Bitcoin Core 31.99.0
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
16static 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
40static 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
53static 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
102static 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
128static 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
178static 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
207static 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
259SECP256K1_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
264SECP256K1_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
269SECP256K1_INLINE static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a) {
270 return a->n[0] & 1;
271}
272
273static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
274 int i;
275 for (i = 9; i >= 0; i--) {
276 if (a->n[i] > b->n[i]) {
277 return 1;
278 }
279 if (a->n[i] < b->n[i]) {
280 return -1;
281 }
282 }
283 return 0;
284}
285
286static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
287 r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
288 r->n[1] = (uint32_t)((a[28] >> 2) & 0x3f) | ((uint32_t)a[27] << 6) | ((uint32_t)a[26] << 14) | ((uint32_t)(a[25] & 0xf) << 22);
289 r->n[2] = (uint32_t)((a[25] >> 4) & 0xf) | ((uint32_t)a[24] << 4) | ((uint32_t)a[23] << 12) | ((uint32_t)(a[22] & 0x3f) << 20);
290 r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18);
291 r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24);
292 r->n[5] = (uint32_t)((a[15] >> 2) & 0x3f) | ((uint32_t)a[14] << 6) | ((uint32_t)a[13] << 14) | ((uint32_t)(a[12] & 0xf) << 22);
293 r->n[6] = (uint32_t)((a[12] >> 4) & 0xf) | ((uint32_t)a[11] << 4) | ((uint32_t)a[10] << 12) | ((uint32_t)(a[9] & 0x3f) << 20);
294 r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
295 r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
296 r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
297}
298
299static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
300 secp256k1_fe_impl_set_b32_mod(r, a);
301 return !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
302}
303
305static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a) {
306 secp256k1_write_be32(&r[0], (a->n[9] << 10) | (a->n[8] >> 16));
307 secp256k1_write_be32(&r[4], (a->n[8] << 16) | (a->n[7] >> 10));
308 secp256k1_write_be32(&r[8], (a->n[7] << 22) | (a->n[6] >> 4));
309 secp256k1_write_be32(&r[12], (a->n[6] << 28) | (a->n[5] << 2) | (a->n[4] >> 24));
310 secp256k1_write_be32(&r[16], (a->n[4] << 8) | (a->n[3] >> 18));
311 secp256k1_write_be32(&r[20], (a->n[3] << 14) | (a->n[2] >> 12));
312 secp256k1_write_be32(&r[24], (a->n[2] << 20) | (a->n[1] >> 6));
313 secp256k1_write_be32(&r[28], (a->n[1] << 26) | a->n[0]);
314}
315
316SECP256K1_INLINE static void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m) {
317 /* For all legal values of m (0..31), the following properties hold: */
318 VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
319 VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
320 VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
321 VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m);
322
323 /* Due to the properties above, the left hand in the subtractions below is never less than
324 * the right hand. */
325 r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
326 r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
327 r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
328 r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
329 r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
330 r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
331 r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
332 r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
333 r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
334 r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
335}
336
337SECP256K1_INLINE static void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a) {
338 r->n[0] *= a;
339 r->n[1] *= a;
340 r->n[2] *= a;
341 r->n[3] *= a;
342 r->n[4] *= a;
343 r->n[5] *= a;
344 r->n[6] *= a;
345 r->n[7] *= a;
346 r->n[8] *= a;
347 r->n[9] *= a;
348}
349
350SECP256K1_INLINE static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a) {
351 r->n[0] += a->n[0];
352 r->n[1] += a->n[1];
353 r->n[2] += a->n[2];
354 r->n[3] += a->n[3];
355 r->n[4] += a->n[4];
356 r->n[5] += a->n[5];
357 r->n[6] += a->n[6];
358 r->n[7] += a->n[7];
359 r->n[8] += a->n[8];
360 r->n[9] += a->n[9];
361}
362
363SECP256K1_INLINE static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a) {
