1 /* Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --inline --static --use-value-barrier --no-wide-int 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 */
2 /* curve description: p256 */
3 /* machine_wordsize = 64 (from "64") */
4 /* requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp */
5 /* m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1") */
6 /* */
7 /* NOTE: In addition to the bounds specified above each function, all */
8 /* functions synthesized for this Montgomery arithmetic require the */
9 /* input to be strictly less than the prime modulus (m), and also */
10 /* require the input to be in the unique saturated representation. */
11 /* All functions also ensure that these two properties are true of */
12 /* return values. */
13 /* */
14 /* Computed values: */
15 /* eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) */
16 /* 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) */
17 /* twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in */
18 /* if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 */
19
20 #include <stdint.h>
21 #include <intrin.h>
22 #if defined(_M_X64)
23 #include <immintrin.h>
24 #endif
25
26 typedef unsigned char fiat_p256_uint1;
27 typedef signed char fiat_p256_int1;
28
29 #define FIAT_P256_FIAT_INLINE inline
30
31 /* The type fiat_p256_montgomery_domain_field_element is a field element in the Montgomery domain. */
32 /* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */
33 typedef uint64_t fiat_p256_montgomery_domain_field_element[4];
34
35 /* The type fiat_p256_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. */
36 /* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */
37 typedef uint64_t fiat_p256_non_montgomery_domain_field_element[4];
38
39 #if (-1 & 3) != 3
40 #error "This code only works on a two's complement system"
41 #endif
42
43 #define fiat_p256_value_barrier_u64(x) (x)
44
45
46 /*
47 * The function fiat_p256_addcarryx_u64 is an addition with carry.
48 *
49 * Postconditions:
50 * out1 = (arg1 + arg2 + arg3) mod 2^64
51 * out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋
52 *
53 * Input Bounds:
54 * arg1: [0x0 ~> 0x1]
55 * arg2: [0x0 ~> 0xffffffffffffffff]
56 * arg3: [0x0 ~> 0xffffffffffffffff]
57 * Output Bounds:
58 * out1: [0x0 ~> 0xffffffffffffffff]
59 * out2: [0x0 ~> 0x1]
60 */
fiat_p256_addcarryx_u64(uint64_t * out1,fiat_p256_uint1 * out2,fiat_p256_uint1 arg1,uint64_t arg2,uint64_t arg3)61 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) {
62 #if defined(_M_X64)
63 *out2 = _addcarry_u64(arg1, arg2, arg3, out1);
64 #else
65 arg2 += arg1;
66 arg1 = arg2 < arg1;
67 arg3 += arg2;
68 arg1 += arg3 < arg2;
69 *out1 = arg3;
70 *out2 = arg1;
71 #endif
72 }
73
74 /*
75 * The function fiat_p256_subborrowx_u64 is a subtraction with borrow.
76 *
77 * Postconditions:
78 * out1 = (-arg1 + arg2 + -arg3) mod 2^64
79 * out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋
80 *
81 * Input Bounds:
82 * arg1: [0x0 ~> 0x1]
83 * arg2: [0x0 ~> 0xffffffffffffffff]
84 * arg3: [0x0 ~> 0xffffffffffffffff]
85 * Output Bounds:
86 * out1: [0x0 ~> 0xffffffffffffffff]
87 * out2: [0x0 ~> 0x1]
88 */
fiat_p256_subborrowx_u64(uint64_t * out1,fiat_p256_uint1 * out2,fiat_p256_uint1 arg1,uint64_t arg2,uint64_t arg3)89 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) {
90 #if defined(_M_X64)
91 *out2 = _subborrow_u64(arg1, arg2, arg3, out1); // NOTE: edited after generation
92 #else
93 *out1 = arg2 - arg3 - arg1;
94 *out2 = (arg2 < arg3) | ((arg2 == arg3) & arg1);
95 #endif
96 }
97
98 /*
99 * The function fiat_p256_mulx_u64 is a multiplication, returning the full double-width result.
100 *
101 * Postconditions:
102 * out1 = (arg1 * arg2) mod 2^64
103 * out2 = ⌊arg1 * arg2 / 2^64⌋
104 *
105 * Input Bounds:
106 * arg1: [0x0 ~> 0xffffffffffffffff]
107 * arg2: [0x0 ~> 0xffffffffffffffff]
108 * Output Bounds:
109 * out1: [0x0 ~> 0xffffffffffffffff]
110 * out2: [0x0 ~> 0xffffffffffffffff]
111 */
fiat_p256_mulx_u64(uint64_t * out1,uint64_t * out2,uint64_t arg1,uint64_t arg2)112 static FIAT_P256_FIAT_INLINE void fiat_p256_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) {
113 // NOTE: edited after generation
114 #if defined(_M_X64)
115 *out1 = _umul128(arg1, arg2, out2);
116 #elif defined(_M_ARM64)
117 *out1 = arg1 * arg2;
118 *out2 = __umulh(arg1, arg2);
119 #else
120 #error "This file is intended for MSVC on X64 or ARM64"
121 #endif
122 }
123
124 /*
125 * The function fiat_p256_cmovznz_u64 is a single-word conditional move.
126 *
127 * Postconditions:
128 * out1 = (if arg1 = 0 then arg2 else arg3)
129 *
130 * Input Bounds:
131 * arg1: [0x0 ~> 0x1]
132 * arg2: [0x0 ~> 0xffffffffffffffff]
133 * arg3: [0x0 ~> 0xffffffffffffffff]
134 * Output Bounds:
135 * out1: [0x0 ~> 0xffffffffffffffff]
136 */
fiat_p256_cmovznz_u64(uint64_t * out1,fiat_p256_uint1 arg1,uint64_t arg2,uint64_t arg3)137 static FIAT_P256_FIAT_INLINE void fiat_p256_cmovznz_u64(uint64_t* out1, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) {
138 fiat_p256_uint1 x1;
139 uint64_t x2;
140 uint64_t x3;
141 x1 = (!(!arg1));
142 x2 = ((fiat_p256_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff));
143 x3 = ((fiat_p256_value_barrier_u64(x2) & arg3) | (fiat_p256_value_barrier_u64((~x2)) & arg2));
144 *out1 = x3;
145 }
146
147 /*
148 * The function fiat_p256_mul multiplies two field elements in the Montgomery domain.
149 *
150 * Preconditions:
151 * 0 ≤ eval arg1 < m
152 * 0 ≤ eval arg2 < m
153 * Postconditions:
154 * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
155 * 0 ≤ eval out1 < m
156 *
157 */
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)158 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) {
159 uint64_t x1;
160 uint64_t x2;
161 uint64_t x3;
162 uint64_t x4;
163 uint64_t x5;
164 uint64_t x6;
165 uint64_t x7;
166 uint64_t x8;
167 uint64_t x9;
168 uint64_t x10;
169 uint64_t x11;
170 uint64_t x12;
171 uint64_t x13;
172 fiat_p256_uint1 x14;
173 uint64_t x15;
174 fiat_p256_uint1 x16;
175 uint64_t x17;
176 fiat_p256_uint1 x18;
177 uint64_t x19;
178 uint64_t x20;
179 uint64_t x21;
180 uint64_t x22;
181 uint64_t x23;
182 uint64_t x24;
183 uint64_t x25;
184 uint64_t x26;
185 fiat_p256_uint1 x27;
186 uint64_t x28;
187 uint64_t x29;
188 fiat_p256_uint1 x30;
189 uint64_t x31;
190 fiat_p256_uint1 x32;
191 uint64_t x33;
192 fiat_p256_uint1 x34;
193 uint64_t x35;
194 fiat_p256_uint1 x36;
195 uint64_t x37;
196 fiat_p256_uint1 x38;
197 uint64_t x39;
198 uint64_t x40;
199 uint64_t x41;
200 uint64_t x42;
201 uint64_t x43;
202 uint64_t x44;
203 uint64_t x45;
204 uint64_t x46;
205 uint64_t x47;
206 fiat_p256_uint1 x48;
207 uint64_t x49;
208 fiat_p256_uint1 x50;
209 uint64_t x51;
210 fiat_p256_uint1 x52;
211 uint64_t x53;
212 uint64_t x54;
213 fiat_p256_uint1 x55;
214 uint64_t x56;
215 fiat_p256_uint1 x57;
216 uint64_t x58;
217 fiat_p256_uint1 x59;
218 uint64_t x60;
219 fiat_p256_uint1 x61;
220 uint64_t x62;
221 fiat_p256_uint1 x63;
222 uint64_t x64;
223 uint64_t x65;
224 uint64_t x66;
225 uint64_t x67;
226 uint64_t x68;
227 uint64_t x69;
228 uint64_t x70;
229 fiat_p256_uint1 x71;
230 uint64_t x72;
231 uint64_t x73;
232 fiat_p256_uint1 x74;
233 uint64_t x75;
234 fiat_p256_uint1 x76;
235 uint64_t x77;
236 fiat_p256_uint1 x78;
237 uint64_t x79;
238 fiat_p256_uint1 x80;
239 uint64_t x81;
240 fiat_p256_uint1 x82;
241 uint64_t x83;
242 uint64_t x84;
243 uint64_t x85;
244 uint64_t x86;
245 uint64_t x87;
246 uint64_t x88;
247 uint64_t x89;
248 uint64_t x90;
249 uint64_t x91;
250 uint64_t x92;
251 fiat_p256_uint1 x93;
252 uint64_t x94;
253 fiat_p256_uint1 x95;
254 uint64_t x96;
255 fiat_p256_uint1 x97;
256 uint64_t x98;
257 uint64_t x99;
258 fiat_p256_uint1 x100;
259 uint64_t x101;
260 fiat_p256_uint1 x102;
261 uint64_t x103;
262 fiat_p256_uint1 x104;
263 uint64_t x105;
264 fiat_p256_uint1 x106;
265 uint64_t x107;
266 fiat_p256_uint1 x108;
267 uint64_t x109;
268 uint64_t x110;
269 uint64_t x111;
270 uint64_t x112;
271 uint64_t x113;
272 uint64_t x114;
273 uint64_t x115;
274 fiat_p256_uint1 x116;
275 uint64_t x117;
276 uint64_t x118;
277 fiat_p256_uint1 x119;
278 uint64_t x120;
279 fiat_p256_uint1 x121;
280 uint64_t x122;
281 fiat_p256_uint1 x123;
282 uint64_t x124;
283 fiat_p256_uint1 x125;
284 uint64_t x126;
285 fiat_p256_uint1 x127;
286 uint64_t x128;
287 uint64_t x129;
288 uint64_t x130;
289 uint64_t x131;
290 uint64_t x132;
291 uint64_t x133;
292 uint64_t x134;
293 uint64_t x135;
294 uint64_t x136;
295 uint64_t x137;
296 fiat_p256_uint1 x138;
297 uint64_t x139;
298 fiat_p256_uint1 x140;
299 uint64_t x141;
300 fiat_p256_uint1 x142;
301 uint64_t x143;
302 uint64_t x144;
303 fiat_p256_uint1 x145;
304 uint64_t x146;
305 fiat_p256_uint1 x147;
306 uint64_t x148;
307 fiat_p256_uint1 x149;
308 uint64_t x150;
309 fiat_p256_uint1 x151;
310 uint64_t x152;
311 fiat_p256_uint1 x153;
312 uint64_t x154;
313 uint64_t x155;
314 uint64_t x156;
315 uint64_t x157;
316 uint64_t x158;
317 uint64_t x159;
318 uint64_t x160;
319 fiat_p256_uint1 x161;
320 uint64_t x162;
321 uint64_t x163;
322 fiat_p256_uint1 x164;
323 uint64_t x165;
324 fiat_p256_uint1 x166;
325 uint64_t x167;
326 fiat_p256_uint1 x168;
327 uint64_t x169;
328 fiat_p256_uint1 x170;
329 uint64_t x171;
330 fiat_p256_uint1 x172;
331 uint64_t x173;
332 uint64_t x174;
333 fiat_p256_uint1 x175;
334 uint64_t x176;
335 fiat_p256_uint1 x177;
336 uint64_t x178;
337 fiat_p256_uint1 x179;
338 uint64_t x180;
339 fiat_p256_uint1 x181;
340 uint64_t x182;
341 fiat_p256_uint1 x183;
342 uint64_t x184;
343 uint64_t x185;
344 uint64_t x186;
345 uint64_t x187;
346 x1 = (arg1[1]);
