Coverage Report

Created: 2024-11-21 06:47

/src/boringssl/third_party/fiat/p256_64.h
Line
Count
Source (jump to first uncovered line)
1
#include <openssl/base.h>
2
#include "../../crypto/internal.h"
3
#if !defined(OPENSSL_NO_ASM) && defined(__GNUC__) && defined(__x86_64__)
4
void fiat_p256_adx_mul(uint64_t*, const uint64_t*, const uint64_t*);
5
void fiat_p256_adx_sqr(uint64_t*, const uint64_t*);
6
#endif
7
8
/* Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --inline --static --use-value-barrier p256 64 '2^256 - 2^224 + 2^192 + 2^96 - 1' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp */
9
/* curve description: p256 */
10
/* machine_wordsize = 64 (from "64") */
11
/* requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp */
12
/* m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1") */
13
/*                                                                    */
14
/* NOTE: In addition to the bounds specified above each function, all */
15
/*   functions synthesized for this Montgomery arithmetic require the */
16
/*   input to be strictly less than the prime modulus (m), and also   */
17
/*   require the input to be in the unique saturated representation.  */
18
/*   All functions also ensure that these two properties are true of  */
19
/*   return values.                                                   */
20
/*  */
21
/* Computed values: */
22
/*   eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) */
23
/*   bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) */
24
/*   twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in */
25
/*                            if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 */
26
27
#include <stdint.h>
28
typedef unsigned char fiat_p256_uint1;
29
typedef signed char fiat_p256_int1;
30
#if defined(__GNUC__) || defined(__clang__)
31
#  define FIAT_P256_FIAT_EXTENSION __extension__
32
#  define FIAT_P256_FIAT_INLINE __inline__
33
#else
34
#  define FIAT_P256_FIAT_EXTENSION
35
#  define FIAT_P256_FIAT_INLINE
36
#endif
37
38
FIAT_P256_FIAT_EXTENSION typedef signed __int128 fiat_p256_int128;
39
FIAT_P256_FIAT_EXTENSION typedef unsigned __int128 fiat_p256_uint128;
40
41
/* The type fiat_p256_montgomery_domain_field_element is a field element in the Montgomery domain. */
42
/* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */
43
typedef uint64_t fiat_p256_montgomery_domain_field_element[4];
44
45
/* The type fiat_p256_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. */
46
/* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */
47
typedef uint64_t fiat_p256_non_montgomery_domain_field_element[4];
48
49
#if (-1 & 3) != 3
50
#error "This code only works on a two's complement system"
51
#endif
52
53
#if !defined(FIAT_P256_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
54
0
static __inline__ uint64_t fiat_p256_value_barrier_u64(uint64_t a) {
55
0
  __asm__("" : "+r"(a) : /* no inputs */);
56
0
  return a;
57
0
}
58
#else
59
#  define fiat_p256_value_barrier_u64(x) (x)
60
#endif
61
62
63
/*
64
 * The function fiat_p256_addcarryx_u64 is an addition with carry.
65
 *
66
 * Postconditions:
67
 *   out1 = (arg1 + arg2 + arg3) mod 2^64
68
 *   out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋
69
 *
70
 * Input Bounds:
71
 *   arg1: [0x0 ~> 0x1]
72
 *   arg2: [0x0 ~> 0xffffffffffffffff]
73
 *   arg3: [0x0 ~> 0xffffffffffffffff]
74
 * Output Bounds:
75
 *   out1: [0x0 ~> 0xffffffffffffffff]
76
 *   out2: [0x0 ~> 0x1]
77
 */
78
0
static FIAT_P256_FIAT_INLINE void fiat_p256_addcarryx_u64(uint64_t* out1, fiat_p256_uint1* out2, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) {
79
0
  fiat_p256_uint128 x1;
80
0
  uint64_t x2;
81
0
  fiat_p256_uint1 x3;
82
0
  x1 = ((arg1 + (fiat_p256_uint128)arg2) + arg3);
83
0
  x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
84
0
  x3 = (fiat_p256_uint1)(x1 >> 64);
85
0
  *out1 = x2;
86
0
  *out2 = x3;
87
0
}
88
89
/*
90
 * The function fiat_p256_subborrowx_u64 is a subtraction with borrow.
91
 *
92
 * Postconditions:
93
 *   out1 = (-arg1 + arg2 + -arg3) mod 2^64
94
 *   out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋
95
 *
96
 * Input Bounds:
97
 *   arg1: [0x0 ~> 0x1]
98
 *   arg2: [0x0 ~> 0xffffffffffffffff]
99
 *   arg3: [0x0 ~> 0xffffffffffffffff]
100
 * Output Bounds:
101
 *   out1: [0x0 ~> 0xffffffffffffffff]
102
 *   out2: [0x0 ~> 0x1]
103
 */
104
0
static FIAT_P256_FIAT_INLINE void fiat_p256_subborrowx_u64(uint64_t* out1, fiat_p256_uint1* out2, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) {
105
0
  fiat_p256_int128 x1;
106
0
  fiat_p256_int1 x2;
107
0
  uint64_t x3;
108
0
  x1 = ((arg2 - (fiat_p256_int128)arg1) - arg3);
109
0
  x2 = (fiat_p256_int1)(x1 >> 64);
110
0
  x3 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
111
0
  *out1 = x3;
112
0
  *out2 = (fiat_p256_uint1)(0x0 - x2);
113
0
}
114
115
/*
116
 * The function fiat_p256_mulx_u64 is a multiplication, returning the full double-width result.
117
 *
118
 * Postconditions:
119
 *   out1 = (arg1 * arg2) mod 2^64
120
 *   out2 = ⌊arg1 * arg2 / 2^64⌋
121
 *
122
 * Input Bounds:
123
 *   arg1: [0x0 ~> 0xffffffffffffffff]
124
 *   arg2: [0x0 ~> 0xffffffffffffffff]
125
 * Output Bounds:
126
 *   out1: [0x0 ~> 0xffffffffffffffff]
127
 *   out2: [0x0 ~> 0xffffffffffffffff]
128
 */
129
0
static FIAT_P256_FIAT_INLINE void fiat_p256_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) {
130
0
  fiat_p256_uint128 x1;
131
0
  uint64_t x2;
132
0
  uint64_t x3;
133
0
  x1 = ((fiat_p256_uint128)arg1 * arg2);
134
0
  x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
135
0
  x3 = (uint64_t)(x1 >> 64);
136
0
  *out1 = x2;
137
0
  *out2 = x3;
138
0
}
139
140
/*
141
 * The function fiat_p256_cmovznz_u64 is a single-word conditional move.
142
 *
143
 * Postconditions:
144
 *   out1 = (if arg1 = 0 then arg2 else arg3)
145
 *
146
 * Input Bounds:
147
 *   arg1: [0x0 ~> 0x1]
148
 *   arg2: [0x0 ~> 0xffffffffffffffff]
149
 *   arg3: [0x0 ~> 0xffffffffffffffff]
150
 * Output Bounds:
151
 *   out1: [0x0 ~> 0xffffffffffffffff]
152
 */
153
0
static FIAT_P256_FIAT_INLINE void fiat_p256_cmovznz_u64(uint64_t* out1, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) {
154
0
  fiat_p256_uint1 x1;
155
0
  uint64_t x2;
156
0
  uint64_t x3;
157
0
  x1 = (!(!arg1));
158
0
  x2 = ((fiat_p256_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff));
159
0
  x3 = ((fiat_p256_value_barrier_u64(x2) & arg3) | (fiat_p256_value_barrier_u64((~x2)) & arg2));
160
0
  *out1 = x3;
161
0
}
162
163
/*
164
 * The function fiat_p256_mul multiplies two field elements in the Montgomery domain.
165
 *
166
 * Preconditions:
167
 *   0 ≤ eval arg1 < m
168
 *   0 ≤ eval arg2 < m
169
 * Postconditions:
170
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
171
 *   0 ≤ eval out1 < m
172
 *
173
 */
174
0
static FIAT_P256_FIAT_INLINE void fiat_p256_mul(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) {
175
0
#if !defined(OPENSSL_NO_ASM) && defined(__GNUC__) && defined(__x86_64__)
176
0
  if (CRYPTO_is_BMI1_capable() && CRYPTO_is_BMI2_capable() &&
177
0
    CRYPTO_is_ADX_capable()) {
178
0
      fiat_p256_adx_mul(out1, arg1, arg2);
179
0
      return;
180
0
  }
181
0
#endif
182
0
  uint64_t x1;
183
0
  uint64_t x2;
184
0
  uint64_t x3;
185
0
  uint64_t x4;
186
0
  uint64_t x5;
187
0
  uint64_t x6;
188
0
  uint64_t x7;
189
0
  uint64_t x8;
190
0
  uint64_t x9;
191
0
  uint64_t x10;
192
0
  uint64_t x11;
193
0
  uint64_t x12;
194
0
  uint64_t x13;
195
0
  fiat_p256_uint1 x14;
196
0
  uint64_t x15;
197
0
  fiat_p256_uint1 x16;
198
0
  uint64_t x17;
199
0
  fiat_p256_uint1 x18;
200
0
  uint64_t x19;
201
0
  uint64_t x20;
202
0
  uint64_t x21;
203
0
  uint64_t x22;
204
0
  uint64_t x23;
205
0
  uint64_t x24;
206
0
  uint64_t x25;
207
0
  uint64_t x26;
208
0
  fiat_p256_uint1 x27;
209
0
  uint64_t x28;
210
0
  uint64_t x29;
211
0
  fiat_p256_uint1 x30;
212
0
  uint64_t x31;
213
0
  fiat_p256_uint1 x32;
214
0
  uint64_t x33;
215
0
  fiat_p256_uint1 x34;
216
0
  uint64_t x35;
217
0
  fiat_p256_uint1 x36;
218
0
  uint64_t x37;
219
0
  fiat_p256_uint1 x38;
220
0
  uint64_t x39;
221
0
  uint64_t x40;
222
0
  uint64_t x41;
223
0
  uint64_t x42;
224
0
  uint64_t x43;
225
0
  uint64_t x44;
226
0
  uint64_t x45;
227
0
  uint64_t x46;
228
0
  uint64_t x47;
229
0
  fiat_p256_uint1 x48;
230
0
  uint64_t x49;
231
0
  fiat_p256_uint1 x50;
232
0
  uint64_t x51;
233
0
  fiat_p256_uint1 x52;
234
0
  uint64_t x53;
235
0
  uint64_t x54;
236
0
  fiat_p256_uint1 x55;
237
0
  uint64_t x56;
238
0
  fiat_p256_uint1 x57;
239
0
  uint64_t x58;
240
0
  fiat_p256_uint1 x59;
241
0
  uint64_t x60;
242
0
  fiat_p256_uint1 x61;
243
0
  uint64_t x62;
244
0
  fiat_p256_uint1 x63;
245
0
  uint64_t x64;
246
0
  uint64_t x65;
247
0
  uint64_t x66;
248
0
  uint64_t x67;
249
0
  uint64_t x68;
250
0
  uint64_t x69;
251
0
  uint64_t x70;
252
0
  fiat_p256_uint1 x71;
253
0
  uint64_t x72;
254
0
  uint64_t x73;
255
0
  fiat_p256_uint1 x74;
256
0
  uint64_t x75;
257
0
  fiat_p256_uint1 x76;
258
0
  uint64_t x77;
259
0
  fiat_p256_uint1 x78;
260
0
  uint64_t x79;
261
0
  fiat_p256_uint1 x80;
262
0
  uint64_t x81;
263
0
  fiat_p256_uint1 x82;
264
0
  uint64_t x83;
265
0
  uint64_t x84;
266
0
  uint64_t x85;
267
0
  uint64_t x86;
268
0
  uint64_t x87;
269
0
  uint64_t x88;
270
0
  uint64_t x89;
271
0
  uint64_t x90;
272
0
  uint64_t x91;
273
0
  uint64_t x92;
274
0
  fiat_p256_uint1 x93;
275
0
  uint64_t x94;
276
0
  fiat_p256_uint1 x95;
277
0
  uint64_t x96;
278
0
  fiat_p256_uint1 x97;
279
0
  uint64_t x98;
280
0
  uint64_t x99;
281
0
  fiat_p256_uint1 x100;
282
0
  uint64_t x101;
283
0
  fiat_p256_uint1 x102;
284
0
  uint64_t x103;
285
0
  fiat_p256_uint1 x104;
286
0
  uint64_t x105;
287
0
  fiat_p256_uint1 x106;
288
0
  uint64_t x107;
289
0
  fiat_p256_uint1 x108;
290
0
  uint64_t x109;
291
0
  uint64_t x110;
292
0
  uint64_t x111;
293
0
  uint64_t x112;
294
0
  uint64_t x113;
295
0
  uint64_t x114;
296
0
  uint64_t x115;
297
0
  fiat_p256_uint1 x116;
298
0
  uint64_t x117;
299
0
  uint64_t x118;
300
0
  fiat_p256_uint1 x119;
301
0
  uint64_t x120;
302
0
  fiat_p256_uint1 x121;
303
0
  uint64_t x122;
304
0
  fiat_p256_uint1 x123;
305
0
  uint64_t x124;
306
0
  fiat_p256_uint1 x125;
307
0
  uint64_t x126;
308
0
  fiat_p256_uint1 x127;
309
0
  uint64_t x128;
310
0
  uint64_t x129;
311
0
  uint64_t x130;
312
0
  uint64_t x131;
313
0
  uint64_t x132;
314
0
  uint64_t x133;
315
0
  uint64_t x134;
316
0
  uint64_t x135;
317
0
  uint64_t x136;
318
0
  uint64_t x137;
319
0
  fiat_p256_uint1 x138;
320
0
  uint64_t x139;
321
0
  fiat_p256_uint1 x140;
322
0
  uint64_t x141;
323
0
  fiat_p256_uint1 x142;
324
0
  uint64_t x143;
325
0
  uint64_t x144;
326
0
  fiat_p256_uint1 x145;
327
0
  uint64_t x146;
328
0
  fiat_p256_uint1 x147;
329
0
  uint64_t x148;
330
0
  fiat_p256_uint1 x149;
331
0
  uint64_t x150;
332
0
  fiat_p256_uint1 x151;
333
0
  uint64_t x152;
334
0
  fiat_p256_uint1 x153;
335
0
  uint64_t x154;
336
0
  uint64_t x155;
337
0
  uint64_t x156;
338
0
  uint64_t x157;
339
0
  uint64_t x158;
340
0
  uint64_t x159;
341
0
  uint64_t x160;
342
0
  fiat_p256_uint1 x161;
343
0
  uint64_t x162;
344
0
  uint64_t x163;
345
0
  fiat_p256_uint1 x164;
346
0
  uint64_t x165;
347
0
  fiat_p256_uint1 x166;
348
0
  uint64_t x167;
349
0
  fiat_p256_uint1 x168;
350
0
  uint64_t x169;
351
0
  fiat_p256_uint1 x170;
352
0
  uint64_t x171;
353
0
  fiat_p256_uint1 x172;
354
0
  uint64_t x173;
355
0
  uint64_t x174;
356
0
  fiat_p256_uint1 x175;
357
0
  uint64_t x176;
358
0
  fiat_p256_uint1 x177;
359
0
  uint64_t x178;
360
0
