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(&ltc_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(&ltc_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(&ltc_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(&ltc_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(&ltc_ecc_fp_lock);
1315    s_ltc_ecc_fp_free_cache();
1316    LTC_MUTEX_UNLOCK(&ltc_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(&ltc_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(&ltc_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(&ltc_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(&ltc_ecc_fp_lock);
1387    for (i = 0; i < FP_ENTRIES; i++) {
1388       fp_cache[i].lock = lock;
1389    }
1390    LTC_MUTEX_UNLOCK(&ltc_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(&ltc_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(&ltc_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(&ltc_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(&ltc_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(&ltc_ecc_fp_lock);
1575    return err;
1576 }
1577 
1578 #endif
1579 
1580 
1581