1 /* LibTomCrypt, modular cryptographic library -- Tom St Denis */
2 /* SPDX-License-Identifier: Unlicense */
3 #include "tomcrypt_private.h"
4
5 /**
6 @file ltc_ecc_fp_mulmod.c
7 ECC Crypto, Tom St Denis
8 */
9
10 #if defined(LTC_MECC) && defined(LTC_MECC_FP)
11 #include <limits.h>
12
13 /* number of entries in the cache */
14 #ifndef FP_ENTRIES
15 #define FP_ENTRIES 16
16 #endif
17
18 /* number of bits in LUT */
19 #ifndef FP_LUT
20 #define FP_LUT 8U
21 #endif
22
23 #if (FP_LUT > 12) || (FP_LUT < 2)
24 #error FP_LUT must be between 2 and 12 inclusively
25 #endif
26
27 /** Our FP cache */
28 static struct {
29 ecc_point *g, /* cached COPY of base point */
30 *LUT[1U<<FP_LUT]; /* fixed point lookup */
31 void *mu; /* copy of the montgomery constant */
32 int lru_count; /* amount of times this entry has been used */
33 int lock; /* flag to indicate cache eviction permitted (0) or not (1) */
34 } fp_cache[FP_ENTRIES];
35
36 LTC_MUTEX_GLOBAL(ltc_ecc_fp_lock)
37
38 /* simple table to help direct the generation of the LUT */
39 static const struct {
40 int ham, terma, termb;
41 } lut_orders[] = {
42 { 0, 0, 0 }, { 1, 0, 0 }, { 1, 0, 0 }, { 2, 1, 2 }, { 1, 0, 0 }, { 2, 1, 4 }, { 2, 2, 4 }, { 3, 3, 4 },
43 { 1, 0, 0 }, { 2, 1, 8 }, { 2, 2, 8 }, { 3, 3, 8 }, { 2, 4, 8 }, { 3, 5, 8 }, { 3, 6, 8 }, { 4, 7, 8 },
44 { 1, 0, 0 }, { 2, 1, 16 }, { 2, 2, 16 }, { 3, 3, 16 }, { 2, 4, 16 }, { 3, 5, 16 }, { 3, 6, 16 }, { 4, 7, 16 },
45 { 2, 8, 16 }, { 3, 9, 16 }, { 3, 10, 16 }, { 4, 11, 16 }, { 3, 12, 16 }, { 4, 13, 16 }, { 4, 14, 16 }, { 5, 15, 16 },
46 { 1, 0, 0 }, { 2, 1, 32 }, { 2, 2, 32 }, { 3, 3, 32 }, { 2, 4, 32 }, { 3, 5, 32 }, { 3, 6, 32 }, { 4, 7, 32 },
47 { 2, 8, 32 }, { 3, 9, 32 }, { 3, 10, 32 }, { 4, 11, 32 }, { 3, 12, 32 }, { 4, 13, 32 }, { 4, 14, 32 }, { 5, 15, 32 },
48 { 2, 16, 32 }, { 3, 17, 32 }, { 3, 18, 32 }, { 4, 19, 32 }, { 3, 20, 32 }, { 4, 21, 32 }, { 4, 22, 32 }, { 5, 23, 32 },
49 { 3, 24, 32 }, { 4, 25, 32 }, { 4, 26, 32 }, { 5, 27, 32 }, { 4, 28, 32 }, { 5, 29, 32 }, { 5, 30, 32 }, { 6, 31, 32 },
50 #if FP_LUT > 6
51 { 1, 0, 0 }, { 2, 1, 64 }, { 2, 2, 64 }, { 3, 3, 64 }, { 2, 4, 64 }, { 3, 5, 64 }, { 3, 6, 64 }, { 4, 7, 64 },
52 { 2, 8, 64 }, { 3, 9, 64 }, { 3, 10, 64 }, { 4, 11, 64 }, { 3, 12, 64 }, { 4, 13, 64 }, { 4, 14, 64 }, { 5, 15, 64 },
53 { 2, 16, 64 }, { 3, 17, 64 }, { 3, 18, 64 }, { 4, 19, 64 }, { 3, 20, 64 }, { 4, 21, 64 }, { 4, 22, 64 }, { 5, 23, 64 },
54 { 3, 24, 64 }, { 4, 25, 64 }, { 4, 26, 64 }, { 5, 27, 64 }, { 4, 28, 64 }, { 5, 29, 64 }, { 5, 30, 64 }, { 6, 31, 64 },
55 { 2, 32, 64 }, { 3, 33, 64 }, { 3, 34, 64 }, { 4, 35, 64 }, { 3, 36, 64 }, { 4, 37, 64 }, { 4, 38, 64 }, { 5, 39, 64 },
56 { 3, 40, 64 }, { 4, 41, 64 }, { 4, 42, 64 }, { 5, 43, 64 }, { 4, 44, 64 }, { 5, 45, 64 }, { 5, 46, 64 }, { 6, 47, 64 },
57 { 3, 48, 64 }, { 4, 49, 64 }, { 4, 50, 64 }, { 5, 51, 64 }, { 4, 52, 64 }, { 5, 53, 64 }, { 5, 54, 64 }, { 6, 55, 64 },
58 { 4, 56, 64 }, { 5, 57, 64 }, { 5, 58, 64 }, { 6, 59, 64 }, { 5, 60, 64 }, { 6, 61, 64 }, { 6, 62, 64 }, { 7, 63, 64 },
59 #if FP_LUT > 7
60 { 1, 0, 0 }, { 2, 1, 128 }, { 2, 2, 128 }, { 3, 3, 128 }, { 2, 4, 128 }, { 3, 5, 128 }, { 3, 6, 128 }, { 4, 7, 128 },
61 { 2, 8, 128 }, { 3, 9, 128 }, { 3, 10, 128 }, { 4, 11, 128 }, { 3, 12, 128 }, { 4, 13, 128 }, { 4, 14, 128 }, { 5, 15, 128 },
62 { 2, 16, 128 }, { 3, 17, 128 }, { 3, 18, 128 }, { 4, 19, 128 }, { 3, 20, 128 }, { 4, 21, 128 }, { 4, 22, 128 }, { 5, 23, 128 },
63 { 3, 24, 128 }, { 4, 25, 128 }, { 4, 26, 128 }, { 5, 27, 128 }, { 4, 28, 128 }, { 5, 29, 128 }, { 5, 30, 128 }, { 6, 31, 128 },
64 { 2, 32, 128 }, { 3, 33, 128 }, { 3, 34, 128 }, { 4, 35, 128 }, { 3, 36, 128 }, { 4, 37, 128 }, { 4, 38, 128 }, { 5, 39, 128 },
65 { 3, 40, 128 }, { 4, 41, 128 }, { 4, 42, 128 }, { 5, 43, 128 }, { 4, 44, 128 }, { 5, 45, 128 }, { 5, 46, 128 }, { 6, 47, 128 },
66 { 3, 48, 128 }, { 4, 49, 128 }, { 4, 50, 128 }, { 5, 51, 128 }, { 4, 52, 128 }, { 5, 53, 128 }, { 5, 54, 128 }, { 6, 55, 128 },
67 { 4, 56, 128 }, { 5, 57, 128 }, { 5, 58, 128 }, { 6, 59, 128 }, { 5, 60, 128 }, { 6, 61, 128 }, { 6, 62, 128 }, { 7, 63, 128 },
68 { 2, 64, 128 }, { 3, 65, 128 }, { 3, 66, 128 }, { 4, 67, 128 }, { 3, 68, 128 }, { 4, 69, 128 }, { 4, 70, 128 }, { 5, 71, 128 },
69 { 3, 72, 128 }, { 4, 73, 128 }, { 4, 74, 128 }, { 5, 75, 128 }, { 4, 76, 128 }, { 5, 77, 128 }, { 5, 78, 128 }, { 6, 79, 128 },
70 { 3, 80, 128 }, { 4, 81, 128 }, { 4, 82, 128 }, { 5, 83, 128 }, { 4, 84, 128 }, { 5, 85, 128 }, { 5, 86, 128 }, { 6, 87, 128 },
71 { 4, 88, 128 }, { 5, 89, 128 }, { 5, 90, 128 }, { 6, 91, 128 }, { 5, 92, 128 }, { 6, 93, 128 }, { 6, 94, 128 }, { 7, 95, 128 },
72 { 3, 96, 128 }, { 4, 97, 128 }, { 4, 98, 128 }, { 5, 99, 128 }, { 4, 100, 128 }, { 5, 101, 128 }, { 5, 102, 128 }, { 6, 103, 128 },
73 { 4, 104, 128 }, { 5, 105, 128 }, { 5, 106, 128 }, { 6, 107, 128 }, { 5, 108, 128 }, { 6, 109, 128 }, { 6, 110, 128 }, { 7, 111, 128 },
74 { 4, 112, 128 }, { 5, 113, 128 }, { 5, 114, 128 }, { 6, 115, 128 }, { 5, 116, 128 }, { 6, 117, 128 }, { 6, 118, 128 }, { 7, 119, 128 },
75 { 5, 120, 128 }, { 6, 121, 128 }, { 6, 122, 128 }, { 7, 123, 128 }, { 6, 124, 128 }, { 7, 125, 128 }, { 7, 126, 128 }, { 8, 127, 128 },
76 #if FP_LUT > 8
77 { 1, 0, 0 }, { 2, 1, 256 }, { 2, 2, 256 }, { 3, 3, 256 }, { 2, 4, 256 }, { 3, 5, 256 }, { 3, 6, 256 }, { 4, 7, 256 },
78 { 2, 8, 256 }, { 3, 9, 256 }, { 3, 10, 256 }, { 4, 11, 256 }, { 3, 12, 256 }, { 4, 13, 256 }, { 4, 14, 256 }, { 5, 15, 256 },
79 { 2, 16, 256 }, { 3, 17, 256 }, { 3, 18, 256 }, { 4, 19, 256 }, { 3, 20, 256 }, { 4, 21, 256 }, { 4, 22, 256 }, { 5, 23, 256 },
80 { 3, 24, 256 }, { 4, 25, 256 }, { 4, 26, 256 }, { 5, 27, 256 }, { 4, 28, 256 }, { 5, 29, 256 }, { 5, 30, 256 }, { 6, 31, 256 },
81 { 2, 32, 256 }, { 3, 33, 256 }, { 3, 34, 256 }, { 4, 35, 256 }, { 3, 36, 256 }, { 4, 37, 256 }, { 4, 38, 256 }, { 5, 39, 256 },
82 { 3, 40, 256 }, { 4, 41, 256 }, { 4, 42, 256 }, { 5, 43, 256 }, { 4, 44, 256 }, { 5, 45, 256 }, { 5, 46, 256 }, { 6, 47, 256 },
83 { 3, 48, 256 }, { 4, 49, 256 }, { 4, 50, 256 }, { 5, 51, 256 }, { 4, 52, 256 }, { 5, 53, 256 }, { 5, 54, 256 }, { 6, 55, 256 },
84 { 4, 56, 256 }, { 5, 57, 256 }, { 5, 58, 256 }, { 6, 59, 256 }, { 5, 60, 256 }, { 6, 61, 256 }, { 6, 62, 256 }, { 7, 63, 256 },
85 { 2, 64, 256 }, { 3, 65, 256 }, { 3, 66, 256 }, { 4, 67, 256 }, { 3, 68, 256 }, { 4, 69, 256 }, { 4, 70, 256 }, { 5, 71, 256 },
86 { 3, 72, 256 }, { 4, 73, 256 }, { 4, 74, 256 }, { 5, 75, 256 }, { 4, 76, 256 }, { 5, 77, 256 }, { 5, 78, 256 }, { 6, 79, 256 },
87 { 3, 80, 256 }, { 4, 81, 256 }, { 4, 82, 256 }, { 5, 83, 256 }, { 4, 84, 256 }, { 5, 85, 256 }, { 5, 86, 256 }, { 6, 87, 256 },
88 { 4, 88, 256 }, { 5, 89, 256 }, { 5, 90, 256 }, { 6, 91, 256 }, { 5, 92, 256 }, { 6, 93, 256 }, { 6, 94, 256 }, { 7, 95, 256 },
89 { 3, 96, 256 }, { 4, 97, 256 }, { 4, 98, 256 }, { 5, 99, 256 }, { 4, 100, 256 }, { 5, 101, 256 }, { 5, 102, 256 }, { 6, 103, 256 },
90 { 4, 104, 256 }, { 5, 105, 256 }, { 5, 106, 256 }, { 6, 107, 256 }, { 5, 108, 256 }, { 6, 109, 256 }, { 6, 110, 256 }, { 7, 111, 256 },
91 { 4, 112, 256 }, { 5, 113, 256 }, { 5, 114, 256 }, { 6, 115, 256 }, { 5, 116, 256 }, { 6, 117, 256 }, { 6, 118, 256 }, { 7, 119, 256 },
92 { 5, 120, 256 }, { 6, 121, 256 }, { 6, 122, 256 }, { 7, 123, 256 }, { 6, 124, 256 }, { 7, 125, 256 }, { 7, 126, 256 }, { 8, 127, 256 },
93 { 2, 128, 256 }, { 3, 129, 256 }, { 3, 130, 256 }, { 4, 131, 256 }, { 3, 132, 256 }, { 4, 133, 256 }, { 4, 134, 256 }, { 5, 135, 256 },
94 { 3, 136, 256 }, { 4, 137, 256 }, { 4, 138, 256 }, { 5, 139, 256 }, { 4, 140, 256 }, { 5, 141, 256 }, { 5, 142, 256 }, { 6, 143, 256 },
95 { 3, 144, 256 }, { 4, 145, 256 }, { 4, 146, 256 }, { 5, 147, 256 }, { 4, 148, 256 }, { 5, 149, 256 }, { 5, 150, 256 }, { 6, 151, 256 },
96 { 4, 152, 256 }, { 5, 153, 256 }, { 5, 154, 256 }, { 6, 155, 256 }, { 5, 156, 256 }, { 6, 157, 256 }, { 6, 158, 256 }, { 7, 159, 256 },
97 { 3, 160, 256 }, { 4, 161, 256 }, { 4, 162, 256 }, { 5, 163, 256 }, { 4, 164, 256 }, { 5, 165, 256 }, { 5, 166, 256 }, { 6, 167, 256 },
98 { 4, 168, 256 }, { 5, 169, 256 }, { 5, 170, 256 }, { 6, 171, 256 }, { 5, 172, 256 }, { 6, 173, 256 }, { 6, 174, 256 }, { 7, 175, 256 },
99 { 4, 176, 256 }, { 5, 177, 256 }, { 5, 178, 256 }, { 6, 179, 256 }, { 5, 180, 256 }, { 6, 181, 256 }, { 6, 182, 256 }, { 7, 183, 256 },
100 { 5, 184, 256 }, { 6, 185, 256 }, { 6, 186, 256 }, { 7, 187, 256 }, { 6, 188, 256 }, { 7, 189, 256 }, { 7, 190, 256 }, { 8, 191, 256 },
101 { 3, 192, 256 }, { 4, 193, 256 }, { 4, 194, 256 }, { 5, 195, 256 }, { 4, 196, 256 }, { 5, 197, 256 }, { 5, 198, 256 }, { 6, 199, 256 },
102 { 4, 200, 256 }, { 5, 201, 256 }, { 5, 202, 256 }, { 6, 203, 256 }, { 5, 204, 256 }, { 6, 205, 256 }, { 6, 206, 256 }, { 7, 207, 256 },
103 { 4, 208, 256 }, { 5, 209, 256 }, { 5, 210, 256 }, { 6, 211, 256 }, { 5, 212, 256 }, { 6, 213, 256 }, { 6, 214, 256 }, { 7, 215, 256 },
104 { 5, 216, 256 }, { 6, 217, 256 }, { 6, 218, 256 }, { 7, 219, 256 }, { 6, 220, 256 }, { 7, 221, 256 }, { 7, 222, 256 }, { 8, 223, 256 },
105 { 4, 224, 256 }, { 5, 225, 256 }, { 5, 226, 256 }, { 6, 227, 256 }, { 5, 228, 256 }, { 6, 229, 256 }, { 6, 230, 256 }, { 7, 231, 256 },
106 { 5, 232, 256 }, { 6, 233, 256 }, { 6, 234, 256 }, { 7, 235, 256 }, { 6, 236, 256 }, { 7, 237, 256 }, { 7, 238, 256 }, { 8, 239, 256 },
107 { 5, 240, 256 }, { 6, 241, 256 }, { 6, 242, 256 }, { 7, 243, 256 }, { 6, 244, 256 }, { 7, 245, 256 }, { 7, 246, 256 }, { 8, 247, 256 },
108 { 6, 248, 256 }, { 7, 249, 256 }, { 7, 250, 256 }, { 8, 251, 256 }, { 7, 252, 256 }, { 8, 253, 256 }, { 8, 254, 256 }, { 9, 255, 256 },
109 #if FP_LUT > 9
110 { 1, 0, 0 }, { 2, 1, 512 }, { 2, 2, 512 }, { 3, 3, 512 }, { 2, 4, 512 }, { 3, 5, 512 }, { 3, 6, 512 }, { 4, 7, 512 },
111 { 2, 8, 512 }, { 3, 9, 512 }, { 3, 10, 512 }, { 4, 11, 512 }, { 3, 12, 512 }, { 4, 13, 512 }, { 4, 14, 512 }, { 5, 15, 512 },
112 { 2, 16, 512 }, { 3, 17, 512 }, { 3, 18, 512 }, { 4, 19, 512 }, { 3, 20, 512 }, { 4, 21, 512 }, { 4, 22, 512 }, { 5, 23, 512 },
113 { 3, 24, 512 }, { 4, 25, 512 }, { 4, 26, 512 }, { 5, 27, 512 }, { 4, 28, 512 }, { 5, 29, 512 }, { 5, 30, 512 }, { 6, 31, 512 },
114 { 2, 32, 512 }, { 3, 33, 512 }, { 3, 34, 512 }, { 4, 35, 512 }, { 3, 36, 512 }, { 4, 37, 512 }, { 4, 38, 512 }, { 5, 39, 512 },
115 { 3, 40, 512 }, { 4, 41, 512 }, { 4, 42, 512 }, { 5, 43, 512 }, { 4, 44, 512 }, { 5, 45, 512 }, { 5, 46, 512 }, { 6, 47, 512 },
116 { 3, 48, 512 }, { 4, 49, 512 }, { 4, 50, 512 }, { 5, 51, 512 }, { 4, 52, 512 }, { 5, 53, 512 }, { 5, 54, 512 }, { 6, 55, 512 },
117 { 4, 56, 512 }, { 5, 57, 512 }, { 5, 58, 512 }, { 6, 59, 512 }, { 5, 60, 512 }, { 6, 61, 512 }, { 6, 62, 512 }, { 7, 63, 512 },
118 { 2, 64, 512 }, { 3, 65, 512 }, { 3, 66, 512 }, { 4, 67, 512 }, { 3, 68, 512 }, { 4, 69, 512 }, { 4, 70, 512 }, { 5, 71, 512 },
119 { 3, 72, 512 }, { 4, 73, 512 }, { 4, 74, 512 }, { 5, 75, 512 }, { 4, 76, 512 }, { 5, 77, 512 }, { 5, 78, 512 }, { 6, 79, 512 },
120 { 3, 80, 512 }, { 4, 81, 512 }, { 4, 82, 512 }, { 5, 83, 512 }, { 4, 84, 512 }, { 5, 85, 512 }, { 5, 86, 512 }, { 6, 87, 512 },
121 { 4, 88, 512 }, { 5, 89, 512 }, { 5, 90, 512 }, { 6, 91, 512 }, { 5, 92, 512 }, { 6, 93, 512 }, { 6, 94, 512 }, { 7, 95, 512 },
122 { 3, 96, 512 }, { 4, 97, 512 }, { 4, 98, 512 }, { 5, 99, 512 }, { 4, 100, 512 }, { 5, 101, 512 }, { 5, 102, 512 }, { 6, 103, 512 },
123 { 4, 104, 512 }, { 5, 105, 512 }, { 5, 106, 512 }, { 6, 107, 512 }, { 5, 108, 512 }, { 6, 109, 512 }, { 6, 110, 512 }, { 7, 111, 512 },
124 { 4, 112, 512 }, { 5, 113, 512 }, { 5, 114, 512 }, { 6, 115, 512 }, { 5, 116, 512 }, { 6, 117, 512 }, { 6, 118, 512 }, { 7, 119, 512 },
125 { 5, 120, 512 }, { 6, 121, 512 }, { 6, 122, 512 }, { 7, 123, 512 }, { 6, 124, 512 }, { 7, 125, 512 }, { 7, 126, 512 }, { 8, 127, 512 },
126 { 2, 128, 512 }, { 3, 129, 512 }, { 3, 130, 512 }, { 4, 131, 512 }, { 3, 132, 512 }, { 4, 133, 512 }, { 4, 134, 512 }, { 5, 135, 512 },
127 { 3, 136, 512 }, { 4, 137, 512 }, { 4, 138, 512 }, { 5, 139, 512 }, { 4, 140, 512 }, { 5, 141, 512 }, { 5, 142, 512 }, { 6, 143, 512 },
128 { 3, 144, 512 }, { 4, 145, 512 }, { 4, 146, 512 }, { 5, 147, 512 }, { 4, 148, 512 }, { 5, 149, 512 }, { 5, 150, 512 }, { 6, 151, 512 },
129 { 4, 152, 512 }, { 5, 153, 512 }, { 5, 154, 512 }, { 6, 155, 512 }, { 5, 156, 512 }, { 6, 157, 512 }, { 6, 158, 512 }, { 7, 159, 512 },
130 { 3, 160, 512 }, { 4, 161, 512 }, { 4, 162, 512 }, { 5, 163, 512 }, { 4, 164, 512 }, { 5, 165, 512 }, { 5, 166, 512 }, { 6, 167, 512 },
131 { 4, 168, 512 }, { 5, 169, 512 }, { 5, 170, 512 }, { 6, 171, 512 }, { 5, 172, 512 }, { 6, 173, 512 }, { 6, 174, 512 }, { 7, 175, 512 },
132 { 4, 176, 512 }, { 5, 177, 512 }, { 5, 178, 512 }, { 6, 179, 512 }, { 5, 180, 512 }, { 6, 181, 512 }, { 6, 182, 512 }, { 7, 183, 512 },
133 { 5, 184, 512 }, { 6, 185, 512 }, { 6, 186, 512 }, { 7, 187, 512 }, { 6, 188, 512 }, { 7, 189, 512 }, { 7, 190, 512 }, { 8, 191, 512 },
134 { 3, 192, 512 }, { 4, 193, 512 }, { 4, 194, 512 }, { 5, 195, 512 }, { 4, 196, 512 }, { 5, 197, 512 }, { 5, 198, 512 }, { 6, 199, 512 },
135 { 4, 200, 512 }, { 5, 201, 512 }, { 5, 202, 512 }, { 6, 203, 512 }, { 5, 204, 512 }, { 6, 205, 512 }, { 6, 206, 512 }, { 7, 207, 512 },
136 { 4, 208, 512 }, { 5, 209, 512 }, { 5, 210, 512 }, { 6, 211, 512 }, { 5, 212, 512 }, { 6, 213, 512 }, { 6, 214, 512 }, { 7, 215, 512 },
