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__))
fiat_p256_value_barrier_u64(uint64_t a)54 static __inline__ uint64_t fiat_p256_value_barrier_u64(uint64_t a) {
55 __asm__("" : "+r"(a) : /* no inputs */);
56 return a;
57 }
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 */
fiat_p256_addcarryx_u64(uint64_t * out1,fiat_p256_uint1 * out2,fiat_p256_uint1 arg1,uint64_t arg2,uint64_t arg3)78 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 fiat_p256_uint128 x1;
80 uint64_t x2;
81 fiat_p256_uint1 x3;
82 x1 = ((arg1 + (fiat_p256_uint128)arg2) + arg3);
83 x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
84 x3 = (fiat_p256_uint1)(x1 >> 64);
85 *out1 = x2;
86 *out2 = x3;
87 }
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 */
fiat_p256_subborrowx_u64(uint64_t * out1,fiat_p256_uint1 * out2,fiat_p256_uint1 arg1,uint64_t arg2,uint64_t arg3)104 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 fiat_p256_int128 x1;
106 fiat_p256_int1 x2;
107 uint64_t x3;
108 x1 = ((arg2 - (fiat_p256_int128)arg1) - arg3);
109 x2 = (fiat_p256_int1)(x1 >> 64);
110 x3 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
111 *out1 = x3;
112 *out2 = (fiat_p256_uint1)(0x0 - x2);
113 }
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 */
fiat_p256_mulx_u64(uint64_t * out1,uint64_t * out2,uint64_t arg1,uint64_t arg2)129 static FIAT_P256_FIAT_INLINE void fiat_p256_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) {
130 fiat_p256_uint128 x1;
131 uint64_t x2;
132 uint64_t x3;
133 x1 = ((fiat_p256_uint128)arg1 * arg2);
134 x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
135 x3 = (uint64_t)(x1 >> 64);
136 *out1 = x2;
137 *out2 = x3;
138 }
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 */
fiat_p256_cmovznz_u64(uint64_t * out1,fiat_p256_uint1 arg1,uint64_t arg2,uint64_t arg3)153 static FIAT_P256_FIAT_INLINE void fiat_p256_cmovznz_u64(uint64_t* out1, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) {
154 fiat_p256_uint1 x1;
155 uint64_t x2;
156 uint64_t x3;
157 x1 = (!(!arg1));
158 x2 = ((fiat_p256_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff));
159 x3 = ((fiat_p256_value_barrier_u64(x2) & arg3) | (fiat_p256_value_barrier_u64((~x2)) & arg2));
160 *out1 = x3;
161 }
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 */
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)174 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 #if !defined(OPENSSL_NO_ASM) && defined(__GNUC__) && defined(__x86_64__)
176 if (CRYPTO_is_BMI1_capable() && CRYPTO_is_BMI2_capable() &&
177 CRYPTO_is_ADX_capable()) {
178 fiat_p256_adx_mul(out1, arg1, arg2);
179 return;
180 }
181 #endif
182 uint64_t x1;
183 uint64_t x2;
184 uint64_t x3;
185 uint64_t x4;
186 uint64_t x5;
187 uint64_t x6;
188 uint64_t x7;
189 uint64_t x8;
190 uint64_t x9;
191 uint64_t x10;
192 uint64_t x11;
193 uint64_t x12;
194 uint64_t x13;
195 fiat_p256_uint1 x14;
196 uint64_t x15;
197 fiat_p256_uint1 x16;
198 uint64_t x17;
199 fiat_p256_uint1 x18;
200 uint64_t x19;
201 uint64_t x20;
202 uint64_t x21;
203 uint64_t x22;
204 uint64_t x23;
205 uint64_t x24;
206 uint64_t x25;
207 uint64_t x26;
208 fiat_p256_uint1 x27;
209 uint64_t x28;
210 uint64_t x29;
211 fiat_p256_uint1 x30;
212 uint64_t x31;
213 fiat_p256_uint1 x32;
214 uint64_t x33;
215 fiat_p256_uint1 x34;
216 uint64_t x35;
217 fiat_p256_uint1 x36;
218 uint64_t x37;
219 fiat_p256_uint1 x38;
220 uint64_t x39;
221 uint64_t x40;
222 uint64_t x41;
223 uint64_t x42;
224 uint64_t x43;
225 uint64_t x44;
226 uint64_t x45;
227 uint64_t x46;
228 uint64_t x47;
229 fiat_p256_uint1 x48;
230 uint64_t x49;
231 fiat_p256_uint1 x50;
232 uint64_t x51;
233 fiat_p256_uint1 x52;
234 uint64_t x53;
235 uint64_t x54;
236 fiat_p256_uint1 x55;
237 uint64_t x56;
238 fiat_p256_uint1 x57;
239 uint64_t x58;
240 fiat_p256_uint1 x59;
241 uint64_t x60;
242 fiat_p256_uint1 x61;
243 uint64_t x62;
244 fiat_p256_uint1 x63;
245 uint64_t x64;
246 uint64_t x65;
247 uint64_t x66;
248 uint64_t x67;
249 uint64_t x68;
250 uint64_t x69;
251 uint64_t x70;
252 fiat_p256_uint1 x71;
253 uint64_t x72;
254 uint64_t x73;
255 fiat_p256_uint1 x74;
256 uint64_t x75;
257 fiat_p256_uint1 x76;
258 uint64_t x77;
259 fiat_p256_uint1 x78;
260 uint64_t x79;
261 fiat_p256_uint1 x80;
262 uint64_t x81;
263 fiat_p256_uint1 x82;
264 uint64_t x83;
265 uint64_t x84;
266 uint64_t x85;
267 uint64_t x86;
268 uint64_t x87;
269 uint64_t x88;
270 uint64_t x89;
271 uint64_t x90;
272 uint64_t x91;
273 uint64_t x92;
274 fiat_p256_uint1 x93;
275 uint64_t x94;
276 fiat_p256_uint1 x95;
277 uint64_t x96;
278 fiat_p256_uint1 x97;
279 uint64_t x98;
280 uint64_t x99;
281 fiat_p256_uint1 x100;
282 uint64_t x101;
283 fiat_p256_uint1 x102;
284 uint64_t x103;
285 fiat_p256_uint1 x104;
286 uint64_t x105;
287 fiat_p256_uint1 x106;
288 uint64_t x107;
289 fiat_p256_uint1 x108;
290 uint64_t x109;
291 uint64_t x110;
292 uint64_t x111;
293 uint64_t x112;
294 uint64_t x113;
295 uint64_t x114;
296 uint64_t x115;
297 fiat_p256_uint1 x116;
298 uint64_t x117;
299 uint64_t x118;
300 fiat_p256_uint1 x119;
301 uint64_t x120;
302 fiat_p256_uint1 x121;
303 uint64_t x122;
304 fiat_p256_uint1 x123;
305 uint64_t x124;
306 fiat_p256_uint1 x125;
307 uint64_t x126;
308 fiat_p256_uint1 x127;
309 uint64_t x128;
310 uint64_t x129;
311 uint64_t x130;
312 uint64_t x131;
313 uint64_t x132;
314 uint64_t x133;
315 uint64_t x134;
316 uint64_t x135;
317 uint64_t x136;
318 uint64_t x137;
319 fiat_p256_uint1 x138;
320 uint64_t x139;
321 fiat_p256_uint1 x140;
322 uint64_t x141;
323 fiat_p256_uint1 x142;
324 uint64_t x143;
325 uint64_t x144;
326 fiat_p256_uint1 x145;
327 uint64_t x146;
328 fiat_p256_uint1 x147;
329 uint64_t x148;
330 fiat_p256_uint1 x149;
331 uint64_t x150;
332 fiat_p256_uint1 x151;
333 uint64_t x152;
334 fiat_p256_uint1 x153;
335 uint64_t x154;
336 uint64_t x155;
337 uint64_t x156;
338 uint64_t x157;
339 uint64_t x158;
340 uint64_t x159;
341 uint64_t x160;
342 fiat_p256_uint1 x161;
343 uint64_t x162;
344 uint64_t x163;
345 fiat_p256_uint1 x164;
346 uint64_t x165;
347 fiat_p256_uint1 x166;
348 uint64_t x167;
349 fiat_p256_uint1 x168;
350 uint64_t x169;
351 fiat_p256_uint1 x170;
352 uint64_t x171;
353 fiat_p256_uint1 x172;
354 uint64_t x173;
355 uint64_t x174;
356 fiat_p256_uint1 x175;
357 uint64_t x176;
358 fiat_p256_uint1 x177;
359 uint64_t x178;
360 fiat_p256_uint1 x179;
361 uint64_t x180;
362 fiat_p256_uint1 x181;
363 uint64_t x182;
364 fiat_p256_uint1 x183;
365 uint64_t x184;
366 uint64_t x185;
367 uint64_t x186;
368 uint64_t x187;
369 x1 = (arg1[1]);
370 x2 = (arg1[2]);
371 x3 = (arg1[3]);
372 x4 = (arg1[0]);
373 fiat_p256_mulx_u64(&x5, &x6, x4, (arg2[3]));
374 fiat_p256_mulx_u64(&x7, &x8, x4, (arg2[2]));
375 fiat_p256_mulx_u64(&x9, &x10, x4, (arg2[1]));
376 fiat_p256_mulx_u64(&x11, &x12, x4, (arg2[0]));
377 fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
378 fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
379 fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
380 x19 = (x18 + x6);
381 fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001));
382 fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff));
383 fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff));
384 fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22);
385 x28 = (x27 + x23);
386 fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24);
387 fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26);
