diff options
Diffstat (limited to 'libtomcrypt/src/math')
| -rw-r--r-- | libtomcrypt/src/math/fp/ltc_ecc_fp_mulmod.c | 1314 | ||||
| -rw-r--r-- | libtomcrypt/src/math/gmp_desc.c | 478 | ||||
| -rw-r--r-- | libtomcrypt/src/math/ltm_desc.c | 483 | ||||
| -rw-r--r-- | libtomcrypt/src/math/multi.c | 61 | ||||
| -rw-r--r-- | libtomcrypt/src/math/rand_prime.c | 87 | ||||
| -rw-r--r-- | libtomcrypt/src/math/tfm_desc.c | 777 |
6 files changed, 3200 insertions, 0 deletions
diff --git a/libtomcrypt/src/math/fp/ltc_ecc_fp_mulmod.c b/libtomcrypt/src/math/fp/ltc_ecc_fp_mulmod.c new file mode 100644 index 0000000..d3c02c3 --- /dev/null +++ b/libtomcrypt/src/math/fp/ltc_ecc_fp_mulmod.c @@ -0,0 +1,1314 @@ +/* LibTomCrypt, modular cryptographic library -- Tom St Denis + * + * LibTomCrypt is a library that provides various cryptographic + * algorithms in a highly modular and flexible manner. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com + */ +#include "tomcrypt.h" + +/** + @file ltc_ecc_fp_mulmod.c + ECC Crypto, Tom St Denis +*/ + +#if defined(MECC) && defined(MECC_FP) +#include <limits.h> + +/* number of entries in the cache */ +#ifndef FP_ENTRIES +#define FP_ENTRIES 16 +#endif + +/* number of bits in LUT */ +#ifndef FP_LUT +#define FP_LUT 8U +#endif + +#if (FP_LUT > 12) || (FP_LUT < 2) + #error FP_LUT must be between 2 and 12 inclusively +#endif + +/** Our FP cache */ +static struct { + ecc_point *g, /* cached COPY of base point */ + *LUT[1U<<FP_LUT]; /* fixed point lookup */ + void *mu; /* copy of the montgomery constant */ + int lru_count; /* amount of times this entry has been used */ +} fp_cache[FP_ENTRIES]; + +LTC_MUTEX_GLOBAL(ltc_ecc_fp_lock) + +/* simple table to help direct the generation of the LUT */ +static const struct { + int ham, terma, termb; +} lut_orders[] = { + { 0, 0, 0 }, { 1, 0, 0 }, { 1, 0, 0 }, { 2, 1, 2 }, { 1, 0, 0 }, { 2, 1, 4 }, { 2, 2, 4 }, { 3, 3, 4 }, + { 1, 0, 0 }, { 2, 1, 8 }, { 2, 2, 8 }, { 3, 3, 8 }, { 2, 4, 8 }, { 3, 5, 8 }, { 3, 6, 8 }, { 4, 7, 8 }, + { 1, 0, 0 }, { 2, 1, 16 }, { 2, 2, 16 }, { 3, 3, 16 }, { 2, 4, 16 }, { 3, 5, 16 }, { 3, 6, 16 }, { 4, 7, 16 }, + { 2, 8, 16 }, { 3, 9, 16 }, { 3, 10, 16 }, { 4, 11, 16 }, { 3, 12, 16 }, { 4, 13, 16 }, { 4, 14, 16 }, { 5, 15, 16 }, + { 1, 0, 0 }, { 2, 1, 32 }, { 2, 2, 32 }, { 3, 3, 32 }, { 2, 4, 32 }, { 3, 5, 32 }, { 3, 6, 32 }, { 4, 7, 32 }, + { 2, 8, 32 }, { 3, 9, 32 }, { 3, 10, 32 }, { 4, 11, 32 }, { 3, 12, 32 }, { 4, 13, 32 }, { 4, 14, 32 }, { 5, 15, 32 }, + { 