364 r->n[0] += a;
365}
366
367#if defined(USE_EXTERNAL_ASM)
368
369/* External assembler implementation */
370void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
371void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
372
373#else
374
375#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
376
377SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
378 uint64_t c, d;
379 uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
380 uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
381 const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
382
383 VERIFY_BITS(a[0], 30);
384 VERIFY_BITS(a[1], 30);
385 VERIFY_BITS(a[2], 30);
386 VERIFY_BITS(a[3], 30);
387 VERIFY_BITS(a[4], 30);
388 VERIFY_BITS(a[5], 30);
389 VERIFY_BITS(a[6], 30);
390 VERIFY_BITS(a[7], 30);
391 VERIFY_BITS(a[8], 30);
392 VERIFY_BITS(a[9], 26);
393 VERIFY_BITS(b[0], 30);
394 VERIFY_BITS(b[1], 30);
395 VERIFY_BITS(b[2], 30);
396 VERIFY_BITS(b[3], 30);
397 VERIFY_BITS(b[4], 30);
398 VERIFY_BITS(b[5], 30);
399 VERIFY_BITS(b[6], 30);
400 VERIFY_BITS(b[7], 30);
401 VERIFY_BITS(b[8], 30);
402 VERIFY_BITS(b[9], 26);
403
410 d = (uint64_t)a[0] * b[9]
411 + (uint64_t)a[1] * b[8]
412 + (uint64_t)a[2] * b[7]
413 + (uint64_t)a[3] * b[6]
414 + (uint64_t)a[4] * b[5]
415 + (uint64_t)a[5] * b[4]
416 + (uint64_t)a[6] * b[3]
417 + (uint64_t)a[7] * b[2]
418 + (uint64_t)a[8] * b[1]
419 + (uint64_t)a[9] * b[0];
420 /* VERIFY_BITS(d, 64); */
421 /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
422 t9 = d & M; d >>= 26;
423 VERIFY_BITS(t9, 26);
424 VERIFY_BITS(d, 38);
425 /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
426
427 c = (uint64_t)a[0] * b[0];
428 VERIFY_BITS(c, 60);
429 /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
430 d += (uint64_t)a[1] * b[9]
431 + (uint64_t)a[2] * b[8]
432 + (uint64_t)a[3] * b[7]
433 + (uint64_t)a[4] * b[6]
434 + (uint64_t)a[5] * b[5]
435 + (uint64_t)a[6] * b[4]
436 + (uint64_t)a[7] * b[3]
437 + (uint64_t)a[8] * b[2]
438 + (uint64_t)a[9] * b[1];
439 VERIFY_BITS(d, 63);
440 /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
441 u0 = d & M; d >>= 26; c += u0 * R0;
442 VERIFY_BITS(u0, 26);
443 VERIFY_BITS(d, 37);
444 VERIFY_BITS(c, 61);
445 /* [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] */
446 t0 = c & M; c >>= 26; c += u0 * R1;
447 VERIFY_BITS(t0, 26);
448 VERIFY_BITS(c, 37);
449 /* [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] */
450 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
451
452 c += (uint64_t)a[0] * b[1]
453 + (uint64_t)a[1] * b[0];
454 VERIFY_BITS(c, 62);
455 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
456 d += (uint64_t)a[2] * b[9]
457 + (uint64_t)a[3] * b[8]
458 + (uint64_t)a[4] * b[7]
459 + (uint64_t)a[5] * b[6]
460 + (uint64_t)a[6] * b[5]
461 + (uint64_t)a[7] * b[4]
462 + (uint64_t)a[8] * b[3]
463 + (uint64_t)a[9] * b[2];
464 VERIFY_BITS(d, 63);
465 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
466 u1 = d & M; d >>= 26; c += u1 * R0;
467 VERIFY_BITS(u1, 26);
468 VERIFY_BITS(d, 37);
469 VERIFY_BITS(c, 63);
470 /* [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] */
471 t1 = c & M; c >>= 26; c += u1 * R1;
472 VERIFY_BITS(t1, 26);
473 VERIFY_BITS(c, 38);
474 /* [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] */
475 /* [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] */
476
477 c += (uint64_t)a[0] * b[2]
478 + (uint64_t)a[1] * b[1]
479 + (uint64_t)a[2] * b[0];
480 VERIFY_BITS(c, 62);
481 /* [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] */
482 d += (uint64_t)a[3] * b[9]
483 + (uint64_t)a[4] * b[8]
484 + (uint64_t)a[5] * b[7]
485 + (uint64_t)a[6] * b[6]
486 + (uint64_t)a[7] * b[5]
487 + (uint64_t)a[8] * b[4]
488 + (uint64_t)a[9] * b[3];
489 VERIFY_BITS(d, 63);
490 /* [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] */
491 u2 = d & M; d >>= 26; c += u2 * R0;
492 VERIFY_BITS(u2, 26);
493 VERIFY_BITS(d, 37);
494 VERIFY_BITS(c, 63);
495 /* [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] */
496 t2 = c & M; c >>= 26; c += u2 * R1;
497 VERIFY_BITS(t2, 26);
498 VERIFY_BITS(c, 38);
499 /* [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] */
500 /* [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] */
501
502 c += (uint64_t)a[0] * b[3]
503 + (uint64_t)a[1] * b[2]
504 + (uint64_t)a[2] * b[1]
505 + (uint64_t)a[3] * b[0];
506 VERIFY_BITS(c, 63);
507 /* [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] */
508 d += (uint64_t)a[4] * b[9]
509 + (uint64_t)a[5] * b[8]
510 + (uint64_t)a[6] * b[7]
511 + (uint64_t)a[7] * b[6]
512 + (uint64_t)a[8] * b[5]
513 + (uint64_t)a[9] * b[4];
