Bitcoin
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 http://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 
13 #ifdef VERIFY
14 static void secp256k1_fe_verify(const secp256k1_fe *a) {
15  const uint32_t *d = a->n;
16  int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
17  r &= (d[0] <= 0x3FFFFFFUL * m);
18  r &= (d[1] <= 0x3FFFFFFUL * m);
19  r &= (d[2] <= 0x3FFFFFFUL * m);
20  r &= (d[3] <= 0x3FFFFFFUL * m);
21  r &= (d[4] <= 0x3FFFFFFUL * m);
22  r &= (d[5] <= 0x3FFFFFFUL * m);
23  r &= (d[6] <= 0x3FFFFFFUL * m);
24  r &= (d[7] <= 0x3FFFFFFUL * m);
25  r &= (d[8] <= 0x3FFFFFFUL * m);
26  r &= (d[9] <= 0x03FFFFFUL * m);
27  r &= (a->magnitude >= 0);
28  r &= (a->magnitude <= 32);
29  if (a->normalized) {
30  r &= (a->magnitude <= 1);
31  if (r && (d[9] == 0x03FFFFFUL)) {
32  uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
33  if (mid == 0x3FFFFFFUL) {
34  r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
35  }
36  }
37  }
38  VERIFY_CHECK(r == 1);
39 }
40 #endif
41 
42 static void secp256k1_fe_normalize(secp256k1_fe *r) {
43  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
44  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
45 
46  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
47  uint32_t m;
48  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
49 
50  /* The first pass ensures the magnitude is 1, ... */
51  t0 += x * 0x3D1UL; t1 += (x << 6);
52  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
53  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
54  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
55  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
56  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
57  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
58  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
59  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
60  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
61 
62  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
63  VERIFY_CHECK(t9 >> 23 == 0);
64 
65  /* At most a single final reduction is needed; check if the value is >= the field characteristic */
66  x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
67  & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
68 
69  /* Apply the final reduction (for constant-time behaviour, we do it always) */
70  t0 += x * 0x3D1UL; t1 += (x << 6);
71  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
72  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
73  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
74  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
75  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
76  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
77  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
78  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
79  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
80 
81  /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
82  VERIFY_CHECK(t9 >> 22 == x);
83 
84  /* Mask off the possible multiple of 2^256 from the final reduction */
85  t9 &= 0x03FFFFFUL;
86 
87  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
88  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
89 
90 #ifdef VERIFY
91  r->magnitude = 1;
92  r->normalized = 1;
93  secp256k1_fe_verify(r);
94 #endif
95 }
96 
97 static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
98  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
99  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
100 
101  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
102  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
103 
104  /* The first pass ensures the magnitude is 1, ... */
105  t0 += x * 0x3D1UL; t1 += (x << 6);
106  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
107  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
108  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
109  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
110  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
111  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
112  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
113  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
114  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
115 
116  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
117  VERIFY_CHECK(t9 >> 23 == 0);
118 
119  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
120  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
121 
122 #ifdef VERIFY
123  r->magnitude = 1;
124  secp256k1_fe_verify(r);
125 #endif
126 }
127 
128 static void secp256k1_fe_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 #ifdef VERIFY
178  r->magnitude = 1;
179  r->normalized = 1;
180  secp256k1_fe_verify(r);
181 #endif
182 }
183 
184 static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
185  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
186  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
187 
188  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
189  uint32_t z0, z1;
190 
191  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
192  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
193 
194  /* The first pass ensures the magnitude is 1, ... */
195  t0 += x * 0x3D1UL; t1 += (x << 6);
196  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL;
197  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