2, 16, 32 }, { 3, 17, 32 }, { 3, 18, 32 }, { 4, 19, 32 }, { 3, 20, 32 }, { 4, 21, 32 }, { 4, 22, 32 }, { 5, 23, 32 }, + { 3, 24, 32 }, { 4, 25, 32 }, { 4, 26, 32 }, { 5, 27, 32 }, { 4, 28, 32 }, { 5, 29, 32 }, { 5, 30, 32 }, { 6, 31, 32 }, +#if FP_LUT > 6 + { 1, 0, 0 }, { 2, 1, 64 }, { 2, 2, 64 }, { 3, 3, 64 }, { 2, 4, 64 }, { 3, 5, 64 }, { 3, 6, 64 }, { 4, 7, 64 }, + { 2, 8, 64 }, { 3, 9, 64 }, { 3, 10, 64 }, { 4, 11, 64 }, { 3, 12, 64 }, { 4, 13, 64 }, { 4, 14, 64 }, { 5, 15, 64 }, + { 2, 16, 64 }, { 3, 17, 64 }, { 3, 18, 64 }, { 4, 19, 64 }, { 3, 20, 64 }, { 4, 21, 64 }, { 4, 22, 64 }, { 5, 23, 64 }, + { 3, 24, 64 }, { 4, 25, 64 }, { 4, 26, 64 }, { 5, 27, 64 }, { 4, 28, 64 }, { 5, 29, 64 }, { 5, 30, 64 }, { 6, 31, 64 }, + { 2, 32, 64 }, { 3, 33, 64 }, { 3, 34, 64 }, { 4, 35, 64 }, { 3, 36, 64 }, { 4, 37, 64 }, { 4, 38, 64 }, { 5, 39, 64 }, + { 3, 40, 64 }, { 4, 41, 64 }, { 4, 42, 64 }, { 5, 43, 64 }, { 4, 44, 64 }, { 5, 45, 64 }, { 5, 46, 64 }, { 6, 47, 64 }, + { 3, 48, 64 }, { 4, 49, 64 }, { 4, 50, 64 }, { 5, 51, 64 }, { 4, 52, 64 }, { 5, 53, 64 }, { 5, 54, 64 }, { 6, 55, 64 }, + { 4, 56, 64 }, { 5, 57, 64 }, { 5, 58, 64 }, { 6, 59, 64 }, { 5, 60, 64 }, { 6, 61, 64 }, { 6, 62, 64 }, { 7, 63, 64 }, +#if FP_LUT > 7 + { 1, 0, 0 }, { 2, 1, 128 }, { 2, 2, 128 }, { 3, 3, 128 }, { 2, 4, 128 }, { 3, 5, 128 }, { 3, 6, 128 }, { 4, 7, 128 }, + { 2, 8, 128 }, { 3, 9, 128 }, { 3, 10, 128 }, { 4, 11, 128 }, { 3, 12, 128 }, { 4, 13, 128 }, { 4, 14, 128 }, { 5, 15, 128 }, + { 2, 16, 128 }, { 3, 17, 128 }, { 3, 18, 128 }, { 4, 19, 128 }, { 3, 20, 128 }, { 4, 21, 128 }, { 4, 22, 128 }, { 5, 23, 128 }, + { 3, 24, 128 }, { 4, 25, 128 }, { 4, 26, 128 }, { 5, 27, 128 }, { 4, 28, 128 }, { 5, 29, 128 }, { 5, 30, 128 }, { 6, 31, 128 }, + { 2, 32, 128 }, { 3, 33, 128 }, { 3, 34, 128 }, { 4, 35, 128 }, { 3, 36, 128 }, { 4, 37, 128 }, { 4, 38, 128 }, { 5, 39, 128 }, + { 3, 40, 128 }, { 4, 41, 128 }, { 4, 42, 128 }, { 5, 43, 128 }, { 4, 44, 128 }, { 5, 45, 128 }, { 5, 46, 128 }, { 6, 47, 128 }, + { 3, 48, 128 }, { 4, 49, 128 }, { 4, 50, 128 }, { 5, 51, 128 }, { 4, 52, 128 }, { 5, 53, 128 }, { 5, 54, 128 }, { 6, 55, 128 }, + { 4, 56, 128 }, { 5, 57, 128 }, { 5, 58, 128 }, { 6, 59, 128 }, { 5, 60, 128 }, { 6, 61, 128 }, { 6, 62, 128 }, { 7, 63, 128 }, + { 2, 64, 128 }, { 3, 65, 128 }, { 3, 66, 128 }, { 4, 67, 128 }, { 3, 68, 128 }, { 4, 69, 128 }, { 4, 70, 128 }, { 5, 71, 128 }, + { 3, 72, 128 }, { 4, 73, 128 }, { 4, 74, 128 }, { 5, 75, 128 }, { 4, 76, 128 }, { 5, 