347 x2 = (arg1[2]);
348 x3 = (arg1[3]);
349 x4 = (arg1[0]);
350 fiat_p256_mulx_u64(&x5, &x6, x4, (arg2[3]));
351 fiat_p256_mulx_u64(&x7, &x8, x4, (arg2[2]));
352 fiat_p256_mulx_u64(&x9, &x10, x4, (arg2[1]));
353 fiat_p256_mulx_u64(&x11, &x12, x4, (arg2[0]));
354 fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
355 fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
356 fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
357 x19 = (x18 + x6);
358 fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001));
359 fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff));
360 fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff));
361 fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22);
362 x28 = (x27 + x23);
363 fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24);
364 fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26);
365 fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28);
366 fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20);
367 fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21);
368 fiat_p256_mulx_u64(&x39, &x40, x1, (arg2[3]));
369 fiat_p256_mulx_u64(&x41, &x42, x1, (arg2[2]));
370 fiat_p256_mulx_u64(&x43, &x44, x1, (arg2[1]));
371 fiat_p256_mulx_u64(&x45, &x46, x1, (arg2[0]));
372 fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43);
373 fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41);
374 fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39);
375 x53 = (x52 + x40);
376 fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45);
377 fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47);
378 fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49);
379 fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51);
380 fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53);
381 fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001));
382 fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff));
383 fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff));
384 fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66);
385 x72 = (x71 + x67);
386 fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68);
387 fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70);
388 fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72);
389 fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64);
390 fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65);
391 x83 = ((uint64_t)x82 + x63);
392 fiat_p256_mulx_u64(&x84, &x85, x2, (arg2[3]));
393 fiat_p256_mulx_u64(&x86, &x87, x2, (arg2[2]));
394 fiat_p256_mulx_u64(&x88, &x89, x2, (arg2[1]));
395 fiat_p256_mulx_u64(&x90, &x91, x2, (arg2[0]));
396 fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88);
397 fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86);
398 fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84);
399 x98 = (x97 + x85);
400 fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90);
401 fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92);
402 fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94);
403 fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96);
404 fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98);
405 fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001));
406 fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff));
407 fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff));
408 fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111);
409 x117 = (x116 + x112);
410 fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113);
411 fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115);
412 fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117);
413 fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109);
414 fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110);
415 x128 = ((uint64_t)x127 + x108);
416 fiat_p256_mulx_u64(&x129, &x130, x3, (arg2[3]));
417 fiat_p256_mulx_u64(&x131, &x132, x3, (arg2[2]));
418 fiat_p256_mulx_u64(&x133, &x134, x3, (arg2[1]));
419 fiat_p256_mulx_u64(&x135, &x136, x3, (arg2[0]));
420 fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133);
421 fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131);
422 fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129);
423 x143 = (x142 + x130);
424 fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135);
425 fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137);
426 fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139);
427 fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141);
428 fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143);
429 fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001));
430 fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff));
431 fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff));
432 fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156);
433 x162 = (x161 + x157);
434 fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158);
435 fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160);
436 fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162);
437 fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154);
438 fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155);
439 x173 = ((uint64_t)x172 + x153);
440 fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff));
441 fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff));
442 fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0);
443 fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001));
444 fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0);
445 fiat_p256_cmovznz_u64(&x184, x183, x174, x165);
446 fiat_p256_cmovznz_u64(&x185, x183, x176, x167);
447 fiat_p256_cmovznz_u64(&x186, x183, x178, x169);
448 fiat_p256_cmovznz_u64(&x187, x183, x180, x171);
449 out1[0] = x184;
450 out1[1] = x185;
451 out1[2] = x186;
452 out1[3] = x187;
453 }
454
455 /*
456 * The function fiat_p256_square squares a field element in the Montgomery domain.
457 *
458 * Preconditions:
459 * 0 ≤ eval arg1 < m
460 * Postconditions:
461 * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m
462 * 0 ≤ eval out1 < m
463 *
464 */
fiat_p256_square(fiat_p256_montgomery_domain_field_element out1,const fiat_p256_montgomery_domain_field_element arg1)465 static FIAT_P256_FIAT_INLINE void fiat_p256_square(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) {
466 uint64_t x1;
467 uint64_t x2;
468 uint64_t x3;
469 uint64_t x4;
470 uint64_t x5;
471 uint64_t x6;
472 uint64_t x7;
473 uint64_t x8;
474 uint64_t x9;
475 uint64_t x10;
476 uint64_t x11;
477 uint64_t x12;
478 uint64_t x13;
479 fiat_p256_uint1 x14;
480 uint64_t x15;
481 fiat_p256_uint1 x16;
482 uint64_t x17;
483 fiat_p256_uint1 x18;
484 uint64_t x19;
485 uint64_t x20;
486 uint64_t x21;
487 uint64_t x22;
488 uint64_t x23;
489 uint64_t x24;
490 uint64_t x25;
491 uint64_t x26;
492 fiat_p256_uint1 x27;
493 uint64_t x28;
494 uint64_t x29;
495 fiat_p256_uint1 x30;
496 uint64_t x31;
497 fiat_p256_uint1 x32;
498 uint64_t x33;
499 fiat_p256_uint1 x34;
500 uint64_t x35;
501 fiat_p256_uint1 x36;
502 uint64_t x37;
503 fiat_p256_uint1 x38;
504 uint64_t x39;
505 uint64_t x40;
506 uint64_t x41;
507 uint64_t x42;
508 uint64_t x43;
509 uint64_t x44;
510 uint64_t x45;
511 uint64_t x46;
512 uint64_t x47;
513 fiat_p256_uint1 x48;
514 uint64_t x49;
515 fiat_p256_uint1 x50;
516 uint64_t x51;
517 fiat_p256_uint1 x52;
518 uint64_t x53;
519 uint64_t x54;
520 fiat_p256_uint1 x55;
521 uint64_t x56;
522 fiat_p256_uint1 x57;
523 uint64_t x58;
524 fiat_p256_uint1 x59;
525 uint64_t x60;
526 fiat_p256_uint1 x61;
527 uint64_t x62;
528 fiat_p256_uint1 x63;
529 uint64_t x64;
530 uint64_t x65;
531 uint64_t x66;
532 uint64_t x67;
533 uint64_t x68;
534 uint64_t x69;
535 uint64_t x70;
536 fiat_p256_uint1 x71;
537 uint64_t x72;
538 uint64_t x73;
539 fiat_p256_uint1 x74;
540 uint64_t x75;
541 fiat_p256_uint1 x76;
542 uint64_t x77;
543 fiat_p256_uint1 x78;
544 uint64_t x79;
545 fiat_p256_uint1 x80;
546 uint64_t x81;
547 fiat_p256_uint1 x82;
548 uint64_t x83;
549 uint64_t x84;
550 uint64_t x85;
551 uint64_t x86;
552 uint64_t x87;
553 uint64_t x88;
554 uint64_t x89;
555 uint64_t x90;
556 uint64_t x91;
557 uint64_t x92;
558 fiat_p256_uint1 x93;
559 uint64_t x94;
560 fiat_p256_uint1 x95;
561 uint64_t x96;
562 fiat_p256_uint1 x97;
563 uint64_t x98;
564 uint64_t x99;
565 fiat_p256_uint1 x100;
566 uint64_t x101;
567 fiat_p256_uint1 x102;
568 uint64_t x103;
569 fiat_p256_uint1 x104;
570 uint64_t x105;
571 fiat_p256_uint1 x106;
572 uint64_t x107;
573 fiat_p256_uint1 x108;
574 uint64_t x109;
575 uint64_t x110;
576 uint64_t x111;
577 uint64_t x112;
578 uint64_t x113;
579 uint64_t x114;
580 uint64_t x115;
581 fiat_p256_uint1 x116;
582 uint64_t x117;
583 uint64_t x118;
584 fiat_p256_uint1 x119;
585 uint64_t x120;
586 fiat_p256_uint1 x121;
587 uint64_t x122;
588 fiat_p256_uint1 x123;
589 uint64_t x124;
590 fiat_p256_uint1 x125;
591 uint64_t x126;
592 fiat_p256_uint1 x127;
593 uint64_t x128;
594 uint64_t x129;
595 uint64_t x130;
596 uint64_t x131;
597 uint64_t x132;
598 uint64_t x133;
599 uint64_t x134;
600 uint64_t x135;
601 uint64_t x136;
602 uint64_t x137;
603 fiat_p256_uint1 x138;
604 uint64_t x139;
605 fiat_p256_uint1 x140;
606 uint64_t x141;
607 fiat_p256_uint1 x142;
608 uint64_t x143;
609 uint64_t x144;
610 fiat_p256_uint1 x145;
611 uint64_t x146;
612 fiat_p256_uint1 x147;
613 uint64_t x148;
614 fiat_p256_uint1 x149;
615 uint64_t x150;
616 fiat_p256_uint1 x151;
617 uint64_t x152;
618 fiat_p256_uint1 x153;
619 uint64_t x154;
620 uint64_t x155;
621 uint64_t x156;
622 uint64_t x157;
623 uint64_t x158;
624 uint64_t x159;
625 uint64_t x160;
626 fiat_p256_uint1 x161;