388 fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28);
389 fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20);
390 fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21);
391 fiat_p256_mulx_u64(&x39, &x40, x1, (arg2[3]));
392 fiat_p256_mulx_u64(&x41, &x42, x1, (arg2[2]));
393 fiat_p256_mulx_u64(&x43, &x44, x1, (arg2[1]));
394 fiat_p256_mulx_u64(&x45, &x46, x1, (arg2[0]));
395 fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43);
396 fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41);
397 fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39);
398 x53 = (x52 + x40);
399 fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45);
400 fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47);
401 fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49);
402 fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51);
403 fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53);
404 fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001));
405 fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff));
406 fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff));
407 fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66);
408 x72 = (x71 + x67);
409 fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68);
410 fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70);
411 fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72);
412 fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64);
413 fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65);
414 x83 = ((uint64_t)x82 + x63);
415 fiat_p256_mulx_u64(&x84, &x85, x2, (arg2[3]));
416 fiat_p256_mulx_u64(&x86, &x87, x2, (arg2[2]));
417 fiat_p256_mulx_u64(&x88, &x89, x2, (arg2[1]));
418 fiat_p256_mulx_u64(&x90, &x91, x2, (arg2[0]));
419 fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88);
420 fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86);
421 fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84);
422 x98 = (x97 + x85);
423 fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90);
424 fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92);
425 fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94);
426 fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96);
427 fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98);
428 fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001));
429 fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff));
430 fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff));
431 fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111);
432 x117 = (x116 + x112);
433 fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113);
434 fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115);
435 fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117);
436 fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109);
437 fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110);
438 x128 = ((uint64_t)x127 + x108);
439 fiat_p256_mulx_u64(&x129, &x130, x3, (arg2[3]));
440 fiat_p256_mulx_u64(&x131, &x132, x3, (arg2[2]));
441 fiat_p256_mulx_u64(&x133, &x134, x3, (arg2[1]));
442 fiat_p256_mulx_u64(&x135, &x136, x3, (arg2[0]));
443 fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133);
444 fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131);
445 fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129);
446 x143 = (x142 + x130);
447 fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135);
448 fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137);
449 fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139);
450 fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141);
451 fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143);
452 fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001));
453 fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff));
454 fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff));
455 fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156);
456 x162 = (x161 + x157);
457 fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158);
458 fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160);
459 fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162);
460 fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154);
461 fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155);
462 x173 = ((uint64_t)x172 + x153);
463 fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff));
464 fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff));
465 fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0);
466 fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001));
467 fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0);
468 fiat_p256_cmovznz_u64(&x184, x183, x174, x165);
469 fiat_p256_cmovznz_u64(&x185, x183, x176, x167);
470 fiat_p256_cmovznz_u64(&x186, x183, x178, x169);
471 fiat_p256_cmovznz_u64(&x187, x183, x180, x171);
472 out1[0] = x184;
473 out1[1] = x185;
474 out1[2] = x186;
475 out1[3] = x187;
476 }
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 */
fiat_p256_square(fiat_p256_montgomery_domain_field_element out1,const fiat_p256_montgomery_domain_field_element arg1)488 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 #if !defined(OPENSSL_NO_ASM) && defined(__GNUC__) && defined(__x86_64__)
490 if (CRYPTO_is_BMI1_capable() && CRYPTO_is_BMI2_capable() &&
491 CRYPTO_is_ADX_capable()) {
492 fiat_p256_adx_sqr(out1, arg1);
493 return;
494 }
495 #endif
496 uint64_t x1;
497 uint64_t x2;
498 uint64_t x3;
499 uint64_t x4;
500 uint64_t x5;
501 uint64_t x6;
502 uint64_t x7;
503 uint64_t x8;
504 uint64_t x9;
505 uint64_t x10;
506 uint64_t x11;
507 uint64_t x12;
508 uint64_t x13;
509 fiat_p256_uint1 x14;
510 uint64_t x15;
511 fiat_p256_uint1 x16;
512 uint64_t x17;
513 fiat_p256_uint1 x18;
514 uint64_t x19;
515 uint64_t x20;
516 uint64_t x21;
517 uint64_t x22;
518 uint64_t x23;
519 uint64_t x24;
520 uint64_t x25;
521 uint64_t x26;
522 fiat_p256_uint1 x27;
523 uint64_t x28;
524 uint64_t x29;
525 fiat_p256_uint1 x30;
526 uint64_t x31;
527 fiat_p256_uint1 x32;
528 uint64_t x33;
529 fiat_p256_uint1 x34;
530 uint64_t x35;
531 fiat_p256_uint1 x36;
532 uint64_t x37;
533 fiat_p256_uint1 x38;
534 uint64_t x39;
535 uint64_t x40;
536 uint64_t x41;
537 uint64_t x42;
538 uint64_t x43;
539 uint64_t x44;
540 uint64_t x45;
541 uint64_t x46;
542 uint64_t x47;
543 fiat_p256_uint1 x48;
544 uint64_t x49;
545 fiat_p256_uint1 x50;
546 uint64_t x51;
547 fiat_p256_uint1 x52;
548 uint64_t x53;
549 uint64_t x54;
550 fiat_p256_uint1 x55;
551 uint64_t x56;
552 fiat_p256_uint1 x57;
553 uint64_t x58;
554 fiat_p256_uint1 x59;
555 uint64_t x60;
556 fiat_p256_uint1 x61;
557 uint64_t x62;
558 fiat_p256_uint1 x63;
559 uint64_t x64;
560 uint64_t x65;
561 uint64_t x66;
562 uint64_t x67;
563 uint64_t x68;
564 uint64_t x69;
565 uint64_t x70;
566 fiat_p256_uint1 x71;
567 uint64_t x72;
568 uint64_t x73;
569 fiat_p256_uint1 x74;
570 uint64_t x75;
571 fiat_p256_uint1 x76;
572 uint64_t x77;
573 fiat_p256_uint1 x78;
574 uint64_t x79;
575 fiat_p256_uint1 x80;
576 uint64_t x81;
577 fiat_p256_uint1 x82;
578 uint64_t x83;
579 uint64_t x84;
580 uint64_t x85;
581 uint64_t x86;
582 uint64_t x87;
583 uint64_t x88;
584 uint64_t x89;
585 uint64_t x90;
586 uint64_t x91;
587 uint64_t x92;
588 fiat_p256_uint1 x93;
589 uint64_t x94;
590 fiat_p256_uint1 x95;
591 uint64_t x96;
592 fiat_p256_uint1 x97;
593 uint64_t x98;
