul(r->Z, p->Z, p->T);
1959    fe_mul(r->T, p->X, p->Y);
1960}
1961
1962/* r = 2 * p */
1963static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p)
1964{
1965    fe t0;
1966
1967    fe_sq(r->X, p->X);
1968    fe_sq(r->Z, p->Y);
1969    fe_sq2(r->T, p->Z);
1970    fe_add(r->Y, p->X, p->Y);
1971    fe_sq(t0, r->Y);
1972    fe_add(r->Y, r->Z, r->X);
1973    fe_sub(r->Z, r->Z, r->X);
1974    fe_sub(r->X, t0, r->Y);
1975    fe_sub(r->T, r->T, r->Z);
1976}
1977
1978/* r = 2 * p */
1979static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
1980{
1981    ge_p2 q;
1982    ge_p3_to_p2(&q, p);
1983    ge_p2_dbl(r, &q);
1984}
1985
1986/* r = p + q */
1987static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
1988{
1989    fe t0;
1990
1991    fe_add(r->X, p->Y, p->X);
1992    fe_sub(r->Y, p->Y, p->X);
1993    fe_mul(r->Z, r->X, q->yplusx);
1994    fe_mul(r->Y, r->Y, q->yminusx);
1995    fe_mul(r->T, q->xy2d, p->T);
1996    fe_add(t0, p->Z, p->Z);
1997    fe_sub(r->X, r->Z, r->Y);
1998    fe_add(r->Y, r->Z, r->Y);
1999    fe_add(r->Z, t0, r->T);
2000    fe_sub(r->T, t0, r->T);
2001}
2002
2003/* r = p - q */
2004static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
2005{
2006    fe t0;
2007
2008    fe_add(r->X, p->Y, p->X);
2009    fe_sub(r->Y, p->Y, p->X);
2010    fe_mul(r->Z, r->X, q->yminusx);
2011    fe_mul(r->Y, r->Y, q->yplusx);
2012    fe_mul(r->T, q->xy2d, p->T);
2013    fe_add(t0, p->Z, p->Z);
2014    fe_sub(r->X, r->Z, r->Y);
2015    fe_add(r->Y, r->Z, r->Y);
2016    fe_sub(r->Z, t0, r->T);
2017    fe_add(r->T, t0, r->T);
2018}
2019
2020/* r = p + q */
2021static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2022{
2023    fe t0;
2024
2025    fe_add(r->X, p->Y, p->X);
2026    fe_sub(r->Y, p->Y, p->X);
2027    fe_mul(r->Z, r->X, q->YplusX);
2028    fe_mul(r->Y, r->Y, q->YminusX);
2029    fe_mul(r->T, q->T2d, p->T);
2030    fe_mul(r->X, p->Z, q->Z);
2031    fe_add(t0, r->X, r->X);
2032    fe_sub(r->X, r->Z, r->Y);
2033    fe_add(r->Y, r->Z, r->Y);
2034    fe_add(r->Z, t0, r->T);
2035    fe_sub(r->T, t0, r->T);
2036}
2037
2038/* r = p - q */
2039static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2040{
2041    fe t0;
2042
2043    fe_add(r->X, p->Y, p->X);
2044    fe_sub(r->Y, p->Y, p->X);
2045    fe_mul(r->Z, r->X, q->YminusX);
2046    fe_mul(r->Y, r->Y, q->YplusX);
2047    fe_mul(r->T, q->T2d, p->T);
2048    fe_mul(r->X, p->Z, q->Z);
2049    fe_add(t0, r->X, r->X);
2050    fe_sub(r->X, r->Z, r->Y);
2051    fe_add(r->Y, r->Z, r->Y);
2052    fe_sub(r->Z, t0, r->T);
2053    fe_add(r->T, t0, r->T);
2054}
2055
2056static uint8_t equal(signed char b, signed char c)
2057{
2058    uint8_t ub = b;
2059    uint8_t uc = c;
2060    uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2061    uint32_t y = x;      /* 0: yes; 1..255: no */
2062    y -= 1;              /* 4294967295: yes; 0..254: no */
2063    y >>= 31;            /* 1: yes; 0: no */
2064    return y;
2065}
2066
2067static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b)
2068{
2069    fe_cmov(t->yplusx, u->yplusx, b);
2070    fe_cmov(t->yminusx, u->yminusx, b);
2071    fe_cmov(t->xy2d, u->xy2d, b);
2072}
2073
2074/* k25519Precomp[i][j] = (j+1)*256^i*B */
2075static const ge_precomp k25519Precomp[32][8] = {
2076    {
2077        {
2078            {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2079             27544626, -11754271, -6079156, 2047605},
2080            {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2081             5043384, 19500929, -15469378},
2082            {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2083             29287919, 11864899, -24514362, -4438546},
2084        },
2085        {
2086            {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2087             -11717903, -3814571, -358445, -10211303},
2088            {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2089             -15616551, 11189268, -26829678, -5319081},
2090            {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2091             -3128826, -9541118, -15472047, -4166697},
2092        },
2093        {
2094            {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2095             27787600, -14772189, 28944400, -1550024},
2096            {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2097             16354577, -11775962, 7689662, 11199574},
2098            {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2099             7512774, 10017326, -17749093, -9920357},
2100        },
2101        {
2102            {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2103             -28926210, 15006023, 3284568, -6276540},
2104            {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2105             7464579, 9656445, 13059162, 10374397},
2106            {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2107             -3839045, -641708, -101325},
2108        },
2109        {
2110            {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2111             32867885, 14515107, -15438304, 10819380},
2112            {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2113             12483688, -12668491, 5581306},
2114            {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2115             28542350, 13850243, -23678021, -15815942},
2116        },
2117        {
2118            {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2119             -19188627, -15224819, -9818940, -12085777},
2120            {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2121             -15689887, 1762328, 14866737},
2122            {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2123             -28236412, 3959421, 27914454, 4383652},
2124        },
2125        {
2126            {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2127             5230134, -23952439, -15175766},
2128            {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2129             20654025, 16520125, 30598449, 7715701},
2130            {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2131             -31400660, 1370708, 29794553, -1409300},
2132        },
2133        {
2134            {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2135             30290735, 10876454, -33154098, 2381726},
2136            {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2137             -6236617, 3696005, -32300832, 15351955},
2138            {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2139             -32961401, -2970515, 29551813, 10109425},
2140        },
2141    },
2142    {
2143        {
2144            {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2145             -2378284, -1627556, 10092783, -4764171},
2146            {27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2147             -32508754, 12005538, -17810127, 12803510},
2148            {17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2149             30364213, -9038194, 18016357, 4397660},
2150        },
2151        {
2152            {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2153             -26619106, 14544525, -17477504, 982639},
2154            {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2155             -4120128, -21047696, 9934963},
2156            {5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2157             -14747930, 4559895, -30123922, -10897950},
2158        },
2159        {
2160            {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2161             24191034, 4541697, -13338309, 5500568},
2162            {12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2163             -17430592, 12264343, 10874051, 13524335},
2164            {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2165             5080568, -22528059, 5376628},
2166        },
2167        {
2168            {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2169             -22321305, -9447443, 4535768, 1569007},
2170            {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2171             -30494562, 3044290, 31848280, 12543772},
2172            {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2173             -27377195, -2062731, 7718482, 14474653},
2174        },
2175        {
2176            {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2177             -7236665, 24316168, -5253567},
2178            {13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2179             33040651, -13424532, -20729456, 8321686},
2180            {21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2181             23845965, -11874838, -9984458, 608372},
2182        },
2183        {
2184            {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2185             1123968, -6780577, 27229399, 23887},
2186            {-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2187             12797024, -6440308, -1633405, 16678954},
2188            {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2189             -1508144, -4795045, -17169265, 4904953},
2190        },
2191        {
2192            {24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2193             5169211, 16191880, 2128236, -4326833},
2194            {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2195             -29806336, 916033, -6882542, -2986532},
2196            {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2197             285431, 2763829, 15736322, 4143876},
2198        },
2199        {
2200            {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2201             -14594663, 23527084, -16458268},
2202            {33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2203             -32625340, 4087881, -15188911, -14416214},
2204            {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2205             4357868, -4774191, -16323038},
2206        },
2207    },
2208    {
2209        {
2210            {6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2211             23365147, -3949732, 7390890, 2759800},
2212            {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2213             -4264057, 1244380, -12919645},
2214            {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2215             9208236, 15886429, 16489664},
2216        },
2217        {
2218            {1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2219             -13693198, 398369, -30606455, -712933},
2220            {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2221             13348553, 12076947, -30836462, 5113182},
2222            {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2223             -30341101, -7336386, 13847711, 5387222},
2224        },
2225        {
2226            {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2227             8763061, 3617786, -19600662, 10370991},
2228            {20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2229             14554437, -8746092, 32232924, 16763880},
2230            {9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2231             11094161, 15689506, 3140038, -16510092},
2232        },
2233        {
2234            {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2235             -27224800, 9448613, -28774454, 366295},
2236            {19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2237             28344573, 8041113, 719605, 11671788},
2238            {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2239             -15266516, 27000813, -10195553},
2240        },
2241        {
2242            {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2243             5336097, 6750977, -14521026},
2244            {11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2245             1695823, -8819122, 8169720, 16220347},
2246            {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2247             -11144307, -2627664, -5990708, -14166033},
2248        },
2249        {
2250            {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2251             27884329, 2847284, 2655861, 1738395},
2252            {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2253             21651608, -3239336, -19087449, -11005278},
2254            {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2255             5821408, 10478196, 8544890},
2256        },
2257        {
2258            {32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2259             19270449, 12217473, 17789017, -3395995},
2260            {-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2261             15479401, -3853233, 30460520, 1052596},
2262            {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2263             27491595, -4612359, 3179268, -9478891},
2264        },
2265        {
2266            {31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2267             -14756777, -16411740, 19072640, -9511060},
2268            {11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2269             5977896, -5215017, 473099, 5040608},
2270            {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2271             28326862, 1721092, -19558642, -3131606},
2272        },
2273    },
2274    {
2275        {
2276            {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2277             8076149, -27868496, 11538389},
2278            {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2279             8754525, 7446702, -5676054, 5797016},
2280            {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2281             2014099, -9050574, -2369172, -5877341},
2282        },
2283        {
2284            {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2285             1192730, -3714199, 15123619, 10811505},
2286            {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
2287             15776356, -28886779, -11974553},
2288            {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
2289             -20654173, -16484855, 4714547, -9600655},
2290        },
2291        {
2292            {15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
2293             24611599, -4543832, -11745876, 12340220},
2294            {12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
2295             9613953, 8241152, 15370987, 9608631},
2296            {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
2297             15866074, -28210621, -8814099},
2298        },
2299        {
2300            {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
2301             858697, 20571223, 8420556},
2302            {14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
2303             33531827, 12516406, -21574435, -12476749},
2304            {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
2305             7256740, 8791136, 15069930},
2306        },
2307        {
2308            {1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
2309             14711875, 4874229, -30663140, -2331391},
2310            {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
2311             -7912378, -33069337, 9234253},
2312            {20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
2313             31559055, -11609587, 18979186, 13396066},
2314        },
2315        {
2316            {24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
2317             -18816887, 13594782, 33514650, 7021958},
2318            {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
2319             -25948728, -3916677, -21480480, 12868082},
2320            {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
2321             -21446107, 2244500, -12455797, -8089383},
2322        },
2323        {
2324            {-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
2325             33086546, 8957937, -15233648, 5540521},
2326            {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
2327             -23710744, -1568984, -16128528, -14962807},
2328            {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
2329             892185, -11513277, -15205948},
2330        },
2331        {
2332            {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
2333             4763127, -19179614, 5867134},
2334            {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
2335             27846559, 5931263, -29749703, -16108455},
2336            {27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
2337             7283490, -15148073, -19526700, 7734629},
2338        },
2339    },
2340    {
2341        {
2342            {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
2343             7585295, -3176626, 18549497, 15302069},
2344            {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
2345             10458790, -6418461, -8872242, 8424746},
2346            {24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
2347             19206234, 7134917, -11284482, -828919},
2348        },
2349        {
2350            {11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
2351             10243738, -14685461, -5066034, 16498837},
2352            {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
2353             -14124238, 6536641, 10543906},
2354            {-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
2355             -2669190, -16625574, -27235709, 8876771},
2356        },
2357        {
2358            {-25742899, -12566864, -15649966, -846607, -33026686, -796288,
2359             -33481822, 15824474, -604426, -9039817},
2360            {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
2361             -4890037, 1657394, 3084098},
2362            {10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
2363             31280319, 14396151, -30233575, 15272409},
2364        },
2365        {
2366            {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
2367             -25173957, -12636138, -25014757, 1950504},
2368            {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
2369             -8384306, -8767532, 15341279, 8373727},
2370            {28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
2371             298136, -10232602, -2878207, 15190420},
2372        },
2373        {
2374            {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
2375             8669718, 2742393, -26033313, -6875003},
2376            {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
2377             9291594, -16247779, -12154742, 6048605},
2378            {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
2379             13934231, 5128323, 11213262, 9168384},
2380        },
2381        {
2382            {-26280513, 11007847, 19408960, -940758, -18592965, -4328580,
2383             -5088060, -11105150, 20470157, -16398701},
2384            {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
2385             -22783952, 14461608, 14042978, 5230683},
2386            {29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
2387             21556951, 3506042, -5933891, -12449708},
2388        },
2389        {
2390            {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683,
2391             -21284170, 8971513, -28539189, 15326563},
2392            {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669,
2393             -15523050, 15300988, -20514118, 9168260},
2394            {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939,
2395             -28948358, 9601605, 33087103, -9011387},
2396        },
2397        {
2398            {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461,
2399             -27444329, -15000531, -5996870, 15664672},
2400            {23294591, -16632613, -22650781, -8470978, 27844204, 11461195,
2401             13099750, -2460356, 18151676, 13417686},
2402            {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065,
2403             1661597, -12551441, 15271676, -15452665},
2404        },
2405    },
2406    {
2407        {
2408            {11433042, -13228665, 8239631, -5279517, -1985436, -725718,
2409             -18698764, 2167544, -6921301, -13440182},
2410            {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379,
2411             -9917708, -8638997, 12215110, 12028277},
2412            {14098400, 6555944, 23007258, 5757252, -15427832, -12950502,
2413             30123440, 4617780, -16900089, -655628},
2414        },
2415        {
2416            {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385,
2417             -15819999, 10154009, 23973261, -12684474},
2418            {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355,
2419             18341390, -11419951, 32013174, -10103539},
2420            {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104,
2421             21911214, 6354752, 4425632, -837822},
2422        },
2423        {
2424            {-10433389, -14612966, 22229858, -3091047, -13191166, 776729,
2425             -17415375, -12020462, 4725005, 14044970},
2426            {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390,
2427             -1411784, -19522291, -16109756},
2428            {-24864089, 12986008, -10898878, -5558584, -11312371, -148526,
2429             19541418, 8180106, 9282262, 10282508},
2430        },
2431        {
2432            {-26205082, 4428547, -8661196, -13194263, 4098402, -14165257,
2433             15522535, 8372215, 5542595, -10702683},
2434            {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360,
2435             -2781891, 6993761, -18093885, 10114655},
2436            {-20107055, -929418, 31422704, 10427861, -7110749, 6150669,
2437             -29091755, -11529146, 25953725, -106158},
2438        },
2439        {
2440            {-4234397, -8039292, -9119125, 3046000, 2101609, -12607294,
2441             19390020, 6094296, -3315279, 12831125},
2442            {-15998678, 7578152, 5310217, 14408357, -33548620, -224739,
2443             31575954, 6326196, 7381791, -2421839},
2444            {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640,
2445             6295303, 8082724, -15362489, 12339664},
2446        },
2447        {
2448            {27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414,
2449             15768922, 25091167, 14856294},
2450            {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300,
2451             -12695493, -22182473, -9012899},
2452            {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039,
2453             -27260765, 13866390, 30146206, 9142070},
2454        },
2455        {
2456            {3924129, -15307516, -13817122, -10054960, 12291820, -668366,
2457             -27702774, 9326384, -8237858, 4171294},
2458            {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944,
2459             26396185, 3731949, 345228, -5462949},
2460            {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387,
