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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#include "util.h"
14
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
18SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
19 secp256k1_uint128 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 secp256k1_u128_mul(&d, a0, b[3]);
44 secp256k1_u128_accum_mul(&d, a1, b[2]);
45 secp256k1_u128_accum_mul(&d, a2, b[1]);
46 secp256k1_u128_accum_mul(&d, a3, b[0]);
47 VERIFY_BITS_128(&d, 114);
48 /* [d 0 0 0] = [p3 0 0 0] */
49 secp256k1_u128_mul(&c, a4, b[4]);
50 VERIFY_BITS_128(&c, 112);
51 /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
52 secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
53 VERIFY_BITS_128(&d, 115);
54 VERIFY_BITS_128(&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 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
57 VERIFY_BITS(t3, 52);
58 VERIFY_BITS_128(&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 secp256k1_u128_accum_mul(&d, a0, b[4]);
62 secp256k1_u128_accum_mul(&d, a1, b[3]);
63 secp256k1_u128_accum_mul(&d, a2, b[2]);
64 secp256k1_u128_accum_mul(&d, a3, b[1]);
65 secp256k1_u128_accum_mul(&d, a4, b[0]);
66 VERIFY_BITS_128(&d, 115);
67 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
68 secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
69 VERIFY_BITS_128(&d, 116);
70 /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
71 t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
72 VERIFY_BITS(t4, 52);
73 VERIFY_BITS_128(&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 secp256k1_u128_mul(&c, a0, b[0]);
81 VERIFY_BITS_128(&c, 112);
82 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
83 secp256k1_u128_accum_mul(&d, a1, b[4]);
84 secp256k1_u128_accum_mul(&d, a2, b[3]);
85 secp256k1_u128_accum_mul(&d, a3, b[2]);
86 secp256k1_u128_accum_mul(&d, a4, b[1]);
87 VERIFY_BITS_128(&d, 114);
88 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
89 u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
90 VERIFY_BITS(u0, 52);
91 VERIFY_BITS_128(&d, 62);
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 secp256k1_u128_accum_mul(&c, u0, R >> 4);
98 VERIFY_BITS_128(&c, 113);
99 /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
100 r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
101 VERIFY_BITS(r[0], 52);
102 VERIFY_BITS_128(&c, 61);
103 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
104
105 secp256k1_u128_accum_mul(&c, a0, b[1]);
106 secp256k1_u128_accum_mul(&c, a1, b[0]);
107 VERIFY_BITS_128(&c, 114);
108 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
109 secp256k1_u128_accum_mul(&d, a2, b[4]);
110 secp256k1_u128_accum_mul(&d, a3, b[3]);
111 secp256k1_u128_accum_mul(&d, a4, b[2]);
112 VERIFY_BITS_128(&d, 114);
113 /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
114 secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
115 VERIFY_BITS_128(&c, 115);
116 VERIFY_BITS_128(&d, 62);
117 /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
118 r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
119 VERIFY_BITS(r[1], 52);
120 VERIFY_BITS_128(&c, 63);
121 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
122
123 secp256k1_u128_accum_mul(&c, a0, b[2]);
124 secp256k1_u128_accum_mul(&c, a1, b[1]);
125 secp256k1_u128_accum_mul(&c, a2, b[0]);
126 VERIFY_BITS_128(&c, 114);
127 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
128 secp256k1_u128_accum_mul(&d, a3, b[4]);
129 secp256k1_u128_accum_mul(&d, a4, b[3]);
130 VERIFY_BITS_128(&d, 114);
131 /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
132 secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
133 VERIFY_BITS_128(&c, 115);
134 VERIFY_BITS_128(&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] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
138 VERIFY_BITS(r[2], 52);
139 VERIFY_BITS_128(&c, 63);
140 /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
141 secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
142 secp256k1_u128_accum_u64(&c, t3);
143 VERIFY_BITS_128(&c, 100);
144 /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
145 r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
146 VERIFY_BITS(r[3], 52);
147 VERIFY_BITS_128(&c, 48);
148 /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
149 r[4] = secp256k1_u128_to_u64(&c) + t4;
150 VERIFY_BITS(r[4], 49);
151 /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
152}
153
154SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
155 secp256k1_uint128 c, d;
156 uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
157 uint64_t t3, t4, tx, u0;
158 const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
159
160 VERIFY_BITS(a[0], 56);
161 VERIFY_BITS(a[1], 56);
162 VERIFY_BITS(a[2], 56);
163 VERIFY_BITS(a[3], 56);
164 VERIFY_BITS(a[4], 52);
165
170
171 secp256k1_u128_mul(&d, a0*2, a3);
172 secp256k1_u128_accum_mul(&d, a1*2, a2);
173 VERIFY_BITS_128(&d, 114);
174 /* [d 0 0 0] = [p3 0 0 0] */
175 secp256k1_u128_mul(&c, a4, a4);
