Bitcoin ABC  0.29.2
P2P Digital Currency
field_10x26_impl.h
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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 "util.h"
11 #include "field.h"
12 #include "modinv32_impl.h"
13 
14 #ifdef VERIFY
15 static void secp256k1_fe_verify(const secp256k1_fe *a) {
16  const uint32_t *d = a->n;
17  int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
18  r &= (d[0] <= 0x3FFFFFFUL * m);
19  r &= (d[1] <= 0x3FFFFFFUL * m);
20  r &= (d[2] <= 0x3FFFFFFUL * m);
21  r &= (d[3] <= 0x3FFFFFFUL * m);
22  r &= (d[4] <= 0x3FFFFFFUL * m);
23  r &= (d[5] <= 0x3FFFFFFUL * m);
24  r &= (d[6] <= 0x3FFFFFFUL * m);
25  r &= (d[7] <= 0x3FFFFFFUL * m);
26  r &= (d[8] <= 0x3FFFFFFUL * m);
27  r &= (d[9] <= 0x03FFFFFUL * m);
28  r &= (a->magnitude >= 0);
29  r &= (a->magnitude <= 32);
30  if (a->normalized) {
31  r &= (a->magnitude <= 1);
32  if (r && (d[9] == 0x03FFFFFUL)) {
33  uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
34  if (mid == 0x3FFFFFFUL) {
35  r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
36  }
37  }
38  }
39  VERIFY_CHECK(r == 1);
40 }
41 #endif
42 
43 static void secp256k1_fe_normalize(secp256k1_fe *r) {
44  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
45  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
46 
47  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
48  uint32_t m;
49  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
50 
51  /* The first pass ensures the magnitude is 1, ... */
52  t0 += x * 0x3D1UL; t1 += (x << 6);
53  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
54  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
55  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
56  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
57  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
58  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
59  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
60  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
61  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
62 
63  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
64  VERIFY_CHECK(t9 >> 23 == 0);
65 
66  /* At most a single final reduction is needed; check if the value is >= the field characteristic */
67  x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
68  & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
69 
70  /* Apply the final reduction (for constant-time behaviour, we do it always) */
71  t0 += x * 0x3D1UL; t1 += (x << 6);
72  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
73  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
74  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
75  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
76  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
77  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
78  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
79  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
80  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
81 
82  /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
83  VERIFY_CHECK(t9 >> 22 == x);
84 
85  /* Mask off the possible multiple of 2^256 from the final reduction */
86  t9 &= 0x03FFFFFUL;
87 
88  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
89  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
90 
91 #ifdef VERIFY
92  r->magnitude = 1;
93  r->normalized = 1;
94  secp256k1_fe_verify(r);
95 #endif
96 }
97 
98 static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
99  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
100  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
101 
102  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
103  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
104 
105  /* The first pass ensures the magnitude is 1, ... */
106  t0 += x * 0x3D1UL; t1 += (x << 6);
107  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
108  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
109  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
110  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
111  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
112  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
113  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
114  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
115  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
116 
117  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
118  VERIFY_CHECK(t9 >> 23 == 0);
119 
120  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
121  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
122 
123 #ifdef VERIFY
124  r->magnitude = 1;
125  secp256k1_fe_verify(r);
126 #endif
127 }
128 
129 static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
130  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
131  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
132 
133  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
134  uint32_t m;
135  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
136 
137  /* The first pass ensures the magnitude is 1, ... */
138  t0 += x * 0x3D1UL; t1 += (x << 6);
139  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
140  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
141  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
142  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
143  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
144  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
145  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
146  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
147  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
148 
149  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
150  VERIFY_CHECK(t9 >> 23 == 0);
151 
152  /* At most a single final reduction is needed; check if the value is >= the field characteristic */
153  x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
