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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 http://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 
18 SECP256K1_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 += (c & M) * R; c >>= 52;
53  VERIFY_BITS(d, 115);
54  VERIFY_BITS(c, 60);
55  /* [c 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 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 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
68  d += c * R;
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 += (d & M) * R; d >>= 52;
133  VERIFY_BITS(c, 115);
134  VERIFY_BITS(d, 62);
135  /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
136 
137  /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
138  r[2] = c & M; c >>= 52;
139  VERIFY_BITS(r[2], 52);
140  VERIFY_BITS(c, 63);
141  /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
142  c += d * R + t3;
143  VERIFY_BITS(c, 100);
144  /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
145  r[3] = c & M; c >>= 52;
146  VERIFY_BITS(r[3], 52);
147  VERIFY_BITS(c, 48);
148  /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
149  c += t4;
150  VERIFY_BITS(c, 49);
151  /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
152  r[4] = c;
153  VERIFY_BITS(r[4], 49);
154  /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
155 }
156 
157 SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
158  uint128_t c, d;
159  uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
160  int64_t t3, t4, tx, u0;
161  const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
162 
163  VERIFY_BITS(a[0], 56);
164  VERIFY_BITS(a[1], 56);
165  VERIFY_BITS(a[2], 56);
166  VERIFY_BITS(a[3], 56);
167  VERIFY_BITS(a[4], 52);
168 
174  d = (uint128_t)(a0*2) * a3
175  + (uint128_t)(a1*2) * a2;
176  VERIFY_BITS(d, 114);
177  /* [d 0 0 0] = [p3 0 0 0] */
178  c = (uint128_t)a4 * a4;
179  VERIFY_BITS(c, 112);
180  /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
181  d += (c & M) * R; c >>= 52;
182  VERIFY_BITS(d, 115);
183  VERIFY_BITS(c, 60);
184  /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
185  t3 = d & M; d >>= 52;
186  VERIFY_BITS(t3, 52);
187  VERIFY_BITS(d, 63);
188  /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
189 
190  a4 *= 2;
191  d += (uint128_t)a0 * a4
192  + (uint128_t)(a1*2) * a3
193  + (uint128_t)a2 * a2;
194  VERIFY_BITS(d, 115);
195  /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
196  d += c * R;
197  VERIFY_BITS(d, 116);
198  /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
199  t4 = d & M; d >>= 52;
200  VERIFY_BITS(t4, 52);
201  VERIFY_BITS(d, 64);
202  /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
203  tx = (t4 >> 48); t4 &= (M >> 4);
204  VERIFY_BITS(tx, 4);
205  VERIFY_BITS(t4, 48);
206  /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
207 
208  c = (uint128_t)a0 * a0;
209  VERIFY_BITS(c, 112);
210  /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
211  d += (uint128_t)a1 * a4
212  + (uint128_t)(a2*2) * a3;
213  VERIFY_BITS(d, 114);
214  /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
215  u0 = d & M; d >>= 52;
216  VERIFY_BITS(u0, 52);
217  VERIFY_BITS(d, 62);
218  /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
219  /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
220  u0 = (u0 << 4) | tx;
221  VERIFY_BITS(u0, 56);
222  /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
223  c += (uint128_t)u0 * (R >> 4);
224  VERIFY_BITS(c, 113);
225  /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
226  r[0] = c & M; c >>= 52;
227  VERIFY_BITS(r[0], 52);
228  VERIFY_BITS(c, 61);
229  /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
230 
231  a0 *= 2;
232  c += (uint128_t)a0 * a1;
233  VERIFY_BITS(c, 114);
234  /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
235  d += (uint128_t)a2 * a4
236  + (uint128_t)a3 * a3;
237  VERIFY_BITS(d, 114);
238  /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
239  c += (d & M) * R; d >>= 52;
240  VERIFY_BITS(c, 115);
241  VERIFY_BITS(d, 62);
242  /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
243  r[1] = c & M; c >>= 52;
244  VERIFY_BITS(r[1], 52);
245  VERIFY_BITS(c, 63);
246  /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
247 
248  c += (uint128_t)a0 * a2
249  + (uint128_t)a1 * a1;
250  VERIFY_BITS(c, 114);
251  /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
252  d += (uint128_t)a3 * a4;
253  VERIFY_BITS(d, 114);
254  /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
255  c += (d & M) * R; d >>= 52;
256  VERIFY_BITS(c, 115);
257  VERIFY_BITS(d, 62);
258  /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
259  r[2] = c & M; c >>= 52;
260  VERIFY_BITS(r[2], 52);
261  VERIFY_BITS(c, 63);
262  /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
263 
264  c += d * R + t3;
265  VERIFY_BITS(c, 100);
266  /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
267  r[3] = c & M; c >>= 52;
268  VERIFY_BITS(r[3], 52);
269  VERIFY_BITS(c, 48);
270  /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
271  c += t4;
272  VERIFY_BITS(c, 49);
273  /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
274  r[4] = c;
275  VERIFY_BITS(r[4], 49);
276  /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
277 }
278 
279 #endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition: util.h:67
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
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:157
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition: secp256k1.h:123
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition: util.h:97
VERIFY_BITS
#define VERIFY_BITS(x, n)
Definition: field_5x52_int128_impl.h:15
M
#define M(x)
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