627 uint64_t x162;
628 uint64_t x163;
629 fiat_p256_uint1 x164;
630 uint64_t x165;
631 fiat_p256_uint1 x166;
632 uint64_t x167;
633 fiat_p256_uint1 x168;
634 uint64_t x169;
635 fiat_p256_uint1 x170;
636 uint64_t x171;
637 fiat_p256_uint1 x172;
638 uint64_t x173;
639 uint64_t x174;
640 fiat_p256_uint1 x175;
641 uint64_t x176;
642 fiat_p256_uint1 x177;
643 uint64_t x178;
644 fiat_p256_uint1 x179;
645 uint64_t x180;
646 fiat_p256_uint1 x181;
647 uint64_t x182;
648 fiat_p256_uint1 x183;
649 uint64_t x184;
650 uint64_t x185;
651 uint64_t x186;
652 uint64_t x187;
653 x1 = (arg1[1]);
654 x2 = (arg1[2]);
655 x3 = (arg1[3]);
656 x4 = (arg1[0]);
657 fiat_p256_mulx_u64(&x5, &x6, x4, (arg1[3]));
658 fiat_p256_mulx_u64(&x7, &x8, x4, (arg1[2]));
659 fiat_p256_mulx_u64(&x9, &x10, x4, (arg1[1]));
660 fiat_p256_mulx_u64(&x11, &x12, x4, (arg1[0]));
661 fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
662 fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
663 fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
664 x19 = (x18 + x6);
665 fiat_p256_mulx_u64(&x20, &x21, x11, UINT64_C(0xffffffff00000001));
666 fiat_p256_mulx_u64(&x22, &x23, x11, UINT32_C(0xffffffff));
667 fiat_p256_mulx_u64(&x24, &x25, x11, UINT64_C(0xffffffffffffffff));
668 fiat_p256_addcarryx_u64(&x26, &x27, 0x0, x25, x22);
669 x28 = (x27 + x23);
670 fiat_p256_addcarryx_u64(&x29, &x30, 0x0, x11, x24);
671 fiat_p256_addcarryx_u64(&x31, &x32, x30, x13, x26);
672 fiat_p256_addcarryx_u64(&x33, &x34, x32, x15, x28);
673 fiat_p256_addcarryx_u64(&x35, &x36, x34, x17, x20);
674 fiat_p256_addcarryx_u64(&x37, &x38, x36, x19, x21);
675 fiat_p256_mulx_u64(&x39, &x40, x1, (arg1[3]));
676 fiat_p256_mulx_u64(&x41, &x42, x1, (arg1[2]));
677 fiat_p256_mulx_u64(&x43, &x44, x1, (arg1[1]));
678 fiat_p256_mulx_u64(&x45, &x46, x1, (arg1[0]));
679 fiat_p256_addcarryx_u64(&x47, &x48, 0x0, x46, x43);
680 fiat_p256_addcarryx_u64(&x49, &x50, x48, x44, x41);
681 fiat_p256_addcarryx_u64(&x51, &x52, x50, x42, x39);
682 x53 = (x52 + x40);
683 fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x31, x45);
684 fiat_p256_addcarryx_u64(&x56, &x57, x55, x33, x47);
685 fiat_p256_addcarryx_u64(&x58, &x59, x57, x35, x49);
686 fiat_p256_addcarryx_u64(&x60, &x61, x59, x37, x51);
687 fiat_p256_addcarryx_u64(&x62, &x63, x61, x38, x53);
688 fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffff00000001));
689 fiat_p256_mulx_u64(&x66, &x67, x54, UINT32_C(0xffffffff));
690 fiat_p256_mulx_u64(&x68, &x69, x54, UINT64_C(0xffffffffffffffff));
691 fiat_p256_addcarryx_u64(&x70, &x71, 0x0, x69, x66);
692 x72 = (x71 + x67);
693 fiat_p256_addcarryx_u64(&x73, &x74, 0x0, x54, x68);
694 fiat_p256_addcarryx_u64(&x75, &x76, x74, x56, x70);
695 fiat_p256_addcarryx_u64(&x77, &x78, x76, x58, x72);
696 fiat_p256_addcarryx_u64(&x79, &x80, x78, x60, x64);
697 fiat_p256_addcarryx_u64(&x81, &x82, x80, x62, x65);
698 x83 = ((uint64_t)x82 + x63);
699 fiat_p256_mulx_u64(&x84, &x85, x2, (arg1[3]));
700 fiat_p256_mulx_u64(&x86, &x87, x2, (arg1[2]));
701 fiat_p256_mulx_u64(&x88, &x89, x2, (arg1[1]));
702 fiat_p256_mulx_u64(&x90, &x91, x2, (arg1[0]));
703 fiat_p256_addcarryx_u64(&x92, &x93, 0x0, x91, x88);
704 fiat_p256_addcarryx_u64(&x94, &x95, x93, x89, x86);
705 fiat_p256_addcarryx_u64(&x96, &x97, x95, x87, x84);
706 x98 = (x97 + x85);
707 fiat_p256_addcarryx_u64(&x99, &x100, 0x0, x75, x90);
708 fiat_p256_addcarryx_u64(&x101, &x102, x100, x77, x92);
709 fiat_p256_addcarryx_u64(&x103, &x104, x102, x79, x94);
710 fiat_p256_addcarryx_u64(&x105, &x106, x104, x81, x96);
711 fiat_p256_addcarryx_u64(&x107, &x108, x106, x83, x98);
712 fiat_p256_mulx_u64(&x109, &x110, x99, UINT64_C(0xffffffff00000001));
713 fiat_p256_mulx_u64(&x111, &x112, x99, UINT32_C(0xffffffff));
714 fiat_p256_mulx_u64(&x113, &x114, x99, UINT64_C(0xffffffffffffffff));
715 fiat_p256_addcarryx_u64(&x115, &x116, 0x0, x114, x111);
716 x117 = (x116 + x112);
717 fiat_p256_addcarryx_u64(&x118, &x119, 0x0, x99, x113);
718 fiat_p256_addcarryx_u64(&x120, &x121, x119, x101, x115);
719 fiat_p256_addcarryx_u64(&x122, &x123, x121, x103, x117);
720 fiat_p256_addcarryx_u64(&x124, &x125, x123, x105, x109);
721 fiat_p256_addcarryx_u64(&x126, &x127, x125, x107, x110);
722 x128 = ((uint64_t)x127 + x108);
723 fiat_p256_mulx_u64(&x129, &x130, x3, (arg1[3]));
724 fiat_p256_mulx_u64(&x131, &x132, x3, (arg1[2]));
725 fiat_p256_mulx_u64(&x133, &x134, x3, (arg1[1]));
726 fiat_p256_mulx_u64(&x135, &x136, x3, (arg1[0]));
727 fiat_p256_addcarryx_u64(&x137, &x138, 0x0, x136, x133);
728 fiat_p256_addcarryx_u64(&x139, &x140, x138, x134, x131);
729 fiat_p256_addcarryx_u64(&x141, &x142, x140, x132, x129);
730 x143 = (x142 + x130);
731 fiat_p256_addcarryx_u64(&x144, &x145, 0x0, x120, x135);
732 fiat_p256_addcarryx_u64(&x146, &x147, x145, x122, x137);
733 fiat_p256_addcarryx_u64(&x148, &x149, x147, x124, x139);
734 fiat_p256_addcarryx_u64(&x150, &x151, x149, x126, x141);
735 fiat_p256_addcarryx_u64(&x152, &x153, x151, x128, x143);
736 fiat_p256_mulx_u64(&x154, &x155, x144, UINT64_C(0xffffffff00000001));
737 fiat_p256_mulx_u64(&x156, &x157, x144, UINT32_C(0xffffffff));
738 fiat_p256_mulx_u64(&x158, &x159, x144, UINT64_C(0xffffffffffffffff));
739 fiat_p256_addcarryx_u64(&x160, &x161, 0x0, x159, x156);
740 x162 = (x161 + x157);
741 fiat_p256_addcarryx_u64(&x163, &x164, 0x0, x144, x158);
742 fiat_p256_addcarryx_u64(&x165, &x166, x164, x146, x160);
743 fiat_p256_addcarryx_u64(&x167, &x168, x166, x148, x162);
744 fiat_p256_addcarryx_u64(&x169, &x170, x168, x150, x154);
745 fiat_p256_addcarryx_u64(&x171, &x172, x170, x152, x155);
746 x173 = ((uint64_t)x172 + x153);
747 fiat_p256_subborrowx_u64(&x174, &x175, 0x0, x165, UINT64_C(0xffffffffffffffff));
748 fiat_p256_subborrowx_u64(&x176, &x177, x175, x167, UINT32_C(0xffffffff));
749 fiat_p256_subborrowx_u64(&x178, &x179, x177, x169, 0x0);
750 fiat_p256_subborrowx_u64(&x180, &x181, x179, x171, UINT64_C(0xffffffff00000001));
751 fiat_p256_subborrowx_u64(&x182, &x183, x181, x173, 0x0);
752 fiat_p256_cmovznz_u64(&x184, x183, x174, x165);
753 fiat_p256_cmovznz_u64(&x185, x183, x176, x167);
754 fiat_p256_cmovznz_u64(&x186, x183, x178, x169);
755 fiat_p256_cmovznz_u64(&x187, x183, x180, x171);
756 out1[0] = x184;
757 out1[1] = x185;
758 out1[2] = x186;
759 out1[3] = x187;
760 }
761
762 /*
763 * The function fiat_p256_add adds two field elements in the Montgomery domain.
764 *
765 * Preconditions:
766 * 0 ≤ eval arg1 < m
767 * 0 ≤ eval arg2 < m
768 * Postconditions:
769 * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
770 * 0 ≤ eval out1 < m
771 *
772 */
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)773 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) {
774 uint64_t x1;
775 fiat_p256_uint1 x2;
776 uint64_t x3;
777 fiat_p256_uint1 x4;
778 uint64_t x5;
779 fiat_p256_uint1 x6;
780 uint64_t x7;
781 fiat_p256_uint1 x8;
782 uint64_t x9;
783 fiat_p256_uint1 x10;
784 uint64_t x11;
785 fiat_p256_uint1 x12;
786 uint64_t x13;
787 fiat_p256_uint1 x14;
788 uint64_t x15;
789 fiat_p256_uint1 x16;
790 uint64_t x17;
791 fiat_p256_uint1 x18;
792 uint64_t x19;
793 uint64_t x20;
794 uint64_t x21;
795 uint64_t x22;
796 fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
797 fiat_p256_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
798 fiat_p256_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
799 fiat_p256_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
800 fiat_p256_subborrowx_u64(&x9, &x10, 0x0, x1, UINT64_C(0xffffffffffffffff));
801 fiat_p256_subborrowx_u64(&x11, &x12, x10, x3, UINT32_C(0xffffffff));
802 fiat_p256_subborrowx_u64(&x13, &x14, x12, x5, 0x0);
803 fiat_p256_subborrowx_u64(&x15, &x16, x14, x7, UINT64_C(0xffffffff00000001));
804 fiat_p256_subborrowx_u64(&x17, &x18, x16, x8, 0x0);
805 fiat_p256_cmovznz_u64(&x19, x18, x9, x1);
806 fiat_p256_cmovznz_u64(&x20, x18, x11, x3);
807 fiat_p256_cmovznz_u64(&x21, x18, x13, x5);
808 fiat_p256_cmovznz_u64(&x22, x18, x15, x7);
809 out1[0] = x19;
810 out1[1] = x20;
811 out1[2] = x21;
812 out1[3] = x22;
813 }
814
815 /*
816 * The function fiat_p256_sub subtracts two field elements in the Montgomery domain.
817 *
818 * Preconditions:
819 * 0 ≤ eval arg1 < m
820 * 0 ≤ eval arg2 < m
821 * Postconditions:
822 * eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
823 * 0 ≤ eval out1 < m
824 *
825 */
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)826 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) {
827 uint64_t x1;
828 fiat_p256_uint1 x2;
829 uint64_t x3;
830 fiat_p256_uint1 x4;
831 uint64_t x5;
832 fiat_p256_uint1 x6;
833 uint64_t x7;
834 fiat_p256_uint1 x8;
835 uint64_t x9;
836 uint64_t x10;
837 fiat_p256_uint1 x11;
838 uint64_t x12;
839 fiat_p256_uint1 x13;
840 uint64_t x14;
841 fiat_p256_uint1 x15;
842 uint64_t x16;
843 fiat_p256_uint1 x17;
844 fiat_p256_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
845 fiat_p256_subborrowx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
846 fiat_p256_subborrowx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
847 fiat_p256_subborrowx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
848 fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
849 fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9);
850 fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff)));
851 fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0);
852 fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001)));
853 out1[0] = x10;
854 out1[1] = x12;
855 out1[2] = x14;
856 out1[3] = x16;
857 }
858
859 /*
860 * The function fiat_p256_opp negates a field element in the Montgomery domain.