594 uint64_t x99;
595 fiat_p256_uint1 x100;
596 uint64_t x101;
597 fiat_p256_uint1 x102;
598 uint64_t x103;
599 fiat_p256_uint1 x104;
600 uint64_t x105;
601 fiat_p256_uint1 x106;
602 uint64_t x107;
603 fiat_p256_uint1 x108;
604 uint64_t x109;
605 uint64_t x110;
606 uint64_t x111;
607 uint64_t x112;
608 uint64_t x113;
609 uint64_t x114;
610 uint64_t x115;
611 fiat_p256_uint1 x116;
612 uint64_t x117;
613 uint64_t x118;
614 fiat_p256_uint1 x119;
615 uint64_t x120;
616 fiat_p256_uint1 x121;
617 uint64_t x122;
618 fiat_p256_uint1 x123;
619 uint64_t x124;
620 fiat_p256_uint1 x125;
621 uint64_t x126;
622 fiat_p256_uint1 x127;
623 uint64_t x128;
624 uint64_t x129;
625 uint64_t x130;
626 uint64_t x131;
627 uint64_t x132;
628 uint64_t x133;
629 uint64_t x134;
630 uint64_t x135;
631 uint64_t x136;
632 uint64_t x137;
633 fiat_p256_uint1 x138;
634 uint64_t x139;
635 fiat_p256_uint1 x140;
636 uint64_t x141;
637 fiat_p256_uint1 x142;
638 uint64_t x143;
639 uint64_t x144;
640 fiat_p256_uint1 x145;
641 uint64_t x146;
642 fiat_p256_uint1 x147;
643 uint64_t x148;
644 fiat_p256_uint1 x149;
645 uint64_t x150;
646 fiat_p256_uint1 x151;
647 uint64_t x152;
648 fiat_p256_uint1 x153;
649 uint64_t x154;
650 uint64_t x155;
651 uint64_t x156;
652 uint64_t x157;
653 uint64_t x158;
654 uint64_t x159;
655 uint64_t x160;
656 fiat_p256_uint1 x161;
657 uint64_t x162;
658 uint64_t x163;
659 fiat_p256_uint1 x164;
660 uint64_t x165;
661 fiat_p256_uint1 x166;
662 uint64_t x167;
663 fiat_p256_uint1 x168;
664 uint64_t x169;
665 fiat_p256_uint1 x170;
666 uint64_t x171;
667 fiat_p256_uint1 x172;
668 uint64_t x173;
669 uint64_t x174;
670 fiat_p256_uint1 x175;
671 uint64_t x176;
672 fiat_p256_uint1 x177;
673 uint64_t x178;
674 fiat_p256_uint1 x179;
675 uint64_t x180;
676 fiat_p256_uint1 x181;
677 uint64_t x182;
678 fiat_p256_uint1 x183;
679 uint64_t x184;
680 uint64_t x185;
681 uint64_t x186;
682 uint64_t x187;
683 x1 = (arg1[1]);
684 x2 = (arg1[2]);
685 x3 = (arg1[3]);
686 x4 = (arg1[0]);
687 fiat_p256_mulx_u64(&x5, &x6, x4, (arg1[3]));
688 fiat_p256_mulx_u64(&x7, &x8, x4, (arg1[2]));
689 fiat_p256_mulx_u64(&x9, &x10, x4, (arg1[1]));
690 fiat_p256_mulx_u64(&x11, &x12, x4, (arg1[0]));
691 fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
692 fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
693 fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
694 x19 = (x18 + x6);
695 fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001));
696 fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff));
697 fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff));
698 fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22);
699 x28 = (x27 + x23);
700 fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24);
701 fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26);
702 fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28);
703 fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20);
704 fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21);
705 fiat_p256_mulx_u64(&x39, &x40, x1, (arg1[3]));
706 fiat_p256_mulx_u64(&x41, &x42, x1, (arg1[2]));
707 fiat_p256_mulx_u64(&x43, &x44, x1, (arg1[1]));
708 fiat_p256_mulx_u64(&x45, &x46, x1, (arg1[0]));
709 fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43);
710 fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41);
711 fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39);
712 x53 = (x52 + x40);
713 fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45);
714 fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47);
715 fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49);
716 fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51);
717 fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53);
718 fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001));
719 fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff));
720 fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff));
721 fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66);
722 x72 = (x71 + x67);
723 fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68);
724 fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70);
725 fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72);
726 fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64);
727 fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65);
728 x83 = ((uint64_t)x82 + x63);
729 fiat_p256_mulx_u64(&x84, &x85, x2, (arg1[3]));
730 fiat_p256_mulx_u64(&x86, &x87, x2, (arg1[2]));
731 fiat_p256_mulx_u64(&x88, &x89, x2, (arg1[1]));
732 fiat_p256_mulx_u64(&x90, &x91, x2, (arg1[0]));
733 fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88);
734 fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86);
735 fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84);
736 x98 = (x97 + x85);
737 fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90);
738 fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92);
739 fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94);
740 fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96);
741 fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98);
742 fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001));
743 fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff));
744 fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff));
745 fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111);
746 x117 = (x116 + x112);
747 fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113);
748 fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115);
749 fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117);
750 fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109);
751 fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110);
752 x128 = ((uint64_t)x127 + x108);
753 fiat_p256_mulx_u64(&x129, &x130, x3, (arg1[3]));
754 fiat_p256_mulx_u64(&x131, &x132, x3, (arg1[2]));
755 fiat_p256_mulx_u64(&x133, &x134, x3, (arg1[1]));
756 fiat_p256_mulx_u64(&x135, &x136, x3, (arg1[0]));
757 fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133);
758 fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131);
759 fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129);
760 x143 = (x142 + x130);
761 fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135);
762 fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137);
763 fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139);
764 fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141);
765 fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143);
766 fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001));
767 fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff));
768 fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff));
769 fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156);
770 x162 = (x161 + x157);
771 fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158);
772 fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160);
773 fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162);
774 fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154);
775 fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155);
776 x173 = ((uint64_t)x172 + x153);
777 fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff));
778 fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff));
779 fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0);
780 fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001));