  fiat_p256_uint1 x179;
361
0
  uint64_t x180;
362
0
  fiat_p256_uint1 x181;
363
0
  uint64_t x182;
364
0
  fiat_p256_uint1 x183;
365
0
  uint64_t x184;
366
0
  uint64_t x185;
367
0
  uint64_t x186;
368
0
  uint64_t x187;
369
0
  x1 = (arg1[1]);
370
0
  x2 = (arg1[2]);
371
0
  x3 = (arg1[3]);
372
0
  x4 = (arg1[0]);
373
0
  fiat_p256_mulx_u64(&x5, &x6, x4, (arg2[3]));
374
0
  fiat_p256_mulx_u64(&x7, &x8, x4, (arg2[2]));
375
0
  fiat_p256_mulx_u64(&x9, &x10, x4, (arg2[1]));
376
0
  fiat_p256_mulx_u64(&x11, &x12, x4, (arg2[0]));
377
0
  fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
378
0
  fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
379
0
  fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
380
0
  x19 = (x18 + x6);
381
0
  fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001));
382
0
  fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff));
383
0
  fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff));
384
0
  fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22);
385
0
  x28 = (x27 + x23);
386
0
  fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24);
387
0
  fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26);
388
0
  fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28);
389
0
  fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20);
390
0
  fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21);
391
0
  fiat_p256_mulx_u64(&x39, &x40, x1, (arg2[3]));
392
0
  fiat_p256_mulx_u64(&x41, &x42, x1, (arg2[2]));
393
0
  fiat_p256_mulx_u64(&x43, &x44, x1, (arg2[1]));
394
0
  fiat_p256_mulx_u64(&x45, &x46, x1, (arg2[0]));
395
0
  fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43);
396
0
  fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41);
397
0
  fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39);
398
0
  x53 = (x52 + x40);
399
0
  fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45);
400
0
  fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47);
401
0
  fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49);
402
0
  fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51);
403
0
  fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53);
404
0
  fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001));
405
0
  fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff));
406
0
  fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff));
407
0
  fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66);
408
0
  x72 = (x71 + x67);
409
0
  fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68);
410
0
  fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70);
411
0
  fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72);
412
0
  fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64);
413
0
  fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65);
414
0
  x83 = ((uint64_t)x82 + x63);
415
0
  fiat_p256_mulx_u64(&x84, &x85, x2, (arg2[3]));
416
0
  fiat_p256_mulx_u64(&x86, &x87, x2, (arg2[2]));
417
0
  fiat_p256_mulx_u64(&x88, &x89, x2, (arg2[1]));
418
0
  fiat_p256_mulx_u64(&x90, &x91, x2, (arg2[0]));
419
0
  fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88);
420
0
  fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86);
421
0
  fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84);
422
0
  x98 = (x97 + x85);
423
0
  fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90);
424
0
  fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92);
425
0
  fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94);
426
0
  fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96);
427
0
  fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98);
428
0
  fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001));
429
0
  fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff));
430
0
  fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff));
431
0
  fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111);
432
0
  x117 = (x116 + x112);
433
0
  fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113);
434
0
  fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115);
435
0
  fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117);
436
0
  fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109);
437
0
  fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110);
438
0
  x128 = ((uint64_t)x127 + x108);
439
0
  fiat_p256_mulx_u64(&x129, &x130, x3, (arg2[3]));
440
0
  fiat_p256_mulx_u64(&x131, &x132, x3, (arg2[2]));
441
0
  fiat_p256_mulx_u64(&x133, &x134, x3, (arg2[1]));
442
0
  fiat_p256_mulx_u64(&x135, &x136, x3, (arg2[0]));
443
0
  fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133);
444
0
  fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131);
445
0
  fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129);
446
0
  x143 = (x142 + x130);
447
0
  fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135);
448
0
  fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137);
449
0
  fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139);
450
0
  fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141);
451
0
  fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143);
452
0
  fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001));
453
0
  fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff));
454
0
  fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff));
455
0
  fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156);
456
0
  x162 = (x161 + x157);
457
0
  fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158);
458
0
  fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160);
459
0
  fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162);
460
0
  fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154);
461
0
  fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155);
462
0
  x173 = ((uint64_t)x172 + x153);
463
0
  fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff));
464
0
  fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff));
465
0
  fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0);
466
0
  fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001));
467
0
  fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0);
468
0
  fiat_p256_cmovznz_u64(&x184, x183, x174, x165);
469
0
  fiat_p256_cmovznz_u64(&x185, x183, x176, x167);
470
0
  fiat_p256_cmovznz_u64(&x186, x183, x178, x169);
471
0
  fiat_p256_cmovznz_u64(&x187, x183, x180, x171);
472
0
  out1[0] = x184;
473
0
  out1[1] = x185;
474
0
  out1[2] = x186;
475
0
  out1[3] = x187;
476
0
}
477
478
/*
479
 * The function fiat_p256_square squares a field element in the Montgomery domain.
480
 *
481
 * Preconditions:
482
 *   0 ≤ eval arg1 < m
483
 * Postconditions:
484
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m
485
 *   0 ≤ eval out1 < m
486
 *
487
 */
488
0
static FIAT_P256_FIAT_INLINE void fiat_p256_square(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) {
489
0
#if !defined(OPENSSL_NO_ASM) && defined(__GNUC__) && defined(__x86_64__)
490
0
  if (CRYPTO_is_BMI1_capable() && CRYPTO_is_BMI2_capable() &&
491
0
    CRYPTO_is_ADX_capable()) {
492
0
      fiat_p256_adx_sqr(out1, arg1);
493
0
      return;
494
0
  }
495
0
#endif
496
0
  uint64_t x1;
497
0
  uint64_t x2;
498
0
  uint64_t x3;
499
0
  uint64_t x4;
500
0
  uint64_t x5;
501
0
  uint64_t x6;
502
0
  uint64_t x7;
503
0
  uint64_t x8;
504
0
  uint64_t x9;
505
0
  uint64_t x10;
506
0
  uint64_t x11;
507
0
  uint64_t x12;
508
0
  uint64_t x13;
509
0
  fiat_p256_uint1 x14;
510
0
  uint64_t x15;
511
0
  fiat_p256_uint1 x16;
512
0
  uint64_t x17;
513
0
  fiat_p256_uint1 x18;
514
0
  uint64_t x19;
515
0
  uint64_t x20;
516
0
  uint64_t x21;
517
0
  uint64_t x22;
518
0
  uint64_t x23;
519
0
  uint64_t x24;
520
0
  uint64_t x25;
521
0
  uint64_t x26;
522
0
  fiat_p256_uint1 x27;
523
0
  uint64_t x28;
524
0
  uint64_t x29;
525
0
  fiat_p256_uint1 x30;
526
0
  uint64_t x31;
527
0
  fiat_p256_uint1 x32;
528
0
  uint64_t x33;
529
0
  fiat_p256_uint1 x34;
530
0
  uint64_t x35;
531
0
  fiat_p256_uint1 x36;
532
0
  uint64_t x37;
533
0
  fiat_p256_uint1 x38;
534
0
  uint64_t x39;
535
0
  uint64_t x40;
536
0
  uint64_t x41;
537
0
  uint64_t x42;
538
0
  uint64_t x43;
539
0
  uint64_t x44;
540
0
  uint64_t x45;
541
0
  uint64_t x46;
542
0
  uint64_t x47;
543
0
  fiat_p256_uint1 x48;
544
0
  uint64_t x49;
545
0
  fiat_p256_uint1 x50;
546
0
  uint64_t x51;
547
0
  fiat_p256_uint1 x52;
548
0
  uint64_t x53;
549
0
  uint64_t x54;
550
0
  fiat_p256_uint1 x55;
551
0
  uint64_t x56;
552
0
  fiat_p256_uint1 x57;
553
0
  uint64_t x58;
554
0
  fiat_p256_uint1 x59;
555
0
  uint64_t x60;
556
0
  fiat_p256_uint1 x61;
557
0
  uint64_t x62;
558
0
  fiat_p256_uint1 x63;
559
0
  uint64_t x64;
560
0
  uint64_t x65;
561
0
  uint64_t x66;
562
0
  uint64_t x67;
563
0
  uint64_t x68;
564
0
  uint64_t x69;
565
0
  uint64_t x70;
566
0
  fiat_p256_uint1 x71;
567
0
  uint64_t x72;
568
0
  uint64_t x73;
569
0
  fiat_p256_uint1 x74;
570
0
  uint64_t x75;
571
0
  fiat_p256_uint1 x76;
572
0
  uint64_t x77;
573
0
  fiat_p256_uint1 x78;
574
0
  uint64_t x79;
575
0
  fiat_p256_uint1 x80;
576
0
  uint64_t x81;
577
0
  fiat_p256_uint1 x82;
578
0
  uint64_t x83;
579
0
  uint64_t x84;
580
0
  uint64_t x85;
581
0
  uint64_t x86;
582
0
  uint64_t x87;
583
0
  uint64_t x88;
584
0
  uint64_t x89;
585
0
  uint64_t x90;
586
0
  uint64_t x91;
587
0
  uint64_t x92;
588
0
  fiat_p256_uint1 x93;
589
0
  uint64_t x94;
590
0
  fiat_p256_uint1 x95;
591
0
  uint64_t x96;
592
0
  fiat_p256_uint1 x97;
593
0
  uint64_t x98;
594
0
  uint64_t x99;
595
0
  fiat_p256_uint1 x100;
596
0
  uint64_t x101;
597
0
  fiat_p256_uint1 x102;
598
0
  uint64_t x103;
599
0
  fiat_p256_uint1 x104;
600
0
  uint64_t x105;
601
0
  fiat_p256_uint1 x106;
602
0
  uint64_t x107;
603
0
  fiat_p256_uint1 x108;
604
0
  uint64_t x109;
605
0
  uint64_t x110;
606
0
  uint64_t x111;
607
0
  uint64_t x112;
608
0
  uint64_t x113;
609
0
  uint64_t x114;
610
0
  uint64_t x115;
611
0
  fiat_p256_uint1 x116;
612
0
  uint64_t x117;
613
0
  uint64_t x118;
614
0
  fiat_p256_uint1 x119;
615
0
  uint64_t x120;
616
0
  fiat_p256_uint1 x121;
617
0
  uint64_t x122;
618
0
  fiat_p256_uint1 x123;
619
0
  uint64_t x124;
620
0
  fiat_p256_uint1 x125;
621
0
  uint64_t x126;
622
0
  fiat_p256_uint1 x127;
623
0
  uint64_t x128;
624
0
  uint64_t x129;
625
0
  uint64_t x130;
626
0
  uint64_t x131;
627
0
  uint64_t x132;
628
0
  uint64_t x133;
629
0
  uint64_t x134;
630
0
  uint64_t x135;
631
0
  uint64_t x136;
632
0
  uint64_t x137;
633
0
  fiat_p256_uint1 x138;
634
0
  uint64_t x139;
635
0
  fiat_p256_uint1 x140;
636
0
  uint64_t x141;
637
0
  fiat_p256_uint1 x142;
638
0
  uint64_t x143;
639
0
  uint64_t x144;
640
0
  fiat_p256_uint1 x145;
641
0
  uint64_t x146;
642
0
  fiat_p256_uint1 x147;
643
0
  uint64_t x148;
644
0
  fiat_p256_uint1 x149;
645
0
  uint64_t x150;
646
0
  fiat_p256_uint1 x151;
647
0
  uint64_t x152;
648
0
  fiat_p256_uint1 x153;
649
0
  uint64_t x154;
650
0
  uint64_t x155;
651
0
  uint64_t x156;
652
0
  uint64_t x157;
653
0
  uint64_t x158;
654
0
  uint64_t x159;
655
0
  uint64_t x160;
656
0
  fiat_p256_uint1 x161;
657
0
  uint64_t x162;
658
0
  uint64_t x163;
659
0
  fiat_p256_uint1 x164;
660
0
  uint64_t x165;
661
0
  fiat_p256_uint1 x166;
662
0
  uint64_t x167;
663
0
  fiat_p256_uint1 x168;
664
0
  uint64_t x169;
665
0
  fiat_p256_uint1 x170;
666
0
  uint64_t x171;
667
0
  fiat_p256_uint1 x172;
668
0
  uint64_t x173;
669
0
  uint64_t x174;
670
0
  fiat_p256_uint1 x175;
671
0
  uint64_t x176;
672
0
  fiat_p256_uint1 x177;
673
0
  uint64_t x178;
674
0
  fiat_p256_uint1 x179;
675
0
  uint64_t x180;
676
0
  fiat_p256_uint1 x181;