2461             2031539, -12391231, -16253183, -13582083},
2462        },
2463        {
2464            {31016211, -16722429, 26371392, -14451233, -5027349, 14854137,
2465             17477601, 3842657, 28012650, -16405420},
2466            {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560,
2467             -9189873, 16292057, -8867157, 3507940},
2468            {29439664, 3537914, 23333589, 6997794, -17555561, -11018068,
2469             -15209202, -15051267, -9164929, 6580396},
2470        },
2471    },
2472    {
2473        {
2474            {-12185861, -7679788, 16438269, 10826160, -8696817, -6235611,
2475             17860444, -9273846, -2095802, 9304567},
2476            {20714564, -4336911, 29088195, 7406487, 11426967, -5095705,
2477             14792667, -14608617, 5289421, -477127},
2478            {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462,
2479             17271490, 12349094, 26939669, -3752294},
2480        },
2481        {
2482            {-12889898, 9373458, 31595848, 16374215, 21471720, 13221525,
2483             -27283495, -12348559, -3698806, 117887},
2484            {22263325, -6560050, 3984570, -11174646, -15114008, -566785,
2485             28311253, 5358056, -23319780, 541964},
2486            {16259219, 3261970, 2309254, -15534474, -16885711, -4581916,
2487             24134070, -16705829, -13337066, -13552195},
2488        },
2489        {
2490            {9378160, -13140186, -22845982, -12745264, 28198281, -7244098,
2491             -2399684, -717351, 690426, 14876244},
2492            {24977353, -314384, -8223969, -13465086, 28432343, -1176353,
2493             -13068804, -12297348, -22380984, 6618999},
2494            {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193,
2495             8044829, -13817328, 32239829, -5652762},
2496        },
2497        {
2498            {-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647,
2499             -10350059, 32779359, 5095274},
2500            {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423,
2501             -24601656, 14506724, 21639561, -2630236},
2502            {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318,
2503             -1289502, -6863535, 17874574, 558605},
2504        },
2505        {
2506            {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700,
2507             33499487, 5080151, 2085892, 5119761},
2508            {-22205145, -2519528, -16381601, 414691, -25019550, 2170430,
2509             30634760, -8363614, -31999993, -5759884},
2510            {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256,
2511             27534430, -7192145, -22351378, 12961482},
2512        },
2513        {
2514            {-24492060, -9570771, 10368194, 11582341, -23397293, -2245287,
2515             16533930, 8206996, -30194652, -5159638},
2516            {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630,
2517             7031275, 7589640, 8945490},
2518            {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393,
2519             7251489, -11182180, 24099109, -14456170},
2520        },
2521        {
2522            {5019558, -7907470, 4244127, -14714356, -26933272, 6453165,
2523             -19118182, -13289025, -6231896, -10280736},
2524            {10853594, 10721687, 26480089, 5861829, -22995819, 1972175,
2525             -1866647, -10557898, -3363451, -6441124},
2526            {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661,
2527             -2008168, -13866408, 7421392},
2528        },
2529        {
2530            {8139927, -6546497, 32257646, -5890546, 30375719, 1886181,
2531             -21175108, 15441252, 28826358, -4123029},
2532            {6267086, 9695052, 7709135, -16603597, -32869068, -1886135,
2533             14795160, -7840124, 13746021, -1742048},
2534            {28584902, 7787108, -6732942, -15050729, 22846041, -7571236,
2535             -3181936, -363524, 4771362, -8419958},
2536        },
2537    },
2538    {
2539        {
2540            {24949256, 6376279, -27466481, -8174608, -18646154, -9930606,
2541             33543569, -12141695, 3569627, 11342593},
2542            {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886,
2543             4608608, 7325975, -14801071},
2544            {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312,
2545             -27400540, 10258390, -17646694, -8186692},
2546        },
2547        {
2548            {11431204, 15823007, 26570245, 14329124, 18029990, 4796082,
2549             -31446179, 15580664, 9280358, -3973687},
2550            {-160783, -10326257, -22855316, -4304997, -20861367, -13621002,
2551             -32810901, -11181622, -15545091, 4387441},
2552            {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370,
2553             -24513992, 8548137, 20617071, -7482001},
2554        },
2555        {
2556            {-938825, -3930586, -8714311, 16124718, 24603125, -6225393,
2557             -13775352, -11875822, 24345683, 10325460},
2558            {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528,
2559             16318175, -1010689, 4766743, 3552007},
2560            {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514,
2561             14481909, 10988822, -3994762},
2562        },
2563        {
2564            {15564307, -14311570, 3101243, 5684148, 30446780, -8051356,
2565             12677127, -6505343, -8295852, 13296005},
2566            {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379,
2567             31521204, 9614054, -30000824, 12074674},
2568            {4771191, -135239, 14290749, -13089852, 27992298, 14998318,
2569             -1413936, -1556716, 29832613, -16391035},
2570        },
2571        {
2572            {7064884, -7541174, -19161962, -5067537, -18891269, -2912736,
2573             25825242, 5293297, -27122660, 13101590},
2574            {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445,
2575             32512469, -5317593, -30356070, -4190957},
2576            {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044,
2577             14413974, 9515896, 19568978, 9628812},
2578        },
2579        {
2580            {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894,
2581             -6106839, -6291786, 3437740},
2582            {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290,
2583             -22961733, 70104, 7463304, 4176122},
2584            {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117,
2585             -32719404, -5322751, 24216882, 5944158},
2586        },
2587        {
2588            {8894125, 7450974, -2664149, -9765752, -28080517, -12389115,
2589             19345746, 14680796, 11632993, 5847885},
2590            {26942781, -2315317, 9129564, -4906607, 26024105, 11769399,
2591             -11518837, 6367194, -9727230, 4782140},
2592            {19916461, -4828410, -22910704, -11414391, 25606324, -5972441,
2593             33253853, 8220911, 6358847, -1873857},
2594        },
2595        {
2596            {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388,
2597             -4480480, -13538503, 1387155},
2598            {19646058, 5720633, -11416706, 12814209, 11607948, 12749789,
2599             14147075, 15156355, -21866831, 11835260},
2600            {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523,
2601             15467869, -26560550, 5052483},
2602        },
2603    },
2604    {
2605        {
2606            {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123,
2607             -12618185, 12228557, -7003677},
2608            {32944382, 14922211, -22844894, 5188528, 21913450, -8719943,
2609             4001465, 13238564, -6114803, 8653815},
2610            {22865569, -4652735, 27603668, -12545395, 14348958, 8234005,
2611             24808405, 5719875, 28483275, 2841751},
2612        },
2613        {
2614            {-16420968, -1113305, -327719, -12107856, 21886282, -15552774,
2615             -1887966, -315658, 19932058, -12739203},
2616            {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912,
2617             3999228, 13239134, -4777469, -13910208},
2618            {1382174, -11694719, 17266790, 9194690, -13324356, 9720081,
2619             20403944, 11284705, -14013818, 3093230},
2620        },
2621        {
2622            {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424,
2623             16271225, -24049421, -6691850},
2624            {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293,
2625             24123614, 15193618, -21652117, -16739389},
2626            {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484,
2627             31870908, 14690798, 17361620, 11864968},
2628        },
2629        {
2630            {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200,
2631             -12331205, -7486601, -25578460, -16240689},
2632            {14668462, -12270235, 26039039, 15305210, 25515617, 4542480,
2633             10453892, 6577524, 9145645, -6443880},
2634            {5974874, 3053895, -9433049, -10385191, -31865124, 3225009,
2635             -7972642, 3936128, -5652273, -3050304},
2636        },
2637        {
2638            {30625386, -4729400, -25555961, -12792866, -20484575, 7695099,
2639             17097188, -16303496, -27999779, 1803632},
2640            {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700,
2641             14911344, 12196514, -21405489, 7047412},
2642            {20093277, 9920966, -11138194, -5343857, 13161587, 12044805,
2643             -32856851, 4124601, -32343828, -10257566},
2644        },
2645        {
2646            {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605,
2647             4752377, -8714640, -21679658, 2288038},
2648            {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457,
2649             29457502, 14625692, -24819617, 12570232},
2650            {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109,
2651             -21159943, -3498680, -11974704, 4724943},
2652        },
2653        {
2654            {17960970, -11775534, -4140968, -9702530, -8876562, -1410617,
2655             -12907383, -8659932, -29576300, 1903856},
2656            {23134274, -14279132, -10681997, -1611936, 20684485, 15770816,
2657             -12989750, 3190296, 26955097, 14109738},
2658            {15308788, 5320727, -30113809, -14318877, 22902008, 7767164,
2659             29425325, -11277562, 31960942, 11934971},
2660        },
2661        {
2662            {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669,
2663             20638173, 4875028, 10491392, 1379718},
2664            {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801,
2665             33518459, 16176658, 21432314, 12180697},
2666            {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205,
2667             1465425, 12689540, -10301319, -13872883},
2668        },
2669    },
2670    {
2671        {
2672            {5414091, -15386041, -21007664, 9643570, 12834970, 1186149,
2673             -2622916, -1342231, 26128231, 6032912},
2674            {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156,
2675             3604025, 8316894, -25875034, -10437358},
2676            {3296484, 6223048, 24680646, -12246460, -23052020, 5903205,
2677             -8862297, -4639164, 12376617, 3188849},
2678        },
2679        {
2680            {29190488, -14659046, 27549113, -1183516, 3520066, -10697301,
2681             32049515, -7309113, -16109234, -9852307},
2682            {-14744486, -9309156, 735818, -598978, -20407687, -5057904,
2683             25246078, -15795669, 18640741, -960977},
2684            {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252,
2685             -31638386, -494430, 10530747, 1053335},
2686        },
2687        {
2688            {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384,
2689             -31462369, -2948985, 24018831, 15026644},
2690            {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631,
2691             25310643, 13003497, -2314791, -15145616},
2692            {-27419985, -603321, -8043984, -1669117, -26092265, 13987819,
2693             -27297622, 187899, -23166419, -2531735},
2694        },
2695        {
2696            {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473,
2697             9716667, 16266922, -5070217, 726099},
2698            {29370922, -6053998, 7334071, -15342259, 9385287, 2247707,
2699             -13661962, -4839461, 30007388, -15823341},
2700            {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109,
2701             730663, 9835848, 4555336},
2702        },
2703        {
2704            {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977,
2705             17693930, 544696, -11985298, 12422646},
2706            {31117226, -12215734, -13502838, 6561947, -9876867, -12757670,
2707             -5118685, -4096706, 29120153, 13924425},
2708            {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820,
2709             -9383939, -11317700, 7240931, -237388},
2710        },
2711        {
2712            {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771,
2713             1222336, 4389483, 3293637, -15551743},
2714            {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533,
2715             -24319580, 7733547, 12796905, -6335822},
2716            {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811,
2717             -28253339, 3647836, 3222231, -11160462},
2718        },
2719        {
2720            {18606113, 1693100, -25448386, -15170272, 4112353, 10045021,
2721             23603893, -2048234, -7550776, 2484985},
2722            {9255317, -3131197, -12156162, -1004256, 13098013, -9214866,
2723             16377220, -2102812, -19802075, -3034702},
2724            {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502,
2725             -31718148, 9936966, -30097688, -10618797},
2726        },
2727        {
2728            {21878590, -5001297, 4338336, 13643897, -3036865, 13160960,
2729             19708896, 5415497, -7360503, -4109293},
2730            {27736861, 10103576, 12500508, 8502413, -3413016, -9633558,
2731             10436918, -1550276, -23659143, -8132100},
2732            {19492550, -12104365, -29681976, -852630, -3208171, 12403437,
2733             30066266, 8367329, 13243957, 8709688},
2734        },
2735    },
2736    {
2737        {
2738            {12015105, 2801261, 28198131, 10151021, 24818120, -4743133,
2739             -11194191, -5645734, 5150968, 7274186},
2740            {2831366, -12492146, 1478975, 6122054, 23825128, -12733586,
2741             31097299, 6083058, 31021603, -9793610},
2742            {-2529932, -2229646, 445613, 10720828, -13849527, -11505937,
2743             -23507731, 16354465, 15067285, -14147707},
2744        },
2745        {
2746            {7840942, 14037873, -33364863, 15934016, -728213, -3642706,
2747             21403988, 1057586, -19379462, -12403220},
2748            {915865, -16469274, 15608285, -8789130, -24357026, 6060030,
2749             -17371319, 8410997, -7220461, 16527025},
2750            {32922597, -556987, 20336074, -16184568, 10903705, -5384487,
2751             16957574, 52992, 23834301, 6588044},
2752        },
2753        {
2754            {32752030, 11232950, 3381995, -8714866, 22652988, -10744103,
2755             17159699, 16689107, -20314580, -1305992},
2756            {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943,
2757             7924251, -2752281, 1976123, -7249027},
2758            {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041,
2759             -3371252, 12331345, -8237197},
2760        },
2761        {
2762            {8651614, -4477032, -16085636, -4996994, 13002507, 2950805,
2763             29054427, -5106970, 10008136, -4667901},
2764            {31486080, 15114593, -14261250, 12951354, 14369431, -7387845,
2765             16347321, -13662089, 8684155, -10532952},
2766            {19443825, 11385320, 24468943, -9659068, -23919258, 2187569,
2767             -26263207, -6086921, 31316348, 14219878},
2768        },
2769        {
2770            {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801,
2771             27146014, 6992409, 29126555, 9207390},
2772            {32382935, 1110093, 18477781, 11028262, -27411763, -7548111,
2773             -4980517, 10843782, -7957600, -14435730},
2774            {2814918, 7836403, 27519878, -7868156, -20894015, -11553689,
2775             -21494559, 8550130, 28346258, 1994730},
2776        },
2777        {
2778            {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307,
2779             -19516951, 7174894, 22628102, 8115180},
2780            {-30405132, 955511, -11133838, -15078069, -32447087, -13278079,
2781             -25651578, 3317160, -9943017, 930272},
2782            {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177,
2783             24091212, -1388970, -22765376, -10650715},
2784        },
2785        {
2786            {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053,
2787             -14839018, -16554220, -1867018, 8398970},
2788            {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670,
2789             22981545, -6291273, 18009408, -15772772},
2790            {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469,
2791             29551787, -3727419, 19288549, 1325865},
2792        },
2793        {
2794            {15100157, -15835752, -23923978, -1005098, -26450192, 15509408,
2795             12376730, -3479146, 33166107, -8042750},
2796            {20909231, 13023121, -9209752, 16251778, -5778415, -8094914,
2797             12412151, 10018715, 2213263, -13878373},
2798            {32529814, -11074689, 30361439, -16689753, -9135940, 1513226,
2799             22922121, 6382134, -5766928, 8371348},
2800        },
2801    },
2802    {
2803        {
2804            {9923462, 11271500, 12616794, 3544722, -29998368, -1721626,
2805             12891687, -8193132, -26442943, 10486144},
2806            {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726,
2807             2610596, -23921530, -11455195},
2808            {5408411, -1136691, -4969122, 10561668, 24145918, 14240566,
2809             31319731, -4235541, 19985175, -3436086},
2810        },
2811        {
2812            {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976,
2813             -17577068, 8849297, 65030, 8370684},
2814            {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277,
2815             -19442942, 6922164, 12743482, -9800518},
2816            {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717,
2817             23783145, 11038569, 18800704, 255233},
2818        },
2819        {
2820            {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847,
2821             9066957, 19258688, -14753793},
2822            {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541,
2823             -31934921, 2209390, -1524053, 2055794},
2824            {580882, 16705327, 5468415, -2683018, -30926419, -14696000,
2825             -7203346, -8994389, -30021019, 7394435},
2826        },
2827        {
2828            {23838809, 1822728, -15738443, 15242727, 8318092, -3733104,
2829             -21672180, -3492205, -4821741, 14799921},
2830            {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804,
2831             13496856, -9056018, 7402518},
2832            {2286874, -4435931, -20042458, -2008336, -13696227, 5038122,
2833             11006906, -15760352, 8205061, 1607563},
2834        },
2835        {
2836            {14414086, -8002132, 3331830, -3208217, 22249151, -5594188,
2837             18364661, -2906958, 30019587, -9029278},
2838            {-27688051, 1585953, -10775053, 931069, -29120221, -11002319,
2839             -14410829, 12029093, 9944378, 8024},
2840            {4368715, -3709630, 29874200, -15022983, -20230386, -11410704,
2841             -16114594, -999085, -8142388, 5640030},
2842        },
2843        {
2844            {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887,
2845             -16694564, 15219798, -14327783},
2846            {27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605,
2847             -1173195, -18342183, 9742717},
2848            {6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614,
2849             7406442, 12420155, 1994844},
2850        },
2851        {
2852            {14012521, -5024720, -18384453, -9578469, -26485342, -3936439,
2853             -13033478, -10909803, 24319929, -6446333},
2854            {16412690, -4507367, 10772641, 15929391, -17068788, -4658621,
2855             10555945, -10484049, -30102368, -4739048},
2856            {22397382, -7767684, -9293161, -12792868, 17166287, -9755136,
2857             -27333065, 6199366, 21880021, -12250760},
2858        },
2859        {
2860            {-4283307, 5368523, -31117018, 8163389, -30323063, 3209128,
2861             16557151, 8890729, 8840445, 4957760},
2862            {-15447727, 709327, -6919446, -10870178, -29777922, 6522332,
2863             -21720181, 12130072, -14796503, 5005757},
2864            {-2114751, -14308128, 23019042, 15765735, -25269683, 6002752,
2865             10183197, -13239326, -16395286, -2176112},
2866        },
2867    },
2868    {
2869        {
2870            {-19025756, 1632005, 13466291, -7995100, -23640451, 16573537,
2871             -32013908, -3057104, 22208662, 2000468},
2872            {3065073, -1412761, -25598674, -361432, -17683065, -5703415,
2873             -8164212, 11248527, -3691214, -7414184},
2874            {10379208, -6045554, 8877319, 1473647, -29291284, -12507580,
2875             16690915, 2553332, -3132688, 16400289},
2876        },
2877        {
2878            {15716668, 1254266, -18472690, 7446274, -8448918, 6344164,
2879             -22097271, -7285580, 26894937, 9132066},
2880            {24158887, 12938817, 11085297, -8177598, -28063478, -4457083,
2881             -30576463, 64452, -6817084, -2692882},
2882            {13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710,
2883             -3418511, -4688006, 2364226},
2884        },
2885        {
2886            {16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024,
2887             -11697457, 15445875, -7798101},
2888            {29004207, -7867081, 28661402, -640412, -12794003, -7943086,
2889             31863255, -4135540, -278050, -15759279},
2890            {-6122061, -14866665, -28614905, 14569919, -10857999, -3591829,
2891             10343412, -6976290, -29828287, -10815811},
2892        },
2893        {
2894            {27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636,
2895             15372179, 17293797, 960709},
2896            {20263915, 11434237, -5765435, 11236810, 13505955, -10857102,
2897             -16111345, 6493122, -19384511, 7639714},