137 { 5, 216, 512 }, { 6, 217, 512 }, { 6, 218, 512 }, { 7, 219, 512 }, { 6, 220, 512 }, { 7, 221, 512 }, { 7, 222, 512 }, { 8, 223, 512 },
138 { 4, 224, 512 }, { 5, 225, 512 }, { 5, 226, 512 }, { 6, 227, 512 }, { 5, 228, 512 }, { 6, 229, 512 }, { 6, 230, 512 }, { 7, 231, 512 },
139 { 5, 232, 512 }, { 6, 233, 512 }, { 6, 234, 512 }, { 7, 235, 512 }, { 6, 236, 512 }, { 7, 237, 512 }, { 7, 238, 512 }, { 8, 239, 512 },
140 { 5, 240, 512 }, { 6, 241, 512 }, { 6, 242, 512 }, { 7, 243, 512 }, { 6, 244, 512 }, { 7, 245, 512 }, { 7, 246, 512 }, { 8, 247, 512 },
141 { 6, 248, 512 }, { 7, 249, 512 }, { 7, 250, 512 }, { 8, 251, 512 }, { 7, 252, 512 }, { 8, 253, 512 }, { 8, 254, 512 }, { 9, 255, 512 },
142 { 2, 256, 512 }, { 3, 257, 512 }, { 3, 258, 512 }, { 4, 259, 512 }, { 3, 260, 512 }, { 4, 261, 512 }, { 4, 262, 512 }, { 5, 263, 512 },
143 { 3, 264, 512 }, { 4, 265, 512 }, { 4, 266, 512 }, { 5, 267, 512 }, { 4, 268, 512 }, { 5, 269, 512 }, { 5, 270, 512 }, { 6, 271, 512 },
144 { 3, 272, 512 }, { 4, 273, 512 }, { 4, 274, 512 }, { 5, 275, 512 }, { 4, 276, 512 }, { 5, 277, 512 }, { 5, 278, 512 }, { 6, 279, 512 },
145 { 4, 280, 512 }, { 5, 281, 512 }, { 5, 282, 512 }, { 6, 283, 512 }, { 5, 284, 512 }, { 6, 285, 512 }, { 6, 286, 512 }, { 7, 287, 512 },
146 { 3, 288, 512 }, { 4, 289, 512 }, { 4, 290, 512 }, { 5, 291, 512 }, { 4, 292, 512 }, { 5, 293, 512 }, { 5, 294, 512 }, { 6, 295, 512 },
147 { 4, 296, 512 }, { 5, 297, 512 }, { 5, 298, 512 }, { 6, 299, 512 }, { 5, 300, 512 }, { 6, 301, 512 }, { 6, 302, 512 }, { 7, 303, 512 },
148 { 4, 304, 512 }, { 5, 305, 512 }, { 5, 306, 512 }, { 6, 307, 512 }, { 5, 308, 512 }, { 6, 309, 512 }, { 6, 310, 512 }, { 7, 311, 512 },
149 { 5, 312, 512 }, { 6, 313, 512 }, { 6, 314, 512 }, { 7, 315, 512 }, { 6, 316, 512 }, { 7, 317, 512 }, { 7, 318, 512 }, { 8, 319, 512 },
150 { 3, 320, 512 }, { 4, 321, 512 }, { 4, 322, 512 }, { 5, 323, 512 }, { 4, 324, 512 }, { 5, 325, 512 }, { 5, 326, 512 }, { 6, 327, 512 },
151 { 4, 328, 512 }, { 5, 329, 512 }, { 5, 330, 512 }, { 6, 331, 512 }, { 5, 332, 512 }, { 6, 333, 512 }, { 6, 334, 512 }, { 7, 335, 512 },
152 { 4, 336, 512 }, { 5, 337, 512 }, { 5, 338, 512 }, { 6, 339, 512 }, { 5, 340, 512 }, { 6, 341, 512 }, { 6, 342, 512 }, { 7, 343, 512 },
153 { 5, 344, 512 }, { 6, 345, 512 }, { 6, 346, 512 }, { 7, 347, 512 }, { 6, 348, 512 }, { 7, 349, 512 }, { 7, 350, 512 }, { 8, 351, 512 },
154 { 4, 352, 512 }, { 5, 353, 512 }, { 5, 354, 512 }, { 6, 355, 512 }, { 5, 356, 512 }, { 6, 357, 512 }, { 6, 358, 512 }, { 7, 359, 512 },
155 { 5, 360, 512 }, { 6, 361, 512 }, { 6, 362, 512 }, { 7, 363, 512 }, { 6, 364, 512 }, { 7, 365, 512 }, { 7, 366, 512 }, { 8, 367, 512 },
156 { 5, 368, 512 }, { 6, 369, 512 }, { 6, 370, 512 }, { 7, 371, 512 }, { 6, 372, 512 }, { 7, 373, 512 }, { 7, 374, 512 }, { 8, 375, 512 },
157 { 6, 376, 512 }, { 7, 377, 512 }, { 7, 378, 512 }, { 8, 379, 512 }, { 7, 380, 512 }, { 8, 381, 512 }, { 8, 382, 512 }, { 9, 383, 512 },
158 { 3, 384, 512 }, { 4, 385, 512 }, { 4, 386, 512 }, { 5, 387, 512 }, { 4, 388, 512 }, { 5, 389, 512 }, { 5, 390, 512 }, { 6, 391, 512 },
159 { 4, 392, 512 }, { 5, 393, 512 }, { 5, 394, 512 }, { 6, 395, 512 }, { 5, 396, 512 }, { 6, 397, 512 }, { 6, 398, 512 }, { 7, 399, 512 },
160 { 4, 400, 512 }, { 5, 401, 512 }, { 5, 402, 512 }, { 6, 403, 512 }, { 5, 404, 512 }, { 6, 405, 512 }, { 6, 406, 512 }, { 7, 407, 512 },
161 { 5, 408, 512 }, { 6, 409, 512 }, { 6, 410, 512 }, { 7, 411, 512 }, { 6, 412, 512 }, { 7, 413, 512 }, { 7, 414, 512 }, { 8, 415, 512 },
162 { 4, 416, 512 }, { 5, 417, 512 }, { 5, 418, 512 }, { 6, 419, 512 }, { 5, 420, 512 }, { 6, 421, 512 }, { 6, 422, 512 }, { 7, 423, 512 },
163 { 5, 424, 512 }, { 6, 425, 512 }, { 6, 426, 512 }, { 7, 427, 512 }, { 6, 428, 512 }, { 7, 429, 512 }, { 7, 430, 512 }, { 8, 431, 512 },
164 { 5, 432, 512 }, { 6, 433, 512 }, { 6, 434, 512 }, { 7, 435, 512 }, { 6, 436, 512 }, { 7, 437, 512 }, { 7, 438, 512 }, { 8, 439, 512 },
165 { 6, 440, 512 }, { 7, 441, 512 }, { 7, 442, 512 }, { 8, 443, 512 }, { 7, 444, 512 }, { 8, 445, 512 }, { 8, 446, 512 }, { 9, 447, 512 },
166 { 4, 448, 512 }, { 5, 449, 512 }, { 5, 450, 512 }, { 6, 451, 512 }, { 5, 452, 512 }, { 6, 453, 512 }, { 6, 454, 512 }, { 7, 455, 512 },
167 { 5, 456, 512 }, { 6, 457, 512 }, { 6, 458, 512 }, { 7, 459, 512 }, { 6, 460, 512 }, { 7, 461, 512 }, { 7, 462, 512 }, { 8, 463, 512 },
168 { 5, 464, 512 }, { 6, 465, 512 }, { 6, 466, 512 }, { 7, 467, 512 }, { 6, 468, 512 }, { 7, 469, 512 }, { 7, 470, 512 }, { 8, 471, 512 },
169 { 6, 472, 512 }, { 7, 473, 512 }, { 7, 474, 512 }, { 8, 475, 512 }, { 7, 476, 512 }, { 8, 477, 512 }, { 8, 478, 512 }, { 9, 479, 512 },
170 { 5, 480, 512 }, { 6, 481, 512 }, { 6, 482, 512 }, { 7, 483, 512 }, { 6, 484, 512 }, { 7, 485, 512 }, { 7, 486, 512 }, { 8, 487, 512 },
171 { 6, 488, 512 }, { 7, 489, 512 }, { 7, 490, 512 }, { 8, 491, 512 }, { 7, 492, 512 }, { 8, 493, 512 }, { 8, 494, 512 }, { 9, 495, 512 },
172 { 6, 496, 512 }, { 7, 497, 512 }, { 7, 498, 512 }, { 8, 499, 512 }, { 7, 500, 512 }, { 8, 501, 512 }, { 8, 502, 512 }, { 9, 503, 512 },
173 { 7, 504, 512 }, { 8, 505, 512 }, { 8, 506, 512 }, { 9, 507, 512 }, { 8, 508, 512 }, { 9, 509, 512 }, { 9, 510, 512 }, { 10, 511, 512 },
174 #if FP_LUT > 10
175 { 1, 0, 0 }, { 2, 1, 1024 }, { 2, 2, 1024 }, { 3, 3, 1024 }, { 2, 4, 1024 }, { 3, 5, 1024 }, { 3, 6, 1024 }, { 4, 7, 1024 },
176 { 2, 8, 1024 }, { 3, 9, 1024 }, { 3, 10, 1024 }, { 4, 11, 1024 }, { 3, 12, 1024 }, { 4, 13, 1024 }, { 4, 14, 1024 }, { 5, 15, 1024 },
177 { 2, 16, 1024 }, { 3, 17, 1024 }, { 3, 18, 1024 }, { 4, 19, 1024 }, { 3, 20, 1024 }, { 4, 21, 1024 }, { 4, 22, 1024 }, { 5, 23, 1024 },
178 { 3, 24, 1024 }, { 4, 25, 1024 }, { 4, 26, 1024 }, { 5, 27, 1024 }, { 4, 28, 1024 }, { 5, 29, 1024 }, { 5, 30, 1024 }, { 6, 31, 1024 },
179 { 2, 32, 1024 }, { 3, 33, 1024 }, { 3, 34, 1024 }, { 4, 35, 1024 }, { 3, 36, 1024 }, { 4, 37, 1024 }, { 4, 38, 1024 }, { 5, 39, 1024 },
180 { 3, 40, 1024 }, { 4, 41, 1024 }, { 4, 42, 1024 }, { 5, 43, 1024 }, { 4, 44, 1024 }, { 5, 45, 1024 }, { 5, 46, 1024 }, { 6, 47, 1024 },
181 { 3, 48, 1024 }, { 4, 49, 1024 }, { 4, 50, 1024 }, { 5, 51, 1024 }, { 4, 52, 1024 }, { 5, 53, 1024 }, { 5, 54, 1024 }, { 6, 55, 1024 },
182 { 4, 56, 1024 }, { 5, 57, 1024 }, { 5, 58, 1024 }, { 6, 59, 1024 }, { 5, 60, 1024 }, { 6, 61, 1024 }, { 6, 62, 1024 }, { 7, 63, 1024 },
183 { 2, 64, 1024 }, { 3, 65, 1024 }, { 3, 66, 1024 }, { 4, 67, 1024 }, { 3, 68, 1024 }, { 4, 69, 1024 }, { 4, 70, 1024 }, { 5, 71, 1024 },
184 { 3, 72, 1024 }, { 4, 73, 1024 }, { 4, 74, 1024 }, { 5, 75, 1024 }, { 4, 76, 1024 }, { 5, 77, 1024 }, { 5, 78, 1024 }, { 6, 79, 1024 },
185 { 3, 80, 1024 }, { 4, 81, 1024 }, { 4, 82, 1024 }, { 5, 83, 1024 }, { 4, 84, 1024 }, { 5, 85, 1024 }, { 5, 86, 1024 }, { 6, 87, 1024 },
186 { 4, 88, 1024 }, { 5, 89, 1024 }, { 5, 90, 1024 }, { 6, 91, 1024 }, { 5, 92, 1024 }, { 6, 93, 1024 }, { 6, 94, 1024 }, { 7, 95, 1024 },
187 { 3, 96, 1024 }, { 4, 97, 1024 }, { 4, 98, 1024 }, { 5, 99, 1024 }, { 4, 100, 1024 }, { 5, 101, 1024 }, { 5, 102, 1024 }, { 6, 103, 1024 },
188 { 4, 104, 1024 }, { 5, 105, 1024 }, { 5, 106, 1024 }, { 6, 107, 1024 }, { 5, 108, 1024 }, { 6, 109, 1024 }, { 6, 110, 1024 }, { 7, 111, 1024 },
189 { 4, 112, 1024 }, { 5, 113, 1024 }, { 5, 114, 1024 }, { 6, 115, 1024 }, { 5, 116, 1024 }, { 6, 117, 1024 }, { 6, 118, 1024 }, { 7, 119, 1024 },
190 { 5, 120, 1024 }, { 6, 121, 1024 }, { 6, 122, 1024 }, { 7, 123, 1024 }, { 6, 124, 1024 }, { 7, 125, 1024 }, { 7, 126, 1024 }, { 8, 127, 1024 },
191 { 2, 128, 1024 }, { 3, 129, 1024 }, { 3, 130, 1024 }, { 4, 131, 1024 }, { 3, 132, 1024 }, { 4, 133, 1024 }, { 4, 134, 1024 }, { 5, 135, 1024 },
192 { 3, 136, 1024 }, { 4, 137, 1024 }, { 4, 138, 1024 }, { 5, 139, 1024 }, { 4, 140, 1024 }, { 5, 141, 1024 }, { 5, 142, 1024 }, { 6, 143, 1024 },
193 { 3, 144, 1024 }, { 4, 145, 1024 }, { 4, 146, 1024 }, { 5, 147, 1024 }, { 4, 148, 1024 }, { 5, 149, 1024 }, { 5, 150, 1024 }, { 6, 151, 1024 },
194 { 4, 152, 1024 }, { 5, 153, 1024 }, { 5, 154, 1024 }, { 6, 155, 1024 }, { 5, 156, 1024 }, { 6, 157, 1024 }, { 6, 158, 1024 }, { 7, 159, 1024 },
195 { 3, 160, 1024 }, { 4, 161, 1024 }, { 4, 162, 1024 }, { 5, 163, 1024 }, { 4, 164, 1024 }, { 5, 165, 1024 }, { 5, 166, 1024 }, { 6, 167, 1024 },
196 { 4, 168, 1024 }, { 5, 169, 1024 }, { 5, 170, 1024 }, { 6, 171, 1024 }, { 5, 172, 1024 }, { 6, 173, 1024 }, { 6, 174, 1024 }, { 7, 175, 1024 },
197 { 4, 176, 1024 }, { 5, 177, 1024 }, { 5, 178, 1024 }, { 6, 179, 1024 }, { 5, 180, 1024 }, { 6, 181, 1024 }, { 6, 182, 1024 }, { 7, 183, 1024 },
198 { 5, 184, 1024 }, { 6, 185, 1024 }, { 6, 186, 1024 }, { 7, 187, 1024 }, { 6, 188, 1024 }, { 7, 189, 1024 }, { 7, 190, 1024 }, { 8, 191, 1024 },
199 { 3, 192, 1024 }, { 4, 193, 1024 }, { 4, 194, 1024 }, { 5, 195, 1024 }, { 4, 196, 1024 }, { 5, 197, 1024 }, { 5, 198, 1024 }, { 6, 199, 1024 },
200 { 4, 200, 1024 }, { 5, 201, 1024 }, { 5, 202, 1024 }, { 6, 203, 1024 }, { 5, 204, 1024 }, { 6, 205, 1024 }, { 6, 206, 1024 }, { 7, 207, 1024 },
201 { 4, 208, 1024 }, { 5, 209, 1024 }, { 5, 210, 1024 }, { 6, 211, 1024 }, { 5, 212, 1024 }, { 6, 213, 1024 }, { 6, 214, 1024 }, { 7, 215, 1024 },
202 { 5, 216, 1024 }, { 6, 217, 1024 }, { 6, 218, 1024 }, { 7, 219, 1024 }, { 6, 220, 1024 }, { 7, 221, 1024 }, { 7, 222, 1024 }, { 8, 223, 1024 },
203 { 4, 224, 1024 }, { 5, 225, 1024 }, { 5, 226, 1024 }, { 6, 227, 1024 }, { 5, 228, 1024 }, { 6, 229, 1024 }, { 6, 230, 1024 }, { 7, 231, 1024 },
204 { 5, 232, 1024 }, { 6, 233, 1024 }, { 6, 234, 1024 }, { 7, 235, 1024 }, { 6, 236, 1024 }, { 7, 237, 1024 }, { 7, 238, 1024 }, { 8, 239, 1024 },
205 { 5, 240, 1024 }, { 6, 241, 1024 }, { 6, 242, 1024 }, { 7, 243, 1024 }, { 6, 244, 1024 }, { 7, 245, 1024 }, { 7, 246, 1024 }, { 8, 247, 1024 },
206 { 6, 248, 1024 }, { 7, 249, 1024 }, { 7, 250, 1024 }, { 8, 251, 1024 }, { 7, 252, 1024 }, { 8, 253, 1024 }, { 8, 254, 1024 }, { 9, 255, 1024 },
207 { 2, 256, 1024 }, { 3, 257, 1024 }, { 3, 258, 1024 }, { 4, 259, 1024 }, { 3, 260, 1024 }, { 4, 261, 1024 }, { 4, 262, 1024 }, { 5, 263, 1024 },
208 { 3, 264, 1024 }, { 4, 265, 1024 }, { 4, 266, 1024 }, { 5, 267, 1024 }, { 4, 268, 1024 }, { 5, 269, 1024 }, { 5, 270, 1024 }, { 6, 271, 1024 },
209 { 3, 272, 1024 }, { 4, 273, 1024 }, { 4, 274, 1024 }, { 5, 275, 1024 }, { 4, 276, 1024 }, { 5, 277, 1024 }, { 5, 278, 1024 }, { 6, 279, 1024 },
210 { 4, 280, 1024 }, { 5, 281, 1024 }, { 5, 282, 1024 }, { 6, 283, 1024 }, { 5, 284, 1024 }, { 6, 285, 1024 }, { 6, 286, 1024 }, { 7, 287, 1024 },
211 { 3, 288, 1024 }, { 4, 289, 1024 }, { 4, 290, 1024 }, { 5, 291, 1024 }, { 4, 292, 1024 }, { 5, 293, 1024 }, { 5, 294, 1024 }, { 6, 295, 1024 },
212 { 4, 296, 1024 }, { 5, 297, 1024 }, { 5, 298, 1024 }, { 6, 299, 1024 }, { 5, 300, 1024 }, { 6, 301, 1024 }, { 6, 302, 1024 }, { 7, 303, 1024 },
213 { 4, 304, 1024 }, { 5, 305, 1024 }, { 5, 306, 1024 }, { 6, 307, 1024 }, { 5, 308, 1024 }, { 6, 309, 1024 }, { 6, 310, 1024 }, { 7, 311, 1024 },
214 { 5, 312, 1024 }, { 6, 313, 1024 }, { 6, 314, 1024 }, { 7, 315, 1024 }, { 6, 316, 1024 }, { 7, 317, 1024 }, { 7, 318, 1024 }, { 8, 319, 1024 },
215 { 3, 320, 1024 }, { 4, 321, 1024 }, { 4, 322, 1024 }, { 5, 323, 1024 }, { 4, 324, 1024 }, { 5, 325, 1024 }, { 5, 326, 1024 }, { 6, 327, 1024 },
216 { 4, 328, 1024 }, { 5, 329, 1024 }, { 5, 330, 1024 }, { 6, 331, 1024 }, { 5, 332, 1024 }, { 6, 333, 1024 }, { 6, 334, 1024 }, { 7, 335, 1024 },
217 { 4, 336, 1024 }, { 5, 337, 1024 }, { 5, 338, 1024 }, { 6, 339, 1024 }, { 5, 340, 1024 }, { 6, 341, 1024 }, { 6, 342, 1024 }, { 7, 343, 1024 },
218 { 5, 344, 1024 }, { 6, 345, 1024 }, { 6, 346, 1024 }, { 7, 347, 1024 }, { 6, 348, 1024 }, { 7, 349, 1024 }, { 7, 350, 1024 }, { 8, 351, 1024 },
219 { 4, 352, 1024 }, { 5, 353, 1024 }, { 5, 354, 1024 }, { 6, 355, 1024 }, { 5, 356, 1024 }, { 6, 357, 1024 }, { 6, 358, 1024 }, { 7, 359, 1024 },
220 { 5, 360, 1024 }, { 6, 361, 1024 }, { 6, 362, 1024 }, { 7, 363, 1024 }, { 6, 364, 1024 }, { 7, 365, 1024 }, { 7, 366, 1024 }, { 8, 367, 1024 },
221 { 5, 368, 1024 }, { 6, 369, 1024 }, { 6, 370, 1024 }, { 7, 371, 1024 }, { 6, 372, 1024 }, { 7, 373, 1024 }, { 7, 374, 1024 }, { 8, 375, 1024 },
222 { 6, 376, 1024 }, { 7, 377, 1024 }, { 7, 378, 1024 }, { 8, 379, 1024 }, { 7, 380, 1024 }, { 8, 381, 1024 }, { 8, 382, 1024 }, { 9, 383, 1024 },
223 { 3, 384, 1024 }, { 4, 385, 1024 }, { 4, 386, 1024 }, { 5, 387, 1024 }, { 4, 388, 1024 }, { 5, 389, 1024 }, { 5, 390, 1024 }, { 6, 391, 1024 },
224 { 4, 392, 1024 }, { 5, 393, 1024 }, { 5, 394, 1024 }, { 6, 395, 1024 }, { 5, 396, 1024 }, { 6, 397, 1024 }, { 6, 398, 1024 }, { 7, 399, 1024 },
225 { 4, 400, 1024 }, { 5, 401, 1024 }, { 5, 402, 1024 }, { 6, 403, 1024 }, { 5, 404, 1024 }, { 6, 405, 1024 }, { 6, 406, 1024 }, { 7, 407, 1024 },
226 { 5, 408, 1024 }, { 6, 409, 1024 }, { 6, 410, 1024 }, { 7, 411, 1024 }, { 6, 412, 1024 }, { 7, 413, 1024 }, { 7, 414, 1024 }, { 8, 415, 1024 },
227 { 4, 416, 1024 }, { 5, 417, 1024 }, { 5, 418, 1024 }, { 6, 419, 1024 }, { 5, 420, 1024 }, { 6, 421, 1024 }, { 6, 422, 1024 }, { 7, 423, 1024 },
228 { 5, 424, 1024 }, { 6, 425, 1024 }, { 6, 426, 1024 }, { 7, 427, 1024 }, { 6, 428, 1024 }, { 7, 429, 1024 }, { 7, 430, 1024 }, { 8, 431, 1024 },
229 { 5, 432, 1024 }, { 6, 433, 1024 }, { 6, 434, 1024 }, { 7, 435, 1024 }, { 6, 436, 1024 }, { 7, 437, 1024 }, { 7, 438, 1024 }, { 8, 439, 1024 },