861 *
862 * Preconditions:
863 * 0 ≤ eval arg1 < m
864 * Postconditions:
865 * eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
866 * 0 ≤ eval out1 < m
867 *
868 */
fiat_p256_opp(fiat_p256_montgomery_domain_field_element out1,const fiat_p256_montgomery_domain_field_element arg1)869 static FIAT_P256_FIAT_INLINE void fiat_p256_opp(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) {
870 uint64_t x1;
871 fiat_p256_uint1 x2;
872 uint64_t x3;
873 fiat_p256_uint1 x4;
874 uint64_t x5;
875 fiat_p256_uint1 x6;
876 uint64_t x7;
877 fiat_p256_uint1 x8;
878 uint64_t x9;
879 uint64_t x10;
880 fiat_p256_uint1 x11;
881 uint64_t x12;
882 fiat_p256_uint1 x13;
883 uint64_t x14;
884 fiat_p256_uint1 x15;
885 uint64_t x16;
886 fiat_p256_uint1 x17;
887 fiat_p256_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0]));
888 fiat_p256_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1]));
889 fiat_p256_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2]));
890 fiat_p256_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3]));
891 fiat_p256_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
892 fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x9);
893 fiat_p256_addcarryx_u64(&x12, &x13, x11, x3, (x9 & UINT32_C(0xffffffff)));
894 fiat_p256_addcarryx_u64(&x14, &x15, x13, x5, 0x0);
895 fiat_p256_addcarryx_u64(&x16, &x17, x15, x7, (x9 & UINT64_C(0xffffffff00000001)));
896 out1[0] = x10;
897 out1[1] = x12;
898 out1[2] = x14;
899 out1[3] = x16;
900 }
901
902 /*
903 * The function fiat_p256_from_montgomery translates a field element out of the Montgomery domain.
904 *
905 * Preconditions:
906 * 0 ≤ eval arg1 < m
907 * Postconditions:
908 * eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
909 * 0 ≤ eval out1 < m
910 *
911 */
fiat_p256_from_montgomery(fiat_p256_non_montgomery_domain_field_element out1,const fiat_p256_montgomery_domain_field_element arg1)912 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) {
913 uint64_t x1;
914 uint64_t x2;
915 uint64_t x3;
916 uint64_t x4;
917 uint64_t x5;
918 uint64_t x6;
919 uint64_t x7;
920 uint64_t x8;
921 fiat_p256_uint1 x9;
922 uint64_t x10;
923 fiat_p256_uint1 x11;
924 uint64_t x12;
925 fiat_p256_uint1 x13;
926 uint64_t x14;
927 fiat_p256_uint1 x15;
928 uint64_t x16;
929 uint64_t x17;
930 uint64_t x18;
931 uint64_t x19;
932 uint64_t x20;
933 uint64_t x21;
934 uint64_t x22;
935 fiat_p256_uint1 x23;
936 uint64_t x24;
937 fiat_p256_uint1 x25;
938 uint64_t x26;
939 fiat_p256_uint1 x27;
940 uint64_t x28;
941 fiat_p256_uint1 x29;
942 uint64_t x30;
943 fiat_p256_uint1 x31;
944 uint64_t x32;
945 fiat_p256_uint1 x33;
946 uint64_t x34;
947 fiat_p256_uint1 x35;
948 uint64_t x36;
949 fiat_p256_uint1 x37;
950 uint64_t x38;
951 uint64_t x39;
952 uint64_t x40;
953 uint64_t x41;
954 uint64_t x42;
955 uint64_t x43;
956 uint64_t x44;
957 fiat_p256_uint1 x45;
958 uint64_t x46;
959 fiat_p256_uint1 x47;
960 uint64_t x48;
961 fiat_p256_uint1 x49;
962 uint64_t x50;
963 fiat_p256_uint1 x51;
964 uint64_t x52;
965 fiat_p256_uint1 x53;
966 uint64_t x54;
967 fiat_p256_uint1 x55;
968 uint64_t x56;
969 fiat_p256_uint1 x57;
970 uint64_t x58;
971 fiat_p256_uint1 x59;
972 uint64_t x60;
973 uint64_t x61;
974 uint64_t x62;
975 uint64_t x63;
976 uint64_t x64;
977 uint64_t x65;
978 uint64_t x66;
979 fiat_p256_uint1 x67;
980 uint64_t x68;
981 fiat_p256_uint1 x69;
982 uint64_t x70;
983 fiat_p256_uint1 x71;
984 uint64_t x72;
985 fiat_p256_uint1 x73;
986 uint64_t x74;
987 fiat_p256_uint1 x75;
988 uint64_t x76;
989 uint64_t x77;
990 fiat_p256_uint1 x78;
991 uint64_t x79;
992 fiat_p256_uint1 x80;
993 uint64_t x81;
994 fiat_p256_uint1 x82;
995 uint64_t x83;
996 fiat_p256_uint1 x84;
997 uint64_t x85;
998 fiat_p256_uint1 x86;
999 uint64_t x87;
1000 uint64_t x88;
1001 uint64_t x89;
1002 uint64_t x90;
1003 x1 = (arg1[0]);
1004 fiat_p256_mulx_u64(&x2, &x3, x1, UINT64_C(0xffffffff00000001));
1005 fiat_p256_mulx_u64(&x4, &x5, x1, UINT32_C(0xffffffff));
1006 fiat_p256_mulx_u64(&x6, &x7, x1, UINT64_C(0xffffffffffffffff));
1007 fiat_p256_addcarryx_u64(&x8, &x9, 0x0, x7, x4);
1008 fiat_p256_addcarryx_u64(&x10, &x11, 0x0, x1, x6);
1009 fiat_p256_addcarryx_u64(&x12, &x13, x11, 0x0, x8);
1010 fiat_p256_addcarryx_u64(&x14, &x15, 0x0, x12, (arg1[1]));
1011 fiat_p256_mulx_u64(&x16, &x17, x14, UINT64_C(0xffffffff00000001));
1012 fiat_p256_mulx_u64(&x18, &x19, x14, UINT32_C(0xffffffff));
1013 fiat_p256_mulx_u64(&x20, &x21, x14, UINT64_C(0xffffffffffffffff));
1014 fiat_p256_addcarryx_u64(&x22, &x23, 0x0, x21, x18);
1015 fiat_p256_addcarryx_u64(&x24, &x25, 0x0, x14, x20);
1016 fiat_p256_addcarryx_u64(&x26, &x27, x25, (x15 + (x13 + (x9 + x5))), x22);
1017 fiat_p256_addcarryx_u64(&x28, &x29, x27, x2, (x23 + x19));
1018 fiat_p256_addcarryx_u64(&x30, &x31, x29, x3, x16);
1019 fiat_p256_addcarryx_u64(&x32, &x33, 0x0, x26, (arg1[2]));
1020 fiat_p256_addcarryx_u64(&x34, &x35, x33, x28, 0x0);
1021 fiat_p256_addcarryx_u64(&x36, &x37, x35, x30, 0x0);
1022 fiat_p256_mulx_u64(&x38, &x39, x32, UINT64_C(0xffffffff00000001));
1023 fiat_p256_mulx_u64(&x40, &x41, x32, UINT32_C(0xffffffff));
1024 fiat_p256_mulx_u64(&x42, &x43, x32, UINT64_C(0xffffffffffffffff));
1025 fiat_p256_addcarryx_u64(&x44, &x45, 0x0, x43, x40);
1026 fiat_p256_addcarryx_u64(&x46, &x47, 0x0, x32, x42);
1027 fiat_p256_addcarryx_u64(&x48, &x49, x47, x34, x44);
1028 fiat_p256_addcarryx_u64(&x50, &x51, x49, x36, (x45 + x41));
1029 fiat_p256_addcarryx_u64(&x52, &x53, x51, (x37 + (x31 + x17)), x38);
1030 fiat_p256_addcarryx_u64(&x54, &x55, 0x0, x48, (arg1[3]));
1031 fiat_p256_addcarryx_u64(&x56, &x57, x55, x50, 0x0);
1032 fiat_p256_addcarryx_u64(&x58, &x59, x57, x52, 0x0);
1033 fiat_p256_mulx_u64(&x60, &x61, x54, UINT64_C(0xffffffff00000001));
1034 fiat_p256_mulx_u64(&x62, &x63, x54, UINT32_C(0xffffffff));
1035 fiat_p256_mulx_u64(&x64, &x65, x54, UINT64_C(0xffffffffffffffff));
1036 fiat_p256_addcarryx_u64(&x66, &x67, 0x0, x65, x62);
1037 fiat_p256_addcarryx_u64(&x68, &x69, 0x0, x54, x64);
1038 fiat_p256_addcarryx_u64(&x70, &x71, x69, x56, x66);
1039 fiat_p256_addcarryx_u64(&x72, &x73, x71, x58, (x67 + x63));
1040 fiat_p256_addcarryx_u64(&x74, &x75, x73, (x59 + (x53 + x39)), x60);
1041 x76 = (x75 + x61);
1042 fiat_p256_subborrowx_u64(&x77, &x78, 0x0, x70, UINT64_C(0xffffffffffffffff));
1043 fiat_p256_subborrowx_u64(&x79, &x80, x78, x72, UINT32_C(0xffffffff));
1044 fiat_p256_subborrowx_u64(&x81, &x82, x80, x74, 0x0);
1045 fiat_p256_subborrowx_u64(&x83, &x84, x82, x76, UINT64_C(0xffffffff00000001));
1046 fiat_p256_subborrowx_u64(&x85, &x86, x84, 0x0, 0x0);
1047 fiat_p256_cmovznz_u64(&x87, x86, x77, x70);
1048 fiat_p256_cmovznz_u64(&x88, x86, x79, x72);
1049 fiat_p256_cmovznz_u64(&x89, x86, x81, x74);
1050 fiat_p256_cmovznz_u64(&x90, x86, x83, x76);
1051 out1[0] = x87;
1052 out1[1] = x88;
1053 out1[2] = x89;
1054 out1[3] = x90;
1055 }
1056
1057 /*
1058 * The function fiat_p256_to_montgomery translates a field element into the Montgomery domain.