2898            {-2830798, -14839232, 25403038, -8215196, -8317012, -16173699,
2899             18006287, -16043750, 29994677, -15808121},
2900        },
2901        {
2902            {9769828, 5202651, -24157398, -13631392, -28051003, -11561624,
2903             -24613141, -13860782, -31184575, 709464},
2904            {12286395, 13076066, -21775189, -1176622, -25003198, 4057652,
2905             -32018128, -8890874, 16102007, 13205847},
2906            {13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170,
2907             8525972, 10151379, 10394400},
2908        },
2909        {
2910            {4024660, -16137551, 22436262, 12276534, -9099015, -2686099,
2911             19698229, 11743039, -33302334, 8934414},
2912            {-15879800, -4525240, -8580747, -2934061, 14634845, -698278,
2913             -9449077, 3137094, -11536886, 11721158},
2914            {17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229,
2915             8835153, -9205489, -1280045},
2916        },
2917        {
2918            {-461409, -7830014, 20614118, 16688288, -7514766, -4807119,
2919             22300304, 505429, 6108462, -6183415},
2920            {-5070281, 12367917, -30663534, 3234473, 32617080, -8422642,
2921             29880583, -13483331, -26898490, -7867459},
2922            {-31975283, 5726539, 26934134, 10237677, -3173717, -605053,
2923             24199304, 3795095, 7592688, -14992079},
2924        },
2925        {
2926            {21594432, -14964228, 17466408, -4077222, 32537084, 2739898,
2927             6407723, 12018833, -28256052, 4298412},
2928            {-20650503, -11961496, -27236275, 570498, 3767144, -1717540,
2929             13891942, -1569194, 13717174, 10805743},
2930            {-14676630, -15644296, 15287174, 11927123, 24177847, -8175568,
2931             -796431, 14860609, -26938930, -5863836},
2932        },
2933    },
2934    {
2935        {
2936            {12962541, 5311799, -10060768, 11658280, 18855286, -7954201,
2937             13286263, -12808704, -4381056, 9882022},
2938            {18512079, 11319350, -20123124, 15090309, 18818594, 5271736,
2939             -22727904, 3666879, -23967430, -3299429},
2940            {-6789020, -3146043, 16192429, 13241070, 15898607, -14206114,
2941             -10084880, -6661110, -2403099, 5276065},
2942        },
2943        {
2944            {30169808, -5317648, 26306206, -11750859, 27814964, 7069267,
2945             7152851, 3684982, 1449224, 13082861},
2946            {10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382,
2947             15056736, -21016438, -8202000},
2948            {-33150110, 3261608, 22745853, 7948688, 19370557, -15177665,
2949             -26171976, 6482814, -10300080, -11060101},
2950        },
2951        {
2952            {32869458, -5408545, 25609743, 15678670, -10687769, -15471071,
2953             26112421, 2521008, -22664288, 6904815},
2954            {29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737,
2955             3841096, -29003639, -6657642},
2956            {10340844, -6630377, -18656632, -2278430, 12621151, -13339055,
2957             30878497, -11824370, -25584551, 5181966},
2958        },
2959        {
2960            {25940115, -12658025, 17324188, -10307374, -8671468, 15029094,
2961             24396252, -16450922, -2322852, -12388574},
2962            {-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390,
2963             12641087, 20603771, -6561742},
2964            {-18882287, -11673380, 24849422, 11501709, 13161720, -4768874,
2965             1925523, 11914390, 4662781, 7820689},
2966        },
2967        {
2968            {12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456,
2969             12172924, 16136752, 15264020},
2970            {-10349955, -14680563, -8211979, 2330220, -17662549, -14545780,
2971             10658213, 6671822, 19012087, 3772772},
2972            {3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732,
2973             -15762884, 20527771, 12988982},
2974        },
2975        {
2976            {-14822485, -5797269, -3707987, 12689773, -898983, -10914866,
2977             -24183046, -10564943, 3299665, -12424953},
2978            {-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197,
2979             6461331, -25583147, 8991218},
2980            {-17226263, 1816362, -1673288, -6086439, 31783888, -8175991,
2981             -32948145, 7417950, -30242287, 1507265},
2982        },
2983        {
2984            {29692663, 6829891, -10498800, 4334896, 20945975, -11906496,
2985             -28887608, 8209391, 14606362, -10647073},
2986            {-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695,
2987             9761487, 4170404, -2085325},
2988            {-11587470, 14855945, -4127778, -1531857, -26649089, 15084046,
2989             22186522, 16002000, -14276837, -8400798},
2990        },
2991        {
2992            {-4811456, 13761029, -31703877, -2483919, -3312471, 7869047,
2993             -7113572, -9620092, 13240845, 10965870},
2994            {-7742563, -8256762, -14768334, -13656260, -23232383, 12387166,
2995             4498947, 14147411, 29514390, 4302863},
2996            {-13413405, -12407859, 20757302, -13801832, 14785143, 8976368,
2997             -5061276, -2144373, 17846988, -13971927},
2998        },
2999    },
3000    {
3001        {
3002            {-2244452, -754728, -4597030, -1066309, -6247172, 1455299,
3003             -21647728, -9214789, -5222701, 12650267},
3004            {-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813,
3005             13770293, -19134326, 10958663},
3006            {22470984, 12369526, 23446014, -5441109, -21520802, -9698723,
3007             -11772496, -11574455, -25083830, 4271862},
3008        },
3009        {
3010            {-25169565, -10053642, -19909332, 15361595, -5984358, 2159192,
3011             75375, -4278529, -32526221, 8469673},
3012            {15854970, 4148314, -8893890, 7259002, 11666551, 13824734,
3013             -30531198, 2697372, 24154791, -9460943},
3014            {15446137, -15806644, 29759747, 14019369, 30811221, -9610191,
3015             -31582008, 12840104, 24913809, 9815020},
3016        },
3017        {
3018            {-4709286, -5614269, -31841498, -12288893, -14443537, 10799414,
3019             -9103676, 13438769, 18735128, 9466238},
3020            {11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821,
3021             -10896103, -22728655, 16199064},
3022            {14576810, 379472, -26786533, -8317236, -29426508, -10812974,
3023             -102766, 1876699, 30801119, 2164795},
3024        },
3025        {
3026            {15995086, 3199873, 13672555, 13712240, -19378835, -4647646,
3027             -13081610, -15496269, -13492807, 1268052},
3028            {-10290614, -3659039, -3286592, 10948818, 23037027, 3794475,
3029             -3470338, -12600221, -17055369, 3565904},
3030            {29210088, -9419337, -5919792, -4952785, 10834811, -13327726,
3031             -16512102, -10820713, -27162222, -14030531},
3032        },
3033        {
3034            {-13161890, 15508588, 16663704, -8156150, -28349942, 9019123,
3035             -29183421, -3769423, 2244111, -14001979},
3036            {-5152875, -3800936, -9306475, -6071583, 16243069, 14684434,
3037             -25673088, -16180800, 13491506, 4641841},
3038            {10813417, 643330, -19188515, -728916, 30292062, -16600078,
3039             27548447, -7721242, 14476989, -12767431},
3040        },
3041        {
3042            {10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937,
3043             -1644259, -27912810, 12651324},
3044            {-31185513, -813383, 22271204, 11835308, 10201545, 15351028,
3045             17099662, 3988035, 21721536, -3148940},
3046            {10202177, -6545839, -31373232, -9574638, -32150642, -8119683,
3047             -12906320, 3852694, 13216206, 14842320},
3048        },
3049        {
3050            {-15815640, -10601066, -6538952, -7258995, -6984659, -6581778,
3051             -31500847, 13765824, -27434397, 9900184},
3052            {14465505, -13833331, -32133984, -14738873, -27443187, 12990492,
3053             33046193, 15796406, -7051866, -8040114},
3054            {30924417, -8279620, 6359016, -12816335, 16508377, 9071735,
3055             -25488601, 15413635, 9524356, -7018878},
3056        },
3057        {
3058            {12274201, -13175547, 32627641, -1785326, 6736625, 13267305,
3059             5237659, -5109483, 15663516, 4035784},
3060            {-2951309, 8903985, 17349946, 601635, -16432815, -4612556,
3061             -13732739, -15889334, -22258478, 4659091},
3062            {-16916263, -4952973, -30393711, -15158821, 20774812, 15897498,
3063             5736189, 15026997, -2178256, -13455585},
3064        },
3065    },
3066    {
3067        {
3068            {-8858980, -2219056, 28571666, -10155518, -474467, -10105698,
3069             -3801496, 278095, 23440562, -290208},
3070            {10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275,
3071             11551483, -16571960, -7442864},
3072            {17932739, -12437276, -24039557, 10749060, 11316803, 7535897,
3073             22503767, 5561594, -3646624, 3898661},
3074        },
3075        {
3076            {7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531,
3077             7152530, 21831162, 1245233},
3078            {26958459, -14658026, 4314586, 8346991, -5677764, 11960072,
3079             -32589295, -620035, -30402091, -16716212},
3080            {-12165896, 9166947, 33491384, 13673479, 29787085, 13096535,
3081             6280834, 14587357, -22338025, 13987525},
3082        },
3083        {
3084            {-24349909, 7778775, 21116000, 15572597, -4833266, -5357778,
3085             -4300898, -5124639, -7469781, -2858068},
3086            {9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781,
3087             6439245, -14581012, 4091397},
3088            {-8426427, 1470727, -28109679, -1596990, 3978627, -5123623,
3089             -19622683, 12092163, 29077877, -14741988},
3090        },
3091        {
3092            {5269168, -6859726, -13230211, -8020715, 25932563, 1763552,
3093             -5606110, -5505881, -20017847, 2357889},
3094            {32264008, -15407652, -5387735, -1160093, -2091322, -3946900,
3095             23104804, -12869908, 5727338, 189038},
3096            {14609123, -8954470, -6000566, -16622781, -14577387, -7743898,
3097             -26745169, 10942115, -25888931, -14884697},
3098        },
3099        {
3100            {20513500, 5557931, -15604613, 7829531, 26413943, -2019404,
3101             -21378968, 7471781, 13913677, -5137875},
3102            {-25574376, 11967826, 29233242, 12948236, -6754465, 4713227,
3103             -8940970, 14059180, 12878652, 8511905},
3104            {-25656801, 3393631, -2955415, -7075526, -2250709, 9366908,
3105             -30223418, 6812974, 5568676, -3127656},
3106        },
3107        {
3108            {11630004, 12144454, 2116339, 13606037, 27378885, 15676917,
3109             -17408753, -13504373, -14395196, 8070818},
3110            {27117696, -10007378, -31282771, -5570088, 1127282, 12772488,
3111             -29845906, 10483306, -11552749, -1028714},
3112            {10637467, -5688064, 5674781, 1072708, -26343588, -6982302,
3113             -1683975, 9177853, -27493162, 15431203},
3114        },
3115        {
3116            {20525145, 10892566, -12742472, 12779443, -29493034, 16150075,
3117             -28240519, 14943142, -15056790, -7935931},
3118            {-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767,
3119             -3239766, -3356550, 9594024},
3120            {-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683,
3121             -6492290, 13352335, -10977084},
3122        },
3123        {
3124            {-1931799, -5407458, 3304649, -12884869, 17015806, -4877091,
3125             -29783850, -7752482, -13215537, -319204},
3126            {20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742,
3127             15077870, -22750759, 14523817},
3128            {27406042, -6041657, 27423596, -4497394, 4996214, 10002360,
3129             -28842031, -4545494, -30172742, -4805667},
3130        },
3131    },
3132    {
3133        {
3134            {11374242, 12660715, 17861383, -12540833, 10935568, 1099227,
3135             -13886076, -9091740, -27727044, 11358504},
3136            {-12730809, 10311867, 1510375, 10778093, -2119455, -9145702,
3137             32676003, 11149336, -26123651, 4985768},
3138            {-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043,
3139             13794114, -19414307, -15621255},
3140        },
3141        {
3142            {6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603,
3143             6970005, -1691065, -9004790},
3144            {1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622,
3145             -5475723, -16796596, -5031438},
3146            {-22273315, -13524424, -64685, -4334223, -18605636, -10921968,
3147             -20571065, -7007978, -99853, -10237333},
3148        },
3149        {
3150            {17747465, 10039260, 19368299, -4050591, -20630635, -16041286,
3151             31992683, -15857976, -29260363, -5511971},
3152            {31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999,
3153             -3744247, 4882242, -10626905},
3154            {29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198,
3155             3272828, -5190932, -4162409},
3156        },
3157        {
3158            {12501286, 4044383, -8612957, -13392385, -32430052, 5136599,
3159             -19230378, -3529697, 330070, -3659409},
3160            {6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522,
3161             -8573892, -271295, 12071499},
3162            {-8365515, -4042521, 25133448, -4517355, -6211027, 2265927,
3163             -32769618, 1936675, -5159697, 3829363},
3164        },
3165        {
3166            {28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550,
3167             -6567787, 26333140, 14267664},
3168            {-11067219, 11871231, 27385719, -10559544, -4585914, -11189312,
3169             10004786, -8709488, -21761224, 8930324},
3170            {-21197785, -16396035, 25654216, -1725397, 12282012, 11008919,
3171             1541940, 4757911, -26491501, -16408940},
3172        },
3173        {
3174            {13537262, -7759490, -20604840, 10961927, -5922820, -13218065,
3175             -13156584, 6217254, -15943699, 13814990},
3176            {-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681,
3177             9257833, -1956526, -1776914},
3178            {-25045300, -10191966, 15366585, 15166509, -13105086, 8423556,
3179             -29171540, 12361135, -18685978, 4578290},
3180        },
3181        {
3182            {24579768, 3711570, 1342322, -11180126, -27005135, 14124956,
3183             -22544529, 14074919, 21964432, 8235257},
3184            {-6528613, -2411497, 9442966, -5925588, 12025640, -1487420,
3185             -2981514, -1669206, 13006806, 2355433},
3186            {-16304899, -13605259, -6632427, -5142349, 16974359, -10911083,
3187             27202044, 1719366, 1141648, -12796236},
3188        },
3189        {
3190            {-12863944, -13219986, -8318266, -11018091, -6810145, -4843894,
3191             13475066, -3133972, 32674895, 13715045},
3192            {11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
3193             -13265253, 16086212, -28740881, -15642093},
3194            {-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
3195             -11709148, 7791794, -27245943, 4383347},
3196        },
3197    },
3198    {
3199        {
3200            {-28970898, 5271447, -1266009, -9736989, -12455236, 16732599,
3201             -4862407, -4906449, 27193557, 6245191},
3202            {-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898,
3203             3260492, 22510453, 8577507},
3204            {-12632451, 11257346, -32692994, 13548177, -721004, 10879011,
3205             31168030, 13952092, -29571492, -3635906},
3206        },
3207        {
3208            {3877321, -9572739, 32416692, 5405324, -11004407, -13656635,
3209             3759769, 11935320, 5611860, 8164018},
3210            {-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
3211             32003002, -8832289, 5773085, -8422109},
3212            {-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
3213             12376320, 31632953, 190926},
3214        },
3215        {
3216            {-24593607, -16138885, -8423991, 13378746, 14162407, 6901328,
3217             -8288749, 4508564, -25341555, -3627528},
3218            {8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941,
3219             -14786005, -1672488, 827625},
3220            {-32720583, -16289296, -32503547, 7101210, 13354605, 2659080,
3221             -1800575, -14108036, -24878478, 1541286},
3222        },
3223        {
3224            {2901347, -1117687, 3880376, -10059388, -17620940, -3612781,
3225             -21802117, -3567481, 20456845, -1885033},
3226            {27019610, 12299467, -13658288, -1603234, -12861660, -4861471,
3227             -19540150, -5016058, 29439641, 15138866},
3228            {21536104, -6626420, -32447818, -10690208, -22408077, 5175814,
3229             -5420040, -16361163, 7779328, 109896},
3230        },
3231        {
3232            {30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390,
3233             12180118, 23177719, -554075},
3234            {26572847, 3405927, -31701700, 12890905, -19265668, 5335866,
3235             -6493768, 2378492, 4439158, -13279347},
3236            {-22716706, 3489070, -9225266, -332753, 18875722, -1140095,
3237             14819434, -12731527, -17717757, -5461437},
3238        },
3239        {
3240            {-5056483, 16566551, 15953661, 3767752, -10436499, 15627060,
3241             -820954, 2177225, 8550082, -15114165},
3242            {-18473302, 16596775, -381660, 15663611, 22860960, 15585581,
3243             -27844109, -3582739, -23260460, -8428588},
3244            {-32480551, 15707275, -8205912, -5652081, 29464558, 2713815,
3245             -22725137, 15860482, -21902570, 1494193},
3246        },
3247        {
3248            {-19562091, -14087393, -25583872, -9299552, 13127842, 759709,
3249             21923482, 16529112, 8742704, 12967017},
3250            {-28464899, 1553205, 32536856, -10473729, -24691605, -406174,
3251             -8914625, -2933896, -29903758, 15553883},
3252            {21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572,
3253             14513274, 19375923, -12647961},
3254        },
3255        {
3256            {8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818,
3257             -6222716, 2862653, 9455043},
3258            {29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124,
3259             -2990080, 15511449, 4789663},
3260            {-20679756, 7004547, 8824831, -9434977, -4045704, -3750736,
3261             -5754762, 108893, 23513200, 16652362},
3262        },
3263    },
3264    {
3265        {
3266            {-33256173, 4144782, -4476029, -6579123, 10770039, -7155542,
3267             -6650416, -12936300, -18319198, 10212860},
3268            {2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801,
3269             2600940, -9988298, -12506466},
3270            {-24645692, 13317462, -30449259, -15653928, 21365574, -10869657,
3271             11344424, 864440, -2499677, -16710063},
3272        },
3273        {
3274            {-26432803, 6148329, -17184412, -14474154, 18782929, -275997,
3275             -22561534, 211300, 2719757, 4940997},
3276            {-1323882, 3911313, -6948744, 14759765, -30027150, 7851207,
3277             21690126, 8518463, 26699843, 5276295},
3278            {-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586,
3279             149635, -15452774, 7159369},
3280        },
3281        {
3282            {9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009,
3283             8312176, 22477218, -8403385},
3284            {18155857, -16504990, 19744716, 9006923, 15154154, -10538976,
3285             24256460, -4864995, -22548173, 9334109},
3286            {2986088, -4911893, 10776628, -3473844, 10620590, -7083203,
3287             -21413845, 14253545, -22587149, 536906},
3288        },
3289        {
3290            {4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551,
3291             10589625, 10838060, -15420424},
3292            {-19342404, 867880, 9277171, -3218459, -14431572, -1986443,
3293             19295826, -15796950, 6378260, 699185},
3294            {7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039,
3295             15693155, -5045064, -13373962},
3296        },
3297        {
3298            {-7737563, -5869402, -14566319, -7406919, 11385654, 13201616,
3299             31730678, -10962840, -3918636, -9669325},
3300            {10188286, -15770834, -7336361, 13427543, 22223443, 14896287,
3301             30743455, 7116568, -21786507, 5427593},
3302            {696102, 13206899, 27047647, -10632082, 15285305, -9853179,
3303             10798490, -4578720, 19236243, 12477404},
3304        },
3305        {
3306            {-11229439, 11243796, -17054270, -8040865, -788228, -8167967,
3307             -3897669, 11180504, -23169516, 7733644},
3308            {17800790, -14036179, -27000429, -11766671, 23887827, 3149671,
3309             23466177, -10538171, 10322027, 15313801},
3310            {26246234, 11968874, 32263343, -5468728, 6830755, -13323031,
3311             -15794704, -101982, -24449242, 10890804},
3312        },
3313        {
3314            {-31365647, 10271363, -12660625, -6267268, 16690207, -13062544,
3315             -14982212, 16484931, 25180797, -5334884},
3316            {-586574, 10376444, -32586414, -11286356, 19801893, 10997610,
3317             2276632, 9482883, 316878, 13820577},
3318            {-9882808, -4510367, -2115506, 16457136, -11100081, 11674996,
3319             30756178, -7515054, 30696930, -3712849},
3320        },
3321        {
3322            {32988917, -9603412, 12499366, 7910787, -10617257, -11931514,
3323             -7342816, -9985397, -32349517, 7392473},
3324            {-8855661, 15927861, 9866406, -3649411, -2396914, -16655781,
3325             -30409476, -9134995, 25112947, -2926644},
3326            {-2504044, -436966, 25621774, -5678772, 15085042, -5479877,
3327             -24884878, -13526194, 5537438, -13914319},
3328        },
3329    },
3330    {
3331        {
3332            {-11225584, 2320285, -9584280, 10149187, -33444663, 5808648,
3333             -14876251, -1729667, 31234590, 6090599},
