• Home
  • Line#
  • Scopes#
  • Navigate#
  • Raw
  • Download
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