1059 *
1060 * Preconditions:
1061 * 0 ≤ eval arg1 < m
1062 * Postconditions:
1063 * eval (from_montgomery out1) mod m = eval arg1 mod m
1064 * 0 ≤ eval out1 < m
1065 *
1066 */
fiat_p256_to_montgomery(fiat_p256_montgomery_domain_field_element out1,const fiat_p256_non_montgomery_domain_field_element arg1)1067 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) {
1068 uint64_t x1;
1069 uint64_t x2;
1070 uint64_t x3;
1071 uint64_t x4;
1072 uint64_t x5;
1073 uint64_t x6;
1074 uint64_t x7;
1075 uint64_t x8;
1076 uint64_t x9;
1077 uint64_t x10;
1078 uint64_t x11;
1079 uint64_t x12;
1080 uint64_t x13;
1081 fiat_p256_uint1 x14;
1082 uint64_t x15;
1083 fiat_p256_uint1 x16;
1084 uint64_t x17;
1085 fiat_p256_uint1 x18;
1086 uint64_t x19;
1087 uint64_t x20;
1088 uint64_t x21;
1089 uint64_t x22;
1090 uint64_t x23;
1091 uint64_t x24;
1092 uint64_t x25;
1093 fiat_p256_uint1 x26;
1094 uint64_t x27;
1095 fiat_p256_uint1 x28;
1096 uint64_t x29;
1097 fiat_p256_uint1 x30;
1098 uint64_t x31;
1099 fiat_p256_uint1 x32;
1100 uint64_t x33;
1101 fiat_p256_uint1 x34;
1102 uint64_t x35;
1103 fiat_p256_uint1 x36;
1104 uint64_t x37;
1105 uint64_t x38;
1106 uint64_t x39;
1107 uint64_t x40;
1108 uint64_t x41;
1109 uint64_t x42;
1110 uint64_t x43;
1111 uint64_t x44;
1112 uint64_t x45;
1113 fiat_p256_uint1 x46;
1114 uint64_t x47;
1115 fiat_p256_uint1 x48;
1116 uint64_t x49;
1117 fiat_p256_uint1 x50;
1118 uint64_t x51;
1119 fiat_p256_uint1 x52;
1120 uint64_t x53;
1121 fiat_p256_uint1 x54;
1122 uint64_t x55;
1123 fiat_p256_uint1 x56;
1124 uint64_t x57;
1125 fiat_p256_uint1 x58;
1126 uint64_t x59;
1127 uint64_t x60;
1128 uint64_t x61;
1129 uint64_t x62;
1130 uint64_t x63;
1131 uint64_t x64;
1132 uint64_t x65;
1133 fiat_p256_uint1 x66;
1134 uint64_t x67;
1135 fiat_p256_uint1 x68;
1136 uint64_t x69;
1137 fiat_p256_uint1 x70;
1138 uint64_t x71;
1139 fiat_p256_uint1 x72;
1140 uint64_t x73;
1141 fiat_p256_uint1 x74;
1142 uint64_t x75;
1143 fiat_p256_uint1 x76;
1144 uint64_t x77;
1145 uint64_t x78;
1146 uint64_t x79;
1147 uint64_t x80;
1148 uint64_t x81;
1149 uint64_t x82;
1150 uint64_t x83;
1151 uint64_t x84;
1152 uint64_t x85;
1153 fiat_p256_uint1 x86;
1154 uint64_t x87;
1155 fiat_p256_uint1 x88;
1156 uint64_t x89;
1157 fiat_p256_uint1 x90;
1158 uint64_t x91;
1159 fiat_p256_uint1 x92;
1160 uint64_t x93;
1161 fiat_p256_uint1 x94;
1162 uint64_t x95;
1163 fiat_p256_uint1 x96;
1164 uint64_t x97;
1165 fiat_p256_uint1 x98;
1166 uint64_t x99;
1167 uint64_t x100;
1168 uint64_t x101;
1169 uint64_t x102;
1170 uint64_t x103;
1171 uint64_t x104;
1172 uint64_t x105;
1173 fiat_p256_uint1 x106;
1174 uint64_t x107;
1175 fiat_p256_uint1 x108;
1176 uint64_t x109;
1177 fiat_p256_uint1 x110;
1178 uint64_t x111;
1179 fiat_p256_uint1 x112;
1180 uint64_t x113;
1181 fiat_p256_uint1 x114;
1182 uint64_t x115;
1183 fiat_p256_uint1 x116;
1184 uint64_t x117;
1185 uint64_t x118;
1186 uint64_t x119;
1187 uint64_t x120;
1188 uint64_t x121;
1189 uint64_t x122;
1190 uint64_t x123;
1191 uint64_t x124;
1192 uint64_t x125;
1193 fiat_p256_uint1 x126;
1194 uint64_t x127;
1195 fiat_p256_uint1 x128;
1196 uint64_t x129;
1197 fiat_p256_uint1 x130;
1198 uint64_t x131;
1199 fiat_p256_uint1 x132;
1200 uint64_t x133;
1201 fiat_p256_uint1 x134;
1202 uint64_t x135;
1203 fiat_p256_uint1 x136;
1204 uint64_t x137;
1205 fiat_p256_uint1 x138;
1206 uint64_t x139;
1207 uint64_t x140;
1208 uint64_t x141;
1209 uint64_t x142;
1210 uint64_t x143;
1211 uint64_t x144;
1212 uint64_t x145;
1213 fiat_p256_uint1 x146;
1214 uint64_t x147;
1215 fiat_p256_uint1 x148;
1216 uint64_t x149;
1217 fiat_p256_uint1 x150;
1218 uint64_t x151;
1219 fiat_p256_uint1 x152;
1220 uint64_t x153;
1221 fiat_p256_uint1 x154;
1222 uint64_t x155;
1223 fiat_p256_uint1 x156;
1224 uint64_t x157;
1225 fiat_p256_uint1 x158;
1226 uint64_t x159;
1227 fiat_p256_uint1 x160;
1228 uint64_t x161;
1229 fiat_p256_uint1 x162;
1230 uint64_t x163;
1231 fiat_p256_uint1 x164;
1232 uint64_t x165;
1233 fiat_p256_uint1 x166;
1234 uint64_t x167;
1235 uint64_t x168;
1236 uint64_t x169;
1237 uint64_t x170;
1238 x1 = (arg1[1]);
1239 x2 = (arg1[2]);
1240 x3 = (arg1[3]);
1241 x4 = (arg1[0]);
1242 fiat_p256_mulx_u64(&x5, &x6, x4, UINT64_C(0x4fffffffd));
1243 fiat_p256_mulx_u64(&x7, &x8, x4, UINT64_C(0xfffffffffffffffe));
1244 fiat_p256_mulx_u64(&x9, &x10, x4, UINT64_C(0xfffffffbffffffff));
1245 fiat_p256_mulx_u64(&x11, &x12, x4, 0x3);
1246 fiat_p256_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
1247 fiat_p256_addcarryx_u64(&x15, &x16, x14, x10, x7);
1248 fiat_p256_addcarryx_u64(&x17, &x18, x16, x8, x5);
1249 fiat_p256_mulx_u64(&x19, &x20, x11, UINT64_C(0xffffffff00000001));
1250 fiat_p256_mulx_u64(&x21, &x22, x11, UINT32_C(0xffffffff));
1251 fiat_p256_mulx_u64(&x23, &x24, x11, UINT64_C(0xffffffffffffffff));
1252 fiat_p256_addcarryx_u64(&x25, &x26, 0x0, x24, x21);
1253 fiat_p256_addcarryx_u64(&x27, &x28, 0x0, x11, x23);
1254 fiat_p256_addcarryx_u64(&x29, &x30, x28, x13, x25);
1255 fiat_p256_addcarryx_u64(&x31, &x32, x30, x15, (x26 + x22));
1256 fiat_p256_addcarryx_u64(&x33, &x34, x32, x17, x19);
1257 fiat_p256_addcarryx_u64(&x35, &x36, x34, (x18 + x6), x20);
1258 fiat_p256_mulx_u64(&x37, &x38, x1, UINT64_C(0x4fffffffd));
1259 fiat_p256_mulx_u64(&x39, &x40, x1, UINT64_C(0xfffffffffffffffe));
1260 fiat_p256_mulx_u64(&x41, &x42, x1, UINT64_C(0xfffffffbffffffff));
1261 fiat_p256_mulx_u64(&x43, &x44, x1, 0x3);
1262 fiat_p256_addcarryx_u64(&x45, &x46, 0x0, x44, x41);
1263 fiat_p256_addcarryx_u64(&x47, &x48, x46, x42, x39);
1264 fiat_p256_addcarryx_u64(&x49, &x50, x48, x40, x37);
1265 fiat_p256_addcarryx_u64(&x51, &x52, 0x0, x29, x43);
1266 fiat_p256_addcarryx_u64(&x53, &x54, x52, x31, x45);
1267 fiat_p256_addcarryx_u64(&x55, &x56, x54, x33, x47);
1268 fiat_p256_addcarryx_u64(&x57, &x58, x56, x35, x49);
1269 fiat_p256_mulx_u64(&x59, &x60, x51, UINT64_C(0xffffffff00000001));
1270 fiat_p256_mulx_u64(&x61, &x62, x51, UINT32_C(0xffffffff));
1271 fiat_p256_mulx_u64(&x63, &x64, x51, UINT64_C(0xffffffffffffffff));
1272 fiat_p256_addcarryx_u64(&x65, &x66, 0x0, x64, x61);
1273 fiat_p256_addcarryx_u64(&x67, &x68, 0x0, x51, x63);
1274 fiat_p256_addcarryx_u64(&x69, &x70, x68, x53, x65);
1275 fiat_p256_addcarryx_u64(&x71, &x72, x70, x55, (x66 + x62));
1276 fiat_p256_addcarryx_u64(&x73, &x74, x72, x57, x59);
1277 fiat_p256_addcarryx_u64(&x75, &x76, x74, (((uint64_t)x58 + x36) + (x50 + x38)), x60);
1278 fiat_p256_mulx_u64(&x77, &x78, x2, UINT64_C(0x4fffffffd));
1279 fiat_p256_mulx_u64(&x79, &x80, x2, UINT64_C(0xfffffffffffffffe));
1280 fiat_p256_mulx_u64(&x81, &x82, x2, UINT64_C(0xfffffffbffffffff));
1281 fiat_p256_mulx_u64(&x83, &x84, x2, 0x3);
1282 fiat_p256_addcarryx_u64(&x85, &x86, 0x0, x84, x81);
1283 fiat_p256_addcarryx_u64(&x87, &x88, x86, x82, x79);
1284 fiat_p256_addcarryx_u64(&x89, &x90, x88, x80, x77);
1285 fiat_p256_addcarryx_u64(&x91, &x92, 0x0, x69, x83);
1286 fiat_p256_addcarryx_u64(&x93, &x94, x92, x71, x85);
1287 fiat_p256_addcarryx_u64(&x95, &x96, x94, x73, x87);
1288 fiat_p256_addcarryx_u64(&x97, &x98, x96, x75, x89);
1289 fiat_p256_mulx_u64(&x99, &x100, x91, UINT64_C(0xffffffff00000001));
1290 fiat_p256_mulx_u64(&x101, &x102, x91, UINT32_C(0xffffffff));
1291 fiat_p256_mulx_u64(&x103, &x104, x91, UINT64_C(0xffffffffffffffff));
1292 fiat_p256_addcarryx_u64(&x105, &x106, 0x0, x104, x101);
1293 fiat_p256_addcarryx_u64(&x107, &x108, 0x0, x91, x103);
1294 fiat_p256_addcarryx_u64(&x109, &x110, x108, x93, x105);
1295 fiat_p256_addcarryx_u64(&x111, &x112, x110, x95, (x106 + x102));
1296 fiat_p256_addcarryx_u64(&x113, &x114, x112, x97, x99);
1297 fiat_p256_addcarryx_u64(&x115, &x116, x114, (((uint64_t)x98 + x76) + (x90 + x78)), x100);
1298 fiat_p256_mulx_u64(&x117, &x118, x3, UINT64_C(0x4fffffffd));