198  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
199  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
200  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
201  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
202  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
203  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
204  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
205  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
206 
207  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
208  VERIFY_CHECK(t9 >> 23 == 0);
209 
210  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
211 }
212 
213 static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
214  uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
215  uint32_t z0, z1;
216  uint32_t x;
217 
218  t0 = r->n[0];
219  t9 = r->n[9];
220 
221  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
222  x = t9 >> 22;
223 
224  /* The first pass ensures the magnitude is 1, ... */
225  t0 += x * 0x3D1UL;
226 
227  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
228  z0 = t0 & 0x3FFFFFFUL;
229  z1 = z0 ^ 0x3D0UL;
230 
231  /* Fast return path should catch the majority of cases */
232  if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) {
233  return 0;
234  }
235 
236  t1 = r->n[1];
237  t2 = r->n[2];
238  t3 = r->n[3];
239  t4 = r->n[4];
240  t5 = r->n[5];
241  t6 = r->n[6];
242  t7 = r->n[7];
243  t8 = r->n[8];
244 
245  t9 &= 0x03FFFFFUL;
246  t1 += (x << 6);
247 
248  t1 += (t0 >> 26);
249  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
250  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
251  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
252  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
253  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
254  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
255  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
256  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
257  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
258 
259  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
260  VERIFY_CHECK(t9 >> 23 == 0);
261 
262  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
263 }
264 
265 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
266  r->n[0] = a;
267  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;
268 #ifdef VERIFY
269  r->magnitude = 1;
270  r->normalized = 1;
271  secp256k1_fe_verify(r);
272 #endif
273 }
274 
275 SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
276  const uint32_t *t = a->n;
277 #ifdef VERIFY
278  VERIFY_CHECK(a->normalized);
279  secp256k1_fe_verify(a);
280 #endif
281  return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
282 }
283 
284 SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
285 #ifdef VERIFY
286  VERIFY_CHECK(a->normalized);
287  secp256k1_fe_verify(a);
288 #endif
289  return a->n[0] & 1;
290 }
291 
292 SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
293  int i;
294 #ifdef VERIFY
295  a->magnitude = 0;
296  a->normalized = 1;
297 #endif
298  for (i=0; i<10; i++) {
299  a->n[i] = 0;
300  }
301 }
302 
303 static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
304  int i;
305 #ifdef VERIFY
306  VERIFY_CHECK(a->normalized);
307  VERIFY_CHECK(b->normalized);
308  secp256k1_fe_verify(a);
309  secp256k1_fe_verify(b);
310 #endif
311  for (i = 9; i >= 0; i--) {
312  if (a->n[i] > b->n[i]) {
313  return 1;
314  }
315  if (a->n[i] < b->n[i]) {
316  return -1;
317  }
318  }
319  return 0;
320 }
321 
322 static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
323  r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
324  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);
325  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);
326  r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18);
327  r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24);
328  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);
329  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);
330  r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
331  r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
332  r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
333 
334  if (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) {
335  return 0;
336  }
337 #ifdef VERIFY
338  r->magnitude = 1;
339  r->normalized = 1;
340  secp256k1_fe_verify(r);
341 #endif
342  return 1;
343 }
344 
346 static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
347 #ifdef VERIFY
348  VERIFY_CHECK(a->normalized);
349  secp256k1_fe_verify(a);
350 #endif
351  r[0] = (a->n[9] >> 14) & 0xff;
352  r[1] = (a->n[9] >> 6) & 0xff;
353  r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3);
354  r[3] = (a->n[8] >> 16) & 0xff;
355  r[4] = (a->n[8] >> 8) & 0xff;
356  r[5] = a->n[8] & 0xff;
357  r[6] = (a->n[7] >> 18) & 0xff;
358  r[7] = (a->n[7] >> 10) & 0xff;
359  r[8] = (a->n[7] >> 2) & 0xff;
360  r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f);
361  r[10] = (a->n[6] >> 12) & 0xff;
362  r[11] = (a->n[6] >> 4) & 0xff;
363  r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf);
364  r[13] = (a->n[5] >> 14) & 0xff;
365  r[14] = (a->n[5] >> 6) & 0xff;
366  r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3);
367  r[16] = (a->n[4] >> 16) & 0xff;
368  r[17] = (a->n[4] >> 8) & 0xff;
369  r[18] = a->n[4] & 0xff;