154  & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
155 
156  if (x) {
157  t0 += 0x3D1UL; t1 += (x << 6);
158  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
159  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
160  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
161  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
162  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
163  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
164  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
165  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
166  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
167 
168  /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
169  VERIFY_CHECK(t9 >> 22 == x);
170 
171  /* Mask off the possible multiple of 2^256 from the final reduction */
172  t9 &= 0x03FFFFFUL;
173  }
174 
175  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
176  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
177 
178 #ifdef VERIFY
179  r->magnitude = 1;
180  r->normalized = 1;
181  secp256k1_fe_verify(r);
182 #endif
183 }
184 
185 static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
186  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
187  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
188 
189  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
190  uint32_t z0, z1;
191 
192  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
193  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
194 
195  /* The first pass ensures the magnitude is 1, ... */
196  t0 += x * 0x3D1UL; t1 += (x << 6);
197  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL;
198  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
199  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
200  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
201  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
202  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
203  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
204  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
205  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
206  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
207 
208  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
209  VERIFY_CHECK(t9 >> 23 == 0);
210 
211  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
212 }
213 
214 static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
215  uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
216  uint32_t z0, z1;
217  uint32_t x;
218 
219  t0 = r->n[0];
220  t9 = r->n[9];
221 
222  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
223  x = t9 >> 22;
224 
225  /* The first pass ensures the magnitude is 1, ... */
226  t0 += x * 0x3D1UL;
227 
228  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
229  z0 = t0 & 0x3FFFFFFUL;
230  z1 = z0 ^ 0x3D0UL;
231 
232  /* Fast return path should catch the majority of cases */
233  if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) {
234  return 0;
235  }
236 
237  t1 = r->n[1];
238  t2 = r->n[2];
239  t3 = r->n[3];
240  t4 = r->n[4];
241  t5 = r->n[5];
242  t6 = r->n[6];
243  t7 = r->n[7];
244  t8 = r->n[8];
245 
246  t9 &= 0x03FFFFFUL;
247  t1 += (x << 6);
248 
249  t1 += (t0 >> 26);
250  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
251  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
252  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
253  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
254  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
255  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
256  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
257  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
258  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
259 
260  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
261  VERIFY_CHECK(t9 >> 23 == 0);
262 
263  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
264 }
265 
266 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
267  r->n[0] = a;
268  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;
269 #ifdef VERIFY
270  r->magnitude = 1;
271  r->normalized = 1;
272  secp256k1_fe_verify(r);
273 #endif
274 }
275 
276 SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
277  const uint32_t *t = a->n;
278 #ifdef VERIFY
279  VERIFY_CHECK(a->normalized);
280  secp256k1_fe_verify(a);
281 #endif
282  return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
283 }
284 
285 SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
286 #ifdef VERIFY
287  VERIFY_CHECK(a->normalized);
288  secp256k1_fe_verify(a);
289 #endif
290  return a->n[0] & 1;
291 }
292 
293 SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
294  int i;
295 #ifdef VERIFY
296  a->magnitude = 0;
297  a->normalized = 1;
298 #endif
299  for (i=0; i<10; i++) {
300  a->n[i] = 0;
301  }
302 }
303 
304 static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
305  int i;
306 #ifdef VERIFY
307  VERIFY_CHECK(a->normalized);
308  VERIFY_CHECK(b->normalized);
309  secp256k1_fe_verify(a);
310  secp256k1_fe_verify(b);
311 #endif
312  for (i = 9; i >= 0; i--) {
313  if (a->n[i] > b->n[i]) {
314  return 1;
315  }
316  if (a->n[i] < b->n[i]) {
317  return -1;
318  }
319  }
320  return 0;
321 }
322 
323 static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
324  int ret;
325  r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
326  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);
327  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);
328  r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18);
329  r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24);
330  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);
331  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);
332  r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
333  r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
334  r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
335 
336  ret = !((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));
