Bitcoin Core  27.99.0
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 "checkmem.h"
11 #include "util.h"
12 #include "field.h"
13 #include "modinv32_impl.h"
14 
15 #ifdef VERIFY
16 static void secp256k1_fe_impl_verify(const secp256k1_fe *a) {
17  const uint32_t *d = a->n;
18  int m = a->normalized ? 1 : 2 * a->magnitude;
19  VERIFY_CHECK(d[0] <= 0x3FFFFFFUL * m);
20  VERIFY_CHECK(d[1] <= 0x3FFFFFFUL * m);
21  VERIFY_CHECK(d[2] <= 0x3FFFFFFUL * m);
22  VERIFY_CHECK(d[3] <= 0x3FFFFFFUL * m);
23  VERIFY_CHECK(d[4] <= 0x3FFFFFFUL * m);
24  VERIFY_CHECK(d[5] <= 0x3FFFFFFUL * m);
25  VERIFY_CHECK(d[6] <= 0x3FFFFFFUL * m);
26  VERIFY_CHECK(d[7] <= 0x3FFFFFFUL * m);
27  VERIFY_CHECK(d[8] <= 0x3FFFFFFUL * m);
28  VERIFY_CHECK(d[9] <= 0x03FFFFFUL * m);
29  if (a->normalized) {
30  if (d[9] == 0x03FFFFFUL) {
31  uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
32  if (mid == 0x3FFFFFFUL) {
33  VERIFY_CHECK((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
34  }
35  }
36  }
37 }
38 #endif
39 
40 static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m) {
41  r->n[0] = 0x3FFFFFFUL * 2 * m;
42  r->n[1] = 0x3FFFFFFUL * 2 * m;
43  r->n[2] = 0x3FFFFFFUL * 2 * m;
44  r->n[3] = 0x3FFFFFFUL * 2 * m;
45  r->n[4] = 0x3FFFFFFUL * 2 * m;
46  r->n[5] = 0x3FFFFFFUL * 2 * m;
47  r->n[6] = 0x3FFFFFFUL * 2 * m;
48  r->n[7] = 0x3FFFFFFUL * 2 * m;
49  r->n[8] = 0x3FFFFFFUL * 2 * m;
50  r->n[9] = 0x03FFFFFUL * 2 * m;
51 }
52 
53 static void secp256k1_fe_impl_normalize(secp256k1_fe *r) {
54  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
55  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
56 
57  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
58  uint32_t m;
59  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
60 
61  /* The first pass ensures the magnitude is 1, ... */
62  t0 += x * 0x3D1UL; t1 += (x << 6);
63  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
64  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
65  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
66  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
67  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
68  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
69  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
70  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
71  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
72 
73  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
74  VERIFY_CHECK(t9 >> 23 == 0);
75 
76  /* At most a single final reduction is needed; check if the value is >= the field characteristic */
77  x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
78  & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
79 
80  /* Apply the final reduction (for constant-time behaviour, we do it always) */
81  t0 += x * 0x3D1UL; t1 += (x << 6);
82  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
83  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
84  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
85  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
86  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
87  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
88  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
89  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
90  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
91 
92  /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
93  VERIFY_CHECK(t9 >> 22 == x);
94 
95  /* Mask off the possible multiple of 2^256 from the final reduction */
96  t9 &= 0x03FFFFFUL;
97 
98  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
99  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
100 }
101 
102 static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r) {
103  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
104  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
105 
106  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
107  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
108 
109  /* The first pass ensures the magnitude is 1, ... */
110  t0 += x * 0x3D1UL; t1 += (x << 6);
111  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
112  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
113  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
114  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
115  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
116  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
117  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
118  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
119  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
120 
121  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
122  VERIFY_CHECK(t9 >> 23 == 0);
123 
124  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
125  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
126 }
127 
128 static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r) {
129  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
130  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
131 
132  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
133  uint32_t m;
134  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
135 
136  /* The first pass ensures the magnitude is 1, ... */
137  t0 += x * 0x3D1UL; t1 += (x << 6);
138  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
139  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
140  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
141  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
142  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
143  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
144  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
145  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
146  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
147 
148  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
149  VERIFY_CHECK(t9 >> 23 == 0);
150 
151  /* At most a single final reduction is needed; check if the value is >= the field characteristic */
152  x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
153  & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
154 
155  if (x) {
156  t0 += 0x3D1UL; t1 += (x << 6);
157  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
158  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
159  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
160  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