514 VERIFY_BITS(d, 63);
515 /* [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] */
516 u3 = d & M; d >>= 26; c += u3 * R0;
517 VERIFY_BITS(u3, 26);
518 VERIFY_BITS(d, 37);
519 /* VERIFY_BITS(c, 64); */
520 /* [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] */
521 t3 = c & M; c >>= 26; c += u3 * R1;
522 VERIFY_BITS(t3, 26);
523 VERIFY_BITS(c, 39);
524 /* [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] */
525 /* [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] */
526
527 c += (uint64_t)a[0] * b[4]
528 + (uint64_t)a[1] * b[3]
529 + (uint64_t)a[2] * b[2]
530 + (uint64_t)a[3] * b[1]
531 + (uint64_t)a[4] * b[0];
532 VERIFY_BITS(c, 63);
533 /* [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] */
534 d += (uint64_t)a[5] * b[9]
535 + (uint64_t)a[6] * b[8]
536 + (uint64_t)a[7] * b[7]
537 + (uint64_t)a[8] * b[6]
538 + (uint64_t)a[9] * b[5];
539 VERIFY_BITS(d, 62);
540 /* [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] */
541 u4 = d & M; d >>= 26; c += u4 * R0;
542 VERIFY_BITS(u4, 26);
543 VERIFY_BITS(d, 36);
544 /* VERIFY_BITS(c, 64); */
545 /* [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] */
546 t4 = c & M; c >>= 26; c += u4 * R1;
547 VERIFY_BITS(t4, 26);
548 VERIFY_BITS(c, 39);
549 /* [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] */
550 /* [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] */
551
552 c += (uint64_t)a[0] * b[5]
553 + (uint64_t)a[1] * b[4]
554 + (uint64_t)a[2] * b[3]
555 + (uint64_t)a[3] * b[2]
556 + (uint64_t)a[4] * b[1]
557 + (uint64_t)a[5] * b[0];
558 VERIFY_BITS(c, 63);
559 /* [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] */
560 d += (uint64_t)a[6] * b[9]
561 + (uint64_t)a[7] * b[8]
562 + (uint64_t)a[8] * b[7]
563 + (uint64_t)a[9] * b[6];
564 VERIFY_BITS(d, 62);
565 /* [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] */
566 u5 = d & M; d >>= 26; c += u5 * R0;
567 VERIFY_BITS(u5, 26);
568 VERIFY_BITS(d, 36);
569 /* VERIFY_BITS(c, 64); */
570 /* [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] */
571 t5 = c & M; c >>= 26; c += u5 * R1;
572 VERIFY_BITS(t5, 26);
573 VERIFY_BITS(c, 39);
574 /* [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] */
575 /* [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] */
576
577 c += (uint64_t)a[0] * b[6]
578 + (uint64_t)a[1] * b[5]
579 + (uint64_t)a[2] * b[4]
580 + (uint64_t)a[3] * b[3]
581 + (uint64_t)a[4] * b[2]
582 + (uint64_t)a[5] * b[1]
583 + (uint64_t)a[6] * b[0];
584 VERIFY_BITS(c, 63);
585 /* [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] */
586 d += (uint64_t)a[7] * b[9]
587 + (uint64_t)a[8] * b[8]
588 + (uint64_t)a[9] * b[7];
589 VERIFY_BITS(d, 61);
590 /* [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] */
591 u6 = d & M; d >>= 26; c += u6 * R0;
592 VERIFY_BITS(u6, 26);
593 VERIFY_BITS(d, 35);
594 /* VERIFY_BITS(c, 64); */
595 /* [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] */
596 t6 = c & M; c >>= 26; c += u6 * R1;
597 VERIFY_BITS(t6, 26);
598 VERIFY_BITS(c, 39);
599 /* [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] */
600 /* [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] */
601
602 c += (uint64_t)a[0] * b[7]
603 + (uint64_t)a[1] * b[6]
604 + (uint64_t)a[2] * b[5]
605 + (uint64_t)a[3] * b[4]
606 + (uint64_t)a[4] * b[3]
607 + (uint64_t)a[5] * b[2]
608 + (uint64_t)a[6] * b[1]
609 + (uint64_t)a[7] * b[0];
610 /* VERIFY_BITS(c, 64); */
611 VERIFY_CHECK(c <= 0x8000007C00000007ULL);
612 /* [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] */
613 d += (uint64_t)a[8] * b[9]
614 + (uint64_t)a[9] * b[8];
615 VERIFY_BITS(d, 58);
616 /* [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] */
617 u7 = d & M; d >>= 26; c += u7 * R0;
618 VERIFY_BITS(u7, 26);
619 VERIFY_BITS(d, 32);
620 /* VERIFY_BITS(c, 64); */
621 VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
622 /* [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] */
623 t7 = c & M; c >>= 26; c += u7 * R1;
624 VERIFY_BITS(t7, 26);
625 VERIFY_BITS(c, 38);
626 /* [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] */
627 /* [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] */
628
629 c += (uint64_t)a[0] * b[8]
630 + (uint64_t)a[1] * b[7]
631 + (uint64_t)a[2] * b[6]
632 + (uint64_t)a[3] * b[5]
633 + (uint64_t)a[4] * b[4]
634 + (uint64_t)a[5] * b[3]
635 + (uint64_t)a[6] * b[2]
636 + (uint64_t)a[7] * b[1]
637 + (uint64_t)a[8] * b[0];
638 /* VERIFY_BITS(c, 64); */
639 VERIFY_CHECK(c <= 0x9000007B80000008ULL);
640 /* [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] */
641 d += (uint64_t)a[9] * b[9];
642 VERIFY_BITS(d, 57);