337 #ifdef VERIFY
338  r->magnitude = 1;
339  if (ret) {
340  r->normalized = 1;
341  secp256k1_fe_verify(r);
342  } else {
343  r->normalized = 0;
344  }
345 #endif
346  return ret;
347 }
348 
350 static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
351 #ifdef VERIFY
352  VERIFY_CHECK(a->normalized);
353  secp256k1_fe_verify(a);
354 #endif
355  r[0] = (a->n[9] >> 14) & 0xff;
356  r[1] = (a->n[9] >> 6) & 0xff;
357  r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3);
358  r[3] = (a->n[8] >> 16) & 0xff;
359  r[4] = (a->n[8] >> 8) & 0xff;
360  r[5] = a->n[8] & 0xff;
361  r[6] = (a->n[7] >> 18) & 0xff;
362  r[7] = (a->n[7] >> 10) & 0xff;
363  r[8] = (a->n[7] >> 2) & 0xff;
364  r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f);
365  r[10] = (a->n[6] >> 12) & 0xff;
366  r[11] = (a->n[6] >> 4) & 0xff;
367  r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf);
368  r[13] = (a->n[5] >> 14) & 0xff;
369  r[14] = (a->n[5] >> 6) & 0xff;
370  r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3);
371  r[16] = (a->n[4] >> 16) & 0xff;
372  r[17] = (a->n[4] >> 8) & 0xff;
373  r[18] = a->n[4] & 0xff;
374  r[19] = (a->n[3] >> 18) & 0xff;
375  r[20] = (a->n[3] >> 10) & 0xff;
376  r[21] = (a->n[3] >> 2) & 0xff;
377  r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f);
378  r[23] = (a->n[2] >> 12) & 0xff;
379  r[24] = (a->n[2] >> 4) & 0xff;
380  r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf);
381  r[26] = (a->n[1] >> 14) & 0xff;
382  r[27] = (a->n[1] >> 6) & 0xff;
383  r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3);
384  r[29] = (a->n[0] >> 16) & 0xff;
385  r[30] = (a->n[0] >> 8) & 0xff;
386  r[31] = a->n[0] & 0xff;
387 }
388 
389 SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
390 #ifdef VERIFY
391  VERIFY_CHECK(a->magnitude <= m);
392  secp256k1_fe_verify(a);
393 #endif
394  r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
395  r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
396  r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
397  r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
398  r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
399  r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
400  r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
401  r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
402  r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
403  r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
404 #ifdef VERIFY
405  r->magnitude = m + 1;
406  r->normalized = 0;
407  secp256k1_fe_verify(r);
408 #endif
409 }
410 
411 SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
412  r->n[0] *= a;
413  r->n[1] *= a;
414  r->n[2] *= a;
415  r->n[3] *= a;
416  r->n[4] *= a;
417  r->n[5] *= a;
418  r->n[6] *= a;
419  r->n[7] *= a;
420  r->n[8] *= a;
421  r->n[9] *= a;
422 #ifdef VERIFY
423  r->magnitude *= a;
424  r->normalized = 0;
425  secp256k1_fe_verify(r);
426 #endif
427 }
428 
429 SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
430 #ifdef VERIFY
431  secp256k1_fe_verify(a);
432 #endif
433  r->n[0] += a->n[0];
434  r->n[1] += a->n[1];
435  r->n[2] += a->n[2];
436  r->n[3] += a->n[3];
437  r->n[4] += a->n[4];
438  r->n[5] += a->n[5];
439  r->n[6] += a->n[6];
440  r->n[7] += a->n[7];
441  r->n[8] += a->n[8];
442  r->n[9] += a->n[9];
443 #ifdef VERIFY
444  r->magnitude += a->magnitude;
445  r->normalized = 0;
446  secp256k1_fe_verify(r);
447 #endif
448 }
449 
450 #if defined(USE_EXTERNAL_ASM)
451 
452 /* External assembler implementation */
453 void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
454 void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
455 
456 #else
457 
458 #ifdef VERIFY
459 #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
460 #else
461 #define VERIFY_BITS(x, n) do { } while(0)
462 #endif
463 
464 SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
465  uint64_t c, d;
466  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
467  uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
468  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
469 
470  VERIFY_BITS(a[0], 30);
471  VERIFY_BITS(a[1], 30);
472  VERIFY_BITS(a[2], 30);
473  VERIFY_BITS(a[3], 30);
474  VERIFY_BITS(a[4], 30);
475  VERIFY_BITS(a[5], 30);
476  VERIFY_BITS(a[6], 30);
477  VERIFY_BITS(a[7], 30);
478  VERIFY_BITS(a[8], 30);
479  VERIFY_BITS(a[9], 26);
480  VERIFY_BITS(b[0], 30);
481  VERIFY_BITS(b[1], 30);
482  VERIFY_BITS(b[2], 30);
483  VERIFY_BITS(b[3], 30);
484  VERIFY_BITS(b[4], 30);
485  VERIFY_BITS(b[5], 30);
486  VERIFY_BITS(b[6], 30);
487  VERIFY_BITS(b[7], 30);
488  VERIFY_BITS(b[8], 30);
489  VERIFY_BITS(b[9], 26);
490 
497  d = (uint64_t)a[0] * b[9]
498  + (uint64_t)a[1] * b[8]
499  + (uint64_t)a[2] * b[7]
500  + (uint64_t)a[3] * b[6]
501  + (uint64_t)a[4] * b[5]
502  + (uint64_t)a[5] * b[4]
503  + (uint64_t)a[6] * b[3]
504  + (uint64_t)a[7] * b[2]
505  + (uint64_t)a[8] * b[1]
506  + (uint64_t)a[9] * b[0];
507  /* VERIFY_BITS(d, 64); */
508  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
509  t9 = d & M; d >>= 26;
510  VERIFY_BITS(t9, 26);
511  VERIFY_BITS(d, 38);
512  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
513 
514  c = (uint64_t)a[0] * b[0];
515  VERIFY_BITS(c, 60);
516  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
517  d += (uint64_t)a[1] * b[9]
518  + (uint64_t)a[2] * b[8]
519  + (uint64_t)a[3] * b[7]
520  + (uint64_t)a[4] * b[6]
521  + (uint64_t)a[5] * b[5]
522  + (uint64_t)a[6] * b[4]
523  + (uint64_t)a[7] * b[3]
524  + (uint64_t)a[8] * b[2]
525  + (uint64_t)a[9] * b[1];
526  VERIFY_BITS(d, 63);
527  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
528  u0 = d & M; d >>= 26; c += u0 * R0;
529  VERIFY_BITS(u0, 26);
530  VERIFY_BITS(d, 37);
531  VERIFY_BITS(c, 61);
532  /* [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] */
533  t0 = c & M; c >>= 26; c += u0 * R1;
534  VERIFY_BITS(t0, 26);
535  VERIFY_BITS(c, 37);
536  /* [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] */