781 fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0);
782 fiat_p256_cmovznz_u64(&x184, x183, x174, x165);
783 fiat_p256_cmovznz_u64(&x185, x183, x176, x167);
784 fiat_p256_cmovznz_u64(&x186, x183, x178, x169);
785 fiat_p256_cmovznz_u64(&x187, x183, x180, x171);
786 out1[0] = x184;
787 out1[1] = x185;
788 out1[2] = x186;
789 out1[3] = x187;
790 }
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 */
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)803 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 uint64_t x1;
805 fiat_p256_uint1 x2;
806 uint64_t x3;
807 fiat_p256_uint1 x4;
808 uint64_t x5;
809 fiat_p256_uint1 x6;
810 uint64_t x7;
811 fiat_p256_uint1 x8;
812 uint64_t x9;
813 fiat_p256_uint1 x10;
814 uint64_t x11;
815 fiat_p256_uint1 x12;
816 uint64_t x13;
817 fiat_p256_uint1 x14;
818 uint64_t x15;
819 fiat_p256_uint1 x16;
820 uint64_t x17;
821 fiat_p256_uint1 x18;
822 uint64_t x19;
823 uint64_t x20;
824 uint64_t x21;
825 uint64_t x22;
826 fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
827 fiat_p256_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
828 fiat_p256_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
829 fiat_p256_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
830 fiat_p256_subborrowx_u64(&x9, &x10, 0x0, x1, UINT64_C(0xffffffffffffffff));
831 fiat_p256_subborrowx_u64(&x11, &x12, x10, x3, UINT32_C(0xffffffff));
832 fiat_p256_subborrowx_u64(&x13, &x14, x12, x5, 0x0);
833 fiat_p256_subborrowx_u64(&x15, &x16, x14, x7, UINT64_C(0xffffffff00000001));
834 fiat_p256_subborrowx_u64(&x17, &x18, x16, x8, 0x0);
835 fiat_p256_cmovznz_u64(&x19, x18, x9, x1);
836 fiat_p256_cmovznz_u64(&x20, x18, x11, x3);
837 fiat_p256_cmovznz_u64(&x21, x18, x13, x5);
838 fiat_p256_cmovznz_u64(&x22, x18, x15, x7);
839 out1[0] = x19;
840 out1[1] = x20;
841 out1[2] = x21;
842 out1[3] = x22;
843 }
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 */
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)856 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 uint64_t x1;
858 fiat_p256_uint1 x2;
859 uint64_t x3;
860 fiat_p256_uint1 x4;
861 uint64_t x5;
862 fiat_p256_uint1 x6;
863 uint64_t x7;
864 fiat_p256_uint1 x8;
865 uint64_t x9;
866 uint64_t x10;
867 fiat_p256_uint1 x11;
868 uint64_t x12;
869 fiat_p256_uint1 x13;
870 uint64_t x14;
871 fiat_p256_uint1 x15;
872 uint64_t x16;
873 fiat_p256_uint1 x17;
874 fiat_p256_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
875 fiat_p256_subborrowx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
876 fiat_p256_subborrowx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
877 fiat_p256_subborrowx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
878 fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
879 fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9);
880 fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff)));
881 fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0);
882 fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001)));
883 out1[0] = x10;
884 out1[1] = x12;
885 out1[2] = x14;
886 out1[3] = x16;
887 }
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 */
fiat_p256_opp(fiat_p256_montgomery_domain_field_element out1,const fiat_p256_montgomery_domain_field_element arg1)899 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 uint64_t x1;
901 fiat_p256_uint1 x2;
902 uint64_t x3;
903 fiat_p256_uint1 x4;
904 uint64_t x5;
905 fiat_p256_uint1 x6;
906 uint64_t x7;
907 fiat_p256_uint1 x8;
908 uint64_t x9;
909 uint64_t x10;
910 fiat_p256_uint1 x11;
911 uint64_t x12;
912 fiat_p256_uint1 x13;
913 uint64_t x14;
914 fiat_p256_uint1 x15;
915 uint64_t x16;
916 fiat_p256_uint1 x17;
917 fiat_p256_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0]));
918 fiat_p256_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1]));
919 fiat_p256_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2]));
920 fiat_p256_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3]));
921 fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
922 fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9);
923 fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff)));
924 fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0);
925 fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001)));
926 out1[0] = x10;
927 out1[1] = x12;
928 out1[2] = x14;
929 out1[3] = x16;
930 }
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 */
fiat_p256_from_montgomery(fiat_p256_non_montgomery_domain_field_element out1,const fiat_p256_montgomery_domain_field_element arg1)942 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 uint64_t x1;
944 uint64_t x2;
945 uint64_t x3;
946 uint64_t x4;
947 uint64_t x5;
948 uint64_t x6;
949 uint64_t x7;
950 uint64_t x8;
951 fiat_p256_uint1 x9;
952 uint64_t x10;
953 fiat_p256_uint1 x11;
954 uint64_t x12;
955 fiat_p256_uint1 x13;
956 uint64_t x14;
957 fiat_p256_uint1 x15;
958 uint64_t x16;
959 uint64_t x17;
960 uint64_t x18;
961 uint64_t x19;
962 uint64_t x20;
963 uint64_t x21;
964 uint64_t x22;
965 fiat_p256_uint1 x23;
966 uint64_t x24;
967 fiat_p256_uint1 x25;
968 uint64_t x26;
969 fiat_p256_uint1 x27;
970 uint64_t x28;
971 fiat_p256_uint1 x29;
972 uint64_t x30;
973 fiat_p256_uint1 x31;
974 uint64_t x32;
975 fiat_p256_uint1 x33;
976 uint64_t x34;
977 fiat_p256_uint1 x35;
978 uint64_t x36;
979 fiat_p256_uint1 x37;
980 uint64_t x38;
981 uint64_t x39;
982 uint64_t x40;
983 uint64_t x41;
984 uint64_t x42;
985 uint64_t x43;
986 uint64_t x44;
987 fiat_p256_uint1 x45;
988 uint64_t x46;
989 fiat_p256_uint1 x47;
990 uint64_t x48;
991 fiat_p256_uint1 x49;
992 uint64_t x50;
993 fiat_p256_uint1 x51;
994 uint64_t x52;
995 fiat_p256_uint1 x53;
996 uint64_t x54;
997 fiat_p256_uint1 x55;
998 uint64_t x56;
999 fiat_p256_uint1 x57;
1000 uint64_t x58;
1001 fiat_p256_uint1 x59;
1002 uint64_t x60;
1003 uint64_t x61;
1004 uint64_t x62;
1005 uint64_t x63;
1006 uint64_t x64;
1007 uint64_t x65;
1008 uint64_t x66;
1009 fiat_p256_uint1 x67;
1010 uint64_t x68;
1011 fiat_p256_uint1 x69;
1012 uint64_t x70;
1013 fiat_p256_uint1 x71;
1014 uint64_t x72;
1015 fiat_p256_uint1 x73;
1016 uint64_t x74;
1017 fiat_p256_uint1 x75;
1018 uint64_t x76;
1019 uint64_t x77;
1020 fiat_p256_uint1 x78;
1021 uint64_t x79;
1022 fiat_p256_uint1 x80;
1023 uint64_t x81;
1024 fiat_p256_uint1 x82;
1025 uint64_t x83;
1026 fiat_p256_uint1 x84;
1027 uint64_t x85;
1028 fiat_p256_uint1 x86;
1029 uint64_t x87;
1030 uint64_t x88;
1031 uint64_t x89;
1032 uint64_t x90;
1033 x1 = (arg1[0]);
1034 fiat_p256_mulx_u64(&x2, &x3, x1, UINT64_C(0xffffffff00000001));
1035 fiat_p256_mulx_u64(&x4, &x5, x1, UINT32_C(0xffffffff));
1036 fiat_p256_mulx_u64(&x6, &x7, x1, UINT64_C(0xffffffffffffffff));
1037 fiat_p256_addcarryx_u64(&x8, &x9, 0x0, x7, x4);
1038 fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x6);
1039 fiat_p256_addcarryx_u64(&x12, &x13, x11, 0x0, x8);
1040 fiat_p256_addcarryx_u64(&x14, &x15, 0x0, x12, (arg1[1]));
1041 fiat_p256_mulx_u64(&x16, &x17, x14, UINT64_C(0xffffffff00000001));
1042 fiat_p256_mulx_u64(&x18, &x19, x14, UINT32_C(0xffffffff));
1043 fiat_p256_mulx_u64(&x20, &x21, x14, UINT64_C(0xffffffffffffffff));
1044 fiat_p256_addcarryx_u64(&x22, &x23, 0x0, x21, x18);
1045 fiat_p256_addcarryx_u64(&x24, &x25, 0x0, x14, x20);
1046 fiat_p256_addcarryx_u64(&x26, &x27, x25, (x15 + (x13 + (x9 + x5))), x22);
1047 fiat_p256_addcarryx_u64(&x28, &x29, x27, x2, (x23 + x19));
