Bitcoin Core  29.1.0
P2P Digital Currency
field_10x26_impl.h
Go to the documentation of this file.
1 /***********************************************************************
2  * Copyright (c) 2013, 2014 Pieter Wuille *
3  * Distributed under the MIT software license, see the accompanying *
4  * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
5  ***********************************************************************/
6 
7 #ifndef SECP256K1_FIELD_REPR_IMPL_H
8 #define SECP256K1_FIELD_REPR_IMPL_H
9 
10 #include "checkmem.h"
11 #include "util.h"
12 #include "field.h"
13 #include "modinv32_impl.h"
14 
15 #ifdef VERIFY
16 static void secp256k1_fe_impl_verify(const secp256k1_fe *a) {
17  const uint32_t *d = a->n;
18  int m = a->normalized ? 1 : 2 * a->magnitude;
19  VERIFY_CHECK(d[0] <= 0x3FFFFFFUL * m);
20  VERIFY_CHECK(d[1] <= 0x3FFFFFFUL * m);
21  VERIFY_CHECK(d[2] <= 0x3FFFFFFUL * m);
22  VERIFY_CHECK(d[3] <= 0x3FFFFFFUL * m);
23  VERIFY_CHECK(d[4] <= 0x3FFFFFFUL * m);
24  VERIFY_CHECK(d[5] <= 0x3FFFFFFUL * m);
25  VERIFY_CHECK(d[6] <= 0x3FFFFFFUL * m);
26  VERIFY_CHECK(d[7] <= 0x3FFFFFFUL * m);
27  VERIFY_CHECK(d[8] <= 0x3FFFFFFUL * m);
28  VERIFY_CHECK(d[9] <= 0x03FFFFFUL * m);
29  if (a->normalized) {
30  if (d[9] == 0x03FFFFFUL) {
31  uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
32  if (mid == 0x3FFFFFFUL) {
33  VERIFY_CHECK((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
34  }
35  }
36  }
37 }
38 #endif
39 
40 static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m) {
41  r->n[0] = 0x3FFFFFFUL * 2 * m;
42  r->n[1] = 0x3FFFFFFUL * 2 * m;
43  r->n[2] = 0x3FFFFFFUL * 2 * m;
44  r->n[3] = 0x3FFFFFFUL * 2 * m;
45  r->n[4] = 0x3FFFFFFUL * 2 * m;
46  r->n[5] = 0x3FFFFFFUL * 2 * m;
47  r->n[6] = 0x3FFFFFFUL * 2 * m;
48  r->n[7] = 0x3FFFFFFUL * 2 * m;
49  r->n[8] = 0x3FFFFFFUL * 2 * m;
50  r->n[9] = 0x03FFFFFUL * 2 * m;
51 }
52 
53 static void secp256k1_fe_impl_normalize(secp256k1_fe *r) {
54  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
55  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
56 
57  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
58  uint32_t m;
59  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
60 
61  /* The first pass ensures the magnitude is 1, ... */
62  t0 += x * 0x3D1UL; t1 += (x << 6);
63  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
64  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
65  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
66  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
67  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
68  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
69  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
70  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
71  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
72 
73  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
74  VERIFY_CHECK(t9 >> 23 == 0);
75 
76  /* At most a single final reduction is needed; check if the value is >= the field characteristic */
77  x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
78  & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
79 
80  /* Apply the final reduction (for constant-time behaviour, we do it always) */
81  t0 += x * 0x3D1UL; t1 += (x << 6);
82  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
83  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
84  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
85  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
86  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
87  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
88  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
89  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
90  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
91 
92  /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
93  VERIFY_CHECK(t9 >> 22 == x);
94 
95  /* Mask off the possible multiple of 2^256 from the final reduction */
96  t9 &= 0x03FFFFFUL;
97 
98  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
99  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
100 }
101 
102 static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r) {
103  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
104  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
105 
106  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
107  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
108 
109  /* The first pass ensures the magnitude is 1, ... */
110  t0 += x * 0x3D1UL; t1 += (x << 6);
111  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
112  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
113  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
114  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
115  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
116  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
117  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
118  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
119  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
120 
121  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
122  VERIFY_CHECK(t9 >> 23 == 0);
123 
124  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
125  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
126 }
127 
128 static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r) {
129  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
130  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
131 
132  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
133  uint32_t m;
134  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
135 
136  /* The first pass ensures the magnitude is 1, ... */
137  t0 += x * 0x3D1UL; t1 += (x << 6);
138  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
139  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
140  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
141  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
142  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
143  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
144  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
145  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
146  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
147 
148  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
149  VERIFY_CHECK(t9 >> 23 == 0);
150 