77, 128 }, { 5, 78, 128 }, { 6, 79, 128 }, + { 3, 80, 128 }, { 4, 81, 128 }, { 4, 82, 128 }, { 5, 83, 128 }, { 4, 84, 128 }, { 5, 85, 128 }, { 5, 86, 128 }, { 6, 87, 128 }, + { 4, 88, 128 }, { 5, 89, 128 }, { 5, 90, 128 }, { 6, 91, 128 }, { 5, 92, 128 }, { 6, 93, 128 }, { 6, 94, 128 }, { 7, 95, 128 }, + { 3, 96, 128 }, { 4, 97, 128 }, { 4, 98, 128 }, { 5, 99, 128 }, { 4, 100, 128 }, { 5, 101, 128 }, { 5, 102, 128 }, { 6, 103, 128 }, + { 4, 104, 128 }, { 5, 105, 128 }, { 5, 106, 128 }, { 6, 107, 128 }, { 5, 108, 128 }, { 6, 109, 128 }, { 6, 110, 128 }, { 7, 111, 128 }, + { 4, 112, 128 }, { 5, 113, 128 }, { 5, 114, 128 }, { 6, 115, 128 }, { 5, 116, 128 }, { 6, 117, 128 }, { 6, 118, 128 }, { 7, 119, 128 }, + { 5, 120, 128 }, { 6, 121, 128 }, { 6, 122, 128 }, { 7, 123, 128 }, { 6, 124, 128 }, { 7, 125, 128 }, { 7, 126, 128 }, { 8, 127, 128 }, +#if FP_LUT > 8 + { 1, 0, 0 }, { 2, 1, 256 }, { 2, 2, 256 }, { 3, 3, 256 }, { 2, 4, 256 }, { 3, 5, 256 }, { 3, 6, 256 }, { 4, 7, 256 }, + { 2, 8, 256 }, { 3, 9, 256 }, { 3, 10, 256 }, { 4, 11, 256 }, { 3, 12, 256 }, { 4, 13, 256 }, { 4, 14, 256 }, { 5, 15, 256 }, + { 2, 16, 256 }, { 3, 17, 256 }, { 3, 18, 256 }, { 4, 19, 256 }, { 3, 20, 256 }, { 4, 21, 256 }, { 4, 22, 256 }, { 5, 23, 256 }, + { 3, 24, 256 }, { 4, 25, 256 }, { 4, 26, 256 }, { 5, 27, 256 }, { 4, 28, 256 }, { 5, 29, 256 }, { 5, 30, 256 }, { 6, 31, 256 }, + { 2, 32, 256 }, { 3, 33, 256 }, { 3, 34, 256 }, { 4, 35, 256 }, { 3, 36, 256 }, { 4, 37, 256 }, { 4, 38, 256 }, { 5, 39, 256 }, + { 3, 40, 256 }, { 4, 41, 256 }, { 4, 42, 256 }, { 5, 43, 256 }, { 4, 44, 256 }, { 5, 45, 256 }, { 5, 46, 256 }, { 6, 47, 256 }, + { 3, 48, 256 }, { 4, 49, 256 }, { 4, 50, 256 }, { 5, 51, 256 }, { 4, 52, 256 }, { 5, 53, 256 }, { 5, 54, 256 }, { 6, 55, 256 }, + { 4, 56, 256 }, { 5, 57, 256 }, { 5, 58, 256 }, { 6, 59, 256 }, { 5, 60, 256 }, { 6, 61, 256 }, { 6, 62, 256 }, { 7, 63, 256 }, + { 2, 64, 256 }, { 3, 65, 256 }, { 3, 66, 256 }, { 4, 67, 256 }, { 3, 68, 256 }, { 4, 69, 256 }, { 4, 70, 256 }, { 5, 71, 256 }, + { 3, 72, 256 }, { 4, 73, 256 }, { 4, 74, 256 }, { 5, 75, 256 }, { 4, 76, 256 }, { 5, 77, 256 }, { 5, 78, 256 }, { 6, 79, 256 }, + { 3, 80, 256 }, { 4, 81, 256 }, { 4, 82, 256 }, { 5, 83, 256 }, { 4, 84, 256 }, { 5, 85, 256 }, { 5, 86, 256 }, { 6, 87, 256 }, + { 4, 88, 256 }, { 5, 89, 256 }, { 5, 90, 256 }, { 6, 91, 256 }, { 5, 92, 256 }, { 6, 93, 256 }, { 6, 94, 256 }, { 7, 95, 256 }, + { 3, 96, 256 }, { 4, 97, 256 }, { 4, 98, 256 }, { 5, 99, 256 }, { 4, 