677
0
  uint64_t x182;
678
0
  fiat_p256_uint1 x183;
679
0
  uint64_t x184;
680
0
  uint64_t x185;
681
0
  uint64_t x186;
682
0
  uint64_t x187;
683
0
  x1 = (arg1[1]);
684
0
  x2 = (arg1[2]);
685
0
  x3 = (arg1[3]);
686
0
  x4 = (arg1[0]);
687
0
  fiat_p256_mulx_u64(&x5, &x6, x4, (arg1[3]));
688
0
  fiat_p256_mulx_u64(&x7, &x8, x4, (arg1[2]));
689
0
  fiat_p256_mulx_u64(&x9, &x10, x4, (arg1[1]));
690
0
  fiat_p256_mulx_u64(&x11, &x12, x4, (arg1[0]));
691
0
  fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
692
0
  fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
693
0
  fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
694
0
  x19 = (x18 + x6);
695
0
  fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001));
696
0
  fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff));
697
0
  fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff));
698
0
  fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22);
699
0
  x28 = (x27 + x23);
700
0
  fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24);
701
0
  fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26);
702
0
  fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28);
703
0
  fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20);
704
0
  fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21);
705
0
  fiat_p256_mulx_u64(&x39, &x40, x1, (arg1[3]));
706
0
  fiat_p256_mulx_u64(&x41, &x42, x1, (arg1[2]));
707
0
  fiat_p256_mulx_u64(&x43, &x44, x1, (arg1[1]));
708
0
  fiat_p256_mulx_u64(&x45, &x46, x1, (arg1[0]));
709
0
  fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43);
710
0
  fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41);
711
0
  fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39);
712
0
  x53 = (x52 + x40);
713
0
  fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45);
714
0
  fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47);
715
0
  fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49);
716
0
  fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51);
717
0
  fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53);
718
0
  fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001));
719
0
  fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff));
720
0
  fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff));
721
0
  fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66);
722
0
  x72 = (x71 + x67);
723
0
  fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68);
724
0
  fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70);
725
0
  fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72);
726
0
  fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64);
727
0
  fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65);
728
0
  x83 = ((uint64_t)x82 + x63);
729
0
  fiat_p256_mulx_u64(&x84, &x85, x2, (arg1[3]));
730
0
  fiat_p256_mulx_u64(&x86, &x87, x2, (arg1[2]));
731
0
  fiat_p256_mulx_u64(&x88, &x89, x2, (arg1[1]));
732
0
  fiat_p256_mulx_u64(&x90, &x91, x2, (arg1[0]));
733
0
  fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88);
734
0
  fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86);
735
0
  fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84);
736
0
  x98 = (x97 + x85);
737
0
  fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90);
738
0
  fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92);
739
0
  fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94);
740
0
  fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96);
741
0
  fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98);
742
0
  fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001));
743
0
  fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff));
744
0
  fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff));
745
0
  fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111);
746
0
  x117 = (x116 + x112);
747
0
  fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113);
748
0
  fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115);
749
0
  fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117);
750
0
  fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109);
751
0
  fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110);
752
0
  x128 = ((uint64_t)x127 + x108);
753
0
  fiat_p256_mulx_u64(&x129, &x130, x3, (arg1[3]));
754
0
  fiat_p256_mulx_u64(&x131, &x132, x3, (arg1[2]));
755
0
  fiat_p256_mulx_u64(&x133, &x134, x3, (arg1[1]));
756
0
  fiat_p256_mulx_u64(&x135, &x136, x3, (arg1[0]));
757
0
  fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133);
758
0
  fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131);
759
0
  fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129);
760
0
  x143 = (x142 + x130);
761
0
  fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135);
762
0
  fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137);
763
0
  fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139);
764
0
  fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141);
765
0
  fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143);
766
0
  fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001));
767
0
  fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff));
768
0
  fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff));
769
0
  fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156);
770
0
  x162 = (x161 + x157);
771
0
  fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158);
772
0
  fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160);
773
0
  fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162);
774
0
  fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154);
775
0
  fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155);
776
0
  x173 = ((uint64_t)x172 + x153);
777
0
  fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff));
778
0
  fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff));
779
0
  fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0);
780
0
  fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001));
781
0
  fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0);
782
0
  fiat_p256_cmovznz_u64(&x184, x183, x174, x165);
783
0
  fiat_p256_cmovznz_u64(&x185, x183, x176, x167);
784
0
  fiat_p256_cmovznz_u64(&x186, x183, x178, x169);
785
0
  fiat_p256_cmovznz_u64(&x187, x183, x180, x171);
786
0
  out1[0] = x184;
787
0
  out1[1] = x185;
788
0
  out1[2] = x186;
789
0
  out1[3] = x187;
790
0
}
791
792
/*
793
 * The function fiat_p256_add adds two field elements in the Montgomery domain.
794
 *
795
 * Preconditions:
796
 *   0 ≤ eval arg1 < m
797
 *   0 ≤ eval arg2 < m
798
 * Postconditions:
799
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
800
 *   0 ≤ eval out1 < m
801
 *
802
 */
803
0
static FIAT_P256_FIAT_INLINE void fiat_p256_add(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) {
804
0
  uint64_t x1;
805
0
  fiat_p256_uint1 x2;
806
0
  uint64_t x3;
807
0
  fiat_p256_uint1 x4;
808
0
  uint64_t x5;
809
0
  fiat_p256_uint1 x6;
810
0
  uint64_t x7;
811
0
  fiat_p256_uint1 x8;
812
0
  uint64_t x9;
813
0
  fiat_p256_uint1 x10;
814
0
  uint64_t x11;
815
0
  fiat_p256_uint1 x12;
816
0
  uint64_t x13;
817
0
  fiat_p256_uint1 x14;
818
0
  uint64_t x15;
819
0
  fiat_p256_uint1 x16;
820
0
  uint64_t x17;
821
0
  fiat_p256_uint1 x18;
822
0
  uint64_t x19;
823
0
  uint64_t x20;
824
0
  uint64_t x21;
825
0
  uint64_t x22;
826
0
  fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
827
0
  fiat_p256_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
828
0
  fiat_p256_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
829
0
  fiat_p256_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
830
0
  fiat_p256_subborrowx_u64(&x9, &x10, 0x0, x1, UINT64_C(0xffffffffffffffff));
831
0
  fiat_p256_subborrowx_u64(&x11, &x12, x10, x3, UINT32_C(0xffffffff));
832
0
  fiat_p256_subborrowx_u64(&x13, &x14, x12, x5, 0x0);
833
0
  fiat_p256_subborrowx_u64(&x15, &x16, x14, x7, UINT64_C(0xffffffff00000001));
834
0
  fiat_p256_subborrowx_u64(&x17, &x18, x16, x8, 0x0);
835
0
  fiat_p256_cmovznz_u64(&x19, x18, x9, x1);
836
0
  fiat_p256_cmovznz_u64(&x20, x18, x11, x3);
837
0
  fiat_p256_cmovznz_u64(&x21, x18, x13, x5);
838
0
  fiat_p256_cmovznz_u64(&x22, x18, x15, x7);
839
0
  out1[0] = x19;
840
0
  out1[1] = x20;
841
0
  out1[2] = x21;
842
0
  out1[3] = x22;
843
0
}
844
845
/*
846
 * The function fiat_p256_sub subtracts two field elements in the Montgomery domain.
847
 *
848
 * Preconditions:
849
 *   0 ≤ eval arg1 < m
850
 *   0 ≤ eval arg2 < m
851
 * Postconditions:
852
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
853
 *   0 ≤ eval out1 < m
854
 *
855
 */
856
0
static FIAT_P256_FIAT_INLINE void fiat_p256_sub(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) {
857
0
  uint64_t x1;
858
0
  fiat_p256_uint1 x2;
859
0
  uint64_t x3;
860
0
  fiat_p256_uint1 x4;
861
0
  uint64_t x5;
862
0
  fiat_p256_uint1 x6;
863
0
  uint64_t x7;
864
0
  fiat_p256_uint1 x8;
865
0
  uint64_t x9;
866
0
  uint64_t x10;
867
0
  fiat_p256_uint1 x11;
868
0
  uint64_t x12;
869
0
  fiat_p256_uint1 x13;
870
0
  uint64_t x14;
871
0
  fiat_p256_uint1 x15;
872
0
  uint64_t x16;
873
0
  fiat_p256_uint1 x17;
874
0
  fiat_p256_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
875
0
  fiat_p256_subborrowx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
876
0
  fiat_p256_subborrowx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
877
0
  fiat_p256_subborrowx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
878
0
  fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
879
0
  fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9);
880
0
  fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff)));
881
0
  fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0);
882
0
  fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001)));
883
0
  out1[0] = x10;
884
0
  out1[1] = x12;
885
0
  out1[2] = x14;
886
0
  out1[3] = x16;
887
0
}
888
889
/*
890
 * The function fiat_p256_opp negates a field element in the Montgomery domain.
891
 *
892
 * Preconditions:
893
 *   0 ≤ eval arg1 < m
894
 * Postconditions:
895
 *   eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
896
 *   0 ≤ eval out1 < m
897
 *
898
 */
899
0
static FIAT_P256_FIAT_INLINE void fiat_p256_opp(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) {
900
0
  uint64_t x1;
901
0
  fiat_p256_uint1 x2;
902
0
  uint64_t x3;
903
0
  fiat_p256_uint1 x4;
904
0
  uint64_t x5;
905
0
  fiat_p256_uint1 x6;
906
0
  uint64_t x7;
907
0
  fiat_p256_uint1 x8;
908
0
  uint64_t x9;
909
0
  uint64_t x10;
910
0
  fiat_p256_uint1 x11;
911
0
  uint64_t x12;
912
0
  fiat_p256_uint1 x13;
913
0
  uint64_t x14;
914
0
  fiat_p256_uint1 x15;
915
0
  uint64_t x16;
916
0
  fiat_p256_uint1 x17;
917
0
  fiat_p256_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0]));
918
0
  fiat_p256_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1]));
919
0
  fiat_p256_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2]));
920
0
  fiat_p256_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3]));
921
0
  fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
922
0
  fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9);
923
0
  fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff)));
924
0
  fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0);
925
0
  fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001)));
926
0
  out1[0] = x10;
927
0
  out1[1] = x12;
928
0
  out1[2] = x14;
929
0
  out1[3] = x16;
930
0
}
931
932
/*
933
 * The function fiat_p256_from_montgomery translates a field element out of the Montgomery domain.