3334            {-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721,
3335             15878753, -6970405, -9034768},
3336            {-27757857, 247744, -15194774, -9002551, 23288161, -10011936,
3337             -23869595, 6503646, 20650474, 1804084},
3338        },
3339        {
3340            {-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995,
3341             -10329713, 27842616, -202328},
3342            {-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656,
3343             5031932, -11375082, 12714369},
3344            {20807691, -7270825, 29286141, 11421711, -27876523, -13868230,
3345             -21227475, 1035546, -19733229, 12796920},
3346        },
3347        {
3348            {12076899, -14301286, -8785001, -11848922, -25012791, 16400684,
3349             -17591495, -12899438, 3480665, -15182815},
3350            {-32361549, 5457597, 28548107, 7833186, 7303070, -11953545,
3351             -24363064, -15921875, -33374054, 2771025},
3352            {-21389266, 421932, 26597266, 6860826, 22486084, -6737172,
3353             -17137485, -4210226, -24552282, 15673397},
3354        },
3355        {
3356            {-20184622, 2338216, 19788685, -9620956, -4001265, -8740893,
3357             -20271184, 4733254, 3727144, -12934448},
3358            {6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594,
3359             7975683, 31123697, -10958981},
3360            {30069250, -11435332, 30434654, 2958439, 18399564, -976289,
3361             12296869, 9204260, -16432438, 9648165},
3362        },
3363        {
3364            {32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266,
3365             5248604, -26008332, -11377501},
3366            {17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711,
3367             15298639, 2662509, -16297073},
3368            {-1172927, -7558695, -4366770, -4287744, -21346413, -8434326,
3369             32087529, -1222777, 32247248, -14389861},
3370        },
3371        {
3372            {14312628, 1221556, 17395390, -8700143, -4945741, -8684635,
3373             -28197744, -9637817, -16027623, -13378845},
3374            {-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502,
3375             9803137, 17597934, 2346211},
3376            {18510800, 15337574, 26171504, 981392, -22241552, 7827556,
3377             -23491134, -11323352, 3059833, -11782870},
3378        },
3379        {
3380            {10141598, 6082907, 17829293, -1947643, 9830092, 13613136,
3381             -25556636, -5544586, -33502212, 3592096},
3382            {33114168, -15889352, -26525686, -13343397, 33076705, 8716171,
3383             1151462, 1521897, -982665, -6837803},
3384            {-32939165, -4255815, 23947181, -324178, -33072974, -12305637,
3385             -16637686, 3891704, 26353178, 693168},
3386        },
3387        {
3388            {30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294,
3389             -400668, 31375464, 14369965},
3390            {-14370654, -7772529, 1510301, 6434173, -18784789, -6262728,
3391             32732230, -13108839, 17901441, 16011505},
3392            {18171223, -11934626, -12500402, 15197122, -11038147, -15230035,
3393             -19172240, -16046376, 8764035, 12309598},
3394        },
3395    },
3396    {
3397        {
3398            {5975908, -5243188, -19459362, -9681747, -11541277, 14015782,
3399             -23665757, 1228319, 17544096, -10593782},
3400            {5811932, -1715293, 3442887, -2269310, -18367348, -8359541,
3401             -18044043, -15410127, -5565381, 12348900},
3402            {-31399660, 11407555, 25755363, 6891399, -3256938, 14872274,
3403             -24849353, 8141295, -10632534, -585479},
3404        },
3405        {
3406            {-12675304, 694026, -5076145, 13300344, 14015258, -14451394,
3407             -9698672, -11329050, 30944593, 1130208},
3408            {8247766, -6710942, -26562381, -7709309, -14401939, -14648910,
3409             4652152, 2488540, 23550156, -271232},
3410            {17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737,
3411             -5908146, -408818, -137719},
3412        },
3413        {
3414            {16091085, -16253926, 18599252, 7340678, 2137637, -1221657,
3415             -3364161, 14550936, 3260525, -7166271},
3416            {-4910104, -13332887, 18550887, 10864893, -16459325, -7291596,
3417             -23028869, -13204905, -12748722, 2701326},
3418            {-8574695, 16099415, 4629974, -16340524, -20786213, -6005432,
3419             -10018363, 9276971, 11329923, 1862132},
3420        },
3421        {
3422            {14763076, -15903608, -30918270, 3689867, 3511892, 10313526,
3423             -21951088, 12219231, -9037963, -940300},
3424            {8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216,
3425             -2909717, -15438168, 11595570},
3426            {15214962, 3537601, -26238722, -14058872, 4418657, -15230761,
3427             13947276, 10730794, -13489462, -4363670},
3428        },
3429        {
3430            {-2538306, 7682793, 32759013, 263109, -29984731, -7955452,
3431             -22332124, -10188635, 977108, 699994},
3432            {-12466472, 4195084, -9211532, 550904, -15565337, 12917920,
3433             19118110, -439841, -30534533, -14337913},
3434            {31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237,
3435             -10051775, 12493932, -5409317},
3436        },
3437        {
3438            {-25680606, 5260744, -19235809, -6284470, -3695942, 16566087,
3439             27218280, 2607121, 29375955, 6024730},
3440            {842132, -2794693, -4763381, -8722815, 26332018, -12405641,
3441             11831880, 6985184, -9940361, 2854096},
3442            {-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645,
3443             960770, 12121869, 16648078},
3444        },
3445        {
3446            {-15218652, 14667096, -13336229, 2013717, 30598287, -464137,
3447             -31504922, -7882064, 20237806, 2838411},
3448            {-19288047, 4453152, 15298546, -16178388, 22115043, -15972604,
3449             12544294, -13470457, 1068881, -12499905},
3450            {-9558883, -16518835, 33238498, 13506958, 30505848, -1114596,
3451             -8486907, -2630053, 12521378, 4845654},
3452        },
3453        {
3454            {-28198521, 10744108, -2958380, 10199664, 7759311, -13088600,
3455             3409348, -873400, -6482306, -12885870},
3456            {-23561822, 6230156, -20382013, 10655314, -24040585, -11621172,
3457             10477734, -1240216, -3113227, 13974498},
3458            {12966261, 15550616, -32038948, -1615346, 21025980, -629444,
3459             5642325, 7188737, 18895762, 12629579},
3460        },
3461    },
3462    {
3463        {
3464            {14741879, -14946887, 22177208, -11721237, 1279741, 8058600,
3465             11758140, 789443, 32195181, 3895677},
3466            {10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575,
3467             -3566119, -8982069, 4429647},
3468            {-2453894, 15725973, -20436342, -10410672, -5803908, -11040220,
3469             -7135870, -11642895, 18047436, -15281743},
3470        },
3471        {
3472            {-25173001, -11307165, 29759956, 11776784, -22262383, -15820455,
3473             10993114, -12850837, -17620701, -9408468},
3474            {21987233, 700364, -24505048, 14972008, -7774265, -5718395,
3475             32155026, 2581431, -29958985, 8773375},
3476            {-25568350, 454463, -13211935, 16126715, 25240068, 8594567,
3477             20656846, 12017935, -7874389, -13920155},
3478        },
3479        {
3480            {6028182, 6263078, -31011806, -11301710, -818919, 2461772,
3481             -31841174, -5468042, -1721788, -2776725},
3482            {-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845,
3483             -4166698, 28408820, 6816612},
3484            {-10358094, -8237829, 19549651, -12169222, 22082623, 16147817,
3485             20613181, 13982702, -10339570, 5067943},
3486        },
3487        {
3488            {-30505967, -3821767, 12074681, 13582412, -19877972, 2443951,
3489             -19719286, 12746132, 5331210, -10105944},
3490            {30528811, 3601899, -1957090, 4619785, -27361822, -15436388,
3491             24180793, -12570394, 27679908, -1648928},
3492            {9402404, -13957065, 32834043, 10838634, -26580150, -13237195,
3493             26653274, -8685565, 22611444, -12715406},
3494        },
3495        {
3496            {22190590, 1118029, 22736441, 15130463, -30460692, -5991321,
3497             19189625, -4648942, 4854859, 6622139},
3498            {-8310738, -2953450, -8262579, -3388049, -10401731, -271929,
3499             13424426, -3567227, 26404409, 13001963},
3500            {-31241838, -15415700, -2994250, 8939346, 11562230, -12840670,
3501             -26064365, -11621720, -15405155, 11020693},
3502        },
3503        {
3504            {1866042, -7949489, -7898649, -10301010, 12483315, 13477547,
3505             3175636, -12424163, 28761762, 1406734},
3506            {-448555, -1777666, 13018551, 3194501, -9580420, -11161737,
3507             24760585, -4347088, 25577411, -13378680},
3508            {-24290378, 4759345, -690653, -1852816, 2066747, 10693769,
3509             -29595790, 9884936, -9368926, 4745410},
3510        },
3511        {
3512            {-9141284, 6049714, -19531061, -4341411, -31260798, 9944276,
3513             -15462008, -11311852, 10931924, -11931931},
3514            {-16561513, 14112680, -8012645, 4817318, -8040464, -11414606,
3515             -22853429, 10856641, -20470770, 13434654},
3516            {22759489, -10073434, -16766264, -1871422, 13637442, -10168091,
3517             1765144, -12654326, 28445307, -5364710},
3518        },
3519        {
3520            {29875063, 12493613, 2795536, -3786330, 1710620, 15181182,
3521             -10195717, -8788675, 9074234, 1167180},
3522            {-26205683, 11014233, -9842651, -2635485, -26908120, 7532294,
3523             -18716888, -9535498, 3843903, 9367684},
3524            {-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123,
3525             8601684, -139197, 4242895},
3526        },
3527    },
3528    {
3529        {
3530            {22092954, -13191123, -2042793, -11968512, 32186753, -11517388,
3531             -6574341, 2470660, -27417366, 16625501},
3532            {-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857,
3533             2602725, -27351616, 14247413},
3534            {6314175, -10264892, -32772502, 15957557, -10157730, 168750,
3535             -8618807, 14290061, 27108877, -1180880},
3536        },
3537        {
3538            {-8586597, -7170966, 13241782, 10960156, -32991015, -13794596,
3539             33547976, -11058889, -27148451, 981874},
3540            {22833440, 9293594, -32649448, -13618667, -9136966, 14756819,
3541             -22928859, -13970780, -10479804, -16197962},
3542            {-7768587, 3326786, -28111797, 10783824, 19178761, 14905060,
3543             22680049, 13906969, -15933690, 3797899},
3544        },
3545        {
3546            {21721356, -4212746, -12206123, 9310182, -3882239, -13653110,
3547             23740224, -2709232, 20491983, -8042152},
3548            {9209270, -15135055, -13256557, -6167798, -731016, 15289673,
3549             25947805, 15286587, 30997318, -6703063},
3550            {7392032, 16618386, 23946583, -8039892, -13265164, -1533858,
3551             -14197445, -2321576, 17649998, -250080},
3552        },
3553        {
3554            {-9301088, -14193827, 30609526, -3049543, -25175069, -1283752,
3555             -15241566, -9525724, -2233253, 7662146},
3556            {-17558673, 1763594, -33114336, 15908610, -30040870, -12174295,
3557             7335080, -8472199, -3174674, 3440183},
3558            {-19889700, -5977008, -24111293, -9688870, 10799743, -16571957,
3559             40450, -4431835, 4862400, 1133},
3560        },
3561        {
3562            {-32856209, -7873957, -5422389, 14860950, -16319031, 7956142,
3563             7258061, 311861, -30594991, -7379421},
3564            {-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763,
3565             16527196, 18278453, 15405622},
3566            {-4381906, 8508652, -19898366, -3674424, -5984453, 15149970,
3567             -13313598, 843523, -21875062, 13626197},
3568        },
3569        {
3570            {2281448, -13487055, -10915418, -2609910, 1879358, 16164207,
3571             -10783882, 3953792, 13340839, 15928663},
3572            {31727126, -7179855, -18437503, -8283652, 2875793, -16390330,
3573             -25269894, -7014826, -23452306, 5964753},
3574            {4100420, -5959452, -17179337, 6017714, -18705837, 12227141,
3575             -26684835, 11344144, 2538215, -7570755},
3576        },
3577        {
3578            {-9433605, 6123113, 11159803, -2156608, 30016280, 14966241,
3579             -20474983, 1485421, -629256, -15958862},
3580            {-26804558, 4260919, 11851389, 9658551, -32017107, 16367492,
3581             -20205425, -13191288, 11659922, -11115118},
3582            {26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568,
3583             -10170080, 33100372, -1306171},
3584        },
3585        {
3586            {15121113, -5201871, -10389905, 15427821, -27509937, -15992507,
3587             21670947, 4486675, -5931810, -14466380},
3588            {16166486, -9483733, -11104130, 6023908, -31926798, -1364923,
3589             2340060, -16254968, -10735770, -10039824},
3590            {28042865, -3557089, -12126526, 12259706, -3717498, -6945899,
3591             6766453, -8689599, 18036436, 5803270},
3592        },
3593    },
3594    {
3595        {
3596            {-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391,
3597             4598332, -6159431, -14117438},
3598            {-31031306, -14256194, 17332029, -2383520, 31312682, -5967183,
3599             696309, 50292, -20095739, 11763584},
3600            {-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117,
3601             -12613632, -19773211, -10713562},
3602        },
3603        {
3604            {30464590, -11262872, -4127476, -12734478, 19835327, -7105613,
3605             -24396175, 2075773, -17020157, 992471},
3606            {18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841,
3607             8080033, -11574335, -10601610},
3608            {19598397, 10334610, 12555054, 2555664, 18821899, -10339780,
3609             21873263, 16014234, 26224780, 16452269},
3610        },
3611        {
3612            {-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804,
3613             -7618186, -20533829, 3698650},
3614            {14187449, 3448569, -10636236, -10810935, -22663880, -3433596,
3615             7268410, -10890444, 27394301, 12015369},
3616            {19695761, 16087646, 28032085, 12999827, 6817792, 11427614,
3617             20244189, -1312777, -13259127, -3402461},
3618        },
3619        {
3620            {30860103, 12735208, -1888245, -4699734, -16974906, 2256940,
3621             -8166013, 12298312, -8550524, -10393462},
3622            {-5719826, -11245325, -1910649, 15569035, 26642876, -7587760,
3623             -5789354, -15118654, -4976164, 12651793},
3624            {-2848395, 9953421, 11531313, -5282879, 26895123, -12697089,
3625             -13118820, -16517902, 9768698, -2533218},
3626        },
3627        {
3628            {-24719459, 1894651, -287698, -4704085, 15348719, -8156530,
3629             32767513, 12765450, 4940095, 10678226},
3630            {18860224, 15980149, -18987240, -1562570, -26233012, -11071856,
3631             -7843882, 13944024, -24372348, 16582019},
3632            {-15504260, 4970268, -29893044, 4175593, -20993212, -2199756,
3633             -11704054, 15444560, -11003761, 7989037},
3634        },
3635        {
3636            {31490452, 5568061, -2412803, 2182383, -32336847, 4531686,
3637             -32078269, 6200206, -19686113, -14800171},
3638            {-17308668, -15879940, -31522777, -2831, -32887382, 16375549,
3639             8680158, -16371713, 28550068, -6857132},
3640            {-28126887, -5688091, 16837845, -1820458, -6850681, 12700016,
3641             -30039981, 4364038, 1155602, 5988841},
3642        },
3643        {
3644            {21890435, -13272907, -12624011, 12154349, -7831873, 15300496,
3645             23148983, -4470481, 24618407, 8283181},
3646            {-33136107, -10512751, 9975416, 6841041, -31559793, 16356536,
3647             3070187, -7025928, 1466169, 10740210},
3648            {-1509399, -15488185, -13503385, -10655916, 32799044, 909394,
3649             -13938903, -5779719, -32164649, -15327040},
3650        },
3651        {
3652            {3960823, -14267803, -28026090, -15918051, -19404858, 13146868,
3653             15567327, 951507, -3260321, -573935},
3654            {24740841, 5052253, -30094131, 8961361, 25877428, 6165135,
3655             -24368180, 14397372, -7380369, -6144105},
3656            {-28888365, 3510803, -28103278, -1158478, -11238128, -10631454,
3657             -15441463, -14453128, -1625486, -6494814},
3658        },
3659    },
3660    {
3661        {
3662            {793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843,
3663             -4885251, -9906200, -621852},
3664            {5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374,
3665             1468826, -6171428, -15186581},
3666            {-4859255, -3779343, -2917758, -6748019, 7778750, 11688288,
3667             -30404353, -9871238, -1558923, -9863646},
3668        },
3669        {
3670            {10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958,
3671             14783338, -30581476, -15757844},
3672            {10566929, 12612572, -31944212, 11118703, -12633376, 12362879,
3673             21752402, 8822496, 24003793, 14264025},
3674            {27713862, -7355973, -11008240, 9227530, 27050101, 2504721,
3675             23886875, -13117525, 13958495, -5732453},
3676        },
3677        {
3678            {-23481610, 4867226, -27247128, 3900521, 29838369, -8212291,
3679             -31889399, -10041781, 7340521, -15410068},
3680            {4646514, -8011124, -22766023, -11532654, 23184553, 8566613,
3681             31366726, -1381061, -15066784, -10375192},
3682            {-17270517, 12723032, -16993061, 14878794, 21619651, -6197576,
3683             27584817, 3093888, -8843694, 3849921},
3684        },
3685        {
3686            {-9064912, 2103172, 25561640, -15125738, -5239824, 9582958,
3687             32477045, -9017955, 5002294, -15550259},
3688            {-12057553, -11177906, 21115585, -13365155, 8808712, -12030708,
3689             16489530, 13378448, -25845716, 12741426},
3690            {-5946367, 10645103, -30911586, 15390284, -3286982, -7118677,
3691             24306472, 15852464, 28834118, -7646072},
3692        },
3693        {
3694            {-17335748, -9107057, -24531279, 9434953, -8472084, -583362,
3695             -13090771, 455841, 20461858, 5491305},
3696            {13669248, -16095482, -12481974, -10203039, -14569770, -11893198,
3697             -24995986, 11293807, -28588204, -9421832},
3698            {28497928, 6272777, -33022994, 14470570, 8906179, -1225630,
3699             18504674, -14165166, 29867745, -8795943},
3700        },
3701        {
3702            {-16207023, 13517196, -27799630, -13697798, 24009064, -6373891,
3703             -6367600, -13175392, 22853429, -4012011},
3704            {24191378, 16712145, -13931797, 15217831, 14542237, 1646131,
3705             18603514, -11037887, 12876623, -2112447},
3706            {17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753,
3707             608397, 16031844, 3723494},
3708        },
3709        {
3710            {-28632773, 12763728, -20446446, 7577504, 33001348, -13017745,
3711             17558842, -7872890, 23896954, -4314245},
3712            {-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064,
3713             7229064, -9919646, -8826859},
3714            {28816045, 298879, -28165016, -15920938, 19000928, -1665890,
3715             -12680833, -2949325, -18051778, -2082915},
3716        },
3717        {
3718            {16000882, -344896, 3493092, -11447198, -29504595, -13159789,
3719             12577740, 16041268, -19715240, 7847707},
3720            {10151868, 10572098, 27312476, 7922682, 14825339, 4723128,
3721             -32855931, -6519018, -10020567, 3852848},
3722            {-11430470, 15697596, -21121557, -4420647, 5386314, 15063598,
3723             16514493, -15932110, 29330899, -15076224},
3724        },
3725    },
3726    {
3727        {
3728            {-25499735, -4378794, -15222908, -6901211, 16615731, 2051784,
3729             3303702, 15490, -27548796, 12314391},
3730            {15683520, -6003043, 18109120, -9980648, 15337968, -5997823,
3731             -16717435, 15921866, 16103996, -3731215},
3732            {-23169824, -10781249, 13588192, -1628807, -3798557, -1074929,
3733             -19273607, 5402699, -29815713, -9841101},
3734        },
3735        {
3736            {23190676, 2384583, -32714340, 3462154, -29903655, -1529132,
3737             -11266856, 8911517, -25205859, 2739713},
3738            {21374101, -3554250, -33524649, 9874411, 15377179, 11831242,
3739             -33529904, 6134907, 4931255, 11987849},
3740            {-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539,
3741             13861388, -30076310, 10117930},
3742        },
3743        {
3744            {-29501170, -10744872, -26163768, 13051539, -25625564, 5089643,
3745             -6325503, 6704079, 12890019, 15728940},
3746            {-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376,
3747             -10428139, 12885167, 8311031},
3748            {-17516482, 5352194, 10384213, -13811658, 7506451, 13453191,
3749             26423267, 4384730, 1888765, -5435404},
3750        },
3751        {
3752            {-25817338, -3107312, -13494599, -3182506, 30896459, -13921729,
3753             -32251644, -12707869, -19464434, -3340243},
3754            {-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245,
3755             14845197, 17151279, -9854116},
3756            {-24830458, -12733720, -15165978, 10367250, -29530908, -265356,
3757             22825805, -7087279, -16866484, 16176525},
3758        },
3759        {
3760            {-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182,
3761             -10363426, -28746253, -10197509},
3762            {-10626600, -4486402, -13320562, -5125317, 3432136, -6393229,
3763             23632037, -1940610, 32808310, 1099883},
3764            {15030977, 5768825, -27451236, -2887299, -6427378, -15361371,
3765             -15277896, -6809350, 2051441, -15225865},