161  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
162  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
163  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
164  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
165  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
166 
167  /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
168  VERIFY_CHECK(t9 >> 22 == x);
169 
170  /* Mask off the possible multiple of 2^256 from the final reduction */
171  t9 &= 0x03FFFFFUL;
172  }
173 
174  r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
175  r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
176 }
177 
178 static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r) {
179  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
180  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
181 
182  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
183  uint32_t z0, z1;
184 
185  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
186  uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
187 
188  /* The first pass ensures the magnitude is 1, ... */
189  t0 += x * 0x3D1UL; t1 += (x << 6);
190  t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL;
191  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
192  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
193  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
194  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
195  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
196  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
197  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
198  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
199  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
200 
201  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
202  VERIFY_CHECK(t9 >> 23 == 0);
203 
204  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
205 }
206 
207 static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r) {
208  uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
209  uint32_t z0, z1;
210  uint32_t x;
211 
212  t0 = r->n[0];
213  t9 = r->n[9];
214 
215  /* Reduce t9 at the start so there will be at most a single carry from the first pass */
216  x = t9 >> 22;
217 
218  /* The first pass ensures the magnitude is 1, ... */
219  t0 += x * 0x3D1UL;
220 
221  /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
222  z0 = t0 & 0x3FFFFFFUL;
223  z1 = z0 ^ 0x3D0UL;
224 
225  /* Fast return path should catch the majority of cases */
226  if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) {
227  return 0;
228  }
229 
230  t1 = r->n[1];
231  t2 = r->n[2];
232  t3 = r->n[3];
233  t4 = r->n[4];
234  t5 = r->n[5];
235  t6 = r->n[6];
236  t7 = r->n[7];
237  t8 = r->n[8];
238 
239  t9 &= 0x03FFFFFUL;
240  t1 += (x << 6);
241 
242  t1 += (t0 >> 26);
243  t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
244  t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
245  t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
246  t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
247  t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
248  t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
249  t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
250  t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
251  z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
252 
253  /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
254  VERIFY_CHECK(t9 >> 23 == 0);
255 
256  return (z0 == 0) | (z1 == 0x3FFFFFFUL);
257 }
258 
259 SECP256K1_INLINE static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a) {
260  r->n[0] = a;
261  r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
262 }
263 
264 SECP256K1_INLINE static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a) {
265  const uint32_t *t = a->n;
266  return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
267 }
268 
269 SECP256K1_INLINE static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a) {
270  return a->n[0] & 1;
271 }
272 
273 SECP256K1_INLINE static void secp256k1_fe_impl_clear(secp256k1_fe *a) {
274  int i;
275  for (i=0; i<10; i++) {
276  a->n[i] = 0;
277  }
278 }
279 
280 static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
281  int i;
282  for (i = 9; i >= 0; i--) {
283  if (a->n[i] > b->n[i]) {
284  return 1;
285  }
286  if (a->n[i] < b->n[i]) {
287  return -1;
288  }
289  }
290  return 0;
291 }
292 
293 static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
294  r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
295  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);
296  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);
297  r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18);
298  r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24);
299  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);
300  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);
301  r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
302  r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
303  r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
304 }
305 
306 static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
307  secp256k1_fe_impl_set_b32_mod(r, a);
308  return !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
309 }
310 
312 static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a) {
313  r[0] = (a->n[9] >> 14) & 0xff;
314  r[1] = (a->n[9] >> 6) & 0xff;
315  r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3);
316  r[3] = (a->n[8] >> 16) & 0xff;
317  r[4] = (a->n[8] >> 8) & 0xff;
318  r[5] = a->n[8] & 0xff;
319  r[6] = (a->n[7] >> 18) & 0xff;
320  r[7] = (a->n[7] >> 10) & 0xff;
321  r[8] = (a->n[7] >> 2) & 0xff;
322  r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f);
323  r[10] = (a->n[6] >> 12) & 0xff;
324  r[11] = (a->n[6] >> 4) & 0xff;
325  r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf);
326  r[13] = (a->n[5] >> 14) & 0xff;
327  r[14] = (a->n[5] >> 6) & 0xff;
328  r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3);
329  r[16] = (a->n[4] >> 16) & 0xff;
330  r[17] = (a->n[4] >> 8) & 0xff;
331  r[18] = a->n[4] & 0xff;
332  r[19] = (a->n[3] >> 18) & 0xff;
333  r[20] = (a->n[3] >> 10) & 0xff;
334  r[21] = (a->n[3] >> 2) & 0xff;
335  r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f);
336  r[23] = (a->n[2] >> 12) & 0xff;
337  r[24] = (a->n[2] >> 4) & 0xff;
338  r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf);