230 { 6, 440, 1024 }, { 7, 441, 1024 }, { 7, 442, 1024 }, { 8, 443, 1024 }, { 7, 444, 1024 }, { 8, 445, 1024 }, { 8, 446, 1024 }, { 9, 447, 1024 },
231 { 4, 448, 1024 }, { 5, 449, 1024 }, { 5, 450, 1024 }, { 6, 451, 1024 }, { 5, 452, 1024 }, { 6, 453, 1024 }, { 6, 454, 1024 }, { 7, 455, 1024 },
232 { 5, 456, 1024 }, { 6, 457, 1024 }, { 6, 458, 1024 }, { 7, 459, 1024 }, { 6, 460, 1024 }, { 7, 461, 1024 }, { 7, 462, 1024 }, { 8, 463, 1024 },
233 { 5, 464, 1024 }, { 6, 465, 1024 }, { 6, 466, 1024 }, { 7, 467, 1024 }, { 6, 468, 1024 }, { 7, 469, 1024 }, { 7, 470, 1024 }, { 8, 471, 1024 },
234 { 6, 472, 1024 }, { 7, 473, 1024 }, { 7, 474, 1024 }, { 8, 475, 1024 }, { 7, 476, 1024 }, { 8, 477, 1024 }, { 8, 478, 1024 }, { 9, 479, 1024 },
235 { 5, 480, 1024 }, { 6, 481, 1024 }, { 6, 482, 1024 }, { 7, 483, 1024 }, { 6, 484, 1024 }, { 7, 485, 1024 }, { 7, 486, 1024 }, { 8, 487, 1024 },
236 { 6, 488, 1024 }, { 7, 489, 1024 }, { 7, 490, 1024 }, { 8, 491, 1024 }, { 7, 492, 1024 }, { 8, 493, 1024 }, { 8, 494, 1024 }, { 9, 495, 1024 },
237 { 6, 496, 1024 }, { 7, 497, 1024 }, { 7, 498, 1024 }, { 8, 499, 1024 }, { 7, 500, 1024 }, { 8, 501, 1024 }, { 8, 502, 1024 }, { 9, 503, 1024 },
238 { 7, 504, 1024 }, { 8, 505, 1024 }, { 8, 506, 1024 }, { 9, 507, 1024 }, { 8, 508, 1024 }, { 9, 509, 1024 }, { 9, 510, 1024 }, { 10, 511, 1024 },
239 { 2, 512, 1024 }, { 3, 513, 1024 }, { 3, 514, 1024 }, { 4, 515, 1024 }, { 3, 516, 1024 }, { 4, 517, 1024 }, { 4, 518, 1024 }, { 5, 519, 1024 },
240 { 3, 520, 1024 }, { 4, 521, 1024 }, { 4, 522, 1024 }, { 5, 523, 1024 }, { 4, 524, 1024 }, { 5, 525, 1024 }, { 5, 526, 1024 }, { 6, 527, 1024 },
241 { 3, 528, 1024 }, { 4, 529, 1024 }, { 4, 530, 1024 }, { 5, 531, 1024 }, { 4, 532, 1024 }, { 5, 533, 1024 }, { 5, 534, 1024 }, { 6, 535, 1024 },
242 { 4, 536, 1024 }, { 5, 537, 1024 }, { 5, 538, 1024 }, { 6, 539, 1024 }, { 5, 540, 1024 }, { 6, 541, 1024 }, { 6, 542, 1024 }, { 7, 543, 1024 },
243 { 3, 544, 1024 }, { 4, 545, 1024 }, { 4, 546, 1024 }, { 5, 547, 1024 }, { 4, 548, 1024 }, { 5, 549, 1024 }, { 5, 550, 1024 }, { 6, 551, 1024 },
244 { 4, 552, 1024 }, { 5, 553, 1024 }, { 5, 554, 1024 }, { 6, 555, 1024 }, { 5, 556, 1024 }, { 6, 557, 1024 }, { 6, 558, 1024 }, { 7, 559, 1024 },
245 { 4, 560, 1024 }, { 5, 561, 1024 }, { 5, 562, 1024 }, { 6, 563, 1024 }, { 5, 564, 1024 }, { 6, 565, 1024 }, { 6, 566, 1024 }, { 7, 567, 1024 },
246 { 5, 568, 1024 }, { 6, 569, 1024 }, { 6, 570, 1024 }, { 7, 571, 1024 }, { 6, 572, 1024 }, { 7, 573, 1024 }, { 7, 574, 1024 }, { 8, 575, 1024 },
247 { 3, 576, 1024 }, { 4, 577, 1024 }, { 4, 578, 1024 }, { 5, 579, 1024 }, { 4, 580, 1024 }, { 5, 581, 1024 }, { 5, 582, 1024 }, { 6, 583, 1024 },
248 { 4, 584, 1024 }, { 5, 585, 1024 }, { 5, 586, 1024 }, { 6, 587, 1024 }, { 5, 588, 1024 }, { 6, 589, 1024 }, { 6, 590, 1024 }, { 7, 591, 1024 },
249 { 4, 592, 1024 }, { 5, 593, 1024 }, { 5, 594, 1024 }, { 6, 595, 1024 }, { 5, 596, 1024 }, { 6, 597, 1024 }, { 6, 598, 1024 }, { 7, 599, 1024 },
250 { 5, 600, 1024 }, { 6, 601, 1024 }, { 6, 602, 1024 }, { 7, 603, 1024 }, { 6, 604, 1024 }, { 7, 605, 1024 }, { 7, 606, 1024 }, { 8, 607, 1024 },
251 { 4, 608, 1024 }, { 5, 609, 1024 }, { 5, 610, 1024 }, { 6, 611, 1024 }, { 5, 612, 1024 }, { 6, 613, 1024 }, { 6, 614, 1024 }, { 7, 615, 1024 },
252 { 5, 616, 1024 }, { 6, 617, 1024 }, { 6, 618, 1024 }, { 7, 619, 1024 }, { 6, 620, 1024 }, { 7, 621, 1024 }, { 7, 622, 1024 }, { 8, 623, 1024 },
253 { 5, 624, 1024 }, { 6, 625, 1024 }, { 6, 626, 1024 }, { 7, 627, 1024 }, { 6, 628, 1024 }, { 7, 629, 1024 }, { 7, 630, 1024 }, { 8, 631, 1024 },
254 { 6, 632, 1024 }, { 7, 633, 1024 }, { 7, 634, 1024 }, { 8, 635, 1024 }, { 7, 636, 1024 }, { 8, 637, 1024 }, { 8, 638, 1024 }, { 9, 639, 1024 },
255 { 3, 640, 1024 }, { 4, 641, 1024 }, { 4, 642, 1024 }, { 5, 643, 1024 }, { 4, 644, 1024 }, { 5, 645, 1024 }, { 5, 646, 1024 }, { 6, 647, 1024 },
256 { 4, 648, 1024 }, { 5, 649, 1024 }, { 5, 650, 1024 }, { 6, 651, 1024 }, { 5, 652, 1024 }, { 6, 653, 1024 }, { 6, 654, 1024 }, { 7, 655, 1024 },
257 { 4, 656, 1024 }, { 5, 657, 1024 }, { 5, 658, 1024 }, { 6, 659, 1024 }, { 5, 660, 1024 }, { 6, 661, 1024 }, { 6, 662, 1024 }, { 7, 663, 1024 },
258 { 5, 664, 1024 }, { 6, 665, 1024 }, { 6, 666, 1024 }, { 7, 667, 1024 }, { 6, 668, 1024 }, { 7, 669, 1024 }, { 7, 670, 1024 }, { 8, 671, 1024 },
259 { 4, 672, 1024 }, { 5, 673, 1024 }, { 5, 674, 1024 }, { 6, 675, 1024 }, { 5, 676, 1024 }, { 6, 677, 1024 }, { 6, 678, 1024 }, { 7, 679, 1024 },
260 { 5, 680, 1024 }, { 6, 681, 1024 }, { 6, 682, 1024 }, { 7, 683, 1024 }, { 6, 684, 1024 }, { 7, 685, 1024 }, { 7, 686, 1024 }, { 8, 687, 1024 },
261 { 5, 688, 1024 }, { 6, 689, 1024 }, { 6, 690, 1024 }, { 7, 691, 1024 }, { 6, 692, 1024 }, { 7, 693, 1024 }, { 7, 694, 1024 }, { 8, 695, 1024 },
262 { 6, 696, 1024 }, { 7, 697, 1024 }, { 7, 698, 1024 }, { 8, 699, 1024 }, { 7, 700, 1024 }, { 8, 701, 1024 }, { 8, 702, 1024 }, { 9, 703, 1024 },
263 { 4, 704, 1024 }, { 5, 705, 1024 }, { 5, 706, 1024 }, { 6, 707, 1024 }, { 5, 708, 1024 }, { 6, 709, 1024 }, { 6, 710, 1024 }, { 7, 711, 1024 },
264 { 5, 712, 1024 }, { 6, 713, 1024 }, { 6, 714, 1024 }, { 7, 715, 1024 }, { 6, 716, 1024 }, { 7, 717, 1024 }, { 7, 718, 1024 }, { 8, 719, 1024 },
265 { 5, 720, 1024 }, { 6, 721, 1024 }, { 6, 722, 1024 }, { 7, 723, 1024 }, { 6, 724, 1024 }, { 7, 725, 1024 }, { 7, 726, 1024 }, { 8, 727, 1024 },
266 { 6, 728, 1024 }, { 7, 729, 1024 }, { 7, 730, 1024 }, { 8, 731, 1024 }, { 7, 732, 1024 }, { 8, 733, 1024 }, { 8, 734, 1024 }, { 9, 735, 1024 },
267 { 5, 736, 1024 }, { 6, 737, 1024 }, { 6, 738, 1024 }, { 7, 739, 1024 }, { 6, 740, 1024 }, { 7, 741, 1024 }, { 7, 742, 1024 }, { 8, 743, 1024 },
268 { 6, 744, 1024 }, { 7, 745, 1024 }, { 7, 746, 1024 }, { 8, 747, 1024 }, { 7, 748, 1024 }, { 8, 749, 1024 }, { 8, 750, 1024 }, { 9, 751, 1024 },
269 { 6, 752, 1024 }, { 7, 753, 1024 }, { 7, 754, 1024 }, { 8, 755, 1024 }, { 7, 756, 1024 }, { 8, 757, 1024 }, { 8, 758, 1024 }, { 9, 759, 1024 },
270 { 7, 760, 1024 }, { 8, 761, 1024 }, { 8, 762, 1024 }, { 9, 763, 1024 }, { 8, 764, 1024 }, { 9, 765, 1024 }, { 9, 766, 1024 }, { 10, 767, 1024 },
271 { 3, 768, 1024 }, { 4, 769, 1024 }, { 4, 770, 1024 }, { 5, 771, 1024 }, { 4, 772, 1024 }, { 5, 773, 1024 }, { 5, 774, 1024 }, { 6, 775, 1024 },
272 { 4, 776, 1024 }, { 5, 777, 1024 }, { 5, 778, 1024 }, { 6, 779, 1024 }, { 5, 780, 1024 }, { 6, 781, 1024 }, { 6, 782, 1024 }, { 7, 783, 1024 },
273 { 4, 784, 1024 }, { 5, 785, 1024 }, { 5, 786, 1024 }, { 6, 787, 1024 }, { 5, 788, 1024 }, { 6, 789, 1024 }, { 6, 790, 1024 }, { 7, 791, 1024 },
274 { 5, 792, 1024 }, { 6, 793, 1024 }, { 6, 794, 1024 }, { 7, 795, 1024 }, { 6, 796, 1024 }, { 7, 797, 1024 }, { 7, 798, 1024 }, { 8, 799, 1024 },
275 { 4, 800, 1024 }, { 5, 801, 1024 }, { 5, 802, 1024 }, { 6, 803, 1024 }, { 5, 804, 1024 }, { 6, 805, 1024 }, { 6, 806, 1024 }, { 7, 807, 1024 },
276 { 5, 808, 1024 }, { 6, 809, 1024 }, { 6, 810, 1024 }, { 7, 811, 1024 }, { 6, 812, 1024 }, { 7, 813, 1024 }, { 7, 814, 1024 }, { 8, 815, 1024 },
277 { 5, 816, 1024 }, { 6, 817, 1024 }, { 6, 818, 1024 }, { 7, 819, 1024 }, { 6, 820, 1024 }, { 7, 821, 1024 }, { 7, 822, 1024 }, { 8, 823, 1024 },
278 { 6, 824, 1024 }, { 7, 825, 1024 }, { 7, 826, 1024 }, { 8, 827, 1024 }, { 7, 828, 1024 }, { 8, 829, 1024 }, { 8, 830, 1024 }, { 9, 831, 1024 },
279 { 4, 832, 1024 }, { 5, 833, 1024 }, { 5, 834, 1024 }, { 6, 835, 1024 }, { 5, 836, 1024 }, { 6, 837, 1024 }, { 6, 838, 1024 }, { 7, 839, 1024 },
280 { 5, 840, 1024 }, { 6, 841, 1024 }, { 6, 842, 1024 }, { 7, 843, 1024 }, { 6, 844, 1024 }, { 7, 845, 1024 }, { 7, 846, 1024 }, { 8, 847, 1024 },
281 { 5, 848, 1024 }, { 6, 849, 1024 }, { 6, 850, 1024 }, { 7, 851, 1024 }, { 6, 852, 1024 }, { 7, 853, 1024 }, { 7, 854, 1024 }, { 8, 855, 1024 },
282 { 6, 856, 1024 }, { 7, 857, 1024 }, { 7, 858, 1024 }, { 8, 859, 1024 }, { 7, 860, 1024 }, { 8, 861, 1024 }, { 8, 862, 1024 }, { 9, 863, 1024 },
283 { 5, 864, 1024 }, { 6, 865, 1024 }, { 6, 866, 1024 }, { 7, 867, 1024 }, { 6, 868, 1024 }, { 7, 869, 1024 }, { 7, 870, 1024 }, { 8, 871, 1024 },
284 { 6, 872, 1024 }, { 7, 873, 1024 }, { 7, 874, 1024 }, { 8, 875, 1024 }, { 7, 876, 1024 }, { 8, 877, 1024 }, { 8, 878, 1024 }, { 9, 879, 1024 },
285 { 6, 880, 1024 }, { 7, 881, 1024 }, { 7, 882, 1024 }, { 8, 883, 1024 }, { 7, 884, 1024 }, { 8, 885, 1024 }, { 8, 886, 1024 }, { 9, 887, 1024 },
286 { 7, 888, 1024 }, { 8, 889, 1024 }, { 8, 890, 1024 }, { 9, 891, 1024 }, { 8, 892, 1024 }, { 9, 893, 1024 }, { 9, 894, 1024 }, { 10, 895, 1024 },
287 { 4, 896, 1024 }, { 5, 897, 1024 }, { 5, 898, 1024 }, { 6, 899, 1024 }, { 5, 900, 1024 }, { 6, 901, 1024 }, { 6, 902, 1024 }, { 7, 903, 1024 },
288 { 5, 904, 1024 }, { 6, 905, 1024 }, { 6, 906, 1024 }, { 7, 907, 1024 }, { 6, 908, 1024 }, { 7, 909, 1024 }, { 7, 910, 1024 }, { 8, 911, 1024 },
289 { 5, 912, 1024 }, { 6, 913, 1024 }, { 6, 914, 1024 }, { 7, 915, 1024 }, { 6, 916, 1024 }, { 7, 917, 1024 }, { 7, 918, 1024 }, { 8, 919, 1024 },
290 { 6, 920, 1024 }, { 7, 921, 1024 }, { 7, 922, 1024 }, { 8, 923, 1024 }, { 7, 924, 1024 }, { 8, 925, 1024 }, { 8, 926, 1024 }, { 9, 927, 1024 },
291 { 5, 928, 1024 }, { 6, 929, 1024 }, { 6, 930, 1024 }, { 7, 931, 1024 }, { 6, 932, 1024 }, { 7, 933, 1024 }, { 7, 934, 1024 }, { 8, 935, 1024 },
292 { 6, 936, 1024 }, { 7, 937, 1024 }, { 7, 938, 1024 }, { 8, 939, 1024 }, { 7, 940, 1024 }, { 8, 941, 1024 }, { 8, 942, 1024 }, { 9, 943, 1024 },
293 { 6, 944, 1024 }, { 7, 945, 1024 }, { 7, 946, 1024 }, { 8, 947, 1024 }, { 7, 948, 1024 }, { 8, 949, 1024 }, { 8, 950, 1024 }, { 9, 951, 1024 },
294 { 7, 952, 1024 }, { 8, 953, 1024 }, { 8, 954, 1024 }, { 9, 955, 1024 }, { 8, 956, 1024 }, { 9, 957, 1024 }, { 9, 958, 1024 }, { 10, 959, 1024 },
295 { 5, 960, 1024 }, { 6, 961, 1024 }, { 6, 962, 1024 }, { 7, 963, 1024 }, { 6, 964, 1024 }, { 7, 965, 1024 }, { 7, 966, 1024 }, { 8, 967, 1024 },
296 { 6, 968, 1024 }, { 7, 969, 1024 }, { 7, 970, 1024 }, { 8, 971, 1024 }, { 7, 972, 1024 }, { 8, 973, 1024 }, { 8, 974, 1024 }, { 9, 975, 1024 },
297 { 6, 976, 1024 }, { 7, 977, 1024 }, { 7, 978, 1024 }, { 8, 979, 1024 }, { 7, 980, 1024 }, { 8, 981, 1024 }, { 8, 982, 1024 }, { 9, 983, 1024 },
298 { 7, 984, 1024 }, { 8, 985, 1024 }, { 8, 986, 1024 }, { 9, 987, 1024 }, { 8, 988, 1024 }, { 9, 989, 1024 }, { 9, 990, 1024 }, { 10, 991, 1024 },
299 { 6, 992, 1024 }, { 7, 993, 1024 }, { 7, 994, 1024 }, { 8, 995, 1024 }, { 7, 996, 1024 }, { 8, 997, 1024 }, { 8, 998, 1024 }, { 9, 999, 1024 },
300 { 7, 1000, 1024 }, { 8, 1001, 1024 }, { 8, 1002, 1024 }, { 9, 1003, 1024 }, { 8, 1004, 1024 }, { 9, 1005, 1024 }, { 9, 1006, 1024 }, { 10, 1007, 1024 },
301 { 7, 1008, 1024 }, { 8, 1009, 1024 }, { 8, 1010, 1024 }, { 9, 1011, 1024 }, { 8, 1012, 1024 }, { 9, 1013, 1024 }, { 9, 1014, 1024 }, { 10, 1015, 1024 },
302 { 8, 1016, 1024 }, { 9, 1017, 1024 }, { 9, 1018, 1024 }, { 10, 1019, 1024 }, { 9, 1020, 1024 }, { 10, 1021, 1024 }, { 10, 1022, 1024 }, { 11, 1023, 1024 },
303 #if FP_LUT > 11
304 { 1, 0, 0 }, { 2, 1, 2048 }, { 2, 2, 2048 }, { 3, 3, 2048 }, { 2, 4, 2048 }, { 3, 5, 2048 }, { 3, 6, 2048 }, { 4, 7, 2048 },
305 { 2, 8, 2048 }, { 3, 9, 2048 }, { 3, 10, 2048 }, { 4, 11, 2048 }, { 3, 12, 2048 }, { 4, 13, 2048 }, { 4, 14, 2048 }, { 5, 15, 2048 },
306 { 2, 16, 2048 }, { 3, 17, 2048 }, { 3, 18, 2048 }, { 4, 19, 2048 }, { 3, 20, 2048 }, { 4, 21, 2048 }, { 4, 22, 2048 }, { 5, 23, 2048 },
307 { 3, 24, 2048 }, { 4, 25, 2048 }, { 4, 26, 2048 }, { 5, 27, 2048 }, { 4, 28, 2048 }, { 5, 29, 2048 }, { 5, 30, 2048 }, { 6, 31, 2048 },
308 { 2, 32, 2048 }, { 3, 33, 2048 }, { 3, 34, 2048 }, { 4, 35, 2048 }, { 3, 36, 2048 }, { 4, 37, 2048 }, { 4, 38, 2048 }, { 5, 39, 2048 },
309 { 3, 40, 2048 }, { 4, 41, 2048 }, { 4, 42, 2048 }, { 5, 43, 2048 }, { 4, 44, 2048 }, { 5, 45, 2048 }, { 5, 46, 2048 }, { 6, 47, 2048 },
310 { 3, 48, 2048 }, { 4, 49, 2048 }, { 4, 50, 2048 }, { 5, 51, 2048 }, { 4, 52, 2048 }, { 5, 53, 2048 }, { 5, 54, 2048 }, { 6, 55, 2048 },
311 { 4, 56, 2048 }, { 5, 57, 2048 }, { 5, 58, 2048 }, { 6, 59, 2048 }, { 5, 60, 2048 }, { 6, 61, 2048 }, { 6, 62, 2048 }, { 7, 63, 2048 },
312 { 2, 64, 2048 }, { 3, 65, 2048 }, { 3, 66, 2048 }, { 4, 67, 2048 }, { 3, 68, 2048 }, { 4, 69, 2048 }, { 4, 70, 2048 }, { 5, 71, 2048 },
313 { 3, 72, 2048 }, { 4, 73, 2048 }, { 4, 74, 2048 }, { 5, 75, 2048 }, { 4, 76, 2048 }, { 5, 77, 2048 }, { 5, 78, 2048 }, { 6, 79, 2048 },
314 { 3, 80, 2048 }, { 4, 81, 2048 }, { 4, 82, 2048 }, { 5, 83, 2048 }, { 4, 84, 2048 }, { 5, 85, 2048 }, { 5, 86, 2048 }, { 6, 87, 2048 },
315 { 4, 88, 2048 }, { 5, 89, 2048 }, { 5, 90, 2048 }, { 6, 91, 2048 }, { 5, 92, 2048 }, { 6, 93, 2048 }, { 6, 94, 2048 }, { 7, 95, 2048 },
316 { 3, 96, 2048 }, { 4, 97, 2048 }, { 4, 98, 2048 }, { 5, 99, 2048 }, { 4, 100, 2048 }, { 5, 101, 2048 }, { 5, 102, 2048 }, { 6, 103, 2048 },
317 { 4, 104, 2048 }, { 5, 105, 2048 }, { 5, 106, 2048 }, { 6, 107, 2048 }, { 5, 108, 2048 }, { 6, 109, 2048 }, { 6, 110, 2048 }, { 7, 111, 2048 },
318 { 4, 112, 2048 }, { 5, 113, 2048 }, { 5, 114, 2048 }, { 6, 115, 2048 }, { 5, 116, 2048 }, { 6, 117, 2048 }, { 6, 118, 2048 }, { 7, 119, 2048 },
319 { 5, 120, 2048 }, { 6, 121, 2048 }, { 6, 122, 2048 }, { 7, 123, 2048 }, { 6, 124, 2048 }, { 7, 125, 2048 }, { 7, 126, 2048 }, { 8, 127, 2048 },
320 { 2, 128, 2048 }, { 3, 129, 2048 }, { 3, 130, 2048 }, { 4, 131, 2048 }, { 3, 132, 2048 }, { 4, 133, 2048 }, { 4, 134, 2048 }, { 5, 135, 2048 },