3766        },
3767        {
3768            {-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398,
3769             -14154188, -22686354, 16633660},
3770            {4577086, -16752288, 13249841, -15304328, 19958763, -14537274,
3771             18559670, -10759549, 8402478, -9864273},
3772            {-28406330, -1051581, -26790155, -907698, -17212414, -11030789,
3773             9453451, -14980072, 17983010, 9967138},
3774        },
3775        {
3776            {-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990,
3777             7806337, 17507396, 3651560},
3778            {-10420457, -4118111, 14584639, 15971087, -15768321, 8861010,
3779             26556809, -5574557, -18553322, -11357135},
3780            {2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121,
3781             8459447, -5605463, -7621941},
3782        },
3783        {
3784            {-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813,
3785             -849066, 17258084, -7977739},
3786            {18164541, -10595176, -17154882, -1542417, 19237078, -9745295,
3787             23357533, -15217008, 26908270, 12150756},
3788            {-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168,
3789             -5537701, -32302074, 16215819},
3790        },
3791    },
3792    {
3793        {
3794            {-6898905, 9824394, -12304779, -4401089, -31397141, -6276835,
3795             32574489, 12532905, -7503072, -8675347},
3796            {-27343522, -16515468, -27151524, -10722951, 946346, 16291093,
3797             254968, 7168080, 21676107, -1943028},
3798            {21260961, -8424752, -16831886, -11920822, -23677961, 3968121,
3799             -3651949, -6215466, -3556191, -7913075},
3800        },
3801        {
3802            {16544754, 13250366, -16804428, 15546242, -4583003, 12757258,
3803             -2462308, -8680336, -18907032, -9662799},
3804            {-2415239, -15577728, 18312303, 4964443, -15272530, -12653564,
3805             26820651, 16690659, 25459437, -4564609},
3806            {-25144690, 11425020, 28423002, -11020557, -6144921, -15826224,
3807             9142795, -2391602, -6432418, -1644817},
3808        },
3809        {
3810            {-23104652, 6253476, 16964147, -3768872, -25113972, -12296437,
3811             -27457225, -16344658, 6335692, 7249989},
3812            {-30333227, 13979675, 7503222, -12368314, -11956721, -4621693,
3813             -30272269, 2682242, 25993170, -12478523},
3814            {4364628, 5930691, 32304656, -10044554, -8054781, 15091131,
3815             22857016, -10598955, 31820368, 15075278},
3816        },
3817        {
3818            {31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788,
3819             -9650886, -17970238, 12833045},
3820            {19073683, 14851414, -24403169, -11860168, 7625278, 11091125,
3821             -19619190, 2074449, -9413939, 14905377},
3822            {24483667, -11935567, -2518866, -11547418, -1553130, 15355506,
3823             -25282080, 9253129, 27628530, -7555480},
3824        },
3825        {
3826            {17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324,
3827             -9157582, -14110875, 15297016},
3828            {510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417,
3829             -11864220, 8683221, 2921426},
3830            {18606791, 11874196, 27155355, -5281482, -24031742, 6265446,
3831             -25178240, -1278924, 4674690, 13890525},
3832        },
3833        {
3834            {13609624, 13069022, -27372361, -13055908, 24360586, 9592974,
3835             14977157, 9835105, 4389687, 288396},
3836            {9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062,
3837             8317628, 23388070, 16052080},
3838            {12720016, 11937594, -31970060, -5028689, 26900120, 8561328,
3839             -20155687, -11632979, -14754271, -10812892},
3840        },
3841        {
3842            {15961858, 14150409, 26716931, -665832, -22794328, 13603569,
3843             11829573, 7467844, -28822128, 929275},
3844            {11038231, -11582396, -27310482, -7316562, -10498527, -16307831,
3845             -23479533, -9371869, -21393143, 2465074},
3846            {20017163, -4323226, 27915242, 1529148, 12396362, 15675764,
3847             13817261, -9658066, 2463391, -4622140},
3848        },
3849        {
3850            {-16358878, -12663911, -12065183, 4996454, -1256422, 1073572,
3851             9583558, 12851107, 4003896, 12673717},
3852            {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325,
3853             14741514, -9103726, 7903886, 2348101},
3854            {24536016, -16515207, 12715592, -3862155, 1511293, 10047386,
3855             -3842346, -7129159, -28377538, 10048127},
3856        },
3857    },
3858    {
3859        {
3860            {-12622226, -6204820, 30718825, 2591312, -10617028, 12192840,
3861             18873298, -7297090, -32297756, 15221632},
3862            {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409,
3863             -21343950, 2095755, 29769758, 6593415},
3864            {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345,
3865             -6118678, 30958054, 8292160},
3866        },
3867        {
3868            {31429822, -13959116, 29173532, 15632448, 12174511, -2760094,
3869             32808831, 3977186, 26143136, -3148876},
3870            {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633,
3871             -1674433, -3758243, -2304625},
3872            {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029,
3873             -1612713, -1535569, -16664475, 8194478},
3874        },
3875        {
3876            {27338066, -7507420, -7414224, 10140405, -19026427, -6589889,
3877             27277191, 8855376, 28572286, 3005164},
3878            {26287124, 4821776, 25476601, -4145903, -3764513, -15788984,
3879             -18008582, 1182479, -26094821, -13079595},
3880            {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192,
3881             -21876275, -13982627, 32208683, -1198248},
3882        },
3883        {
3884            {-16657702, 2817643, -10286362, 14811298, 6024667, 13349505,
3885             -27315504, -10497842, -27672585, -11539858},
3886            {15941029, -9405932, -21367050, 8062055, 31876073, -238629,
3887             -15278393, -1444429, 15397331, -4130193},
3888            {8934485, -13485467, -23286397, -13423241, -32446090, 14047986,
3889             31170398, -1441021, -27505566, 15087184},
3890        },
3891        {
3892            {-18357243, -2156491, 24524913, -16677868, 15520427, -6360776,
3893             -15502406, 11461896, 16788528, -5868942},
3894            {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433,
3895             -3770287, -10323320, 31322514, -11615635},
3896            {21426655, -5650218, -13648287, -5347537, -28812189, -4920970,
3897             -18275391, -14621414, 13040862, -12112948},
3898        },
3899        {
3900            {11293895, 12478086, -27136401, 15083750, -29307421, 14748872,
3901             14555558, -13417103, 1613711, 4896935},
3902            {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460,
3903             2825960, -4897045, -23971776, -11267415},
3904            {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618,
3905             20615400, 12405433, -23753030, -8436416},
3906        },
3907        {
3908            {-7091295, 12556208, -20191352, 9025187, -17072479, 4333801,
3909             4378436, 2432030, 23097949, -566018},
3910            {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264,
3911             10103221, -18512313, 2424778},
3912            {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
3913             1344109, -3642553, 12412659},
3914        },
3915        {
3916            {-24001791, 7690286, 14929416, -168257, -32210835, -13412986,
3917             24162697, -15326504, -3141501, 11179385},
3918            {18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
3919             -6001441, -1486897, -18684645, -11443503},
3920            {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
3921             13403813, 11052904, 5219329},
3922        },
3923    },
3924    {
3925        {
3926            {20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
3927             31186971, -3973730, 9014762, -8579056},
3928            {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
3929             -33102500, 9160280, 8473550, -3256838},
3930            {24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
3931             -7689309, -16335821, -24568481, 11788948},
3932        },
3933        {
3934            {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
3935             -20037437, 10410733, -24568470, -1458691},
3936            {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
3937             11871841, -12505194, -18513325, 8464118},
3938            {-23400612, 8348507, -14585951, -861714, -3950205, -6373419,
3939             14325289, 8628612, 33313881, -8370517},
3940        },
3941        {
3942            {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
3943             -24805667, -10236854, -8940735, -5818269},
3944            {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
3945             15989197, -12838188, 28358192, -4253904},
3946            {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
3947             -16637684, 4072016, -5351664, 5596589},
3948        },
3949        {
3950            {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
3951             29266239, 2557221, 1768301, 15373193},
3952            {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
3953             -4504991, -24660491, 3442910},
3954            {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
3955             22597931, 7176455, -18585478, 13365930},
3956        },
3957        {
3958            {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
3959             -8570186, -9689599, -3031667},
3960            {25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
3961             683793, -11823784, 15723479, -15163481},
3962            {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
3963             11879682, 5400171, 519526, -1235876},
3964        },
3965        {
3966            {22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
3967             -20353881, 7315967, 16648397, 7605640},
3968            {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
3969             23994942, -5281555, -9468848, 4763278},
3970            {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
3971             31088447, -7764523, -11356529, 728112},
3972        },
3973        {
3974            {26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
3975             -4273545, -12555558, -29365436, -5498272},
3976            {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
3977             12327945, 10750447, 10014012},
3978            {-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
3979             -27481051, -666732, 3424691, 7540221},
3980        },
3981        {
3982            {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
3983             -16317219, -9244265, 15258046},
3984            {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
3985             2711395, 1062915, -5136345},
3986            {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
3987             -6066489, 12194497, 32960380, 1459310},
3988        },
3989    },
3990    {
3991        {
3992            {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
3993             -6101885, 18638003, -11174937},
3994            {31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
3995             9012486, -7584354, -6643087, -5442636},
3996            {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
3997             9677543, -32294889, -6456008},
3998        },
3999        {
4000            {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
4001             -7839692, -7852844, -8138429},
4002            {-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
4003             -27333451, 10754588, -9431476, 5203576},
4004            {31834314, 14135496, -770007, 5159118, 20917671, -16768096,
4005             -7467973, -7337524, 31809243, 7347066},
4006        },
4007        {
4008            {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
4009             19797970, -12211255, 15192876, -2087490},
4010            {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
4011             10609330, 12694420, 33473243, -13382104},
4012            {33184999, 11180355, 15832085, -11385430, -1633671, 225884,
4013             15089336, -11023903, -6135662, 14480053},
4014        },
4015        {
4016            {31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
4017             5496208, 13685227, 27595050, 8737275},
4018            {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
4019             -31008351, -12610604, 26498114, 66511},
4020            {22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
4021             30540766, -4286747, -13327787, -7515095},
4022        },
4023        {
4024            {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
4025             8205540, 13585437, -17127465, 15115439},
4026            {23711543, -672915, 31206561, -8362711, 6164647, -9709987,
4027             -33535882, -1426096, 8236921, 16492939},
4028            {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
4029             19574902, 10071562, 6708380, -6222424},
4030        },
4031        {
4032            {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
4033             9328700, 29955601, -11678310},
4034            {3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
4035             -25892142, -12635595, -9917575, 6216608},
4036            {-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
4037             24822830, -6146567, -26767480, 7525079},
4038        },
4039        {
4040            {-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
4041             -910336, -2782495, -19386633, 11994101},
4042            {21691500, -13624626, -641331, -14367021, 3285881, -3483596,
4043             -25064666, 9718258, -7477437, 13381418},
4044            {18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
4045             23111648, -6375247, 28535282, 15779576},
4046        },
4047        {
4048            {30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
4049             -14068454, 12021730, 9955285, -16303356},
4050            {9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
4051             -18426029, 9924399, 20194861, 13380996},
4052            {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
4053             -1984914, 15707771, 26342023, 10146099},
4054        },
4055    },
4056    {
4057        {
4058            {-26016874, -219943, 21339191, -41388, 19745256, -2878700,
4059             -29637280, 2227040, 21612326, -545728},
4060            {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
4061             25764461, 12243797, -20856566, 11649658},
4062            {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
4063             6114064, 33514190, 2333242},
4064        },
4065        {
4066            {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
4067             -6679750, -12670638, 24350578, -13450001},
4068            {-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
4069             -31536088, -10406836, 8317860, 12352766},
4070            {18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
4071             -23552096, -2287550, 20712163, 6719373},
4072        },
4073        {
4074            {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
4075             -3763210, 26224235, -3297458},
4076            {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
4077             21728352, 9493610, 18620611, -16428628},
4078            {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
4079             -5269471, -9725556, -30701573, -16479657},
4080        },
4081        {
4082            {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
4083             12248509, -5240639, 13735342, 1934062},
4084            {25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
4085             -15136294, -3765346, -21277997, 5473616},
4086            {31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
4087             -7125085, 12469656, 29111212, -5451014},
4088        },
4089        {
4090            {24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
4091             24367466, 6388839, -10295587, 452383},
4092            {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
4093             -24236251, -5915248, 15766062, 8407814},
4094            {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
4095             -8917023, -4388953, -8067909, 2276718},
4096        },
4097        {
4098            {30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
4099             -23827587, 5096219, 22740376, -7303417},
4100            {2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
4101             24051124, 13742383, -15637599, 13295222},
4102            {33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
4103             -17720195, -4612972, -4451357, -14669444},
4104        },
4105        {
4106            {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
4107             -2469266, -4141880, 7770569, 9620597},
4108            {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
4109             -1694323, -33502340, -14767970},
4110            {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
4111             1220118, 30494170, -11440799},
4112        },
4113        {
4114            {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
4115             -26739026, 926050, -1684339, -13333647},
4116            {13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
4117             9021034, 9078865, 3353509, 4033511},
4118            {-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
4119             23161163, 8839127, 27485041, 7356032},
4120        },
4121    },
4122    {
4123        {
4124            {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
4125             2625015, 28431036, -16771834},
4126            {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
4127             -22545972, 14150565, 15970762, 4099461},
4128            {29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
4129             13617293, -9937143, 11465739, 8317062},
4130        },
4131        {
4132            {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
4133             14898637, 3848455, 20969334, -5157516},
4134            {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
4135             -21610826, -3649888, 11177095, 14989547},
4136            {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
4137             13515641, 2581286, -28487508, 9930240},
4138        },
4139        {
4140            {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
4141             18345767, -13403753, 16291481, -5314038},
4142            {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
4143             6957617, 4368891, 9788741},
4144            {16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
4145             -21722536, -8613148, 16250552, -11111103},
4146        },
4147        {
4148            {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
4149             10604807, -30190403, 4782747},
4150            {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
4151             -9981571, 4383045, 22546403, 437323},
4152            {31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
4153             27343084, 2786261, -30633590, -14097016},
4154        },
4155        {
4156            {-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
4157             -19690631, 2355319, -19284671, -6114373},
4158            {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
4159             18952177, 15496498, -29380133, 11754228},
4160            {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
4161             7141596, 11724556, 22761615, -10134141},
4162        },
4163        {
4164            {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
4165             -28741185, -12227393, 32851222, 11717399},
4166            {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
4167             31474879, 3483633, -1193175, -4030831},
4168            {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
4169             33142652, 6546660, -19985279, -3948376},
4170        },
4171        {
4172            {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
4173             -8537131, -12833048, -30772034, -15486313},
4174            {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
4175             -31135347, -16049879, 10928917, 3011958},
4176            {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
4177             -30831056, -12805180, 18008031, 10258577},
4178        },
4179        {
4180            {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4181             -1853465, 1367120, 25127874, 6671743},
4182            {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4183             21382910, 11042292, 25838796, 4642684},
4184            {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4185             30468147, -13900640, 18423289, 4177476},
4186        },
4187    },
4188};
4189
4190static uint8_t negative(signed char b)
4191{
4192    uint32_t x = b;
4193
4194    x >>= 31; /* 1: yes; 0: no */
4195    return x;
4196}
4197
4198static void table_select(ge_precomp *t, int pos, signed char b)
4199{
4200    ge_precomp minust;
4201    uint8_t bnegative = negative(b);
4202    uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4203
4204    ge_precomp_0(t);
4205    cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4206    cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4207    cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4208    cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4209    cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4210    cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4211    cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4212    cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4213    fe_copy(minust.yplusx, t->yminusx);
4214    fe_copy(minust.yminusx, t->yplusx);
4215    fe_neg(minust.xy2d, t->xy2d);
4216    cmov(t, &minust, bnegative);
4217}
4218
4219/*
4220 * h = a * B
4221 *
4222 * where a = a[0]+256*a[1]+...+256^31 a[31]
4223 * B is the Ed25519 base point (x,4/5) with x positive.