934
 *
935
 * Preconditions:
936
 *   0 ≤ eval arg1 < m
937
 * Postconditions:
938
 *   eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
939
 *   0 ≤ eval out1 < m
940
 *
941
 */
942
0
static FIAT_P256_FIAT_INLINE void fiat_p256_from_montgomery(fiat_p256_non_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) {
943
0
  uint64_t x1;
944
0
  uint64_t x2;
945
0
  uint64_t x3;
946
0
  uint64_t x4;
947
0
  uint64_t x5;
948
0
  uint64_t x6;
949
0
  uint64_t x7;
950
0
  uint64_t x8;
951
0
  fiat_p256_uint1 x9;
952
0
  uint64_t x10;
953
0
  fiat_p256_uint1 x11;
954
0
  uint64_t x12;
955
0
  fiat_p256_uint1 x13;
956
0
  uint64_t x14;
957
0
  fiat_p256_uint1 x15;
958
0
  uint64_t x16;
959
0
  uint64_t x17;
960
0
  uint64_t x18;
961
0
  uint64_t x19;
962
0
  uint64_t x20;
963
0
  uint64_t x21;
964
0
  uint64_t x22;
965
0
  fiat_p256_uint1 x23;
966
0
  uint64_t x24;
967
0
  fiat_p256_uint1 x25;
968
0
  uint64_t x26;
969
0
  fiat_p256_uint1 x27;
970
0
  uint64_t x28;
971
0
  fiat_p256_uint1 x29;
972
0
  uint64_t x30;
973
0
  fiat_p256_uint1 x31;
974
0
  uint64_t x32;
975
0
  fiat_p256_uint1 x33;
976
0
  uint64_t x34;
977
0
  fiat_p256_uint1 x35;
978
0
  uint64_t x36;
979
0
  fiat_p256_uint1 x37;
980
0
  uint64_t x38;
981
0
  uint64_t x39;
982
0
  uint64_t x40;
983
0
  uint64_t x41;
984
0
  uint64_t x42;
985
0
  uint64_t x43;
986
0
  uint64_t x44;
987
0
  fiat_p256_uint1 x45;
988
0
  uint64_t x46;
989
0
  fiat_p256_uint1 x47;
990
0
  uint64_t x48;
991
0
  fiat_p256_uint1 x49;
992
0
  uint64_t x50;
993
0
  fiat_p256_uint1 x51;
994
0
  uint64_t x52;
995
0
  fiat_p256_uint1 x53;
996
0
  uint64_t x54;
997
0
  fiat_p256_uint1 x55;
998
0
  uint64_t x56;
999
0
  fiat_p256_uint1 x57;
1000
0
  uint64_t x58;
1001
0
  fiat_p256_uint1 x59;
1002
0
  uint64_t x60;
1003
0
  uint64_t x61;
1004
0
  uint64_t x62;
1005
0
  uint64_t x63;
1006
0
  uint64_t x64;
1007
0
  uint64_t x65;
1008
0
  uint64_t x66;
1009
0
  fiat_p256_uint1 x67;
1010
0
  uint64_t x68;
1011
0
  fiat_p256_uint1 x69;
1012
0
  uint64_t x70;
1013
0
  fiat_p256_uint1 x71;
1014
0
  uint64_t x72;
1015
0
  fiat_p256_uint1 x73;
1016
0
  uint64_t x74;
1017
0
  fiat_p256_uint1 x75;
1018
0
  uint64_t x76;
1019
0
  uint64_t x77;
1020
0
  fiat_p256_uint1 x78;
1021
0
  uint64_t x79;
1022
0
  fiat_p256_uint1 x80;
1023
0
  uint64_t x81;
1024
0
  fiat_p256_uint1 x82;
1025
0
  uint64_t x83;
1026
0
  fiat_p256_uint1 x84;
1027
0
  uint64_t x85;
1028
0
  fiat_p256_uint1 x86;
1029
0
  uint64_t x87;
1030
0
  uint64_t x88;
1031
0
  uint64_t x89;
1032
0
  uint64_t x90;
1033
0
  x1 = (arg1[0]);
1034
0
  fiat_p256_mulx_u64(&x2, &x3, x1, UINT64_C(0xffffffff00000001));
1035
0
  fiat_p256_mulx_u64(&x4, &x5, x1, UINT32_C(0xffffffff));
1036
0
  fiat_p256_mulx_u64(&x6, &x7, x1, UINT64_C(0xffffffffffffffff));
1037
0
  fiat_p256_addcarryx_u64(&x8, &x9, 0x0, x7, x4);
1038
0
  fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x6);
1039
0
  fiat_p256_addcarryx_u64(&x12, &x13, x11, 0x0, x8);
1040
0
  fiat_p256_addcarryx_u64(&x14, &x15, 0x0, x12, (arg1[1]));
1041
0
  fiat_p256_mulx_u64(&x16, &x17, x14, UINT64_C(0xffffffff00000001));
1042
0
  fiat_p256_mulx_u64(&x18, &x19, x14, UINT32_C(0xffffffff));
1043
0
  fiat_p256_mulx_u64(&x20, &x21, x14, UINT64_C(0xffffffffffffffff));
1044
0
  fiat_p256_addcarryx_u64(&x22, &x23, 0x0, x21, x18);
1045
0
  fiat_p256_addcarryx_u64(&x24, &x25, 0x0, x14, x20);
1046
0
  fiat_p256_addcarryx_u64(&x26, &x27, x25, (x15 + (x13 + (x9 + x5))), x22);
1047
0
  fiat_p256_addcarryx_u64(&x28, &x29, x27, x2, (x23 + x19));
1048
0
  fiat_p256_addcarryx_u64(&x30, &x31, x29, x3, x16);
1049
0
  fiat_p256_addcarryx_u64(&x32, &x33, 0x0, x26, (arg1[2]));
1050
0
  fiat_p256_addcarryx_u64(&x34, &x35, x33, x28, 0x0);
1051
0
  fiat_p256_addcarryx_u64(&x36, &x37, x35, x30, 0x0);
1052
0
  fiat_p256_mulx_u64(&x38, &x39, x32, UINT64_C(0xffffffff00000001));
1053
0
  fiat_p256_mulx_u64(&x40, &x41, x32, UINT32_C(0xffffffff));
1054
0
  fiat_p256_mulx_u64(&x42, &x43, x32, UINT64_C(0xffffffffffffffff));
1055
0
  fiat_p256_addcarryx_u64(&x44, &x45, 0x0, x43, x40);
1056
0
  fiat_p256_addcarryx_u64(&x46, &x47, 0x0, x32, x42);
1057
0
  fiat_p256_addcarryx_u64(&x48, &x49, x47, x34, x44);
1058
0
  fiat_p256_addcarryx_u64(&x50, &x51, x49, x36, (x45 + x41));
1059
0
  fiat_p256_addcarryx_u64(&x52, &x53, x51, (x37 + (x31 + x17)), x38);
1060
0
  fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x48, (arg1[3]));
1061
0
  fiat_p256_addcarryx_u64(&x56, &x57, x55, x50, 0x0);
1062
0
  fiat_p256_addcarryx_u64(&x58, &x59, x57, x52, 0x0);
1063
0
  fiat_p256_mulx_u64(&x60, &x61, x54, UINT64_C(0xffffffff00000001));
1064
0
  fiat_p256_mulx_u64(&x62, &x63, x54, UINT32_C(0xffffffff));
1065
0
  fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffffffffffff));
1066
0
  fiat_p256_addcarryx_u64(&x66, &x67, 0x0, x65, x62);
1067
0
  fiat_p256_addcarryx_u64(&x68, &x69, 0x0, x54, x64);
1068
0
  fiat_p256_addcarryx_u64(&x70, &x71, x69, x56, x66);
1069
0
  fiat_p256_addcarryx_u64(&x72, &x73, x71, x58, (x67 + x63));
1070
0
  fiat_p256_addcarryx_u64(&x74, &x75, x73, (x59 + (x53 + x39)), x60);
1071
0
  x76 = (x75 + x61);
1072
0
  fiat_p256_subborrowx_u64(&x77, &x78, 0x0, x70, UINT64_C(0xffffffffffffffff));
1073
0
  fiat_p256_subborrowx_u64(&x79, &x80, x78, x72, UINT32_C(0xffffffff));
1074
0
  fiat_p256_subborrowx_u64(&x81, &x82, x80, x74, 0x0);
1075
0
  fiat_p256_subborrowx_u64(&x83, &x84, x82, x76, UINT64_C(0xffffffff00000001));
1076
0
  fiat_p256_subborrowx_u64(&x85, &x86, x84, 0x0, 0x0);
1077
0
  fiat_p256_cmovznz_u64(&x87, x86, x77, x70);
1078
0
  fiat_p256_cmovznz_u64(&x88, x86, x79, x72);
1079
0
  fiat_p256_cmovznz_u64(&x89, x86, x81, x74);
1080
0
  fiat_p256_cmovznz_u64(&x90, x86, x83, x76);
1081
0
  out1[0] = x87;
1082
0
  out1[1] = x88;
1083
0
  out1[2] = x89;
1084
0
  out1[3] = x90;
1085
0
}
1086
1087
/*
1088
 * The function fiat_p256_to_montgomery translates a field element into the Montgomery domain.