339  r[26] = (a->n[1] >> 14) & 0xff;
340  r[27] = (a->n[1] >> 6) & 0xff;
341  r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3);
342  r[29] = (a->n[0] >> 16) & 0xff;
343  r[30] = (a->n[0] >> 8) & 0xff;
344  r[31] = a->n[0] & 0xff;
345 }
346 
347 SECP256K1_INLINE static void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m) {
348  /* For all legal values of m (0..31), the following properties hold: */
349  VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
350  VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
351  VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
352  VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m);
353 
354  /* Due to the properties above, the left hand in the subtractions below is never less than
355  * the right hand. */
356  r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
357  r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
358  r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
359  r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
360  r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
361  r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
362  r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
363  r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
364  r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
365  r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
366 }
367 
368 SECP256K1_INLINE static void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a) {
369  r->n[0] *= a;
370  r->n[1] *= a;
371  r->n[2] *= a;
372  r->n[3] *= a;
373  r->n[4] *= a;
374  r->n[5] *= a;
375  r->n[6] *= a;
376  r->n[7] *= a;
377  r->n[8] *= a;
378  r->n[9] *= a;
379 }
380 
381 SECP256K1_INLINE static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a) {
382  r->n[0] += a->n[0];
383  r->n[1] += a->n[1];
384  r->n[2] += a->n[2];
385  r->n[3] += a->n[3];
386  r->n[4] += a->n[4];
387  r->n[5] += a->n[5];
388  r->n[6] += a->n[6];
389  r->n[7] += a->n[7];
390  r->n[8] += a->n[8];
391  r->n[9] += a->n[9];
392 }
393 
394 SECP256K1_INLINE static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a) {
395  r->n[0] += a;
396 }
397 
398 #if defined(USE_EXTERNAL_ASM)
399 
400 /* External assembler implementation */
401 void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
402 void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
403 
404 #else
405 
406 #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
407 
408 SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
409  uint64_t c, d;
410  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
411  uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
412  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
413 
414  VERIFY_BITS(a[0], 30);
415  VERIFY_BITS(a[1], 30);
416  VERIFY_BITS(a[2], 30);
417  VERIFY_BITS(a[3], 30);
418  VERIFY_BITS(a[4], 30);
419  VERIFY_BITS(a[5], 30);
420  VERIFY_BITS(a[6], 30);
421  VERIFY_BITS(a[7], 30);
422  VERIFY_BITS(a[8], 30);
423  VERIFY_BITS(a[9], 26);
424  VERIFY_BITS(b[0], 30);
425  VERIFY_BITS(b[1], 30);
426  VERIFY_BITS(b[2], 30);
427  VERIFY_BITS(b[3], 30);
428  VERIFY_BITS(b[4], 30);
429  VERIFY_BITS(b[5], 30);
430  VERIFY_BITS(b[6], 30);
431  VERIFY_BITS(b[7], 30);
432  VERIFY_BITS(b[8], 30);
433  VERIFY_BITS(b[9], 26);
434 
441  d = (uint64_t)a[0] * b[9]
442  + (uint64_t)a[1] * b[8]
443  + (uint64_t)a[2] * b[7]
444  + (uint64_t)a[3] * b[6]
445  + (uint64_t)a[4] * b[5]
446  + (uint64_t)a[5] * b[4]
447  + (uint64_t)a[6] * b[3]
448  + (uint64_t)a[7] * b[2]
449  + (uint64_t)a[8] * b[1]
450  + (uint64_t)a[9] * b[0];
451  /* VERIFY_BITS(d, 64); */
452  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
453  t9 = d & M; d >>= 26;
454  VERIFY_BITS(t9, 26);
455  VERIFY_BITS(d, 38);
456  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
457 
458  c = (uint64_t)a[0] * b[0];
459  VERIFY_BITS(c, 60);
460  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
461  d += (uint64_t)a[1] * b[9]
462  + (uint64_t)a[2] * b[8]
463  + (uint64_t)a[3] * b[7]
464  + (uint64_t)a[4] * b[6]
465  + (uint64_t)a[5] * b[5]
466  + (uint64_t)a[6] * b[4]
467  + (uint64_t)a[7] * b[3]
468  + (uint64_t)a[8] * b[2]
469  + (uint64_t)a[9] * b[1];
470  VERIFY_BITS(d, 63);
471  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
472  u0 = d & M; d >>= 26; c += u0 * R0;
473  VERIFY_BITS(u0, 26);
474  VERIFY_BITS(d, 37);
475  VERIFY_BITS(c, 61);
476  /* [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] */
477  t0 = c & M; c >>= 26; c += u0 * R1;
478  VERIFY_BITS(t0, 26);
479  VERIFY_BITS(c, 37);
480  /* [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] */
481  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
482 
483  c += (uint64_t)a[0] * b[1]
484  + (uint64_t)a[1] * b[0];
485  VERIFY_BITS(c, 62);
486  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
487  d += (uint64_t)a[2] * b[9]
488  + (uint64_t)a[3] * b[8]
489  + (uint64_t)a[4] * b[7]
490  + (uint64_t)a[5] * b[6]
491  + (uint64_t)a[6] * b[5]
492  + (uint64_t)a[7] * b[4]
493  + (uint64_t)a[8] * b[3]
494  + (uint64_t)a[9] * b[2];
495  VERIFY_BITS(d, 63);
496  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
497  u1 = d & M; d >>= 26; c += u1 * R0;
498  VERIFY_BITS(u1, 26);
499  VERIFY_BITS(d, 37);
500  VERIFY_BITS(c, 63);
501  /* [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] */
502  t1 = c & M; c >>= 26; c += u1 * R1;
503  VERIFY_BITS(t1, 26);
504  VERIFY_BITS(c, 38);
505  /* [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] */
506  /* [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] */
507 
508  c += (uint64_t)a[0] * b[2]
509  + (uint64_t)a[1] * b[1]
510  + (uint64_t)a[2] * b[0];
511  VERIFY_BITS(c, 62);
512  /* [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] */
513  d += (uint64_t)a[3] * b[9]
514  + (uint64_t)a[4] * b[8]
515  + (uint64_t)a[5] * b[7]
516  + (uint64_t)a[6] * b[6]
517  + (uint64_t)a[7] * b[5]
518  + (uint64_t)a[8] * b[4]
519  + (uint64_t)a[9] * b[3];
520  VERIFY_BITS(d, 63);
521  /* [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] */
522  u2 = d & M; d >>= 26; c += u2 * R0;
523  VERIFY_BITS(u2, 26);
524  VERIFY_BITS(d, 37);
525  VERIFY_BITS(c, 63);
526  /* [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] */
527  t2 = c & M; c >>= 26; c += u2 * R1;
528  VERIFY_BITS(t2, 26);
529  VERIFY_BITS(c, 38);
530  /* [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] */
531  /* [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] */