370  r[19] = (a->n[3] >> 18) & 0xff;
371  r[20] = (a->n[3] >> 10) & 0xff;
372  r[21] = (a->n[3] >> 2) & 0xff;
373  r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f);
374  r[23] = (a->n[2] >> 12) & 0xff;
375  r[24] = (a->n[2] >> 4) & 0xff;
376  r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf);
377  r[26] = (a->n[1] >> 14) & 0xff;
378  r[27] = (a->n[1] >> 6) & 0xff;
379  r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3);
380  r[29] = (a->n[0] >> 16) & 0xff;
381  r[30] = (a->n[0] >> 8) & 0xff;
382  r[31] = a->n[0] & 0xff;
383 }
384 
385 SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
386 #ifdef VERIFY
387  VERIFY_CHECK(a->magnitude <= m);
388  secp256k1_fe_verify(a);
389 #endif
390  r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
391  r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
392  r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
393  r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
394  r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
395  r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
396  r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
397  r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
398  r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
399  r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
400 #ifdef VERIFY
401  r->magnitude = m + 1;
402  r->normalized = 0;
403  secp256k1_fe_verify(r);
404 #endif
405 }
406 
407 SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
408  r->n[0] *= a;
409  r->n[1] *= a;
410  r->n[2] *= a;
411  r->n[3] *= a;
412  r->n[4] *= a;
413  r->n[5] *= a;
414  r->n[6] *= a;
415  r->n[7] *= a;
416  r->n[8] *= a;
417  r->n[9] *= a;
418 #ifdef VERIFY
419  r->magnitude *= a;
420  r->normalized = 0;
421  secp256k1_fe_verify(r);
422 #endif
423 }
424 
425 SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
426 #ifdef VERIFY
427  secp256k1_fe_verify(a);
428 #endif
429  r->n[0] += a->n[0];
430  r->n[1] += a->n[1];
431  r->n[2] += a->n[2];
432  r->n[3] += a->n[3];
433  r->n[4] += a->n[4];
434  r->n[5] += a->n[5];
435  r->n[6] += a->n[6];
436  r->n[7] += a->n[7];
437  r->n[8] += a->n[8];
438  r->n[9] += a->n[9];
439 #ifdef VERIFY
440  r->magnitude += a->magnitude;
441  r->normalized = 0;
442  secp256k1_fe_verify(r);
443 #endif
444 }
445 
446 #if defined(USE_EXTERNAL_ASM)
447 
448 /* External assembler implementation */
449 void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
450 void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
451 
452 #else
453 
454 #ifdef VERIFY
455 #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
456 #else
457 #define VERIFY_BITS(x, n) do { } while(0)
458 #endif
459 
460 SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
461  uint64_t c, d;
462  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
463  uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
464  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
465 
466  VERIFY_BITS(a[0], 30);
467  VERIFY_BITS(a[1], 30);
468  VERIFY_BITS(a[2], 30);
469  VERIFY_BITS(a[3], 30);
470  VERIFY_BITS(a[4], 30);
471  VERIFY_BITS(a[5], 30);
472  VERIFY_BITS(a[6], 30);
473  VERIFY_BITS(a[7], 30);
474  VERIFY_BITS(a[8], 30);
475  VERIFY_BITS(a[9], 26);
476  VERIFY_BITS(b[0], 30);
477  VERIFY_BITS(b[1], 30);
478  VERIFY_BITS(b[2], 30);
479  VERIFY_BITS(b[3], 30);
480  VERIFY_BITS(b[4], 30);
481  VERIFY_BITS(b[5], 30);
482  VERIFY_BITS(b[6], 30);
483  VERIFY_BITS(b[7], 30);
484  VERIFY_BITS(b[8], 30);
485  VERIFY_BITS(b[9], 26);
486 
493  d = (uint64_t)a[0] * b[9]
494  + (uint64_t)a[1] * b[8]
495  + (uint64_t)a[2] * b[7]
496  + (uint64_t)a[3] * b[6]
497  + (uint64_t)a[4] * b[5]
498  + (uint64_t)a[5] * b[4]
499  + (uint64_t)a[6] * b[3]
500  + (uint64_t)a[7] * b[2]
501  + (uint64_t)a[8] * b[1]
502  + (uint64_t)a[9] * b[0];
503  /* VERIFY_BITS(d, 64); */
504  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
505  t9 = d & M; d >>= 26;
506  VERIFY_BITS(t9, 26);
507  VERIFY_BITS(d, 38);
508  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
509 
510  c = (uint64_t)a[0] * b[0];
511  VERIFY_BITS(c, 60);
512  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
513  d += (uint64_t)a[1] * b[9]
514  + (uint64_t)a[2] * b[8]
515  + (uint64_t)a[3] * b[7]
516  + (uint64_t)a[4] * b[6]
517  + (uint64_t)a[5] * b[5]
518  + (uint64_t)a[6] * b[4]
519  + (uint64_t)a[7] * b[3]
520  + (uint64_t)a[8] * b[2]
521  + (uint64_t)a[9] * b[1];
522  VERIFY_BITS(d, 63);
523  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
524  u0 = d & M; d >>= 26; c += u0 * R0;
525  VERIFY_BITS(u0, 26);
526  VERIFY_BITS(d, 37);
527  VERIFY_BITS(c, 61);
528  /* [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] */
529  t0 = c & M; c >>= 26; c += u0 * R1;
530  VERIFY_BITS(t0, 26);
531  VERIFY_BITS(c, 37);
532  /* [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] */
533  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
534 
535  c += (uint64_t)a[0] * b[1]
536  + (uint64_t)a[1] * b[0];
537  VERIFY_BITS(c, 62);
538  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
539  d += (uint64_t)a[2] * b[9]
540  + (uint64_t)a[3] * b[8]
541  + (uint64_t)a[4] * b[7]
542  + (uint64_t)a[5] * b[6]
543  + (uint64_t)a[6] * b[5]
544  + (uint64_t)a[7] * b[4]
545  + (uint64_t)a[8] * b[3]
546  + (uint64_t)a[9] * b[2];
547  VERIFY_BITS(d, 63);
548  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
549  u1 = d & M; d >>= 26; c += u1 * R0;
550  VERIFY_BITS(u1, 26);