1089
 *
1090
 * Preconditions:
1091
 *   0 ≤ eval arg1 < m
1092
 * Postconditions:
1093
 *   eval (from_montgomery out1) mod m = eval arg1 mod m
1094
 *   0 ≤ eval out1 < m
1095
 *
1096
 */
1097
0
static FIAT_P256_FIAT_INLINE void fiat_p256_to_montgomery(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_non_montgomery_domain_field_element arg1) {
1098
0
  uint64_t x1;
1099
0
  uint64_t x2;
1100
0
  uint64_t x3;
1101
0
  uint64_t x4;
1102
0
  uint64_t x5;
1103
0
  uint64_t x6;
1104
0
  uint64_t x7;
1105
0
  uint64_t x8;
1106
0
  uint64_t x9;
1107
0
  uint64_t x10;
1108
0
  uint64_t x11;
1109
0
  uint64_t x12;
1110
0
  uint64_t x13;
1111
0
  fiat_p256_uint1 x14;
1112
0
  uint64_t x15;
1113
0
  fiat_p256_uint1 x16;
1114
0
  uint64_t x17;
1115
0
  fiat_p256_uint1 x18;
1116
0
  uint64_t x19;
1117
0
  uint64_t x20;
1118
0
  uint64_t x21;
1119
0
  uint64_t x22;
1120
0
  uint64_t x23;
1121
0
  uint64_t x24;
1122
0
  uint64_t x25;
1123
0
  fiat_p256_uint1 x26;
1124
0
  uint64_t x27;
1125
0
  fiat_p256_uint1 x28;
1126
0
  uint64_t x29;
1127
0
  fiat_p256_uint1 x30;
1128
0
  uint64_t x31;
1129
0
  fiat_p256_uint1 x32;
1130
0
  uint64_t x33;
1131
0
  fiat_p256_uint1 x34;
1132
0
  uint64_t x35;
1133
0
  fiat_p256_uint1 x36;
1134
0
  uint64_t x37;
1135
0
  uint64_t x38;
1136
0
  uint64_t x39;
1137
0
  uint64_t x40;
1138
0
  uint64_t x41;
1139
0
  uint64_t x42;
1140
0
  uint64_t x43;
1141
0
  uint64_t x44;
1142
0
  uint64_t x45;
1143
0
  fiat_p256_uint1 x46;
1144
0
  uint64_t x47;
1145
0
  fiat_p256_uint1 x48;
1146
0
  uint64_t x49;
1147
0
  fiat_p256_uint1 x50;
1148
0
  uint64_t x51;
1149
0
  fiat_p256_uint1 x52;
1150
0
  uint64_t x53;
1151
0
  fiat_p256_uint1 x54;
1152
0
  uint64_t x55;
1153
0
  fiat_p256_uint1 x56;
1154
0
  uint64_t x57;
1155
0
  fiat_p256_uint1 x58;
1156
0
  uint64_t x59;
1157
0
  uint64_t x60;
1158
0
  uint64_t x61;
1159
0
  uint64_t x62;
1160
0
  uint64_t x63;
1161
0
  uint64_t x64;
1162
0
  uint64_t x65;
1163
0
  fiat_p256_uint1 x66;
1164
0
  uint64_t x67;
1165
0
  fiat_p256_uint1 x68;
1166
0
  uint64_t x69;
1167
0
  fiat_p256_uint1 x70;
1168
0
  uint64_t x71;
1169
0
  fiat_p256_uint1 x72;
1170
0
  uint64_t x73;
1171
0
  fiat_p256_uint1 x74;
1172
0
  uint64_t x75;
1173
0
  fiat_p256_uint1 x76;
1174
0
  uint64_t x77;
1175
0
  uint64_t x78;
1176
0
  uint64_t x79;
1177
0
  uint64_t x80;
1178
0
  uint64_t x81;
1179
0
  uint64_t x82;
1180
0
  uint64_t x83;
1181
0
  uint64_t x84;
1182
0
  uint64_t x85;
1183
0
  fiat_p256_uint1 x86;
1184
0
  uint64_t x87;
1185
0
  fiat_p256_uint1 x88;
1186
0
  uint64_t x89;
1187
0
  fiat_p256_uint1 x90;
1188
0
  uint64_t x91;
1189
0
  fiat_p256_uint1 x92;
1190
0
  uint64_t x93;
1191
0
  fiat_p256_uint1 x94;
1192
0
  uint64_t x95;
1193
0
  fiat_p256_uint1 x96;
1194
0
  uint64_t x97;
1195
0
  fiat_p256_uint1 x98;
1196
0
  uint64_t x99;
1197
0
  uint64_t x100;
1198
0
  uint64_t x101;
1199
0
  uint64_t x102;
1200
0
  uint64_t x103;
1201
0
  uint64_t x104;
1202
0
  uint64_t x105;
1203
0
  fiat_p256_uint1 x106;
1204
0
  uint64_t x107;
1205
0
  fiat_p256_uint1 x108;
1206
0
  uint64_t x109;
1207
0
  fiat_p256_uint1 x110;
1208
0
  uint64_t x111;
1209
0
  fiat_p256_uint1 x112;
1210
0
  uint64_t x113;
1211
0
  fiat_p256_uint1 x114;
1212
0
  uint64_t x115;
1213
0
  fiat_p256_uint1 x116;
1214
0
  uint64_t x117;
1215
0
  uint64_t x118;
1216
0
  uint64_t x119;
1217
0
  uint64_t x120;
1218
0
  uint64_t x121;
1219
0
  uint64_t x122;
1220
0
  uint64_t x123;
1221
0
  uint64_t x124;
1222
0
  uint64_t x125;
1223
0
  fiat_p256_uint1 x126;
1224
0
  uint64_t x127;
1225
0
  fiat_p256_uint1 x128;
1226
0
  uint64_t x129;
1227
0
  fiat_p256_uint1 x130;
1228
0
  uint64_t x131;
1229
0
  fiat_p256_uint1 x132;
1230
0
  uint64_t x133;
1231
0
  fiat_p256_uint1 x134;
1232
0
  uint64_t x135;
1233
0
  fiat_p256_uint1 x136;
1234
0
  uint64_t x137;
1235
0
  fiat_p256_uint1 x138;
1236
0
  uint64_t x139;
1237
0
  uint64_t x140;
1238
0
  uint64_t x141;
1239
0
  uint64_t x142;
1240
0
  uint64_t x143;
1241
0
  uint64_t x144;
1242
0
  uint64_t x145;
1243
0
  fiat_p256_uint1 x146;
1244
0
  uint64_t x147;
1245
0
  fiat_p256_uint1 x148;
1246
0
  uint64_t x149;
1247
0
  fiat_p256_uint1 x150;
1248
0
  uint64_t x151;
1249
0
  fiat_p256_uint1 x152;
1250
0
  uint64_t x153;
1251
0
  fiat_p256_uint1 x154;
1252
0
  uint64_t x155;
1253
0
  fiat_p256_uint1 x156;
1254
0
  uint64_t x157;
1255
0
  fiat_p256_uint1 x158;
1256
0
  uint64_t x159;
1257
0
  fiat_p256_uint1 x160;
1258
0
  uint64_t x161;
1259
0
  fiat_p256_uint1 x162;
1260
0
  uint64_t x163;
1261
0
  fiat_p256_uint1 x164;
1262
0
  uint64_t x165;
1263
0
  fiat_p256_uint1 x166;
1264
0
  uint64_t x167;
1265
0
  uint64_t x168;
1266
0
  uint64_t x169;
1267
0
  uint64_t x170;
1268
0
  x1 = (arg1[1]);
1269
0
  x2 = (arg1[2]);
1270
0
  x3 = (arg1[3]);
1271
0
  x4 = (arg1[0]);
1272
0
  fiat_p256_mulx_u64(&x5, &x6, x4, UINT64_C(0x4fffffffd));
1273
0
  fiat_p256_mulx_u64(&x7, &x8, x4, UINT64_C(0xfffffffffffffffe));
1274
0
  fiat_p256_mulx_u64(&x9, &x10, x4, UINT64_C(0xfffffffbffffffff));
1275
0
  fiat_p256_mulx_u64(&x11, &x12, x4, 0x3);
1276
0
  fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
1277
0
  fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
1278
0
  fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
1279
0
  fiat_p256_mulx_u64(&x19, &x20, x11, UINT64_C(0xffffffff00000001));
1280
0
  fiat_p256_mulx_u64(&x21, &x22, x11, UINT32_C(0xffffffff));
1281
0
  fiat_p256_mulx_u64(&x23, &x24, x11, UINT64_C(0xffffffffffffffff));
1282
0
  fiat_p256_addcarryx_u64(&x25, &x26, 0x0, x24, x21);
1283
0
  fiat_p256_addcarryx_u64(&x27, &x28, 0x0, x11, x23);
1284
0
  fiat_p256_addcarryx_u64(&x29, &x30, x28, x13, x25);
1285
0
  fiat_p256_addcarryx_u64(&x31, &x32, x30, x15, (x26 + x22));
1286
0
  fiat_p256_addcarryx_u64(&x33, &x34, x32, x17, x19);
1287
0
  fiat_p256_addcarryx_u64(&x35, &x36, x34, (x18 + x6), x20);
1288
0
  fiat_p256_mulx_u64(&x37, &x38, x1, UINT64_C(0x4fffffffd));
1289
0
  fiat_p256_mulx_u64(&x39, &x40, x1, UINT64_C(0xfffffffffffffffe));
1290
0
  fiat_p256_mulx_u64(&x41, &x42, x1, UINT64_C(0xfffffffbffffffff));
1291
0
  fiat_p256_mulx_u64(&x43, &x44, x1, 0x3);
1292
0
  fiat_p256_addcarryx_u64(&x45, &x46, 0x0, x44, x41);
1293
0
  fiat_p256_addcarryx_u64(&x47, &x48, x46, x42, x39);
1294
0
  fiat_p256_addcarryx_u64(&x49, &x50, x48, x40, x37);
1295
0
  fiat_p256_addcarryx_u64(&x51, &x52, 0x0, x29, x43);
1296
0
  fiat_p256_addcarryx_u64(&x53, &x54, x52, x31, x45);
1297
0
  fiat_p256_addcarryx_u64(&x55, &x56, x54, x33, x47);
1298
0
  fiat_p256_addcarryx_u64(&x57, &x58, x56, x35, x49);
1299
0
  fiat_p256_mulx_u64(&x59, &x60, x51, UINT64_C(0xffffffff00000001));
1300
0
  fiat_p256_mulx_u64(&x61, &x62, x51, UINT32_C(0xffffffff));
1301
0
  fiat_p256_mulx_u64(&x63, &x64, x51, UINT64_C(0xffffffffffffffff));
1302
0
  fiat_p256_addcarryx_u64(&x65, &x66, 0x0, x64, x61);
1303
0
  fiat_p256_addcarryx_u64(&x67, &x68, 0x0, x51, x63);
1304
0
  fiat_p256_addcarryx_u64(&x69, &x70, x68, x53, x65);
1305
0
  fiat_p256_addcarryx_u64(&x71, &x72, x70, x55, (x66 + x62));
1306
0
  fiat_p256_addcarryx_u64(&x73, &x74, x72, x57, x59);
1307
0
  fiat_p256_addcarryx_u64(&x75, &x76, x74, (((uint64_t)x58 + x36) + (x50 + x38)), x60);
1308
0
  fiat_p256_mulx_u64(&x77, &x78, x2, UINT64_C(0x4fffffffd));
1309
0
  fiat_p256_mulx_u64(&x79, &x80, x2, UINT64_C(0xfffffffffffffffe));
1310
0
  fiat_p256_mulx_u64(&x81, &x82, x2, UINT64_C(0xfffffffbffffffff));
1311
0
  fiat_p256_mulx_u64(&x83, &x84, x2, 0x3);
1312
0
  fiat_p256_addcarryx_u64(&x85, &x86, 0x0, x84, x81);
1313
0
  fiat_p256_addcarryx_u64(&x87, &x88, x86, x82, x79);
1314
0
  fiat_p256_addcarryx_u64(&x89, &x90, x88, x80, x77);
1315
0
  fiat_p256_addcarryx_u64(&x91, &x92, 0x0, x69, x83);
1316
0
  fiat_p256_addcarryx_u64(&x93, &x94, x92, x71, x85);
1317
0
  fiat_p256_addcarryx_u64(&x95, &x96, x94, x73, x87);
1318
0
  fiat_p256_addcarryx_u64(&x97, &x98, x96, x75, x89);
1319
0
  fiat_p256_mulx_u64(&x99, &x100, x91, UINT64_C(0xffffffff00000001));
1320
0
  fiat_p256_mulx_u64(&x101, &x102, x91, UINT32_C(0xffffffff));
1321
0
  fiat_p256_mulx_u64(&x103, &x104, x91, UINT64_C(0xffffffffffffffff));
1322
0
  fiat_p256_addcarryx_u64(&x105, &x106, 0x0, x104, x101);
1323
0
  fiat_p256_addcarryx_u64(&x107, &x108, 0x0, x91, x103);
1324
0
  fiat_p256_addcarryx_u64(&x109, &x110, x108, x93, x105);
1325
0
  fiat_p256_addcarryx_u64(&x111, &x112, x110, x95, (x106 + x102));
1326
0
  fiat_p256_addcarryx_u64(&x113, &x114, x112, x97, x99);
1327
0
  fiat_p256_addcarryx_u64(&x115, &x116, x114, (((uint64_t)x98 + x76) + (x90 + x78)), x100);
1328
0
  fiat_p256_mulx_u64(&x117, &x118, x3, UINT64_C(0x4fffffffd));
1329
0
  fiat_p256_mulx_u64(&x119, &x120, x3, UINT64_C(0xfffffffffffffffe));
1330
0
  fiat_p256_mulx_u64(&x121, &x122, x3, UINT64_C(0xfffffffbffffffff));
1331
0
  fiat_p256_mulx_u64(&x123, &x124, x3, 0x3);
1332
0
  fiat_p256_addcarryx_u64(&x125, &x126, 0x0, x124, x121);
1333
0
  fiat_p256_addcarryx_u64(&x127, &x128, x126, x122, x119);
1334
0
  fiat_p256_addcarryx_u64(&x129, &x130, x128, x120, x117);
1335
0
  fiat_p256_addcarryx_u64(&x131, &x132, 0x0, x109, x123);
1336
0
  fiat_p256_addcarryx_u64(&x133, &x134, x132, x111, x125);
1337
0
  fiat_p256_addcarryx_u64(&x135, &x136, x134, x113, x127);
1338
0
  fiat_p256_addcarryx_u64(&x137, &x138, x136, x115, x129);
1339
0
  fiat_p256_mulx_u64(&x139, &x140, x131, UINT64_C(0xffffffff00000001));
1340
0
  fiat_p256_mulx_u64(&x141, &x142, x131, UINT32_C(0xffffffff));
1341
0
  fiat_p256_mulx_u64(&x143, &x144, x131, UINT64_C(0xffffffffffffffff));
1342
0
  fiat_p256_addcarryx_u64(&x145, &x146, 0x0, x144, x141);
1343
0
  fiat_p256_addcarryx_u64(&x147, &x148, 0x0, x131, x143);
1344
0
  fiat_p256_addcarryx_u64(&x149, &x150, x148, x133, x145);
1345
0
  fiat_p256_addcarryx_u64(&x151, &x152, x150, x135, (x146 + x142));
1346
0
  fiat_p256_addcarryx_u64(&x153, &x154, x152, x137, x139);
1347
0
  fiat_p256_addcarryx_u64(&x155, &x156, x154, (((uint64_t)x138 + x116) + (x130 + x118)), x140);
1348
0
  fiat_p256_subborrowx_u64(&x157, &x158, 0x0, x149, UINT64_C(0xffffffffffffffff));
1349
0
  fiat_p256_subborrowx_u64(&x159, &x160, x158, x151, UINT32_C(0xffffffff));
1350
0
  fiat_p256_subborrowx_u64(&x161, &x162, x160, x153, 0x0);
1351
0
  fiat_p256_subborrowx_u64(&x163, &x164, x162, x155, UINT64_C(0xffffffff00000001));
1352
0
  fiat_p256_subborrowx_u64(&x165, &x166, x164, x156, 0x0);
1353
0
  fiat_p256_cmovznz_u64(&x167, x166, x157, x149);
1354
0
  fiat_p256_cmovznz_u64(&x168, x166, x159, x151);
1355
0
  fiat_p256_cmovznz_u64(&x169, x166, x161, x153);
1356
0
  fiat_p256_cmovznz_u64(&x170, x166, x163, x155);
1357
0
  out1[0] = x167;
1358
0
  out1[1] = x168;
1359
0
  out1[2] = x169;
1360
0
  out1[3] = x170;
1361
0
}
1362
1363
/*
1364
 * The function fiat_p256_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
1365
 *
1366
 * Preconditions:
1367
 *   0 ≤ eval arg1 < m
1368
 * Postconditions:
1369
 *   out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0
1370
 *
1371
 * Input Bounds:
1372
 *   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1373
 * Output Bounds:
1374
 *   out1: [0x0 ~> 0xffffffffffffffff]
1375
 */
1376
0
static FIAT_P256_FIAT_INLINE void fiat_p256_nonzero(uint64_t* out1, const uint64_t arg1[4]) {
1377
0
  uint64_t x1;
1378
0
  x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3]))));
1379
0
  *out1 = x1;
1380
0
}
1381
1382
/*
1383
 * The function fiat_p256_selectznz is a multi-limb conditional select.