532 
533  c += (uint64_t)a[0] * b[3]
534  + (uint64_t)a[1] * b[2]
535  + (uint64_t)a[2] * b[1]
536  + (uint64_t)a[3] * b[0];
537  VERIFY_BITS(c, 63);
538  /* [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] */
539  d += (uint64_t)a[4] * b[9]
540  + (uint64_t)a[5] * b[8]
541  + (uint64_t)a[6] * b[7]
542  + (uint64_t)a[7] * b[6]
543  + (uint64_t)a[8] * b[5]
544  + (uint64_t)a[9] * b[4];
545  VERIFY_BITS(d, 63);
546  /* [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] */
547  u3 = d & M; d >>= 26; c += u3 * R0;
548  VERIFY_BITS(u3, 26);
549  VERIFY_BITS(d, 37);
550  /* VERIFY_BITS(c, 64); */
551  /* [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] */
552  t3 = c & M; c >>= 26; c += u3 * R1;
553  VERIFY_BITS(t3, 26);
554  VERIFY_BITS(c, 39);
555  /* [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] */
556  /* [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] */
557 
558  c += (uint64_t)a[0] * b[4]
559  + (uint64_t)a[1] * b[3]
560  + (uint64_t)a[2] * b[2]
561  + (uint64_t)a[3] * b[1]
562  + (uint64_t)a[4] * b[0];
563  VERIFY_BITS(c, 63);
564  /* [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] */
565  d += (uint64_t)a[5] * b[9]
566  + (uint64_t)a[6] * b[8]
567  + (uint64_t)a[7] * b[7]
568  + (uint64_t)a[8] * b[6]
569  + (uint64_t)a[9] * b[5];
570  VERIFY_BITS(d, 62);
571  /* [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] */
572  u4 = d & M; d >>= 26; c += u4 * R0;
573  VERIFY_BITS(u4, 26);
574  VERIFY_BITS(d, 36);
575  /* VERIFY_BITS(c, 64); */
576  /* [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] */
577  t4 = c & M; c >>= 26; c += u4 * R1;
578  VERIFY_BITS(t4, 26);
579  VERIFY_BITS(c, 39);
580  /* [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] */
581  /* [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] */
582 
583  c += (uint64_t)a[0] * b[5]
584  + (uint64_t)a[1] * b[4]
585  + (uint64_t)a[2] * b[3]
586  + (uint64_t)a[3] * b[2]
587  + (uint64_t)a[4] * b[1]
588  + (uint64_t)a[5] * b[0];
589  VERIFY_BITS(c, 63);
590  /* [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] */
591  d += (uint64_t)a[6] * b[9]
592  + (uint64_t)a[7] * b[8]
593  + (uint64_t)a[8] * b[7]
594  + (uint64_t)a[9] * b[6];
595  VERIFY_BITS(d, 62);
596  /* [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] */
597  u5 = d & M; d >>= 26; c += u5 * R0;
598  VERIFY_BITS(u5, 26);
599  VERIFY_BITS(d, 36);
600  /* VERIFY_BITS(c, 64); */
601  /* [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] */
602  t5 = c & M; c >>= 26; c += u5 * R1;
603  VERIFY_BITS(t5, 26);
604  VERIFY_BITS(c, 39);
605  /* [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] */
606  /* [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] */
607 
608  c += (uint64_t)a[0] * b[6]
609  + (uint64_t)a[1] * b[5]
610  + (uint64_t)a[2] * b[4]
611  + (uint64_t)a[3] * b[3]
612  + (uint64_t)a[4] * b[2]
613  + (uint64_t)a[5] * b[1]
614  + (uint64_t)a[6] * b[0];
615  VERIFY_BITS(c, 63);
616  /* [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] */
617  d += (uint64_t)a[7] * b[9]
618  + (uint64_t)a[8] * b[8]
619  + (uint64_t)a[9] * b[7];
620  VERIFY_BITS(d, 61);
621  /* [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] */
622  u6 = d & M; d >>= 26; c += u6 * R0;
623  VERIFY_BITS(u6, 26);
624  VERIFY_BITS(d, 35);
625  /* VERIFY_BITS(c, 64); */
626  /* [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] */
627  t6 = c & M; c >>= 26; c += u6 * R1;
628  VERIFY_BITS(t6, 26);
629  VERIFY_BITS(c, 39);
630  /* [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] */
631  /* [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] */
632 
633  c += (uint64_t)a[0] * b[7]
634  + (uint64_t)a[1] * b[6]
635  + (uint64_t)a[2] * b[5]
636  + (uint64_t)a[3] * b[4]
637  + (uint64_t)a[4] * b[3]
638  + (uint64_t)a[5] * b[2]
639  + (uint64_t)a[6] * b[1]
640  + (uint64_t)a[7] * b[0];
641  /* VERIFY_BITS(c, 64); */
642  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
643  /* [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] */
644  d += (uint64_t)a[8] * b[9]
645  + (uint64_t)a[9] * b[8];
646  VERIFY_BITS(d, 58);
647  /* [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] */
648  u7 = d & M; d >>= 26; c += u7 * R0;
649  VERIFY_BITS(u7, 26);
650  VERIFY_BITS(d, 32);
651  /* VERIFY_BITS(c, 64); */
652  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
653  /* [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] */
654  t7 = c & M; c >>= 26; c += u7 * R1;
655  VERIFY_BITS(t7, 26);
656  VERIFY_BITS(c, 38);
657  /* [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] */
658  /* [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] */
659 
660  c += (uint64_t)a[0] * b[8]
661  + (uint64_t)a[1] * b[7]
662  + (uint64_t)a[2] * b[6]
663  + (uint64_t)a[3] * b[5]
664  + (uint64_t)a[4] * b[4]
665  + (uint64_t)a[5] * b[3]
666  + (uint64_t)a[6] * b[2]
667  + (uint64_t)a[7] * b[1]
668  + (uint64_t)a[8] * b[0];
669  /* VERIFY_BITS(c, 64); */
670  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
671  /* [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] */
672  d += (uint64_t)a[9] * b[9];
673  VERIFY_BITS(d, 57);
674  /* [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] */
675  u8 = d & M; d >>= 26; c += u8 * R0;
676  VERIFY_BITS(u8, 26);
677  VERIFY_BITS(d, 31);
678  /* VERIFY_BITS(c, 64); */
679  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
680  /* [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] */
681 
682  r[3] = t3;
683  VERIFY_BITS(r[3], 26);
684  /* [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] */
685  r[4] = t4;
686  VERIFY_BITS(r[4], 26);
687  /* [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] */
688  r[5] = t5;
689  VERIFY_BITS(r[5], 26);
690  /* [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] */
691  r[6] = t6;
692  VERIFY_BITS(r[6], 26);
693  /* [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] */
694  r[7] = t7;
695  VERIFY_BITS(r[7], 26);
696  /* [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] */
697 
698  r[8] = c & M; c >>= 26; c += u8 * R1;
699  VERIFY_BITS(r[8], 26);
700  VERIFY_BITS(c, 39);
701  /* [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] */
702  /* [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] */
703  c += d * R0 + t9;
704  VERIFY_BITS(c, 45);
705  /* [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] */
706  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