100, 256 }, { 5, 101, 256 }, { 5, 102, 256 }, { 6, 103, 256 }, + { 4, 104, 256 }, { 5, 105, 256 }, { 5, 106, 256 }, { 6, 107, 256 }, { 5, 108, 256 }, { 6, 109, 256 }, { 6, 110, 256 }, { 7, 111, 256 }, + { 4, 112, 256 }, { 5, 113, 256 }, { 5, 114, 256 }, { 6, 115, 256 }, { 5, 116, 256 }, { 6, 117, 256 }, { 6, 118, 256 }, { 7, 119, 256 }, + { 5, 120, 256 }, { 6, 121, 256 }, { 6, 122, 256 }, { 7, 123, 256 }, { 6, 124, 256 }, { 7, 125, 256 }, { 7, 126, 256 }, { 8, 127, 256 }, + { 2, 128, 256 }, { 3, 129, 256 }, { 3, 130, 256 }, { 4, 131, 256 }, { 3, 132, 256 }, { 4, 133, 256 }, { 4, 134, 256 }, { 5, 135, 256 }, + { 3, 136, 256 }, { 4, 137, 256 }, { 4, 138, 256 }, { 5, 139, 256 }, { 4, 140, 256 }, { 5, 141, 256 }, { 5, 142, 256 }, { 6, 143, 256 }, + { 3, 144, 256 }, { 4, 145, 256 }, { 4, 146, 256 }, { 5, 147, 256 }, { 4, 148, 256 }, { 5, 149, 256 }, { 5, 150, 256 }, { 6, 151, 256 }, + { 4, 152, 256 }, { 5, 153, 256 }, { 5, 154, 256 }, { 6, 155, 256 }, { 5, 156, 256 }, { 6, 157, 256 }, { 6, 158, 256 }, { 7, 159, 256 }, + { 3, 160, 256 }, { 4, 161, 256 }, { 4, 162, 256 }, { 5, 163, 256 }, { 4, 164, 256 }, { 5, 165, 256 }, { 5, 166, 256 }, { 6, 167, 256 }, + { 4, 168, 256 }, { 5, 169, 256 }, { 5, 170, 256 }, { 6, 171, 256 }, { 5, 172, 256 }, { 6, 173, 256 }, { 6, 174, 256 }, { 7, 175, 256 }, + { 4, 176, 256 }, { 5, 177, 256 }, { 5, 178, 256 }, { 6, 179, 256 }, { 5, 180, 256 }, { 6, 181, 256 }, { 6, 182, 256 }, { 7, 183, 256 }, + { 5, 184, 256 }, { 6, 185, 256 }, { 6, 186, 256 }, { 7, 187, 256 }, { 6, 188, 256 }, { 7, 189, 256 }, { 7, 190, 256 }, { 8, 191, 256 }, + { 3, 192, 256 }, { 4, 193, 256 }, { 4, 194, 256 }, { 5, 195, 256 }, { 4, 196, 256 }, { 5, 197, 256 }, { 5, 198, 256 }, { 6, 199, 256 }, + { 4, 200, 256 }, { 5, 201, 256 }, { 5, 202, 256 }, { 6, 203, 256 }, { 5, 204, 256 }, { 6, 205, 256 }, { 6, 206, 256 }, { 7, 207, 256 }, + { 4, 208, 256 }, { 5, 209, 256 }, { 5, 210, 256 }, { 6, 211, 256 }, { 5, 212, 256 }, { 6, 213, 256 }, { 6, 214, 256 }, { 7, 215, 256 }, + { 5, 216, 256 }, { 6, 217, 256 }, { 6, 218, 256 }, { 7, 219, 256 }, { 6, 220, 256 }, { 7, 221, 256 }, { 7, 222, 256 }, { 8, 223, 256 }, + { 4, 224, 256 }, { 5, 225, 256 }, { 5, 226, 256 }, { 6, 227, 256 }, { 5, 228, 256 }, { 6, 229, 256 }, { 6, 230, 256 }, { 7, 231, 256 }, + { 5, 232, 256 }, { 6, 233, 256 }, { 6, 234, 256 }, { 7, 235, 256 }, { 6, 236, 256 }, { 7, 237, 256 }, { 7, 238, 256 }, { 8, 239, 256 }, + { 5, 240, 256 }, { 6, 241, 256 }, { 6, 242, 256 }, { 7, 243, 256 }, { 6, 