321 { 3, 136, 2048 }, { 4, 137, 2048 }, { 4, 138, 2048 }, { 5, 139, 2048 }, { 4, 140, 2048 }, { 5, 141, 2048 }, { 5, 142, 2048 }, { 6, 143, 2048 },
322 { 3, 144, 2048 }, { 4, 145, 2048 }, { 4, 146, 2048 }, { 5, 147, 2048 }, { 4, 148, 2048 }, { 5, 149, 2048 }, { 5, 150, 2048 }, { 6, 151, 2048 },
323 { 4, 152, 2048 }, { 5, 153, 2048 }, { 5, 154, 2048 }, { 6, 155, 2048 }, { 5, 156, 2048 }, { 6, 157, 2048 }, { 6, 158, 2048 }, { 7, 159, 2048 },
324 { 3, 160, 2048 }, { 4, 161, 2048 }, { 4, 162, 2048 }, { 5, 163, 2048 }, { 4, 164, 2048 }, { 5, 165, 2048 }, { 5, 166, 2048 }, { 6, 167, 2048 },
325 { 4, 168, 2048 }, { 5, 169, 2048 }, { 5, 170, 2048 }, { 6, 171, 2048 }, { 5, 172, 2048 }, { 6, 173, 2048 }, { 6, 174, 2048 }, { 7, 175, 2048 },
326 { 4, 176, 2048 }, { 5, 177, 2048 }, { 5, 178, 2048 }, { 6, 179, 2048 }, { 5, 180, 2048 }, { 6, 181, 2048 }, { 6, 182, 2048 }, { 7, 183, 2048 },
327 { 5, 184, 2048 }, { 6, 185, 2048 }, { 6, 186, 2048 }, { 7, 187, 2048 }, { 6, 188, 2048 }, { 7, 189, 2048 }, { 7, 190, 2048 }, { 8, 191, 2048 },
328 { 3, 192, 2048 }, { 4, 193, 2048 }, { 4, 194, 2048 }, { 5, 195, 2048 }, { 4, 196, 2048 }, { 5, 197, 2048 }, { 5, 198, 2048 }, { 6, 199, 2048 },
329 { 4, 200, 2048 }, { 5, 201, 2048 }, { 5, 202, 2048 }, { 6, 203, 2048 }, { 5, 204, 2048 }, { 6, 205, 2048 }, { 6, 206, 2048 }, { 7, 207, 2048 },
330 { 4, 208, 2048 }, { 5, 209, 2048 }, { 5, 210, 2048 }, { 6, 211, 2048 }, { 5, 212, 2048 }, { 6, 213, 2048 }, { 6, 214, 2048 }, { 7, 215, 2048 },
331 { 5, 216, 2048 }, { 6, 217, 2048 }, { 6, 218, 2048 }, { 7, 219, 2048 }, { 6, 220, 2048 }, { 7, 221, 2048 }, { 7, 222, 2048 }, { 8, 223, 2048 },
332 { 4, 224, 2048 }, { 5, 225, 2048 }, { 5, 226, 2048 }, { 6, 227, 2048 }, { 5, 228, 2048 }, { 6, 229, 2048 }, { 6, 230, 2048 }, { 7, 231, 2048 },
333 { 5, 232, 2048 }, { 6, 233, 2048 }, { 6, 234, 2048 }, { 7, 235, 2048 }, { 6, 236, 2048 }, { 7, 237, 2048 }, { 7, 238, 2048 }, { 8, 239, 2048 },
334 { 5, 240, 2048 }, { 6, 241, 2048 }, { 6, 242, 2048 }, { 7, 243, 2048 }, { 6, 244, 2048 }, { 7, 245, 2048 }, { 7, 246, 2048 }, { 8, 247, 2048 },
335 { 6, 248, 2048 }, { 7, 249, 2048 }, { 7, 250, 2048 }, { 8, 251, 2048 }, { 7, 252, 2048 }, { 8, 253, 2048 }, { 8, 254, 2048 }, { 9, 255, 2048 },
336 { 2, 256, 2048 }, { 3, 257, 2048 }, { 3, 258, 2048 }, { 4, 259, 2048 }, { 3, 260, 2048 }, { 4, 261, 2048 }, { 4, 262, 2048 }, { 5, 263, 2048 },
337 { 3, 264, 2048 }, { 4, 265, 2048 }, { 4, 266, 2048 }, { 5, 267, 2048 }, { 4, 268, 2048 }, { 5, 269, 2048 }, { 5, 270, 2048 }, { 6, 271, 2048 },
338 { 3, 272, 2048 }, { 4, 273, 2048 }, { 4, 274, 2048 }, { 5, 275, 2048 }, { 4, 276, 2048 }, { 5, 277, 2048 }, { 5, 278, 2048 }, { 6, 279, 2048 },
339 { 4, 280, 2048 }, { 5, 281, 2048 }, { 5, 282, 2048 }, { 6, 283, 2048 }, { 5, 284, 2048 }, { 6, 285, 2048 }, { 6, 286, 2048 }, { 7, 287, 2048 },
340 { 3, 288, 2048 }, { 4, 289, 2048 }, { 4, 290, 2048 }, { 5, 291, 2048 }, { 4, 292, 2048 }, { 5, 293, 2048 }, { 5, 294, 2048 }, { 6, 295, 2048 },
341 { 4, 296, 2048 }, { 5, 297, 2048 }, { 5, 298, 2048 }, { 6, 299, 2048 }, { 5, 300, 2048 }, { 6, 301, 2048 }, { 6, 302, 2048 }, { 7, 303, 2048 },
342 { 4, 304, 2048 }, { 5, 305, 2048 }, { 5, 306, 2048 }, { 6, 307, 2048 }, { 5, 308, 2048 }, { 6, 309, 2048 }, { 6, 310, 2048 }, { 7, 311, 2048 },
343 { 5, 312, 2048 }, { 6, 313, 2048 }, { 6, 314, 2048 }, { 7, 315, 2048 }, { 6, 316, 2048 }, { 7, 317, 2048 }, { 7, 318, 2048 }, { 8, 319, 2048 },
344 { 3, 320, 2048 }, { 4, 321, 2048 }, { 4, 322, 2048 }, { 5, 323, 2048 }, { 4, 324, 2048 }, { 5, 325, 2048 }, { 5, 326, 2048 }, { 6, 327, 2048 },
345 { 4, 328, 2048 }, { 5, 329, 2048 }, { 5, 330, 2048 }, { 6, 331, 2048 }, { 5, 332, 2048 }, { 6, 333, 2048 }, { 6, 334, 2048 }, { 7, 335, 2048 },
346 { 4, 336, 2048 }, { 5, 337, 2048 }, { 5, 338, 2048 }, { 6, 339, 2048 }, { 5, 340, 2048 }, { 6, 341, 2048 }, { 6, 342, 2048 }, { 7, 343, 2048 },
347 { 5, 344, 2048 }, { 6, 345, 2048 }, { 6, 346, 2048 }, { 7, 347, 2048 }, { 6, 348, 2048 }, { 7, 349, 2048 }, { 7, 350, 2048 }, { 8, 351, 2048 },
348 { 4, 352, 2048 }, { 5, 353, 2048 }, { 5, 354, 2048 }, { 6, 355, 2048 }, { 5, 356, 2048 }, { 6, 357, 2048 }, { 6, 358, 2048 }, { 7, 359, 2048 },
349 { 5, 360, 2048 }, { 6, 361, 2048 }, { 6, 362, 2048 }, { 7, 363, 2048 }, { 6, 364, 2048 }, { 7, 365, 2048 }, { 7, 366, 2048 }, { 8, 367, 2048 },
350 { 5, 368, 2048 }, { 6, 369, 2048 }, { 6, 370, 2048 }, { 7, 371, 2048 }, { 6, 372, 2048 }, { 7, 373, 2048 }, { 7, 374, 2048 }, { 8, 375, 2048 },
351 { 6, 376, 2048 }, { 7, 377, 2048 }, { 7, 378, 2048 }, { 8, 379, 2048 }, { 7, 380, 2048 }, { 8, 381, 2048 }, { 8, 382, 2048 }, { 9, 383, 2048 },
352 { 3, 384, 2048 }, { 4, 385, 2048 }, { 4, 386, 2048 }, { 5, 387, 2048 }, { 4, 388, 2048 }, { 5, 389, 2048 }, { 5, 390, 2048 }, { 6, 391, 2048 },
353 { 4, 392, 2048 }, { 5, 393, 2048 }, { 5, 394, 2048 }, { 6, 395, 2048 }, { 5, 396, 2048 }, { 6, 397, 2048 }, { 6, 398, 2048 }, { 7, 399, 2048 },
354 { 4, 400, 2048 }, { 5, 401, 2048 }, { 5, 402, 2048 }, { 6, 403, 2048 }, { 5, 404, 2048 }, { 6, 405, 2048 }, { 6, 406, 2048 }, { 7, 407, 2048 },
355 { 5, 408, 2048 }, { 6, 409, 2048 }, { 6, 410, 2048 }, { 7, 411, 2048 }, { 6, 412, 2048 }, { 7, 413, 2048 }, { 7, 414, 2048 }, { 8, 415, 2048 },
356 { 4, 416, 2048 }, { 5, 417, 2048 }, { 5, 418, 2048 }, { 6, 419, 2048 }, { 5, 420, 2048 }, { 6, 421, 2048 }, { 6, 422, 2048 }, { 7, 423, 2048 },
357 { 5, 424, 2048 }, { 6, 425, 2048 }, { 6, 426, 2048 }, { 7, 427, 2048 }, { 6, 428, 2048 }, { 7, 429, 2048 }, { 7, 430, 2048 }, { 8, 431, 2048 },
358 { 5, 432, 2048 }, { 6, 433, 2048 }, { 6, 434, 2048 }, { 7, 435, 2048 }, { 6, 436, 2048 }, { 7, 437, 2048 }, { 7, 438, 2048 }, { 8, 439, 2048 },
359 { 6, 440, 2048 }, { 7, 441, 2048 }, { 7, 442, 2048 }, { 8, 443, 2048 }, { 7, 444, 2048 }, { 8, 445, 2048 }, { 8, 446, 2048 }, { 9, 447, 2048 },
360 { 4, 448, 2048 }, { 5, 449, 2048 }, { 5, 450, 2048 }, { 6, 451, 2048 }, { 5, 452, 2048 }, { 6, 453, 2048 }, { 6, 454, 2048 }, { 7, 455, 2048 },
361 { 5, 456, 2048 }, { 6, 457, 2048 }, { 6, 458, 2048 }, { 7, 459, 2048 }, { 6, 460, 2048 }, { 7, 461, 2048 }, { 7, 462, 2048 }, { 8, 463, 2048 },
362 { 5, 464, 2048 }, { 6, 465, 2048 }, { 6, 466, 2048 }, { 7, 467, 2048 }, { 6, 468, 2048 }, { 7, 469, 2048 }, { 7, 470, 2048 }, { 8, 471, 2048 },
363 { 6, 472, 2048 }, { 7, 473, 2048 }, { 7, 474, 2048 }, { 8, 475, 2048 }, { 7, 476, 2048 }, { 8, 477, 2048 }, { 8, 478, 2048 }, { 9, 479, 2048 },
364 { 5, 480, 2048 }, { 6, 481, 2048 }, { 6, 482, 2048 }, { 7, 483, 2048 }, { 6, 484, 2048 }, { 7, 485, 2048 }, { 7, 486, 2048 }, { 8, 487, 2048 },
365 { 6, 488, 2048 }, { 7, 489, 2048 }, { 7, 490, 2048 }, { 8, 491, 2048 }, { 7, 492, 2048 }, { 8, 493, 2048 }, { 8, 494, 2048 }, { 9, 495, 2048 },
366 { 6, 496, 2048 }, { 7, 497, 2048 }, { 7, 498, 2048 }, { 8, 499, 2048 }, { 7, 500, 2048 }, { 8, 501, 2048 }, { 8, 502, 2048 }, { 9, 503, 2048 },
367 { 7, 504, 2048 }, { 8, 505, 2048 }, { 8, 506, 2048 }, { 9, 507, 2048 }, { 8, 508, 2048 }, { 9, 509, 2048 }, { 9, 510, 2048 }, { 10, 511, 2048 },
368 { 2, 512, 2048 }, { 3, 513, 2048 }, { 3, 514, 2048 }, { 4, 515, 2048 }, { 3, 516, 2048 }, { 4, 517, 2048 }, { 4, 518, 2048 }, { 5, 519, 2048 },
369 { 3, 520, 2048 }, { 4, 521, 2048 }, { 4, 522, 2048 }, { 5, 523, 2048 }, { 4, 524, 2048 }, { 5, 525, 2048 }, { 5, 526, 2048 }, { 6, 527, 2048 },
370 { 3, 528, 2048 }, { 4, 529, 2048 }, { 4, 530, 2048 }, { 5, 531, 2048 }, { 4, 532, 2048 }, { 5, 533, 2048 }, { 5, 534, 2048 }, { 6, 535, 2048 },
371 { 4, 536, 2048 }, { 5, 537, 2048 }, { 5, 538, 2048 }, { 6, 539, 2048 }, { 5, 540, 2048 }, { 6, 541, 2048 }, { 6, 542, 2048 }, { 7, 543, 2048 },
372 { 3, 544, 2048 }, { 4, 545, 2048 }, { 4, 546, 2048 }, { 5, 547, 2048 }, { 4, 548, 2048 }, { 5, 549, 2048 }, { 5, 550, 2048 }, { 6, 551, 2048 },
373 { 4, 552, 2048 }, { 5, 553, 2048 }, { 5, 554, 2048 }, { 6, 555, 2048 }, { 5, 556, 2048 }, { 6, 557, 2048 }, { 6, 558, 2048 }, { 7, 559, 2048 },
374 { 4, 560, 2048 }, { 5, 561, 2048 }, { 5, 562, 2048 }, { 6, 563, 2048 }, { 5, 564, 2048 }, { 6, 565, 2048 }, { 6, 566, 2048 }, { 7, 567, 2048 },
375 { 5, 568, 2048 }, { 6, 569, 2048 }, { 6, 570, 2048 }, { 7, 571, 2048 }, { 6, 572, 2048 }, { 7, 573, 2048 }, { 7, 574, 2048 }, { 8, 575, 2048 },
376 { 3, 576, 2048 }, { 4, 577, 2048 }, { 4, 578, 2048 }, { 5, 579, 2048 }, { 4, 580, 2048 }, { 5, 581, 2048 }, { 5, 582, 2048 }, { 6, 583, 2048 },
377 { 4, 584, 2048 }, { 5, 585, 2048 }, { 5, 586, 2048 }, { 6, 587, 2048 }, { 5, 588, 2048 }, { 6, 589, 2048 }, { 6, 590, 2048 }, { 7, 591, 2048 },
378 { 4, 592, 2048 }, { 5, 593, 2048 }, { 5, 594, 2048 }, { 6, 595, 2048 }, { 5, 596, 2048 }, { 6, 597, 2048 }, { 6, 598, 2048 }, { 7, 599, 2048 },
379 { 5, 600, 2048 }, { 6, 601, 2048 }, { 6, 602, 2048 }, { 7, 603, 2048 }, { 6, 604, 2048 }, { 7, 605, 2048 }, { 7, 606, 2048 }, { 8, 607, 2048 },
380 { 4, 608, 2048 }, { 5, 609, 2048 }, { 5, 610, 2048 }, { 6, 611, 2048 }, { 5, 612, 2048 }, { 6, 613, 2048 }, { 6, 614, 2048 }, { 7, 615, 2048 },
381 { 5, 616, 2048 }, { 6, 617, 2048 }, { 6, 618, 2048 }, { 7, 619, 2048 }, { 6, 620, 2048 }, { 7, 621, 2048 }, { 7, 622, 2048 }, { 8, 623, 2048 },
382 { 5, 624, 2048 }, { 6, 625, 2048 }, { 6, 626, 2048 }, { 7, 627, 2048 }, { 6, 628, 2048 }, { 7, 629, 2048 }, { 7, 630, 2048 }, { 8, 631, 2048 },
383 { 6, 632, 2048 }, { 7, 633, 2048 }, { 7, 634, 2048 }, { 8, 635, 2048 }, { 7, 636, 2048 }, { 8, 637, 2048 }, { 8, 638, 2048 }, { 9, 639, 2048 },
384 { 3, 640, 2048 }, { 4, 641, 2048 }, { 4, 642, 2048 }, { 5, 643, 2048 }, { 4, 644, 2048 }, { 5, 645, 2048 }, { 5, 646, 2048 }, { 6, 647, 2048 },
385 { 4, 648, 2048 }, { 5, 649, 2048 }, { 5, 650, 2048 }, { 6, 651, 2048 }, { 5, 652, 2048 }, { 6, 653, 2048 }, { 6, 654, 2048 }, { 7, 655, 2048 },
386 { 4, 656, 2048 }, { 5, 657, 2048 }, { 5, 658, 2048 }, { 6, 659, 2048 }, { 5, 660, 2048 }, { 6, 661, 2048 }, { 6, 662, 2048 }, { 7, 663, 2048 },
387 { 5, 664, 2048 }, { 6, 665, 2048 }, { 6, 666, 2048 }, { 7, 667, 2048 }, { 6, 668, 2048 }, { 7, 669, 2048 }, { 7, 670, 2048 }, { 8, 671, 2048 },
388 { 4, 672, 2048 }, { 5, 673, 2048 }, { 5, 674, 2048 }, { 6, 675, 2048 }, { 5, 676, 2048 }, { 6, 677, 2048 }, { 6, 678, 2048 }, { 7, 679, 2048 },
389 { 5, 680, 2048 }, { 6, 681, 2048 }, { 6, 682, 2048 }, { 7, 683, 2048 }, { 6, 684, 2048 }, { 7, 685, 2048 }, { 7, 686, 2048 }, { 8, 687, 2048 },
390 { 5, 688, 2048 }, { 6, 689, 2048 }, { 6, 690, 2048 }, { 7, 691, 2048 }, { 6, 692, 2048 }, { 7, 693, 2048 }, { 7, 694, 2048 }, { 8, 695, 2048 },
391 { 6, 696, 2048 }, { 7, 697, 2048 }, { 7, 698, 2048 }, { 8, 699, 2048 }, { 7, 700, 2048 }, { 8, 701, 2048 }, { 8, 702, 2048 }, { 9, 703, 2048 },
392 { 4, 704, 2048 }, { 5, 705, 2048 }, { 5, 706, 2048 }, { 6, 707, 2048 }, { 5, 708, 2048 }, { 6, 709, 2048 }, { 6, 710, 2048 }, { 7, 711, 2048 },
393 { 5, 712, 2048 }, { 6, 713, 2048 }, { 6, 714, 2048 }, { 7, 715, 2048 }, { 6, 716, 2048 }, { 7, 717, 2048 }, { 7, 718, 2048 }, { 8, 719, 2048 },
394 { 5, 720, 2048 }, { 6, 721, 2048 }, { 6, 722, 2048 }, { 7, 723, 2048 }, { 6, 724, 2048 }, { 7, 725, 2048 }, { 7, 726, 2048 }, { 8, 727, 2048 },
395 { 6, 728, 2048 }, { 7, 729, 2048 }, { 7, 730, 2048 }, { 8, 731, 2048 }, { 7, 732, 2048 }, { 8, 733, 2048 }, { 8, 734, 2048 }, { 9, 735, 2048 },
396 { 5, 736, 2048 }, { 6, 737, 2048 }, { 6, 738, 2048 }, { 7, 739, 2048 }, { 6, 740, 2048 }, { 7, 741, 2048 }, { 7, 742, 2048 }, { 8, 743, 2048 },
397 { 6, 744, 2048 }, { 7, 745, 2048 }, { 7, 746, 2048 }, { 8, 747, 2048 }, { 7, 748, 2048 }, { 8, 749, 2048 }, { 8, 750, 2048 }, { 9, 751, 2048 },
398 { 6, 752, 2048 }, { 7, 753, 2048 }, { 7, 754, 2048 }, { 8, 755, 2048 }, { 7, 756, 2048 }, { 8, 757, 2048 }, { 8, 758, 2048 }, { 9, 759, 2048 },
399 { 7, 760, 2048 }, { 8, 761, 2048 }, { 8, 762, 2048 }, { 9, 763, 2048 }, { 8, 764, 2048 }, { 9, 765, 2048 }, { 9, 766, 2048 }, { 10, 767, 2048 },
400 { 3, 768, 2048 }, { 4, 769, 2048 }, { 4, 770, 2048 }, { 5, 771, 2048 }, { 4, 772, 2048 }, { 5, 773, 2048 }, { 5, 774, 2048 }, { 6, 775, 2048 },
401 { 4, 776, 2048 }, { 5, 777, 2048 }, { 5, 778, 2048 }, { 6, 779, 2048 }, { 5, 780, 2048 }, { 6, 781, 2048 }, { 6, 782, 2048 }, { 7, 783, 2048 },
402 { 4, 784, 2048 }, { 5, 785, 2048 }, { 5, 786, 2048 }, { 6, 787, 2048 }, { 5, 788, 2048 }, { 6, 789, 2048 }, { 6, 790, 2048 }, { 7, 791, 2048 },
403 { 5, 792, 2048 }, { 6, 793, 2048 }, { 6, 794, 2048 }, { 7, 795, 2048 }, { 6, 796, 2048 }, { 7, 797, 2048 }, { 7, 798, 2048 }, { 8, 799, 2048 },
404 { 4, 800, 2048 }, { 5, 801, 2048 }, { 5, 802, 2048 }, { 6, 803, 2048 }, { 5, 804, 2048 }, { 6, 805, 2048 }, { 6, 806, 2048 }, { 7, 807, 2048 },
405 { 5, 808, 2048 }, { 6, 809, 2048 }, { 6, 810, 2048 }, { 7, 811, 2048 }, { 6, 812, 2048 }, { 7, 813, 2048 }, { 7, 814, 2048 }, { 8, 815, 2048 },
406 { 5, 816, 2048 }, { 6, 817, 2048 }, { 6, 818, 2048 }, { 7, 819, 2048 }, { 6, 820, 2048 }, { 7, 821, 2048 }, { 7, 822, 2048 }, { 8, 823, 2048 },
407 { 6, 824, 2048 }, { 7, 825, 2048 }, { 7, 826, 2048 }, { 8, 827, 2048 }, { 7, 828, 2048 }, { 8, 829, 2048 }, { 8, 830, 2048 }, { 9, 831, 2048 },
408 { 4, 832, 2048 }, { 5, 833, 2048 }, { 5, 834, 2048 }, { 6, 835, 2048 }, { 5, 836, 2048 }, { 6, 837, 2048 }, { 6, 838, 2048 }, { 7, 839, 2048 },
409 { 5, 840, 2048 }, { 6, 841, 2048 }, { 6, 842, 2048 }, { 7, 843, 2048 }, { 6, 844, 2048 }, { 7, 845, 2048 }, { 7, 846, 2048 }, { 8, 847, 2048 },