1384
 *
1385
 * Postconditions:
1386
 *   eval out1 = (if arg1 = 0 then eval arg2 else eval arg3)
1387
 *
1388
 * Input Bounds:
1389
 *   arg1: [0x0 ~> 0x1]
1390
 *   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1391
 *   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1392
 * Output Bounds:
1393
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1394
 */
1395
0
static FIAT_P256_FIAT_INLINE void fiat_p256_selectznz(uint64_t out1[4], fiat_p256_uint1 arg1, const uint64_t arg2[4], const uint64_t arg3[4]) {
1396
0
  uint64_t x1;
1397
0
  uint64_t x2;
1398
0
  uint64_t x3;
1399
0
  uint64_t x4;
1400
0
  fiat_p256_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]));
1401
0
  fiat_p256_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]));
1402
0
  fiat_p256_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]));
1403
0
  fiat_p256_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]));
1404
0
  out1[0] = x1;
1405
0
  out1[1] = x2;
1406
0
  out1[2] = x3;
1407
0
  out1[3] = x4;
1408
0
}
1409
1410
/*
1411
 * The function fiat_p256_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
1412
 *
1413
 * Preconditions:
1414
 *   0 ≤ eval arg1 < m
1415
 * Postconditions:
1416
 *   out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
1417
 *
1418
 * Input Bounds:
1419
 *   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1420
 * Output Bounds:
1421
 *   out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]]
1422
 */
1423
0
static FIAT_P256_FIAT_INLINE void fiat_p256_to_bytes(uint8_t out1[32], const uint64_t arg1[4]) {
1424
0
  uint64_t x1;
1425
0
  uint64_t x2;
1426
0
  uint64_t x3;
1427
0
  uint64_t x4;
1428
0
  uint8_t x5;
1429
0
  uint64_t x6;
1430
0
  uint8_t x7;
1431
0
  uint64_t x8;
1432
0
  uint8_t x9;
1433
0
  uint64_t x10;
1434
0
  uint8_t x11;
1435
0
  uint64_t x12;
1436
0
  uint8_t x13;
1437
0
  uint64_t x14;
1438
0
  uint8_t x15;
1439
0
  uint64_t x16;
1440
0
  uint8_t x17;
1441
0
  uint8_t x18;
1442
0
  uint8_t x19;
1443
0
  uint64_t x20;
1444
0
  uint8_t x21;
1445
0
  uint64_t x22;
1446
0
  uint8_t x23;
1447
0
  uint64_t x24;
1448
0
  uint8_t x25;
1449
0
  uint64_t x26;
1450
0
  uint8_t x27;
1451
0
  uint64_t x28;
1452
0
  uint8_t x29;
1453
0
  uint64_t x30;
1454
0
  uint8_t x31;
1455
0
  uint8_t x32;
1456
0
  uint8_t x33;
1457
0
  uint64_t x34;
1458
0
  uint8_t x35;
1459
0
  uint64_t x36;
1460
0
  uint8_t x37;
1461
0
  uint64_t x38;
1462
0
  uint8_t x39;
1463
0
  uint64_t x40;
1464
0
  uint8_t x41;
1465
0
  uint64_t x42;
1466
0
  uint8_t x43;
1467
0
  uint64_t x44;
1468
0
  uint8_t x45;
1469
0
  uint8_t x46;
1470
0
  uint8_t x47;
1471
0
  uint64_t x48;
1472
0
  uint8_t x49;
1473
0
  uint64_t x50;
1474
0
  uint8_t x51;
1475
0
  uint64_t x52;
1476
0
  uint8_t x53;
1477
0
  uint64_t x54;
1478
0
  uint8_t x55;
1479
0
  uint64_t x56;
1480
0
  uint8_t x57;
1481
0
  uint64_t x58;
1482
0
  uint8_t x59;
1483
0
  uint8_t x60;
1484
0
  x1 = (arg1[3]);
1485
0
  x2 = (arg1[2]);
1486
0
  x3 = (arg1[1]);
1487
0
  x4 = (arg1[0]);
1488
0
  x5 = (uint8_t)(x4 & UINT8_C(0xff));
1489
0
  x6 = (x4 >> 8);
1490
0
  x7 = (uint8_t)(x6 & UINT8_C(0xff));
1491
0
  x8 = (x6 >> 8);
1492
0
  x9 = (uint8_t)(x8 & UINT8_C(0xff));
1493
0
  x10 = (x8 >> 8);
1494
0
  x11 = (uint8_t)(x10 & UINT8_C(0xff));
1495
0
  x12 = (x10 >> 8);
1496
0
  x13 = (uint8_t)(x12 & UINT8_C(0xff));
1497
0
  x14 = (x12 >> 8);
1498
0
  x15 = (uint8_t)(x14 & UINT8_C(0xff));
1499
0
  x16 = (x14 >> 8);
1500
0
  x17 = (uint8_t)(x16 & UINT8_C(0xff));
1501
0
  x18 = (uint8_t)(x16 >> 8);
1502
0
  x19 = (uint8_t)(x3 & UINT8_C(0xff));
1503
0
  x20 = (x3 >> 8);
1504
0
  x21 = (uint8_t)(x20 & UINT8_C(0xff));
1505
0
  x22 = (x20 >> 8);
1506
0
  x23 = (uint8_t)(x22 & UINT8_C(0xff));
1507
0
  x24 = (x22 >> 8);
1508
0
  x25 = (uint8_t)(x24 & UINT8_C(0xff));
1509
0
  x26 = (x24 >> 8);
1510
0
  x27 = (uint8_t)(x26 & UINT8_C(0xff));
1511
0
  x28 = (x26 >> 8);
1512
0
  x29 = (uint8_t)(x28 & UINT8_C(0xff));
1513
0
  x30 = (x28 >> 8);
1514
0
  x31 = (uint8_t)(x30 & UINT8_C(0xff));
1515
0
  x32 = (uint8_t)(x30 >> 8);
1516
0
  x33 = (uint8_t)(x2 & UINT8_C(0xff));
1517
0
  x34 = (x2 >> 8);
1518
0
  x35 = (uint8_t)(x34 & UINT8_C(0xff));
1519
0
  x36 = (x34 >> 8);
1520
0
  x37 = (uint8_t)(x36 & UINT8_C(0xff));
1521
0
  x38 = (x36 >> 8);
1522
0
  x39 = (uint8_t)(x38 & UINT8_C(0xff));
1523
0
  x40 = (x38 >> 8);
1524
0
  x41 = (uint8_t)(x40 & UINT8_C(0xff));
1525
0
  x42 = (x40 >> 8);
1526
0
  x43 = (uint8_t)(x42 & UINT8_C(0xff));
1527
0
  x44 = (x42 >> 8);
1528
0
  x45 = (uint8_t)(x44 & UINT8_C(0xff));
1529
0
  x46 = (uint8_t)(x44 >> 8);
1530
0
  x47 = (uint8_t)(x1 & UINT8_C(0xff));
1531
0
  x48 = (x1 >> 8);
1532
0
  x49 = (uint8_t)(x48 & UINT8_C(0xff));
1533
0
  x50 = (x48 >> 8);
1534
0
  x51 = (uint8_t)(x50 & UINT8_C(0xff));
1535
0
  x52 = (x50 >> 8);
1536
0
  x53 = (uint8_t)(x52 & UINT8_C(0xff));
1537
0
  x54 = (x52 >> 8);
1538
0
  x55 = (uint8_t)(x54 & UINT8_C(0xff));
1539
0
  x56 = (x54 >> 8);
1540
0
  x57 = (uint8_t)(x56 & UINT8_C(0xff));
1541
0
  x58 = (x56 >> 8);
1542
0
  x59 = (uint8_t)(x58 & UINT8_C(0xff));
1543
0
  x60 = (uint8_t)(x58 >> 8);
1544
0
  out1[0] = x5;
1545
0
  out1[1] = x7;
1546
0
  out1[2] = x9;
1547
0
  out1[3] = x11;
1548
0
  out1[4] = x13;
1549
0
  out1[5] = x15;
1550
0
  out1[6] = x17;
1551
0
  out1[7] = x18;
1552
0
  out1[8] = x19;
1553
0
  out1[9] = x21;
1554
0
  out1[10] = x23;
1555
0
  out1[11] = x25;
1556
0
  out1[12] = x27;
1557
0
  out1[13] = x29;
1558
0
  out1[14] = x31;
1559
0
  out1[15] = x32;
1560
0
  out1[16] = x33;
1561
0
  out1[17] = x35;
1562
0
  out1[18] = x37;
1563
0
  out1[19] = x39;
1564
0
  out1[20] = x41;
1565
0
  out1[21] = x43;
1566
0
  out1[22] = x45;
1567
0
  out1[23] = x46;
1568
0
  out1[24] = x47;
1569
0
  out1[25] = x49;
1570
0
  out1[26] = x51;
1571
0
  out1[27] = x53;
1572
0
  out1[28] = x55;
1573
0
  out1[29] = x57;
1574
0
  out1[30] = x59;
1575
0
  out1[31] = x60;
1576
0
}
1577
1578
/*
1579
 * The function fiat_p256_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
1580
 *
1581
 * Preconditions:
1582
 *   0 ≤ bytes_eval arg1 < m
1583
 * Postconditions:
1584
 *   eval out1 mod m = bytes_eval arg1 mod m
1585
 *   0 ≤ eval out1 < m
1586
 *
1587
 * Input Bounds:
1588
 *   arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]]
1589
 * Output Bounds:
1590
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1591
 */
1592
0
static FIAT_P256_FIAT_INLINE void fiat_p256_from_bytes(uint64_t out1[4], const uint8_t arg1[32]) {
1593
0
  uint64_t x1;
1594
0
  uint64_t x2;
1595
0
  uint64_t x3;
1596
0
  uint64_t x4;
1597
0
  uint64_t x5;
1598
0
  uint64_t x6;
1599
0
  uint64_t x7;
1600
0
  uint8_t x8;
1601
0
  uint64_t x9;
1602
0
  uint64_t x10;
1603
0
  uint64_t x11;
1604
0
  uint64_t x12;
1605
0
  uint64_t x13;
1606
0
  uint64_t x14;
1607
0
  uint64_t x15;
1608
0
  uint8_t x16;
1609
0
  uint64_t x17;
1610
0
  uint64_t x18;
1611
0
  uint64_t x19;
1612
0
  uint64_t x20;
1613
0
  uint64_t x21;
1614
0
  uint64_t x22;
1615
0
  uint64_t x23;
1616
0
  uint8_t x24;
1617
0
  uint64_t x25;
1618
0
  uint64_t x26;
1619
0
  uint64_t x27;
1620
0
  uint64_t x28;
1621
0
  uint64_t x29;
1622
0
  uint64_t x30;
1623
0
  uint64_t x31;
1624
0
  uint8_t x32;
1625
0
  uint64_t x33;
1626
0
  uint64_t x34;
1627
0
  uint64_t x35;
1628
0
  uint64_t x36;
1629
0
  uint64_t x37;
1630
0
  uint64_t x38;
1631
0
  uint64_t x39;
1632
0
  uint64_t x40;
1633
0
  uint64_t x41;
1634
0
  uint64_t x42;
1635
0
  uint64_t x43;
1636
0
  uint64_t x44;
1637
0
  uint64_t x45;
1638
0
  uint64_t x46;
1639
0
  uint64_t x47;
1640
0
  uint64_t x48;
1641
0
  uint64_t x49;
1642
0
  uint64_t x50;
1643
0
  uint64_t x51;
1644
0
  uint64_t x52;
1645
0
  uint64_t x53;
1646
0
  uint64_t x54;
1647