151  /* At most a single final reduction is needed; check if the value is >= the field characteristic */
152  x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
153  & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
154 
155  if (x) {
156  t0 += 0x3D1UL; t1 += (x << 6);
157  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
158  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
159  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
160  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
161  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
162  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
163  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
164  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
165  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
166 
167  /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
168  VERIFY_CHECK(t9 >> 22 == x);
169 
170  /* Mask off the possible multiple of 2^256 from the final reduction */
171  t9 &= 0x03FFFFFUL;
172  }
173 
174  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
175  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
176 }
177 
178 static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r) {
179  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
180  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
181 
182  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
183  uint32_t z0, z1;
184 
185  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
186  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
187 
188  /* The first pass ensures the magnitude is 1, ... */
189  t0 += x * 0x3D1UL; t1 += (x << 6);
190  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL;
191  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
192  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
193  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
194  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
195  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
196  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
197  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
198  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
199  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
200 
201  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
202  VERIFY_CHECK(t9 >> 23 == 0);
203 
204  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
205 }
206 
207 static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r) {
208  uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
209  uint32_t z0, z1;
210  uint32_t x;
211 
212  t0 = r->n[0];
213  t9 = r->n[9];
214 
215  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
216  x = t9 >> 22;
217 
218  /* The first pass ensures the magnitude is 1, ... */
219  t0 += x * 0x3D1UL;
220 
221  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
222  z0 = t0 & 0x3FFFFFFUL;
223  z1 = z0 ^ 0x3D0UL;
224 
225  /* Fast return path should catch the majority of cases */
226  if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) {
227  return 0;
228  }
229 
230  t1 = r->n[1];
231  t2 = r->n[2];
232  t3 = r->n[3];
233  t4 = r->n[4];
234  t5 = r->n[5];
235  t6 = r->n[6];
236  t7 = r->n[7];
237  t8 = r->n[8];
238 
239  t9 &= 0x03FFFFFUL;
240  t1 += (x << 6);
241 
242  t1 += (t0 >> 26);
243  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
244  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
245  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
246  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
247  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
248  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
249  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
250  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
251  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
252 
253  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
254  VERIFY_CHECK(t9 >> 23 == 0);
255 
256  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
257 }
258 
259 SECP256K1_INLINE static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a) {
260  r->n[0] = a;
261  r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
262 }
263 
264 SECP256K1_INLINE static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a) {
265  const uint32_t *t = a->n;
266  return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
267 }
268 
269 SECP256K1_INLINE static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a) {
270  return a->n[0] & 1;
271 }
272 
273 static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
274  int i;
275  for (i = 9; i >= 0; i--) {
276  if (a->n[i] > b->n[i]) {
277  return 1;
278  }
279  if (a->n[i] < b->n[i]) {
280  return -1;
281  }
282  }
283  return 0;
284 }
285 
286 static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
287  r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
288  r->n[1] = (uint32_t)((a[28] >> 2) & 0x3f) | ((uint32_t)a[27] << 6) | ((uint32_t)a[26] << 14) | ((uint32_t)(a[25] & 0xf) << 22);
289  r->n[2] = (uint32_t)((a[25] >> 4) & 0xf) | ((uint32_t)a[24] << 4) | ((uint32_t)a[23] << 12) | ((uint32_t)(a[22] & 0x3f) << 20);
290  r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18);
291  r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24);
292  r->n[5] = (uint32_t)((a[15] >> 2) & 0x3f) | ((uint32_t)a[14] << 6) | ((uint32_t)a[13] << 14) | ((uint32_t)(a[12] & 0xf) << 22);
293  r->n[6] = (uint32_t)((a[12] >> 4) & 0xf) | ((uint32_t)a[11] << 4) | ((uint32_t)a[10] << 12) | ((uint32_t)(a[9] & 0x3f) << 20);
294  r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
295  r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
296  r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
297 }
298 
299 static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
300  secp256k1_fe_impl_set_b32_mod(r, a);
301  return !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
302 }
303 
305 static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a) {
306  r[0] = (a->n[9] >> 14) & 0xff;
307  r[1] = (a->n[9] >> 6) & 0xff;
308  r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3);
309  r[3] = (a->n[8] >> 16) & 0xff;
310  r[4] = (a->n[8] >> 8) & 0xff;
311  r[5] = a->n[8] & 0xff;
312  r[6] = (a->n[7] >> 18) & 0xff;
313  r[7] = (a->n[7] >> 10) & 0xff;
314  r[8] = (a->n[7] >> 2) & 0xff;
315  r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f);
316  r[10] = (a->n[6] >> 12) & 0xff;