410 { 5, 848, 2048 }, { 6, 849, 2048 }, { 6, 850, 2048 }, { 7, 851, 2048 }, { 6, 852, 2048 }, { 7, 853, 2048 }, { 7, 854, 2048 }, { 8, 855, 2048 },
411 { 6, 856, 2048 }, { 7, 857, 2048 }, { 7, 858, 2048 }, { 8, 859, 2048 }, { 7, 860, 2048 }, { 8, 861, 2048 }, { 8, 862, 2048 }, { 9, 863, 2048 },
412 { 5, 864, 2048 }, { 6, 865, 2048 }, { 6, 866, 2048 }, { 7, 867, 2048 }, { 6, 868, 2048 }, { 7, 869, 2048 }, { 7, 870, 2048 }, { 8, 871, 2048 },
413 { 6, 872, 2048 }, { 7, 873, 2048 }, { 7, 874, 2048 }, { 8, 875, 2048 }, { 7, 876, 2048 }, { 8, 877, 2048 }, { 8, 878, 2048 }, { 9, 879, 2048 },
414 { 6, 880, 2048 }, { 7, 881, 2048 }, { 7, 882, 2048 }, { 8, 883, 2048 }, { 7, 884, 2048 }, { 8, 885, 2048 }, { 8, 886, 2048 }, { 9, 887, 2048 },
415 { 7, 888, 2048 }, { 8, 889, 2048 }, { 8, 890, 2048 }, { 9, 891, 2048 }, { 8, 892, 2048 }, { 9, 893, 2048 }, { 9, 894, 2048 }, { 10, 895, 2048 },
416 { 4, 896, 2048 }, { 5, 897, 2048 }, { 5, 898, 2048 }, { 6, 899, 2048 }, { 5, 900, 2048 }, { 6, 901, 2048 }, { 6, 902, 2048 }, { 7, 903, 2048 },
417 { 5, 904, 2048 }, { 6, 905, 2048 }, { 6, 906, 2048 }, { 7, 907, 2048 }, { 6, 908, 2048 }, { 7, 909, 2048 }, { 7, 910, 2048 }, { 8, 911, 2048 },
418 { 5, 912, 2048 }, { 6, 913, 2048 }, { 6, 914, 2048 }, { 7, 915, 2048 }, { 6, 916, 2048 }, { 7, 917, 2048 }, { 7, 918, 2048 }, { 8, 919, 2048 },
419 { 6, 920, 2048 }, { 7, 921, 2048 }, { 7, 922, 2048 }, { 8, 923, 2048 }, { 7, 924, 2048 }, { 8, 925, 2048 }, { 8, 926, 2048 }, { 9, 927, 2048 },
420 { 5, 928, 2048 }, { 6, 929, 2048 }, { 6, 930, 2048 }, { 7, 931, 2048 }, { 6, 932, 2048 }, { 7, 933, 2048 }, { 7, 934, 2048 }, { 8, 935, 2048 },
421 { 6, 936, 2048 }, { 7, 937, 2048 }, { 7, 938, 2048 }, { 8, 939, 2048 }, { 7, 940, 2048 }, { 8, 941, 2048 }, { 8, 942, 2048 }, { 9, 943, 2048 },
422 { 6, 944, 2048 }, { 7, 945, 2048 }, { 7, 946, 2048 }, { 8, 947, 2048 }, { 7, 948, 2048 }, { 8, 949, 2048 }, { 8, 950, 2048 }, { 9, 951, 2048 },
423 { 7, 952, 2048 }, { 8, 953, 2048 }, { 8, 954, 2048 }, { 9, 955, 2048 }, { 8, 956, 2048 }, { 9, 957, 2048 }, { 9, 958, 2048 }, { 10, 959, 2048 },
424 { 5, 960, 2048 }, { 6, 961, 2048 }, { 6, 962, 2048 }, { 7, 963, 2048 }, { 6, 964, 2048 }, { 7, 965, 2048 }, { 7, 966, 2048 }, { 8, 967, 2048 },
425 { 6, 968, 2048 }, { 7, 969, 2048 }, { 7, 970, 2048 }, { 8, 971, 2048 }, { 7, 972, 2048 }, { 8, 973, 2048 }, { 8, 974, 2048 }, { 9, 975, 2048 },
426 { 6, 976, 2048 }, { 7, 977, 2048 }, { 7, 978, 2048 }, { 8, 979, 2048 }, { 7, 980, 2048 }, { 8, 981, 2048 }, { 8, 982, 2048 }, { 9, 983, 2048 },
427 { 7, 984, 2048 }, { 8, 985, 2048 }, { 8, 986, 2048 }, { 9, 987, 2048 }, { 8, 988, 2048 }, { 9, 989, 2048 }, { 9, 990, 2048 }, { 10, 991, 2048 },
428 { 6, 992, 2048 }, { 7, 993, 2048 }, { 7, 994, 2048 }, { 8, 995, 2048 }, { 7, 996, 2048 }, { 8, 997, 2048 }, { 8, 998, 2048 }, { 9, 999, 2048 },
429 { 7, 1000, 2048 }, { 8, 1001, 2048 }, { 8, 1002, 2048 }, { 9, 1003, 2048 }, { 8, 1004, 2048 }, { 9, 1005, 2048 }, { 9, 1006, 2048 }, { 10, 1007, 2048 },
430 { 7, 1008, 2048 }, { 8, 1009, 2048 }, { 8, 1010, 2048 }, { 9, 1011, 2048 }, { 8, 1012, 2048 }, { 9, 1013, 2048 }, { 9, 1014, 2048 }, { 10, 1015, 2048 },
431 { 8, 1016, 2048 }, { 9, 1017, 2048 }, { 9, 1018, 2048 }, { 10, 1019, 2048 }, { 9, 1020, 2048 }, { 10, 1021, 2048 }, { 10, 1022, 2048 }, { 11, 1023, 2048 },
432 { 2, 1024, 2048 }, { 3, 1025, 2048 }, { 3, 1026, 2048 }, { 4, 1027, 2048 }, { 3, 1028, 2048 }, { 4, 1029, 2048 }, { 4, 1030, 2048 }, { 5, 1031, 2048 },
433 { 3, 1032, 2048 }, { 4, 1033, 2048 }, { 4, 1034, 2048 }, { 5, 1035, 2048 }, { 4, 1036, 2048 }, { 5, 1037, 2048 }, { 5, 1038, 2048 }, { 6, 1039, 2048 },
434 { 3, 1040, 2048 }, { 4, 1041, 2048 }, { 4, 1042, 2048 }, { 5, 1043, 2048 }, { 4, 1044, 2048 }, { 5, 1045, 2048 }, { 5, 1046, 2048 }, { 6, 1047, 2048 },
435 { 4, 1048, 2048 }, { 5, 1049, 2048 }, { 5, 1050, 2048 }, { 6, 1051, 2048 }, { 5, 1052, 2048 }, { 6, 1053, 2048 }, { 6, 1054, 2048 }, { 7, 1055, 2048 },
436 { 3, 1056, 2048 }, { 4, 1057, 2048 }, { 4, 1058, 2048 }, { 5, 1059, 2048 }, { 4, 1060, 2048 }, { 5, 1061, 2048 }, { 5, 1062, 2048 }, { 6, 1063, 2048 },
437 { 4, 1064, 2048 }, { 5, 1065, 2048 }, { 5, 1066, 2048 }, { 6, 1067, 2048 }, { 5, 1068, 2048 }, { 6, 1069, 2048 }, { 6, 1070, 2048 }, { 7, 1071, 2048 },
438 { 4, 1072, 2048 }, { 5, 1073, 2048 }, { 5, 1074, 2048 }, { 6, 1075, 2048 }, { 5, 1076, 2048 }, { 6, 1077, 2048 }, { 6, 1078, 2048 }, { 7, 1079, 2048 },
439 { 5, 1080, 2048 }, { 6, 1081, 2048 }, { 6, 1082, 2048 }, { 7, 1083, 2048 }, { 6, 1084, 2048 }, { 7, 1085, 2048 }, { 7, 1086, 2048 }, { 8, 1087, 2048 },
440 { 3, 1088, 2048 }, { 4, 1089, 2048 }, { 4, 1090, 2048 }, { 5, 1091, 2048 }, { 4, 1092, 2048 }, { 5, 1093, 2048 }, { 5, 1094, 2048 }, { 6, 1095, 2048 },
441 { 4, 1096, 2048 }, { 5, 1097, 2048 }, { 5, 1098, 2048 }, { 6, 1099, 2048 }, { 5, 1100, 2048 }, { 6, 1101, 2048 }, { 6, 1102, 2048 }, { 7, 1103, 2048 },
442 { 4, 1104, 2048 }, { 5, 1105, 2048 }, { 5, 1106, 2048 }, { 6, 1107, 2048 }, { 5, 1108, 2048 }, { 6, 1109, 2048 }, { 6, 1110, 2048 }, { 7, 1111, 2048 },
443 { 5, 1112, 2048 }, { 6, 1113, 2048 }, { 6, 1114, 2048 }, { 7, 1115, 2048 }, { 6, 1116, 2048 }, { 7, 1117, 2048 }, { 7, 1118, 2048 }, { 8, 1119, 2048 },
444 { 4, 1120, 2048 }, { 5, 1121, 2048 }, { 5, 1122, 2048 }, { 6, 1123, 2048 }, { 5, 1124, 2048 }, { 6, 1125, 2048 }, { 6, 1126, 2048 }, { 7, 1127, 2048 },
445 { 5, 1128, 2048 }, { 6, 1129, 2048 }, { 6, 1130, 2048 }, { 7, 1131, 2048 }, { 6, 1132, 2048 }, { 7, 1133, 2048 }, { 7, 1134, 2048 }, { 8, 1135, 2048 },
446 { 5, 1136, 2048 }, { 6, 1137, 2048 }, { 6, 1138, 2048 }, { 7, 1139, 2048 }, { 6, 1140, 2048 }, { 7, 1141, 2048 }, { 7, 1142, 2048 }, { 8, 1143, 2048 },
447 { 6, 1144, 2048 }, { 7, 1145, 2048 }, { 7, 1146, 2048 }, { 8, 1147, 2048 }, { 7, 1148, 2048 }, { 8, 1149, 2048 }, { 8, 1150, 2048 }, { 9, 1151, 2048 },
448 { 3, 1152, 2048 }, { 4, 1153, 2048 }, { 4, 1154, 2048 }, { 5, 1155, 2048 }, { 4, 1156, 2048 }, { 5, 1157, 2048 }, { 5, 1158, 2048 }, { 6, 1159, 2048 },
449 { 4, 1160, 2048 }, { 5, 1161, 2048 }, { 5, 1162, 2048 }, { 6, 1163, 2048 }, { 5, 1164, 2048 }, { 6, 1165, 2048 }, { 6, 1166, 2048 }, { 7, 1167, 2048 },
450 { 4, 1168, 2048 }, { 5, 1169, 2048 }, { 5, 1170, 2048 }, { 6, 1171, 2048 }, { 5, 1172, 2048 }, { 6, 1173, 2048 }, { 6, 1174, 2048 }, { 7, 1175, 2048 },
451 { 5, 1176, 2048 }, { 6, 1177, 2048 }, { 6, 1178, 2048 }, { 7, 1179, 2048 }, { 6, 1180, 2048 }, { 7, 1181, 2048 }, { 7, 1182, 2048 }, { 8, 1183, 2048 },
452 { 4, 1184, 2048 }, { 5, 1185, 2048 }, { 5, 1186, 2048 }, { 6, 1187, 2048 }, { 5, 1188, 2048 }, { 6, 1189, 2048 }, { 6, 1190, 2048 }, { 7, 1191, 2048 },
453 { 5, 1192, 2048 }, { 6, 1193, 2048 }, { 6, 1194, 2048 }, { 7, 1195, 2048 }, { 6, 1196, 2048 }, { 7, 1197, 2048 }, { 7, 1198, 2048 }, { 8, 1199, 2048 },
454 { 5, 1200, 2048 }, { 6, 1201, 2048 }, { 6, 1202, 2048 }, { 7, 1203, 2048 }, { 6, 1204, 2048 }, { 7, 1205, 2048 }, { 7, 1206, 2048 }, { 8, 1207, 2048 },
455 { 6, 1208, 2048 }, { 7, 1209, 2048 }, { 7, 1210, 2048 }, { 8, 1211, 2048 }, { 7, 1212, 2048 }, { 8, 1213, 2048 }, { 8, 1214, 2048 }, { 9, 1215, 2048 },
456 { 4, 1216, 2048 }, { 5, 1217, 2048 }, { 5, 1218, 2048 }, { 6, 1219, 2048 }, { 5, 1220, 2048 }, { 6, 1221, 2048 }, { 6, 1222, 2048 }, { 7, 1223, 2048 },
457 { 5, 1224, 2048 }, { 6, 1225, 2048 }, { 6, 1226, 2048 }, { 7, 1227, 2048 }, { 6, 1228, 2048 }, { 7, 1229, 2048 }, { 7, 1230, 2048 }, { 8, 1231, 2048 },
458 { 5, 1232, 2048 }, { 6, 1233, 2048 }, { 6, 1234, 2048 }, { 7, 1235, 2048 }, { 6, 1236, 2048 }, { 7, 1237, 2048 }, { 7, 1238, 2048 }, { 8, 1239, 2048 },
459 { 6, 1240, 2048 }, { 7, 1241, 2048 }, { 7, 1242, 2048 }, { 8, 1243, 2048 }, { 7, 1244, 2048 }, { 8, 1245, 2048 }, { 8, 1246, 2048 }, { 9, 1247, 2048 },
460 { 5, 1248, 2048 }, { 6, 1249, 2048 }, { 6, 1250, 2048 }, { 7, 1251, 2048 }, { 6, 1252, 2048 }, { 7, 1253, 2048 }, { 7, 1254, 2048 }, { 8, 1255, 2048 },
461 { 6, 1256, 2048 }, { 7, 1257, 2048 }, { 7, 1258, 2048 }, { 8, 1259, 2048 }, { 7, 1260, 2048 }, { 8, 1261, 2048 }, { 8, 1262, 2048 }, { 9, 1263, 2048 },
462 { 6, 1264, 2048 }, { 7, 1265, 2048 }, { 7, 1266, 2048 }, { 8, 1267, 2048 }, { 7, 1268, 2048 }, { 8, 1269, 2048 }, { 8, 1270, 2048 }, { 9, 1271, 2048 },
463 { 7, 1272, 2048 }, { 8, 1273, 2048 }, { 8, 1274, 2048 }, { 9, 1275, 2048 }, { 8, 1276, 2048 }, { 9, 1277, 2048 }, { 9, 1278, 2048 }, { 10, 1279, 2048 },
464 { 3, 1280, 2048 }, { 4, 1281, 2048 }, { 4, 1282, 2048 }, { 5, 1283, 2048 }, { 4, 1284, 2048 }, { 5, 1285, 2048 }, { 5, 1286, 2048 }, { 6, 1287, 2048 },
465 { 4, 1288, 2048 }, { 5, 1289, 2048 }, { 5, 1290, 2048 }, { 6, 1291, 2048 }, { 5, 1292, 2048 }, { 6, 1293, 2048 }, { 6, 1294, 2048 }, { 7, 1295, 2048 },
466 { 4, 1296, 2048 }, { 5, 1297, 2048 }, { 5, 1298, 2048 }, { 6, 1299, 2048 }, { 5, 1300, 2048 }, { 6, 1301, 2048 }, { 6, 1302, 2048 }, { 7, 1303, 2048 },
467 { 5, 1304, 2048 }, { 6, 1305, 2048 }, { 6, 1306, 2048 }, { 7, 1307, 2048 }, { 6, 1308, 2048 }, { 7, 1309, 2048 }, { 7, 1310, 2048 }, { 8, 1311, 2048 },
468 { 4, 1312, 2048 }, { 5, 1313, 2048 }, { 5, 1314, 2048 }, { 6, 1315, 2048 }, { 5, 1316, 2048 }, { 6, 1317, 2048 }, { 6, 1318, 2048 }, { 7, 1319, 2048 },
469 { 5, 1320, 2048 }, { 6, 1321, 2048 }, { 6, 1322, 2048 }, { 7, 1323, 2048 }, { 6, 1324, 2048 }, { 7, 1325, 2048 }, { 7, 1326, 2048 }, { 8, 1327, 2048 },
470 { 5, 1328, 2048 }, { 6, 1329, 2048 }, { 6, 1330, 2048 }, { 7, 1331, 2048 }, { 6, 1332, 2048 }, { 7, 1333, 2048 }, { 7, 1334, 2048 }, { 8, 1335, 2048 },
471 { 6, 1336, 2048 }, { 7, 1337, 2048 }, { 7, 1338, 2048 }, { 8, 1339, 2048 }, { 7, 1340, 2048 }, { 8, 1341, 2048 }, { 8, 1342, 2048 }, { 9, 1343, 2048 },
472 { 4, 1344, 2048 }, { 5, 1345, 2048 }, { 5, 1346, 2048 }, { 6, 1347, 2048 }, { 5, 1348, 2048 }, { 6, 1349, 2048 }, { 6, 1350, 2048 }, { 7, 1351, 2048 },
473 { 5, 1352, 2048 }, { 6, 1353, 2048 }, { 6, 1354, 2048 }, { 7, 1355, 2048 }, { 6, 1356, 2048 }, { 7, 1357, 2048 }, { 7, 1358, 2048 }, { 8, 1359, 2048 },
474 { 5, 1360, 2048 }, { 6, 1361, 2048 }, { 6, 1362, 2048 }, { 7, 1363, 2048 }, { 6, 1364, 2048 }, { 7, 1365, 2048 }, { 7, 1366, 2048 }, { 8, 1367, 2048 },
475 { 6, 1368, 2048 }, { 7, 1369, 2048 }, { 7, 1370, 2048 }, { 8, 1371, 2048 }, { 7, 1372, 2048 }, { 8, 1373, 2048 }, { 8, 1374, 2048 }, { 9, 1375, 2048 },
476 { 5, 1376, 2048 }, { 6, 1377, 2048 }, { 6, 1378, 2048 }, { 7, 1379, 2048 }, { 6, 1380, 2048 }, { 7, 1381, 2048 }, { 7, 1382, 2048 }, { 8, 1383, 2048 },
477 { 6, 1384, 2048 }, { 7, 1385, 2048 }, { 7, 1386, 2048 }, { 8, 1387, 2048 }, { 7, 1388, 2048 }, { 8, 1389, 2048 }, { 8, 1390, 2048 }, { 9, 1391, 2048 },
478 { 6, 1392, 2048 }, { 7, 1393, 2048 }, { 7, 1394, 2048 }, { 8, 1395, 2048 }, { 7, 1396, 2048 }, { 8, 1397, 2048 }, { 8, 1398, 2048 }, { 9, 1399, 2048 },
479 { 7, 1400, 2048 }, { 8, 1401, 2048 }, { 8, 1402, 2048 }, { 9, 1403, 2048 }, { 8, 1404, 2048 }, { 9, 1405, 2048 }, { 9, 1406, 2048 }, { 10, 1407, 2048 },
480 { 4, 1408, 2048 }, { 5, 1409, 2048 }, { 5, 1410, 2048 }, { 6, 1411, 2048 }, { 5, 1412, 2048 }, { 6, 1413, 2048 }, { 6, 1414, 2048 }, { 7, 1415, 2048 },
481 { 5, 1416, 2048 }, { 6, 1417, 2048 }, { 6, 1418, 2048 }, { 7, 1419, 2048 }, { 6, 1420, 2048 }, { 7, 1421, 2048 }, { 7, 1422, 2048 }, { 8, 1423, 2048 },
482 { 5, 1424, 2048 }, { 6, 1425, 2048 }, { 6, 1426, 2048 }, { 7, 1427, 2048 }, { 6, 1428, 2048 }, { 7, 1429, 2048 }, { 7, 1430, 2048 }, { 8, 1431, 2048 },
483 { 6, 1432, 2048 }, { 7, 1433, 2048 }, { 7, 1434, 2048 }, { 8, 1435, 2048 }, { 7, 1436, 2048 }, { 8, 1437, 2048 }, { 8, 1438, 2048 }, { 9, 1439, 2048 },
484 { 5, 1440, 2048 }, { 6, 1441, 2048 }, { 6, 1442, 2048 }, { 7, 1443, 2048 }, { 6, 1444, 2048 }, { 7, 1445, 2048 }, { 7, 1446, 2048 }, { 8, 1447, 2048 },
485 { 6, 1448, 2048 }, { 7, 1449, 2048 }, { 7, 1450, 2048 }, { 8, 1451, 2048 }, { 7, 1452, 2048 }, { 8, 1453, 2048 }, { 8, 1454, 2048 }, { 9, 1455, 2048 },
486 { 6, 1456, 2048 }, { 7, 1457, 2048 }, { 7, 1458, 2048 }, { 8, 1459, 2048 }, { 7, 1460, 2048 }, { 8, 1461, 2048 }, { 8, 1462, 2048 }, { 9, 1463, 2048 },
487 { 7, 1464, 2048 }, { 8, 1465, 2048 }, { 8, 1466, 2048 }, { 9, 1467, 2048 }, { 8, 1468, 2048 }, { 9, 1469, 2048 }, { 9, 1470, 2048 }, { 10, 1471, 2048 },
488 { 5, 1472, 2048 }, { 6, 1473, 2048 }, { 6, 1474, 2048 }, { 7, 1475, 2048 }, { 6, 1476, 2048 }, { 7, 1477, 2048 }, { 7, 1478, 2048 }, { 8, 1479, 2048 },
489 { 6, 1480, 2048 }, { 7, 1481, 2048 }, { 7, 1482, 2048 }, { 8, 1483, 2048 }, { 7, 1484, 2048 }, { 8, 1485, 2048 }, { 8, 1486, 2048 }, { 9, 1487, 2048 },
490 { 6, 1488, 2048 }, { 7, 1489, 2048 }, { 7, 1490, 2048 }, { 8, 1491, 2048 }, { 7, 1492, 2048 }, { 8, 1493, 2048 }, { 8, 1494, 2048 }, { 9, 1495, 2048 },
491 { 7, 1496, 2048 }, { 8, 1497, 2048 }, { 8, 1498, 2048 }, { 9, 1499, 2048 }, { 8, 1500, 2048 }, { 9, 1501, 2048 }, { 9, 1502, 2048 }, { 10, 1503, 2048 },
492 { 6, 1504, 2048 }, { 7, 1505, 2048 }, { 7, 1506, 2048 }, { 8, 1507, 2048 }, { 7, 1508, 2048 }, { 8, 1509, 2048 }, { 8, 1510, 2048 }, { 9, 1511, 2048 },
493 { 7, 1512, 2048 }, { 8, 1513, 2048 }, { 8, 1514, 2048 }, { 9, 1515, 2048 }, { 8, 1516, 2048 }, { 9, 1517, 2048 }, { 9, 1518, 2048 }, { 10, 1519, 2048 },
494 { 7, 1520, 2048 }, { 8, 1521, 2048 }, { 8, 1522, 2048 }, { 9, 1523, 2048 }, { 8, 1524, 2048 }, { 9, 1525, 2048 }, { 9, 1526, 2048 }, { 10, 1527, 2048 },
495 { 8, 1528, 2048 }, { 9, 1529, 2048 }, { 9, 1530, 2048 }, { 10, 1531, 2048 }, { 9, 1532, 2048 }, { 10, 1533, 2048 }, { 10, 1534, 2048 }, { 11, 1535, 2048 },