537  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
538 
539  c += (uint64_t)a[0] * b[1]
540  + (uint64_t)a[1] * b[0];
541  VERIFY_BITS(c, 62);
542  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
543  d += (uint64_t)a[2] * b[9]
544  + (uint64_t)a[3] * b[8]
545  + (uint64_t)a[4] * b[7]
546  + (uint64_t)a[5] * b[6]
547  + (uint64_t)a[6] * b[5]
548  + (uint64_t)a[7] * b[4]
549  + (uint64_t)a[8] * b[3]
550  + (uint64_t)a[9] * b[2];
551  VERIFY_BITS(d, 63);
552  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
553  u1 = d & M; d >>= 26; c += u1 * R0;
554  VERIFY_BITS(u1, 26);
555  VERIFY_BITS(d, 37);
556  VERIFY_BITS(c, 63);
557  /* [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] */
558  t1 = c & M; c >>= 26; c += u1 * R1;
559  VERIFY_BITS(t1, 26);
560  VERIFY_BITS(c, 38);
561  /* [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] */
562  /* [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] */
563 
564  c += (uint64_t)a[0] * b[2]
565  + (uint64_t)a[1] * b[1]
566  + (uint64_t)a[2] * b[0];
567  VERIFY_BITS(c, 62);
568  /* [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] */
569  d += (uint64_t)a[3] * b[9]
570  + (uint64_t)a[4] * b[8]
571  + (uint64_t)a[5] * b[7]
572  + (uint64_t)a[6] * b[6]
573  + (uint64_t)a[7] * b[5]
574  + (uint64_t)a[8] * b[4]
575  + (uint64_t)a[9] * b[3];
576  VERIFY_BITS(d, 63);
577  /* [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] */
578  u2 = d & M; d >>= 26; c += u2 * R0;
579  VERIFY_BITS(u2, 26);
580  VERIFY_BITS(d, 37);
581  VERIFY_BITS(c, 63);
582  /* [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] */
583  t2 = c & M; c >>= 26; c += u2 * R1;
584  VERIFY_BITS(t2, 26);
585  VERIFY_BITS(c, 38);
586  /* [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] */
587  /* [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] */
588 
589  c += (uint64_t)a[0] * b[3]
590  + (uint64_t)a[1] * b[2]
591  + (uint64_t)a[2] * b[1]
592  + (uint64_t)a[3] * b[0];
593  VERIFY_BITS(c, 63);
594  /* [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] */
595  d += (uint64_t)a[4] * b[9]
596  + (uint64_t)a[5] * b[8]
597  + (uint64_t)a[6] * b[7]
598  + (uint64_t)a[7] * b[6]
599  + (uint64_t)a[8] * b[5]
600  + (uint64_t)a[9] * b[4];
601  VERIFY_BITS(d, 63);
602  /* [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] */
603  u3 = d & M; d >>= 26; c += u3 * R0;
604  VERIFY_BITS(u3, 26);
605  VERIFY_BITS(d, 37);
606  /* VERIFY_BITS(c, 64); */
607  /* [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] */
608  t3 = c & M; c >>= 26; c += u3 * R1;
609  VERIFY_BITS(t3, 26);
610  VERIFY_BITS(c, 39);
611  /* [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] */
612  /* [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] */
613 
614  c += (uint64_t)a[0] * b[4]
615  + (uint64_t)a[1] * b[3]
616  + (uint64_t)a[2] * b[2]
617  + (uint64_t)a[3] * b[1]
618  + (uint64_t)a[4] * b[0];
619  VERIFY_BITS(c, 63);
620  /* [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] */
621  d += (uint64_t)a[5] * b[9]
622  + (uint64_t)a[6] * b[8]
623  + (uint64_t)a[7] * b[7]
624  + (uint64_t)a[8] * b[6]
625  + (uint64_t)a[9] * b[5];
626  VERIFY_BITS(d, 62);
627  /* [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] */
628  u4 = d & M; d >>= 26; c += u4 * R0;
629  VERIFY_BITS(u4, 26);
630  VERIFY_BITS(d, 36);
631  /* VERIFY_BITS(c, 64); */
632  /* [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] */
633  t4 = c & M; c >>= 26; c += u4 * R1;
634  VERIFY_BITS(t4, 26);
635  VERIFY_BITS(c, 39);
636  /* [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] */
637  /* [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] */
638 
639  c += (uint64_t)a[0] * b[5]
640  + (uint64_t)a[1] * b[4]
641  + (uint64_t)a[2] * b[3]
642  + (uint64_t)a[3] * b[2]
643  + (uint64_t)a[4] * b[1]
644  + (uint64_t)a[5] * b[0];
645  VERIFY_BITS(c, 63);
646  /* [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] */
647  d += (uint64_t)a[6] * b[9]
648  + (uint64_t)a[7] * b[8]
649  + (uint64_t)a[8] * b[7]
650  + (uint64_t)a[9] * b[6];
651  VERIFY_BITS(d, 62);
652  /* [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] */
653  u5 = d & M; d >>= 26; c += u5 * R0;
654  VERIFY_BITS(u5, 26);
655  VERIFY_BITS(d, 36);
656  /* VERIFY_BITS(c, 64); */
657  /* [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] */
658  t5 = c & M; c >>= 26; c += u5 * R1;
659  VERIFY_BITS(t5, 26);
660  VERIFY_BITS(c, 39);
661  /* [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] */
662  /* [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] */
663 
664  c += (uint64_t)a[0] * b[6]
665  + (uint64_t)a[1] * b[5]
666  + (uint64_t)a[2] * b[4]
667  + (uint64_t)a[3] * b[3]
668  + (uint64_t)a[4] * b[2]
669  + (uint64_t)a[5] * b[1]
670  + (uint64_t)a[6] * b[0];
671  VERIFY_BITS(c, 63);
672  /* [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] */
673  d += (uint64_t)a[7] * b[9]
674  + (uint64_t)a[8] * b[8]
675  + (uint64_t)a[9] * b[7];
676  VERIFY_BITS(d, 61);
677  /* [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] */
678  u6 = d & M; d >>= 26; c += u6 * R0;
679  VERIFY_BITS(u6, 26);
680  VERIFY_BITS(d, 35);
681  /* VERIFY_BITS(c, 64); */
682  /* [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] */
683  t6 = c & M; c >>= 26; c += u6 * R1;
684  VERIFY_BITS(t6, 26);
685  VERIFY_BITS(c, 39);
686  /* [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] */
687  /* [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] */
688 
689  c += (uint64_t)a[0] * b[7]
690  + (uint64_t)a[1] * b[6]
691  + (uint64_t)a[2] * b[5]
692  + (uint64_t)a[3] * b[4]
693  + (uint64_t)a[4] * b[3]
694  + (uint64_t)a[5] * b[2]
695  + (uint64_t)a[6] * b[1]
696  + (uint64_t)a[7] * b[0];
697  /* VERIFY_BITS(c, 64); */
698  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
699  /* [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] */
700  d += (uint64_t)a[8] * b[9]
701  + (uint64_t)a[9] * b[8];
702  VERIFY_BITS(d, 58);