551  VERIFY_BITS(d, 37);
552  VERIFY_BITS(c, 63);
553  /* [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] */
554  t1 = c & M; c >>= 26; c += u1 * R1;
555  VERIFY_BITS(t1, 26);
556  VERIFY_BITS(c, 38);
557  /* [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] */
558  /* [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] */
559 
560  c += (uint64_t)a[0] * b[2]
561  + (uint64_t)a[1] * b[1]
562  + (uint64_t)a[2] * b[0];
563  VERIFY_BITS(c, 62);
564  /* [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] */
565  d += (uint64_t)a[3] * b[9]
566  + (uint64_t)a[4] * b[8]
567  + (uint64_t)a[5] * b[7]
568  + (uint64_t)a[6] * b[6]
569  + (uint64_t)a[7] * b[5]
570  + (uint64_t)a[8] * b[4]
571  + (uint64_t)a[9] * b[3];
572  VERIFY_BITS(d, 63);
573  /* [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] */
574  u2 = d & M; d >>= 26; c += u2 * R0;
575  VERIFY_BITS(u2, 26);
576  VERIFY_BITS(d, 37);
577  VERIFY_BITS(c, 63);
578  /* [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] */
579  t2 = c & M; c >>= 26; c += u2 * R1;
580  VERIFY_BITS(t2, 26);
581  VERIFY_BITS(c, 38);
582  /* [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] */
583  /* [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] */
584 
585  c += (uint64_t)a[0] * b[3]
586  + (uint64_t)a[1] * b[2]
587  + (uint64_t)a[2] * b[1]
588  + (uint64_t)a[3] * b[0];
589  VERIFY_BITS(c, 63);
590  /* [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] */
591  d += (uint64_t)a[4] * b[9]
592  + (uint64_t)a[5] * b[8]
593  + (uint64_t)a[6] * b[7]
594  + (uint64_t)a[7] * b[6]
595  + (uint64_t)a[8] * b[5]
596  + (uint64_t)a[9] * b[4];
597  VERIFY_BITS(d, 63);
598  /* [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] */
599  u3 = d & M; d >>= 26; c += u3 * R0;
600  VERIFY_BITS(u3, 26);
601  VERIFY_BITS(d, 37);
602  /* VERIFY_BITS(c, 64); */
603  /* [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] */
604  t3 = c & M; c >>= 26; c += u3 * R1;
605  VERIFY_BITS(t3, 26);
606  VERIFY_BITS(c, 39);
607  /* [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] */
608  /* [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] */
609 
610  c += (uint64_t)a[0] * b[4]
611  + (uint64_t)a[1] * b[3]
612  + (uint64_t)a[2] * b[2]
613  + (uint64_t)a[3] * b[1]
614  + (uint64_t)a[4] * b[0];
615  VERIFY_BITS(c, 63);
616  /* [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] */
617  d += (uint64_t)a[5] * b[9]
618  + (uint64_t)a[6] * b[8]
619  + (uint64_t)a[7] * b[7]
620  + (uint64_t)a[8] * b[6]
621  + (uint64_t)a[9] * b[5];
622  VERIFY_BITS(d, 62);
623  /* [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] */
624  u4 = d & M; d >>= 26; c += u4 * R0;
625  VERIFY_BITS(u4, 26);
626  VERIFY_BITS(d, 36);
627  /* VERIFY_BITS(c, 64); */
628  /* [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] */
629  t4 = c & M; c >>= 26; c += u4 * R1;
630  VERIFY_BITS(t4, 26);
631  VERIFY_BITS(c, 39);
632  /* [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] */
633  /* [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] */
634 
635  c += (uint64_t)a[0] * b[5]
636  + (uint64_t)a[1] * b[4]
637  + (uint64_t)a[2] * b[3]
638  + (uint64_t)a[3] * b[2]
639  + (uint64_t)a[4] * b[1]
640  + (uint64_t)a[5] * b[0];
641  VERIFY_BITS(c, 63);
642  /* [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] */
643  d += (uint64_t)a[6] * b[9]
644  + (uint64_t)a[7] * b[8]
645  + (uint64_t)a[8] * b[7]
646  + (uint64_t)a[9] * b[6];
647  VERIFY_BITS(d, 62);
648  /* [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] */
649  u5 = d & M; d >>= 26; c += u5 * R0;
650  VERIFY_BITS(u5, 26);
651  VERIFY_BITS(d, 36);
652  /* VERIFY_BITS(c, 64); */
653  /* [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] */
654  t5 = c & M; c >>= 26; c += u5 * R1;
655  VERIFY_BITS(t5, 26);
656  VERIFY_BITS(c, 39);
657  /* [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] */
658  /* [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] */
659 
660  c += (uint64_t)a[0] * b[6]
661  + (uint64_t)a[1] * b[5]
662  + (uint64_t)a[2] * b[4]
663  + (uint64_t)a[3] * b[3]
664  + (uint64_t)a[4] * b[2]
665  + (uint64_t)a[5] * b[1]
666  + (uint64_t)a[6] * b[0];
667  VERIFY_BITS(c, 63);
668  /* [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] */
669  d += (uint64_t)a[7] * b[9]
670  + (uint64_t)a[8] * b[8]
671  + (uint64_t)a[9] * b[7];
672  VERIFY_BITS(d, 61);
673  /* [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] */
674  u6 = d & M; d >>= 26; c += u6 * R0;
675  VERIFY_BITS(u6, 26);
676  VERIFY_BITS(d, 35);
677  /* VERIFY_BITS(c, 64); */
678  /* [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] */
679  t6 = c & M; c >>= 26; c += u6 * R1;
680  VERIFY_BITS(t6, 26);
681  VERIFY_BITS(c, 39);
682  /* [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] */
683  /* [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] */
684 
685  c += (uint64_t)a[0] * b[7]
686  + (uint64_t)a[1] * b[6]
687  + (uint64_t)a[2] * b[5]
688  + (uint64_t)a[3] * b[4]
689  + (uint64_t)a[4] * b[3]
690  + (uint64_t)a[5] * b[2]
691  + (uint64_t)a[6] * b[1]
692  + (uint64_t)a[7] * b[0];
693  /* VERIFY_BITS(c, 64); */
694  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
695  /* [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] */
696  d += (uint64_t)a[8] * b[9]
697  + (uint64_t)a[9] * b[8];
698  VERIFY_BITS(d, 58);
699  /* [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] */