317  r[11] = (a->n[6] >> 4) & 0xff;
318  r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf);
319  r[13] = (a->n[5] >> 14) & 0xff;
320  r[14] = (a->n[5] >> 6) & 0xff;
321  r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3);
322  r[16] = (a->n[4] >> 16) & 0xff;
323  r[17] = (a->n[4] >> 8) & 0xff;
324  r[18] = a->n[4] & 0xff;
325  r[19] = (a->n[3] >> 18) & 0xff;
326  r[20] = (a->n[3] >> 10) & 0xff;
327  r[21] = (a->n[3] >> 2) & 0xff;
328  r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f);
329  r[23] = (a->n[2] >> 12) & 0xff;
330  r[24] = (a->n[2] >> 4) & 0xff;
331  r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf);
332  r[26] = (a->n[1] >> 14) & 0xff;
333  r[27] = (a->n[1] >> 6) & 0xff;
334  r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3);
335  r[29] = (a->n[0] >> 16) & 0xff;
336  r[30] = (a->n[0] >> 8) & 0xff;
337  r[31] = a->n[0] & 0xff;
338 }
339 
340 SECP256K1_INLINE static void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m) {
341  /* For all legal values of m (0..31), the following properties hold: */
342  VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
343  VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
344  VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
345  VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m);
346 
347  /* Due to the properties above, the left hand in the subtractions below is never less than
348  * the right hand. */
349  r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
350  r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
351  r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
352  r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
353  r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
354  r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
355  r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
356  r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
357  r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
358  r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
359 }
360 
361 SECP256K1_INLINE static void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a) {
362  r->n[0] *= a;
363  r->n[1] *= a;
364  r->n[2] *= a;
365  r->n[3] *= a;
366  r->n[4] *= a;
367  r->n[5] *= a;
368  r->n[6] *= a;
369  r->n[7] *= a;
370  r->n[8] *= a;
371  r->n[9] *= a;
372 }
373 
374 SECP256K1_INLINE static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a) {
375  r->n[0] += a->n[0];
376  r->n[1] += a->n[1];
377  r->n[2] += a->n[2];
378  r->n[3] += a->n[3];
379  r->n[4] += a->n[4];
380  r->n[5] += a->n[5];
381  r->n[6] += a->n[6];
382  r->n[7] += a->n[7];
383  r->n[8] += a->n[8];
384  r->n[9] += a->n[9];
385 }
386 
387 SECP256K1_INLINE static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a) {
388  r->n[0] += a;
389 }
390 
391 #if defined(USE_EXTERNAL_ASM)
392 
393 /* External assembler implementation */
394 void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
395 void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
396 
397 #else
398 
399 #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
400 
401 SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
402  uint64_t c, d;
403  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
404  uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
405  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
406 
407  VERIFY_BITS(a[0], 30);
408  VERIFY_BITS(a[1], 30);
409  VERIFY_BITS(a[2], 30);
410  VERIFY_BITS(a[3], 30);
411  VERIFY_BITS(a[4], 30);
412  VERIFY_BITS(a[5], 30);
413  VERIFY_BITS(a[6], 30);
414  VERIFY_BITS(a[7], 30);
415  VERIFY_BITS(a[8], 30);
416  VERIFY_BITS(a[9], 26);
417  VERIFY_BITS(b[0], 30);
418  VERIFY_BITS(b[1], 30);
419  VERIFY_BITS(b[2], 30);
420  VERIFY_BITS(b[3], 30);
421  VERIFY_BITS(b[4], 30);
422  VERIFY_BITS(b[5], 30);
423  VERIFY_BITS(b[6], 30);
424  VERIFY_BITS(b[7], 30);
425  VERIFY_BITS(b[8], 30);
426  VERIFY_BITS(b[9], 26);
427 
434  d = (uint64_t)a[0] * b[9]
435  + (uint64_t)a[1] * b[8]
436  + (uint64_t)a[2] * b[7]
437  + (uint64_t)a[3] * b[6]
438  + (uint64_t)a[4] * b[5]
439  + (uint64_t)a[5] * b[4]
440  + (uint64_t)a[6] * b[3]
441  + (uint64_t)a[7] * b[2]
442  + (uint64_t)a[8] * b[1]
443  + (uint64_t)a[9] * b[0];
444  /* VERIFY_BITS(d, 64); */
445  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
446  t9 = d & M; d >>= 26;
447  VERIFY_BITS(t9, 26);
448  VERIFY_BITS(d, 38);
449  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
450 
451  c = (uint64_t)a[0] * b[0];
452  VERIFY_BITS(c, 60);
453  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
454  d += (uint64_t)a[1] * b[9]
455  + (uint64_t)a[2] * b[8]
456  + (uint64_t)a[3] * b[7]
457  + (uint64_t)a[4] * b[6]
458  + (uint64_t)a[5] * b[5]
459  + (uint64_t)a[6] * b[4]
460  + (uint64_t)a[7] * b[3]
461  + (uint64_t)a[8] * b[2]
462  + (uint64_t)a[9] * b[1];
463  VERIFY_BITS(d, 63);
464  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
465  u0 = d & M; d >>= 26; c += u0 * R0;
466  VERIFY_BITS(u0, 26);
467  VERIFY_BITS(d, 37);
468  VERIFY_BITS(c, 61);
469  /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
470  t0 = c & M; c >>= 26; c += u0 * R1;
471  VERIFY_BITS(t0, 26);
472  VERIFY_BITS(c, 37);
473  /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
474  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
475 
476  c += (uint64_t)a[0] * b[1]
477  + (uint64_t)a[1] * b[0];
478  VERIFY_BITS(c, 62);
479  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
480  d += (uint64_t)a[2] * b[9]
481  + (uint64_t)a[3] * b[8]
482  + (uint64_t)a[4] * b[7]
483  + (uint64_t)a[5] * b[6]
484  + (uint64_t)a[6] * b[5]
485  + (uint64_t)a[7] * b[4]
486  + (uint64_t)a[8] * b[3]
487  + (uint64_t)a[9] * b[2];
488  VERIFY_BITS(d, 63);
489  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
490  u1 = d & M; d >>= 26; c += u1 * R0;
491  VERIFY_BITS(u1, 26);
492  VERIFY_BITS(d, 37);
493  VERIFY_BITS(c, 63);
494  /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
495  t1 = c & M; c >>= 26; c += u1 * R1;
496  VERIFY_BITS(t1, 26);
497  VERIFY_BITS(c, 38);
498  /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
499  /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
500 
501  c += (uint64_t)a[0] * b[2]
502  + (uint64_t)a[1] * b[1]
503  + (uint64_t)a[2] * b[0];
504  VERIFY_BITS(c, 62);
505  /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
506  d += (uint64_t)a[3] * b[9]
507  + (uint64_t)a[4] * b[8]