1299 fiat_p256_mulx_u64(&x119, &x120, x3, UINT64_C(0xfffffffffffffffe));
1300 fiat_p256_mulx_u64(&x121, &x122, x3, UINT64_C(0xfffffffbffffffff));
1301 fiat_p256_mulx_u64(&x123, &x124, x3, 0x3);
1302 fiat_p256_addcarryx_u64(&x125, &x126, 0x0, x124, x121);
1303 fiat_p256_addcarryx_u64(&x127, &x128, x126, x122, x119);
1304 fiat_p256_addcarryx_u64(&x129, &x130, x128, x120, x117);
1305 fiat_p256_addcarryx_u64(&x131, &x132, 0x0, x109, x123);
1306 fiat_p256_addcarryx_u64(&x133, &x134, x132, x111, x125);
1307 fiat_p256_addcarryx_u64(&x135, &x136, x134, x113, x127);
1308 fiat_p256_addcarryx_u64(&x137, &x138, x136, x115, x129);
1309 fiat_p256_mulx_u64(&x139, &x140, x131, UINT64_C(0xffffffff00000001));
1310 fiat_p256_mulx_u64(&x141, &x142, x131, UINT32_C(0xffffffff));
1311 fiat_p256_mulx_u64(&x143, &x144, x131, UINT64_C(0xffffffffffffffff));
1312 fiat_p256_addcarryx_u64(&x145, &x146, 0x0, x144, x141);
1313 fiat_p256_addcarryx_u64(&x147, &x148, 0x0, x131, x143);
1314 fiat_p256_addcarryx_u64(&x149, &x150, x148, x133, x145);
1315 fiat_p256_addcarryx_u64(&x151, &x152, x150, x135, (x146 + x142));
1316 fiat_p256_addcarryx_u64(&x153, &x154, x152, x137, x139);
1317 fiat_p256_addcarryx_u64(&x155, &x156, x154, (((uint64_t)x138 + x116) + (x130 + x118)), x140);
1318 fiat_p256_subborrowx_u64(&x157, &x158, 0x0, x149, UINT64_C(0xffffffffffffffff));
1319 fiat_p256_subborrowx_u64(&x159, &x160, x158, x151, UINT32_C(0xffffffff));
1320 fiat_p256_subborrowx_u64(&x161, &x162, x160, x153, 0x0);
1321 fiat_p256_subborrowx_u64(&x163, &x164, x162, x155, UINT64_C(0xffffffff00000001));
1322 fiat_p256_subborrowx_u64(&x165, &x166, x164, x156, 0x0);
1323 fiat_p256_cmovznz_u64(&x167, x166, x157, x149);
1324 fiat_p256_cmovznz_u64(&x168, x166, x159, x151);
1325 fiat_p256_cmovznz_u64(&x169, x166, x161, x153);
1326 fiat_p256_cmovznz_u64(&x170, x166, x163, x155);
1327 out1[0] = x167;
1328 out1[1] = x168;
1329 out1[2] = x169;
1330 out1[3] = x170;
1331 }
1332
1333 /*
1334 * The function fiat_p256_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
1335 *
1336 * Preconditions:
1337 * 0 ≤ eval arg1 < m
1338 * Postconditions:
1339 * out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0
1340 *
1341 * Input Bounds:
1342 * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1343 * Output Bounds:
1344 * out1: [0x0 ~> 0xffffffffffffffff]
1345 */
fiat_p256_nonzero(uint64_t * out1,const uint64_t arg1[4])1346 static FIAT_P256_FIAT_INLINE void fiat_p256_nonzero(uint64_t* out1, const uint64_t arg1[4]) {
1347 uint64_t x1;
1348 x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3]))));
1349 *out1 = x1;
1350 }
1351
1352 /*
1353 * The function fiat_p256_selectznz is a multi-limb conditional select.
1354 *
1355 * Postconditions:
1356 * out1 = (if arg1 = 0 then arg2 else arg3)
1357 *
1358 * Input Bounds:
1359 * arg1: [0x0 ~> 0x1]
1360 * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1361 * arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1362 * Output Bounds:
1363 * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1364 */
fiat_p256_selectznz(uint64_t out1[4],fiat_p256_uint1 arg1,const uint64_t arg2[4],const uint64_t arg3[4])1365 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]) {
1366 uint64_t x1;
1367 uint64_t x2;
1368 uint64_t x3;
1369 uint64_t x4;
1370 fiat_p256_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]));
1371 fiat_p256_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]));
1372 fiat_p256_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]));
1373 fiat_p256_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]));
1374 out1[0] = x1;
1375 out1[1] = x2;
1376 out1[2] = x3;
1377 out1[3] = x4;
1378 }
1379
1380 /*
1381 * The function fiat_p256_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
1382 *
1383 * Preconditions:
1384 * 0 ≤ eval arg1 < m
1385 * Postconditions:
1386 * out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
1387 *
1388 * Input Bounds:
1389 * arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1390 * Output Bounds:
1391 * 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]]
1392 */
fiat_p256_to_bytes(uint8_t out1[32],const uint64_t arg1[4])1393 static FIAT_P256_FIAT_INLINE void fiat_p256_to_bytes(uint8_t out1[32], const uint64_t arg1[4]) {
1394 uint64_t x1;
1395 uint64_t x2;
1396 uint64_t x3;
1397 uint64_t x4;
1398 uint8_t x5;
1399 uint64_t x6;
1400 uint8_t x7;
1401 uint64_t x8;
1402 uint8_t x9;
1403 uint64_t x10;
1404 uint8_t x11;
1405 uint64_t x12;
1406 uint8_t x13;
1407 uint64_t x14;
1408 uint8_t x15;
1409 uint64_t x16;
1410 uint8_t x17;
1411 uint8_t x18;
1412 uint8_t x19;
1413 uint64_t x20;
1414 uint8_t x21;
1415 uint64_t x22;
1416 uint8_t x23;
1417 uint64_t x24;
1418 uint8_t x25;
1419 uint64_t x26;
1420 uint8_t x27;
1421 uint64_t x28;
1422 uint8_t x29;
1423 uint64_t x30;
1424 uint8_t x31;
1425 uint8_t x32;
1426 uint8_t x33;
1427 uint64_t x34;
1428 uint8_t x35;
1429 uint64_t x36;
1430 uint8_t x37;
1431 uint64_t x38;
1432 uint8_t x39;
1433 uint64_t x40;
1434 uint8_t x41;
1435 uint64_t x42;
1436 uint8_t x43;
1437 uint64_t x44;
1438 uint8_t x45;
1439 uint8_t x46;
1440 uint8_t x47;
1441 uint64_t x48;
1442 uint8_t x49;
1443 uint64_t x50;
1444 uint8_t x51;
1445 uint64_t x52;
1446 uint8_t x53;
1447 uint64_t x54;
1448 uint8_t x55;
1449 uint64_t x56;
1450 uint8_t x57;
1451 uint64_t x58;
1452 uint8_t x59;
1453 uint8_t x60;
1454 x1 = (arg1[3]);
1455 x2 = (arg1[2]);
1456 x3 = (arg1[1]);
1457 x4 = (arg1[0]);
1458 x5 = (uint8_t)(x4 & UINT8_C(0xff));
1459 x6 = (x4 >> 8);
1460 x7 = (uint8_t)(x6 & UINT8_C(0xff));
1461 x8 = (x6 >> 8);
1462 x9 = (uint8_t)(x8 & UINT8_C(0xff));
1463 x10 = (x8 >> 8);
1464 x11 = (uint8_t)(x10 & UINT8_C(0xff));
1465 x12 = (x10 >> 8);
1466 x13 = (uint8_t)(x12 & UINT8_C(0xff));
1467 x14 = (x12 >> 8);
1468 x15 = (uint8_t)(x14 & UINT8_C(0xff));
1469 x16 = (x14 >> 8);
1470 x17 = (uint8_t)(x16 & UINT8_C(0xff));
1471 x18 = (uint8_t)(x16 >> 8);
1472 x19 = (uint8_t)(x3 & UINT8_C(0xff));
1473 x20 = (x3 >> 8);
1474 x21 = (uint8_t)(x20 & UINT8_C(0xff));
1475 x22 = (x20 >> 8);
1476 x23 = (uint8_t)(x22 & UINT8_C(0xff));
1477 x24 = (x22 >> 8);
1478 x25 = (uint8_t)(x24 & UINT8_C(0xff));
1479 x26 = (x24 >> 8);
1480 x27 = (uint8_t)(x26 & UINT8_C(0xff));
1481 x28 = (x26 >> 8);
1482 x29 = (uint8_t)(x28 & UINT8_C(0xff));
1483 x30 = (x28 >> 8);
1484 x31 = (uint8_t)(x30 & UINT8_C(0xff));
1485 x32 = (uint8_t)(x30 >> 8);
1486 x33 = (uint8_t)(x2 & UINT8_C(0xff));
1487 x34 = (x2 >> 8);
1488 x35 = (uint8_t)(x34 & UINT8_C(0xff));
1489 x36 = (x34 >> 8);
1490 x37 = (uint8_t)(x36 & UINT8_C(0xff));
1491 x38 = (x36 >> 8);
1492 x39 = (uint8_t)(x38 & UINT8_C(0xff));
1493 x40 = (x38 >> 8);
1494 x41 = (uint8_t)(x40 & UINT8_C(0xff));
1495 x42 = (x40 >> 8);
1496 x43 = (uint8_t)(x42 & UINT8_C(0xff));
1497 x44 = (x42 >> 8);
1498 x45 = (uint8_t)(x44 & UINT8_C(0xff));
1499 x46 = (uint8_t)(x44 >> 8);
1500 x47 = (uint8_t)(x1 & UINT8_C(0xff));
1501 x48 = (x1 >> 8);
1502 x49 = (uint8_t)(x48 & UINT8_C(0xff));
1503 x50 = (x48 >> 8);
1504 x51 = (uint8_t)(x50 & UINT8_C(0xff));
1505 x52 = (x50 >> 8);
1506 x53 = (uint8_t)(x52 & UINT8_C(0xff));
1507 x54 = (x52 >> 8);
1508 x55 = (uint8_t)(x54 & UINT8_C(0xff));
1509 x56 = (x54 >> 8);
1510 x57 = (uint8_t)(x56 & UINT8_C(0xff));
1511 x58 = (x56 >> 8);
1512 x59 = (uint8_t)(x58 & UINT8_C(0xff));
1513 x60 = (uint8_t)(x58 >> 8);
1514 out1[0] = x5;
1515 out1[1] = x7;
1516 out1[2] = x9;
1517 out1[3] = x11;
1518 out1[4] = x13;
1519 out1[5] = x15;
1520 out1[6] = x17;
1521 out1[7] = x18;
1522 out1[8] = x19;
1523 out1[9] = x21;
1524 out1[10] = x23;
1525 out1[11] = x25;
1526 out1[12] = x27;
1527 out1[13] = x29;
1528 out1[14] = x31;
1529 out1[15] = x32;
1530 out1[16] = x33;
1531 out1[17] = x35;