700  u7 = d & M; d >>= 26; c += u7 * R0;
701  VERIFY_BITS(u7, 26);
702  VERIFY_BITS(d, 32);
703  /* VERIFY_BITS(c, 64); */
704  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
705  /* [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] */
706  t7 = c & M; c >>= 26; c += u7 * R1;
707  VERIFY_BITS(t7, 26);
708  VERIFY_BITS(c, 38);
709  /* [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] */
710  /* [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] */
711 
712  c += (uint64_t)a[0] * b[8]
713  + (uint64_t)a[1] * b[7]
714  + (uint64_t)a[2] * b[6]
715  + (uint64_t)a[3] * b[5]
716  + (uint64_t)a[4] * b[4]
717  + (uint64_t)a[5] * b[3]
718  + (uint64_t)a[6] * b[2]
719  + (uint64_t)a[7] * b[1]
720  + (uint64_t)a[8] * b[0];
721  /* VERIFY_BITS(c, 64); */
722  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
723  /* [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] */
724  d += (uint64_t)a[9] * b[9];
725  VERIFY_BITS(d, 57);
726  /* [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] */
727  u8 = d & M; d >>= 26; c += u8 * R0;
728  VERIFY_BITS(u8, 26);
729  VERIFY_BITS(d, 31);
730  /* VERIFY_BITS(c, 64); */
731  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
732  /* [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] */
733 
734  r[3] = t3;
735  VERIFY_BITS(r[3], 26);
736  /* [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] */
737  r[4] = t4;
738  VERIFY_BITS(r[4], 26);
739  /* [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] */
740  r[5] = t5;
741  VERIFY_BITS(r[5], 26);
742  /* [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] */
743  r[6] = t6;
744  VERIFY_BITS(r[6], 26);
745  /* [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] */
746  r[7] = t7;
747  VERIFY_BITS(r[7], 26);
748  /* [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] */
749 
750  r[8] = c & M; c >>= 26; c += u8 * R1;
751  VERIFY_BITS(r[8], 26);
752  VERIFY_BITS(c, 39);
753  /* [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] */
754  /* [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] */
755  c += d * R0 + t9;
756  VERIFY_BITS(c, 45);
757  /* [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] */
758  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
759  VERIFY_BITS(r[9], 22);
760  VERIFY_BITS(c, 46);
761  /* [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] */
762  /* [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] */
763  /* [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] */
764 
765  d = c * (R0 >> 4) + t0;
766  VERIFY_BITS(d, 56);
767  /* [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] */
768  r[0] = d & M; d >>= 26;
769  VERIFY_BITS(r[0], 26);
770  VERIFY_BITS(d, 30);
771  /* [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] */
772  d += c * (R1 >> 4) + t1;
773  VERIFY_BITS(d, 53);
774  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
775  /* [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] */
776  /* [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] */
777  r[1] = d & M; d >>= 26;
778  VERIFY_BITS(r[1], 26);
779  VERIFY_BITS(d, 27);
780  VERIFY_CHECK(d <= 0x4000000ULL);
781  /* [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] */
782  d += t2;
783  VERIFY_BITS(d, 27);
784  /* [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] */
785  r[2] = d;
786  VERIFY_BITS(r[2], 27);
787  /* [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] */
788 }
789 
790 SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
791  uint64_t c, d;
792  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
793  uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
794  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
795 
796  VERIFY_BITS(a[0], 30);
797  VERIFY_BITS(a[1], 30);
798  VERIFY_BITS(a[2], 30);
799  VERIFY_BITS(a[3], 30);
800  VERIFY_BITS(a[4], 30);
801  VERIFY_BITS(a[5], 30);
802  VERIFY_BITS(a[6], 30);
803  VERIFY_BITS(a[7], 30);
804  VERIFY_BITS(a[8], 30);
805  VERIFY_BITS(a[9], 26);
806 
812  d = (uint64_t)(a[0]*2) * a[9]
813  + (uint64_t)(a[1]*2) * a[8]
814  + (uint64_t)(a[2]*2) * a[7]
815  + (uint64_t)(a[3]*2) * a[6]
816  + (uint64_t)(a[4]*2) * a[5];
817  /* VERIFY_BITS(d, 64); */
818  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
819  t9 = d & M; d >>= 26;
820  VERIFY_BITS(t9, 26);
821  VERIFY_BITS(d, 38);
822  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
823 
824  c = (uint64_t)a[0] * a[0];
825  VERIFY_BITS(c, 60);
826  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
827  d += (uint64_t)(a[1]*2) * a[9]
828  + (uint64_t)(a[2]*2) * a[8]
829  + (uint64_t)(a[3]*2) * a[7]
830  + (uint64_t)(a[4]*2) * a[6]
831  + (uint64_t)a[5] * a[5];
832  VERIFY_BITS(d, 63);
833  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
834  u0 = d & M; d >>= 26; c += u0 * R0;
835  VERIFY_BITS(u0, 26);
836  VERIFY_BITS(d, 37);
837  VERIFY_BITS(c, 61);
838  /* [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] */
839  t0 = c & M; c >>= 26; c += u0 * R1;
840  VERIFY_BITS(t0, 26);
841  VERIFY_BITS(c, 37);
842  /* [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] */
843  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
844 
845  c += (uint64_t)(a[0]*2) * a[1];
846  VERIFY_BITS(c, 62);
847  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
848  d += (uint64_t)(a[2]*2) * a[9]
849  + (uint64_t)(a[3]*2) * a[8]
850  + (uint64_t)(a[4]*2) * a[7]