496 { 3, 1536, 2048 }, { 4, 1537, 2048 }, { 4, 1538, 2048 }, { 5, 1539, 2048 }, { 4, 1540, 2048 }, { 5, 1541, 2048 }, { 5, 1542, 2048 }, { 6, 1543, 2048 },
497 { 4, 1544, 2048 }, { 5, 1545, 2048 }, { 5, 1546, 2048 }, { 6, 1547, 2048 }, { 5, 1548, 2048 }, { 6, 1549, 2048 }, { 6, 1550, 2048 }, { 7, 1551, 2048 },
498 { 4, 1552, 2048 }, { 5, 1553, 2048 }, { 5, 1554, 2048 }, { 6, 1555, 2048 }, { 5, 1556, 2048 }, { 6, 1557, 2048 }, { 6, 1558, 2048 }, { 7, 1559, 2048 },
499 { 5, 1560, 2048 }, { 6, 1561, 2048 }, { 6, 1562, 2048 }, { 7, 1563, 2048 }, { 6, 1564, 2048 }, { 7, 1565, 2048 }, { 7, 1566, 2048 }, { 8, 1567, 2048 },
500 { 4, 1568, 2048 }, { 5, 1569, 2048 }, { 5, 1570, 2048 }, { 6, 1571, 2048 }, { 5, 1572, 2048 }, { 6, 1573, 2048 }, { 6, 1574, 2048 }, { 7, 1575, 2048 },
501 { 5, 1576, 2048 }, { 6, 1577, 2048 }, { 6, 1578, 2048 }, { 7, 1579, 2048 }, { 6, 1580, 2048 }, { 7, 1581, 2048 }, { 7, 1582, 2048 }, { 8, 1583, 2048 },
502 { 5, 1584, 2048 }, { 6, 1585, 2048 }, { 6, 1586, 2048 }, { 7, 1587, 2048 }, { 6, 1588, 2048 }, { 7, 1589, 2048 }, { 7, 1590, 2048 }, { 8, 1591, 2048 },
503 { 6, 1592, 2048 }, { 7, 1593, 2048 }, { 7, 1594, 2048 }, { 8, 1595, 2048 }, { 7, 1596, 2048 }, { 8, 1597, 2048 }, { 8, 1598, 2048 }, { 9, 1599, 2048 },
504 { 4, 1600, 2048 }, { 5, 1601, 2048 }, { 5, 1602, 2048 }, { 6, 1603, 2048 }, { 5, 1604, 2048 }, { 6, 1605, 2048 }, { 6, 1606, 2048 }, { 7, 1607, 2048 },
505 { 5, 1608, 2048 }, { 6, 1609, 2048 }, { 6, 1610, 2048 }, { 7, 1611, 2048 }, { 6, 1612, 2048 }, { 7, 1613, 2048 }, { 7, 1614, 2048 }, { 8, 1615, 2048 },
506 { 5, 1616, 2048 }, { 6, 1617, 2048 }, { 6, 1618, 2048 }, { 7, 1619, 2048 }, { 6, 1620, 2048 }, { 7, 1621, 2048 }, { 7, 1622, 2048 }, { 8, 1623, 2048 },
507 { 6, 1624, 2048 }, { 7, 1625, 2048 }, { 7, 1626, 2048 }, { 8, 1627, 2048 }, { 7, 1628, 2048 }, { 8, 1629, 2048 }, { 8, 1630, 2048 }, { 9, 1631, 2048 },
508 { 5, 1632, 2048 }, { 6, 1633, 2048 }, { 6, 1634, 2048 }, { 7, 1635, 2048 }, { 6, 1636, 2048 }, { 7, 1637, 2048 }, { 7, 1638, 2048 }, { 8, 1639, 2048 },
509 { 6, 1640, 2048 }, { 7, 1641, 2048 }, { 7, 1642, 2048 }, { 8, 1643, 2048 }, { 7, 1644, 2048 }, { 8, 1645, 2048 }, { 8, 1646, 2048 }, { 9, 1647, 2048 },
510 { 6, 1648, 2048 }, { 7, 1649, 2048 }, { 7, 1650, 2048 }, { 8, 1651, 2048 }, { 7, 1652, 2048 }, { 8, 1653, 2048 }, { 8, 1654, 2048 }, { 9, 1655, 2048 },
511 { 7, 1656, 2048 }, { 8, 1657, 2048 }, { 8, 1658, 2048 }, { 9, 1659, 2048 }, { 8, 1660, 2048 }, { 9, 1661, 2048 }, { 9, 1662, 2048 }, { 10, 1663, 2048 },
512 { 4, 1664, 2048 }, { 5, 1665, 2048 }, { 5, 1666, 2048 }, { 6, 1667, 2048 }, { 5, 1668, 2048 }, { 6, 1669, 2048 }, { 6, 1670, 2048 }, { 7, 1671, 2048 },
513 { 5, 1672, 2048 }, { 6, 1673, 2048 }, { 6, 1674, 2048 }, { 7, 1675, 2048 }, { 6, 1676, 2048 }, { 7, 1677, 2048 }, { 7, 1678, 2048 }, { 8, 1679, 2048 },
514 { 5, 1680, 2048 }, { 6, 1681, 2048 }, { 6, 1682, 2048 }, { 7, 1683, 2048 }, { 6, 1684, 2048 }, { 7, 1685, 2048 }, { 7, 1686, 2048 }, { 8, 1687, 2048 },
515 { 6, 1688, 2048 }, { 7, 1689, 2048 }, { 7, 1690, 2048 }, { 8, 1691, 2048 }, { 7, 1692, 2048 }, { 8, 1693, 2048 }, { 8, 1694, 2048 }, { 9, 1695, 2048 },
516 { 5, 1696, 2048 }, { 6, 1697, 2048 }, { 6, 1698, 2048 }, { 7, 1699, 2048 }, { 6, 1700, 2048 }, { 7, 1701, 2048 }, { 7, 1702, 2048 }, { 8, 1703, 2048 },
517 { 6, 1704, 2048 }, { 7, 1705, 2048 }, { 7, 1706, 2048 }, { 8, 1707, 2048 }, { 7, 1708, 2048 }, { 8, 1709, 2048 }, { 8, 1710, 2048 }, { 9, 1711, 2048 },
518 { 6, 1712, 2048 }, { 7, 1713, 2048 }, { 7, 1714, 2048 }, { 8, 1715, 2048 }, { 7, 1716, 2048 }, { 8, 1717, 2048 }, { 8, 1718, 2048 }, { 9, 1719, 2048 },
519 { 7, 1720, 2048 }, { 8, 1721, 2048 }, { 8, 1722, 2048 }, { 9, 1723, 2048 }, { 8, 1724, 2048 }, { 9, 1725, 2048 }, { 9, 1726, 2048 }, { 10, 1727, 2048 },
520 { 5, 1728, 2048 }, { 6, 1729, 2048 }, { 6, 1730, 2048 }, { 7, 1731, 2048 }, { 6, 1732, 2048 }, { 7, 1733, 2048 }, { 7, 1734, 2048 }, { 8, 1735, 2048 },
521 { 6, 1736, 2048 }, { 7, 1737, 2048 }, { 7, 1738, 2048 }, { 8, 1739, 2048 }, { 7, 1740, 2048 }, { 8, 1741, 2048 }, { 8, 1742, 2048 }, { 9, 1743, 2048 },
522 { 6, 1744, 2048 }, { 7, 1745, 2048 }, { 7, 1746, 2048 }, { 8, 1747, 2048 }, { 7, 1748, 2048 }, { 8, 1749, 2048 }, { 8, 1750, 2048 }, { 9, 1751, 2048 },
523 { 7, 1752, 2048 }, { 8, 1753, 2048 }, { 8, 1754, 2048 }, { 9, 1755, 2048 }, { 8, 1756, 2048 }, { 9, 1757, 2048 }, { 9, 1758, 2048 }, { 10, 1759, 2048 },
524 { 6, 1760, 2048 }, { 7, 1761, 2048 }, { 7, 1762, 2048 }, { 8, 1763, 2048 }, { 7, 1764, 2048 }, { 8, 1765, 2048 }, { 8, 1766, 2048 }, { 9, 1767, 2048 },
525 { 7, 1768, 2048 }, { 8, 1769, 2048 }, { 8, 1770, 2048 }, { 9, 1771, 2048 }, { 8, 1772, 2048 }, { 9, 1773, 2048 }, { 9, 1774, 2048 }, { 10, 1775, 2048 },
526 { 7, 1776, 2048 }, { 8, 1777, 2048 }, { 8, 1778, 2048 }, { 9, 1779, 2048 }, { 8, 1780, 2048 }, { 9, 1781, 2048 }, { 9, 1782, 2048 }, { 10, 1783, 2048 },
527 { 8, 1784, 2048 }, { 9, 1785, 2048 }, { 9, 1786, 2048 }, { 10, 1787, 2048 }, { 9, 1788, 2048 }, { 10, 1789, 2048 }, { 10, 1790, 2048 }, { 11, 1791, 2048 },
528 { 4, 1792, 2048 }, { 5, 1793, 2048 }, { 5, 1794, 2048 }, { 6, 1795, 2048 }, { 5, 1796, 2048 }, { 6, 1797, 2048 }, { 6, 1798, 2048 }, { 7, 1799, 2048 },
529 { 5, 1800, 2048 }, { 6, 1801, 2048 }, { 6, 1802, 2048 }, { 7, 1803, 2048 }, { 6, 1804, 2048 }, { 7, 1805, 2048 }, { 7, 1806, 2048 }, { 8, 1807, 2048 },
530 { 5, 1808, 2048 }, { 6, 1809, 2048 }, { 6, 1810, 2048 }, { 7, 1811, 2048 }, { 6, 1812, 2048 }, { 7, 1813, 2048 }, { 7, 1814, 2048 }, { 8, 1815, 2048 },
531 { 6, 1816, 2048 }, { 7, 1817, 2048 }, { 7, 1818, 2048 }, { 8, 1819, 2048 }, { 7, 1820, 2048 }, { 8, 1821, 2048 }, { 8, 1822, 2048 }, { 9, 1823, 2048 },
532 { 5, 1824, 2048 }, { 6, 1825, 2048 }, { 6, 1826, 2048 }, { 7, 1827, 2048 }, { 6, 1828, 2048 }, { 7, 1829, 2048 }, { 7, 1830, 2048 }, { 8, 1831, 2048 },
533 { 6, 1832, 2048 }, { 7, 1833, 2048 }, { 7, 1834, 2048 }, { 8, 1835, 2048 }, { 7, 1836, 2048 }, { 8, 1837, 2048 }, { 8, 1838, 2048 }, { 9, 1839, 2048 },
534 { 6, 1840, 2048 }, { 7, 1841, 2048 }, { 7, 1842, 2048 }, { 8, 1843, 2048 }, { 7, 1844, 2048 }, { 8, 1845, 2048 }, { 8, 1846, 2048 }, { 9, 1847, 2048 },
535 { 7, 1848, 2048 }, { 8, 1849, 2048 }, { 8, 1850, 2048 }, { 9, 1851, 2048 }, { 8, 1852, 2048 }, { 9, 1853, 2048 }, { 9, 1854, 2048 }, { 10, 1855, 2048 },
536 { 5, 1856, 2048 }, { 6, 1857, 2048 }, { 6, 1858, 2048 }, { 7, 1859, 2048 }, { 6, 1860, 2048 }, { 7, 1861, 2048 }, { 7, 1862, 2048 }, { 8, 1863, 2048 },
537 { 6, 1864, 2048 }, { 7, 1865, 2048 }, { 7, 1866, 2048 }, { 8, 1867, 2048 }, { 7, 1868, 2048 }, { 8, 1869, 2048 }, { 8, 1870, 2048 }, { 9, 1871, 2048 },
538 { 6, 1872, 2048 }, { 7, 1873, 2048 }, { 7, 1874, 2048 }, { 8, 1875, 2048 }, { 7, 1876, 2048 }, { 8, 1877, 2048 }, { 8, 1878, 2048 }, { 9, 1879, 2048 },
539 { 7, 1880, 2048 }, { 8, 1881, 2048 }, { 8, 1882, 2048 }, { 9, 1883, 2048 }, { 8, 1884, 2048 }, { 9, 1885, 2048 }, { 9, 1886, 2048 }, { 10, 1887, 2048 },
540 { 6, 1888, 2048 }, { 7, 1889, 2048 }, { 7, 1890, 2048 }, { 8, 1891, 2048 }, { 7, 1892, 2048 }, { 8, 1893, 2048 }, { 8, 1894, 2048 }, { 9, 1895, 2048 },
541 { 7, 1896, 2048 }, { 8, 1897, 2048 }, { 8, 1898, 2048 }, { 9, 1899, 2048 }, { 8, 1900, 2048 }, { 9, 1901, 2048 }, { 9, 1902, 2048 }, { 10, 1903, 2048 },
542 { 7, 1904, 2048 }, { 8, 1905, 2048 }, { 8, 1906, 2048 }, { 9, 1907, 2048 }, { 8, 1908, 2048 }, { 9, 1909, 2048 }, { 9, 1910, 2048 }, { 10, 1911, 2048 },
543 { 8, 1912, 2048 }, { 9, 1913, 2048 }, { 9, 1914, 2048 }, { 10, 1915, 2048 }, { 9, 1916, 2048 }, { 10, 1917, 2048 }, { 10, 1918, 2048 }, { 11, 1919, 2048 },
544 { 5, 1920, 2048 }, { 6, 1921, 2048 }, { 6, 1922, 2048 }, { 7, 1923, 2048 }, { 6, 1924, 2048 }, { 7, 1925, 2048 }, { 7, 1926, 2048 }, { 8, 1927, 2048 },
545 { 6, 1928, 2048 }, { 7, 1929, 2048 }, { 7, 1930, 2048 }, { 8, 1931, 2048 }, { 7, 1932, 2048 }, { 8, 1933, 2048 }, { 8, 1934, 2048 }, { 9, 1935, 2048 },
546 { 6, 1936, 2048 }, { 7, 1937, 2048 }, { 7, 1938, 2048 }, { 8, 1939, 2048 }, { 7, 1940, 2048 }, { 8, 1941, 2048 }, { 8, 1942, 2048 }, { 9, 1943, 2048 },
547 { 7, 1944, 2048 }, { 8, 1945, 2048 }, { 8, 1946, 2048 }, { 9, 1947, 2048 }, { 8, 1948, 2048 }, { 9, 1949, 2048 }, { 9, 1950, 2048 }, { 10, 1951, 2048 },
548 { 6, 1952, 2048 }, { 7, 1953, 2048 }, { 7, 1954, 2048 }, { 8, 1955, 2048 }, { 7, 1956, 2048 }, { 8, 1957, 2048 }, { 8, 1958, 2048 }, { 9, 1959, 2048 },
549 { 7, 1960, 2048 }, { 8, 1961, 2048 }, { 8, 1962, 2048 }, { 9, 1963, 2048 }, { 8, 1964, 2048 }, { 9, 1965, 2048 }, { 9, 1966, 2048 }, { 10, 1967, 2048 },
550 { 7, 1968, 2048 }, { 8, 1969, 2048 }, { 8, 1970, 2048 }, { 9, 1971, 2048 }, { 8, 1972, 2048 }, { 9, 1973, 2048 }, { 9, 1974, 2048 }, { 10, 1975, 2048 },
551 { 8, 1976, 2048 }, { 9, 1977, 2048 }, { 9, 1978, 2048 }, { 10, 1979, 2048 }, { 9, 1980, 2048 }, { 10, 1981, 2048 }, { 10, 1982, 2048 }, { 11, 1983, 2048 },
552 { 6, 1984, 2048 }, { 7, 1985, 2048 }, { 7, 1986, 2048 }, { 8, 1987, 2048 }, { 7, 1988, 2048 }, { 8, 1989, 2048 }, { 8, 1990, 2048 }, { 9, 1991, 2048 },
553 { 7, 1992, 2048 }, { 8, 1993, 2048 }, { 8, 1994, 2048 }, { 9, 1995, 2048 }, { 8, 1996, 2048 }, { 9, 1997, 2048 }, { 9, 1998, 2048 }, { 10, 1999, 2048 },
554 { 7, 2000, 2048 }, { 8, 2001, 2048 }, { 8, 2002, 2048 }, { 9, 2003, 2048 }, { 8, 2004, 2048 }, { 9, 2005, 2048 }, { 9, 2006, 2048 }, { 10, 2007, 2048 },
555 { 8, 2008, 2048 }, { 9, 2009, 2048 }, { 9, 2010, 2048 }, { 10, 2011, 2048 }, { 9, 2012, 2048 }, { 10, 2013, 2048 }, { 10, 2014, 2048 }, { 11, 2015, 2048 },
556 { 7, 2016, 2048 }, { 8, 2017, 2048 }, { 8, 2018, 2048 }, { 9, 2019, 2048 }, { 8, 2020, 2048 }, { 9, 2021, 2048 }, { 9, 2022, 2048 }, { 10, 2023, 2048 },
557 { 8, 2024, 2048 }, { 9, 2025, 2048 }, { 9, 2026, 2048 }, { 10, 2027, 2048 }, { 9, 2028, 2048 }, { 10, 2029, 2048 }, { 10, 2030, 2048 }, { 11, 2031, 2048 },
558 { 8, 2032, 2048 }, { 9, 2033, 2048 }, { 9, 2034, 2048 }, { 10, 2035, 2048 }, { 9, 2036, 2048 }, { 10, 2037, 2048 }, { 10, 2038, 2048 }, { 11, 2039, 2048 },
559 { 9, 2040, 2048 }, { 10, 2041, 2048 }, { 10, 2042, 2048 }, { 11, 2043, 2048 }, { 10, 2044, 2048 }, { 11, 2045, 2048 }, { 11, 2046, 2048 }, { 12, 2047, 2048 },
560 #endif
561 #endif
562 #endif
563 #endif
564 #endif
565 #endif
566 };
567
568 /* find a hole and free as required, return -1 if no hole found */
s_find_hole(void)569 static int s_find_hole(void)
570 {
571 unsigned x;
572 int y, z;
573 for (z = -1, y = INT_MAX, x = 0; x < FP_ENTRIES; x++) {
574 if (fp_cache[x].lru_count < y && fp_cache[x].lock == 0) {
575 z = x;
576 y = fp_cache[x].lru_count;
577 }
578 }
579
580 /* decrease all */
581 for (x = 0; x < FP_ENTRIES; x++) {
582 if (fp_cache[x].lru_count > 3) {
583 --(fp_cache[x].lru_count);
584 }
585 }
586
587 /* free entry z */
588 if (z >= 0 && fp_cache[z].g) {
589 if (fp_cache[z].mu != NULL) {
590 mp_clear(fp_cache[z].mu);
591 fp_cache[z].mu = NULL;
592 }
593 ltc_ecc_del_point(fp_cache[z].g);
594 fp_cache[z].g = NULL;
595 for (x = 0; x < (1U<<FP_LUT); x++) {
596 ltc_ecc_del_point(fp_cache[z].LUT[x]);
597 fp_cache[z].LUT[x] = NULL;
598 }
599 fp_cache[z].lru_count = 0;
600 }
601 return z;
602 }
603
604 /* determine if a base is already in the cache and if so, where */
s_find_base(ecc_point * g)605 static int s_find_base(ecc_point *g)
606 {
607 int x;
608 for (x = 0; x < FP_ENTRIES; x++) {
609 if (fp_cache[x].g != NULL &&
610 mp_cmp(fp_cache[x].g->x, g->x) == LTC_MP_EQ &&
611 mp_cmp(fp_cache[x].g->y, g->y) == LTC_MP_EQ &&
612 mp_cmp(fp_cache[x].g->z, g->z) == LTC_MP_EQ) {
613 break;
614 }
615 }
616 if (x == FP_ENTRIES) {
617 x = -1;
618 }
619 return x;
620 }
621
622 /* add a new base to the cache */
s_add_entry(int idx,ecc_point * g)623 static int s_add_entry(int idx, ecc_point *g)
624 {
625 unsigned x, y;
626
627 /* allocate base and LUT */
628 fp_cache[idx].g = ltc_ecc_new_point();
629 if (fp_cache[idx].g == NULL) {
630 return CRYPT_MEM;
631 }
632
633 /* copy x and y */
634 if ((mp_copy(g->x, fp_cache[idx].g->x) != CRYPT_OK) ||
635 (mp_copy(g->y, fp_cache[idx].g->y) != CRYPT_OK) ||
636 (mp_copy(g->z, fp_cache[idx].g->z) != CRYPT_OK)) {
637 ltc_ecc_del_point(fp_cache[idx].g);
638 fp_cache[idx].g = NULL;
639 return CRYPT_MEM;
640 }
641
642 for (x = 0; x < (1U<<FP_LUT); x++) {
643 fp_cache[idx].LUT[x] = ltc_ecc_new_point();
644 if (fp_cache[idx].LUT[x] == NULL) {
645 for (y = 0; y < x; y++) {
646 ltc_ecc_del_point(fp_cache[idx].LUT[y]);
647 fp_cache[idx].LUT[y] = NULL;
648 }
649 ltc_ecc_del_point(fp_cache[idx].g);
650 fp_cache[idx].g = NULL;
651 fp_cache[idx].lru_count = 0;
652 return CRYPT_MEM;
653 }
654 }
655
656 fp_cache[idx].lru_count = 0;
657 return CRYPT_OK;
658 }
659
660 /* build the LUT by spacing the bits of the input by #modulus/FP_LUT bits apart
661 *
662 * The algorithm builds patterns in increasing bit order by first making all
663 * single bit input patterns, then all two bit input patterns and so on
664 */
s_build_lut(int idx,void * a,void * modulus,void * mp,void * mu)665 static int s_build_lut(int idx, void *a, void *modulus, void *mp, void *mu)
666 {
667 unsigned x, y, err, bitlen, lut_gap;
668 void *tmp;
669
670 tmp = NULL;
671
672 /* sanity check to make sure lut_order table is of correct size, should compile out to a NOP if true */
673 if ((sizeof(lut_orders) / sizeof(lut_orders[0])) < (1U<<FP_LUT)) {
674 err = CRYPT_INVALID_ARG;
675 goto DONE;
676 }