1048 fiat_p256_addcarryx_u64(&x30, &x31, x29, x3, x16);
1049 fiat_p256_addcarryx_u64(&x32, &x33, 0x0, x26, (arg1[2]));
1050 fiat_p256_addcarryx_u64(&x34, &x35, x33, x28, 0x0);
1051 fiat_p256_addcarryx_u64(&x36, &x37, x35, x30, 0x0);
1052 fiat_p256_mulx_u64(&x38, &x39, x32, UINT64_C(0xffffffff00000001));
1053 fiat_p256_mulx_u64(&x40, &x41, x32, UINT32_C(0xffffffff));
1054 fiat_p256_mulx_u64(&x42, &x43, x32, UINT64_C(0xffffffffffffffff));
1055 fiat_p256_addcarryx_u64(&x44, &x45, 0x0, x43, x40);
1056 fiat_p256_addcarryx_u64(&x46, &x47, 0x0, x32, x42);
1057 fiat_p256_addcarryx_u64(&x48, &x49, x47, x34, x44);
1058 fiat_p256_addcarryx_u64(&x50, &x51, x49, x36, (x45 + x41));
1059 fiat_p256_addcarryx_u64(&x52, &x53, x51, (x37 + (x31 + x17)), x38);
1060 fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x48, (arg1[3]));
1061 fiat_p256_addcarryx_u64(&x56, &x57, x55, x50, 0x0);
1062 fiat_p256_addcarryx_u64(&x58, &x59, x57, x52, 0x0);
1063 fiat_p256_mulx_u64(&x60, &x61, x54, UINT64_C(0xffffffff00000001));
1064 fiat_p256_mulx_u64(&x62, &x63, x54, UINT32_C(0xffffffff));
1065 fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffffffffffff));
1066 fiat_p256_addcarryx_u64(&x66, &x67, 0x0, x65, x62);
1067 fiat_p256_addcarryx_u64(&x68, &x69, 0x0, x54, x64);
1068 fiat_p256_addcarryx_u64(&x70, &x71, x69, x56, x66);
1069 fiat_p256_addcarryx_u64(&x72, &x73, x71, x58, (x67 + x63));
1070 fiat_p256_addcarryx_u64(&x74, &x75, x73, (x59 + (x53 + x39)), x60);
1071 x76 = (x75 + x61);
1072 fiat_p256_subborrowx_u64(&x77, &x78, 0x0, x70, UINT64_C(0xffffffffffffffff));
1073 fiat_p256_subborrowx_u64(&x79, &x80, x78, x72, UINT32_C(0xffffffff));
1074 fiat_p256_subborrowx_u64(&x81, &x82, x80, x74, 0x0);
1075 fiat_p256_subborrowx_u64(&x83, &x84, x82, x76, UINT64_C(0xffffffff00000001));
1076 fiat_p256_subborrowx_u64(&x85, &x86, x84, 0x0, 0x0);
1077 fiat_p256_cmovznz_u64(&x87, x86, x77, x70);
1078 fiat_p256_cmovznz_u64(&x88, x86, x79, x72);
1079 fiat_p256_cmovznz_u64(&x89, x86, x81, x74);
1080 fiat_p256_cmovznz_u64(&x90, x86, x83, x76);
1081 out1[0] = x87;
1082 out1[1] = x88;
1083 out1[2] = x89;
1084 out1[3] = x90;
1085 }
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 */
fiat_p256_to_montgomery(fiat_p256_montgomery_domain_field_element out1,const fiat_p256_non_montgomery_domain_field_element arg1)1097 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 uint64_t x1;
1099 uint64_t x2;
1100 uint64_t x3;
1101 uint64_t x4;
1102 uint64_t x5;
1103 uint64_t x6;
1104 uint64_t x7;
1105 uint64_t x8;
1106 uint64_t x9;
1107 uint64_t x10;
1108 uint64_t x11;
1109 uint64_t x12;
1110 uint64_t x13;
1111 fiat_p256_uint1 x14;
1112 uint64_t x15;
1113 fiat_p256_uint1 x16;
1114 uint64_t x17;
1115 fiat_p256_uint1 x18;
1116 uint64_t x19;
1117 uint64_t x20;
1118 uint64_t x21;
1119 uint64_t x22;
1120 uint64_t x23;
1121 uint64_t x24;
1122 uint64_t x25;
1123 fiat_p256_uint1 x26;
1124 uint64_t x27;
1125 fiat_p256_uint1 x28;
1126 uint64_t x29;
1127 fiat_p256_uint1 x30;
1128 uint64_t x31;
1129 fiat_p256_uint1 x32;
1130 uint64_t x33;
1131 fiat_p256_uint1 x34;
1132 uint64_t x35;
1133 fiat_p256_uint1 x36;
1134 uint64_t x37;
1135 uint64_t x38;
1136 uint64_t x39;
1137 uint64_t x40;
1138 uint64_t x41;
1139 uint64_t x42;
1140 uint64_t x43;
1141 uint64_t x44;
1142 uint64_t x45;
1143 fiat_p256_uint1 x46;
1144 uint64_t x47;
1145 fiat_p256_uint1 x48;
1146 uint64_t x49;
1147 fiat_p256_uint1 x50;
1148 uint64_t x51;
1149 fiat_p256_uint1 x52;
1150 uint64_t x53;
1151 fiat_p256_uint1 x54;
1152 uint64_t x55;
1153 fiat_p256_uint1 x56;
1154 uint64_t x57;
1155 fiat_p256_uint1 x58;
1156 uint64_t x59;
1157 uint64_t x60;
1158 uint64_t x61;
1159 uint64_t x62;
1160 uint64_t x63;
1161 uint64_t x64;
1162 uint64_t x65;
1163 fiat_p256_uint1 x66;
1164 uint64_t x67;
1165 fiat_p256_uint1 x68;
1166 uint64_t x69;
1167 fiat_p256_uint1 x70;
1168 uint64_t x71;
1169 fiat_p256_uint1 x72;
1170 uint64_t x73;
1171 fiat_p256_uint1 x74;
1172 uint64_t x75;
1173 fiat_p256_uint1 x76;
1174 uint64_t x77;
1175 uint64_t x78;
1176 uint64_t x79;
1177 uint64_t x80;
1178 uint64_t x81;
1179 uint64_t x82;
1180 uint64_t x83;
1181 uint64_t x84;
1182 uint64_t x85;
1183 fiat_p256_uint1 x86;
1184 uint64_t x87;
1185 fiat_p256_uint1 x88;
1186 uint64_t x89;
1187 fiat_p256_uint1 x90;
1188 uint64_t x91;
1189 fiat_p256_uint1 x92;
1190 uint64_t x93;
1191 fiat_p256_uint1 x94;
1192 uint64_t x95;
1193 fiat_p256_uint1 x96;
1194 uint64_t x97;
1195 fiat_p256_uint1 x98;
1196 uint64_t x99;
1197 uint64_t x100;
1198 uint64_t x101;
1199 uint64_t x102;
1200 uint64_t x103;
1201 uint64_t x104;
1202 uint64_t x105;
1203 fiat_p256_uint1 x106;
1204 uint64_t x107;
1205 fiat_p256_uint1 x108;
1206 uint64_t x109;
1207 fiat_p256_uint1 x110;
1208 uint64_t x111;
1209 fiat_p256_uint1 x112;
1210 uint64_t x113;
1211 fiat_p256_uint1 x114;
1212 uint64_t x115;
1213 fiat_p256_uint1 x116;
1214 uint64_t x117;
1215 uint64_t x118;
1216 uint64_t x119;
1217 uint64_t x120;
1218 uint64_t x121;
1219 uint64_t x122;
1220 uint64_t x123;
1221 uint64_t x124;
1222 uint64_t x125;
1223 fiat_p256_uint1 x126;
1224 uint64_t x127;
1225 fiat_p256_uint1 x128;
1226 uint64_t x129;
1227 fiat_p256_uint1 x130;
1228 uint64_t x131;
1229 fiat_p256_uint1 x132;
1230 uint64_t x133;
1231 fiat_p256_uint1 x134;
1232 uint64_t x135;
1233 fiat_p256_uint1 x136;
1234 uint64_t x137;
1235 fiat_p256_uint1 x138;
1236 uint64_t x139;
1237 uint64_t x140;
1238 uint64_t x141;
1239 uint64_t x142;
1240 uint64_t x143;
1241 uint64_t x144;
1242 uint64_t x145;
1243 fiat_p256_uint1 x146;
1244 uint64_t x147;
1245 fiat_p256_uint1 x148;
1246 uint64_t x149;
1247 fiat_p256_uint1 x150;
1248 uint64_t x151;
1249 fiat_p256_uint1 x152;
1250 uint64_t x153;
1251 fiat_p256_uint1 x154;
1252 uint64_t x155;
1253 fiat_p256_uint1 x156;
1254 uint64_t x157;
1255 fiat_p256_uint1 x158;
1256 uint64_t x159;
1257 fiat_p256_uint1 x160;
1258 uint64_t x161;
1259 fiat_p256_uint1 x162;
1260 uint64_t x163;
1261 fiat_p256_uint1 x164;
1262 uint64_t x165;
1263 fiat_p256_uint1 x166;
1264 uint64_t x167;
1265 uint64_t x168;
1266 uint64_t x169;
1267 uint64_t x170;
1268 x1 = (arg1[1]);
1269 x2 = (arg1[2]);
1270 x3 = (arg1[3]);
1271 x4 = (arg1[0]);
1272 fiat_p256_mulx_u64(&x5, &x6, x4, UINT64_C(0x4fffffffd));
1273 fiat_p256_mulx_u64(&x7, &x8, x4, UINT64_C(0xfffffffffffffffe));
1274 fiat_p256_mulx_u64(&x9, &x10, x4, UINT64_C(0xfffffffbffffffff));
1275 fiat_p256_mulx_u64(&x11, &x12, x4, 0x3);
1276 fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
1277 fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
1278 fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
1279 fiat_p256_mulx_u64(&x19, &x20, x11, UINT64_C(0xffffffff00000001));
1280 fiat_p256_mulx_u64(&x21, &x22, x11, UINT32_C(0xffffffff));
1281 fiat_p256_mulx_u64(&x23, &x24, x11, UINT64_C(0xffffffffffffffff));
1282 fiat_p256_addcarryx_u64(&x25, &x26, 0x0, x24, x21);
1283 fiat_p256_addcarryx_u64(&x27, &x28, 0x0, x11, x23);
1284 fiat_p256_addcarryx_u64(&x29, &x30, x28, x13, x25);
1285 fiat_p256_addcarryx_u64(&x31, &x32, x30, x15, (x26 + x22));
1286 fiat_p256_addcarryx_u64(&x33, &x34, x32, x17, x19);
1287 fiat_p256_addcarryx_u64(&x35, &x36, x34, (x18 + x6), x20);
1288 fiat_p256_mulx_u64(&x37, &x38, x1, UINT64_C(0x4fffffffd));
1289 fiat_p256_mulx_u64(&x39, &x40, x1, UINT64_C(0xfffffffffffffffe));
1290 fiat_p256_mulx_u64(&x41, &x42, x1, UINT64_C(0xfffffffbffffffff));