851  + (uint64_t)(a[5]*2) * a[6];
852  VERIFY_BITS(d, 63);
853  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
854  u1 = d & M; d >>= 26; c += u1 * R0;
855  VERIFY_BITS(u1, 26);
856  VERIFY_BITS(d, 37);
857  VERIFY_BITS(c, 63);
858  /* [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] */
859  t1 = c & M; c >>= 26; c += u1 * R1;
860  VERIFY_BITS(t1, 26);
861  VERIFY_BITS(c, 38);
862  /* [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] */
863  /* [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] */
864 
865  c += (uint64_t)(a[0]*2) * a[2]
866  + (uint64_t)a[1] * a[1];
867  VERIFY_BITS(c, 62);
868  /* [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] */
869  d += (uint64_t)(a[3]*2) * a[9]
870  + (uint64_t)(a[4]*2) * a[8]
871  + (uint64_t)(a[5]*2) * a[7]
872  + (uint64_t)a[6] * a[6];
873  VERIFY_BITS(d, 63);
874  /* [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] */
875  u2 = d & M; d >>= 26; c += u2 * R0;
876  VERIFY_BITS(u2, 26);
877  VERIFY_BITS(d, 37);
878  VERIFY_BITS(c, 63);
879  /* [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] */
880  t2 = c & M; c >>= 26; c += u2 * R1;
881  VERIFY_BITS(t2, 26);
882  VERIFY_BITS(c, 38);
883  /* [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] */
884  /* [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] */
885 
886  c += (uint64_t)(a[0]*2) * a[3]
887  + (uint64_t)(a[1]*2) * a[2];
888  VERIFY_BITS(c, 63);
889  /* [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] */
890  d += (uint64_t)(a[4]*2) * a[9]
891  + (uint64_t)(a[5]*2) * a[8]
892  + (uint64_t)(a[6]*2) * a[7];
893  VERIFY_BITS(d, 63);
894  /* [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] */
895  u3 = d & M; d >>= 26; c += u3 * R0;
896  VERIFY_BITS(u3, 26);
897  VERIFY_BITS(d, 37);
898  /* VERIFY_BITS(c, 64); */
899  /* [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] */
900  t3 = c & M; c >>= 26; c += u3 * R1;
901  VERIFY_BITS(t3, 26);
902  VERIFY_BITS(c, 39);
903  /* [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] */
904  /* [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] */
905 
906  c += (uint64_t)(a[0]*2) * a[4]
907  + (uint64_t)(a[1]*2) * a[3]
908  + (uint64_t)a[2] * a[2];
909  VERIFY_BITS(c, 63);
910  /* [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] */
911  d += (uint64_t)(a[5]*2) * a[9]
912  + (uint64_t)(a[6]*2) * a[8]
913  + (uint64_t)a[7] * a[7];
914  VERIFY_BITS(d, 62);
915  /* [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] */
916  u4 = d & M; d >>= 26; c += u4 * R0;
917  VERIFY_BITS(u4, 26);
918  VERIFY_BITS(d, 36);
919  /* VERIFY_BITS(c, 64); */
920  /* [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] */
921  t4 = c & M; c >>= 26; c += u4 * R1;
922  VERIFY_BITS(t4, 26);
923  VERIFY_BITS(c, 39);
924  /* [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] */
925  /* [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] */
926 
927  c += (uint64_t)(a[0]*2) * a[5]
928  + (uint64_t)(a[1]*2) * a[4]
929  + (uint64_t)(a[2]*2) * a[3];
930  VERIFY_BITS(c, 63);
931  /* [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] */
932  d += (uint64_t)(a[6]*2) * a[9]
933  + (uint64_t)(a[7]*2) * a[8];
934  VERIFY_BITS(d, 62);
935  /* [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] */
936  u5 = d & M; d >>= 26; c += u5 * R0;
937  VERIFY_BITS(u5, 26);
938  VERIFY_BITS(d, 36);
939  /* VERIFY_BITS(c, 64); */
940  /* [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] */
941  t5 = c & M; c >>= 26; c += u5 * R1;
942  VERIFY_BITS(t5, 26);
943  VERIFY_BITS(c, 39);
944  /* [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] */
945  /* [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] */
946 
947  c += (uint64_t)(a[0]*2) * a[6]
948  + (uint64_t)(a[1]*2) * a[5]
949  + (uint64_t)(a[2]*2) * a[4]
950  + (uint64_t)a[3] * a[3];
951  VERIFY_BITS(c, 63);
952  /* [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] */
953  d += (uint64_t)(a[7]*2) * a[9]
954  + (uint64_t)a[8] * a[8];
955  VERIFY_BITS(d, 61);
956  /* [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] */
957  u6 = d & M; d >>= 26; c += u6 * R0;
958  VERIFY_BITS(u6, 26);
959  VERIFY_BITS(d, 35);
960  /* VERIFY_BITS(c, 64); */
961  /* [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] */
962  t6 = c & M; c >>= 26; c += u6 * R1;
963  VERIFY_BITS(t6, 26);
964  VERIFY_BITS(c, 39);
965  /* [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] */
966  /* [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] */
967 
968  c += (uint64_t)(a[0]*2) * a[7]
969  + (uint64_t)(a[1]*2) * a[6]
970  + (uint64_t)(a[2]*2) * a[5]
971  + (uint64_t)(a[3]*2) * a[4];
972  /* VERIFY_BITS(c, 64); */
973  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
974  /* [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] */
975  d += (uint64_t)(a[8]*2) * a[9];
976  VERIFY_BITS(d, 58);
977  /* [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] */
978  u7 = d & M; d >>= 26; c += u7 * R0;
979  VERIFY_BITS(u7, 26);
980  VERIFY_BITS(d, 32);
981  /* VERIFY_BITS(c, 64); */
982  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
983  /* [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] */
984  t7 = c & M; c >>= 26; c += u7 * R1;
985  VERIFY_BITS(t7, 26);
986  VERIFY_BITS(c, 38);
987  /* [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] */
988  /* [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] */
989 