677
678 /* get bitlen and round up to next multiple of FP_LUT */
679 bitlen = mp_unsigned_bin_size(modulus) << 3;
680 x = bitlen % FP_LUT;
681 if (x) {
682 bitlen += FP_LUT - x;
683 }
684 lut_gap = bitlen / FP_LUT;
685
686 /* init the mu */
687 if ((err = mp_init_copy(&fp_cache[idx].mu, mu)) != CRYPT_OK) {
688 goto ERR;
689 }
690
691 /* copy base */
692 if ((mp_mulmod(fp_cache[idx].g->x, mu, modulus, fp_cache[idx].LUT[1]->x) != CRYPT_OK) ||
693 (mp_mulmod(fp_cache[idx].g->y, mu, modulus, fp_cache[idx].LUT[1]->y) != CRYPT_OK) ||
694 (mp_mulmod(fp_cache[idx].g->z, mu, modulus, fp_cache[idx].LUT[1]->z) != CRYPT_OK)) { goto ERR; }
695
696 /* make all single bit entries */
697 for (x = 1; x < FP_LUT; x++) {
698 if ((mp_copy(fp_cache[idx].LUT[1<<(x-1)]->x, fp_cache[idx].LUT[1<<x]->x) != CRYPT_OK) ||
699 (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->y, fp_cache[idx].LUT[1<<x]->y) != CRYPT_OK) ||
700 (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->z, fp_cache[idx].LUT[1<<x]->z) != CRYPT_OK)) { goto ERR; }
701
702 /* now double it bitlen/FP_LUT times */
703 for (y = 0; y < lut_gap; y++) {
704 if ((err = ltc_mp.ecc_ptdbl(fp_cache[idx].LUT[1<<x], fp_cache[idx].LUT[1<<x], a, modulus, mp)) != CRYPT_OK) {
705 goto ERR;
706 }
707 }
708 }
709
710 /* now make all entries in increase order of hamming weight */
711 for (x = 2; x <= FP_LUT; x++) {
712 for (y = 0; y < (1UL<<FP_LUT); y++) {
713 if (lut_orders[y].ham != (int)x) continue;
714
715 /* perform the add */
716 if ((err = ltc_mp.ecc_ptadd(fp_cache[idx].LUT[lut_orders[y].terma], fp_cache[idx].LUT[lut_orders[y].termb],
717 fp_cache[idx].LUT[y], a, modulus, mp)) != CRYPT_OK) {
718 goto ERR;
719 }
720 }
721 }
722
723 /* now map all entries back to affine space to make point addition faster */
724 if ((err = mp_init(&tmp)) != CRYPT_OK) { goto ERR; }
725 for (x = 1; x < (1UL<<FP_LUT); x++) {
726 /* convert z to normal from montgomery */
727 if ((err = mp_montgomery_reduce(fp_cache[idx].LUT[x]->z, modulus, mp)) != CRYPT_OK) { goto ERR; }
728
729 /* invert it */
730 if ((err = mp_invmod(fp_cache[idx].LUT[x]->z, modulus, fp_cache[idx].LUT[x]->z)) != CRYPT_OK) { goto ERR; }
731
732 /* now square it */
733 if ((err = mp_sqrmod(fp_cache[idx].LUT[x]->z, modulus, tmp)) != CRYPT_OK) { goto ERR; }
734
735 /* fix x */
736 if ((err = mp_mulmod(fp_cache[idx].LUT[x]->x, tmp, modulus, fp_cache[idx].LUT[x]->x)) != CRYPT_OK) { goto ERR; }
737
738 /* get 1/z^3 */
739 if ((err = mp_mulmod(tmp, fp_cache[idx].LUT[x]->z, modulus, tmp)) != CRYPT_OK) { goto ERR; }
740
741 /* fix y */
742 if ((err = mp_mulmod(fp_cache[idx].LUT[x]->y, tmp, modulus, fp_cache[idx].LUT[x]->y)) != CRYPT_OK) { goto ERR; }
743
744 /* free z */
745 mp_clear(fp_cache[idx].LUT[x]->z);
746 fp_cache[idx].LUT[x]->z = NULL;
747 }
748 mp_clear(tmp);
749
750 return CRYPT_OK;
751 ERR:
752 err = CRYPT_MEM;
753 DONE:
754 for (y = 0; y < (1U<<FP_LUT); y++) {
755 ltc_ecc_del_point(fp_cache[idx].LUT[y]);
756 fp_cache[idx].LUT[y] = NULL;
757 }
758 ltc_ecc_del_point(fp_cache[idx].g);
759 fp_cache[idx].g = NULL;
760 fp_cache[idx].lru_count = 0;
761 if (fp_cache[idx].mu != NULL) {
762 mp_clear(fp_cache[idx].mu);
763 fp_cache[idx].mu = NULL;
764 }
765 if (tmp != NULL) {
766 mp_clear(tmp);
767 }
768 return err;
769 }
770
771 /* perform a fixed point ECC mulmod */
s_accel_fp_mul(int idx,void * k,ecc_point * R,void * a,void * modulus,void * mp,int map)772 static int s_accel_fp_mul(int idx, void *k, ecc_point *R, void *a, void *modulus, void *mp, int map)
773 {
774 unsigned char kb[128];
775 int x;
776 unsigned y, z, err, bitlen, bitpos, lut_gap, first;
777 void *tk, *order;
778
779 /* if it's smaller than modulus we fine */
780 if (mp_unsigned_bin_size(k) > mp_unsigned_bin_size(modulus)) {
781 /* find order */
782 y = mp_unsigned_bin_size(modulus);
783 for (x = 0; ltc_ecc_sets[x].size; x++) {
784 if (y <= (unsigned)ltc_ecc_sets[x].size) break;
785 }
786
787 /* back off if we are on the 521 bit curve */
788 if (y == 66) --x;
789
790 if ((err = mp_init(&order)) != CRYPT_OK) {
791 return err;
792 }
793 if ((err = mp_read_radix(order, ltc_ecc_sets[x].order, 16)) != CRYPT_OK) {
794 mp_clear(&order);
795 return err;
796 }
797
798 /* k must be less than modulus */
799 if (mp_cmp(k, order) != LTC_MP_LT) {
800 if ((err = mp_init(&tk)) != CRYPT_OK) {
801 mp_clear(order);
802 return err;
803 }
804 if ((err = mp_mod(k, order, tk)) != CRYPT_OK) {
805 mp_clear(tk);
806 mp_clear(order);
807 return err;
808 }
809 } else {
810 tk = k;
811 }
812 mp_clear(order);
813 } else {
814 tk = k;
815 }
816
817 /* get bitlen and round up to next multiple of FP_LUT */
818 bitlen = mp_unsigned_bin_size(modulus) << 3;
819 x = bitlen % FP_LUT;
820 if (x) {
821 bitlen += FP_LUT - x;
822 }
823 lut_gap = bitlen / FP_LUT;
824
825 /* get the k value */
826 if (mp_unsigned_bin_size(tk) > (sizeof(kb) - 2)) {
827 if (tk != k) {
828 mp_clear(tk);
829 }
830 return CRYPT_BUFFER_OVERFLOW;
831 }
832
833 /* store k */
834 zeromem(kb, sizeof(kb));
835 if ((err = mp_to_unsigned_bin(tk, kb)) != CRYPT_OK) {
836 if (tk != k) {
837 mp_clear(tk);
838 }
839 return err;
840 }
841
842 /* let's reverse kb so it's little endian */
843 x = 0;
844 y = mp_unsigned_bin_size(tk) - 1;
845 if (tk != k) {
846 mp_clear(tk);
847 }
848 while ((unsigned)x < y) {
849 z = kb[x]; kb[x] = kb[y]; kb[y] = z;
850 ++x; --y;
851 }
852
853 /* at this point we can start, yipee */
854 first = 1;
855 for (x = lut_gap-1; x >= 0; x--) {
856 /* extract FP_LUT bits from kb spread out by lut_gap bits and offset by x bits from the start */
857 bitpos = x;
858 for (y = z = 0; y < FP_LUT; y++) {
859 z |= ((kb[bitpos>>3] >> (bitpos&7)) & 1) << y;
860 bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid the mult in each loop */
861 }
862
863 /* double if not first */
864 if (!first) {
865 if ((err = ltc_mp.ecc_ptdbl(R, R, a, modulus, mp)) != CRYPT_OK) {
866 return err;
867 }
868 }
869
870 /* add if not first, otherwise copy */
871 if (!first && z) {
872 if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx].LUT[z], R, a, modulus, mp)) != CRYPT_OK) {
873 return err;
874 }
875 } else if (z) {
876 if ((mp_copy(fp_cache[idx].LUT[z]->x, R->x) != CRYPT_OK) ||
877 (mp_copy(fp_cache[idx].LUT[z]->y, R->y) != CRYPT_OK) ||
878 (mp_copy(fp_cache[idx].mu, R->z) != CRYPT_OK)) { return CRYPT_MEM; }
879 first = 0;
880 }
881 }
882 z = 0;
883 zeromem(kb, sizeof(kb));
884 /* map R back from projective space */
885 if (map) {
886 err = ltc_ecc_map(R, modulus, mp);
887 } else {
888 err = CRYPT_OK;
889 }
890 return err;
891 }
892
893 #ifdef LTC_ECC_SHAMIR
894 /* perform a fixed point ECC mulmod */
ss_accel_fp_mul2add(int idx1,int idx2,void * kA,void * kB,ecc_point * R,void * a,void * modulus,void * mp)895 static int ss_accel_fp_mul2add(int idx1, int idx2,
896 void *kA, void *kB,
897 ecc_point *R, void *a, void *modulus, void *mp)
898 {
899 unsigned char kb[2][128];
900 int x;
901 unsigned y, z, err, bitlen, bitpos, lut_gap, first, zA, zB;
902 void *tka, *tkb, *order;
903
904 /* if it's smaller than modulus we fine */
905 if (mp_unsigned_bin_size(kA) > mp_unsigned_bin_size(modulus)) {
906 /* find order */
907 y = mp_unsigned_bin_size(modulus);
908 for (x = 0; ltc_ecc_sets[x].size; x++) {
909 if (y <= (unsigned)ltc_ecc_sets[x].size) break;
910 }
911
912 /* back off if we are on the 521 bit curve */
913 if (y == 66) --x;
914
915 if ((err = mp_init(&order)) != CRYPT_OK) {
916 return err;
917 }
918 if ((err = mp_read_radix(order, ltc_ecc_sets[x].order, 16)) != CRYPT_OK) {
919 mp_clear(&order);
920 return err;
921 }
922
923 /* kA must be less than modulus */
924 if (mp_cmp(kA, order) != LTC_MP_LT) {
925 if ((err = mp_init(&tka)) != CRYPT_OK) {
926 mp_clear(order);
927 return err;
928 }
929 if ((err = mp_mod(kA, order, tka)) != CRYPT_OK) {
930 mp_clear(tka);
931 mp_clear(order);
932 return err;
933 }
934 } else {
935 tka = kA;
936 }
937 mp_clear(order);
938 } else {
939 tka = kA;
940 }
941
942 /* if it's smaller than modulus we fine */
943 if (mp_unsigned_bin_size(kB) > mp_unsigned_bin_size(modulus)) {
944 /* find order */
945 y = mp_unsigned_bin_size(modulus);
946 for (x = 0; ltc_ecc_sets[x].size; x++) {
947 if (y <= (unsigned)ltc_ecc_sets[x].size) break;
948 }
949
950 /* back off if we are on the 521 bit curve */
951 if (y == 66) --x;
952
953 if ((err = mp_init(&order)) != CRYPT_OK) {
954 return err;
955 }
956 if ((err = mp_read_radix(order, ltc_ecc_sets[x].order, 16)) != CRYPT_OK) {
957 mp_clear(&order);
958 return err;
959 }
960
961 /* kB must be less than modulus */
962 if (mp_cmp(kB, order) != LTC_MP_LT) {
963 if ((err = mp_init(&tkb)) != CRYPT_OK) {
964 mp_clear(order);
965 return err;
966 }
967 if ((err = mp_mod(kB, order, tkb)) != CRYPT_OK) {
968 mp_clear(tkb);
969 mp_clear(order);
970 return err;
971 }
972 } else {
973 tkb = kB;
974 }
975 mp_clear(order);
976 } else {
977 tkb = kB;
978 }
979
980 /* get bitlen and round up to next multiple of FP_LUT */
981 bitlen = mp_unsigned_bin_size(modulus) << 3;
982 x = bitlen % FP_LUT;
983 if (x) {
984 bitlen += FP_LUT - x;
985 }
986 lut_gap = bitlen / FP_LUT;
987
988 /* get the k value */
989 if ((mp_unsigned_bin_size(tka) > (sizeof(kb[0]) - 2)) || (mp_unsigned_bin_size(tkb) > (sizeof(kb[0]) - 2)) ) {
990 if (tka != kA) {
991 mp_clear(tka);
992 }
993 if (tkb != kB) {
994 mp_clear(tkb);
995 }
996 return CRYPT_BUFFER_OVERFLOW;
997 }
998
999 /* store k */
1000 zeromem(kb, sizeof(kb));
1001 if ((err = mp_to_unsigned_bin(tka, kb[0])) != CRYPT_OK) {
1002 if (tka != kA) {
1003 mp_clear(tka);
1004 }
1005 if (tkb != kB) {
1006 mp_clear(tkb);
1007 }
1008 return err;
1009 }
1010
1011 /* let's reverse kb so it's little endian */
1012 x = 0;
1013 y = mp_unsigned_bin_size(tka) - 1;
1014 if (tka != kA) {
1015 mp_clear(tka);
1016 }
1017 while ((unsigned)x < y) {
1018 z = kb[0][x]; kb[0][x] = kb[0][y]; kb[0][y] = z;
1019 ++x; --y;
1020 }
1021
1022 /* store b */
1023 if ((err = mp_to_unsigned_bin(tkb, kb[1])) != CRYPT_OK) {
1024 if (tkb != kB) {
1025 mp_clear(tkb);
1026 }
1027 return err;
1028 }
1029
1030 x = 0;
1031 y = mp_unsigned_bin_size(tkb) - 1;
1032 if (tkb != kB) {
1033 mp_clear(tkb);
1034 }
1035 while ((unsigned)x < y) {
1036 z = kb[1][x]; kb[1][x] = kb[1][y]; kb[1][y] = z;
1037 ++x; --y;
1038 }
1039
1040 /* at this point we can start, yipee */
1041 first = 1;
1042 for (x = lut_gap-1; x >= 0; x--) {
1043 /* extract FP_LUT bits from kb spread out by lut_gap bits and offset by x bits from the start */
1044 bitpos = x;
1045 for (y = zA = zB = 0; y < FP_LUT; y++) {
1046 zA |= ((kb[0][bitpos>>3] >> (bitpos&7)) & 1) << y;
1047 zB |= ((kb[1][bitpos>>3] >> (bitpos&7)) & 1) << y;
1048 bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid the mult in each loop */
1049 }
1050
1051 /* double if not first */
1052 if (!first) {
1053 if ((err = ltc_mp.ecc_ptdbl(R, R, a, modulus, mp)) != CRYPT_OK) {
1054 return err;
1055 }
1056 }
1057
1058 /* add if not first, otherwise copy */
1059 if (!first) {
1060 if (zA) {
1061 if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx1].LUT[zA], R, a, modulus, mp)) != CRYPT_OK) {
1062 return err;
1063 }
1064 }
1065 if (zB) {
1066 if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx2].LUT[zB], R, a, modulus, mp)) != CRYPT_OK) {
1067 return err;
1068 }
1069 }
1070 } else {
1071 if (zA) {
1072 if ((mp_copy(fp_cache[idx1].LUT[zA]->x, R->x) != CRYPT_OK) ||
1073 (mp_copy(fp_cache[idx1].LUT[zA]->y, R->y) != CRYPT_OK) ||
1074 (mp_copy(fp_cache[idx1].mu, R->z) != CRYPT_OK)) { return CRYPT_MEM; }
1075 first = 0;
1076 }
1077 if (zB && first == 0) {
1078 if (zB) {
1079 if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx2].LUT[zB], R, a, modulus, mp)) != CRYPT_OK) {
1080 return err;
1081 }
1082 }
1083 } else if (zB && first == 1) {
1084 if ((mp_copy(fp_cache[idx2].LUT[zB]->x, R->x) != CRYPT_OK) ||
1085 (mp_copy(fp_cache[idx2].LUT[zB]->y, R->y) != CRYPT_OK) ||
1086 (mp_copy(fp_cache[idx2].mu, R->z) != CRYPT_OK)) { return CRYPT_MEM; }
1087 first = 0;
1088 }
1089 }
1090 }
1091 zeromem(kb, sizeof(kb));
1092 return ltc_ecc_map(R, modulus, mp);
1093 }
1094
1095 /** ECC Fixed Point mulmod global
1096 Computes kA*A + kB*B = C using Shamir's Trick
1097 @param A First point to multiply
1098 @param kA What to multiple A by
1099 @param B Second point to multiply
1100 @param kB What to multiple B by
1101 @param C [out] Destination point (can overlap with A or B)
1102 @param modulus Modulus for curve
1103 @return CRYPT_OK on success
1104 */
ltc_ecc_fp_mul2add(ecc_point * A,void * kA,ecc_point * B,void * kB,ecc_point * C,void * a,void * modulus)1105 int ltc_ecc_fp_mul2add(ecc_point *A, void *kA,
1106 ecc_point *B, void *kB,
1107 ecc_point *C,
1108 void *a,
1109 void *modulus)
1110 {
1111 int idx1, idx2, err;
1112 void *mp, *mu;
1113
1114 mp = NULL;
1115 mu = NULL;
1116 LTC_MUTEX_LOCK(<c_ecc_fp_lock);
1117 /* find point */
1118 idx1 = s_find_base(A);
1119
1120 /* no entry? */
1121 if (idx1 == -1) {
1122 /* find hole and add it */
1123 if ((idx1 = s_find_hole()) >= 0) {
1124 if ((err = s_add_entry(idx1, A)) != CRYPT_OK) {
1125 goto LBL_ERR;
1126 }
1127 }
1128 }
1129 if (idx1 != -1) {
1130 /* increment LRU */
1131 ++(fp_cache[idx1].lru_count);
1132 }
1133
1134 /* find point */
1135 idx2 = s_find_base(B);
1136
1137 /* no entry? */
1138 if (idx2 == -1) {