1291 fiat_p256_mulx_u64(&x43, &x44, x1, 0x3);
1292 fiat_p256_addcarryx_u64(&x45, &x46, 0x0, x44, x41);
1293 fiat_p256_addcarryx_u64(&x47, &x48, x46, x42, x39);
1294 fiat_p256_addcarryx_u64(&x49, &x50, x48, x40, x37);
1295 fiat_p256_addcarryx_u64(&x51, &x52, 0x0, x29, x43);
1296 fiat_p256_addcarryx_u64(&x53, &x54, x52, x31, x45);
1297 fiat_p256_addcarryx_u64(&x55, &x56, x54, x33, x47);
1298 fiat_p256_addcarryx_u64(&x57, &x58, x56, x35, x49);
1299 fiat_p256_mulx_u64(&x59, &x60, x51, UINT64_C(0xffffffff00000001));
1300 fiat_p256_mulx_u64(&x61, &x62, x51, UINT32_C(0xffffffff));
1301 fiat_p256_mulx_u64(&x63, &x64, x51, UINT64_C(0xffffffffffffffff));
1302 fiat_p256_addcarryx_u64(&x65, &x66, 0x0, x64, x61);
1303 fiat_p256_addcarryx_u64(&x67, &x68, 0x0, x51, x63);
1304 fiat_p256_addcarryx_u64(&x69, &x70, x68, x53, x65);
1305 fiat_p256_addcarryx_u64(&x71, &x72, x70, x55, (x66 + x62));
1306 fiat_p256_addcarryx_u64(&x73, &x74, x72, x57, x59);
1307 fiat_p256_addcarryx_u64(&x75, &x76, x74, (((uint64_t)x58 + x36) + (x50 + x38)), x60);
1308 fiat_p256_mulx_u64(&x77, &x78, x2, UINT64_C(0x4fffffffd));
1309 fiat_p256_mulx_u64(&x79, &x80, x2, UINT64_C(0xfffffffffffffffe));
1310 fiat_p256_mulx_u64(&x81, &x82, x2, UINT64_C(0xfffffffbffffffff));
1311 fiat_p256_mulx_u64(&x83, &x84, x2, 0x3);
1312 fiat_p256_addcarryx_u64(&x85, &x86, 0x0, x84, x81);
1313 fiat_p256_addcarryx_u64(&x87, &x88, x86, x82, x79);
1314 fiat_p256_addcarryx_u64(&x89, &x90, x88, x80, x77);
1315 fiat_p256_addcarryx_u64(&x91, &x92, 0x0, x69, x83);
1316 fiat_p256_addcarryx_u64(&x93, &x94, x92, x71, x85);
1317 fiat_p256_addcarryx_u64(&x95, &x96, x94, x73, x87);
1318 fiat_p256_addcarryx_u64(&x97, &x98, x96, x75, x89);
1319 fiat_p256_mulx_u64(&x99, &x100, x91, UINT64_C(0xffffffff00000001));
1320 fiat_p256_mulx_u64(&x101, &x102, x91, UINT32_C(0xffffffff));
1321 fiat_p256_mulx_u64(&x103, &x104, x91, UINT64_C(0xffffffffffffffff));
1322 fiat_p256_addcarryx_u64(&x105, &x106, 0x0, x104, x101);
1323 fiat_p256_addcarryx_u64(&x107, &x108, 0x0, x91, x103);
1324 fiat_p256_addcarryx_u64(&x109, &x110, x108, x93, x105);
1325 fiat_p256_addcarryx_u64(&x111, &x112, x110, x95, (x106 + x102));
1326 fiat_p256_addcarryx_u64(&x113, &x114, x112, x97, x99);
1327 fiat_p256_addcarryx_u64(&x115, &x116, x114, (((uint64_t)x98 + x76) + (x90 + x78)), x100);
1328 fiat_p256_mulx_u64(&x117, &x118, x3, UINT64_C(0x4fffffffd));
1329 fiat_p256_mulx_u64(&x119, &x120, x3, UINT64_C(0xfffffffffffffffe));
1330 fiat_p256_mulx_u64(&x121, &x122, x3, UINT64_C(0xfffffffbffffffff));
1331 fiat_p256_mulx_u64(&x123, &x124, x3, 0x3);
1332 fiat_p256_addcarryx_u64(&x125, &x126, 0x0, x124, x121);
1333 fiat_p256_addcarryx_u64(&x127, &x128, x126, x122, x119);
1334 fiat_p256_addcarryx_u64(&x129, &x130, x128, x120, x117);
1335 fiat_p256_addcarryx_u64(&x131, &x132, 0x0, x109, x123);
1336 fiat_p256_addcarryx_u64(&x133, &x134, x132, x111, x125);
1337 fiat_p256_addcarryx_u64(&x135, &x136, x134, x113, x127);
1338 fiat_p256_addcarryx_u64(&x137, &x138, x136, x115, x129);
1339 fiat_p256_mulx_u64(&x139, &x140, x131, UINT64_C(0xffffffff00000001));
1340 fiat_p256_mulx_u64(&x141, &x142, x131, UINT32_C(0xffffffff));
1341 fiat_p256_mulx_u64(&x143, &x144, x131, UINT64_C(0xffffffffffffffff));
1342 fiat_p256_addcarryx_u64(&x145, &x146, 0x0, x144, x141);
1343 fiat_p256_addcarryx_u64(&x147, &x148, 0x0, x131, x143);
1344 fiat_p256_addcarryx_u64(&x149, &x150, x148, x133, x145);
1345 fiat_p256_addcarryx_u64(&x151, &x152, x150, x135, (x146 + x142));
1346 fiat_p256_addcarryx_u64(&x153, &x154, x152, x137, x139);
1347 fiat_p256_addcarryx_u64(&x155, &x156, x154, (((uint64_t)x138 + x116) + (x130 + x118)), x140);
1348 fiat_p256_subborrowx_u64(&x157, &x158, 0x0, x149, UINT64_C(0xffffffffffffffff));
1349 fiat_p256_subborrowx_u64(&x159, &x160, x158, x151, UINT32_C(0xffffffff));
1350 fiat_p256_subborrowx_u64(&x161, &x162, x160, x153, 0x0);
1351 fiat_p256_subborrowx_u64(&x163, &x164, x162, x155, UINT64_C(0xffffffff00000001));
1352 fiat_p256_subborrowx_u64(&x165, &x166, x164, x156, 0x0);
1353 fiat_p256_cmovznz_u64(&x167, x166, x157, x149);
1354 fiat_p256_cmovznz_u64(&x168, x166, x159, x151);
1355 fiat_p256_cmovznz_u64(&x169, x166, x161, x153);
1356 fiat_p256_cmovznz_u64(&x170, x166, x163, x155);
1357 out1[0] = x167;
1358 out1[1] = x168;
1359 out1[2] = x169;
1360 out1[3] = x170;
1361 }
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 */
fiat_p256_nonzero(uint64_t * out1,const uint64_t arg1[4])1376 static FIAT_P256_FIAT_INLINE void fiat_p256_nonzero(uint64_t* out1, const uint64_t arg1[4]) {
1377 uint64_t x1;
1378 x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3]))));
1379 *out1 = x1;
1380 }
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 */
fiat_p256_selectznz(uint64_t out1[4],fiat_p256_uint1 arg1,const uint64_t arg2[4],const uint64_t arg3[4])1395 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 uint64_t x1;
1397 uint64_t x2;
1398 uint64_t x3;
1399 uint64_t x4;
1400 fiat_p256_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]));
1401 fiat_p256_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]));
1402 fiat_p256_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]));
1403 fiat_p256_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]));
1404 out1[0] = x1;
1405 out1[1] = x2;
1406 out1[2] = x3;
1407 out1[3] = x4;
1408 }
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 */
fiat_p256_to_bytes(uint8_t out1[32],const uint64_t arg1[4])1423 static FIAT_P256_FIAT_INLINE void fiat_p256_to_bytes(uint8_t out1[32], const uint64_t arg1[4]) {
1424 uint64_t x1;
1425 uint64_t x2;
1426 uint64_t x3;
1427 uint64_t x4;
1428 uint8_t x5;
1429 uint64_t x6;
1430 uint8_t x7;
1431 uint64_t x8;
1432 uint8_t x9;
1433 uint64_t x10;
1434 uint8_t x11;
1435 uint64_t x12;
1436 uint8_t x13;
1437 uint64_t x14;
1438 uint8_t x15;
1439 uint64_t x16;
1440 uint8_t x17;
1441 uint8_t x18;
1442 uint8_t x19;
1443 uint64_t x20;
1444 uint8_t x21;
1445 uint64_t x22;
1446 uint8_t x23;
1447 uint64_t x24;
1448 uint8_t x25;
1449 uint64_t x26;
1450 uint8_t x27;
1451 uint64_t x28;
1452 uint8_t x29;
1453 uint64_t x30;
1454 uint8_t x31;
1455 uint8_t x32;
1456 uint8_t x33;
1457 uint64_t x34;
1458 uint8_t x35;
1459 uint64_t x36;
1460 uint8_t x37;
1461 uint64_t x38;
1462 uint8_t x39;
1463 uint64_t x40;
1464 uint8_t x41;
1465 uint64_t x42;
1466 uint8_t x43;
1467 uint64_t x44;
1468 uint8_t x45;
1469 uint8_t x46;
1470 uint8_t x47;
1471 uint64_t x48;
1472 uint8_t x49;
1473 uint64_t x50;
1474 uint8_t x51;
1475 uint64_t x52;
1476 uint8_t x53;
1477 uint64_t x54;
1478 uint8_t x55;
1479 uint64_t x56;
1480 uint8_t x57;
1481 uint64_t x58;
1482 uint8_t x59;
1483 uint8_t x60;
1484 x1 = (arg1[3]);
1485 x2 = (arg1[2]);
1486 x3 = (arg1[1]);
1487 x4 = (arg1[0]);
1488 x5 = (uint8_t)(x4 & UINT8_C(0xff));
1489 x6 = (x4 >> 8);
1490 x7 = (uint8_t)(x6 & UINT8_C(0xff));
1491 x8 = (x6 >> 8);
1492 x9 = (uint8_t)(x8 & UINT8_C(0xff));
1493 x10 = (x8 >> 8);
1494 x11 = (uint8_t)(x10 & UINT8_C(0xff));
1495 x12 = (x10 >> 8);
1496 x13 = (uint8_t)(x12 & UINT8_C(0xff));
1497 x14 = (x12 >> 8);
1498 x15 = (uint8_t)(x14 & UINT8_C(0xff));
1499 x16 = (x14 >> 8);
1500 x17 = (uint8_t)(x16 & UINT8_C(0xff));
1501 x18 = (uint8_t)(x16 >> 8);
1502 x19 = (uint8_t)(x3 & UINT8_C(0xff));
1503 x20 = (x3 >> 8);
1504 x21 = (uint8_t)(x20 & UINT8_C(0xff));
1505 x22 = (x20 >> 8);
1506 x23 = (uint8_t)(x22 & UINT8_C(0xff));
1507 x24 = (x22 >> 8);