643 /* [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] */
644 u8 = d & M; d >>= 26; c += u8 * R0;
645 VERIFY_BITS(u8, 26);
646 VERIFY_BITS(d, 31);
647 /* VERIFY_BITS(c, 64); */
648 VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
649 /* [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] */
650
651 r[3] = t3;
652 VERIFY_BITS(r[3], 26);
653 /* [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] */
654 r[4] = t4;
655 VERIFY_BITS(r[4], 26);
656 /* [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] */
657 r[5] = t5;
658 VERIFY_BITS(r[5], 26);
659 /* [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] */
660 r[6] = t6;
661 VERIFY_BITS(r[6], 26);
662 /* [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] */
663 r[7] = t7;
664 VERIFY_BITS(r[7], 26);
665 /* [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] */
666
667 r[8] = c & M; c >>= 26; c += u8 * R1;
668 VERIFY_BITS(r[8], 26);
669 VERIFY_BITS(c, 39);
670 /* [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] */
671 /* [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] */
672 c += d * R0 + t9;
673 VERIFY_BITS(c, 45);
674 /* [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] */
675 r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
676 VERIFY_BITS(r[9], 22);
677 VERIFY_BITS(c, 46);
678 /* [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] */
679 /* [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] */
680 /* [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] */
681
682 d = c * (R0 >> 4) + t0;
683 VERIFY_BITS(d, 56);
684 /* [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] */
685 r[0] = d & M; d >>= 26;
686 VERIFY_BITS(r[0], 26);
687 VERIFY_BITS(d, 30);
688 /* [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] */
689 d += c * (R1 >> 4) + t1;
690 VERIFY_BITS(d, 53);
691 VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
692 /* [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] */
693 /* [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] */
694 r[1] = d & M; d >>= 26;
695 VERIFY_BITS(r[1], 26);
696 VERIFY_BITS(d, 27);
697 VERIFY_CHECK(d <= 0x4000000ULL);
698 /* [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] */
699 d += t2;
700 VERIFY_BITS(d, 27);
701 /* [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] */
702 r[2] = d;
703 VERIFY_BITS(r[2], 27);
704 /* [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] */
705}
706
707SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
708 uint64_t c, d;
709 uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
710 uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
711 const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
712
713 VERIFY_BITS(a[0], 30);
714 VERIFY_BITS(a[1], 30);
715 VERIFY_BITS(a[2], 30);
716 VERIFY_BITS(a[3], 30);
717 VERIFY_BITS(a[4], 30);
718 VERIFY_BITS(a[5], 30);
719 VERIFY_BITS(a[6], 30);
720 VERIFY_BITS(a[7], 30);
721 VERIFY_BITS(a[8], 30);
722 VERIFY_BITS(a[9], 26);
723
729 d = (uint64_t)(a[0]*2) * a[9]
730 + (uint64_t)(a[1]*2) * a[8]
731 + (uint64_t)(a[2]*2) * a[7]
732 + (uint64_t)(a[3]*2) * a[6]
733 + (uint64_t)(a[4]*2) * a[5];
734 /* VERIFY_BITS(d, 64); */
735 /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
736 t9 = d & M; d >>= 26;
737 VERIFY_BITS(t9, 26);
738 VERIFY_BITS(d, 38);
739 /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
740
741 c = (uint64_t)a[0] * a[0];
742 VERIFY_BITS(c, 60);
743 /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
744 d += (uint64_t)(a[1]*2) * a[9]
745 + (uint64_t)(a[2]*2) * a[8]
746 + (uint64_t)(a[3]*2) * a[7]
747 + (uint64_t)(a[4]*2) * a[6]
748 + (uint64_t)a[5] * a[5];
749 VERIFY_BITS(d, 63);
750 /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
751 u0 = d & M; d >>= 26; c += u0 * R0;
752 VERIFY_BITS(u0, 26);
753 VERIFY_BITS(d, 37);
754 VERIFY_BITS(c, 61);
755 /* [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] */
756 t0 = c & M; c >>= 26; c += u0 * R1;
757 VERIFY_BITS(t0, 26);
758 VERIFY_BITS(c, 37);
759 /* [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] */
760 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
761
762 c += (uint64_t)(a[0]*2) * a[1];
763 VERIFY_BITS(c, 62);
764 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
765 d += (uint64_t)(a[2]*2) * a[9]
766 + (uint64_t)(a[3]*2) * a[8]
767 + (uint64_t)(a[4]*2) * a[7]
768 + (uint64_t)(a[5]*2) * a[6];
769 VERIFY_BITS(d, 63);
770 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
771 u1 = d & M; d >>= 26; c += u1 * R0;
772 VERIFY_BITS(u1, 26);
773 VERIFY_BITS(d, 37);
774 VERIFY_BITS(c, 63);
775 /* [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] */