176 VERIFY_BITS_128(&c, 112);
177 /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
178 secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
179 VERIFY_BITS_128(&d, 115);
180 VERIFY_BITS_128(&c, 48);
181 /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
182 t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
183 VERIFY_BITS(t3, 52);
184 VERIFY_BITS_128(&d, 63);
185 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
186
187 a4 *= 2;
188 secp256k1_u128_accum_mul(&d, a0, a4);
189 secp256k1_u128_accum_mul(&d, a1*2, a3);
190 secp256k1_u128_accum_mul(&d, a2, a2);
191 VERIFY_BITS_128(&d, 115);
192 /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
193 secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
194 VERIFY_BITS_128(&d, 116);
195 /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
196 t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
197 VERIFY_BITS(t4, 52);
198 VERIFY_BITS_128(&d, 64);
199 /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
200 tx = (t4 >> 48); t4 &= (M >> 4);
201 VERIFY_BITS(tx, 4);
202 VERIFY_BITS(t4, 48);
203 /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
204
205 secp256k1_u128_mul(&c, a0, a0);
206 VERIFY_BITS_128(&c, 112);
207 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
208 secp256k1_u128_accum_mul(&d, a1, a4);
209 secp256k1_u128_accum_mul(&d, a2*2, a3);
210 VERIFY_BITS_128(&d, 114);
211 /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
212 u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
213 VERIFY_BITS(u0, 52);
214 VERIFY_BITS_128(&d, 62);
215 /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
216 /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
217 u0 = (u0 << 4) | tx;
218 VERIFY_BITS(u0, 56);
219 /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
220 secp256k1_u128_accum_mul(&c, u0, R >> 4);
221 VERIFY_BITS_128(&c, 113);
222 /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
223 r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
224 VERIFY_BITS(r[0], 52);
225 VERIFY_BITS_128(&c, 61);
226 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
227
228 a0 *= 2;
229 secp256k1_u128_accum_mul(&c, a0, a1);
230 VERIFY_BITS_128(&c, 114);
231 /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
232 secp256k1_u128_accum_mul(&d, a2, a4);
233 secp256k1_u128_accum_mul(&d, a3, a3);
234 VERIFY_BITS_128(&d, 114);
235 /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
236 secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
237 VERIFY_BITS_128(&c, 115);
238 VERIFY_BITS_128(&d, 62);
239 /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
240 r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
241 VERIFY_BITS(r[1], 52);
242 VERIFY_BITS_128(&c, 63);
243 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
244
245 secp256k1_u128_accum_mul(&c, a0, a2);
246 secp256k1_u128_accum_mul(&c, a1, a1);
247 VERIFY_BITS_128(&c, 114);
248 /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
249 secp256k1_u128_accum_mul(&d, a3, a4);
250 VERIFY_BITS_128(&d, 114);
251 /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
252 secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
253 VERIFY_BITS_128(&c, 115);
254 VERIFY_BITS_128(&d, 50);
255 /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
256 r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
257 VERIFY_BITS(r[2], 52);
258 VERIFY_BITS_128(&c, 63);
259 /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
260
261 secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
262 secp256k1_u128_accum_u64(&c, t3);
263 VERIFY_BITS_128(&c, 100);
264 /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
265 r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
266 VERIFY_BITS(r[3], 52);
267 VERIFY_BITS_128(&c, 48);
268 /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
269 r[4] = secp256k1_u128_to_u64(&c) + t4;
270 VERIFY_BITS(r[4], 49);
271 /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
272}
273
274#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */
VERIFY_BITS_128
#define VERIFY_BITS_128(x, n)
Definition field_5x52_int128_impl.h:16
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:154
secp256k1_u128_rshift
static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n)
Definition int128_native_impl.h:23
secp256k1_u128_accum_u64
static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a)
Definition int128_native_impl.h:19
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:15
secp256k1_u128_mul
static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b)
Definition int128_native_impl.h:11
secp256k1_u128_to_u64
static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a)
Definition int128_native_impl.h:28
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition util.h:54
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition util.h:159
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition util.h:194
secp256k1_uint128
Definition int128_struct.h:7
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