1508 x25 = (uint8_t)(x24 & UINT8_C(0xff));
1509 x26 = (x24 >> 8);
1510 x27 = (uint8_t)(x26 & UINT8_C(0xff));
1511 x28 = (x26 >> 8);
1512 x29 = (uint8_t)(x28 & UINT8_C(0xff));
1513 x30 = (x28 >> 8);
1514 x31 = (uint8_t)(x30 & UINT8_C(0xff));
1515 x32 = (uint8_t)(x30 >> 8);
1516 x33 = (uint8_t)(x2 & UINT8_C(0xff));
1517 x34 = (x2 >> 8);
1518 x35 = (uint8_t)(x34 & UINT8_C(0xff));
1519 x36 = (x34 >> 8);
1520 x37 = (uint8_t)(x36 & UINT8_C(0xff));
1521 x38 = (x36 >> 8);
1522 x39 = (uint8_t)(x38 & UINT8_C(0xff));
1523 x40 = (x38 >> 8);
1524 x41 = (uint8_t)(x40 & UINT8_C(0xff));
1525 x42 = (x40 >> 8);
1526 x43 = (uint8_t)(x42 & UINT8_C(0xff));
1527 x44 = (x42 >> 8);
1528 x45 = (uint8_t)(x44 & UINT8_C(0xff));
1529 x46 = (uint8_t)(x44 >> 8);
1530 x47 = (uint8_t)(x1 & UINT8_C(0xff));
1531 x48 = (x1 >> 8);
1532 x49 = (uint8_t)(x48 & UINT8_C(0xff));
1533 x50 = (x48 >> 8);
1534 x51 = (uint8_t)(x50 & UINT8_C(0xff));
1535 x52 = (x50 >> 8);
1536 x53 = (uint8_t)(x52 & UINT8_C(0xff));
1537 x54 = (x52 >> 8);
1538 x55 = (uint8_t)(x54 & UINT8_C(0xff));
1539 x56 = (x54 >> 8);
1540 x57 = (uint8_t)(x56 & UINT8_C(0xff));
1541 x58 = (x56 >> 8);
1542 x59 = (uint8_t)(x58 & UINT8_C(0xff));
1543 x60 = (uint8_t)(x58 >> 8);
1544 out1[0] = x5;
1545 out1[1] = x7;
1546 out1[2] = x9;
1547 out1[3] = x11;
1548 out1[4] = x13;
1549 out1[5] = x15;
1550 out1[6] = x17;
1551 out1[7] = x18;
1552 out1[8] = x19;
1553 out1[9] = x21;
1554 out1[10] = x23;
1555 out1[11] = x25;
1556 out1[12] = x27;
1557 out1[13] = x29;
1558 out1[14] = x31;
1559 out1[15] = x32;
1560 out1[16] = x33;
1561 out1[17] = x35;
1562 out1[18] = x37;
1563 out1[19] = x39;
1564 out1[20] = x41;
1565 out1[21] = x43;
1566 out1[22] = x45;
1567 out1[23] = x46;
1568 out1[24] = x47;
1569 out1[25] = x49;
1570 out1[26] = x51;
1571 out1[27] = x53;
1572 out1[28] = x55;
1573 out1[29] = x57;
1574 out1[30] = x59;
1575 out1[31] = x60;
1576 }
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 */
fiat_p256_from_bytes(uint64_t out1[4],const uint8_t arg1[32])1592 static FIAT_P256_FIAT_INLINE void fiat_p256_from_bytes(uint64_t out1[4], const uint8_t arg1[32]) {
1593 uint64_t x1;
1594 uint64_t x2;
1595 uint64_t x3;
1596 uint64_t x4;
1597 uint64_t x5;
1598 uint64_t x6;
1599 uint64_t x7;
1600 uint8_t x8;
1601 uint64_t x9;
1602 uint64_t x10;
1603 uint64_t x11;
1604 uint64_t x12;
1605 uint64_t x13;
1606 uint64_t x14;
1607 uint64_t x15;
1608 uint8_t x16;
1609 uint64_t x17;
1610 uint64_t x18;
1611 uint64_t x19;
1612 uint64_t x20;
1613 uint64_t x21;
1614 uint64_t x22;
1615 uint64_t x23;
1616 uint8_t x24;
1617 uint64_t x25;
1618 uint64_t x26;
1619 uint64_t x27;
1620 uint64_t x28;
1621 uint64_t x29;
1622 uint64_t x30;
1623 uint64_t x31;
1624 uint8_t x32;
1625 uint64_t x33;
1626 uint64_t x34;
1627 uint64_t x35;
1628 uint64_t x36;
1629 uint64_t x37;
1630 uint64_t x38;
1631 uint64_t x39;
1632 uint64_t x40;
1633 uint64_t x41;
1634 uint64_t x42;
1635 uint64_t x43;
1636 uint64_t x44;
1637 uint64_t x45;
1638 uint64_t x46;
1639 uint64_t x47;
1640 uint64_t x48;
1641 uint64_t x49;
1642 uint64_t x50;
1643 uint64_t x51;
1644 uint64_t x52;
1645 uint64_t x53;
1646 uint64_t x54;
1647 uint64_t x55;
1648 uint64_t x56;
1649 uint64_t x57;
1650 uint64_t x58;
1651 uint64_t x59;
1652 uint64_t x60;
1653 x1 = ((uint64_t)(arg1[31]) << 56);
1654 x2 = ((uint64_t)(arg1[30]) << 48);
1655 x3 = ((uint64_t)(arg1[29]) << 40);
1656 x4 = ((uint64_t)(arg1[28]) << 32);
1657 x5 = ((uint64_t)(arg1[27]) << 24);
1658 x6 = ((uint64_t)(arg1[26]) << 16);
1659 x7 = ((uint64_t)(arg1[25]) << 8);
1660 x8 = (arg1[24]);
1661 x9 = ((uint64_t)(arg1[23]) << 56);
1662 x10 = ((uint64_t)(arg1[22]) << 48);
1663 x11 = ((uint64_t)(arg1[21]) << 40);
1664 x12 = ((uint64_t)(arg1[20]) << 32);
1665 x13 = ((uint64_t)(arg1[19]) << 24);
1666 x14 = ((uint64_t)(arg1[18]) << 16);
1667 x15 = ((uint64_t)(arg1[17]) << 8);
1668 x16 = (arg1[16]);
1669 x17 = ((uint64_t)(arg1[15]) << 56);
1670 x18 = ((uint64_t)(arg1[14]) << 48);
1671 x19 = ((uint64_t)(arg1[13]) << 40);
1672 x20 = ((uint64_t)(arg1[12]) << 32);
1673 x21 = ((uint64_t)(arg1[11]) << 24);
1674 x22 = ((uint64_t)(arg1[10]) << 16);
1675 x23 = ((uint64_t)(arg1[9]) << 8);
1676 x24 = (arg1[8]);
1677 x25 = ((uint64_t)(arg1[7]) << 56);
1678 x26 = ((uint64_t)(arg1[6]) << 48);
1679 x27 = ((uint64_t)(arg1[5]) << 40);
1680 x28 = ((uint64_t)(arg1[4]) << 32);
1681 x29 = ((uint64_t)(arg1[3]) << 24);
1682 x30 = ((uint64_t)(arg1[2]) << 16);
1683 x31 = ((uint64_t)(arg1[1]) << 8);
1684 x32 = (arg1[0]);
1685 x33 = (x31 + (uint64_t)x32);
1686 x34 = (x30 + x33);
1687 x35 = (x29 + x34);
1688 x36 = (x28 + x35);
1689 x37 = (x27 + x36);
1690 x38 = (x26 + x37);
1691 x39 = (x25 + x38);
1692 x40 = (x23 + (uint64_t)x24);
1693 x41 = (x22 + x40);
1694 x42 = (x21 + x41);
1695 x43 = (x20 + x42);
1696 x44 = (x19 + x43);
1697 x45 = (x18 + x44);
1698 x46 = (x17 + x45);
1699 x47 = (x15 + (uint64_t)x16);
1700 x48 = (x14 + x47);
1701 x49 = (x13 + x48);
1702 x50 = (x12 + x49);
1703 x51 = (x11 + x50);
1704 x52 = (x10 + x51);
1705 x53 = (x9 + x52);
1706 x54 = (x7 + (uint64_t)x8);
1707 x55 = (x6 + x54);
1708 x56 = (x5 + x55);
1709 x57 = (x4 + x56);
1710 x58 = (x3 + x57);
1711 x59 = (x2 + x58);
1712 x60 = (x1 + x59);
1713 out1[0] = x39;
1714 out1[1] = x46;
1715 out1[2] = x53;
1716 out1[3] = x60;
1717 }
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 */
fiat_p256_set_one(fiat_p256_montgomery_domain_field_element out1)1727 static FIAT_P256_FIAT_INLINE void fiat_p256_set_one(fiat_p256_montgomery_domain_field_element out1) {
1728 out1[0] = 0x1;
1729 out1[1] = UINT64_C(0xffffffff00000000);
1730 out1[2] = UINT64_C(0xffffffffffffffff);
1731 out1[3] = UINT32_C(0xfffffffe);
1732 }
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 */
fiat_p256_msat(uint64_t out1[5])1744 static FIAT_P256_FIAT_INLINE void fiat_p256_msat(uint64_t out1[5]) {
1745 out1[0] = UINT64_C(0xffffffffffffffff);
1746 out1[1] = UINT32_C(0xffffffff);
1747 out1[2] = 0x0;
1748 out1[3] = UINT64_C(0xffffffff00000001);
1749 out1[4] = 0x0;
1750 }
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 */
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])1782 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 uint64_t x1;
1784 fiat_p256_uint1 x2;
1785 fiat_p256_uint1 x3;
1786 uint64_t x4;
1787 fiat_p256_uint1 x5;
1788 uint64_t x6;
1789 uint64_t x7;
1790 uint64_t x8;
1791 uint64_t x9;
1792 uint64_t x10;
1793 uint64_t x11;
1794 uint64_t x12;
1795 fiat_p256_uint1 x13;
1796 uint64_t x14;
1797 fiat_p256_uint1 x15;
1798 uint64_t x16;
1799 fiat_p256_uint1 x17;
1800 uint64_t x18;
1801 fiat_p256_uint1 x19;
1802 uint64_t x20;
1803 fiat_p256_uint1 x21;
1804 uint64_t x22;
1805 uint64_t x23;
1806 uint64_t x24;
1807 uint64_t x25;
1808 uint64_t x26;
1809 uint64_t x27;
1810 uint64_t x28;
1811 uint64_t x29;
1812 uint64_t x30;
1813 uint64_t x31;
1814 fiat_p256_uint1 x32;
1815 uint64_t x33;
1816 fiat_p256_uint1 x34;
1817 uint64_t x35;
1818 fiat_p256_uint1 x36;
1819 uint64_t x37;
1820 fiat_p256_uint1 x38;
1821 uint64_t x39;
1822 fiat_p256_uint1 x40;
1823 uint64_t x41;
1824 fiat_p256_uint1 x42;
1825 uint64_t x43;
1826 fiat_p256_uint1 x44;
1827 uint64_t x45;
1828 fiat_p256_uint1 x46;
1829 uint64_t x47;
1830 fiat_p256_uint1 x48;
1831 uint64_t x49;
1832 uint64_t x50;
1833 uint64_t x51;
1834 uint64_t x52;
1835 uint64_t x53;
1836 fiat_p256_uint1 x54;
1837 uint64_t x55;
1838 fiat_p256_uint1 x56;
1839 uint64_t x57;