776 t1 = c & M; c >>= 26; c += u1 * R1;
777 VERIFY_BITS(t1, 26);
778 VERIFY_BITS(c, 38);
779 /* [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] */
780 /* [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] */
781
782 c += (uint64_t)(a[0]*2) * a[2]
783 + (uint64_t)a[1] * a[1];
784 VERIFY_BITS(c, 62);
785 /* [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] */
786 d += (uint64_t)(a[3]*2) * a[9]
787 + (uint64_t)(a[4]*2) * a[8]
788 + (uint64_t)(a[5]*2) * a[7]
789 + (uint64_t)a[6] * a[6];
790 VERIFY_BITS(d, 63);
791 /* [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] */
792 u2 = d & M; d >>= 26; c += u2 * R0;
793 VERIFY_BITS(u2, 26);
794 VERIFY_BITS(d, 37);
795 VERIFY_BITS(c, 63);
796 /* [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] */
797 t2 = c & M; c >>= 26; c += u2 * R1;
798 VERIFY_BITS(t2, 26);
799 VERIFY_BITS(c, 38);
800 /* [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] */
801 /* [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] */
802
803 c += (uint64_t)(a[0]*2) * a[3]
804 + (uint64_t)(a[1]*2) * a[2];
805 VERIFY_BITS(c, 63);
806 /* [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] */
807 d += (uint64_t)(a[4]*2) * a[9]
808 + (uint64_t)(a[5]*2) * a[8]
809 + (uint64_t)(a[6]*2) * a[7];
810 VERIFY_BITS(d, 63);
811 /* [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] */
812 u3 = d & M; d >>= 26; c += u3 * R0;
813 VERIFY_BITS(u3, 26);
814 VERIFY_BITS(d, 37);
815 /* VERIFY_BITS(c, 64); */
816 /* [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] */
817 t3 = c & M; c >>= 26; c += u3 * R1;
818 VERIFY_BITS(t3, 26);
819 VERIFY_BITS(c, 39);
820 /* [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] */
821 /* [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] */
822
823 c += (uint64_t)(a[0]*2) * a[4]
824 + (uint64_t)(a[1]*2) * a[3]
825 + (uint64_t)a[2] * a[2];
826 VERIFY_BITS(c, 63);
827 /* [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] */
828 d += (uint64_t)(a[5]*2) * a[9]
829 + (uint64_t)(a[6]*2) * a[8]
830 + (uint64_t)a[7] * a[7];
831 VERIFY_BITS(d, 62);
832 /* [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] */
833 u4 = d & M; d >>= 26; c += u4 * R0;
834 VERIFY_BITS(u4, 26);
835 VERIFY_BITS(d, 36);
836 /* VERIFY_BITS(c, 64); */
837 /* [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] */
838 t4 = c & M; c >>= 26; c += u4 * R1;
839 VERIFY_BITS(t4, 26);
840 VERIFY_BITS(c, 39);
841 /* [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] */
842 /* [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] */
843
844 c += (uint64_t)(a[0]*2) * a[5]
845 + (uint64_t)(a[1]*2) * a[4]
846 + (uint64_t)(a[2]*2) * a[3];
847 VERIFY_BITS(c, 63);
848 /* [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] */
849 d += (uint64_t)(a[6]*2) * a[9]
850 + (uint64_t)(a[7]*2) * a[8];
851 VERIFY_BITS(d, 62);
852 /* [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] */
853 u5 = d & M; d >>= 26; c += u5 * R0;
854 VERIFY_BITS(u5, 26);
855 VERIFY_BITS(d, 36);
856 /* VERIFY_BITS(c, 64); */
857 /* [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] */
858 t5 = c & M; c >>= 26; c += u5 * R1;
859 VERIFY_BITS(t5, 26);
860 VERIFY_BITS(c, 39);
861 /* [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] */
862 /* [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] */
863
864 c += (uint64_t)(a[0]*2) * a[6]
865 + (uint64_t)(a[1]*2) * a[5]
866 + (uint64_t)(a[2]*2) * a[4]
867 + (uint64_t)a[3] * a[3];
868 VERIFY_BITS(c, 63);
869 /* [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] */
870 d += (uint64_t)(a[7]*2) * a[9]
871 + (uint64_t)a[8] * a[8];
872 VERIFY_BITS(d, 61);
873 /* [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] */
874 u6 = d & M; d >>= 26; c += u6 * R0;
875 VERIFY_BITS(u6, 26);
876 VERIFY_BITS(d, 35);
877 /* VERIFY_BITS(c, 64); */
878 /* [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] */
879 t6 = c & M; c >>= 26; c += u6 * R1;
880 VERIFY_BITS(t6, 26);
881 VERIFY_BITS(c, 39);
882 /* [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] */
883 /* [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] */
884
885 c += (uint64_t)(a[0]*2) * a[7]
886 + (uint64_t)(a[1]*2) * a[6]
887 + (uint64_t)(a[2]*2) * a[5]
888 + (uint64_t)(a[3]*2) * a[4];
889 /* VERIFY_BITS(c, 64); */
890 VERIFY_CHECK(c <= 0x8000007C00000007ULL);
891 /* [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] */
892 d += (uint64_t)(a[8]*2) * a[9];
893 VERIFY_BITS(d, 58);
894 /* [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] */
895 u7 = d & M; d >>= 26; c += u7 * R0;
896 VERIFY_BITS(u7, 26);
897 VERIFY_BITS(d, 32);
898 /* VERIFY_BITS(c, 64); */