707  VERIFY_BITS(r[9], 22);
708  VERIFY_BITS(c, 46);
709  /* [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] */
710  /* [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] */
711  /* [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] */
712 
713  d = c * (R0 >> 4) + t0;
714  VERIFY_BITS(d, 56);
715  /* [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] */
716  r[0] = d & M; d >>= 26;
717  VERIFY_BITS(r[0], 26);
718  VERIFY_BITS(d, 30);
719  /* [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] */
720  d += c * (R1 >> 4) + t1;
721  VERIFY_BITS(d, 53);
722  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
723  /* [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] */
724  /* [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] */
725  r[1] = d & M; d >>= 26;
726  VERIFY_BITS(r[1], 26);
727  VERIFY_BITS(d, 27);
728  VERIFY_CHECK(d <= 0x4000000ULL);
729  /* [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] */
730  d += t2;
731  VERIFY_BITS(d, 27);
732  /* [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] */
733  r[2] = d;
734  VERIFY_BITS(r[2], 27);
735  /* [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] */
736 }
737 
738 SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
739  uint64_t c, d;
740  uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
741  uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
742  const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
743 
744  VERIFY_BITS(a[0], 30);
745  VERIFY_BITS(a[1], 30);
746  VERIFY_BITS(a[2], 30);
747  VERIFY_BITS(a[3], 30);
748  VERIFY_BITS(a[4], 30);
749  VERIFY_BITS(a[5], 30);
750  VERIFY_BITS(a[6], 30);
751  VERIFY_BITS(a[7], 30);
752  VERIFY_BITS(a[8], 30);
753  VERIFY_BITS(a[9], 26);
754 
760  d = (uint64_t)(a[0]*2) * a[9]
761  + (uint64_t)(a[1]*2) * a[8]
762  + (uint64_t)(a[2]*2) * a[7]
763  + (uint64_t)(a[3]*2) * a[6]
764  + (uint64_t)(a[4]*2) * a[5];
765  /* VERIFY_BITS(d, 64); */
766  /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
767  t9 = d & M; d >>= 26;
768  VERIFY_BITS(t9, 26);
769  VERIFY_BITS(d, 38);
770  /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
771 
772  c = (uint64_t)a[0] * a[0];
773  VERIFY_BITS(c, 60);
774  /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
775  d += (uint64_t)(a[1]*2) * a[9]
776  + (uint64_t)(a[2]*2) * a[8]
777  + (uint64_t)(a[3]*2) * a[7]
778  + (uint64_t)(a[4]*2) * a[6]
779  + (uint64_t)a[5] * a[5];
780  VERIFY_BITS(d, 63);
781  /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
782  u0 = d & M; d >>= 26; c += u0 * R0;
783  VERIFY_BITS(u0, 26);
784  VERIFY_BITS(d, 37);
785  VERIFY_BITS(c, 61);
786  /* [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] */
787  t0 = c & M; c >>= 26; c += u0 * R1;
788  VERIFY_BITS(t0, 26);
789  VERIFY_BITS(c, 37);
790  /* [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] */
791  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
792 
793  c += (uint64_t)(a[0]*2) * a[1];
794  VERIFY_BITS(c, 62);
795  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
796  d += (uint64_t)(a[2]*2) * a[9]
797  + (uint64_t)(a[3]*2) * a[8]
798  + (uint64_t)(a[4]*2) * a[7]
799  + (uint64_t)(a[5]*2) * a[6];
800  VERIFY_BITS(d, 63);
801  /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
802  u1 = d & M; d >>= 26; c += u1 * R0;
803  VERIFY_BITS(u1, 26);
804  VERIFY_BITS(d, 37);
805  VERIFY_BITS(c, 63);
806  /* [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] */
807  t1 = c & M; c >>= 26; c += u1 * R1;
808  VERIFY_BITS(t1, 26);
809  VERIFY_BITS(c, 38);
810  /* [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] */
811  /* [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] */
812 
813  c += (uint64_t)(a[0]*2) * a[2]
814  + (uint64_t)a[1] * a[1];
815  VERIFY_BITS(c, 62);
816  /* [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] */
817  d += (uint64_t)(a[3]*2) * a[9]
818  + (uint64_t)(a[4]*2) * a[8]
819  + (uint64_t)(a[5]*2) * a[7]
820  + (uint64_t)a[6] * a[6];
821  VERIFY_BITS(d, 63);
822  /* [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] */
823  u2 = d & M; d >>= 26; c += u2 * R0;
824  VERIFY_BITS(u2, 26);
825  VERIFY_BITS(d, 37);
826  VERIFY_BITS(c, 63);
827  /* [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] */
828  t2 = c & M; c >>= 26; c += u2 * R1;
829  VERIFY_BITS(t2, 26);
830  VERIFY_BITS(c, 38);
831  /* [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] */
832  /* [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] */
833 
834  c += (uint64_t)(a[0]*2) * a[3]
835  + (uint64_t)(a[1]*2) * a[2];
836  VERIFY_BITS(c, 63);
837  /* [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] */
838  d += (uint64_t)(a[4]*2) * a[9]
839  + (uint64_t)(a[5]*2) * a[8]
840  + (uint64_t)(a[6]*2) * a[7];
841  VERIFY_BITS(d, 63);
842  /* [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] */
843  u3 = d & M; d >>= 26; c += u3 * R0;
844  VERIFY_BITS(u3, 26);
845  VERIFY_BITS(d, 37);
846  /* VERIFY_BITS(c, 64); */
847  /* [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] */
848  t3 = c & M; c >>= 26; c += u3 * R1;
849  VERIFY_BITS(t3, 26);
850  VERIFY_BITS(c, 39);
851  /* [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] */
852  /* [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] */
853 
854  c += (uint64_t)(a[0]*2) * a[4]
855  + (uint64_t)(a[1]*2) * a[3]
856  + (uint64_t)a[2] * a[2];
857  VERIFY_BITS(c, 63);
858  /* [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] */
859  d += (uint64_t)(a[5]*2) * a[9]
860  + (uint64_t)(a[6]*2) * a[8]
861  + (uint64_t)a[7] * a[7];
862  VERIFY_BITS(d, 62);
863  /* [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] */
864  u4 = d & M; d >>= 26; c += u4 * R0;
865  VERIFY_BITS(u4, 26);
866  VERIFY_BITS(d, 36);
867  /* VERIFY_BITS(c, 64); */
868  /* [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] */
869  t4 = c & M; c >>= 26; c += u4 * R1;
870  VERIFY_BITS(t4, 26);
871  VERIFY_BITS(c, 39);
872  /* [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] */
873  /* [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] */
874 
875  c += (uint64_t)(a[0]*2) * a[5]
876  + (uint64_t)(a[1]*2) * a[4]
877  + (uint64_t)(a[2]*2) * a[3];
878  VERIFY_BITS(c, 63);
879  /* [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] */
880  d += (uint64_t)(a[6]*2) * a[9]
881  + (uint64_t)(a[7]*2) * a[8];
882  VERIFY_BITS(d, 62);
883  /* [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] */