1840 fiat_p256_uint1 x58;
1841 uint64_t x59;
1842 fiat_p256_uint1 x60;
1843 uint64_t x61;
1844 uint64_t x62;
1845 fiat_p256_uint1 x63;
1846 uint64_t x64;
1847 fiat_p256_uint1 x65;
1848 uint64_t x66;
1849 fiat_p256_uint1 x67;
1850 uint64_t x68;
1851 fiat_p256_uint1 x69;
1852 uint64_t x70;
1853 uint64_t x71;
1854 uint64_t x72;
1855 uint64_t x73;
1856 fiat_p256_uint1 x74;
1857 uint64_t x75;
1858 uint64_t x76;
1859 uint64_t x77;
1860 uint64_t x78;
1861 uint64_t x79;
1862 uint64_t x80;
1863 fiat_p256_uint1 x81;
1864 uint64_t x82;
1865 fiat_p256_uint1 x83;
1866 uint64_t x84;
1867 fiat_p256_uint1 x85;
1868 uint64_t x86;
1869 fiat_p256_uint1 x87;
1870 uint64_t x88;
1871 fiat_p256_uint1 x89;
1872 uint64_t x90;
1873 uint64_t x91;
1874 uint64_t x92;
1875 uint64_t x93;
1876 uint64_t x94;
1877 fiat_p256_uint1 x95;
1878 uint64_t x96;
1879 fiat_p256_uint1 x97;
1880 uint64_t x98;
1881 fiat_p256_uint1 x99;
1882 uint64_t x100;
1883 fiat_p256_uint1 x101;
1884 uint64_t x102;
1885 fiat_p256_uint1 x103;
1886 uint64_t x104;
1887 fiat_p256_uint1 x105;
1888 uint64_t x106;
1889 fiat_p256_uint1 x107;
1890 uint64_t x108;
1891 fiat_p256_uint1 x109;
1892 uint64_t x110;
1893 fiat_p256_uint1 x111;
1894 uint64_t x112;
1895 fiat_p256_uint1 x113;
1896 uint64_t x114;
1897 uint64_t x115;
1898 uint64_t x116;
1899 uint64_t x117;
1900 uint64_t x118;
1901 uint64_t x119;
1902 uint64_t x120;
1903 uint64_t x121;
1904 uint64_t x122;
1905 uint64_t x123;
1906 uint64_t x124;
1907 uint64_t x125;
1908 uint64_t x126;
1909 fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (~arg1), 0x1);
1910 x3 = (fiat_p256_uint1)((fiat_p256_uint1)(x1 >> 63) & (fiat_p256_uint1)((arg3[0]) & 0x1));
1911 fiat_p256_addcarryx_u64(&x4, &x5, 0x0, (~arg1), 0x1);
1912 fiat_p256_cmovznz_u64(&x6, x3, arg1, x4);
1913 fiat_p256_cmovznz_u64(&x7, x3, (arg2[0]), (arg3[0]));
1914 fiat_p256_cmovznz_u64(&x8, x3, (arg2[1]), (arg3[1]));
1915 fiat_p256_cmovznz_u64(&x9, x3, (arg2[2]), (arg3[2]));
1916 fiat_p256_cmovznz_u64(&x10, x3, (arg2[3]), (arg3[3]));
1917 fiat_p256_cmovznz_u64(&x11, x3, (arg2[4]), (arg3[4]));
1918 fiat_p256_addcarryx_u64(&x12, &x13, 0x0, 0x1, (~(arg2[0])));
1919 fiat_p256_addcarryx_u64(&x14, &x15, x13, 0x0, (~(arg2[1])));
1920 fiat_p256_addcarryx_u64(&x16, &x17, x15, 0x0, (~(arg2[2])));
1921 fiat_p256_addcarryx_u64(&x18, &x19, x17, 0x0, (~(arg2[3])));
1922 fiat_p256_addcarryx_u64(&x20, &x21, x19, 0x0, (~(arg2[4])));
1923 fiat_p256_cmovznz_u64(&x22, x3, (arg3[0]), x12);
1924 fiat_p256_cmovznz_u64(&x23, x3, (arg3[1]), x14);
1925 fiat_p256_cmovznz_u64(&x24, x3, (arg3[2]), x16);
1926 fiat_p256_cmovznz_u64(&x25, x3, (arg3[3]), x18);
1927 fiat_p256_cmovznz_u64(&x26, x3, (arg3[4]), x20);
1928 fiat_p256_cmovznz_u64(&x27, x3, (arg4[0]), (arg5[0]));
1929 fiat_p256_cmovznz_u64(&x28, x3, (arg4[1]), (arg5[1]));
1930 fiat_p256_cmovznz_u64(&x29, x3, (arg4[2]), (arg5[2]));
1931 fiat_p256_cmovznz_u64(&x30, x3, (arg4[3]), (arg5[3]));
1932 fiat_p256_addcarryx_u64(&x31, &x32, 0x0, x27, x27);
1933 fiat_p256_addcarryx_u64(&x33, &x34, x32, x28, x28);
1934 fiat_p256_addcarryx_u64(&x35, &x36, x34, x29, x29);
1935 fiat_p256_addcarryx_u64(&x37, &x38, x36, x30, x30);
1936 fiat_p256_subborrowx_u64(&x39, &x40, 0x0, x31, UINT64_C(0xffffffffffffffff));
1937 fiat_p256_subborrowx_u64(&x41, &x42, x40, x33, UINT32_C(0xffffffff));
1938 fiat_p256_subborrowx_u64(&x43, &x44, x42, x35, 0x0);
1939 fiat_p256_subborrowx_u64(&x45, &x46, x44, x37, UINT64_C(0xffffffff00000001));
1940 fiat_p256_subborrowx_u64(&x47, &x48, x46, x38, 0x0);
1941 x49 = (arg4[3]);
1942 x50 = (arg4[2]);
1943 x51 = (arg4[1]);
1944 x52 = (arg4[0]);
1945 fiat_p256_subborrowx_u64(&x53, &x54, 0x0, 0x0, x52);
1946 fiat_p256_subborrowx_u64(&x55, &x56, x54, 0x0, x51);
1947 fiat_p256_subborrowx_u64(&x57, &x58, x56, 0x0, x50);
1948 fiat_p256_subborrowx_u64(&x59, &x60, x58, 0x0, x49);
1949 fiat_p256_cmovznz_u64(&x61, x60, 0x0, UINT64_C(0xffffffffffffffff));
1950 fiat_p256_addcarryx_u64(&x62, &x63, 0x0, x53, x61);
1951 fiat_p256_addcarryx_u64(&x64, &x65, x63, x55, (x61 & UINT32_C(0xffffffff)));
1952 fiat_p256_addcarryx_u64(&x66, &x67, x65, x57, 0x0);
1953 fiat_p256_addcarryx_u64(&x68, &x69, x67, x59, (x61 & UINT64_C(0xffffffff00000001)));
1954 fiat_p256_cmovznz_u64(&x70, x3, (arg5[0]), x62);
1955 fiat_p256_cmovznz_u64(&x71, x3, (arg5[1]), x64);
1956 fiat_p256_cmovznz_u64(&x72, x3, (arg5[2]), x66);
1957 fiat_p256_cmovznz_u64(&x73, x3, (arg5[3]), x68);
1958 x74 = (fiat_p256_uint1)(x22 & 0x1);
1959 fiat_p256_cmovznz_u64(&x75, x74, 0x0, x7);
1960 fiat_p256_cmovznz_u64(&x76, x74, 0x0, x8);
1961 fiat_p256_cmovznz_u64(&x77, x74, 0x0, x9);
1962 fiat_p256_cmovznz_u64(&x78, x74, 0x0, x10);
1963 fiat_p256_cmovznz_u64(&x79, x74, 0x0, x11);
1964 fiat_p256_addcarryx_u64(&x80, &x81, 0x0, x22, x75);
1965 fiat_p256_addcarryx_u64(&x82, &x83, x81, x23, x76);
1966 fiat_p256_addcarryx_u64(&x84, &x85, x83, x24, x77);
1967 fiat_p256_addcarryx_u64(&x86, &x87, x85, x25, x78);
1968 fiat_p256_addcarryx_u64(&x88, &x89, x87, x26, x79);
1969 fiat_p256_cmovznz_u64(&x90, x74, 0x0, x27);
1970 fiat_p256_cmovznz_u64(&x91, x74, 0x0, x28);
1971 fiat_p256_cmovznz_u64(&x92, x74, 0x0, x29);
1972 fiat_p256_cmovznz_u64(&x93, x74, 0x0, x30);
1973 fiat_p256_addcarryx_u64(&x94, &x95, 0x0, x70, x90);
1974 fiat_p256_addcarryx_u64(&x96, &x97, x95, x71, x91);
1975 fiat_p256_addcarryx_u64(&x98, &x99, x97, x72, x92);
1976 fiat_p256_addcarryx_u64(&x100, &x101, x99, x73, x93);
1977 fiat_p256_subborrowx_u64(&x102, &x103, 0x0, x94, UINT64_C(0xffffffffffffffff));
1978 fiat_p256_subborrowx_u64(&x104, &x105, x103, x96, UINT32_C(0xffffffff));
1979 fiat_p256_subborrowx_u64(&x106, &x107, x105, x98, 0x0);
1980 fiat_p256_subborrowx_u64(&x108, &x109, x107, x100, UINT64_C(0xffffffff00000001));
1981 fiat_p256_subborrowx_u64(&x110, &x111, x109, x101, 0x0);
1982 fiat_p256_addcarryx_u64(&x112, &x113, 0x0, x6, 0x1);
1983 x114 = ((x80 >> 1) | ((x82 << 63) & UINT64_C(0xffffffffffffffff)));
1984 x115 = ((x82 >> 1) | ((x84 << 63) & UINT64_C(0xffffffffffffffff)));
1985 x116 = ((x84 >> 1) | ((x86 << 63) & UINT64_C(0xffffffffffffffff)));
1986 x117 = ((x86 >> 1) | ((x88 << 63) & UINT64_C(0xffffffffffffffff)));
1987 x118 = ((x88 & UINT64_C(0x8000000000000000)) | (x88 >> 1));
1988 fiat_p256_cmovznz_u64(&x119, x48, x39, x31);
1989 fiat_p256_cmovznz_u64(&x120, x48, x41, x33);
1990 fiat_p256_cmovznz_u64(&x121, x48, x43, x35);
1991 fiat_p256_cmovznz_u64(&x122, x48, x45, x37);
1992 fiat_p256_cmovznz_u64(&x123, x111, x102, x94);
1993 fiat_p256_cmovznz_u64(&x124, x111, x104, x96);
1994 fiat_p256_cmovznz_u64(&x125, x111, x106, x98);
1995 fiat_p256_cmovznz_u64(&x126, x111, x108, x100);
1996 *out1 = x112;
1997 out2[0] = x7;
1998 out2[1] = x8;
1999 out2[2] = x9;
2000 out2[3] = x10;
2001 out2[4] = x11;
2002 out3[0] = x114;
2003 out3[1] = x115;
2004 out3[2] = x116;
2005 out3[3] = x117;
2006 out3[4] = x118;
2007 out4[0] = x119;
2008 out4[1] = x120;
2009 out4[2] = x121;
2010 out4[3] = x122;
2011 out5[0] = x123;
2012 out5[1] = x124;
2013 out5[2] = x125;
2014 out5[3] = x126;
2015 }
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 */
fiat_p256_divstep_precomp(uint64_t out1[4])2027 static FIAT_P256_FIAT_INLINE void fiat_p256_divstep_precomp(uint64_t out1[4]) {
2028 out1[0] = UINT64_C(0x67ffffffb8000000);
2029 out1[1] = UINT64_C(0xc000000038000000);
2030 out1[2] = UINT64_C(0xd80000007fffffff);
2031 out1[3] = UINT64_C(0x2fffffffffffffff);
2032 }
2033