990  c += (uint64_t)(a[0]*2) * a[8]
991  + (uint64_t)(a[1]*2) * a[7]
992  + (uint64_t)(a[2]*2) * a[6]
993  + (uint64_t)(a[3]*2) * a[5]
994  + (uint64_t)a[4] * a[4];
995  /* VERIFY_BITS(c, 64); */
996  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
997  /* [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] */
998  d += (uint64_t)a[9] * a[9];
999  VERIFY_BITS(d, 57);
1000  /* [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] */
1001  u8 = d & M; d >>= 26; c += u8 * R0;
1002  VERIFY_BITS(u8, 26);
1003  VERIFY_BITS(d, 31);
1004  /* VERIFY_BITS(c, 64); */
1005  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
1006  /* [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] */
1007 
1008  r[3] = t3;
1009  VERIFY_BITS(r[3], 26);
1010  /* [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] */
1011  r[4] = t4;
1012  VERIFY_BITS(r[4], 26);
1013  /* [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] */
1014  r[5] = t5;
1015  VERIFY_BITS(r[5], 26);
1016  /* [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] */
1017  r[6] = t6;
1018  VERIFY_BITS(r[6], 26);
1019  /* [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] */
1020  r[7] = t7;
1021  VERIFY_BITS(r[7], 26);
1022  /* [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] */
1023 
1024  r[8] = c & M; c >>= 26; c += u8 * R1;
1025  VERIFY_BITS(r[8], 26);
1026  VERIFY_BITS(c, 39);
1027  /* [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] */
1028  /* [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] */
1029  c += d * R0 + t9;
1030  VERIFY_BITS(c, 45);
1031  /* [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] */
1032  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
1033  VERIFY_BITS(r[9], 22);
1034  VERIFY_BITS(c, 46);
1035  /* [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] */
1036  /* [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] */
1037  /* [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] */
1038 
1039  d = c * (R0 >> 4) + t0;
1040  VERIFY_BITS(d, 56);
1041  /* [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] */
1042  r[0] = d & M; d >>= 26;
1043  VERIFY_BITS(r[0], 26);
1044  VERIFY_BITS(d, 30);
1045  /* [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] */
1046  d += c * (R1 >> 4) + t1;
1047  VERIFY_BITS(d, 53);
1048  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
1049  /* [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] */
1050  /* [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] */
1051  r[1] = d & M; d >>= 26;
1052  VERIFY_BITS(r[1], 26);
1053  VERIFY_BITS(d, 27);
1054  VERIFY_CHECK(d <= 0x4000000ULL);
1055  /* [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] */
1056  d += t2;
1057  VERIFY_BITS(d, 27);
1058  /* [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] */
1059  r[2] = d;
1060  VERIFY_BITS(r[2], 27);
1061  /* [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] */
1062 }
1063 #endif
1064 
1065 static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
1066 #ifdef VERIFY
1067  VERIFY_CHECK(a->magnitude <= 8);
1068  VERIFY_CHECK(b->magnitude <= 8);
1069  secp256k1_fe_verify(a);
1070  secp256k1_fe_verify(b);
1071  VERIFY_CHECK(r != b);
1072  VERIFY_CHECK(a != b);
1073 #endif
1074  secp256k1_fe_mul_inner(r->n, a->n, b->n);
1075 #ifdef VERIFY
1076  r->magnitude = 1;
1077  r->normalized = 0;
1078  secp256k1_fe_verify(r);
1079 #endif
1080 }
1081 
1082 static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
1083 #ifdef VERIFY
1084  VERIFY_CHECK(a->magnitude <= 8);
1085  secp256k1_fe_verify(a);
1086 #endif
1087  secp256k1_fe_sqr_inner(r->n, a->n);
1088 #ifdef VERIFY
1089  r->magnitude = 1;
1090  r->normalized = 0;
1091  secp256k1_fe_verify(r);
1092 #endif
1093 }
1094 
1095 static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
1096  uint32_t mask0, mask1;
1097  mask0 = flag + ~((uint32_t)0);
1098  mask1 = ~mask0;
1099  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1100  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1101  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1102  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1103  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1104  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1105  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1106  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1107  r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
1108  r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
1109 #ifdef VERIFY
1110  if (a->magnitude > r->magnitude) {
1111  r->magnitude = a->magnitude;
1112  }
1113  r->normalized &= a->normalized;
1114 #endif
1115 }
1116 
1117 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
1118  uint32_t mask0, mask1;
1119  mask0 = flag + ~((uint32_t)0);
1120  mask1 = ~mask0;
1121  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1122  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1123  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1124  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1125  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1126  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1127  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1128  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1129 }
1130 
1131 static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
1132 #ifdef VERIFY
1133  VERIFY_CHECK(a->normalized);
1134 #endif