899 VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
900 /* [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] */
901 t7 = c & M; c >>= 26; c += u7 * R1;
902 VERIFY_BITS(t7, 26);
903 VERIFY_BITS(c, 38);
904 /* [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] */
905 /* [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] */
906
907 c += (uint64_t)(a[0]*2) * a[8]
908 + (uint64_t)(a[1]*2) * a[7]
909 + (uint64_t)(a[2]*2) * a[6]
910 + (uint64_t)(a[3]*2) * a[5]
911 + (uint64_t)a[4] * a[4];
912 /* VERIFY_BITS(c, 64); */
913 VERIFY_CHECK(c <= 0x9000007B80000008ULL);
914 /* [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] */
915 d += (uint64_t)a[9] * a[9];
916 VERIFY_BITS(d, 57);
917 /* [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] */
918 u8 = d & M; d >>= 26; c += u8 * R0;
919 VERIFY_BITS(u8, 26);
920 VERIFY_BITS(d, 31);
921 /* VERIFY_BITS(c, 64); */
922 VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
923 /* [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] */
924
925 r[3] = t3;
926 VERIFY_BITS(r[3], 26);
927 /* [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] */
928 r[4] = t4;
929 VERIFY_BITS(r[4], 26);
930 /* [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] */
931 r[5] = t5;
932 VERIFY_BITS(r[5], 26);
933 /* [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] */
934 r[6] = t6;
935 VERIFY_BITS(r[6], 26);
936 /* [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] */
937 r[7] = t7;
938 VERIFY_BITS(r[7], 26);
939 /* [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] */
940
941 r[8] = c & M; c >>= 26; c += u8 * R1;
942 VERIFY_BITS(r[8], 26);
943 VERIFY_BITS(c, 39);
944 /* [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] */
945 /* [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] */
946 c += d * R0 + t9;
947 VERIFY_BITS(c, 45);
948 /* [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] */
949 r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
950 VERIFY_BITS(r[9], 22);
951 VERIFY_BITS(c, 46);
952 /* [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] */
953 /* [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] */
954 /* [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] */
955
956 d = c * (R0 >> 4) + t0;
957 VERIFY_BITS(d, 56);
958 /* [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] */
959 r[0] = d & M; d >>= 26;
960 VERIFY_BITS(r[0], 26);
961 VERIFY_BITS(d, 30);
962 /* [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] */
963 d += c * (R1 >> 4) + t1;
964 VERIFY_BITS(d, 53);
965 VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
966 /* [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] */
967 /* [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] */
968 r[1] = d & M; d >>= 26;
969 VERIFY_BITS(r[1], 26);
970 VERIFY_BITS(d, 27);
971 VERIFY_CHECK(d <= 0x4000000ULL);
972 /* [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] */
973 d += t2;
974 VERIFY_BITS(d, 27);
975 /* [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] */
976 r[2] = d;
977 VERIFY_BITS(r[2], 27);
978 /* [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] */
979}
980#endif
981
982SECP256K1_INLINE static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
983 secp256k1_fe_mul_inner(r->n, a->n, b->n);
984}
985
986SECP256K1_INLINE static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
987 secp256k1_fe_sqr_inner(r->n, a->n);
988}
989
990SECP256K1_INLINE static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
991 uint32_t mask0, mask1;
992 volatile int vflag = flag;
993 VERIFY_CHECK(flag == 0 || flag == 1);
994 SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
995 mask0 = vflag + ~((uint32_t)0);
996 mask1 = ~mask0;
997 r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
998 r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
999 r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1000 r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1001 r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1002 r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1003 r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1004 r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1005 r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
1006 r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
1007}
1008
1009static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r) {
1010 uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
1011 t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
1012 uint32_t one = (uint32_t)1;
1013 uint32_t mask = -(t0 & one) >> 6;
1014
1015 /* Bounds analysis (over the rationals).