4224 *
4225 * Preconditions:
4226 *   a[31] <= 127
4227 */
4228static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a)
4229{
4230    signed char e[64];
4231    signed char carry;
4232    ge_p1p1 r;
4233    ge_p2 s;
4234    ge_precomp t;
4235    int i;
4236
4237    for (i = 0; i < 32; ++i) {
4238        e[2 * i + 0] = (a[i] >> 0) & 15;
4239        e[2 * i + 1] = (a[i] >> 4) & 15;
4240    }
4241    /* each e[i] is between 0 and 15 */
4242    /* e[63] is between 0 and 7 */
4243
4244    carry = 0;
4245    for (i = 0; i < 63; ++i) {
4246        e[i] += carry;
4247        carry = e[i] + 8;
4248        carry >>= 4;
4249        e[i] -= carry << 4;
4250    }
4251    e[63] += carry;
4252    /* each e[i] is between -8 and 8 */
4253
4254    ge_p3_0(h);
4255    for (i = 1; i < 64; i += 2) {
4256        table_select(&t, i / 2, e[i]);
4257        ge_madd(&r, h, &t);
4258        ge_p1p1_to_p3(h, &r);
4259    }
4260
4261    ge_p3_dbl(&r, h);
4262    ge_p1p1_to_p2(&s, &r);
4263    ge_p2_dbl(&r, &s);
4264    ge_p1p1_to_p2(&s, &r);
4265    ge_p2_dbl(&r, &s);
4266    ge_p1p1_to_p2(&s, &r);
4267    ge_p2_dbl(&r, &s);
4268    ge_p1p1_to_p3(h, &r);
4269
4270    for (i = 0; i < 64; i += 2) {
4271        table_select(&t, i / 2, e[i]);
4272        ge_madd(&r, h, &t);
4273        ge_p1p1_to_p3(h, &r);
4274    }
4275
4276    OPENSSL_cleanse(e, sizeof(e));
4277}
4278
4279#if !defined(BASE_2_51_IMPLEMENTED)
4280/*
4281 * Replace (f,g) with (g,f) if b == 1;
4282 * replace (f,g) with (f,g) if b == 0.
4283 *
4284 * Preconditions: b in {0,1}.
4285 */
4286static void fe_cswap(fe f, fe g, unsigned int b)
4287{
4288    size_t i;
4289
4290    b = 0-b;
4291    for (i = 0; i < 10; i++) {
4292        int32_t x = f[i] ^ g[i];
4293        x &= b;
4294        f[i] ^= x;
4295        g[i] ^= x;
4296    }
4297}
4298
4299/*
4300 * h = f * 121666
4301 *
4302 * Can overlap h with f.
4303 *
4304 * Preconditions:
4305 *    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
4306 *
4307 * Postconditions:
4308 *    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
4309 */
4310static void fe_mul121666(fe h, fe f)
4311{
4312    int32_t f0 = f[0];
4313    int32_t f1 = f[1];
4314    int32_t f2 = f[2];
4315    int32_t f3 = f[3];
4316    int32_t f4 = f[4];
4317    int32_t f5 = f[5];
4318    int32_t f6 = f[6];
4319    int32_t f7 = f[7];
4320    int32_t f8 = f[8];
4321    int32_t f9 = f[9];
4322    int64_t h0 = f0 * (int64_t) 121666;
4323    int64_t h1 = f1 * (int64_t) 121666;
4324    int64_t h2 = f2 * (int64_t) 121666;
4325    int64_t h3 = f3 * (int64_t) 121666;
4326    int64_t h4 = f4 * (int64_t) 121666;
4327    int64_t h5 = f5 * (int64_t) 121666;
4328    int64_t h6 = f6 * (int64_t) 121666;
4329    int64_t h7 = f7 * (int64_t) 121666;
4330    int64_t h8 = f8 * (int64_t) 121666;
4331    int64_t h9 = f9 * (int64_t) 121666;
4332    int64_t carry0;
4333    int64_t carry1;
4334    int64_t carry2;
4335    int64_t carry3;
4336    int64_t carry4;
4337    int64_t carry5;
4338    int64_t carry6;
4339    int64_t carry7;
4340    int64_t carry8;
4341    int64_t carry9;
4342
4343    carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4344    carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4345    carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4346    carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4347    carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4348
4349    carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4350    carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4351    carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4352    carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4353    carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4354
4355    h[0] = (int32_t)h0;
4356    h[1] = (int32_t)h1;
4357    h[2] = (int32_t)h2;
4358    h[3] = (int32_t)h3;
4359    h[4] = (int32_t)h4;
4360    h[5] = (int32_t)h5;
4361    h[6] = (int32_t)h6;
4362    h[7] = (int32_t)h7;
4363    h[8] = (int32_t)h8;
4364    h[9] = (int32_t)h9;
4365}
4366
4367static void x25519_scalar_mult_generic(uint8_t out[32],
4368                                       const uint8_t scalar[32],
4369                                       const uint8_t point[32]) {
4370    fe x1, x2, z2, x3, z3, tmp0, tmp1;
4371    uint8_t e[32];
4372    unsigned swap = 0;
4373    int pos;
4374
4375    memcpy(e, scalar, 32);
4376    e[0] &= 248;
4377    e[31] &= 127;
4378    e[31] |= 64;
4379    fe_frombytes(x1, point);
4380    fe_1(x2);
4381    fe_0(z2);
4382    fe_copy(x3, x1);
4383    fe_1(z3);
4384
4385    for (pos = 254; pos >= 0; --pos) {
4386        unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4387        swap ^= b;
4388        fe_cswap(x2, x3, swap);
4389        fe_cswap(z2, z3, swap);
4390        swap = b;
4391        fe_sub(tmp0, x3, z3);
4392        fe_sub(tmp1, x2, z2);
4393        fe_add(x2, x2, z2);
4394        fe_add(z2, x3, z3);
4395        fe_mul(z3, tmp0, x2);
4396        fe_mul(z2, z2, tmp1);
4397        fe_sq(tmp0, tmp1);
4398        fe_sq(tmp1, x2);
4399        fe_add(x3, z3, z2);
4400        fe_sub(z2, z3, z2);
4401        fe_mul(x2, tmp1, tmp0);
4402        fe_sub(tmp1, tmp1, tmp0);
4403        fe_sq(z2, z2);
4404        fe_mul121666(z3, tmp1);
4405        fe_sq(x3, x3);
4406        fe_add(tmp0, tmp0, z3);
4407        fe_mul(z3, x1, z2);
4408        fe_mul(z2, tmp1, tmp0);
4409    }
4410
4411    fe_invert(z2, z2);
4412    fe_mul(x2, x2, z2);
4413    fe_tobytes(out, x2);
4414
4415    OPENSSL_cleanse(e, sizeof(e));
4416}
4417
4418static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4419                               const uint8_t point[32]) {
4420    x25519_scalar_mult_generic(out, scalar, point);
4421}
4422#endif
4423
4424static void slide(signed char *r, const uint8_t *a)
4425{
4426    int i;
4427    int b;
4428    int k;
4429
4430    for (i = 0; i < 256; ++i) {
4431        r[i] = 1 & (a[i >> 3] >> (i & 7));
4432    }
4433
4434    for (i = 0; i < 256; ++i) {
4435        if (r[i]) {
4436            for (b = 1; b <= 6 && i + b < 256; ++b) {
4437                if (r[i + b]) {
4438                    if (r[i] + (r[i + b] << b) <= 15) {
4439                        r[i] += r[i + b] << b;
4440                        r[i + b] = 0;
4441                    } else if (r[i] - (r[i + b] << b) >= -15) {
4442                        r[i] -= r[i + b] << b;
4443                        for (k = i + b; k < 256; ++k) {
4444                            if (!r[k]) {
4445                                r[k] = 1;
4446                                break;
4447                            }
4448                            r[k] = 0;
4449                        }
4450                    } else {
4451                        break;
4452                    }
4453                }
4454            }
4455        }
4456    }
4457}
4458
4459static const ge_precomp Bi[8] = {
4460    {
4461        {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4462         -11754271, -6079156, 2047605},
4463        {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4464         5043384, 19500929, -15469378},
4465        {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4466         11864899, -24514362, -4438546},
4467    },
4468    {
4469        {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4470         -14772189, 28944400, -1550024},
4471        {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4472         -11775962, 7689662, 11199574},
4473        {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4474         10017326, -17749093, -9920357},
4475    },
4476    {
4477        {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4478         14515107, -15438304, 10819380},
4479        {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4480         12483688, -12668491, 5581306},
4481        {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4482         13850243, -23678021, -15815942},
4483    },
4484    {
4485        {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4486         5230134, -23952439, -15175766},
4487        {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4488         16520125, 30598449, 7715701},
4489        {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4490         1370708, 29794553, -1409300},
4491    },
4492    {
4493        {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4494         -1361450, -13062696, 13821877},
4495        {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4496         -7212327, 18853322, -14220951},
4497        {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4498         -10431137, 2207753, -3209784},
4499    },
4500    {
4501        {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4502         -663000, -31111463, -16132436},
4503        {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4504         15725684, 171356, 6466918},
4505        {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4506         -14088058, -30714912, 16193877},
4507    },
4508    {
4509        {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4510         4729455, -18074513, 9256800},
4511        {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4512         9761698, -19827198, 630305},
4513        {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4514         -15960994, -2449256, -14291300},
4515    },
4516    {
4517        {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4518         15033784, 25105118, -7894876},
4519        {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4520         1573892, -2625887, 2198790, -15804619},
4521        {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4522         -16236442, -32461234, -12290683},
4523    },
4524};
4525
4526/*
4527 * r = a * A + b * B
4528 *
4529 * where a = a[0]+256*a[1]+...+256^31 a[31].
4530 * and b = b[0]+256*b[1]+...+256^31 b[31].
4531 * B is the Ed25519 base point (x,4/5) with x positive.
4532 */
4533static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
4534                                         const ge_p3 *A, const uint8_t *b)
4535{
4536    signed char aslide[256];
4537    signed char bslide[256];
4538    ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4539    ge_p1p1 t;
4540    ge_p3 u;
4541    ge_p3 A2;
4542    int i;
4543
4544    slide(aslide, a);
4545    slide(bslide, b);
4546
4547    ge_p3_to_cached(&Ai[0], A);
4548    ge_p3_dbl(&t, A);
4549    ge_p1p1_to_p3(&A2, &t);
4550    ge_add(&t, &A2, &Ai[0]);
4551    ge_p1p1_to_p3(&u, &t);
4552    ge_p3_to_cached(&Ai[1], &u);
4553    ge_add(&t, &A2, &Ai[1]);
4554    ge_p1p1_to_p3(&u, &t);
4555    ge_p3_to_cached(&Ai[2], &u);
4556    ge_add(&t, &A2, &Ai[2]);
4557    ge_p1p1_to_p3(&u, &t);
4558    ge_p3_to_cached(&Ai[3], &u);
4559    ge_add(&t, &A2, &Ai[3]);
4560    ge_p1p1_to_p3(&u, &t);
4561    ge_p3_to_cached(&Ai[4], &u);
4562    ge_add(&t, &A2, &Ai[4]);
4563    ge_p1p1_to_p3(&u, &t);
4564    ge_p3_to_cached(&Ai[5], &u);
4565    ge_add(&t, &A2, &Ai[5]);
4566    ge_p1p1_to_p3(&u, &t);
4567    ge_p3_to_cached(&Ai[6], &u);
4568    ge_add(&t, &A2, &Ai[6]);
4569    ge_p1p1_to_p3(&u, &t);
4570    ge_p3_to_cached(&Ai[7], &u);
4571
4572    ge_p2_0(r);
4573
4574    for (i = 255; i >= 0; --i) {
4575        if (aslide[i] || bslide[i]) {
4576            break;
4577        }
4578    }
4579
4580    for (; i >= 0; --i) {
4581        ge_p2_dbl(&t, r);
4582
4583        if (aslide[i] > 0) {
4584            ge_p1p1_to_p3(&u, &t);
4585            ge_add(&t, &u, &Ai[aslide[i] / 2]);
4586        } else if (aslide[i] < 0) {
4587            ge_p1p1_to_p3(&u, &t);
4588            ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4589        }
4590
4591        if (bslide[i] > 0) {
4592            ge_p1p1_to_p3(&u, &t);
4593            ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4594        } else if (bslide[i] < 0) {
4595            ge_p1p1_to_p3(&u, &t);
4596            ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4597        }
4598
4599        ge_p1p1_to_p2(r, &t);
4600    }
4601}
4602
4603/*
4604 * The set of scalars is \Z/l
4605 * where l = 2^252 + 27742317777372353535851937790883648493.
4606 *
4607 * Input:
4608 *   s[0]+256*s[1]+...+256^63*s[63] = s
4609 *
4610 * Output:
4611 *   s[0]+256*s[1]+...+256^31*s[31] = s mod l
4612 *   where l = 2^252 + 27742317777372353535851937790883648493.
4613 *   Overwrites s in place.
4614*/
4615static void x25519_sc_reduce(uint8_t *s)
4616{
4617    int64_t s0  = kBottom21Bits &  load_3(s);
4618    int64_t s1  = kBottom21Bits & (load_4(s +  2) >> 5);
4619    int64_t s2  = kBottom21Bits & (load_3(s +  5) >> 2);
4620    int64_t s3  = kBottom21Bits & (load_4(s +  7) >> 7);
4621    int64_t s4  = kBottom21Bits & (load_4(s + 10) >> 4);
4622    int64_t s5  = kBottom21Bits & (load_3(s + 13) >> 1);
4623    int64_t s6  = kBottom21Bits & (load_4(s + 15) >> 6);
4624    int64_t s7  = kBottom21Bits & (load_3(s + 18) >> 3);
4625    int64_t s8  = kBottom21Bits &  load_3(s + 21);
4626    int64_t s9  = kBottom21Bits & (load_4(s + 23) >> 5);
4627    int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4628    int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4629    int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4630    int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4631    int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4632    int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4633    int64_t s16 = kBottom21Bits &  load_3(s + 42);
4634    int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4635    int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4636    int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4637    int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4638    int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4639    int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4640    int64_t s23 =                 (load_4(s + 60) >> 3);
4641    int64_t carry0;
4642    int64_t carry1;
4643    int64_t carry2;
4644    int64_t carry3;
4645    int64_t carry4;
4646    int64_t carry5;
4647    int64_t carry6;
4648    int64_t carry7;
4649    int64_t carry8;
4650    int64_t carry9;
4651    int64_t carry10;
4652    int64_t carry11;
4653    int64_t carry12;
4654    int64_t carry13;
4655    int64_t carry14;
4656    int64_t carry15;
4657    int64_t carry16;
4658
4659    s11 += s23 * 666643;
4660    s12 += s23 * 470296;
4661    s13 += s23 * 654183;
4662    s14 -= s23 * 997805;
4663    s15 += s23 * 136657;
4664    s16 -= s23 * 683901;
4665    s23  = 0;
4666
4667    s10 += s22 * 666643;
4668    s11 += s22 * 470296;
4669    s12 += s22 * 654183;
4670    s13 -= s22 * 997805;
4671    s14 += s22 * 136657;
4672    s15 -= s22 * 683901;
4673    s22  = 0;
4674
4675    s9  += s21 * 666643;
4676    s10 += s21 * 470296;
4677    s11 += s21 * 654183;
4678    s12 -= s21 * 997805;
4679    s13 += s21 * 136657;
4680    s14 -= s21 * 683901;
4681    s21  = 0;
4682