1135  r->n[0] = a->n[0] | a->n[1] << 26;
1136  r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
1137  r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
1138  r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
1139  r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
1140  r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
1141  r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
1142  r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
1143 }
1144 
1145 static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
1146  r->n[0] = a->n[0] & 0x3FFFFFFUL;
1147  r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
1148  r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
1149  r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
1150  r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
1151  r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
1152  r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
1153  r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
1154  r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
1155  r->n[9] = a->n[7] >> 10;
1156 #ifdef VERIFY
1157  r->magnitude = 1;
1158  r->normalized = 1;
1159 #endif
1160 }
1161 
1162 #endif /* SECP256K1_FIELD_REPR_IMPL_H */
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition: util.h:67
secp256k1_fe_from_storage
static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a)
Definition: field_10x26_impl.h:1145
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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:1065
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static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag)
Definition: field_10x26_impl.h:1117
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Definition: field_10x26.h:12
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static SECP256K1_INLINE void secp256k1_fe_clear(secp256k1_fe *a)
Definition: field_10x26_impl.h:292
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static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1131
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static SECP256K1_INLINE void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a)
Definition: field_10x26_impl.h:790
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uint32_t n[8]
Definition: field_10x26.h:44
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static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a)
Definition: field_10x26_impl.h:322
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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:1095
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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:460
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m
Definition: linearize-data.py:266
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static SECP256K1_INLINE int secp256k1_fe_is_odd(const secp256k1_fe *a)
Definition: field_10x26_impl.h:284
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#define SECP256K1_INLINE
Definition: secp256k1.h:123
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static SECP256K1_INLINE void secp256k1_fe_mul_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:407
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unsigned int uint32_t
Definition: stdint.h:21
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static SECP256K1_INLINE void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:425
secp256k1_fe_normalize_weak
static void secp256k1_fe_normalize_weak(secp256k1_fe *r)
Definition: field_10x26_impl.h:97
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static void secp256k1_fe_normalize(secp256k1_fe *r)
Definition: field_10x26_impl.h:42
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unsigned long long uint64_t
Definition: stdint.h:22
secp256k1_fe_negate
static SECP256K1_INLINE void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m)
Definition: field_10x26_impl.h:385
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition: util.h:97
secp256k1_fe_cmp_var
static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b)
Definition: field_10x26_impl.h:303
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static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r)
Definition: field_10x26_impl.h:184
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uint32_t n[10]
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static SECP256K1_INLINE int secp256k1_fe_is_zero(const secp256k1_fe *a)
Definition: field_10x26_impl.h:275
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static void secp256k1_fe_normalize_var(secp256k1_fe *r)
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static SECP256K1_INLINE void secp256k1_fe_set_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:265
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#define VERIFY_BITS(x, n)
Definition: field_10x26_impl.h:457
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static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r)
Definition: field_10x26_impl.h:213
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Definition: field_10x26.h:43
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static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:346
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static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1082
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