703  /* [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] */
704  u7 = d & M; d >>= 26; c += u7 * R0;
705  VERIFY_BITS(u7, 26);
706  VERIFY_BITS(d, 32);
707  /* VERIFY_BITS(c, 64); */
708  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
709  /* [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] */
710  t7 = c & M; c >>= 26; c += u7 * R1;
711  VERIFY_BITS(t7, 26);
712  VERIFY_BITS(c, 38);
713  /* [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] */
714  /* [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] */
715 
716  c += (uint64_t)a[0] * b[8]
717  + (uint64_t)a[1] * b[7]
718  + (uint64_t)a[2] * b[6]
719  + (uint64_t)a[3] * b[5]
720  + (uint64_t)a[4] * b[4]
721  + (uint64_t)a[5] * b[3]
722  + (uint64_t)a[6] * b[2]
723  + (uint64_t)a[7] * b[1]
724  + (uint64_t)a[8] * b[0];
725  /* VERIFY_BITS(c, 64); */
726  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
727  /* [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] */
728  d += (uint64_t)a[9] * b[9];
729  VERIFY_BITS(d, 57);
730  /* [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] */
731  u8 = d & M; d >>= 26; c += u8 * R0;
732  VERIFY_BITS(u8, 26);
733  VERIFY_BITS(d, 31);
734  /* VERIFY_BITS(c, 64); */
735  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
736  /* [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] */
737 
738  r[3] = t3;
739  VERIFY_BITS(r[3], 26);
740  /* [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] */
741  r[4] = t4;
742  VERIFY_BITS(r[4], 26);
743  /* [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] */
744  r[5] = t5;
745  VERIFY_BITS(r[5], 26);
746  /* [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] */
747  r[6] = t6;
748  VERIFY_BITS(r[6], 26);
749  /* [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] */
750  r[7] = t7;
751  VERIFY_BITS(r[7], 26);
752  /* [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] */
753 
754  r[8] = c & M; c >>= 26; c += u8 * R1;
755  VERIFY_BITS(r[8], 26);
756  VERIFY_BITS(c, 39);
757  /* [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] */
758  /* [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] */
759  c += d * R0 + t9;
760  VERIFY_BITS(c, 45);
761  /* [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] */
762  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
763  VERIFY_BITS(r[9], 22);
764  VERIFY_BITS(c, 46);
765  /* [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] */
766  /* [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] */
767  /* [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] */
768 
769  d = c * (R0 >> 4) + t0;
770  VERIFY_BITS(d, 56);
771  /* [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] */
772  r[0] = d & M; d >>= 26;
773  VERIFY_BITS(r[0], 26);
774  VERIFY_BITS(d, 30);
775  /* [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] */
776  d += c * (R1 >> 4) + t1;
777  VERIFY_BITS(d, 53);
778  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
779  /* [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] */
780  /* [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] */
781  r[1] = d & M; d >>= 26;
782  VERIFY_BITS(r[1], 26);
783  VERIFY_BITS(d, 27);
784  VERIFY_CHECK(d <= 0x4000000ULL);
785  /* [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] */
786  d += t2;
787  VERIFY_BITS(d, 27);
788  /* [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] */
789  r[2] = d;
790  VERIFY_BITS(r[2], 27);
791  /* [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] */
792 }
793 
794 SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
795  uint64_t c, d;
796  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
797  uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
798  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
799 
800  VERIFY_BITS(a[0], 30);
801  VERIFY_BITS(a[1], 30);
802  VERIFY_BITS(a[2], 30);
803  VERIFY_BITS(a[3], 30);
804  VERIFY_BITS(a[4], 30);
805  VERIFY_BITS(a[5], 30);
806  VERIFY_BITS(a[6], 30);
807  VERIFY_BITS(a[7], 30);
808  VERIFY_BITS(a[8], 30);
809  VERIFY_BITS(a[9], 26);
810 
816  d = (uint64_t)(a[0]*2) * a[9]
817  + (uint64_t)(a[1]*2) * a[8]
818  + (uint64_t)(a[2]*2) * a[7]
819  + (uint64_t)(a[3]*2) * a[6]
820  + (uint64_t)(a[4]*2) * a[5];
821  /* VERIFY_BITS(d, 64); */
822  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
823  t9 = d & M; d >>= 26;
824  VERIFY_BITS(t9, 26);
825  VERIFY_BITS(d, 38);
826  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
827 
828  c = (uint64_t)a[0] * a[0];
829  VERIFY_BITS(c, 60);
830  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
831  d += (uint64_t)(a[1]*2) * a[9]
832  + (uint64_t)(a[2]*2) * a[8]
833  + (uint64_t)(a[3]*2) * a[7]
834  + (uint64_t)(a[4]*2) * a[6]
835  + (uint64_t)a[5] * a[5];
836  VERIFY_BITS(d, 63);
837  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
838  u0 = d & M; d >>= 26; c += u0 * R0;
839  VERIFY_BITS(u0, 26);
840  VERIFY_BITS(d, 37);
841  VERIFY_BITS(c, 61);
842  /* [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] */
843  t0 = c & M; c >>= 26; c += u0 * R1;
844  VERIFY_BITS(t0, 26);
845  VERIFY_BITS(c, 37);
846  /* [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] */
847  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
848 
849  c += (uint64_t)(a[0]*2) * a[1];
850  VERIFY_BITS(c, 62);
851  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
852  d += (uint64_t)(a[2]*2) * a[9]
853  + (uint64_t)(a[3]*2) * a[8]
854  + (uint64_t)(a[4]*2) * a[7]
855  + (uint64_t)(a[5]*2) * a[6];
856  VERIFY_BITS(d, 63);
857  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
858  u1 = d & M; d >>= 26; c += u1 * R0;
859  VERIFY_BITS(u1, 26);
860  VERIFY_BITS(d, 37);
861  VERIFY_BITS(c, 63);
862  /* [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] */
863  t1 = c & M; c >>= 26; c += u1 * R1;
864  VERIFY_BITS(t1, 26);
865  VERIFY_BITS(c, 38);
866  /* [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] */
867  /* [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] */