508  + (uint64_t)a[5] * b[7]
509  + (uint64_t)a[6] * b[6]
510  + (uint64_t)a[7] * b[5]
511  + (uint64_t)a[8] * b[4]
512  + (uint64_t)a[9] * b[3];
513  VERIFY_BITS(d, 63);
514  /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
515  u2 = d & M; d >>= 26; c += u2 * R0;
516  VERIFY_BITS(u2, 26);
517  VERIFY_BITS(d, 37);
518  VERIFY_BITS(c, 63);
519  /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
520  t2 = c & M; c >>= 26; c += u2 * R1;
521  VERIFY_BITS(t2, 26);
522  VERIFY_BITS(c, 38);
523  /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
524  /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
525 
526  c += (uint64_t)a[0] * b[3]
527  + (uint64_t)a[1] * b[2]
528  + (uint64_t)a[2] * b[1]
529  + (uint64_t)a[3] * b[0];
530  VERIFY_BITS(c, 63);
531  /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
532  d += (uint64_t)a[4] * b[9]
533  + (uint64_t)a[5] * b[8]
534  + (uint64_t)a[6] * b[7]
535  + (uint64_t)a[7] * b[6]
536  + (uint64_t)a[8] * b[5]
537  + (uint64_t)a[9] * b[4];
538  VERIFY_BITS(d, 63);
539  /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
540  u3 = d & M; d >>= 26; c += u3 * R0;
541  VERIFY_BITS(u3, 26);
542  VERIFY_BITS(d, 37);
543  /* VERIFY_BITS(c, 64); */
544  /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
545  t3 = c & M; c >>= 26; c += u3 * R1;
546  VERIFY_BITS(t3, 26);
547  VERIFY_BITS(c, 39);
548  /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
549  /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
550 
551  c += (uint64_t)a[0] * b[4]
552  + (uint64_t)a[1] * b[3]
553  + (uint64_t)a[2] * b[2]
554  + (uint64_t)a[3] * b[1]
555  + (uint64_t)a[4] * b[0];
556  VERIFY_BITS(c, 63);
557  /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
558  d += (uint64_t)a[5] * b[9]
559  + (uint64_t)a[6] * b[8]
560  + (uint64_t)a[7] * b[7]
561  + (uint64_t)a[8] * b[6]
562  + (uint64_t)a[9] * b[5];
563  VERIFY_BITS(d, 62);
564  /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
565  u4 = d & M; d >>= 26; c += u4 * R0;
566  VERIFY_BITS(u4, 26);
567  VERIFY_BITS(d, 36);
568  /* VERIFY_BITS(c, 64); */
569  /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
570  t4 = c & M; c >>= 26; c += u4 * R1;
571  VERIFY_BITS(t4, 26);
572  VERIFY_BITS(c, 39);
573  /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
574  /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
575 
576  c += (uint64_t)a[0] * b[5]
577  + (uint64_t)a[1] * b[4]
578  + (uint64_t)a[2] * b[3]
579  + (uint64_t)a[3] * b[2]
580  + (uint64_t)a[4] * b[1]
581  + (uint64_t)a[5] * b[0];
582  VERIFY_BITS(c, 63);
583  /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
584  d += (uint64_t)a[6] * b[9]
585  + (uint64_t)a[7] * b[8]
586  + (uint64_t)a[8] * b[7]
587  + (uint64_t)a[9] * b[6];
588  VERIFY_BITS(d, 62);
589  /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
590  u5 = d & M; d >>= 26; c += u5 * R0;
591  VERIFY_BITS(u5, 26);
592  VERIFY_BITS(d, 36);
593  /* VERIFY_BITS(c, 64); */
594  /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
595  t5 = c & M; c >>= 26; c += u5 * R1;
596  VERIFY_BITS(t5, 26);
597  VERIFY_BITS(c, 39);
598  /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
599  /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
600 
601  c += (uint64_t)a[0] * b[6]
602  + (uint64_t)a[1] * b[5]
603  + (uint64_t)a[2] * b[4]
604  + (uint64_t)a[3] * b[3]
605  + (uint64_t)a[4] * b[2]
606  + (uint64_t)a[5] * b[1]
607  + (uint64_t)a[6] * b[0];
608  VERIFY_BITS(c, 63);
609  /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
610  d += (uint64_t)a[7] * b[9]
611  + (uint64_t)a[8] * b[8]
612  + (uint64_t)a[9] * b[7];
613  VERIFY_BITS(d, 61);
614  /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
615  u6 = d & M; d >>= 26; c += u6 * R0;
616  VERIFY_BITS(u6, 26);
617  VERIFY_BITS(d, 35);
618  /* VERIFY_BITS(c, 64); */
619  /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
620  t6 = c & M; c >>= 26; c += u6 * R1;
621  VERIFY_BITS(t6, 26);
622  VERIFY_BITS(c, 39);
623  /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
624  /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
625 
626  c += (uint64_t)a[0] * b[7]
627  + (uint64_t)a[1] * b[6]
628  + (uint64_t)a[2] * b[5]
629  + (uint64_t)a[3] * b[4]
630  + (uint64_t)a[4] * b[3]
631  + (uint64_t)a[5] * b[2]
632  + (uint64_t)a[6] * b[1]
633  + (uint64_t)a[7] * b[0];
634  /* VERIFY_BITS(c, 64); */
635  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
636  /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
637  d += (uint64_t)a[8] * b[9]
638  + (uint64_t)a[9] * b[8];
639  VERIFY_BITS(d, 58);
640  /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
641  u7 = d & M; d >>= 26; c += u7 * R0;
642  VERIFY_BITS(u7, 26);
643  VERIFY_BITS(d, 32);
644  /* VERIFY_BITS(c, 64); */
645  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
646  /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
647  t7 = c & M; c >>= 26; c += u7 * R1;
648  VERIFY_BITS(t7, 26);
649  VERIFY_BITS(c, 38);
650  /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
651  /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
652 
653  c += (uint64_t)a[0] * b[8]
654  + (uint64_t)a[1] * b[7]
655  + (uint64_t)a[2] * b[6]
656  + (uint64_t)a[3] * b[5]
657  + (uint64_t)a[4] * b[4]
658  + (uint64_t)a[5] * b[3]
659  + (uint64_t)a[6] * b[2]
660  + (uint64_t)a[7] * b[1]
661  + (uint64_t)a[8] * b[0];
662  /* VERIFY_BITS(c, 64); */
663  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
664  /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
665  d += (uint64_t)a[9] * b[9];
666  VERIFY_BITS(d, 57);
667  /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
668  u8 = d & M; d >>= 26; c += u8 * R0;
669  VERIFY_BITS(u8, 26);
670  VERIFY_BITS(d, 31);
671  /* VERIFY_BITS(c, 64); */
672  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
673  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
674 
675  r[3] = t3;
676  VERIFY_BITS(r[3], 26);
677  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
678  r[4] = t4;
679  VERIFY_BITS(r[4], 26);
680  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
681  r[5] = t5;
682  VERIFY_BITS(r[5], 26);
683  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
684  r[6] = t6;
685  VERIFY_BITS(r[6], 26);
686  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
687  r[7] = t7;
688  VERIFY_BITS(r[7], 26);
689  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
690 