1532 out1[18] = x37;
1533 out1[19] = x39;
1534 out1[20] = x41;
1535 out1[21] = x43;
1536 out1[22] = x45;
1537 out1[23] = x46;
1538 out1[24] = x47;
1539 out1[25] = x49;
1540 out1[26] = x51;
1541 out1[27] = x53;
1542 out1[28] = x55;
1543 out1[29] = x57;
1544 out1[30] = x59;
1545 out1[31] = x60;
1546 }
1547
1548 /*
1549 * The function fiat_p256_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
1550 *
1551 * Preconditions:
1552 * 0 ≤ bytes_eval arg1 < m
1553 * Postconditions:
1554 * eval out1 mod m = bytes_eval arg1 mod m
1555 * 0 ≤ eval out1 < m
1556 *
1557 * Input Bounds:
1558 * 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]]
1559 * Output Bounds:
1560 * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1561 */
fiat_p256_from_bytes(uint64_t out1[4],const uint8_t arg1[32])1562 static FIAT_P256_FIAT_INLINE void fiat_p256_from_bytes(uint64_t out1[4], const uint8_t arg1[32]) {
1563 uint64_t x1;
1564 uint64_t x2;
1565 uint64_t x3;
1566 uint64_t x4;
1567 uint64_t x5;
1568 uint64_t x6;
1569 uint64_t x7;
1570 uint8_t x8;
1571 uint64_t x9;
1572 uint64_t x10;
1573 uint64_t x11;
1574 uint64_t x12;
1575 uint64_t x13;
1576 uint64_t x14;
1577 uint64_t x15;
1578 uint8_t x16;
1579 uint64_t x17;
1580 uint64_t x18;
1581 uint64_t x19;
1582 uint64_t x20;
1583 uint64_t x21;
1584 uint64_t x22;
1585 uint64_t x23;
1586 uint8_t x24;
1587 uint64_t x25;
1588 uint64_t x26;
1589 uint64_t x27;
1590 uint64_t x28;
1591 uint64_t x29;
1592 uint64_t x30;
1593 uint64_t x31;
1594 uint8_t x32;
1595 uint64_t x33;
1596 uint64_t x34;
1597 uint64_t x35;
1598 uint64_t x36;
1599 uint64_t x37;
1600 uint64_t x38;
1601 uint64_t x39;
1602 uint64_t x40;
1603 uint64_t x41;
1604 uint64_t x42;
1605 uint64_t x43;
1606 uint64_t x44;
1607 uint64_t x45;
1608 uint64_t x46;
1609 uint64_t x47;
1610 uint64_t x48;
1611 uint64_t x49;
1612 uint64_t x50;
1613 uint64_t x51;
1614 uint64_t x52;
1615 uint64_t x53;
1616 uint64_t x54;
1617 uint64_t x55;
1618 uint64_t x56;
1619 uint64_t x57;
1620 uint64_t x58;
1621 uint64_t x59;
1622 uint64_t x60;
1623 x1 = ((uint64_t)(arg1[31]) << 56);
1624 x2 = ((uint64_t)(arg1[30]) << 48);
1625 x3 = ((uint64_t)(arg1[29]) << 40);
1626 x4 = ((uint64_t)(arg1[28]) << 32);
1627 x5 = ((uint64_t)(arg1[27]) << 24);
1628 x6 = ((uint64_t)(arg1[26]) << 16);
1629 x7 = ((uint64_t)(arg1[25]) << 8);
1630 x8 = (arg1[24]);
1631 x9 = ((uint64_t)(arg1[23]) << 56);
1632 x10 = ((uint64_t)(arg1[22]) << 48);
1633 x11 = ((uint64_t)(arg1[21]) << 40);
1634 x12 = ((uint64_t)(arg1[20]) << 32);
1635 x13 = ((uint64_t)(arg1[19]) << 24);
1636 x14 = ((uint64_t)(arg1[18]) << 16);
1637 x15 = ((uint64_t)(arg1[17]) << 8);
1638 x16 = (arg1[16]);
1639 x17 = ((uint64_t)(arg1[15]) << 56);
1640 x18 = ((uint64_t)(arg1[14]) << 48);
1641 x19 = ((uint64_t)(arg1[13]) << 40);
1642 x20 = ((uint64_t)(arg1[12]) << 32);
1643 x21 = ((uint64_t)(arg1[11]) << 24);
1644 x22 = ((uint64_t)(arg1[10]) << 16);
1645 x23 = ((uint64_t)(arg1[9]) << 8);
1646 x24 = (arg1[8]);
1647 x25 = ((uint64_t)(arg1[7]) << 56);
1648 x26 = ((uint64_t)(arg1[6]) << 48);
1649 x27 = ((uint64_t)(arg1[5]) << 40);
1650 x28 = ((uint64_t)(arg1[4]) << 32);
1651 x29 = ((uint64_t)(arg1[3]) << 24);
1652 x30 = ((uint64_t)(arg1[2]) << 16);
1653 x31 = ((uint64_t)(arg1[1]) << 8);
1654 x32 = (arg1[0]);
1655 x33 = (x31 + (uint64_t)x32);
1656 x34 = (x30 + x33);
1657 x35 = (x29 + x34);
1658 x36 = (x28 + x35);
1659 x37 = (x27 + x36);
1660 x38 = (x26 + x37);
1661 x39 = (x25 + x38);
1662 x40 = (x23 + (uint64_t)x24);
1663 x41 = (x22 + x40);
1664 x42 = (x21 + x41);
1665 x43 = (x20 + x42);
1666 x44 = (x19 + x43);
1667 x45 = (x18 + x44);
1668 x46 = (x17 + x45);
1669 x47 = (x15 + (uint64_t)x16);
1670 x48 = (x14 + x47);
1671 x49 = (x13 + x48);
1672 x50 = (x12 + x49);
1673 x51 = (x11 + x50);
1674 x52 = (x10 + x51);
1675 x53 = (x9 + x52);
1676 x54 = (x7 + (uint64_t)x8);
1677 x55 = (x6 + x54);
1678 x56 = (x5 + x55);
1679 x57 = (x4 + x56);
1680 x58 = (x3 + x57);
1681 x59 = (x2 + x58);
1682 x60 = (x1 + x59);
1683 out1[0] = x39;
1684 out1[1] = x46;
1685 out1[2] = x53;
1686 out1[3] = x60;
1687 }
1688
1689 /*
1690 * The function fiat_p256_set_one returns the field element one in the Montgomery domain.
1691 *
1692 * Postconditions:
1693 * eval (from_montgomery out1) mod m = 1 mod m
1694 * 0 ≤ eval out1 < m
1695 *
1696 */
fiat_p256_set_one(fiat_p256_montgomery_domain_field_element out1)1697 static FIAT_P256_FIAT_INLINE void fiat_p256_set_one(fiat_p256_montgomery_domain_field_element out1) {
1698 out1[0] = 0x1;
1699 out1[1] = UINT64_C(0xffffffff00000000);
1700 out1[2] = UINT64_C(0xffffffffffffffff);
1701 out1[3] = UINT32_C(0xfffffffe);
1702 }
1703
1704 /*
1705 * The function fiat_p256_msat returns the saturated representation of the prime modulus.
1706 *
1707 * Postconditions:
1708 * twos_complement_eval out1 = m
1709 * 0 ≤ eval out1 < m
1710 *
1711 * Output Bounds:
1712 * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1713 */
fiat_p256_msat(uint64_t out1[5])1714 static FIAT_P256_FIAT_INLINE void fiat_p256_msat(uint64_t out1[5]) {
1715 out1[0] = UINT64_C(0xffffffffffffffff);
1716 out1[1] = UINT32_C(0xffffffff);
1717 out1[2] = 0x0;
1718 out1[3] = UINT64_C(0xffffffff00000001);
1719 out1[4] = 0x0;
1720 }
1721
1722 /*
1723 * The function fiat_p256_divstep computes a divstep.
1724 *
1725 * Preconditions:
1726 * 0 ≤ eval arg4 < m
1727 * 0 ≤ eval arg5 < m
1728 * Postconditions:
1729 * out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1)
1730 * twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2)
1731 * 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⌋)
1732 * 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)
1733 * 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)
1734 * 0 ≤ eval out5 < m
1735 * 0 ≤ eval out5 < m
1736 * 0 ≤ eval out2 < m
1737 * 0 ≤ eval out3 < m
1738 *
1739 * Input Bounds:
1740 * arg1: [0x0 ~> 0xffffffffffffffff]
1741 * arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1742 * arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1743 * arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1744 * arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1745 * Output Bounds:
1746 * out1: [0x0 ~> 0xffffffffffffffff]
1747 * out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1748 * out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1749 * out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1750 * out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1751 */
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])1752 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]) {
1753 uint64_t x1;
1754 fiat_p256_uint1 x2;
1755 fiat_p256_uint1 x3;
1756 uint64_t x4;
1757 fiat_p256_uint1 x5;
1758 uint64_t x6;
1759 uint64_t x7;
1760 uint64_t x8;
1761 uint64_t x9;
1762 uint64_t x10;
1763 uint64_t x11;
1764 uint64_t x12;
1765 fiat_p256_uint1 x13;
1766 uint64_t x14;
1767 fiat_p256_uint1 x15;
1768 uint64_t x16;
1769 fiat_p256_uint1 x17;
1770 uint64_t x18;
1771 fiat_p256_uint1 x19;
1772 uint64_t x20;
1773 fiat_p256_uint1 x21;
1774 uint64_t x22;
1775 uint64_t x23;
1776 uint64_t x24;
1777 uint64_t x25;
1778 uint64_t x26;
1779 uint64_t x27;
1780 uint64_t x28;
1781 uint64_t x29;
1782 uint64_t x30;
1783 uint64_t x31;
1784 fiat_p256_uint1 x32;
1785 uint64_t x33;
1786 fiat_p256_uint1 x34;
1787 uint64_t x35;
1788 fiat_p256_uint1 x36;
1789 uint64_t x37;
1790 fiat_p256_uint1 x38;
1791 uint64_t x39;
1792 fiat_p256_uint1 x40;
1793 uint64_t x41;
1794 fiat_p256_uint1 x42;
1795 uint64_t x43;
1796 fiat_p256_uint1 x44;
1797 uint64_t x45;
1798 fiat_p256_uint1 x46;
1799 uint64_t x47;
1800 fiat_p256_uint1 x48;
1801 uint64_t x49;
1802 uint64_t x50;
1803 uint64_t x51;
1804 uint64_t x52;
1805 uint64_t x53;
1806 fiat_p256_uint1 x54;
