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field_5x52_int128_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_INNER5X52_IMPL_H
8#define SECP256K1_FIELD_INNER5X52_IMPL_H
9
10#include <stdint.h>
11
12#ifdef VERIFY
13#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
14#else
15#define VERIFY_BITS(x, n) do { } while(0)
16#endif
17
18SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
19 uint128_t c, d;
20 uint64_t t3, t4, tx, u0;
21 uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
22 const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
23
24 VERIFY_BITS(a[0], 56);
25 VERIFY_BITS(a[1], 56);
26 VERIFY_BITS(a[2], 56);
27 VERIFY_BITS(a[3], 56);
28 VERIFY_BITS(a[4], 52);
29 VERIFY_BITS(b[0], 56);
30 VERIFY_BITS(b[1], 56);
31 VERIFY_BITS(b[2], 56);
32 VERIFY_BITS(b[3], 56);
33 VERIFY_BITS(b[4], 52);
34 VERIFY_CHECK(r != b);
35 VERIFY_CHECK(a != b);
36
37 /* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
38 * for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x).
39 * for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4)
40 * Note that [x 0 0 0 0 0] = [x*R].
41 */
42
43 d = (uint128_t)a0 * b[3]
44 + (uint128_t)a1 * b[2]
45 + (uint128_t)a2 * b[1]
46 + (uint128_t)a3 * b[0];
47 VERIFY_BITS(d, 114);
48 /* [d 0 0 0] = [p3 0 0 0] */
49 c = (uint128_t)a4 * b[4];
50 VERIFY_BITS(c, 112);
51 /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
52 d += (uint128_t)R * (uint64_t)c; c >>= 64;
53 VERIFY_BITS(d, 115);
54 VERIFY_BITS(c, 48);
55 /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
56 t3 = d & M; d >>= 52;
57 VERIFY_BITS(t3, 52);
58 VERIFY_BITS(d, 63);
59 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
60
61 d += (uint128_t)a0 * b[4]
62 + (uint128_t)a1 * b[3]
63 + (uint128_t)a2 * b[2]
64 + (uint128_t)a3 * b[1]
65 + (uint128_t)a4 * b[0];
66 VERIFY_BITS(d, 115);
67 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
68 d += (uint128_t)(R << 12) * (uint64_t)c;
69 VERIFY_BITS(d, 116);
70 /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
71 t4 = d & M; d >>= 52;
72 VERIFY_BITS(t4, 52);
73 VERIFY_BITS(d, 64);
74 /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
75 tx = (t4 >> 48); t4 &= (M >> 4);
76 VERIFY_BITS(tx, 4);
77 VERIFY_BITS(t4, 48);
78 /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
79
80 c = (uint128_t)a0 * b[0];
81 VERIFY_BITS(c, 112);
82 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
83 d += (uint128_t)a1 * b[4]
84 + (uint128_t)a2 * b[3]
85 + (uint128_t)a3 * b[2]
86 + (uint128_t)a4 * b[1];
87 VERIFY_BITS(d, 115);
88 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
89 u0 = d & M; d >>= 52;
90 VERIFY_BITS(u0, 52);
91 VERIFY_BITS(d, 63);
92 /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
93 /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
94 u0 = (u0 << 4) | tx;
95 VERIFY_BITS(u0, 56);
96 /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
97 c += (uint128_t)u0 * (R >> 4);
98 VERIFY_BITS(c, 115);
99 /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
100 r[0] = c & M; c >>= 52;
101 VERIFY_BITS(r[0], 52);
102 VERIFY_BITS(c, 61);
103 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
104
105 c += (uint128_t)a0 * b[1]
106 + (uint128_t)a1 * b[0];
107 VERIFY_BITS(c, 114);
108 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
109 d += (uint128_t)a2 * b[4]
110 + (uint128_t)a3 * b[3]
111 + (uint128_t)a4 * b[2];
112 VERIFY_BITS(d, 114);
113 /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
114 c += (d & M) * R; d >>= 52;
115 VERIFY_BITS(c, 115);
116 VERIFY_BITS(d, 62);
117 /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
118 r[1] = c & M; c >>= 52;
119 VERIFY_BITS(r[1], 52);
120 VERIFY_BITS(c, 63);
121 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
122
123 c += (uint128_t)a0 * b[2]
124 + (uint128_t)a1 * b[1]
125 + (uint128_t)a2 * b[0];
126 VERIFY_BITS(c, 114);
127 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
128 d += (uint128_t)a3 * b[4]
129 + (uint128_t)a4 * b[3];
130 VERIFY_BITS(d, 114);
131 /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
132 c += (uint128_t)R * (uint64_t)d; d >>= 64;
133 VERIFY_BITS(c, 115);
134 VERIFY_BITS(d, 50);
135 /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
136
137 r[2] = c & M; c >>= 52;
138 VERIFY_BITS(r[2], 52);
139 VERIFY_BITS(c, 63);
140 /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
141 c += (uint128_t)(R << 12) * (uint64_t)d + t3;
142 VERIFY_BITS(c, 100);
143 /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
144 r[3] = c & M; c >>= 52;
145 VERIFY_BITS(r[3], 52);
146 VERIFY_BITS(c, 48);
147 /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
148 c += t4;
149 VERIFY_BITS(c, 49);
150 /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