691  r[8] = c & M; c >>= 26; c += u8 * R1;
692  VERIFY_BITS(r[8], 26);
693  VERIFY_BITS(c, 39);
694  /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
695  /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
696  c += d * R0 + t9;
697  VERIFY_BITS(c, 45);
698  /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
699  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
700  VERIFY_BITS(r[9], 22);
701  VERIFY_BITS(c, 46);
702  /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
703  /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
704  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
705 
706  d = c * (R0 >> 4) + t0;
707  VERIFY_BITS(d, 56);
708  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
709  r[0] = d & M; d >>= 26;
710  VERIFY_BITS(r[0], 26);
711  VERIFY_BITS(d, 30);
712  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
713  d += c * (R1 >> 4) + t1;
714  VERIFY_BITS(d, 53);
715  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
716  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
717  /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
718  r[1] = d & M; d >>= 26;
719  VERIFY_BITS(r[1], 26);
720  VERIFY_BITS(d, 27);
721  VERIFY_CHECK(d <= 0x4000000ULL);
722  /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
723  d += t2;
724  VERIFY_BITS(d, 27);
725  /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
726  r[2] = d;
727  VERIFY_BITS(r[2], 27);
728  /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
729 }
730 
731 SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
732  uint64_t c, d;
733  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
734  uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
735  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
736 
737  VERIFY_BITS(a[0], 30);
738  VERIFY_BITS(a[1], 30);
739  VERIFY_BITS(a[2], 30);
740  VERIFY_BITS(a[3], 30);
741  VERIFY_BITS(a[4], 30);
742  VERIFY_BITS(a[5], 30);
743  VERIFY_BITS(a[6], 30);
744  VERIFY_BITS(a[7], 30);
745  VERIFY_BITS(a[8], 30);
746  VERIFY_BITS(a[9], 26);
747 
753  d = (uint64_t)(a[0]*2) * a[9]
754  + (uint64_t)(a[1]*2) * a[8]
755  + (uint64_t)(a[2]*2) * a[7]
756  + (uint64_t)(a[3]*2) * a[6]
757  + (uint64_t)(a[4]*2) * a[5];
758  /* VERIFY_BITS(d, 64); */
759  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
760  t9 = d & M; d >>= 26;
761  VERIFY_BITS(t9, 26);
762  VERIFY_BITS(d, 38);
763  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
764 
765  c = (uint64_t)a[0] * a[0];
766  VERIFY_BITS(c, 60);
767  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
768  d += (uint64_t)(a[1]*2) * a[9]
769  + (uint64_t)(a[2]*2) * a[8]
770  + (uint64_t)(a[3]*2) * a[7]
771  + (uint64_t)(a[4]*2) * a[6]
772  + (uint64_t)a[5] * a[5];
773  VERIFY_BITS(d, 63);
774  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
775  u0 = d & M; d >>= 26; c += u0 * R0;
776  VERIFY_BITS(u0, 26);
777  VERIFY_BITS(d, 37);
778  VERIFY_BITS(c, 61);
779  /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
780  t0 = c & M; c >>= 26; c += u0 * R1;
781  VERIFY_BITS(t0, 26);
782  VERIFY_BITS(c, 37);
783  /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
784  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
785 
786  c += (uint64_t)(a[0]*2) * a[1];
787  VERIFY_BITS(c, 62);
788  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
789  d += (uint64_t)(a[2]*2) * a[9]
790  + (uint64_t)(a[3]*2) * a[8]
791  + (uint64_t)(a[4]*2) * a[7]
792  + (uint64_t)(a[5]*2) * a[6];
793  VERIFY_BITS(d, 63);
794  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
795  u1 = d & M; d >>= 26; c += u1 * R0;
796  VERIFY_BITS(u1, 26);
797  VERIFY_BITS(d, 37);
798  VERIFY_BITS(c, 63);
799  /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
800  t1 = c & M; c >>= 26; c += u1 * R1;
801  VERIFY_BITS(t1, 26);
802  VERIFY_BITS(c, 38);
803  /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
804  /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
805 
806  c += (uint64_t)(a[0]*2) * a[2]
807  + (uint64_t)a[1] * a[1];
808  VERIFY_BITS(c, 62);
809  /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
810  d += (uint64_t)(a[3]*2) * a[9]
811  + (uint64_t)(a[4]*2) * a[8]
812  + (uint64_t)(a[5]*2) * a[7]
813  + (uint64_t)a[6] * a[6];
814  VERIFY_BITS(d, 63);
815  /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
816  u2 = d & M; d >>= 26; c += u2 * R0;
817  VERIFY_BITS(u2, 26);
818  VERIFY_BITS(d, 37);
819  VERIFY_BITS(c, 63);
820  /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
821  t2 = c & M; c >>= 26; c += u2 * R1;
822  VERIFY_BITS(t2, 26);
823  VERIFY_BITS(c, 38);
824  /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
825  /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
826 
827  c += (uint64_t)(a[0]*2) * a[3]
828  + (uint64_t)(a[1]*2) * a[2];
829  VERIFY_BITS(c, 63);
830  /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
831  d += (uint64_t)(a[4]*2) * a[9]
832  + (uint64_t)(a[5]*2) * a[8]
833  + (uint64_t)(a[6]*2) * a[7];
834  VERIFY_BITS(d, 63);
835  /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
836  u3 = d & M; d >>= 26; c += u3 * R0;
837  VERIFY_BITS(u3, 26);
838  VERIFY_BITS(d, 37);
839  /* VERIFY_BITS(c, 64); */
840  /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
841  t3 = c & M; c >>= 26; c += u3 * R1;
842  VERIFY_BITS(t3, 26);
843  VERIFY_BITS(c, 39);
844  /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
845  /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
846 
847  c += (uint64_t)(a[0]*2) * a[4]
848  + (uint64_t)(a[1]*2) * a[3]
849  + (uint64_t)a[2] * a[2];
850  VERIFY_BITS(c, 63);
851  /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
852  d += (uint64_t)(a[5]*2) * a[9]
853  + (uint64_t)(a[6]*2) * a[8]
854  + (uint64_t)a[7] * a[7];
855  VERIFY_BITS(d, 62);
856  /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
857  u4 = d & M; d >>= 26; c += u4 * R0;
858  VERIFY_BITS(u4, 26);
859  VERIFY_BITS(d, 36);
860  /* VERIFY_BITS(c, 64); */
861  /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
862  t4 = c & M; c >>= 26; c += u4 * R1;
863  VERIFY_BITS(t4, 26);
864  VERIFY_BITS(c, 39);
865  /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
866  /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
867 
868  c += (uint64_t)(a[0]*2) * a[5]
869  + (uint64_t)(a[1]*2) * a[4]
870  + (uint64_t)(a[2]*2) * a[3];
871  VERIFY_BITS(c, 63);
872  /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