4683    s8  += s20 * 666643;
4684    s9  += s20 * 470296;
4685    s10 += s20 * 654183;
4686    s11 -= s20 * 997805;
4687    s12 += s20 * 136657;
4688    s13 -= s20 * 683901;
4689    s20  = 0;
4690
4691    s7  += s19 * 666643;
4692    s8  += s19 * 470296;
4693    s9  += s19 * 654183;
4694    s10 -= s19 * 997805;
4695    s11 += s19 * 136657;
4696    s12 -= s19 * 683901;
4697    s19  = 0;
4698
4699    s6  += s18 * 666643;
4700    s7  += s18 * 470296;
4701    s8  += s18 * 654183;
4702    s9  -= s18 * 997805;
4703    s10 += s18 * 136657;
4704    s11 -= s18 * 683901;
4705    s18  = 0;
4706
4707    carry6 = (s6 + (1 << 20)) >> 21;
4708    s7  += carry6;
4709    s6  -= carry6 * (1 << 21);
4710    carry8 = (s8 + (1 << 20)) >> 21;
4711    s9  += carry8;
4712    s8  -= carry8 * (1 << 21);
4713    carry10 = (s10 + (1 << 20)) >> 21;
4714    s11 += carry10;
4715    s10 -= carry10 * (1 << 21);
4716    carry12 = (s12 + (1 << 20)) >> 21;
4717    s13 += carry12;
4718    s12 -= carry12 * (1 << 21);
4719    carry14 = (s14 + (1 << 20)) >> 21;
4720    s15 += carry14;
4721    s14 -= carry14 * (1 << 21);
4722    carry16 = (s16 + (1 << 20)) >> 21;
4723    s17 += carry16;
4724    s16 -= carry16 * (1 << 21);
4725
4726    carry7 = (s7 + (1 << 20)) >> 21;
4727    s8  += carry7;
4728    s7  -= carry7 * (1 << 21);
4729    carry9 = (s9 + (1 << 20)) >> 21;
4730    s10 += carry9;
4731    s9  -= carry9 * (1 << 21);
4732    carry11 = (s11 + (1 << 20)) >> 21;
4733    s12 += carry11;
4734    s11 -= carry11 * (1 << 21);
4735    carry13 = (s13 + (1 << 20)) >> 21;
4736    s14 += carry13;
4737    s13 -= carry13 * (1 << 21);
4738    carry15 = (s15 + (1 << 20)) >> 21;
4739    s16 += carry15;
4740    s15 -= carry15 * (1 << 21);
4741
4742    s5  += s17 * 666643;
4743    s6  += s17 * 470296;
4744    s7  += s17 * 654183;
4745    s8  -= s17 * 997805;
4746    s9  += s17 * 136657;
4747    s10 -= s17 * 683901;
4748    s17  = 0;
4749
4750    s4  += s16 * 666643;
4751    s5  += s16 * 470296;
4752    s6  += s16 * 654183;
4753    s7  -= s16 * 997805;
4754    s8  += s16 * 136657;
4755    s9  -= s16 * 683901;
4756    s16  = 0;
4757
4758    s3  += s15 * 666643;
4759    s4  += s15 * 470296;
4760    s5  += s15 * 654183;
4761    s6  -= s15 * 997805;
4762    s7  += s15 * 136657;
4763    s8  -= s15 * 683901;
4764    s15  = 0;
4765
4766    s2  += s14 * 666643;
4767    s3  += s14 * 470296;
4768    s4  += s14 * 654183;
4769    s5  -= s14 * 997805;
4770    s6  += s14 * 136657;
4771    s7  -= s14 * 683901;
4772    s14  = 0;
4773
4774    s1  += s13 * 666643;
4775    s2  += s13 * 470296;
4776    s3  += s13 * 654183;
4777    s4  -= s13 * 997805;
4778    s5  += s13 * 136657;
4779    s6  -= s13 * 683901;
4780    s13  = 0;
4781
4782    s0  += s12 * 666643;
4783    s1  += s12 * 470296;
4784    s2  += s12 * 654183;
4785    s3  -= s12 * 997805;
4786    s4  += s12 * 136657;
4787    s5  -= s12 * 683901;
4788    s12  = 0;
4789
4790    carry0 = (s0 + (1 << 20)) >> 21;
4791    s1  += carry0;
4792    s0  -= carry0 * (1 << 21);
4793    carry2 = (s2 + (1 << 20)) >> 21;
4794    s3  += carry2;
4795    s2  -= carry2 * (1 << 21);
4796    carry4 = (s4 + (1 << 20)) >> 21;
4797    s5  += carry4;
4798    s4  -= carry4 * (1 << 21);
4799    carry6 = (s6 + (1 << 20)) >> 21;
4800    s7 += carry6;
4801    s6 -= carry6 * (1 << 21);
4802    carry8 = (s8 + (1 << 20)) >> 21;
4803    s9  += carry8;
4804    s8  -= carry8 * (1 << 21);
4805    carry10 = (s10 + (1 << 20)) >> 21;
4806    s11 += carry10;
4807    s10 -= carry10 * (1 << 21);
4808
4809    carry1 = (s1 + (1 << 20)) >> 21;
4810    s2  += carry1;
4811    s1  -= carry1 * (1 << 21);
4812    carry3 = (s3 + (1 << 20)) >> 21;
4813    s4  += carry3;
4814    s3  -= carry3 * (1 << 21);
4815    carry5 = (s5 + (1 << 20)) >> 21;
4816    s6  += carry5;
4817    s5  -= carry5 * (1 << 21);
4818    carry7 = (s7 + (1 << 20)) >> 21;
4819    s8  += carry7;
4820    s7  -= carry7 * (1 << 21);
4821    carry9 = (s9 + (1 << 20)) >> 21;
4822    s10 += carry9;
4823    s9  -= carry9 * (1 << 21);
4824    carry11 = (s11 + (1 << 20)) >> 21;
4825    s12 += carry11;
4826    s11 -= carry11 * (1 << 21);
4827
4828    s0  += s12 * 666643;
4829    s1  += s12 * 470296;
4830    s2  += s12 * 654183;
4831    s3  -= s12 * 997805;
4832    s4  += s12 * 136657;
4833    s5  -= s12 * 683901;
4834    s12  = 0;
4835
4836    carry0 = s0 >> 21;
4837    s1  += carry0;
4838    s0  -= carry0 * (1 << 21);
4839    carry1 = s1 >> 21;
4840    s2  += carry1;
4841    s1  -= carry1 * (1 << 21);
4842    carry2 = s2 >> 21;
4843    s3  += carry2;
4844    s2  -= carry2 * (1 << 21);
4845    carry3 = s3 >> 21;
4846    s4  += carry3;
4847    s3  -= carry3 * (1 << 21);
4848    carry4 = s4 >> 21;
4849    s5  += carry4;
4850    s4  -= carry4 * (1 << 21);
4851    carry5 = s5 >> 21;
4852    s6  += carry5;
4853    s5  -= carry5 * (1 << 21);
4854    carry6 = s6 >> 21;
4855    s7  += carry6;
4856    s6  -= carry6 * (1 << 21);
4857    carry7 = s7 >> 21;
4858    s8  += carry7;
4859    s7  -= carry7 * (1 << 21);
4860    carry8 = s8 >> 21;
4861    s9  += carry8;
4862    s8  -= carry8 * (1 << 21);
4863    carry9 = s9 >> 21;
4864    s10 += carry9;
4865    s9  -= carry9 * (1 << 21);
4866    carry10 = s10 >> 21;
4867    s11 += carry10;
4868    s10 -= carry10 * (1 << 21);
4869    carry11 = s11 >> 21;
4870    s12 += carry11;
4871    s11 -= carry11 * (1 << 21);
4872
4873    s0  += s12 * 666643;
4874    s1  += s12 * 470296;
4875    s2  += s12 * 654183;
4876    s3  -= s12 * 997805;
4877    s4  += s12 * 136657;
4878    s5  -= s12 * 683901;
4879    s12  = 0;
4880
4881    carry0 = s0 >> 21;
4882    s1  += carry0;
4883    s0  -= carry0 * (1 << 21);
4884    carry1 = s1 >> 21;
4885    s2  += carry1;
4886    s1  -= carry1 * (1 << 21);
4887    carry2 = s2 >> 21;
4888    s3  += carry2;
4889    s2  -= carry2 * (1 << 21);
4890    carry3 = s3 >> 21;
4891    s4  += carry3;
4892    s3  -= carry3 * (1 << 21);
4893    carry4 = s4 >> 21;
4894    s5  += carry4;
4895    s4  -= carry4 * (1 << 21);
4896    carry5 = s5 >> 21;
4897    s6  += carry5;
4898    s5  -= carry5 * (1 << 21);
4899    carry6 = s6 >> 21;
4900    s7  += carry6;
4901    s6  -= carry6 * (1 << 21);
4902    carry7 = s7 >> 21;
4903    s8  += carry7;
4904    s7  -= carry7 * (1 << 21);
4905    carry8 = s8 >> 21;
4906    s9  += carry8;
4907    s8  -= carry8 * (1 << 21);
4908    carry9 = s9 >> 21;
4909    s10 += carry9;
4910    s9  -= carry9 * (1 << 21);
4911    carry10 = s10 >> 21;
4912    s11 += carry10;
4913    s10 -= carry10 * (1 << 21);
4914
4915    s[ 0] = (uint8_t) (s0  >>  0);
4916    s[ 1] = (uint8_t) (s0  >>  8);
4917    s[ 2] = (uint8_t)((s0  >> 16) | (s1  <<  5));
4918    s[ 3] = (uint8_t) (s1  >>  3);
4919    s[ 4] = (uint8_t) (s1  >> 11);
4920    s[ 5] = (uint8_t)((s1  >> 19) | (s2  <<  2));
4921    s[ 6] = (uint8_t) (s2  >>  6);
4922    s[ 7] = (uint8_t)((s2  >> 14) | (s3  <<  7));
4923    s[ 8] = (uint8_t) (s3  >>  1);
4924    s[ 9] = (uint8_t) (s3  >>  9);
4925    s[10] = (uint8_t)((s3  >> 17) | (s4  <<  4));
4926    s[11] = (uint8_t) (s4  >>  4);
4927    s[12] = (uint8_t) (s4  >> 12);
4928    s[13] = (uint8_t)((s4  >> 20) | (s5  <<  1));
4929    s[14] = (uint8_t) (s5  >>  7);
4930    s[15] = (uint8_t)((s5  >> 15) | (s6  <<  6));
4931    s[16] = (uint8_t) (s6  >>  2);
4932    s[17] = (uint8_t) (s6  >> 10);
4933    s[18] = (uint8_t)((s6  >> 18) | (s7  <<  3));
4934    s[19] = (uint8_t) (s7  >>  5);
4935    s[20] = (uint8_t) (s7  >> 13);
4936    s[21] = (uint8_t) (s8  >>  0);
4937    s[22] = (uint8_t) (s8  >>  8);
4938    s[23] = (uint8_t)((s8  >> 16) | (s9  <<  5));
4939    s[24] = (uint8_t) (s9  >>  3);
4940    s[25] = (uint8_t) (s9  >> 11);
4941    s[26] = (uint8_t)((s9  >> 19) | (s10 <<  2));
4942    s[27] = (uint8_t) (s10 >>  6);
4943    s[28] = (uint8_t)((s10 >> 14) | (s11 <<  7));
4944    s[29] = (uint8_t) (s11 >>  1);
4945    s[30] = (uint8_t) (s11 >>  9);
4946    s[31] = (uint8_t) (s11 >> 17);
4947}
4948
4949/*
4950 * Input:
4951 *   a[0]+256*a[1]+...+256^31*a[31] = a
4952 *   b[0]+256*b[1]+...+256^31*b[31] = b
4953 *   c[0]+256*c[1]+...+256^31*c[31] = c
4954 *
4955 * Output:
4956 *   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
4957 *   where l = 2^252 + 27742317777372353535851937790883648493.
4958 */
4959static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
4960                      const uint8_t *c)
4961{
4962    int64_t a0  = kBottom21Bits &  load_3(a);
4963    int64_t a1  = kBottom21Bits & (load_4(a +  2) >> 5);
4964    int64_t a2  = kBottom21Bits & (load_3(a +  5) >> 2);
4965    int64_t a3  = kBottom21Bits & (load_4(a +  7) >> 7);
4966    int64_t a4  = kBottom21Bits & (load_4(a + 10) >> 4);
4967    int64_t a5  = kBottom21Bits & (load_3(a + 13) >> 1);
4968    int64_t a6  = kBottom21Bits & (load_4(a + 15) >> 6);
4969    int64_t a7  = kBottom21Bits & (load_3(a + 18) >> 3);
4970    int64_t a8  = kBottom21Bits &  load_3(a + 21);
4971    int64_t a9  = kBottom21Bits & (load_4(a + 23) >> 5);
4972    int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4973    int64_t a11 =                 (load_4(a + 28) >> 7);
4974    int64_t b0  = kBottom21Bits &  load_3(b);
4975    int64_t b1  = kBottom21Bits & (load_4(b +  2) >> 5);
4976    int64_t b2  = kBottom21Bits & (load_3(b +  5) >> 2);
4977    int64_t b3  = kBottom21Bits & (load_4(b +  7) >> 7);
4978    int64_t b4  = kBottom21Bits & (load_4(b + 10) >> 4);
4979    int64_t b5  = kBottom21Bits & (load_3(b + 13) >> 1);
4980    int64_t b6  = kBottom21Bits & (load_4(b + 15) >> 6);
4981    int64_t b7  = kBottom21Bits & (load_3(b + 18) >> 3);
4982    int64_t b8  = kBottom21Bits &  load_3(b + 21);
4983    int64_t b9  = kBottom21Bits & (load_4(b + 23) >> 5);
4984    int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4985    int64_t b11 =                 (load_4(b + 28) >> 7);
4986    int64_t c0  = kBottom21Bits &  load_3(c);
4987    int64_t c1  = kBottom21Bits & (load_4(c +  2) >> 5);
4988    int64_t c2  = kBottom21Bits & (load_3(c +  5) >> 2);
4989    int64_t c3  = kBottom21Bits & (load_4(c +  7) >> 7);
4990    int64_t c4  = kBottom21Bits & (load_4(c + 10) >> 4);
4991    int64_t c5  = kBottom21Bits & (load_3(c + 13) >> 1);
4992    int64_t c6  = kBottom21Bits & (load_4(c + 15) >> 6);
4993    int64_t c7  = kBottom21Bits & (load_3(c + 18) >> 3);
4994    int64_t c8  = kBottom21Bits &  load_3(c + 21);
4995    int64_t c9  = kBottom21Bits & (load_4(c + 23) >> 5);
4996    int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
4997    int64_t c11 =                 (load_4(c + 28) >> 7);
4998    int64_t s0;
4999    int64_t s1;
5000    int64_t s2;
5001    int64_t s3;
5002    int64_t s4;
5003    int64_t s5;
5004    int64_t s6;
5005    int64_t s7;
5006    int64_t s8;
5007    int64_t s9;
5008    int64_t s10;
5009    int64_t s11;
5010    int64_t s12;
5011    int64_t s13;
5012    int64_t s14;
5013    int64_t s15;
5014    int64_t s16;
5015    int64_t s17;
5016    int64_t s18;
5017    int64_t s19;
5018    int64_t s20;
5019    int64_t s21;
5020    int64_t s22;
5021    int64_t s23;
5022    int64_t carry0;
5023    int64_t carry1;
5024    int64_t carry2;
5025    int64_t carry3;
5026    int64_t carry4;
5027    int64_t carry5;
5028    int64_t carry6;
5029    int64_t carry7;
5030    int64_t carry8;
5031    int64_t carry9;
5032    int64_t carry10;
5033    int64_t carry11;
5034    int64_t carry12;
5035    int64_t carry13;
5036    int64_t carry14;
5037    int64_t carry15;
5038    int64_t carry16;
5039    int64_t carry17;
5040    int64_t carry18;
5041    int64_t carry19;
5042    int64_t carry20;
5043    int64_t carry21;
5044    int64_t carry22;
5045
5046    s0  = c0   +   a0 * b0;
5047    s1  = c1   +   a0 * b1   +   a1 * b0;
5048    s2  = c2   +   a0 * b2   +   a1 * b1   +   a2 * b0;
5049    s3  = c3   +   a0 * b3   +   a1 * b2   +   a2 * b1  +   a3 * b0;
5050    s4  = c4   +   a0 * b4   +   a1 * b3   +   a2 * b2  +   a3 * b1  +   a4 * b0;
5051    s5  = c5   +   a0 * b5   +   a1 * b4   +   a2 * b3  +   a3 * b2  +   a4 * b1  +   a5 * b0;
5052    s6  = c6   +   a0 * b6   +   a1 * b5   +   a2 * b4  +   a3 * b3  +   a4 * b2  +   a5 * b1 +   a6 * b0;
5053    s7  = c7   +   a0 * b7   +   a1 * b6   +   a2 * b5  +   a3 * b4  +   a4 * b3  +   a5 * b2 +   a6 * b1   +   a7 * b0;
5054    s8  = c8   +   a0 * b8   +   a1 * b7   +   a2 * b6  +   a3 * b5  +   a4 * b4  +   a5 * b3 +   a6 * b2   +   a7 * b1   +   a8 * b0;
5055    s9  = c9   +   a0 * b9   +   a1 * b8   +   a2 * b7  +   a3 * b6  +   a4 * b5  +   a5 * b4 +   a6 * b3   +   a7 * b2   +   a8 * b1  +   a9 * b0;
5056    s10 = c10  +   a0 * b10  +   a1 * b9   +   a2 * b8  +   a3 * b7  +   a4 * b6  +   a5 * b5 +   a6 * b4   +   a7 * b3   +   a8 * b2  +   a9 * b1  +  a10 * b0;
5057    s11 = c11  +   a0 * b11  +   a1 * b10  +   a2 * b9  +   a3 * b8  +   a4 * b7  +   a5 * b6 +   a6 * b5   +   a7 * b4   +   a8 * b3  +   a9 * b2  +  a10 * b1  +  a11 * b0;
5058    s12 =          a1 * b11  +   a2 * b10  +   a3 * b9  +   a4 * b8  +   a5 * b7  +   a6 * b6 +   a7 * b5   +   a8 * b4   +   a9 * b3  +  a10 * b2  +  a11 * b1;
5059    s13 =          a2 * b11  +   a3 * b10  +   a4 * b9  +   a5 * b8  +   a6 * b7  +   a7 * b6 +   a8 * b5   +   a9 * b4   +  a10 * b3  +  a11 * b2;
5060    s14 =          a3 * b11  +   a4 * b10  +   a5 * b9  +   a6 * b8  +   a7 * b7  +   a8 * b6 +   a9 * b5   +  a10 * b4   +  a11 * b3;
5061    s15 =          a4 * b11  +   a5 * b10  +   a6 * b9  +   a7 * b8  +   a8 * b7  +   a9 * b6 +  a10 * b5   +  a11 * b4;
5062    s16 =          a5 * b11  +   a6 * b10  +   a7 * b9  +   a8 * b8  +   a9 * b7  +  a10 * b6 +  a11 * b5;
5063    s17 =          a6 * b11  +   a7 * b10  +   a8 * b9  +   a9 * b8  +  a10 * b7  +  a11 * b6;
5064    s18 =          a7 * b11  +   a8 * b10  +   a9 * b9  +  a10 * b8  +  a11 * b7;
5065    s19 =          a8 * b11  +   a9 * b10  +  a10 * b9  +  a11 * b8;
5066    s20 =          a9 * b11  +  a10 * b10  +  a11 * b9;
5067    s21 =         a10 * b11  +  a11 * b10;
5068    s22 =         a11 * b11;
5069    s23 =         0;
5070
5071    carry0 = (s0 + (1 << 20)) >> 21;
5072    s1  += carry0;
5073    s0  -= carry0 * (1 << 21);
5074    carry2 = (s2 + (1 << 20)) >> 21;
5075    s3  += carry2;
5076    s2  -= carry2 * (1 << 21);
5077    carry4 = (s4 + (1 << 20)) >> 21;
5078    s5  += carry4;
5079    s4  -= carry4 * (1 << 21);
5080    carry6 = (s6 + (1 << 20)) >> 21;
5081    s7  += carry6;
5082    s6  -= carry6 * (1 << 21);
5083    carry8 = (s8 + (1 << 20)) >> 21;
5084    s9  += carry8;
5085    s8  -= carry8 * (1 << 21);
5086    carry10 = (s10 + (1 << 20)) >> 21;
5087    s11 += carry10;
5088    s10 -= carry10 * (1 << 21);
5089    carry12 = (s12 + (1 << 20)) >> 21;
5090    s13 += carry12;
5091    s12 -= carry12 * (1 << 21);
5092    carry14 = (s14 + (1 << 20)) >> 21;
5093    s15 += carry14;
5094    s14 -= carry14 * (1 << 21);
5095    carry16 = (s16 + (1 << 20)) >> 21;
5096    s17 += carry16;
5097    s16 -= carry16 * (1 << 21);
5098    carry18 = (s18 + (1 << 20)) >> 21;
5099    s19 += carry18;