884  u5 = d & M; d >>= 26; c += u5 * R0;
885  VERIFY_BITS(u5, 26);
886  VERIFY_BITS(d, 36);
887  /* VERIFY_BITS(c, 64); */
888  /* [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] */
889  t5 = c & M; c >>= 26; c += u5 * R1;
890  VERIFY_BITS(t5, 26);
891  VERIFY_BITS(c, 39);
892  /* [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] */
893  /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
894 
895  c += (uint64_t)(a[0]*2) * a[6]
896  + (uint64_t)(a[1]*2) * a[5]
897  + (uint64_t)(a[2]*2) * a[4]
898  + (uint64_t)a[3] * a[3];
899  VERIFY_BITS(c, 63);
900  /* [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] */
901  d += (uint64_t)(a[7]*2) * a[9]
902  + (uint64_t)a[8] * a[8];
903  VERIFY_BITS(d, 61);
904  /* [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] */
905  u6 = d & M; d >>= 26; c += u6 * R0;
906  VERIFY_BITS(u6, 26);
907  VERIFY_BITS(d, 35);
908  /* VERIFY_BITS(c, 64); */
909  /* [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] */
910  t6 = c & M; c >>= 26; c += u6 * R1;
911  VERIFY_BITS(t6, 26);
912  VERIFY_BITS(c, 39);
913  /* [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] */
914  /* [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] */
915 
916  c += (uint64_t)(a[0]*2) * a[7]
917  + (uint64_t)(a[1]*2) * a[6]
918  + (uint64_t)(a[2]*2) * a[5]
919  + (uint64_t)(a[3]*2) * a[4];
920  /* VERIFY_BITS(c, 64); */
921  VERIFY_CHECK(c <= 0x8000007C00000007ULL);
922  /* [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] */
923  d += (uint64_t)(a[8]*2) * a[9];
924  VERIFY_BITS(d, 58);
925  /* [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] */
926  u7 = d & M; d >>= 26; c += u7 * R0;
927  VERIFY_BITS(u7, 26);
928  VERIFY_BITS(d, 32);
929  /* VERIFY_BITS(c, 64); */
930  VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
931  /* [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] */
932  t7 = c & M; c >>= 26; c += u7 * R1;
933  VERIFY_BITS(t7, 26);
934  VERIFY_BITS(c, 38);
935  /* [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] */
936  /* [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] */
937 
938  c += (uint64_t)(a[0]*2) * a[8]
939  + (uint64_t)(a[1]*2) * a[7]
940  + (uint64_t)(a[2]*2) * a[6]
941  + (uint64_t)(a[3]*2) * a[5]
942  + (uint64_t)a[4] * a[4];
943  /* VERIFY_BITS(c, 64); */
944  VERIFY_CHECK(c <= 0x9000007B80000008ULL);
945  /* [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] */
946  d += (uint64_t)a[9] * a[9];
947  VERIFY_BITS(d, 57);
948  /* [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] */
949  u8 = d & M; d >>= 26; c += u8 * R0;
950  VERIFY_BITS(u8, 26);
951  VERIFY_BITS(d, 31);
952  /* VERIFY_BITS(c, 64); */
953  VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
954  /* [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] */
955 
956  r[3] = t3;
957  VERIFY_BITS(r[3], 26);
958  /* [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] */
959  r[4] = t4;
960  VERIFY_BITS(r[4], 26);
961  /* [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] */
962  r[5] = t5;
963  VERIFY_BITS(r[5], 26);
964  /* [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] */
965  r[6] = t6;
966  VERIFY_BITS(r[6], 26);
967  /* [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] */
968  r[7] = t7;
969  VERIFY_BITS(r[7], 26);
970  /* [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] */
971 
972  r[8] = c & M; c >>= 26; c += u8 * R1;
973  VERIFY_BITS(r[8], 26);
974  VERIFY_BITS(c, 39);
975  /* [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] */
976  /* [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] */
977  c += d * R0 + t9;
978  VERIFY_BITS(c, 45);
979  /* [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] */
980  r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
981  VERIFY_BITS(r[9], 22);
982  VERIFY_BITS(c, 46);
983  /* [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] */
984  /* [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] */
985  /* [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] */
986 
987  d = c * (R0 >> 4) + t0;
988  VERIFY_BITS(d, 56);
989  /* [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] */
990  r[0] = d & M; d >>= 26;
991  VERIFY_BITS(r[0], 26);
992  VERIFY_BITS(d, 30);
993  /* [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] */
994  d += c * (R1 >> 4) + t1;
995  VERIFY_BITS(d, 53);
996  VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
997  /* [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] */
998  /* [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] */
999  r[1] = d & M; d >>= 26;
1000  VERIFY_BITS(r[1], 26);
1001  VERIFY_BITS(d, 27);
1002  VERIFY_CHECK(d <= 0x4000000ULL);
1003  /* [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] */
1004  d += t2;
1005  VERIFY_BITS(d, 27);
1006  /* [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] */
1007  r[2] = d;
1008  VERIFY_BITS(r[2], 27);
1009  /* [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] */
1010 }
1011 #endif
1012 
1013 SECP256K1_INLINE static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
1014  secp256k1_fe_mul_inner(r->n, a->n, b->n);
1015 }
1016 
1017 SECP256K1_INLINE static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
1018  secp256k1_fe_sqr_inner(r->n, a->n);
1019 }
1020 
1021 SECP256K1_INLINE static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
1022  uint32_t mask0, mask1;
1023  volatile int vflag = flag;
1024  SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
1025  mask0 = vflag + ~((uint32_t)0);
1026  mask1 = ~mask0;
1027  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1028  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1029  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1030  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1031  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1032  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1033  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1034  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1035  r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
1036  r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
1037 }
1038 
1039 static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r) {
1040  uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
1041  t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
1042  uint32_t one = (uint32_t)1;
1043  uint32_t mask = -(t0 & one) >> 6;
1044 
1045  /* Bounds analysis (over the rationals).