868 
869  c += (uint64_t)(a[0]*2) * a[2]
870  + (uint64_t)a[1] * a[1];
871  VERIFY_BITS(c, 62);
872  /* [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] */
873  d += (uint64_t)(a[3]*2) * a[9]
874  + (uint64_t)(a[4]*2) * a[8]
875  + (uint64_t)(a[5]*2) * a[7]
876  + (uint64_t)a[6] * a[6];
877  VERIFY_BITS(d, 63);
878  /* [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] */
879  u2 = d & M; d >>= 26; c += u2 * R0;
880  VERIFY_BITS(u2, 26);
881  VERIFY_BITS(d, 37);
882  VERIFY_BITS(c, 63);
883  /* [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] */
884  t2 = c & M; c >>= 26; c += u2 * R1;
885  VERIFY_BITS(t2, 26);
886  VERIFY_BITS(c, 38);
887  /* [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] */
888  /* [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] */
889 
890  c += (uint64_t)(a[0]*2) * a[3]
891  + (uint64_t)(a[1]*2) * a[2];
892  VERIFY_BITS(c, 63);
893  /* [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] */
894  d += (uint64_t)(a[4]*2) * a[9]
895  + (uint64_t)(a[5]*2) * a[8]
896  + (uint64_t)(a[6]*2) * a[7];
897  VERIFY_BITS(d, 63);
898  /* [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] */
899  u3 = d & M; d >>= 26; c += u3 * R0;
900  VERIFY_BITS(u3, 26);
901  VERIFY_BITS(d, 37);
902  /* VERIFY_BITS(c, 64); */
903  /* [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] */
904  t3 = c & M; c >>= 26; c += u3 * R1;
905  VERIFY_BITS(t3, 26);
906  VERIFY_BITS(c, 39);
907  /* [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] */
908  /* [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] */
909 
910  c += (uint64_t)(a[0]*2) * a[4]
911  + (uint64_t)(a[1]*2) * a[3]
912  + (uint64_t)a[2] * a[2];
913  VERIFY_BITS(c, 63);
914  /* [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] */
915  d += (uint64_t)(a[5]*2) * a[9]
916  + (uint64_t)(a[6]*2) * a[8]
917  + (uint64_t)a[7] * a[7];
918  VERIFY_BITS(d, 62);
919  /* [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] */
920  u4 = d & M; d >>= 26; c += u4 * R0;
921  VERIFY_BITS(u4, 26);
922  VERIFY_BITS(d, 36);
923  /* VERIFY_BITS(c, 64); */
924  /* [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] */
925  t4 = c & M; c >>= 26; c += u4 * R1;
926  VERIFY_BITS(t4, 26);
927  VERIFY_BITS(c, 39);
928  /* [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] */
929  /* [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] */
930 
931  c += (uint64_t)(a[0]*2) * a[5]
932  + (uint64_t)(a[1]*2) * a[4]
933  + (uint64_t)(a[2]*2) * a[3];
934  VERIFY_BITS(c, 63);
935  /* [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] */
936  d += (uint64_t)(a[6]*2) * a[9]
937  + (uint64_t)(a[7]*2) * a[8];
938  VERIFY_BITS(d, 62);
939  /* [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] */
940  u5 = d & M; d >>= 26; c += u5 * R0;
941  VERIFY_BITS(u5, 26);
942  VERIFY_BITS(d, 36);
943  /* VERIFY_BITS(c, 64); */
944  /* [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] */
945  t5 = c & M; c >>= 26; c += u5 * R1;
946  VERIFY_BITS(t5, 26);
947  VERIFY_BITS(c, 39);
948  /* [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] */
949  /* [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] */
950 
951  c += (uint64_t)(a[0]*2) * a[6]
952  + (uint64_t)(a[1]*2) * a[5]
953  + (uint64_t)(a[2]*2) * a[4]
954  + (uint64_t)a[3] * a[3];
955  VERIFY_BITS(c, 63);
956  /* [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] */
957  d += (uint64_t)(a[7]*2) * a[9]
958  + (uint64_t)a[8] * a[8];
959  VERIFY_BITS(d, 61);
960  /* [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] */
961  u6 = d & M; d >>= 26; c += u6 * R0;
962  VERIFY_BITS(u6, 26);
963  VERIFY_BITS(d, 35);
964  /* VERIFY_BITS(c, 64); */
965  /* [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] */
966  t6 = c & M; c >>= 26; c += u6 * R1;
967  VERIFY_BITS(t6, 26);
968  VERIFY_BITS(c, 39);
969  /* [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] */
970  /* [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] */
971 
972  c += (uint64_t)(a[0]*2) * a[7]
973  + (uint64_t)(a[1]*2) * a[6]
974  + (uint64_t)(a[2]*2) * a[5]
975  + (uint64_t)(a[3]*2) * a[4];
976  /* VERIFY_BITS(c, 64); */
977  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
978  /* [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] */
979  d += (uint64_t)(a[8]*2) * a[9];
980  VERIFY_BITS(d, 58);
981  /* [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] */
982  u7 = d & M; d >>= 26; c += u7 * R0;
983  VERIFY_BITS(u7, 26);
984  VERIFY_BITS(d, 32);
985  /* VERIFY_BITS(c, 64); */
986  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
987  /* [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] */
988  t7 = c & M; c >>= 26; c += u7 * R1;
989  VERIFY_BITS(t7, 26);
990  VERIFY_BITS(c, 38);
991  /* [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] */
992  /* [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] */
993 
994  c += (uint64_t)(a[0]*2) * a[8]
995  + (uint64_t)(a[1]*2) * a[7]
996  + (uint64_t)(a[2]*2) * a[6]
997  + (uint64_t)(a[3]*2) * a[5]
998  + (uint64_t)a[4] * a[4];
999  /* VERIFY_BITS(c, 64); */
1000  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
1001  /* [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] */
1002  d += (uint64_t)a[9] * a[9];
1003  VERIFY_BITS(d, 57);
1004  /* [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] */
1005  u8 = d & M; d >>= 26; c += u8 * R0;
1006  VERIFY_BITS(u8, 26);
1007  VERIFY_BITS(d, 31);
1008  /* VERIFY_BITS(c, 64); */
1009  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
1010  /* [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] */
1011 
1012  r[3] = t3;
1013  VERIFY_BITS(r[3], 26);
1014  /* [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] */
1015  r[4] = t4;
1016  VERIFY_BITS(r[4], 26);
1017  /* [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] */
1018  r[5] = t5;
1019  VERIFY_BITS(r[5], 26);
1020  /* [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] */
1021  r[6] = t6;