1139 /* find hole and add it */
1140 if ((idx2 = s_find_hole()) >= 0) {
1141 if ((err = s_add_entry(idx2, B)) != CRYPT_OK) {
1142 goto LBL_ERR;
1143 }
1144 }
1145 }
1146 if (idx2 != -1) {
1147 /* increment LRU */
1148 ++(fp_cache[idx2].lru_count);
1149 }
1150
1151 /* if it's 2 build the LUT, if it's higher just use the LUT */
1152 if (idx1 >= 0 && fp_cache[idx1].lru_count == 2) {
1153 /* compute mp */
1154 if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; }
1155
1156 /* compute mu */
1157 if ((err = mp_init(&mu)) != CRYPT_OK) {
1158 goto LBL_ERR;
1159 }
1160 if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) {
1161 goto LBL_ERR;
1162 }
1163
1164 /* build the LUT */
1165 if ((err = s_build_lut(idx1, a, modulus, mp, mu)) != CRYPT_OK) {
1166 goto LBL_ERR;;
1167 }
1168 }
1169
1170 /* if it's 2 build the LUT, if it's higher just use the LUT */
1171 if (idx2 >= 0 && fp_cache[idx2].lru_count == 2) {
1172 if (mp == NULL) {
1173 /* compute mp */
1174 if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; }
1175
1176 /* compute mu */
1177 if ((err = mp_init(&mu)) != CRYPT_OK) {
1178 goto LBL_ERR;
1179 }
1180 if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) {
1181 goto LBL_ERR;
1182 }
1183 }
1184
1185 /* build the LUT */
1186 if ((err = s_build_lut(idx2, a, modulus, mp, mu)) != CRYPT_OK) {
1187 goto LBL_ERR;;
1188 }
1189 }
1190
1191
1192 if (idx1 >=0 && idx2 >= 0 && fp_cache[idx1].lru_count >= 2 && fp_cache[idx2].lru_count >= 2) {
1193 if (mp == NULL) {
1194 /* compute mp */
1195 if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; }
1196 }
1197 err = ss_accel_fp_mul2add(idx1, idx2, kA, kB, C, a, modulus, mp);
1198 } else {
1199 err = ltc_ecc_mul2add(A, kA, B, kB, C, a, modulus);
1200 }
1201 LBL_ERR:
1202 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1203 if (mp != NULL) {
1204 mp_montgomery_free(mp);
1205 }
1206 if (mu != NULL) {
1207 mp_clear(mu);
1208 }
1209 return err;
1210 }
1211 #endif
1212
1213 /** ECC Fixed Point mulmod global
1214 @param k The multiplicand
1215 @param G Base point to multiply
1216 @param R [out] Destination of product
1217 @param a ECC curve parameter a
1218 @param modulus The modulus for the curve
1219 @param map [boolean] If non-zero maps the point back to affine co-ordinates, otherwise it's left in jacobian-montgomery form
1220 @return CRYPT_OK if successful
1221 */
ltc_ecc_fp_mulmod(void * k,ecc_point * G,ecc_point * R,void * a,void * modulus,int map)1222 int ltc_ecc_fp_mulmod(void *k, ecc_point *G, ecc_point *R, void *a, void *modulus, int map)
1223 {
1224 int idx, err;
1225 void *mp, *mu;
1226
1227 mp = NULL;
1228 mu = NULL;
1229 LTC_MUTEX_LOCK(<c_ecc_fp_lock);
1230 /* find point */
1231 idx = s_find_base(G);
1232
1233 /* no entry? */
1234 if (idx == -1) {
1235 /* find hole and add it */
1236 idx = s_find_hole();
1237
1238 if (idx >= 0) {
1239 if ((err = s_add_entry(idx, G)) != CRYPT_OK) {
1240 goto LBL_ERR;
1241 }
1242 }
1243 }
1244 if (idx != -1) {
1245 /* increment LRU */
1246 ++(fp_cache[idx].lru_count);
1247 }
1248
1249
1250 /* if it's 2 build the LUT, if it's higher just use the LUT */
1251 if (idx >= 0 && fp_cache[idx].lru_count == 2) {
1252 /* compute mp */
1253 if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; }
1254
1255 /* compute mu */
1256 if ((err = mp_init(&mu)) != CRYPT_OK) {
1257 goto LBL_ERR;
1258 }
1259 if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) {
1260 goto LBL_ERR;
1261 }
1262
1263 /* build the LUT */
1264 if ((err = s_build_lut(idx, a, modulus, mp, mu)) != CRYPT_OK) {
1265 goto LBL_ERR;;
1266 }
1267 }
1268
1269 if (idx >= 0 && fp_cache[idx].lru_count >= 2) {
1270 if (mp == NULL) {
1271 /* compute mp */
1272 if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; }
1273 }
1274 err = s_accel_fp_mul(idx, k, R, a, modulus, mp, map);
1275 } else {
1276 err = ltc_ecc_mulmod(k, G, R, a, modulus, map);
1277 }
1278 LBL_ERR:
1279 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1280 if (mp != NULL) {
1281 mp_montgomery_free(mp);
1282 }
1283 if (mu != NULL) {
1284 mp_clear(mu);
1285 }
1286 return err;
1287 }
1288
1289 /* helper function for freeing the cache ... must be called with the cache mutex locked */
s_ltc_ecc_fp_free_cache(void)1290 static void s_ltc_ecc_fp_free_cache(void)
1291 {
1292 unsigned x, y;
1293 for (x = 0; x < FP_ENTRIES; x++) {
1294 if (fp_cache[x].g != NULL) {
1295 for (y = 0; y < (1U<<FP_LUT); y++) {
1296 ltc_ecc_del_point(fp_cache[x].LUT[y]);
1297 fp_cache[x].LUT[y] = NULL;
1298 }
1299 ltc_ecc_del_point(fp_cache[x].g);
1300 fp_cache[x].g = NULL;
1301 if (fp_cache[x].mu != NULL) {
1302 mp_clear(fp_cache[x].mu);
1303 fp_cache[x].mu = NULL;
1304 }
1305 fp_cache[x].lru_count = 0;
1306 fp_cache[x].lock = 0;
1307 }
1308 }
1309 }
1310
1311 /** Free the Fixed Point cache */
ltc_ecc_fp_free(void)1312 void ltc_ecc_fp_free(void)
1313 {
1314 LTC_MUTEX_LOCK(<c_ecc_fp_lock);
1315 s_ltc_ecc_fp_free_cache();
1316 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1317 }
1318
1319 /** Add a point to the cache and initialize the LUT
1320 @param g The point to add
1321 @param modulus Modulus for curve
1322 @param lock Flag to indicate if this entry should be locked into the cache or not
1323 @return CRYPT_OK on success
1324 */
1325 int
ltc_ecc_fp_add_point(ecc_point * g,void * modulus,int lock)1326 ltc_ecc_fp_add_point(ecc_point *g, void *modulus, int lock)
1327 {
1328 int idx;
1329 int err;
1330 void *mp = NULL;
1331 void *mu = NULL;
1332
1333 LTC_MUTEX_LOCK(<c_ecc_fp_lock);
1334 if ((idx = s_find_base(g)) >= 0) {
1335 /* it is already in the cache ... just check that the LUT is initialized */
1336 if(fp_cache[idx].lru_count >= 2) {
1337 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1338 return CRYPT_OK;
1339 }
1340 }
1341
1342 if(idx == -1 && (idx = s_find_hole()) == -1) {
1343 err = CRYPT_BUFFER_OVERFLOW;
1344 goto LBL_ERR;
1345 }
1346 if ((err = s_add_entry(idx, g)) != CRYPT_OK) {
1347 goto LBL_ERR;
1348 }
1349 /* compute mp */
1350 if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) {
1351 goto LBL_ERR;
1352 }
1353
1354 /* compute mu */
1355 if ((err = mp_init(&mu)) != CRYPT_OK) {
1356 goto LBL_ERR;
1357 }
1358 if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) {
1359 goto LBL_ERR;
1360 }
1361
1362 /* build the LUT */
1363 if ((err = s_build_lut(idx, a, modulus, mp, mu)) != CRYPT_OK) {
1364 goto LBL_ERR;
1365 }
1366 fp_cache[idx].lru_count = 2;
1367 fp_cache[idx].lock = lock;
1368 LBL_ERR:
1369 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1370 if (mp != NULL) {
1371 mp_montgomery_free(mp);
1372 }
1373 if (mu != NULL) {
1374 mp_clear(mu);
1375 }
1376 return err;
1377 }
1378
1379 /** Prevent/permit the FP cache from being updated
1380 @param flag If flag is 0, remove cache lock (unlock), otherwise lock it
1381 */
ltc_ecc_fp_tablelock(int lock)1382 void ltc_ecc_fp_tablelock(int lock)
1383 {
1384 int i;
1385
1386 LTC_MUTEX_LOCK(<c_ecc_fp_lock);
1387 for (i = 0; i < FP_ENTRIES; i++) {
1388 fp_cache[i].lock = lock;
1389 }
1390 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1391 }
1392
1393 /** Export the current cache as a binary packet
1394 @param out [out] pointer to malloc'ed space containing the packet
1395 @param outlen [out] size of exported packet
1396 @return CRYPT_OK if successful
1397 */
ltc_ecc_fp_save_state(unsigned char ** out,unsigned long * outlen)1398 int ltc_ecc_fp_save_state(unsigned char **out, unsigned long *outlen)
1399 {
1400 ltc_asn1_list *cache_entry;
1401 unsigned int i, j, k;
1402 unsigned long fp_entries, fp_lut, num_entries;
1403 int err;
1404
1405 LTC_ARGCHK(out != NULL);
1406 LTC_ARGCHK(outlen != NULL);
1407
1408 fp_entries = FP_ENTRIES;
1409 fp_lut = FP_LUT;
1410 num_entries = 0;
1411
1412 LTC_MUTEX_LOCK(<c_ecc_fp_lock);
1413 /*
1414 * build the list;
1415 Cache DEFINITIONS ::=
1416 BEGIN
1417 CacheDump ::= SEQUENCE {
1418 numEntries SHORTINTEGER,
1419 maxEntries SHORTINTEGER,
1420 numLUT SHORTINTEGER,
1421 cache SEQUENCE OF INTEGER
1422 }
1423 END
1424 *
1425 */
1426 /*
1427 * The cache itself is a point (3 INTEGERS),
1428 * the LUT as pairs of INTEGERS (2 * 1<<FP_LUT),
1429 * and the mu INTEGER
1430 */
1431 cache_entry = XCALLOC(FP_ENTRIES*(2*(1U<<FP_LUT)+4)+3, sizeof(ltc_asn1_list));
1432 if (cache_entry == NULL) {
1433 err = CRYPT_MEM;
1434 goto save_err;
1435 }
1436 j = 1; /* handle the zero'th element later */
1437
1438 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_SHORT_INTEGER, &fp_entries, 1);
1439 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_SHORT_INTEGER, &fp_lut, 1);
1440
1441 for (i = 0; i < FP_ENTRIES; i++) {
1442 /*
1443 * do not save empty entries, or entries that have not yet had the lut built
1444 */
1445 if (fp_cache[i].g == NULL || fp_cache[i].lru_count < 2) {
1446 continue;
1447 }
1448 num_entries++;
1449 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].g->x, 1);
1450 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].g->y, 1);
1451 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].g->z, 1);
1452 for (k = 0; k < (1U<<FP_LUT); k++) {
1453 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].LUT[k]->x, 1);
1454 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].LUT[k]->y, 1);
1455 }
1456 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].mu, 1);
1457 }
1458 LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_EOL, 0, 0);
1459
1460 LTC_SET_ASN1(cache_entry, 0, LTC_ASN1_SHORT_INTEGER, &num_entries, 1);
1461
1462 if ((err = der_length_sequence(cache_entry, j, outlen)) != CRYPT_OK) {
1463 goto save_err;
1464 }
1465 if ((*out = XMALLOC(*outlen)) == NULL) {
1466 err = CRYPT_MEM;
1467 goto save_err;
1468 }
1469 err = der_encode_sequence(cache_entry, j, *out, outlen);
1470 save_err:
1471 XFREE(cache_entry);
1472 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1473 return err;
1474 }
1475
1476 /** Import a binary packet into the current cache
1477 @param in [in] pointer to packet
1478 @param inlen [in] size of packet (bytes)
1479 @return CRYPT_OK if successful
1480 */
ltc_ecc_fp_restore_state(unsigned char * in,unsigned long inlen)1481 int ltc_ecc_fp_restore_state(unsigned char *in, unsigned long inlen)
1482 {
1483 int err;
1484 ltc_asn1_list *asn1_list;
1485 unsigned long num_entries, fp_entries, fp_lut;
1486 unsigned long i, j;
1487 unsigned int x;
1488
1489 LTC_ARGCHK(in != NULL);
1490 if (inlen == 0) {
1491 return CRYPT_INVALID_ARG;
1492 }
1493
1494 /* zero indecies */
1495 i = 0;
1496 j = 0;
1497 asn1_list = NULL;
1498
1499 LTC_MUTEX_LOCK(<c_ecc_fp_lock);
1500 /*
1501 * start with an empty cache
1502 */
1503 s_ltc_ecc_fp_free_cache();
1504
1505 /*
1506 * decode the input packet: It consists of a sequence with a few
1507 * integers (including the FP_ENTRIES and FP_LUT sizes), followed by a
1508 * SEQUENCE which is the cache itself.
1509 *
1510 * use standard decoding for the first part, then flexible for the second
1511 */
1512 if((err = der_decode_sequence_multi(in, inlen,
1513 LTC_ASN1_SHORT_INTEGER, 1, &num_entries,
1514 LTC_ASN1_SHORT_INTEGER, 1, &fp_entries,
1515 LTC_ASN1_SHORT_INTEGER, 1, &fp_lut,
1516 LTC_ASN1_EOL, 0, 0)) != CRYPT_OK) {
1517 goto ERR_OUT;
1518 }
1519 if (fp_entries != FP_ENTRIES || fp_lut != FP_LUT || num_entries > fp_entries) {
1520 err = CRYPT_INVALID_PACKET;
1521 goto ERR_OUT;
1522 }
1523 if ((asn1_list = XCALLOC(3+num_entries*(4+2*(1<<FP_LUT))+1, sizeof(ltc_asn1_list))) == NULL) {
1524 err = CRYPT_MEM;
1525 goto ERR_OUT;
1526 }
1527 j = 0;
1528 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_SHORT_INTEGER, &num_entries, 1);
1529 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_SHORT_INTEGER, &fp_entries, 1);
1530 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_SHORT_INTEGER, &fp_lut, 1);
1531 for (i = 0; i < num_entries; i++) {
1532 if((fp_cache[i].g = ltc_ecc_new_point()) == NULL) {
1533 err = CRYPT_MEM;
1534 goto ERR_OUT;
1535 }
1536 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].g->x, 1);
1537 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].g->y, 1);
1538 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].g->z, 1);
1539 for (x = 0; x < (1U<<FP_LUT); x++) {
1540 /* since we don't store z in the cache, don't use ltc_ecc_new_point()
1541 * (which allocates space for z, only to have to free it later) */
1542 ecc_point *p = XCALLOC(1, sizeof(*p));
1543
1544 if (p == NULL) {
1545 err = CRYPT_MEM;
1546 goto ERR_OUT;
1547 }
1548 fp_cache[i].LUT[x] = p;
1549 if ((err = mp_init_multi(&p->x, &p->y, LTC_NULL)) != CRYPT_OK) {
1550 goto ERR_OUT;
1551 }
1552 p->z = NULL;
1553 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, p->x, 1);
1554 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, p->y, 1);
1555 }
1556 if((err = mp_init(&fp_cache[i].mu)) != CRYPT_OK) {
1557 goto ERR_OUT;
1558 }
1559 LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].mu, 1);
1560 fp_cache[i].lru_count = 3;
1561 fp_cache[i].lock = 1;
1562 }
1563
1564 if ((err = der_decode_sequence(in, inlen, asn1_list, j)) != CRYPT_OK) {
1565 goto ERR_OUT;
1566 }
1567 XFREE(asn1_list);
1568 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1569 return CRYPT_OK;
1570 ERR_OUT:
1571 if(asn1_list)
1572 XFREE(asn1_list);
1573 s_ltc_ecc_fp_free_cache();
1574 LTC_MUTEX_UNLOCK(<c_ecc_fp_lock);
1575 return err;
1576 }
1577
1578 #endif
1579
1580
1581