1807 uint64_t x55;
1808 fiat_p256_uint1 x56;
1809 uint64_t x57;
1810 fiat_p256_uint1 x58;
1811 uint64_t x59;
1812 fiat_p256_uint1 x60;
1813 uint64_t x61;
1814 uint64_t x62;
1815 fiat_p256_uint1 x63;
1816 uint64_t x64;
1817 fiat_p256_uint1 x65;
1818 uint64_t x66;
1819 fiat_p256_uint1 x67;
1820 uint64_t x68;
1821 fiat_p256_uint1 x69;
1822 uint64_t x70;
1823 uint64_t x71;
1824 uint64_t x72;
1825 uint64_t x73;
1826 fiat_p256_uint1 x74;
1827 uint64_t x75;
1828 uint64_t x76;
1829 uint64_t x77;
1830 uint64_t x78;
1831 uint64_t x79;
1832 uint64_t x80;
1833 fiat_p256_uint1 x81;
1834 uint64_t x82;
1835 fiat_p256_uint1 x83;
1836 uint64_t x84;
1837 fiat_p256_uint1 x85;
1838 uint64_t x86;
1839 fiat_p256_uint1 x87;
1840 uint64_t x88;
1841 fiat_p256_uint1 x89;
1842 uint64_t x90;
1843 uint64_t x91;
1844 uint64_t x92;
1845 uint64_t x93;
1846 uint64_t x94;
1847 fiat_p256_uint1 x95;
1848 uint64_t x96;
1849 fiat_p256_uint1 x97;
1850 uint64_t x98;
1851 fiat_p256_uint1 x99;
1852 uint64_t x100;
1853 fiat_p256_uint1 x101;
1854 uint64_t x102;
1855 fiat_p256_uint1 x103;
1856 uint64_t x104;
1857 fiat_p256_uint1 x105;
1858 uint64_t x106;
1859 fiat_p256_uint1 x107;
1860 uint64_t x108;
1861 fiat_p256_uint1 x109;
1862 uint64_t x110;
1863 fiat_p256_uint1 x111;
1864 uint64_t x112;
1865 fiat_p256_uint1 x113;
1866 uint64_t x114;
1867 uint64_t x115;
1868 uint64_t x116;
1869 uint64_t x117;
1870 uint64_t x118;
1871 uint64_t x119;
1872 uint64_t x120;
1873 uint64_t x121;
1874 uint64_t x122;
1875 uint64_t x123;
1876 uint64_t x124;
1877 uint64_t x125;
1878 uint64_t x126;
1879 fiat_p256_addcarryx_u64(&x1, &x2, 0x0, (~arg1), 0x1);
1880 x3 = (fiat_p256_uint1)((fiat_p256_uint1)(x1 >> 63) & (fiat_p256_uint1)((arg3[0]) & 0x1));
1881 fiat_p256_addcarryx_u64(&x4, &x5, 0x0, (~arg1), 0x1);
1882 fiat_p256_cmovznz_u64(&x6, x3, arg1, x4);
1883 fiat_p256_cmovznz_u64(&x7, x3, (arg2[0]), (arg3[0]));
1884 fiat_p256_cmovznz_u64(&x8, x3, (arg2[1]), (arg3[1]));
1885 fiat_p256_cmovznz_u64(&x9, x3, (arg2[2]), (arg3[2]));
1886 fiat_p256_cmovznz_u64(&x10, x3, (arg2[3]), (arg3[3]));
1887 fiat_p256_cmovznz_u64(&x11, x3, (arg2[4]), (arg3[4]));
1888 fiat_p256_addcarryx_u64(&x12, &x13, 0x0, 0x1, (~(arg2[0])));
1889 fiat_p256_addcarryx_u64(&x14, &x15, x13, 0x0, (~(arg2[1])));
1890 fiat_p256_addcarryx_u64(&x16, &x17, x15, 0x0, (~(arg2[2])));
1891 fiat_p256_addcarryx_u64(&x18, &x19, x17, 0x0, (~(arg2[3])));
1892 fiat_p256_addcarryx_u64(&x20, &x21, x19, 0x0, (~(arg2[4])));
1893 fiat_p256_cmovznz_u64(&x22, x3, (arg3[0]), x12);
1894 fiat_p256_cmovznz_u64(&x23, x3, (arg3[1]), x14);
1895 fiat_p256_cmovznz_u64(&x24, x3, (arg3[2]), x16);
1896 fiat_p256_cmovznz_u64(&x25, x3, (arg3[3]), x18);
1897 fiat_p256_cmovznz_u64(&x26, x3, (arg3[4]), x20);
1898 fiat_p256_cmovznz_u64(&x27, x3, (arg4[0]), (arg5[0]));
1899 fiat_p256_cmovznz_u64(&x28, x3, (arg4[1]), (arg5[1]));
1900 fiat_p256_cmovznz_u64(&x29, x3, (arg4[2]), (arg5[2]));
1901 fiat_p256_cmovznz_u64(&x30, x3, (arg4[3]), (arg5[3]));
1902 fiat_p256_addcarryx_u64(&x31, &x32, 0x0, x27, x27);
1903 fiat_p256_addcarryx_u64(&x33, &x34, x32, x28, x28);
1904 fiat_p256_addcarryx_u64(&x35, &x36, x34, x29, x29);
1905 fiat_p256_addcarryx_u64(&x37, &x38, x36, x30, x30);
1906 fiat_p256_subborrowx_u64(&x39, &x40, 0x0, x31, UINT64_C(0xffffffffffffffff));
1907 fiat_p256_subborrowx_u64(&x41, &x42, x40, x33, UINT32_C(0xffffffff));
1908 fiat_p256_subborrowx_u64(&x43, &x44, x42, x35, 0x0);
1909 fiat_p256_subborrowx_u64(&x45, &x46, x44, x37, UINT64_C(0xffffffff00000001));
1910 fiat_p256_subborrowx_u64(&x47, &x48, x46, x38, 0x0);
1911 x49 = (arg4[3]);
1912 x50 = (arg4[2]);
1913 x51 = (arg4[1]);
1914 x52 = (arg4[0]);
1915 fiat_p256_subborrowx_u64(&x53, &x54, 0x0, 0x0, x52);
1916 fiat_p256_subborrowx_u64(&x55, &x56, x54, 0x0, x51);
1917 fiat_p256_subborrowx_u64(&x57, &x58, x56, 0x0, x50);
1918 fiat_p256_subborrowx_u64(&x59, &x60, x58, 0x0, x49);
1919 fiat_p256_cmovznz_u64(&x61, x60, 0x0, UINT64_C(0xffffffffffffffff));
1920 fiat_p256_addcarryx_u64(&x62, &x63, 0x0, x53, x61);
1921 fiat_p256_addcarryx_u64(&x64, &x65, x63, x55, (x61 & UINT32_C(0xffffffff)));
1922 fiat_p256_addcarryx_u64(&x66, &x67, x65, x57, 0x0);
1923 fiat_p256_addcarryx_u64(&x68, &x69, x67, x59, (x61 & UINT64_C(0xffffffff00000001)));
1924 fiat_p256_cmovznz_u64(&x70, x3, (arg5[0]), x62);
1925 fiat_p256_cmovznz_u64(&x71, x3, (arg5[1]), x64);
1926 fiat_p256_cmovznz_u64(&x72, x3, (arg5[2]), x66);
1927 fiat_p256_cmovznz_u64(&x73, x3, (arg5[3]), x68);
1928 x74 = (fiat_p256_uint1)(x22 & 0x1);
1929 fiat_p256_cmovznz_u64(&x75, x74, 0x0, x7);
1930 fiat_p256_cmovznz_u64(&x76, x74, 0x0, x8);
1931 fiat_p256_cmovznz_u64(&x77, x74, 0x0, x9);
1932 fiat_p256_cmovznz_u64(&x78, x74, 0x0, x10);
1933 fiat_p256_cmovznz_u64(&x79, x74, 0x0, x11);
1934 fiat_p256_addcarryx_u64(&x80, &x81, 0x0, x22, x75);
1935 fiat_p256_addcarryx_u64(&x82, &x83, x81, x23, x76);
1936 fiat_p256_addcarryx_u64(&x84, &x85, x83, x24, x77);
1937 fiat_p256_addcarryx_u64(&x86, &x87, x85, x25, x78);
1938 fiat_p256_addcarryx_u64(&x88, &x89, x87, x26, x79);
1939 fiat_p256_cmovznz_u64(&x90, x74, 0x0, x27);
1940 fiat_p256_cmovznz_u64(&x91, x74, 0x0, x28);
1941 fiat_p256_cmovznz_u64(&x92, x74, 0x0, x29);
1942 fiat_p256_cmovznz_u64(&x93, x74, 0x0, x30);
1943 fiat_p256_addcarryx_u64(&x94, &x95, 0x0, x70, x90);
1944 fiat_p256_addcarryx_u64(&x96, &x97, x95, x71, x91);
1945 fiat_p256_addcarryx_u64(&x98, &x99, x97, x72, x92);
1946 fiat_p256_addcarryx_u64(&x100, &x101, x99, x73, x93);
1947 fiat_p256_subborrowx_u64(&x102, &x103, 0x0, x94, UINT64_C(0xffffffffffffffff));
1948 fiat_p256_subborrowx_u64(&x104, &x105, x103, x96, UINT32_C(0xffffffff));
1949 fiat_p256_subborrowx_u64(&x106, &x107, x105, x98, 0x0);
1950 fiat_p256_subborrowx_u64(&x108, &x109, x107, x100, UINT64_C(0xffffffff00000001));
1951 fiat_p256_subborrowx_u64(&x110, &x111, x109, x101, 0x0);
1952 fiat_p256_addcarryx_u64(&x112, &x113, 0x0, x6, 0x1);
1953 x114 = ((x80 >> 1) | ((x82 << 63) & UINT64_C(0xffffffffffffffff)));
1954 x115 = ((x82 >> 1) | ((x84 << 63) & UINT64_C(0xffffffffffffffff)));
1955 x116 = ((x84 >> 1) | ((x86 << 63) & UINT64_C(0xffffffffffffffff)));
1956 x117 = ((x86 >> 1) | ((x88 << 63) & UINT64_C(0xffffffffffffffff)));
1957 x118 = ((x88 & UINT64_C(0x8000000000000000)) | (x88 >> 1));
1958 fiat_p256_cmovznz_u64(&x119, x48, x39, x31);
1959 fiat_p256_cmovznz_u64(&x120, x48, x41, x33);
1960 fiat_p256_cmovznz_u64(&x121, x48, x43, x35);
1961 fiat_p256_cmovznz_u64(&x122, x48, x45, x37);
1962 fiat_p256_cmovznz_u64(&x123, x111, x102, x94);
1963 fiat_p256_cmovznz_u64(&x124, x111, x104, x96);
1964 fiat_p256_cmovznz_u64(&x125, x111, x106, x98);
1965 fiat_p256_cmovznz_u64(&x126, x111, x108, x100);
1966 *out1 = x112;
1967 out2[0] = x7;
1968 out2[1] = x8;
1969 out2[2] = x9;
1970 out2[3] = x10;
1971 out2[4] = x11;
1972 out3[0] = x114;
1973 out3[1] = x115;
1974 out3[2] = x116;
1975 out3[3] = x117;
1976 out3[4] = x118;
1977 out4[0] = x119;
1978 out4[1] = x120;
1979 out4[2] = x121;
1980 out4[3] = x122;
1981 out5[0] = x123;
1982 out5[1] = x124;
1983 out5[2] = x125;
1984 out5[3] = x126;
1985 }
1986
1987 /*
1988 * The function fiat_p256_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).
1989 *
1990 * Postconditions:
1991 * 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⌋)
1992 * 0 ≤ eval out1 < m
1993 *
1994 * Output Bounds:
1995 * out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
1996 */
fiat_p256_divstep_precomp(uint64_t out1[4])1997 static FIAT_P256_FIAT_INLINE void fiat_p256_divstep_precomp(uint64_t out1[4]) {
1998 out1[0] = UINT64_C(0x67ffffffb8000000);
1999 out1[1] = UINT64_C(0xc000000038000000);
2000 out1[2] = UINT64_C(0xd80000007fffffff);
2001 out1[3] = UINT64_C(0x2fffffffffffffff);
2002 }
2003