1046  *
1047  * Let m = r->magnitude
1048  * C = 0x3FFFFFFUL * 2
1049  * D = 0x03FFFFFUL * 2
1050  *
1051  * Initial bounds: t0..t8 <= C * m
1052  * t9 <= D * m
1053  */
1054 
1055  t0 += 0x3FFFC2FUL & mask;
1056  t1 += 0x3FFFFBFUL & mask;
1057  t2 += mask;
1058  t3 += mask;
1059  t4 += mask;
1060  t5 += mask;
1061  t6 += mask;
1062  t7 += mask;
1063  t8 += mask;
1064  t9 += mask >> 4;
1065 
1066  VERIFY_CHECK((t0 & one) == 0);
1067 
1068  /* t0..t8: added <= C/2
1069  * t9: added <= D/2
1070  *
1071  * Current bounds: t0..t8 <= C * (m + 1/2)
1072  * t9 <= D * (m + 1/2)
1073  */
1074 
1075  r->n[0] = (t0 >> 1) + ((t1 & one) << 25);
1076  r->n[1] = (t1 >> 1) + ((t2 & one) << 25);
1077  r->n[2] = (t2 >> 1) + ((t3 & one) << 25);
1078  r->n[3] = (t3 >> 1) + ((t4 & one) << 25);
1079  r->n[4] = (t4 >> 1) + ((t5 & one) << 25);
1080  r->n[5] = (t5 >> 1) + ((t6 & one) << 25);
1081  r->n[6] = (t6 >> 1) + ((t7 & one) << 25);
1082  r->n[7] = (t7 >> 1) + ((t8 & one) << 25);
1083  r->n[8] = (t8 >> 1) + ((t9 & one) << 25);
1084  r->n[9] = (t9 >> 1);
1085 
1086  /* t0..t8: shifted right and added <= C/4 + 1/2
1087  * t9: shifted right
1088  *
1089  * Current bounds: t0..t8 <= C * (m/2 + 1/2)
1090  * t9 <= D * (m/2 + 1/4)
1091  *
1092  * Therefore the output magnitude (M) has to be set such that:
1093  * t0..t8: C * M >= C * (m/2 + 1/2)
1094  * t9: D * M >= D * (m/2 + 1/4)
1095  *
1096  * It suffices for all limbs that, for any input magnitude m:
1097  * M >= m/2 + 1/2
1098  *
1099  * and since we want the smallest such integer value for M:
1100  * M == floor(m/2) + 1
1101  */
1102 }
1103 
1104 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
1105  uint32_t mask0, mask1;
1106  volatile int vflag = flag;
1107  SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
1108  mask0 = vflag + ~((uint32_t)0);
1109  mask1 = ~mask0;
1110  r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1111  r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1112  r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1113  r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1114  r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1115  r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1116  r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1117  r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1118 }
1119 
1120 static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
1121  r->n[0] = a->n[0] | a->n[1] << 26;
1122  r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
1123  r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
1124  r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
1125  r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
1126  r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
1127  r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
1128  r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
1129 }
1130 
1131 static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
1132  r->n[0] = a->n[0] & 0x3FFFFFFUL;
1133  r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
1134  r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
1135  r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
1136  r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
1137  r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
1138  r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
1139  r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
1140  r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
1141  r->n[9] = a->n[7] >> 10;
1142 }
1143 
1144 static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) {
1145  const uint32_t M26 = UINT32_MAX >> 6;
1146  const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4],
1147  a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8];
1148 
1149  /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and
1150  * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8).
1151  */
1152  VERIFY_CHECK(a0 >> 30 == 0);
1153  VERIFY_CHECK(a1 >> 30 == 0);
1154  VERIFY_CHECK(a2 >> 30 == 0);
1155  VERIFY_CHECK(a3 >> 30 == 0);
1156  VERIFY_CHECK(a4 >> 30 == 0);
1157  VERIFY_CHECK(a5 >> 30 == 0);
1158  VERIFY_CHECK(a6 >> 30 == 0);
1159  VERIFY_CHECK(a7 >> 30 == 0);
1160  VERIFY_CHECK(a8 >> 16 == 0);
1161 
1162  r->n[0] = a0 & M26;
1163  r->n[1] = (a0 >> 26 | a1 << 4) & M26;
1164  r->n[2] = (a1 >> 22 | a2 << 8) & M26;
1165  r->n[3] = (a2 >> 18 | a3 << 12) & M26;
1166  r->n[4] = (a3 >> 14 | a4 << 16) & M26;
1167  r->n[5] = (a4 >> 10 | a5 << 20) & M26;
1168  r->n[6] = (a5 >> 6 | a6 << 24) & M26;
1169  r->n[7] = (a6 >> 2 ) & M26;
1170  r->n[8] = (a6 >> 28 | a7 << 2) & M26;
1171  r->n[9] = (a7 >> 24 | a8 << 6);
1172 }
1173 
1174 static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) {
1175  const uint32_t M30 = UINT32_MAX >> 2;
1176  const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4],
1177  a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9];
1178 
1179  r->v[0] = (a0 | a1 << 26) & M30;
1180  r->v[1] = (a1 >> 4 | a2 << 22) & M30;
1181  r->v[2] = (a2 >> 8 | a3 << 18) & M30;
1182  r->v[3] = (a3 >> 12 | a4 << 14) & M30;
1183  r->v[4] = (a4 >> 16 | a5 << 10) & M30;
1184  r->v[5] = (a5 >> 20 | a6 << 6) & M30;
1185  r->v[6] = (a6 >> 24 | a7 << 2
1186  | a8 << 28) & M30;
1187  r->v[7] = (a8 >> 2 | a9 << 24) & M30;
1188  r->v[8] = a9 >> 6;
1189 }
1190 
1191 static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = {
1192  {{-0x3D1, -4, 0, 0, 0, 0, 0, 0, 65536}},
1193  0x2DDACACFL
1194 };
1195 
1196 static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x) {
1197  secp256k1_fe tmp = *x;
1198  secp256k1_modinv32_signed30 s;
1199 
1200  secp256k1_fe_normalize(&tmp);
1201  secp256k1_fe_to_signed30(&s, &tmp);
1202  secp256k1_modinv32(&s, &secp256k1_const_modinfo_fe);
1203  secp256k1_fe_from_signed30(r, &s);
1204 }
1205 
1206 static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
1207  secp256k1_fe tmp = *x;
1208  secp256k1_modinv32_signed30 s;
1209 
1210  secp256k1_fe_normalize_var(&tmp);
1211  secp256k1_fe_to_signed30(&s, &tmp);
1212  secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_fe);
1213  secp256k1_fe_from_signed30(r, &s);
1214 }
1215 
1216 static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x) {
1217  secp256k1_fe tmp;
1218  secp256k1_modinv32_signed30 s;
1219  int jac, ret;
1220 
1221  tmp = *x;
1222  secp256k1_fe_normalize_var(&tmp);
1223  /* secp256k1_jacobi32_maybe_var cannot deal with input 0. */
1224  if (secp256k1_fe_is_zero(&tmp)) return 1;
1225  secp256k1_fe_to_signed30(&s, &tmp);
1226  jac = secp256k1_jacobi32_maybe_var(&s, &secp256k1_const_modinfo_fe);
1227  if (jac == 0) {
1228  /* secp256k1_jacobi32_maybe_var failed to compute the Jacobi symbol. Fall back