873  d += (uint64_t)(a[6]*2) * a[9]
874  + (uint64_t)(a[7]*2) * a[8];
875  VERIFY_BITS(d, 62);
876  /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
877  u5 = d & M; d >>= 26; c += u5 * R0;
878  VERIFY_BITS(u5, 26);
879  VERIFY_BITS(d, 36);
880  /* VERIFY_BITS(c, 64); */
881  /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
882  t5 = c & M; c >>= 26; c += u5 * R1;
883  VERIFY_BITS(t5, 26);
884  VERIFY_BITS(c, 39);
885  /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
886  /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
887 
888  c += (uint64_t)(a[0]*2) * a[6]
889  + (uint64_t)(a[1]*2) * a[5]
890  + (uint64_t)(a[2]*2) * a[4]
891  + (uint64_t)a[3] * a[3];
892  VERIFY_BITS(c, 63);
893  /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
894  d += (uint64_t)(a[7]*2) * a[9]
895  + (uint64_t)a[8] * a[8];
896  VERIFY_BITS(d, 61);
897  /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
898  u6 = d & M; d >>= 26; c += u6 * R0;
899  VERIFY_BITS(u6, 26);
900  VERIFY_BITS(d, 35);
901  /* VERIFY_BITS(c, 64); */
902  /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
903  t6 = c & M; c >>= 26; c += u6 * R1;
904  VERIFY_BITS(t6, 26);
905  VERIFY_BITS(c, 39);
906  /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
907  /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
908 
909  c += (uint64_t)(a[0]*2) * a[7]
910  + (uint64_t)(a[1]*2) * a[6]
911  + (uint64_t)(a[2]*2) * a[5]
912  + (uint64_t)(a[3]*2) * a[4];
913  /* VERIFY_BITS(c, 64); */
914  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
915  /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
916  d += (uint64_t)(a[8]*2) * a[9];
917  VERIFY_BITS(d, 58);
918  /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
919  u7 = d & M; d >>= 26; c += u7 * R0;
920  VERIFY_BITS(u7, 26);
921  VERIFY_BITS(d, 32);
922  /* VERIFY_BITS(c, 64); */
923  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
924  /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
925  t7 = c & M; c >>= 26; c += u7 * R1;
926  VERIFY_BITS(t7, 26);
927  VERIFY_BITS(c, 38);
928  /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
929  /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
930 
931  c += (uint64_t)(a[0]*2) * a[8]
932  + (uint64_t)(a[1]*2) * a[7]
933  + (uint64_t)(a[2]*2) * a[6]
934  + (uint64_t)(a[3]*2) * a[5]
935  + (uint64_t)a[4] * a[4];
936  /* VERIFY_BITS(c, 64); */
937  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
938  /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
939  d += (uint64_t)a[9] * a[9];
940  VERIFY_BITS(d, 57);
941  /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
942  u8 = d & M; d >>= 26; c += u8 * R0;
943  VERIFY_BITS(u8, 26);
944  VERIFY_BITS(d, 31);
945  /* VERIFY_BITS(c, 64); */
946  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
947  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
948 
949  r[3] = t3;
950  VERIFY_BITS(r[3], 26);
951  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
952  r[4] = t4;
953  VERIFY_BITS(r[4], 26);
954  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
955  r[5] = t5;
956  VERIFY_BITS(r[5], 26);
957  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
958  r[6] = t6;
959  VERIFY_BITS(r[6], 26);
960  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
961  r[7] = t7;
962  VERIFY_BITS(r[7], 26);
963  /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
964 
965  r[8] = c & M; c >>= 26; c += u8 * R1;
966  VERIFY_BITS(r[8], 26);
967  VERIFY_BITS(c, 39);
968  /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
969  /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
970  c += d * R0 + t9;
971  VERIFY_BITS(c, 45);
972  /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
973  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
974  VERIFY_BITS(r[9], 22);
975  VERIFY_BITS(c, 46);
976  /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
977  /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
978  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
979 
980  d = c * (R0 >> 4) + t0;
981  VERIFY_BITS(d, 56);
982  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
983  r[0] = d & M; d >>= 26;
984  VERIFY_BITS(r[0], 26);
985  VERIFY_BITS(d, 30);
986  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
987  d += c * (R1 >> 4) + t1;
988  VERIFY_BITS(d, 53);
989  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
990  /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
991  /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
992  r[1] = d & M; d >>= 26;
993  VERIFY_BITS(r[1], 26);
994  VERIFY_BITS(d, 27);
995  VERIFY_CHECK(d <= 0x4000000ULL);
996  /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
997  d += t2;
998  VERIFY_BITS(d, 27);
999  /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
1000  r[2] = d;
1001  VERIFY_BITS(r[2], 27);
1002  /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
1003 }
1004 #endif
1005 
1006 SECP256K1_INLINE static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
1007  secp256k1_fe_mul_inner(r->n, a->n, b->n);
1008 }
1009 
1010 SECP256K1_INLINE static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
1011  secp256k1_fe_sqr_inner(r->n, a->n);
1012 }
1013 
1014 SECP256K1_INLINE static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
1015  uint32_t mask0, mask1;
1016  volatile int vflag = flag;
1017  SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
1018  mask0 = vflag + ~((uint32_t)0);
1019  mask1 = ~mask0;
1020  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1021  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1022  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1023  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1024  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1025  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1026  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1027  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1028  r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
1029  r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
1030 }
1031 
1032 static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r) {
1033  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
1034  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
1035  uint32_t one = (uint32_t)1;
1036  uint32_t mask = -(t0 & one) >> 6;
1037 
1038  /* Bounds analysis (over the rationals).