1016 *
1017 * Let m = r->magnitude
1018 * C = 0x3FFFFFFUL * 2
1019 * D = 0x03FFFFFUL * 2
1020 *
1021 * Initial bounds: t0..t8 <= C * m
1022 * t9 <= D * m
1023 */
1024
1025 t0 += 0x3FFFC2FUL & mask;
1026 t1 += 0x3FFFFBFUL & mask;
1027 t2 += mask;
1028 t3 += mask;
1029 t4 += mask;
1030 t5 += mask;
1031 t6 += mask;
1032 t7 += mask;
1033 t8 += mask;
1034 t9 += mask >> 4;
1035
1036 VERIFY_CHECK((t0 & one) == 0);
1037
1038 /* t0..t8: added <= C/2
1039 * t9: added <= D/2
1040 *
1041 * Current bounds: t0..t8 <= C * (m + 1/2)
1042 * t9 <= D * (m + 1/2)
1043 */
1044
1045 r->n[0] = (t0 >> 1) + ((t1 & one) << 25);
1046 r->n[1] = (t1 >> 1) + ((t2 & one) << 25);
1047 r->n[2] = (t2 >> 1) + ((t3 & one) << 25);
1048 r->n[3] = (t3 >> 1) + ((t4 & one) << 25);
1049 r->n[4] = (t4 >> 1) + ((t5 & one) << 25);
1050 r->n[5] = (t5 >> 1) + ((t6 & one) << 25);
1051 r->n[6] = (t6 >> 1) + ((t7 & one) << 25);
1052 r->n[7] = (t7 >> 1) + ((t8 & one) << 25);
1053 r->n[8] = (t8 >> 1) + ((t9 & one) << 25);
1054 r->n[9] = (t9 >> 1);
1055
1056 /* t0..t8: shifted right and added <= C/4 + 1/2
1057 * t9: shifted right
1058 *
1059 * Current bounds: t0..t8 <= C * (m/2 + 1/2)
1060 * t9 <= D * (m/2 + 1/4)
1061 *
1062 * Therefore the output magnitude (M) has to be set such that:
1063 * t0..t8: C * M >= C * (m/2 + 1/2)
1064 * t9: D * M >= D * (m/2 + 1/4)
1065 *
1066 * It suffices for all limbs that, for any input magnitude m:
1067 * M >= m/2 + 1/2
1068 *
1069 * and since we want the smallest such integer value for M:
1070 * M == floor(m/2) + 1
1071 */
1072}
1073
1074static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
1075 uint32_t mask0, mask1;
1076 volatile int vflag = flag;
1077 VERIFY_CHECK(flag == 0 || flag == 1);
1078 SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
1079 mask0 = vflag + ~((uint32_t)0);
1080 mask1 = ~mask0;
1081 r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1082 r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1083 r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1084 r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1085 r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1086 r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1087 r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1088 r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1089}
1090
1091static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
1092 r->n[0] = a->n[0] | a->n[1] << 26;
1093 r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
1094 r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
1095 r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
1096 r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
1097 r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
1098 r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
1099 r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
1100}
1101
1102static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
1103 r->n[0] = a->n[0] & 0x3FFFFFFUL;
1104 r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
1105 r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
1106 r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
1107 r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
1108 r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
1109 r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
1110 r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
1111 r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
1112 r->n[9] = a->n[7] >> 10;
1113}
1114
1115static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) {
1116 const uint32_t M26 = UINT32_MAX >> 6;
1117 const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4],
1118 a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8];
1119
1120 /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and
1121 * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8).
1122 */
1123 VERIFY_CHECK(a0 >> 30 == 0);
1124 VERIFY_CHECK(a1 >> 30 == 0);
1125 VERIFY_CHECK(a2 >> 30 == 0);
1126 VERIFY_CHECK(a3 >> 30 == 0);
1127 VERIFY_CHECK(a4 >> 30 == 0);
1128 VERIFY_CHECK(a5 >> 30 == 0);
1129 VERIFY_CHECK(a6 >> 30 == 0);
1130 VERIFY_CHECK(a7 >> 30 == 0);
1131 VERIFY_CHECK(a8 >> 16 == 0);
1132
1133 r->n[0] = a0 & M26;
1134 r->n[1] = (a0 >> 26 | a1 << 4) & M26;
1135 r->n[2] = (a1 >> 22 | a2 << 8) & M26;
1136 r->n[3] = (a2 >> 18 | a3 << 12) & M26;
1137 r->n[4] = (a3 >> 14 | a4 << 16) & M26;
1138 r->n[5] = (a4 >> 10 | a5 << 20) & M26;
1139 r->n[6] = (a5 >> 6 | a6 << 24) & M26;
1140 r->n[7] = (a6 >> 2 ) & M26;
1141 r->n[8] = (a6 >> 28 | a7 << 2) & M26;
1142 r->n[9] = (a7 >> 24 | a8 << 6);
1143}
1144
1145static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) {
1146 const uint32_t M30 = UINT32_MAX >> 2;
1147 const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4],
1148 a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9];
1149
1150 r->v[0] = (a0 | a1 << 26) & M30;
1151 r->v[1] = (a1 >> 4 | a2 << 22) & M30;
1152 r->v[2] = (a2 >> 8 | a3 << 18) & M30;
1153 r->v[3] = (a3 >> 12 | a4 << 14) & M30;
1154 r->v[4] = (a4 >> 16 | a5 << 10) & M30;
1155 r->v[5] = (a5 >> 20 | a6 << 6) & M30;
1156 r->v[6] = (a6 >> 24 | a7 << 2
1157 | a8 << 28) & M30;
1158 r->v[7] = (a8 >> 2 | a9 << 24) & M30;
1159 r->v[8] = a9 >> 6;
1160}
1161
1162static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = {
1163 {{-0x3D1, -4, 0, 0, 0, 0, 0, 0, 65536}},
1164 0x2DDACACFL
1165};
1166
1167static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x) {
1168 secp256k1_fe tmp = *x;
1169 secp256k1_modinv32_signed30 s;
1170
1171 secp256k1_fe_normalize(&tmp);
1172 secp256k1_fe_to_signed30(&s, &tmp);
1173 secp256k1_modinv32(&s, &secp256k1_const_modinfo_fe);
1174 secp256k1_fe_from_signed30(r, &s);
1175}
1176
1177static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
1178 secp256k1_fe tmp = *x;
1179 secp256k1_modinv32_signed30 s;
1180
1181 secp256k1_fe_normalize_var(&tmp);
1182 secp256k1_fe_to_signed30(&s, &tmp);
1183 secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_fe);
1184 secp256k1_fe_from_signed30(r, &s);
1185}
1186
1187static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x) {
1188 secp256k1_fe tmp;
1189 secp256k1_modinv32_signed30 s;
1190 int jac, ret;
1191
1192 tmp = *x;
