Bitcoin ABC 0.32.11
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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#include "int128.h"
13
14#ifdef VERIFY
15#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
16#define VERIFY_BITS_128(x, n) VERIFY_CHECK(secp256k1_u128_check_bits((x), (n)))
17#else
18#define VERIFY_BITS(x, n) do { } while(0)
19#define VERIFY_BITS_128(x, n) do { } while(0)
20#endif
21
22SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
23 secp256k1_uint128 c, d;
24 uint64_t t3, t4, tx, u0;
25 uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
26 const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
27
28 VERIFY_BITS(a[0], 56);
29 VERIFY_BITS(a[1], 56);
30 VERIFY_BITS(a[2], 56);
31 VERIFY_BITS(a[3], 56);
32 VERIFY_BITS(a[4], 52);
33 VERIFY_BITS(b[0], 56);
34 VERIFY_BITS(b[1], 56);
35 VERIFY_BITS(b[2], 56);
36 VERIFY_BITS(b[3], 56);
37 VERIFY_BITS(b[4], 52);
38 VERIFY_CHECK(r != b);
39 VERIFY_CHECK(a != b);
40
41 /* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
42 * for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x).
43 * for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4)
44 * Note that [x 0 0 0 0 0] = [x*R].
45 */
46
47 secp256k1_u128_mul(&d, a0, b[3]);
48 secp256k1_u128_accum_mul(&d, a1, b[2]);
49 secp256k1_u128_accum_mul(&d, a2, b[1]);
50 secp256k1_u128_accum_mul(&d, a3, b[0]);
51 VERIFY_BITS_128(&d, 114);
52 /* [d 0 0 0] = [p3 0 0 0] */
53 secp256k1_u128_mul(&c, a4, b[4]);
54 VERIFY_BITS_128(&c, 112);
55 /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
56 secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
57 VERIFY_BITS_128(&d, 115);
58 VERIFY_BITS_128(&c, 48);
59 /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
60 t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
61 VERIFY_BITS(t3, 52);
62 VERIFY_BITS_128(&d, 63);
63 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
64
65 secp256k1_u128_accum_mul(&d, a0, b[4]);
66 secp256k1_u128_accum_mul(&d, a1, b[3]);
67 secp256k1_u128_accum_mul(&d, a2, b[2]);
68 secp256k1_u128_accum_mul(&d, a3, b[1]);
69 secp256k1_u128_accum_mul(&d, a4, b[0]);
70 VERIFY_BITS_128(&d, 115);
71 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
72 secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
73 VERIFY_BITS_128(&d, 116);
74 /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
75 t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
76 VERIFY_BITS(t4, 52);
77 VERIFY_BITS_128(&d, 64);
78 /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
79 tx = (t4 >> 48); t4 &= (M >> 4);
80 VERIFY_BITS(tx, 4);
81 VERIFY_BITS(t4, 48);
82 /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
83
84 secp256k1_u128_mul(&c, a0, b[0]);
85 VERIFY_BITS_128(&c, 112);
86 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
87 secp256k1_u128_accum_mul(&d, a1, b[4]);
88 secp256k1_u128_accum_mul(&d, a2, b[3]);
89 secp256k1_u128_accum_mul(&d, a3, b[2]);
90 secp256k1_u128_accum_mul(&d, a4, b[1]);
91 VERIFY_BITS_128(&d, 115);
92 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
93 u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
94 VERIFY_BITS(u0, 52);
95 VERIFY_BITS_128(&d, 63);
96 /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
97 /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
98 u0 = (u0 << 4) | tx;
99 VERIFY_BITS(u0, 56);
100 /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
101 secp256k1_u128_accum_mul(&c, u0, R >> 4);
102 VERIFY_BITS_128(&c, 115);
103 /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
104 r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
105 VERIFY_BITS(r[0], 52);
106 VERIFY_BITS_128(&c, 61);
107 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
108
109 secp256k1_u128_accum_mul(&c, a0, b[1]);
110 secp256k1_u128_accum_mul(&c, a1, b[0]);
111 VERIFY_BITS_128(&c, 114);
112 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
113 secp256k1_u128_accum_mul(&d, a2, b[4]);
114 secp256k1_u128_accum_mul(&d, a3, b[3]);
115 secp256k1_u128_accum_mul(&d, a4, b[2]);
116 VERIFY_BITS_128(&d, 114);
117 /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
118 secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
119 VERIFY_BITS_128(&c, 115);
120 VERIFY_BITS_128(&d, 62);
121 /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
122 r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
123 VERIFY_BITS(r[1], 52);
124 VERIFY_BITS_128(&c, 63);
125 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
126
127 secp256k1_u128_accum_mul(&c, a0, b[2]);
128 secp256k1_u128_accum_mul(&c, a1, b[1]);
129 secp256k1_u128_accum_mul(&c, a2, b[0]);
130 VERIFY_BITS_128(&c, 114);
131 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
132 secp256k1_u128_accum_mul(&d, a3, b[4]);
133 secp256k1_u128_accum_mul(&d, a4, b[3]);
134 VERIFY_BITS_128(&d, 114);
135 /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
136 secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
137 VERIFY_BITS_128(&c, 115);
138 VERIFY_BITS_128(&d, 50);
139 /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
140
141 r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
142 VERIFY_BITS(r[2], 52);
143 VERIFY_BITS_128(&c, 63);
144 /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
145 secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
146 secp256k1_u128_accum_u64(&c, t3);
147 VERIFY_BITS_128(&c, 100);
148 /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
149 r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
150 VERIFY_BITS(r[3], 52);
151 VERIFY_BITS_128(&c, 48);
152 /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
153 r[4] = secp256k1_u128_to_u64(&c) + t4;
154 VERIFY_BITS(r[4], 49);
155 /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