1022  VERIFY_BITS(r[6], 26);
1023  /* [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] */
1024  r[7] = t7;
1025  VERIFY_BITS(r[7], 26);
1026  /* [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] */
1027 
1028  r[8] = c & M; c >>= 26; c += u8 * R1;
1029  VERIFY_BITS(r[8], 26);
1030  VERIFY_BITS(c, 39);
1031  /* [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] */
1032  /* [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] */
1033  c += d * R0 + t9;
1034  VERIFY_BITS(c, 45);
1035  /* [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] */
1036  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
1037  VERIFY_BITS(r[9], 22);
1038  VERIFY_BITS(c, 46);
1039  /* [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] */
1040  /* [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] */
1041  /* [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] */
1042 
1043  d = c * (R0 >> 4) + t0;
1044  VERIFY_BITS(d, 56);
1045  /* [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] */
1046  r[0] = d & M; d >>= 26;
1047  VERIFY_BITS(r[0], 26);
1048  VERIFY_BITS(d, 30);
1049  /* [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] */
1050  d += c * (R1 >> 4) + t1;
1051  VERIFY_BITS(d, 53);
1052  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
1053  /* [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] */
1054  /* [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] */
1055  r[1] = d & M; d >>= 26;
1056  VERIFY_BITS(r[1], 26);
1057  VERIFY_BITS(d, 27);
1058  VERIFY_CHECK(d <= 0x4000000ULL);
1059  /* [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] */
1060  d += t2;
1061  VERIFY_BITS(d, 27);
1062  /* [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] */
1063  r[2] = d;
1064  VERIFY_BITS(r[2], 27);
1065  /* [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] */
1066 }
1067 #endif
1068 
1069 static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
1070 #ifdef VERIFY
1071  VERIFY_CHECK(a->magnitude <= 8);
1072  VERIFY_CHECK(b->magnitude <= 8);
1073  secp256k1_fe_verify(a);
1074  secp256k1_fe_verify(b);
1075  VERIFY_CHECK(r != b);
1076  VERIFY_CHECK(a != b);
1077 #endif
1078  secp256k1_fe_mul_inner(r->n, a->n, b->n);
1079 #ifdef VERIFY
1080  r->magnitude = 1;
1081  r->normalized = 0;
1082  secp256k1_fe_verify(r);
1083 #endif
1084 }
1085 
1086 static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
1087 #ifdef VERIFY
1088  VERIFY_CHECK(a->magnitude <= 8);
1089  secp256k1_fe_verify(a);
1090 #endif
1091  secp256k1_fe_sqr_inner(r->n, a->n);
1092 #ifdef VERIFY
1093  r->magnitude = 1;
1094  r->normalized = 0;
1095  secp256k1_fe_verify(r);
1096 #endif
1097 }
1098 
1099 static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
1100  uint32_t mask0, mask1;
1101  VG_CHECK_VERIFY(r->n, sizeof(r->n));
1102  mask0 = flag + ~((uint32_t)0);
1103  mask1 = ~mask0;
1104  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1105  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1106  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1107  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1108  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1109  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1110  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1111  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1112  r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
1113  r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
1114 #ifdef VERIFY
1115  if (flag) {
1116  r->magnitude = a->magnitude;
1117  r->normalized = a->normalized;
1118  }
1119 #endif
1120 }
1121 
1122 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
1123  uint32_t mask0, mask1;
1124  VG_CHECK_VERIFY(r->n, sizeof(r->n));
1125  mask0 = flag + ~((uint32_t)0);
1126  mask1 = ~mask0;
1127  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1128  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1129  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1130  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1131  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1132  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1133  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1134  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1135 }
1136 
1137 static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
1138 #ifdef VERIFY
1139  VERIFY_CHECK(a->normalized);
1140 #endif
1141  r->n[0] = a->n[0] | a->n[1] << 26;
1142  r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
1143  r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
1144  r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
1145  r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
1146  r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
1147  r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
1148  r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
1149 }
1150 
1151 static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
1152  r->n[0] = a->n[0] & 0x3FFFFFFUL;
1153  r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
1154  r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
1155  r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
1156  r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
1157  r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
1158  r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
1159  r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
1160  r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
1161  r->n[9] = a->n[7] >> 10;
1162 #ifdef VERIFY
1163  r->magnitude = 1;
1164  r->normalized = 1;
1165 #endif
1166 }
1167 
1168 static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) {
1169  const uint32_t M26 = UINT32_MAX >> 6;
1170  const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4],
1171  a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8];
1172 
1173  /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and
1174  * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8).