151 r[4] = c;
152 VERIFY_BITS(r[4], 49);
153 /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
154}
155
156SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
157 uint128_t c, d;
158 uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
159 int64_t t3, t4, tx, u0;
160 const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
161
162 VERIFY_BITS(a[0], 56);
163 VERIFY_BITS(a[1], 56);
164 VERIFY_BITS(a[2], 56);
165 VERIFY_BITS(a[3], 56);
166 VERIFY_BITS(a[4], 52);
167
173 d = (uint128_t)(a0*2) * a3
174 + (uint128_t)(a1*2) * a2;
175 VERIFY_BITS(d, 114);
176 /* [d 0 0 0] = [p3 0 0 0] */
177 c = (uint128_t)a4 * a4;
178 VERIFY_BITS(c, 112);
179 /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
180 d += (uint128_t)R * (uint64_t)c; c >>= 64;
181 VERIFY_BITS(d, 115);
182 VERIFY_BITS(c, 48);
183 /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
184 t3 = d & M; d >>= 52;
185 VERIFY_BITS(t3, 52);
186 VERIFY_BITS(d, 63);
187 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
188
189 a4 *= 2;
190 d += (uint128_t)a0 * a4
191 + (uint128_t)(a1*2) * a3
192 + (uint128_t)a2 * a2;
193 VERIFY_BITS(d, 115);
194 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
195 d += (uint128_t)(R << 12) * (uint64_t)c;
196 VERIFY_BITS(d, 116);
197 /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
198 t4 = d & M; d >>= 52;
199 VERIFY_BITS(t4, 52);
200 VERIFY_BITS(d, 64);
201 /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
202 tx = (t4 >> 48); t4 &= (M >> 4);
203 VERIFY_BITS(tx, 4);
204 VERIFY_BITS(t4, 48);
205 /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
206
207 c = (uint128_t)a0 * a0;
208 VERIFY_BITS(c, 112);
209 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
210 d += (uint128_t)a1 * a4
211 + (uint128_t)(a2*2) * a3;
212 VERIFY_BITS(d, 114);
213 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
214 u0 = d & M; d >>= 52;
215 VERIFY_BITS(u0, 52);
216 VERIFY_BITS(d, 62);
217 /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
218 /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
219 u0 = (u0 << 4) | tx;
220 VERIFY_BITS(u0, 56);
221 /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
222 c += (uint128_t)u0 * (R >> 4);
223 VERIFY_BITS(c, 113);
224 /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
225 r[0] = c & M; c >>= 52;
226 VERIFY_BITS(r[0], 52);
227 VERIFY_BITS(c, 61);
228 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
229
230 a0 *= 2;
231 c += (uint128_t)a0 * a1;
232 VERIFY_BITS(c, 114);
233 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
234 d += (uint128_t)a2 * a4
235 + (uint128_t)a3 * a3;
236 VERIFY_BITS(d, 114);
237 /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
238 c += (d & M) * R; d >>= 52;
239 VERIFY_BITS(c, 115);
240 VERIFY_BITS(d, 62);
241 /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
242 r[1] = c & M; c >>= 52;
243 VERIFY_BITS(r[1], 52);
244 VERIFY_BITS(c, 63);
245 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
246
247 c += (uint128_t)a0 * a2
248 + (uint128_t)a1 * a1;
249 VERIFY_BITS(c, 114);
250 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
251 d += (uint128_t)a3 * a4;
252 VERIFY_BITS(d, 114);
253 /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
254 c += (uint128_t)R * (uint64_t)d; d >>= 64;
255 VERIFY_BITS(c, 115);
256 VERIFY_BITS(d, 50);
257 /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
258 r[2] = c & M; c >>= 52;
259 VERIFY_BITS(r[2], 52);
260 VERIFY_BITS(c, 63);
261 /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
262
263 c += (uint128_t)(R << 12) * (uint64_t)d + t3;
264 VERIFY_BITS(c, 100);
265 /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
266 r[3] = c & M; c >>= 52;
267 VERIFY_BITS(r[3], 52);
268 VERIFY_BITS(c, 48);
269 /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
270 c += t4;
271 VERIFY_BITS(c, 49);
272 /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
273 r[4] = c;
274 VERIFY_BITS(r[4], 49);
275 /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
276}
277
278#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */
secp256k1_fe_mul_inner
static SECP256K1_INLINE void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t *SECP256K1_RESTRICT b)
Definition: field_5x52_int128_impl.h:18
VERIFY_BITS
#define VERIFY_BITS(x, n)
Definition: field_5x52_int128_impl.h:15
secp256k1_fe_sqr_inner
static SECP256K1_INLINE void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a)
Definition: field_5x52_int128_impl.h:156
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition: util.h:68
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition: util.h:160
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition: secp256k1.h:127
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