5100    s18 -= carry18 * (1 << 21);
5101    carry20 = (s20 + (1 << 20)) >> 21;
5102    s21 += carry20;
5103    s20 -= carry20 * (1 << 21);
5104    carry22 = (s22 + (1 << 20)) >> 21;
5105    s23 += carry22;
5106    s22 -= carry22 * (1 << 21);
5107
5108    carry1 = (s1 + (1 << 20)) >> 21;
5109    s2  += carry1;
5110    s1  -= carry1 * (1 << 21);
5111    carry3 = (s3 + (1 << 20)) >> 21;
5112    s4  += carry3;
5113    s3  -= carry3 * (1 << 21);
5114    carry5 = (s5 + (1 << 20)) >> 21;
5115    s6  += carry5;
5116    s5  -= carry5 * (1 << 21);
5117    carry7 = (s7 + (1 << 20)) >> 21;
5118    s8  += carry7;
5119    s7  -= carry7 * (1 << 21);
5120    carry9 = (s9 + (1 << 20)) >> 21;
5121    s10 += carry9;
5122    s9  -= carry9 * (1 << 21);
5123    carry11 = (s11 + (1 << 20)) >> 21;
5124    s12 += carry11;
5125    s11 -= carry11 * (1 << 21);
5126    carry13 = (s13 + (1 << 20)) >> 21;
5127    s14 += carry13;
5128    s13 -= carry13 * (1 << 21);
5129    carry15 = (s15 + (1 << 20)) >> 21;
5130    s16 += carry15;
5131    s15 -= carry15 * (1 << 21);
5132    carry17 = (s17 + (1 << 20)) >> 21;
5133    s18 += carry17;
5134    s17 -= carry17 * (1 << 21);
5135    carry19 = (s19 + (1 << 20)) >> 21;
5136    s20 += carry19;
5137    s19 -= carry19 * (1 << 21);
5138    carry21 = (s21 + (1 << 20)) >> 21;
5139    s22 += carry21;
5140    s21 -= carry21 * (1 << 21);
5141
5142    s11 += s23 * 666643;
5143    s12 += s23 * 470296;
5144    s13 += s23 * 654183;
5145    s14 -= s23 * 997805;
5146    s15 += s23 * 136657;
5147    s16 -= s23 * 683901;
5148    s23  = 0;
5149
5150    s10 += s22 * 666643;
5151    s11 += s22 * 470296;
5152    s12 += s22 * 654183;
5153    s13 -= s22 * 997805;
5154    s14 += s22 * 136657;
5155    s15 -= s22 * 683901;
5156    s22  = 0;
5157
5158    s9  += s21 * 666643;
5159    s10 += s21 * 470296;
5160    s11 += s21 * 654183;
5161    s12 -= s21 * 997805;
5162    s13 += s21 * 136657;
5163    s14 -= s21 * 683901;
5164    s21  = 0;
5165
5166    s8  += s20 * 666643;
5167    s9  += s20 * 470296;
5168    s10 += s20 * 654183;
5169    s11 -= s20 * 997805;
5170    s12 += s20 * 136657;
5171    s13 -= s20 * 683901;
5172    s20  = 0;
5173
5174    s7  += s19 * 666643;
5175    s8  += s19 * 470296;
5176    s9  += s19 * 654183;
5177    s10 -= s19 * 997805;
5178    s11 += s19 * 136657;
5179    s12 -= s19 * 683901;
5180    s19  = 0;
5181
5182    s6  += s18 * 666643;
5183    s7  += s18 * 470296;
5184    s8  += s18 * 654183;
5185    s9  -= s18 * 997805;
5186    s10 += s18 * 136657;
5187    s11 -= s18 * 683901;
5188    s18  = 0;
5189
5190    carry6 = (s6 + (1 << 20)) >> 21;
5191    s7  += carry6;
5192    s6  -= carry6 * (1 << 21);
5193    carry8 = (s8 + (1 << 20)) >> 21;
5194    s9  += carry8;
5195    s8  -= carry8 * (1 << 21);
5196    carry10 = (s10 + (1 << 20)) >> 21;
5197    s11 += carry10;
5198    s10 -= carry10 * (1 << 21);
5199    carry12 = (s12 + (1 << 20)) >> 21;
5200    s13 += carry12;
5201    s12 -= carry12 * (1 << 21);
5202    carry14 = (s14 + (1 << 20)) >> 21;
5203    s15 += carry14;
5204    s14 -= carry14 * (1 << 21);
5205    carry16 = (s16 + (1 << 20)) >> 21;
5206    s17 += carry16;
5207    s16 -= carry16 * (1 << 21);
5208
5209    carry7 = (s7 + (1 << 20)) >> 21;
5210    s8  += carry7;
5211    s7  -= carry7 * (1 << 21);
5212    carry9 = (s9 + (1 << 20)) >> 21;
5213    s10 += carry9;
5214    s9  -= carry9 * (1 << 21);
5215    carry11 = (s11 + (1 << 20)) >> 21;
5216    s12 += carry11;
5217    s11 -= carry11 * (1 << 21);
5218    carry13 = (s13 + (1 << 20)) >> 21;
5219    s14 += carry13;
5220    s13 -= carry13 * (1 << 21);
5221    carry15 = (s15 + (1 << 20)) >> 21;
5222    s16 += carry15;
5223    s15 -= carry15 * (1 << 21);
5224
5225    s5  += s17 * 666643;
5226    s6  += s17 * 470296;
5227    s7  += s17 * 654183;
5228    s8  -= s17 * 997805;
5229    s9  += s17 * 136657;
5230    s10 -= s17 * 683901;
5231    s17  = 0;
5232
5233    s4  += s16 * 666643;
5234    s5  += s16 * 470296;
5235    s6  += s16 * 654183;
5236    s7  -= s16 * 997805;
5237    s8  += s16 * 136657;
5238    s9  -= s16 * 683901;
5239    s16  = 0;
5240
5241    s3  += s15 * 666643;
5242    s4  += s15 * 470296;
5243    s5  += s15 * 654183;
5244    s6  -= s15 * 997805;
5245    s7  += s15 * 136657;
5246    s8  -= s15 * 683901;
5247    s15  = 0;
5248
5249    s2  += s14 * 666643;
5250    s3  += s14 * 470296;
5251    s4  += s14 * 654183;
5252    s5  -= s14 * 997805;
5253    s6  += s14 * 136657;
5254    s7  -= s14 * 683901;
5255    s14  = 0;
5256
5257    s1  += s13 * 666643;
5258    s2  += s13 * 470296;
5259    s3  += s13 * 654183;
5260    s4  -= s13 * 997805;
5261    s5  += s13 * 136657;
5262    s6  -= s13 * 683901;
5263    s13  = 0;
5264
5265    s0  += s12 * 666643;
5266    s1  += s12 * 470296;
5267    s2  += s12 * 654183;
5268    s3  -= s12 * 997805;
5269    s4  += s12 * 136657;
5270    s5  -= s12 * 683901;
5271    s12 = 0;
5272
5273    carry0 = (s0 + (1 << 20)) >> 21;
5274    s1  += carry0;
5275    s0  -= carry0 * (1 << 21);
5276    carry2 = (s2 + (1 << 20)) >> 21;
5277    s3  += carry2;
5278    s2  -= carry2 * (1 << 21);
5279    carry4 = (s4 + (1 << 20)) >> 21;
5280    s5  += carry4;
5281    s4  -= carry4 * (1 << 21);
5282    carry6 = (s6 + (1 << 20)) >> 21;
5283    s7  += carry6;
5284    s6  -= carry6 * (1 << 21);
5285    carry8 = (s8 + (1 << 20)) >> 21;
5286    s9  += carry8;
5287    s8  -= carry8 * (1 << 21);
5288    carry10 = (s10 + (1 << 20)) >> 21;
5289    s11 += carry10;
5290    s10 -= carry10 * (1 << 21);
5291
5292    carry1 = (s1 + (1 << 20)) >> 21;
5293    s2  += carry1;
5294    s1  -= carry1 * (1 << 21);
5295    carry3 = (s3 + (1 << 20)) >> 21;
5296    s4  += carry3;
5297    s3  -= carry3 * (1 << 21);
5298    carry5 = (s5 + (1 << 20)) >> 21;
5299    s6  += carry5;
5300    s5  -= carry5 * (1 << 21);
5301    carry7 = (s7 + (1 << 20)) >> 21;
5302    s8  += carry7;
5303    s7  -= carry7 * (1 << 21);
5304    carry9 = (s9 + (1 << 20)) >> 21;
5305    s10 += carry9;
5306    s9  -= carry9 * (1 << 21);
5307    carry11 = (s11 + (1 << 20)) >> 21;
5308    s12 += carry11;
5309    s11 -= carry11 * (1 << 21);
5310
5311    s0  += s12 * 666643;
5312    s1  += s12 * 470296;
5313    s2  += s12 * 654183;
5314    s3  -= s12 * 997805;
5315    s4  += s12 * 136657;
5316    s5  -= s12 * 683901;
5317    s12  = 0;
5318
5319    carry0 = s0 >> 21;
5320    s1  += carry0;
5321    s0  -= carry0 * (1 << 21);
5322    carry1 = s1 >> 21;
5323    s2  += carry1;
5324    s1  -= carry1 * (1 << 21);
5325    carry2 = s2 >> 21;
5326    s3  += carry2;
5327    s2  -= carry2 * (1 << 21);
5328    carry3 = s3 >> 21;
5329    s4  += carry3;
5330    s3  -= carry3 * (1 << 21);
5331    carry4 = s4 >> 21;
5332    s5  += carry4;
5333    s4  -= carry4 * (1 << 21);
5334    carry5 = s5 >> 21;
5335    s6  += carry5;
5336    s5  -= carry5 * (1 << 21);
5337    carry6 = s6 >> 21;
5338    s7  += carry6;
5339    s6  -= carry6 * (1 << 21);
5340    carry7 = s7 >> 21;
5341    s8  += carry7;
5342    s7  -= carry7 * (1 << 21);
5343    carry8 = s8 >> 21;
5344    s9  += carry8;
5345    s8  -= carry8 * (1 << 21);
5346    carry9 = s9 >> 21;
5347    s10 += carry9;
5348    s9  -= carry9 * (1 << 21);
5349    carry10 = s10 >> 21;
5350    s11 += carry10;
5351    s10 -= carry10 * (1 << 21);
5352    carry11 = s11 >> 21;
5353    s12 += carry11;
5354    s11 -= carry11 * (1 << 21);
5355
5356    s0  += s12 * 666643;
5357    s1  += s12 * 470296;
5358    s2  += s12 * 654183;
5359    s3  -= s12 * 997805;
5360    s4  += s12 * 136657;
5361    s5  -= s12 * 683901;
5362    s12  = 0;
5363
5364    carry0 = s0 >> 21;
5365    s1  += carry0;
5366    s0  -= carry0 * (1 << 21);
5367    carry1 = s1 >> 21;
5368    s2  += carry1;
5369    s1  -= carry1 * (1 << 21);
5370    carry2 = s2 >> 21;
5371    s3  += carry2;
5372    s2  -= carry2 * (1 << 21);
5373    carry3 = s3 >> 21;
5374    s4  += carry3;
5375    s3  -= carry3 * (1 << 21);
5376    carry4 = s4 >> 21;
5377    s5  += carry4;
5378    s4  -= carry4 * (1 << 21);
5379    carry5 = s5 >> 21;
5380    s6  += carry5;
5381    s5  -= carry5 * (1 << 21);
5382    carry6 = s6 >> 21;
5383    s7  += carry6;
5384    s6  -= carry6 * (1 << 21);
5385    carry7 = s7 >> 21;
5386    s8  += carry7;
5387    s7  -= carry7 * (1 << 21);
5388    carry8 = s8 >> 21;
5389    s9  += carry8;
5390    s8  -= carry8 * (1 << 21);
5391    carry9 = s9 >> 21;
5392    s10 += carry9;
5393    s9  -= carry9 * (1 << 21);
5394    carry10 = s10 >> 21;
5395    s11 += carry10;
5396    s10 -= carry10 * (1 << 21);
5397
5398    s[ 0] = (uint8_t) (s0  >>  0);
5399    s[ 1] = (uint8_t) (s0  >>  8);
5400    s[ 2] = (uint8_t)((s0  >> 16) | (s1 << 5));
5401    s[ 3] = (uint8_t) (s1  >>  3);
5402    s[ 4] = (uint8_t) (s1  >> 11);
5403    s[ 5] = (uint8_t)((s1  >> 19) | (s2 << 2));
5404    s[ 6] = (uint8_t) (s2  >>  6);
5405    s[ 7] = (uint8_t)((s2  >> 14) | (s3 << 7));
5406    s[ 8] = (uint8_t) (s3  >>  1);
5407    s[ 9] = (uint8_t) (s3  >>  9);
5408    s[10] = (uint8_t)((s3  >> 17) | (s4 << 4));
5409    s[11] = (uint8_t) (s4  >>  4);
5410    s[12] = (uint8_t) (s4  >> 12);
5411    s[13] = (uint8_t)((s4  >> 20) | (s5 << 1));
5412    s[14] = (uint8_t) (s5  >>  7);
5413    s[15] = (uint8_t)((s5  >> 15) | (s6 << 6));
5414    s[16] = (uint8_t) (s6  >>  2);
5415    s[17] = (uint8_t) (s6  >> 10);
5416    s[18] = (uint8_t)((s6  >> 18) | (s7 << 3));
5417    s[19] = (uint8_t) (s7  >>  5);
5418    s[20] = (uint8_t) (s7  >> 13);
5419    s[21] = (uint8_t) (s8  >>  0);
5420    s[22] = (uint8_t) (s8  >>  8);
5421    s[23] = (uint8_t)((s8  >> 16) | (s9 << 5));
5422    s[24] = (uint8_t) (s9  >>  3);
5423    s[25] = (uint8_t) (s9  >> 11);
5424    s[26] = (uint8_t)((s9  >> 19) | (s10 << 2));
5425    s[27] = (uint8_t) (s10 >>  6);
5426    s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
5427    s[29] = (uint8_t) (s11 >>  1);
5428    s[30] = (uint8_t) (s11 >>  9);
5429    s[31] = (uint8_t) (s11 >> 17);
5430}
5431
5432int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
5433                 const uint8_t public_key[32], const uint8_t private_key[32])
5434{
5435    uint8_t az[SHA512_DIGEST_LENGTH];
5436    uint8_t nonce[SHA512_DIGEST_LENGTH];
5437    ge_p3 R;
5438    uint8_t hram[SHA512_DIGEST_LENGTH];
5439    SHA512_CTX hash_ctx;
5440
5441    SHA512_Init(&hash_ctx);
5442    SHA512_Update(&hash_ctx, private_key, 32);
5443    SHA512_Final(az, &hash_ctx);
5444
5445    az[0] &= 248;
5446    az[31] &= 63;
5447    az[31] |= 64;
5448
5449    SHA512_Init(&hash_ctx);
5450    SHA512_Update(&hash_ctx, az + 32, 32);
5451    SHA512_Update(&hash_ctx, message, message_len);
5452    SHA512_Final(nonce, &hash_ctx);
5453
5454    x25519_sc_reduce(nonce);
5455    ge_scalarmult_base(&R, nonce);
5456    ge_p3_tobytes(out_sig, &R);
5457
5458    SHA512_Init(&hash_ctx);
5459    SHA512_Update(&hash_ctx, out_sig, 32);
5460    SHA512_Update(&hash_ctx, public_key, 32);
5461    SHA512_Update(&hash_ctx, message, message_len);
5462    SHA512_Final(hram, &hash_ctx);
5463
5464    x25519_sc_reduce(hram);
5465    sc_muladd(out_sig + 32, hram, az, nonce);
5466
5467    OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx));
5468    OPENSSL_cleanse(nonce, sizeof(nonce));
5469    OPENSSL_cleanse(az, sizeof(az));
5470
5471    return 1;
5472}
5473
5474static const char allzeroes[15];
5475
5476int ED25519_verify(const uint8_t *message, size_t message_len,
5477                   const uint8_t signature[64], const uint8_t public_key[32])
5478{
5479    int i;
5480    ge_p3 A;
5481    const uint8_t *r, *s;
5482    SHA512_CTX hash_ctx;
5483    ge_p2 R;
5484    uint8_t rcheck[32];
5485    uint8_t h[SHA512_DIGEST_LENGTH];
5486    /* 27742317777372353535851937790883648493 in little endian format */
5487    const uint8_t l_low[16] = {
5488        0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5489        0xDE, 0xF9, 0xDE, 0x14
5490    };
5491
5492    r = signature;
5493    s = signature + 32;
5494
5495    /*
5496     * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5497     *
5498     * If not the signature is publicly invalid. Since it's public we can do the
5499     * check in variable time.
5500     *
5501     * First check the most significant byte
5502     */
5503    if (s[31] > 0x10)
5504        return 0;
5505    if (s[31] == 0x10) {
5506        /*
5507         * Most significant byte indicates a value close to 2^252 so check the
5508         * rest
5509         */
5510        if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5511            return 0;
5512        for (i = 15; i >= 0; i--) {
5513            if (s[i] < l_low[i])
5514                break;
5515            if (s[i] > l_low[i])
5516                return 0;
5517        }
5518        if (i < 0)
5519            return 0;
5520    }
5521
5522    if (ge_frombytes_vartime(&A, public_key) != 0) {
5523        return 0;
5524    }
5525
5526    fe_neg(A.X, A.X);
5527    fe_neg(A.T, A.T);
5528
5529    SHA512_Init(&hash_ctx);
5530    SHA512_Update(&hash_ctx, r, 32);
5531    SHA512_Update(&hash_ctx, public_key, 32);
5532    SHA512_Update(&hash_ctx, message, message_len);
5533    SHA512_Final(h, &hash_ctx);
5534
5535    x25519_sc_reduce(h);
5536
5537    ge_double_scalarmult_vartime(&R, h, &A, s);
5538
5539    ge_tobytes(rcheck, &R);
5540
5541    return CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5542}
5543
5544void ED25519_public_from_private(uint8_t out_public_key[32],
5545                                 const uint8_t private_key[32])
5546{
5547    uint8_t az[SHA512_DIGEST_LENGTH];
5548    ge_p3 A;
5549
5550    SHA512(private_key, 32, az);
5551
5552    az[0] &= 248;
5553    az[31] &= 63;
5554    az[31] |= 64;
5555
5556    ge_scalarmult_base(&A, az);
5557    ge_p3_tobytes(out_public_key, &A);
5558
5559    OPENSSL_cleanse(az, sizeof(az));
5560}
5561
5562int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5563           const uint8_t peer_public_value[32])
5564{
5565    static const uint8_t kZeros[32] = {0};
5566    x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5567    /* The all-zero output results when the input is a point of small order. */
5568    return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5569}
5570
5571void X25519_public_from_private(uint8_t out_public_value[32],
5572                                const uint8_t private_key[32])
5573{
5574    uint8_t e[32];
5575    ge_p3 A;
5576    fe zplusy, zminusy, zminusy_inv;
5577
5578    memcpy(e, private_key, 32);
5579    e[0] &= 248;
5580    e[31] &= 127;
5581    e[31] |= 64;
5582
5583    ge_scalarmult_base(&A, e);
5584
5585    /*
5586     * We only need the u-coordinate of the curve25519 point.
5587     * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5588     * u=(Z+Y)/(Z-Y).
5589     */
5590    fe_add(zplusy, A.Z, A.Y);
5591    fe_sub(zminusy, A.Z, A.Y);
5592    fe_invert(zminusy_inv, zminusy);
5593    fe_mul(zplusy, zplusy, zminusy_inv);
5594    fe_tobytes(out_public_value, zplusy);
5595
5596    OPENSSL_cleanse(e, sizeof(e));
5597}
5598