1175  */
1176  VERIFY_CHECK(a0 >> 30 == 0);
1177  VERIFY_CHECK(a1 >> 30 == 0);
1178  VERIFY_CHECK(a2 >> 30 == 0);
1179  VERIFY_CHECK(a3 >> 30 == 0);
1180  VERIFY_CHECK(a4 >> 30 == 0);
1181  VERIFY_CHECK(a5 >> 30 == 0);
1182  VERIFY_CHECK(a6 >> 30 == 0);
1183  VERIFY_CHECK(a7 >> 30 == 0);
1184  VERIFY_CHECK(a8 >> 16 == 0);
1185 
1186  r->n[0] = a0 & M26;
1187  r->n[1] = (a0 >> 26 | a1 << 4) & M26;
1188  r->n[2] = (a1 >> 22 | a2 << 8) & M26;
1189  r->n[3] = (a2 >> 18 | a3 << 12) & M26;
1190  r->n[4] = (a3 >> 14 | a4 << 16) & M26;
1191  r->n[5] = (a4 >> 10 | a5 << 20) & M26;
1192  r->n[6] = (a5 >> 6 | a6 << 24) & M26;
1193  r->n[7] = (a6 >> 2 ) & M26;
1194  r->n[8] = (a6 >> 28 | a7 << 2) & M26;
1195  r->n[9] = (a7 >> 24 | a8 << 6);
1196 
1197 #ifdef VERIFY
1198  r->magnitude = 1;
1199  r->normalized = 1;
1200  secp256k1_fe_verify(r);
1201 #endif
1202 }
1203 
1204 static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) {
1205  const uint32_t M30 = UINT32_MAX >> 2;
1206  const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4],
1207  a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9];
1208 
1209 #ifdef VERIFY
1210  VERIFY_CHECK(a->normalized);
1211 #endif
1212 
1213  r->v[0] = (a0 | a1 << 26) & M30;
1214  r->v[1] = (a1 >> 4 | a2 << 22) & M30;
1215  r->v[2] = (a2 >> 8 | a3 << 18) & M30;
1216  r->v[3] = (a3 >> 12 | a4 << 14) & M30;
1217  r->v[4] = (a4 >> 16 | a5 << 10) & M30;
1218  r->v[5] = (a5 >> 20 | a6 << 6) & M30;
1219  r->v[6] = (a6 >> 24 | a7 << 2
1220  | a8 << 28) & M30;
1221  r->v[7] = (a8 >> 2 | a9 << 24) & M30;
1222  r->v[8] = a9 >> 6;
1223 }
1224 
1225 static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = {
1226  {{-0x3D1, -4, 0, 0, 0, 0, 0, 0, 65536}},
1227  0x2DDACACFL
1228 };
1229 
1230 static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
1231  secp256k1_fe tmp;
1232  secp256k1_modinv32_signed30 s;
1233 
1234  tmp = *x;
1235  secp256k1_fe_normalize(&tmp);
1236  secp256k1_fe_to_signed30(&s, &tmp);
1237  secp256k1_modinv32(&s, &secp256k1_const_modinfo_fe);
1238  secp256k1_fe_from_signed30(r, &s);
1239 
1240  VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
1241 }
1242 
1243 static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
1244  secp256k1_fe tmp;
1245  secp256k1_modinv32_signed30 s;
1246 
1247  tmp = *x;
1248  secp256k1_fe_normalize_var(&tmp);
1249  secp256k1_fe_to_signed30(&s, &tmp);
1250  secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_fe);
1251  secp256k1_fe_from_signed30(r, &s);
1252 
1253  VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
1254 }
1255 
1256 #endif /* SECP256K1_FIELD_REPR_IMPL_H */
secp256k1_fe_set_int
static SECP256K1_INLINE void secp256k1_fe_set_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:266
secp256k1_fe_normalize_weak
static void secp256k1_fe_normalize_weak(secp256k1_fe *r)
Definition: field_10x26_impl.h:98
secp256k1_fe_sqr_inner
static SECP256K1_INLINE void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a)
Definition: field_10x26_impl.h:794
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static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe
Definition: field_10x26_impl.h:1225
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static SECP256K1_INLINE int secp256k1_fe_is_zero(const secp256k1_fe *a)
Definition: field_10x26_impl.h:276
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static void secp256k1_fe_normalize_var(secp256k1_fe *r)
Definition: field_10x26_impl.h:129
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static SECP256K1_INLINE void secp256k1_fe_mul_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:411
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static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe *SECP256K1_RESTRICT b)
Definition: field_10x26_impl.h:1069
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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:464
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static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a)
Definition: field_10x26_impl.h:323
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static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag)
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Definition: field_10x26_impl.h:214
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static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag)
Definition: field_10x26_impl.h:1099
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static SECP256K1_INLINE void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m)
Definition: field_10x26_impl.h:389
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static void secp256k1_fe_normalize(secp256k1_fe *r)
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#define VERIFY_BITS(x, n)
Definition: field_10x26_impl.h:461
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static SECP256K1_INLINE int secp256k1_fe_is_odd(const secp256k1_fe *a)
Definition: field_10x26_impl.h:285
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Definition: field_10x26_impl.h:293
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static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1137
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static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a)
Definition: field_10x26_impl.h:1151
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static void secp256k1_fe_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:350
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static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r)
Definition: field_10x26_impl.h:185
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static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b)
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static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x)
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static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
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static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
modinv32_impl.h
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#define VG_CHECK_VERIFY(x, y)
Definition: util.h:88
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Definition: util.h:68
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#define SECP256K1_RESTRICT
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