1193 secp256k1_fe_normalize_var(&tmp);
1194 /* secp256k1_jacobi32_maybe_var cannot deal with input 0. */
1195 if (secp256k1_fe_is_zero(&tmp)) return 1;
1196 secp256k1_fe_to_signed30(&s, &tmp);
1197 jac = secp256k1_jacobi32_maybe_var(&s, &secp256k1_const_modinfo_fe);
1198 if (jac == 0) {
1199 /* secp256k1_jacobi32_maybe_var failed to compute the Jacobi symbol. Fall back
1200 * to computing a square root. This should be extremely rare with random
1201 * input (except in VERIFY mode, where a lower iteration count is used). */
1202 secp256k1_fe dummy;
1203 ret = secp256k1_fe_sqrt(&dummy, &tmp);
1204 } else {
1205 ret = jac >= 0;
1206 }
1207 return ret;
1208}
1209
1210#endif /* SECP256K1_FIELD_REPR_IMPL_H */
ret
int ret
Definition: bitcoin-cli.cpp:1691
SECP256K1_CHECKMEM_CHECK_VERIFY
#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len)
Definition: checkmem.h:114
u8
unsigned char u8
Definition: crypto_diff_fuzz_chacha20.cpp:21
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static int secp256k1_fe_sqrt(secp256k1_fe *SECP256K1_RESTRICT r, const secp256k1_fe *SECP256K1_RESTRICT a)
Compute a square root of a field element.
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#define secp256k1_fe_normalize_var
Definition: field.h:80
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#define secp256k1_fe_is_zero
Definition: field.h:84
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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:1009
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Definition: field_10x26_impl.h:286
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Definition: field_10x26_impl.h:102
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static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x)
Definition: field_10x26_impl.h:1187
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static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a)
Convert a field element to a 32-byte big endian value.
Definition: field_10x26_impl.h:305
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static SECP256K1_INLINE void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:350
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static SECP256K1_INLINE void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a)
Definition: field_10x26_impl.h:707
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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:1162
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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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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:377
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static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a)
Definition: field_10x26_impl.h:1115
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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:1074
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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:316
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static SECP256K1_INLINE void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:337
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static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b)
Definition: field_10x26_impl.h:273
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#define VERIFY_BITS(x, n)
Definition: field_10x26_impl.h:375
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Definition: field_10x26_impl.h:178
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Definition: field_10x26_impl.h:1177
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static SECP256K1_INLINE void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:986
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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:1102
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static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a)
Definition: field_10x26_impl.h:1145
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Definition: field_10x26_impl.h:1091
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static SECP256K1_INLINE void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a)
Definition: field_10x26_impl.h:363
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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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Definition: field_10x26_impl.h:53
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static SECP256K1_INLINE int secp256k1_fe_impl_is_odd(const secp256k1_fe *a)
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static SECP256K1_INLINE void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe *SECP256K1_RESTRICT b)
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static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
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static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
secp256k1_jacobi32_maybe_var
static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
modinv32_impl.h
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Definition: test_vectors_musig2_generate.py:72
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition: util.h:53
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static SECP256K1_INLINE void secp256k1_write_be32(unsigned char *p, uint32_t x)
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#define VERIFY_CHECK(cond)
Definition: util.h:169
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Definition: field_10x26.h:50
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uint32_t n[8]
Definition: field_10x26.h:51
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This field implementation represents the value as 10 uint32_t limbs in base 2^26.
Definition: field_10x26.h:14
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uint32_t n[10]
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Definition: modinv32.h:19
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Definition: modinv32.h:15
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Definition: modinv32.h:16
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