1039  *
1040  * Let m = r->magnitude
1041  * C = 0x3FFFFFFUL * 2
1042  * D = 0x03FFFFFUL * 2
1043  *
1044  * Initial bounds: t0..t8 <= C * m
1045  * t9 <= D * m
1046  */
1047 
1048  t0 += 0x3FFFC2FUL & mask;
1049  t1 += 0x3FFFFBFUL & mask;
1050  t2 += mask;
1051  t3 += mask;
1052  t4 += mask;
1053  t5 += mask;
1054  t6 += mask;
1055  t7 += mask;
1056  t8 += mask;
1057  t9 += mask >> 4;
1058 
1059  VERIFY_CHECK((t0 & one) == 0);
1060 
1061  /* t0..t8: added <= C/2
1062  * t9: added <= D/2
1063  *
1064  * Current bounds: t0..t8 <= C * (m + 1/2)
1065  * t9 <= D * (m + 1/2)
1066  */
1067 
1068  r->n[0] = (t0 >> 1) + ((t1 & one) << 25);
1069  r->n[1] = (t1 >> 1) + ((t2 & one) << 25);
1070  r->n[2] = (t2 >> 1) + ((t3 & one) << 25);
1071  r->n[3] = (t3 >> 1) + ((t4 & one) << 25);
1072  r->n[4] = (t4 >> 1) + ((t5 & one) << 25);
1073  r->n[5] = (t5 >> 1) + ((t6 & one) << 25);
1074  r->n[6] = (t6 >> 1) + ((t7 & one) << 25);
1075  r->n[7] = (t7 >> 1) + ((t8 & one) << 25);
1076  r->n[8] = (t8 >> 1) + ((t9 & one) << 25);
1077  r->n[9] = (t9 >> 1);
1078 
1079  /* t0..t8: shifted right and added <= C/4 + 1/2
1080  * t9: shifted right
1081  *
1082  * Current bounds: t0..t8 <= C * (m/2 + 1/2)
1083  * t9 <= D * (m/2 + 1/4)
1084  *
1085  * Therefore the output magnitude (M) has to be set such that:
1086  * t0..t8: C * M >= C * (m/2 + 1/2)
1087  * t9: D * M >= D * (m/2 + 1/4)
1088  *
1089  * It suffices for all limbs that, for any input magnitude m:
1090  * M >= m/2 + 1/2
1091  *
1092  * and since we want the smallest such integer value for M:
1093  * M == floor(m/2) + 1
1094  */
1095 }
1096 
1097 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
1098  uint32_t mask0, mask1;
1099  volatile int vflag = flag;
1100  SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
1101  mask0 = vflag + ~((uint32_t)0);
1102  mask1 = ~mask0;
1103  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1104  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1105  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1106  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1107  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1108  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1109  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1110  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1111 }
1112 
1113 static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
1114  r->n[0] = a->n[0] | a->n[1] << 26;
1115  r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
1116  r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
1117  r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
1118  r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
1119  r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
1120  r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
1121  r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
1122 }
1123 
1124 static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
1125  r->n[0] = a->n[0] & 0x3FFFFFFUL;
1126  r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
1127  r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
1128  r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
1129  r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
1130  r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
1131  r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
1132  r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
1133  r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
1134  r->n[9] = a->n[7] >> 10;
1135 }
1136 
1137 static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) {
1138  const uint32_t M26 = UINT32_MAX >> 6;
1139  const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4],
1140  a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8];
1141 
1142  /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and
1143  * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8).
1144  */
1145  VERIFY_CHECK(a0 >> 30 == 0);
1146  VERIFY_CHECK(a1 >> 30 == 0);
1147  VERIFY_CHECK(a2 >> 30 == 0);
1148  VERIFY_CHECK(a3 >> 30 == 0);
1149  VERIFY_CHECK(a4 >> 30 == 0);
1150  VERIFY_CHECK(a5 >> 30 == 0);
1151  VERIFY_CHECK(a6 >> 30 == 0);
1152  VERIFY_CHECK(a7 >> 30 == 0);
1153  VERIFY_CHECK(a8 >> 16 == 0);
1154 
1155  r->n[0] = a0 & M26;
1156  r->n[1] = (a0 >> 26 | a1 << 4) & M26;
1157  r->n[2] = (a1 >> 22 | a2 << 8) & M26;
1158  r->n[3] = (a2 >> 18 | a3 << 12) & M26;
1159  r->n[4] = (a3 >> 14 | a4 << 16) & M26;
1160  r->n[5] = (a4 >> 10 | a5 << 20) & M26;
1161  r->n[6] = (a5 >> 6 | a6 << 24) & M26;
1162  r->n[7] = (a6 >> 2 ) & M26;
1163  r->n[8] = (a6 >> 28 | a7 << 2) & M26;
1164  r->n[9] = (a7 >> 24 | a8 << 6);
1165 }
1166 
1167 static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) {
1168  const uint32_t M30 = UINT32_MAX >> 2;
1169  const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4],
1170  a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9];
1171 
1172  r->v[0] = (a0 | a1 << 26) & M30;
1173  r->v[1] = (a1 >> 4 | a2 << 22) & M30;
1174  r->v[2] = (a2 >> 8 | a3 << 18) & M30;
1175  r->v[3] = (a3 >> 12 | a4 << 14) & M30;
1176  r->v[4] = (a4 >> 16 | a5 << 10) & M30;
1177  r->v[5] = (a5 >> 20 | a6 << 6) & M30;
1178  r->v[6] = (a6 >> 24 | a7 << 2
1179  | a8 << 28) & M30;
1180  r->v[7] = (a8 >> 2 | a9 << 24) & M30;
1181  r->v[8] = a9 >> 6;
1182 }
1183 
1184 static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = {
1185  {{-0x3D1, -4, 0, 0, 0, 0, 0, 0, 65536}},
1186  0x2DDACACFL
1187 };
1188 
1189 static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x) {
1190  secp256k1_fe tmp = *x;
1191  secp256k1_modinv32_signed30 s;
1192 
1193  secp256k1_fe_normalize(&tmp);
1194  secp256k1_fe_to_signed30(&s, &tmp);
1195  secp256k1_modinv32(&s, &secp256k1_const_modinfo_fe);
1196  secp256k1_fe_from_signed30(r, &s);
1197 }
1198 
1199 static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
1200  secp256k1_fe tmp = *x;
1201  secp256k1_modinv32_signed30 s;
1202 
1203  secp256k1_fe_normalize_var(&tmp);
1204  secp256k1_fe_to_signed30(&s, &tmp);
1205  secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_fe);
1206  secp256k1_fe_from_signed30(r, &s);
1207 }
1208 
1209 static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x) {
1210  secp256k1_fe tmp;
1211  secp256k1_modinv32_signed30 s;
1212  int jac, ret;
1213 
1214  tmp = *x;
1215  secp256k1_fe_normalize_var(&tmp);
1216  /* secp256k1_jacobi32_maybe_var cannot deal with input 0. */
1217  if (secp256k1_fe_is_zero(&tmp)) return 1;
1218  secp256k1_fe_to_signed30(&s, &tmp);
1219  jac = secp256k1_jacobi32_maybe_var(&s, &secp256k1_const_modinfo_fe);
1220  if (jac == 0) {
1221  /* secp256k1_jacobi32_maybe_var failed to compute the Jacobi symbol. Fall back
1222  * to computing a square root. This should be extremely rare with random
1223  * input (except in VERIFY mode, where a lower iteration count is used). */
1224  secp256k1_fe dummy;
1225  ret = secp256k1_fe_sqrt(&dummy, &tmp);
1226  } else {
1227  ret = jac >= 0;
1228  }
1229  return ret;
1230 }
1231 
1232 #endif /* SECP256K1_FIELD_REPR_IMPL_H */
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition: util.h:159
secp256k1_fe_impl_half
static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r)
Definition: field_10x26_impl.h:1032
secp256k1_modinv32_modinfo
Definition: modinv32.h:19
secp256k1_fe_storage_cmov
static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag)
Definition: field_10x26_impl.h:1097
secp256k1_fe
This field implementation represents the value as 10 uint32_t limbs in base 2^26. ...