0
  uint64_t x55;
1648
0
  uint64_t x56;
1649
0
  uint64_t x57;
1650
0
  uint64_t x58;
1651
0
  uint64_t x59;
1652
0
  uint64_t x60;
1653
0
  x1 = ((uint64_t)(arg1[31]) << 56);
1654
0
  x2 = ((uint64_t)(arg1[30]) << 48);
1655
0
  x3 = ((uint64_t)(arg1[29]) << 40);
1656
0
  x4 = ((uint64_t)(arg1[28]) << 32);
1657
0
  x5 = ((uint64_t)(arg1[27]) << 24);
1658
0
  x6 = ((uint64_t)(arg1[26]) << 16);
1659
0
  x7 = ((uint64_t)(arg1[25]) << 8);
1660
0
  x8 = (arg1[24]);
1661
0
  x9 = ((uint64_t)(arg1[23]) << 56);
1662
0
  x10 = ((uint64_t)(arg1[22]) << 48);
1663
0
  x11 = ((uint64_t)(arg1[21]) << 40);
1664
0
  x12 = ((uint64_t)(arg1[20]) << 32);
1665
0
  x13 = ((uint64_t)(arg1[19]) << 24);
1666
0
  x14 = ((uint64_t)(arg1[18]) << 16);
1667
0
  x15 = ((uint64_t)(arg1[17]) << 8);
1668
0
  x16 = (arg1[16]);
1669
0
  x17 = ((uint64_t)(arg1[15]) << 56);
1670
0
  x18 = ((uint64_t)(arg1[14]) << 48);
1671
0
  x19 = ((uint64_t)(arg1[13]) << 40);
1672
0
  x20 = ((uint64_t)(arg1[12]) << 32);
1673
0
  x21 = ((uint64_t)(arg1[11]) << 24);
1674
0
  x22 = ((uint64_t)(arg1[10]) << 16);
1675
0
  x23 = ((uint64_t)(arg1[9]) << 8);
1676
0
  x24 = (arg1[8]);
1677
0
  x25 = ((uint64_t)(arg1[7]) << 56);
1678
0
  x26 = ((uint64_t)(arg1[6]) << 48);
1679
0
  x27 = ((uint64_t)(arg1[5]) << 40);
1680
0
  x28 = ((uint64_t)(arg1[4]) << 32);
1681
0
  x29 = ((uint64_t)(arg1[3]) << 24);
1682
0
  x30 = ((uint64_t)(arg1[2]) << 16);
1683
0
  x31 = ((uint64_t)(arg1[1]) << 8);
1684
0
  x32 = (arg1[0]);
1685
0
  x33 = (x31 + (uint64_t)x32);
1686
0
  x34 = (x30 + x33);
1687
0
  x35 = (x29 + x34);
1688
0
  x36 = (x28 + x35);
1689
0
  x37 = (x27 + x36);
1690
0
  x38 = (x26 + x37);
1691
0
  x39 = (x25 + x38);
1692
0
  x40 = (x23 + (uint64_t)x24);
1693
0
  x41 = (x22 + x40);
1694
0
  x42 = (x21 + x41);
1695
0
  x43 = (x20 + x42);
1696
0
  x44 = (x19 + x43);
1697
0
  x45 = (x18 + x44);
1698
0
  x46 = (x17 + x45);
1699
0
  x47 = (x15 + (uint64_t)x16);
1700
0
  x48 = (x14 + x47);
1701
0
  x49 = (x13 + x48);
1702
0
  x50 = (x12 + x49);
1703
0
  x51 = (x11 + x50);
1704
0
  x52 = (x10 + x51);
1705
0
  x53 = (x9 + x52);
1706
0
  x54 = (x7 + (uint64_t)x8);
1707
0
  x55 = (x6 + x54);
1708
0
  x56 = (x5 + x55);
1709
0
  x57 = (x4 + x56);
1710
0
  x58 = (x3 + x57);
1711
0
  x59 = (x2 + x58);
1712
0
  x60 = (x1 + x59);
1713
0
  out1[0] = x39;
1714
0
  out1[1] = x46;
1715
0
  out1[2] = x53;
1716
0
  out1[3] = x60;
1717
0
}
1718
1719
/*
1720
 * The function fiat_p256_set_one returns the field element one in the Montgomery domain.
1721
 *
1722
 * Postconditions:
1723
 *   eval (from_montgomery out1) mod m = 1 mod m
1724
 *   0 ≤ eval out1 < m
1725
 *
1726
 */
1727
0
static FIAT_P256_FIAT_INLINE void fiat_p256_set_one(fiat_p256_montgomery_domain_field_element out1) {
1728
0
  out1[0] = 0x1;
1729
0
  out1[1] = UINT64_C(0xffffffff00000000);
1730
0
  out1[2] = UINT64_C(0xffffffffffffffff);
1731
0
  out1[3] = UINT32_C(0xfffffffe);
1732
0
}
1733
1734
/*
1735
 * The function fiat_p256_msat returns the saturated representation of the prime modulus.
1736
 *
1737
 * Postconditions:
1738
 *   twos_complement_eval out1 = m
1739
 *   0 ≤ eval out1 < m
1740
 *
1741
 * Output Bounds:
1742
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1743
 */
1744
0
static FIAT_P256_FIAT_INLINE void fiat_p256_msat(uint64_t out1[5]) {
1745
0
  out1[0] = UINT64_C(0xffffffffffffffff);
1746
0
  out1[1] = UINT32_C(0xffffffff);
1747
0
  out1[2] = 0x0;
1748
0
  out1[3] = UINT64_C(0xffffffff00000001);
1749
0
  out1[4] = 0x0;
1750
0
}
1751
1752
/*
1753
 * The function fiat_p256_divstep computes a divstep.
1754
 *
1755
 * Preconditions:
1756
 *   0 ≤ eval arg4 < m
1757
 *   0 ≤ eval arg5 < m
1758
 * Postconditions:
1759
 *   out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1)
1760
 *   twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2)
1761
 *   twos_complement_eval out3 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then ⌊(twos_complement_eval arg3 - twos_complement_eval arg2) / 2⌋ else ⌊(twos_complement_eval arg3 + (twos_complement_eval arg3 mod 2) * twos_complement_eval arg2) / 2⌋)
1762
 *   eval (from_montgomery out4) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (2 * eval (from_montgomery arg5)) mod m else (2 * eval (from_montgomery arg4)) mod m)
1763
 *   eval (from_montgomery out5) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (eval (from_montgomery arg4) - eval (from_montgomery arg4)) mod m else (eval (from_montgomery arg5) + (twos_complement_eval arg3 mod 2) * eval (from_montgomery arg4)) mod m)
1764
 *   0 ≤ eval out5 < m
1765
 *   0 ≤ eval out5 < m
1766
 *   0 ≤ eval out2 < m
1767
 *   0 ≤ eval out3 < m
1768
 *
1769
 * Input Bounds:
1770
 *   arg1: [0x0 ~> 0xffffffffffffffff]
1771
 *   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1772
 *   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1773
 *   arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1774
 *   arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1775
 * Output Bounds:
1776
 *   out1: [0x0 ~> 0xffffffffffffffff]
1777
 *   out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1778
 *   out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1779
 *   out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1780
 *   out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1781
 */
1782
0
static FIAT_P256_FIAT_INLINE void fiat_p256_divstep(uint64_t* out1, uint64_t out2[5], uint64_t out3[5], uint64_t out4[4], uint64_t out5[4], uint64_t arg1, const uint64_t arg2[5], const uint64_t arg3[5], const uint64_t arg4[4], const uint64_t arg5[4]) {
1783
0
  uint64_t x1;
1784
0
  fiat_p256_uint1 x2;
1785
0
  fiat_p256_uint1 x3;
1786
0
  uint64_t x4;
1787
0
  fiat_p256_uint1 x5;
1788
0
  uint64_t x6;
1789
0
  uint64_t x7;
1790
0
  uint64_t x8;
1791
0
  uint64_t x9;
1792
0
  uint64_t x10;
1793
0
  uint64_t x11;
1794
0
  uint64_t x12;
1795
0
  fiat_p256_uint1 x13;
1796
0
  uint64_t x14;
1797
0
  fiat_p256_uint1 x15;
1798
0
  uint64_t x16;
1799
0
  fiat_p256_uint1 x17;
1800
0
  uint64_t x18;
1801
0
  fiat_p256_uint1 x19;
1802
0
  uint64_t x20;
1803
0
  fiat_p256_uint1 x21;
1804
0
  uint64_t x22;
1805
0
  uint64_t x23;
1806
0
  uint64_t x24;
1807
0
  uint64_t x25;
1808
0
  uint64_t x26;
1809
0
  uint64_t x27;
1810
0
  uint64_t x28;
1811
0
  uint64_t x29;
1812
0
  uint64_t x30;
1813
0
  uint64_t x31;
1814
0
  fiat_p256_uint1 x32;
1815
0
  uint64_t x33;
1816
0
  fiat_p256_uint1 x34;
1817
0
  uint64_t x35;
1818
0
  fiat_p256_uint1 x36;
1819
0
  uint64_t x37;
1820
0
  fiat_p256_uint1 x38;
1821
0
  uint64_t x39;
1822
0
  fiat_p256_uint1 x40;
1823
0
  uint64_t x41;
1824
0
  fiat_p256_uint1 x42;
1825
0
  uint64_t x43;
1826
0
  fiat_p256_uint1 x44;
1827
0
  uint64_t x45;
1828
0
  fiat_p256_uint1 x46;
1829
0
  uint64_t x47;
1830
0
  fiat_p256_uint1 x48;
1831
0
  uint64_t x49;
1832
0
  uint64_t x50;
1833
0
  uint64_t x51;
1834
0
  uint64_t x52;
1835
0
  uint64_t x53;
1836
0
  fiat_p256_uint1 x54;
1837
0
  uint64_t x55;
1838
0
  fiat_p256_uint1 x56;
1839
0
  uint64_t x57;
1840
0
  fiat_p256_uint1 x58;
1841
0
  uint64_t x59;
1842
0
  fiat_p256_uint1 x60;
1843
0
  uint64_t x61;
1844
0
  uint64_t x62;
1845
0
  fiat_p256_uint1 x63;
1846
0
  uint64_t x64;
1847
0
  fiat_p256_uint1 x65;
1848
0
  uint64_t x66;
1849
0
  fiat_p256_uint1 x67;
1850
0
  uint64_t x68;
1851
0
  fiat_p256_uint1 x69;
1852
0
  uint64_t x70;
1853
0
  uint64_t x71;
1854
0
  uint64_t x72;
1855
0
  uint64_t x73;
1856
0
  fiat_p256_uint1 x74;
1857
0
  uint64_t x75;
1858
0
  uint64_t x76;
1859
0
  uint64_t x77;
1860
0
  uint64_t x78;
1861
0
  uint64_t x79;
1862
0
  uint64_t x80;
1863
0
  fiat_p256_uint1 x81;
1864
0
  uint64_t x82;
1865
0
  fiat_p256_uint1 x83;
1866
0
  uint64_t x84;
1867
0