156}
157
158SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
159 secp256k1_uint128 c, d;
160 uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
161 int64_t t3, t4, tx, u0;
162 const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
163
164 VERIFY_BITS(a[0], 56);
165 VERIFY_BITS(a[1], 56);
166 VERIFY_BITS(a[2], 56);
167 VERIFY_BITS(a[3], 56);
168 VERIFY_BITS(a[4], 52);
169
175 secp256k1_u128_mul(&d, a0*2, a3);
176 secp256k1_u128_accum_mul(&d, a1*2, a2);
177 VERIFY_BITS_128(&d, 114);
178 /* [d 0 0 0] = [p3 0 0 0] */
179 secp256k1_u128_mul(&c, a4, a4);
180 VERIFY_BITS_128(&c, 112);
181 /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
182 secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
183 VERIFY_BITS_128(&d, 115);
184 VERIFY_BITS_128(&c, 48);
185 /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
186 t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
187 VERIFY_BITS(t3, 52);
188 VERIFY_BITS_128(&d, 63);
189 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
190
191 a4 *= 2;
192 secp256k1_u128_accum_mul(&d, a0, a4);
193 secp256k1_u128_accum_mul(&d, a1*2, a3);
194 secp256k1_u128_accum_mul(&d, a2, a2);
195 VERIFY_BITS_128(&d, 115);
196 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
197 secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
198 VERIFY_BITS_128(&d, 116);
199 /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
200 t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
201 VERIFY_BITS(t4, 52);
202 VERIFY_BITS_128(&d, 64);
203 /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
204 tx = (t4 >> 48); t4 &= (M >> 4);
205 VERIFY_BITS(tx, 4);
206 VERIFY_BITS(t4, 48);
207 /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
208
209 secp256k1_u128_mul(&c, a0, a0);
210 VERIFY_BITS_128(&c, 112);
211 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
212 secp256k1_u128_accum_mul(&d, a1, a4);
213 secp256k1_u128_accum_mul(&d, a2*2, a3);
214 VERIFY_BITS_128(&d, 114);
215 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
216 u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
217 VERIFY_BITS(u0, 52);
218 VERIFY_BITS_128(&d, 62);
219 /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
220 /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
221 u0 = (u0 << 4) | tx;
222 VERIFY_BITS(u0, 56);
223 /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
224 secp256k1_u128_accum_mul(&c, u0, R >> 4);
225 VERIFY_BITS_128(&c, 113);
226 /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
227 r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
228 VERIFY_BITS(r[0], 52);
229 VERIFY_BITS_128(&c, 61);
230 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
231
232 a0 *= 2;
233 secp256k1_u128_accum_mul(&c, a0, a1);
234 VERIFY_BITS_128(&c, 114);
235 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
236 secp256k1_u128_accum_mul(&d, a2, a4);
237 secp256k1_u128_accum_mul(&d, a3, a3);
238 VERIFY_BITS_128(&d, 114);
239 /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
240 secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
241 VERIFY_BITS_128(&c, 115);
242 VERIFY_BITS_128(&d, 62);
243 /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
244 r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
245 VERIFY_BITS(r[1], 52);
246 VERIFY_BITS_128(&c, 63);
247 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
248
249 secp256k1_u128_accum_mul(&c, a0, a2);
250 secp256k1_u128_accum_mul(&c, a1, a1);
251 VERIFY_BITS_128(&c, 114);
252 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
253 secp256k1_u128_accum_mul(&d, a3, a4);
254 VERIFY_BITS_128(&d, 114);
255 /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
256 secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
257 VERIFY_BITS_128(&c, 115);
258 VERIFY_BITS_128(&d, 50);
259 /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
260 r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
261 VERIFY_BITS(r[2], 52);
262 VERIFY_BITS_128(&c, 63);
263 /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
264
265 secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
266 secp256k1_u128_accum_u64(&c, t3);
267 VERIFY_BITS_128(&c, 100);
268 /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
269 r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
270 VERIFY_BITS(r[3], 52);
271 VERIFY_BITS_128(&c, 48);
272 /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
273 r[4] = secp256k1_u128_to_u64(&c) + t4;
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 */
VERIFY_BITS_128
#define VERIFY_BITS_128(x, n)
Definition: field_5x52_int128_impl.h:19
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:22
VERIFY_BITS
#define VERIFY_BITS(x, n)
Definition: field_5x52_int128_impl.h:18
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:158
secp256k1_u128_rshift
static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n)
Definition: int128_native_impl.h:22
secp256k1_u128_accum_u64
static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a)
Definition: int128_native_impl.h:18
secp256k1_u128_accum_mul
static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b)
Definition: int128_native_impl.h:14
secp256k1_u128_mul
static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b)
Definition: int128_native_impl.h:10
secp256k1_u128_to_u64
static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a)
Definition: int128_native_impl.h:27
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition: util.h:96
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition: util.h:156
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition: secp256k1.h:131
secp256k1_uint128
Definition: int128_struct.h:7
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