Definition: field_10x26.h:14
ret
int ret
Definition: bitcoin-cli.cpp:1358
secp256k1_fe_impl_cmov
static SECP256K1_INLINE void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag)
Definition: field_10x26_impl.h:1014
secp256k1_fe_sqrt
static int secp256k1_fe_sqrt(secp256k1_fe *SECP256K1_RESTRICT r, const secp256k1_fe *SECP256K1_RESTRICT a)
Compute a square root of a field element.
secp256k1_fe_impl_sqr
static SECP256K1_INLINE void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1010
secp256k1_fe_impl_normalizes_to_zero_var
static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r)
Definition: field_10x26_impl.h:207
secp256k1_fe_is_zero
#define secp256k1_fe_is_zero
Definition: field.h:84
secp256k1_fe_sqr_inner
static SECP256K1_INLINE void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a)
Definition: field_10x26_impl.h:731
secp256k1_jacobi32_maybe_var
static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
secp256k1_fe_impl_normalizes_to_zero
static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r)
Definition: field_10x26_impl.h:178
secp256k1_fe_impl_add_int
static SECP256K1_INLINE void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:387
secp256k1_fe_impl_set_int
static SECP256K1_INLINE void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:259
secp256k1_fe_impl_set_b32_mod
static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a)
Definition: field_10x26_impl.h:286
modinv32_impl.h
secp256k1_fe_impl_get_bounds
static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m)
Definition: field_10x26_impl.h:40
secp256k1_fe_impl_normalize
static void secp256k1_fe_impl_normalize(secp256k1_fe *r)
Definition: field_10x26_impl.h:53
secp256k1_fe_impl_is_zero
static SECP256K1_INLINE int secp256k1_fe_impl_is_zero(const secp256k1_fe *a)
Definition: field_10x26_impl.h:264
secp256k1_fe_impl_normalize_weak
static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r)
Definition: field_10x26_impl.h:102
secp256k1_fe_impl_inv_var
static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x)
Definition: field_10x26_impl.h:1199
secp256k1_fe_storage::n
uint32_t n[8]
Definition: field_10x26.h:51
secp256k1_fe_impl_from_storage
static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a)
Definition: field_10x26_impl.h:1124
secp256k1_fe_impl_is_square_var
static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x)
Definition: field_10x26_impl.h:1209
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition: util.h:54
secp256k1_fe_mul_inner
static SECP256K1_INLINE void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t *SECP256K1_RESTRICT b)
Definition: field_10x26_impl.h:401
secp256k1_fe_impl_cmp_var
static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b)
Definition: field_10x26_impl.h:273
secp256k1_fe_impl_mul
static SECP256K1_INLINE void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe *SECP256K1_RESTRICT b)
Definition: field_10x26_impl.h:1006
secp256k1_const_modinfo_fe
static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe
Definition: field_10x26_impl.h:1184
secp256k1_fe_impl_normalize_var
static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r)
Definition: field_10x26_impl.h:128
secp256k1_modinv32_var
static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
secp256k1_fe_impl_is_odd
static SECP256K1_INLINE int secp256k1_fe_impl_is_odd(const secp256k1_fe *a)
Definition: field_10x26_impl.h:269
secp256k1_fe_from_signed30
static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a)
Definition: field_10x26_impl.h:1137
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition: util.h:194
secp256k1_modinv32_signed30
Definition: modinv32.h:15
secp256k1_modinv32_signed30::v
int32_t v[9]
Definition: modinv32.h:16
secp256k1_fe_impl_negate_unchecked
static SECP256K1_INLINE void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m)
Definition: field_10x26_impl.h:340
secp256k1_fe_impl_to_storage
static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1113
secp256k1_fe::n
uint32_t n[10]
Definition: field_10x26.h:22
secp256k1_fe_impl_get_b32
static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a)
Convert a field element to a 32-byte big endian value.
Definition: field_10x26_impl.h:305
secp256k1_fe_impl_inv
static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x)
Definition: field_10x26_impl.h:1189
secp256k1_modinv32
static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
VERIFY_BITS
#define VERIFY_BITS(x, n)
Definition: field_10x26_impl.h:399
secp256k1_fe_normalize
#define secp256k1_fe_normalize
Definition: field.h:78
secp256k1_fe_normalize_var
#define secp256k1_fe_normalize_var
Definition: field.h:80
secp256k1_fe_impl_add
static SECP256K1_INLINE void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:374
secp256k1_fe_to_signed30
static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1167
test_vectors_musig2_generate.s
tuple s
Definition: test_vectors_musig2_generate.py:72
SECP256K1_CHECKMEM_CHECK_VERIFY
#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len)
Definition: checkmem.h:99
u8
unsigned char u8
Definition: crypto_diff_fuzz_chacha20.cpp:21
secp256k1_fe_storage
Definition: field_10x26.h:50
secp256k1_fe_impl_mul_int_unchecked
static SECP256K1_INLINE void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:361
secp256k1_fe_impl_set_b32_limit
static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a)
Definition: field_10x26_impl.h:299
Generated on Wed Sep 3 2025 12:00:00 for Bitcoin Core by   doxygen 1.8.14