1229  * to computing a square root. This should be extremely rare with random
1230  * input (except in VERIFY mode, where a lower iteration count is used). */
1231  secp256k1_fe dummy;
1232  ret = secp256k1_fe_sqrt(&dummy, &tmp);
1233  } else {
1234  ret = jac >= 0;
1235  }
1236  return ret;
1237 }
1238 
1239 #endif /* SECP256K1_FIELD_REPR_IMPL_H */
ret
int ret
Definition: bitcoin-cli.cpp:1271
SECP256K1_CHECKMEM_CHECK_VERIFY
#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len)
Definition: checkmem.h:99
u8
unsigned char u8
Definition: crypto_diff_fuzz_chacha20.cpp:21
secp256k1_fe_sqrt
static int secp256k1_fe_sqrt(secp256k1_fe *SECP256K1_RESTRICT r, const secp256k1_fe *SECP256K1_RESTRICT a)
Compute a square root of a field element.
secp256k1_fe_normalize_var
#define secp256k1_fe_normalize_var
Definition: field.h:80
secp256k1_fe_is_zero
#define secp256k1_fe_is_zero
Definition: field.h:85
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#define secp256k1_fe_normalize
Definition: field.h:78
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static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r)
Definition: field_10x26_impl.h:1039
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static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a)
Definition: field_10x26_impl.h:293
secp256k1_fe_impl_normalize_weak
static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r)
Definition: field_10x26_impl.h:102
secp256k1_fe_impl_is_square_var
static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x)
Definition: field_10x26_impl.h:1216
secp256k1_fe_impl_get_b32
static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a)
Convert a field element to a 32-byte big endian value.
Definition: field_10x26_impl.h:312
secp256k1_fe_impl_add
static SECP256K1_INLINE void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:381
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static SECP256K1_INLINE void secp256k1_fe_impl_clear(secp256k1_fe *a)
Definition: field_10x26_impl.h:273
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static SECP256K1_INLINE void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a)
Definition: field_10x26_impl.h:738
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static SECP256K1_INLINE void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:259
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static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe
Definition: field_10x26_impl.h:1191
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static SECP256K1_INLINE int secp256k1_fe_impl_is_zero(const secp256k1_fe *a)
Definition: field_10x26_impl.h:264
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static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m)
Definition: field_10x26_impl.h:40
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Definition: field_10x26_impl.h:306
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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:408
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Definition: field_10x26_impl.h:1144
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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:1104
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static SECP256K1_INLINE void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m)
Definition: field_10x26_impl.h:347
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static SECP256K1_INLINE void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:368
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static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b)
Definition: field_10x26_impl.h:280
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#define VERIFY_BITS(x, n)
Definition: field_10x26_impl.h:406
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static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r)
Definition: field_10x26_impl.h:178
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Definition: field_10x26_impl.h:1206
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static SECP256K1_INLINE void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1017
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static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a)
Definition: field_10x26_impl.h:1131
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static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1174
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static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1120
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Definition: field_10x26_impl.h:394
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static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r)
Definition: field_10x26_impl.h:207
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static void secp256k1_fe_impl_normalize(secp256k1_fe *r)
Definition: field_10x26_impl.h:53
secp256k1_fe_impl_cmov
static SECP256K1_INLINE void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag)
Definition: field_10x26_impl.h:1021
secp256k1_fe_impl_inv
static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x)
Definition: field_10x26_impl.h:1196
secp256k1_fe_impl_normalize_var
static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r)
Definition: field_10x26_impl.h:128
secp256k1_fe_impl_is_odd
static SECP256K1_INLINE int secp256k1_fe_impl_is_odd(const secp256k1_fe *a)
Definition: field_10x26_impl.h:269
secp256k1_fe_impl_mul
static SECP256K1_INLINE void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe *SECP256K1_RESTRICT b)
Definition: field_10x26_impl.h:1013
secp256k1_modinv32_var
static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
secp256k1_modinv32
static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
secp256k1_jacobi32_maybe_var
static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
modinv32_impl.h
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition: util.h:48
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition: util.h:153
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition: util.h:185
secp256k1_fe_storage
Definition: field_10x26.h:50
secp256k1_fe_storage::n
uint32_t n[8]
Definition: field_10x26.h:51
secp256k1_fe
This field implementation represents the value as 10 uint32_t limbs in base 2^26.
Definition: field_10x26.h:14
secp256k1_fe::n
uint32_t n[10]
Definition: field_10x26.h:22
secp256k1_modinv32_modinfo
Definition: modinv32.h:19
secp256k1_modinv32_signed30
Definition: modinv32.h:15
secp256k1_modinv32_signed30::v
int32_t v[9]
Definition: modinv32.h:16
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