  fiat_p256_uint1 x85;
1868
0
  uint64_t x86;
1869
0
  fiat_p256_uint1 x87;
1870
0
  uint64_t x88;
1871
0
  fiat_p256_uint1 x89;
1872
0
  uint64_t x90;
1873
0
  uint64_t x91;
1874
0
  uint64_t x92;
1875
0
  uint64_t x93;
1876
0
  uint64_t x94;
1877
0
  fiat_p256_uint1 x95;
1878
0
  uint64_t x96;
1879
0
  fiat_p256_uint1 x97;
1880
0
  uint64_t x98;
1881
0
  fiat_p256_uint1 x99;
1882
0
  uint64_t x100;
1883
0
  fiat_p256_uint1 x101;
1884
0
  uint64_t x102;
1885
0
  fiat_p256_uint1 x103;
1886
0
  uint64_t x104;
1887
0
  fiat_p256_uint1 x105;
1888
0
  uint64_t x106;
1889
0
  fiat_p256_uint1 x107;
1890
0
  uint64_t x108;
1891
0
  fiat_p256_uint1 x109;
1892
0
  uint64_t x110;
1893
0
  fiat_p256_uint1 x111;
1894
0
  uint64_t x112;
1895
0
  fiat_p256_uint1 x113;
1896
0
  uint64_t x114;
1897
0
  uint64_t x115;
1898
0
  uint64_t x116;
1899
0
  uint64_t x117;
1900
0
  uint64_t x118;
1901
0
  uint64_t x119;
1902
0
  uint64_t x120;
1903
0
  uint64_t x121;
1904
0
  uint64_t x122;
1905
0
  uint64_t x123;
1906
0
  uint64_t x124;
1907
0
  uint64_t x125;
1908
0
  uint64_t x126;
1909
0
  fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (~arg1), 0x1);
1910
0
  x3 = (fiat_p256_uint1)((fiat_p256_uint1)(x1 >> 63) & (fiat_p256_uint1)((arg3[0]) & 0x1));
1911
0
  fiat_p256_addcarryx_u64(&x4, &x5, 0x0, (~arg1), 0x1);
1912
0
  fiat_p256_cmovznz_u64(&x6, x3, arg1, x4);
1913
0
  fiat_p256_cmovznz_u64(&x7, x3, (arg2[0]), (arg3[0]));
1914
0
  fiat_p256_cmovznz_u64(&x8, x3, (arg2[1]), (arg3[1]));
1915
0
  fiat_p256_cmovznz_u64(&x9, x3, (arg2[2]), (arg3[2]));
1916
0
  fiat_p256_cmovznz_u64(&x10, x3, (arg2[3]), (arg3[3]));
1917
0
  fiat_p256_cmovznz_u64(&x11, x3, (arg2[4]), (arg3[4]));
1918
0
  fiat_p256_addcarryx_u64(&x12, &x13, 0x0, 0x1, (~(arg2[0])));
1919
0
  fiat_p256_addcarryx_u64(&x14, &x15, x13, 0x0, (~(arg2[1])));
1920
0
  fiat_p256_addcarryx_u64(&x16, &x17, x15, 0x0, (~(arg2[2])));
1921
0
  fiat_p256_addcarryx_u64(&x18, &x19, x17, 0x0, (~(arg2[3])));
1922
0
  fiat_p256_addcarryx_u64(&x20, &x21, x19, 0x0, (~(arg2[4])));
1923
0
  fiat_p256_cmovznz_u64(&x22, x3, (arg3[0]), x12);
1924
0
  fiat_p256_cmovznz_u64(&x23, x3, (arg3[1]), x14);
1925
0
  fiat_p256_cmovznz_u64(&x24, x3, (arg3[2]), x16);
1926
0
  fiat_p256_cmovznz_u64(&x25, x3, (arg3[3]), x18);
1927
0
  fiat_p256_cmovznz_u64(&x26, x3, (arg3[4]), x20);
1928
0
  fiat_p256_cmovznz_u64(&x27, x3, (arg4[0]), (arg5[0]));
1929
0
  fiat_p256_cmovznz_u64(&x28, x3, (arg4[1]), (arg5[1]));
1930
0
  fiat_p256_cmovznz_u64(&x29, x3, (arg4[2]), (arg5[2]));
1931
0
  fiat_p256_cmovznz_u64(&x30, x3, (arg4[3]), (arg5[3]));
1932
0
  fiat_p256_addcarryx_u64(&x31, &x32, 0x0, x27, x27);
1933
0
  fiat_p256_addcarryx_u64(&x33, &x34, x32, x28, x28);
1934
0
  fiat_p256_addcarryx_u64(&x35, &x36, x34, x29, x29);
1935
0
  fiat_p256_addcarryx_u64(&x37, &x38, x36, x30, x30);
1936
0
  fiat_p256_subborrowx_u64(&x39, &x40, 0x0, x31, UINT64_C(0xffffffffffffffff));
1937
0
  fiat_p256_subborrowx_u64(&x41, &x42, x40, x33, UINT32_C(0xffffffff));
1938
0
  fiat_p256_subborrowx_u64(&x43, &x44, x42, x35, 0x0);
1939
0
  fiat_p256_subborrowx_u64(&x45, &x46, x44, x37, UINT64_C(0xffffffff00000001));
1940
0
  fiat_p256_subborrowx_u64(&x47, &x48, x46, x38, 0x0);
1941
0
  x49 = (arg4[3]);
1942
0
  x50 = (arg4[2]);
1943
0
  x51 = (arg4[1]);
1944
0
  x52 = (arg4[0]);
1945
0
  fiat_p256_subborrowx_u64(&x53, &x54, 0x0, 0x0, x52);
1946
0
  fiat_p256_subborrowx_u64(&x55, &x56, x54, 0x0, x51);
1947
0
  fiat_p256_subborrowx_u64(&x57, &x58, x56, 0x0, x50);
1948
0
  fiat_p256_subborrowx_u64(&x59, &x60, x58, 0x0, x49);
1949
0
  fiat_p256_cmovznz_u64(&x61, x60, 0x0, UINT64_C(0xffffffffffffffff));
1950
0
  fiat_p256_addcarryx_u64(&x62, &x63, 0x0, x53, x61);
1951
0
  fiat_p256_addcarryx_u64(&x64, &x65, x63, x55, (x61 & UINT32_C(0xffffffff)));
1952
0
  fiat_p256_addcarryx_u64(&x66, &x67, x65, x57, 0x0);
1953
0
  fiat_p256_addcarryx_u64(&x68, &x69, x67, x59, (x61 & UINT64_C(0xffffffff00000001)));
1954
0
  fiat_p256_cmovznz_u64(&x70, x3, (arg5[0]), x62);
1955
0
  fiat_p256_cmovznz_u64(&x71, x3, (arg5[1]), x64);
1956
0
  fiat_p256_cmovznz_u64(&x72, x3, (arg5[2]), x66);
1957
0
  fiat_p256_cmovznz_u64(&x73, x3, (arg5[3]), x68);
1958
0
  x74 = (fiat_p256_uint1)(x22 & 0x1);
1959
0
  fiat_p256_cmovznz_u64(&x75, x74, 0x0, x7);
1960
0
  fiat_p256_cmovznz_u64(&x76, x74, 0x0, x8);
1961
0
  fiat_p256_cmovznz_u64(&x77, x74, 0x0, x9);
1962
0
  fiat_p256_cmovznz_u64(&x78, x74, 0x0, x10);
1963
0
  fiat_p256_cmovznz_u64(&x79, x74, 0x0, x11);
1964
0
  fiat_p256_addcarryx_u64(&x80, &x81, 0x0, x22, x75);
1965
0
  fiat_p256_addcarryx_u64(&x82, &x83, x81, x23, x76);
1966
0
  fiat_p256_addcarryx_u64(&x84, &x85, x83, x24, x77);
1967
0
  fiat_p256_addcarryx_u64(&x86, &x87, x85, x25, x78);
1968
0
  fiat_p256_addcarryx_u64(&x88, &x89, x87, x26, x79);
1969
0
  fiat_p256_cmovznz_u64(&x90, x74, 0x0, x27);
1970
0
  fiat_p256_cmovznz_u64(&x91, x74, 0x0, x28);
1971
0
  fiat_p256_cmovznz_u64(&x92, x74, 0x0, x29);
1972
0
  fiat_p256_cmovznz_u64(&x93, x74, 0x0, x30);
1973
0
  fiat_p256_addcarryx_u64(&x94, &x95, 0x0, x70, x90);
1974
0
  fiat_p256_addcarryx_u64(&x96, &x97, x95, x71, x91);
1975
0
  fiat_p256_addcarryx_u64(&x98, &x99, x97, x72, x92);
1976
0
  fiat_p256_addcarryx_u64(&x100, &x101, x99, x73, x93);
1977
0
  fiat_p256_subborrowx_u64(&x102, &x103, 0x0, x94, UINT64_C(0xffffffffffffffff));
1978
0
  fiat_p256_subborrowx_u64(&x104, &x105, x103, x96, UINT32_C(0xffffffff));
1979
0
  fiat_p256_subborrowx_u64(&x106, &x107, x105, x98, 0x0);
1980
0
  fiat_p256_subborrowx_u64(&x108, &x109, x107, x100, UINT64_C(0xffffffff00000001));
1981
0
  fiat_p256_subborrowx_u64(&x110, &x111, x109, x101, 0x0);
1982
0
  fiat_p256_addcarryx_u64(&x112, &x113, 0x0, x6, 0x1);
1983
0
  x114 = ((x80 >> 1) | ((x82 << 63) & UINT64_C(0xffffffffffffffff)));
1984
0
  x115 = ((x82 >> 1) | ((x84 << 63) & UINT64_C(0xffffffffffffffff)));
1985
0
  x116 = ((x84 >> 1) | ((x86 << 63) & UINT64_C(0xffffffffffffffff)));
1986
0
  x117 = ((x86 >> 1) | ((x88 << 63) & UINT64_C(0xffffffffffffffff)));
1987
0
  x118 = ((x88 & UINT64_C(0x8000000000000000)) | (x88 >> 1));
1988
0
  fiat_p256_cmovznz_u64(&x119, x48, x39, x31);
1989
0
  fiat_p256_cmovznz_u64(&x120, x48, x41, x33);
1990
0
  fiat_p256_cmovznz_u64(&x121, x48, x43, x35);
1991
0
  fiat_p256_cmovznz_u64(&x122, x48, x45, x37);
1992
0
  fiat_p256_cmovznz_u64(&x123, x111, x102, x94);
1993
0
  fiat_p256_cmovznz_u64(&x124, x111, x104, x96);
1994
0
  fiat_p256_cmovznz_u64(&x125, x111, x106, x98);
1995
0
  fiat_p256_cmovznz_u64(&x126, x111, x108, x100);
1996
0
  *out1 = x112;
1997
0
  out2[0] = x7;
1998
0
  out2[1] = x8;
1999
0
  out2[2] = x9;
2000
0
  out2[3] = x10;
2001
0
  out2[4] = x11;
2002
0
  out3[0] = x114;
2003
0
  out3[1] = x115;
2004
0
  out3[2] = x116;
2005
0
  out3[3] = x117;
2006
0
  out3[4] = x118;
2007
0
  out4[0] = x119;
2008
0
  out4[1] = x120;
2009
0
  out4[2] = x121;
2010
0
  out4[3] = x122;
2011
0
  out5[0] = x123;
2012
0
  out5[1] = x124;
2013
0
  out5[2] = x125;
2014
0
  out5[3] = x126;
2015
0
}
2016
2017
/*
2018
 * The function fiat_p256_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).
2019
 *
2020
 * Postconditions:
2021
 *   eval (from_montgomery out1) = ⌊(m - 1) / 2⌋^(if ⌊log2 m⌋ + 1 < 46 then ⌊(49 * (⌊log2 m⌋ + 1) + 80) / 17⌋ else ⌊(49 * (⌊log2 m⌋ + 1) + 57) / 17⌋)
2022
 *   0 ≤ eval out1 < m
2023
 *
2024
 * Output Bounds:
2025
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
2026
 */
2027
0
static FIAT_P256_FIAT_INLINE void fiat_p256_divstep_precomp(uint64_t out1[4]) {
2028
0
  out1[0] = UINT64_C(0x67ffffffb8000000);
2029
0
  out1[1] = UINT64_C(0xc000000038000000);
2030
0
  out1[2] = UINT64_C(0xd80000007fffffff);
2031
0
  out1[3] = UINT64_C(0x2fffffffffffffff);
2032
0
}