244, 256 }, { 7, 245, 256 }, { 7, 246, 256 }, { 8, 247, 256 }, + { 6, 248, 256 }, { 7, 249, 256 }, { 7, 250, 256 }, { 8, 251, 256 }, { 7, 252, 256 }, { 8, 253, 256 }, { 8, 254, 256 }, { 9, 255, 256 }, +#if FP_LUT > 9 + { 1, 0, 0 }, { 2, 1, 512 }, { 2, 2, 512 }, { 3, 3, 512 }, { 2, 4, 512 }, { 3, 5, 512 }, { 3, 6, 512 }, { 4, 7, 512 }, + { 2, 8, 512 }, { 3, 9, 512 }, { 3, 10, 512 }, { 4, 11, 512 }, { 3, 12, 512 }, { 4, 13, 512 }, { 4, 14, 512 }, { 5, 15, 512 }, + { 2, 16, 512 }, { 3, 17, 512 }, { 3, 18, 512 }, { 4, 19, 512 }, { 3, 20, 512 }, { 4, 21, 512 }, { 4, 22, 512 }, { 5, 23, 512 }, + { 3, 24, 512 }, { 4, 25, 512 }, { 4, 26, 512 }, { 5, 27, 512 }, { 4, 28, 512 }, { 5, 29, 512 }, { 5, 30, 512 }, { 6, 31, 512 }, + { 2, 32, 512 }, { 3, 33, 512 }, { 3, 34, 512 }, { 4, 35, 512 }, { 3, 36, 512 }, { 4, 37, 512 }, { 4, 38, 512 }, { 5, 39, 512 }, + { 3, 40, 512 }, { 4, 41, 512 }, { 4, 42, 512 }, { 5, 43, 512 }, { 4, 44, 512 }, { 5, 45, 512 }, { 5, 46, 512 }, { 6, 47, 512 }, + { 3, 48, 512 }, { 4, 49, 512 }, { 4, 50, 512 }, { 5, 51, 512 }, { 4, 52, 512 }, { 5, 53, 512 }, { 5, 54, 512 }, { 6, 55, 512 }, + { 4, 56, 512 }, { 5, 57, 512 }, { 5, 58, 512 }, { 6, 59, 512 }, { 5, 60, 512 }, { 6, 61, 512 }, { 6, 62, 512 }, { 7, 63, 512 }, + { 2, 64, 512 }, { 3, 65, 512 }, { 3, 66, 512 }, { 4, 67, 512 }, { 3, 68, 512 }, { 4, 69, 512 }, { 4, 70, 512 }, { 5, 71, 512 }, + { 3, 72, 512 }, { 4, 73, 512 }, { 4, 74, 512 }, { 5, 75, 512 }, { 4, 76, 512 }, { 5, 77, 512 }, { 5, 78, 512 }, { 6, 79, 512 }, + { 3, 80, 512 }, { 4, 81, 512 }, { 4, 82, 512 }, { 5, 83, 512 }, { 4, 84, 512 }, { 5, 85, 512 }, { 5, 86, 512 }, { 6, 87, 512 }, + { 4, 88, 512 }, { 5, 89, 512 }, { 5, 90, 512 }, { 6, 91, 512 }, { 5, 92, 512 }, { 6, 93, 512 }, { 6, 94, 512 }, { 7, 95, 512 }, + { 3, 96, 512 }, { 4, 97, 512 }, { 4, 98, 512 }, { 5, 99, 512 }, { 4, 100, 512 }, { 5, 101, 512 }, { 5, 102, 512 }, { 6, 103, 512 }, + { 4, 104, 512 }, { 5, 105, 512 }, { 5, 106, 512 }, { 6, 107, 512 }, { 5, 108, 512 }, { 6, 109, 512 }, { 6, 110, 512 }, { 7, 111, 512 }, + { 4, 112, 512 }, { 5, 113, 512 }, { 5, 114, 512 }, { 6, 115, 512 }, { 5, 116, 512 }, { 6, 117, 512 }, { 6, 118, 512 }, { 7, 119, 512 }, + { 5, 120, 512 }, { 6, 121, 512 }, { 6, 122, 512 }, { 7, 123, 512 }, { 6, 124, 512 }, { 7, 125, 512 }, { 7, 126, 512 }, { 8, 127, 512 }, + { 2, 128, 512 }, { 3, 129, 512 }, { 3, 130, 512 }, { 4, 131, 512 }, { 3, 132, 512 }, { 4, 133, 512 }, { 4, 134, 512 }, { 5, 135, 512 }, + { 3, 136, 512 }, { 4, 137, 512 }, { 4, 138, 512 }, { 5, 139, 512 }, { 4, 140, 512 }, { 5, 141, 512 }, { 5, 142, 512 }, { 6, 143, 512 }, + { 3, 144, 512 }, { 4, 145, 512 }, { 4, 146, 512 }, { 5, 147, 512 }, { 4, 148, 512 }, { 5, 149, 512 }, { 5, 150, 512 }, { 6, 151, 512 }, + { 4, 152, 512 }, { 5, 153, 512 }, { 5, 154, 512 }, { 6, 155, 512 }, { 5, 156, 512 }, { 6, 157, 512 }, { 6, 158, 512 }, { 7, 159, 512 }, + { 3, 160, 512 }, { 4, 161, 512 }, { 4, 162, 512 }, { 5, 163, 512 }, { 4, 164, 512 }, { 5, 165, 512 }, { 5, 166, 512 }, { 6, 167, 512 }, + { 4, 168, 512 }, { 5, 169, 512 }, { 5, 170, 512 }, { 6, 171, 512 }, { 5, 172, 512 }, { 6, 173, 512 }, { 6, 174, 512 }, { 7, 175, 512 }, + { 4, 176, 512 }, { 5, 177, 512 }, { 5, 178, 512 }, { 6, 179, 512 }, { 5, 180, 512 }, { 6, 181, 512 }, { 6, 182, 512 }, { 7, 183, 512 }, + { 5, 184, 512 }, { 6, 185, 512 }, { 6, 186, 512 }, { 7, 187, 512 }, { 6, 188, 512 }, { 7, 189, 512 }, { 7, 190, 512 }, { 8, 191, 512 }, + { 3, 192, 512 }, { 4, 193, 512 }, { 4, 194, 512 }, { 5, 195, 512 }, { 4, 196, 512 }, { 5, 197, 512 }, { 5, 198, 512 }, { 6, 199, 512 }, + { 4, 200, 512 }, { 5, 201, 512 }, { 5, 202, 512 }, { 6, 203, 512 }, { 5, 204, 512 }, { 6, 205, 512 }, { 6, 206, 512 }, { 7, 207, 512 }, + { 4, 208, 512 }, { 5, 209, 512 }, { 5, 210, 512 }, { 6, 211, 512 }, { 5, 212, 512 }, { 6, 213, 512 }, { 6, 214, 512 }, { 7, 215, 512 }, + { 5, 216, 512 }, { 6, 217, 512 }, { 6, 218, 512 }, { 7, 219, 512 }, { 6, 220, 512 }, { 7, 221, 512 }, { 7, 222, 512 }, { 8, 223, 512 }, + { 4, 224, 512 }, { 5, 225, 512 }, { 5, 226, 512 }, { 6, 227, 512 }, { 5, 228, 512 }, { 6, 229, 512 }, { 6, 230, 512 }, { 7, 231, 512 }, + { 5, 232, 512 }, { 6, 233, 512 }, { 6, 234, 512 }, { 7, 235, 512 }, { 6, 236, 512 }, { 7, 237, 512 }, { 7, 238, 512 }, { 8, 239, 512 }, + { 5, 240, 512 }, { 6, 241, 512 }, { 6, 242, 512 }, { 7, 243, 512 }, { 6, 244, 512 }, { 7, 245, 512 }, { 7, 246, 512 }, { 8, 247, 512 }, + { 6, 248, 512 }, { 7, 249, 512 }, { 7, 250, 512 }, { 8, 251, 512 }, { 7, 252, 512 }, { 8, 253, 512 }, { 8, 254, 512 }, { 9, 255, 512 }, + { 2, 256, 512 }, { 3, 257, 512 }, { 3, 258, 512 }, { 4, 259, 512 }, { 3, 260, 512 }, { 4, 261, 512 }, { 4, 262, 512 }, { 5, 263, 512 }, + { 3, 264, 512 }, { 4, 265, 512 }, { 4, 266, 512 }, { 5, 267, 512 }, { 4, 268, 512 }, { 5, 269, 512 }, { 5, 270, 512 }, { 6, 271, 512 }, + { 3, 272, 512 }, { 4, 273, 512 }, { 4, 274, 512 }, { 5, 275, 512 }, { 4, 276, 512 }, { 5, 277, 512 }, { 5, 278, 512 }, { 6, 279, 512 }, + { 4, 280, 512 }, { 5, 281, 512 }, { 5, 282, 512 }, { 6, 283, 512 }, { 5, 284, 512 }, { 6, 285, 512 }, { 6, 286, 512 }, { 7, 287, 512 }, + { 3, 288, 512 }, { 4, 289, 512 }, { 4, 290, 512 }, { 5, 291, 512 }, { 4, 292, 512 }, { 5, 293, 512 }, { 5, 294, 512 }, { 6, 295, 512 }, + { 4, 296, 512 }, { 5, 297, 512 }, { 5, 298, 512 }, { 6, 299, 512 }, { 5, 300, 512 }, { 6, 301, 512 }, { 6, 302, 512 }, { 7, 303, 512 }, + { 4, 304, 512 }, { 5, 305, 512 }, { 5, 306, 512 }, { 6, 307, 512 }, { 5, 308, 512 }, { 6, 309, 512 }, { 6, 310, 512 }, { 7, 311, 512 }, + { 5, 312, 512 }, { 6, 313, 512 }, { 6, 314, 512 }, { 7, 315, 512 }, { 6, 316, 512 }, { 7, 317, 512 }, { 7, 318, 512 }, { 8, 319, 512 }, + { 3, 320, 512 }, { 4, 321, 512 }, { 4, 322, 512 }, { 5, 323, 512 }, { 4, 324, 512 }, { 5, 325, 512 }, { 5, 326, 512 }, { 6, 327, 512 }, + { 4, 328, 512 }, { 5, 329, 512 }, { 5, 330, 512 }, { 6, 331, 512 }, { 5, 332, 512 }, { 6, 333, 512 }, { 6, 334, 512 }, { 7, 335, 512 }, + { 4, 336, 512 }, { 5, 337, 512 }, { 5, 338, 512 }, { 6, 339, 512 }, { 5, 340, 512 }, { 6, 341, 512 }, { 6, 342, 512 }, { 7, 343, 512 }, + { 5, 344, 512 }, { 6, 345, 512 }, { 6, 346, 512 }, { 7, 347, 512 }, { 6, 348, 512 }, { 7, 349, 512 }, { 7, 350, 512 }, { 8, 351, 512 }, + { 4, 352, 512 }, { 5, 353, 512 }, { 5, 354, 512 }, { 6, 355, 512 }, { 5, 356, 512 }, { 6, 357, 512 }, { 6, 358, 512 }, { 7, 359, 512 }, + { 5, 360, 512 }, { 6, 361, 512 }, { 6, 362, 512 }, { 7, 363, 512 }, { 6, 364, 512 }, { 7, 365, 512 }, { 7, 366, 512 }, { 8, 367, 512 }, + { 5, 368, 512 }, { 6, 369, 512 }, { 6, 370, 512 }, { 7, 371, 512 }, { 6, 372, 512 }, { 7, 373, 512 }, { 7, 374, 512 }, { 8, 375, 512 }, + { 6, 376, 512 }, { 7, 377, 512 }, { 7, 378, 512 }, { 8, 379, 512 }, { 7, 380, 512 }, { 8, 381, 512 }, { 8, 382, 512 }, { 9, 383, 512 }, + { 3, 384, 512 }, { 4, 385, 512 }, { 4, 386, 512 }, { 5, 387, 512 }, { 4, 388, 512 }, { 5, 389, 512 }, { 5, 390, 512 }, { 6, 391, 512 }, + { 4, 392, 512 }, { 5, 393, 512 }, { 5, 394, 512 }, { 6, 395, 512 }, { 5, 396, 512 }, { 6, 397, 512 }, { 6, 398, 512 }, { 7, 399, 512 }, + { 4, 400, 512 }, { 5, 401, 512 }, { 5, 402, 512 }, { 6, 403, 512 }, { 5, 404, 512 }, { 6, 405, 512 }, { 6, 406, 512 }, { 7, 407, 512 }, + { 5, 408, 512 }, { 6, 409, 512 }, { 6, 410, 512 }, { 7, 411, 512 }, { 6, 412, 512 }, { 7, 413, 512 }, { 7, 414, 512 }, { 8, 415, 512 }, + { 4, 416, 512 }, { 5, 417, 512 }, { 5, 418, 512 }, { 6, 419, 512 }, { 5, 420, 512 }, { 6, 421, 512 }, { 6, 422, 512 }, { 7, 423, 512 }, + { 5, 424, 512 }, { 6, 425, 512 }, { 6, 426, 512 }, { 7, 427, 512 }, { 6, 428, 512 }, { 7, 429, 512 }, { 7, 430, 512 }, { 8, 431, 512 }, + { 5, 432, 512 }, { 6, 433, 512 }, { 6, 434, 512 }, { 7, 435, 512 }, { 6, 436, 512 }, { 7, 437, 512 }, { 7, 438, 512 }, { 8, 439, 512 }, + { 6, 440, 512 }, { 7, 441, 512 }, { 7, 442, 512 }, { 8, 443, 512 }, { 7, 444, 512 }, { 8, 445, 512 }, { 8, 446, 512 }, { 9, 447, 512 }, + { 4, 448, 512 }, { 5, 449, 512 }, { 5, 450, 512 }, { 6, 451, 512 }, { 5, 452, 512 }, { 6, 453, 512 }, { 6, 454, 512 }, { 7, 455, 512 }, + { 5, 456, 512 }, { 6, 457, 512 }, { 6, 458, 512 }, { 7, 459, 512 }, { 6, 460, 512 }, { 7, 461, 512 }, { 7, 462, 512 }, { 8, 463, 512 }, + { 5, 464, 512 }, { 6, 465, 512 }, { 6, 466, 512 }, { 7, 467, 512 }, { 6, 468, 512 }, { 7, 469, 512 }, { 7, 470, 512 }, { 8, 471, 512 }, + { 6, 472, 512 }, { 7, 473, 512 }, { 7, 474, 512 }, { 8, 475, 512 }, { 7, 476, 512 }, { 8, 477, 512 }, { 8, 478, 512 }, { 9, 479, 512 }, + { 5, 480, 512 }, { 6, 481, 512 }, { 6, 482, 512 }, { 7, 483, 512 }, { 6, 484, 512 }, { 7, 485, 512 }, { 7, 486, 512 }, { 8, 487, 512 }, + { 6, 488, 512 }, { 7, 489, 512 }, { 7, 490, 512 }, { 8, 491, 512 }, { 7, 492, 512 }, { 8, 493, 512 }, { 8, 494, 512 }, { 9, 495, 512 }, + { 6, 496, 512 }, { 7, 497, 512 }, { 7, 498, 512 }, { 8, 499, 512 }, { 7, 500, 512 }, { 8, 501, 512 }, { 8, 502, 512 }, { 9, 503, 512 }, + { 7, 504, 512 }, { 8, 505, 512 }, { 8, 506, 512 }, { 9, 507, 512 }, { 8, 508, 512 }, { 9, 509, 512 }, { 9, 510, 512 }, { 10, 511, 512 }, +#if FP_LUT > 10 + { 1, 0, 0 }, { 2, 1, 1024 }, { 2, 2, 1024 }, { 3, 3, 1024 }, { 2, 4, 1024 }, { 3, 5, 1024 }, { 3, 6, 1024 }, { 4, 7, 1024 }, + { 2, 8, 1024 }, { 3, 9, 1024 }, { 3, 10, 1024 }, { 4, 11, 1024 }, { 3, 12, 1024 }, { 4, 13, 1024 }, { 4, 14, 1024 }, { 5, 15, 1024 }, + { 2, 16, 1024 }, { 3, 17, 1024 }, { 3, 18, 1024 }, { 4, 19, 1024 }, { 3, 20, 1024 }, { 4, 21, 1024 }, { 4, 22, 1024 }, { 5, 23, 1024 }, + { 3, 24, 1024 }, { 4, 25, 1024 }, { 4, 26, 1024 }, { 5, 27, 1024 }, { 4, 28, 1024 }, { 5, 29, 1024 }, { 5, 30, 1024 }, { 6, 31, 1024 }, + { 2, 32, 1024 }, { 3, 33, 1024 }, { 3, 34, 1024 }, { 4, 35, 1024 }, { 3, 36, 1024 }, { 4, 37, 1024 }, { 4, 38, 1024 }, { 5, 39, 1024 }, + { 3, 40, 1024 }, { 4, 41, 1024 }, { 4, 42, 1024 }, { 5, 43, 1024 }, { 4, 44, 1024 }, { 5, 45, 1024 }, { 5, 46, 1024 }, { 6, 47, 1024 }, + { 3, 48, 1024 }, { 4, 49, 1024 }, { 4, 50, 1024 }, { 5, 51, 1024 }, { 4, 52, 1024 }, { 5, 53, 1024 }, { 5, 54, 1024 }, { 6, 55, 1024 }, + { 4, 56, 1024 }, { 5, 57, 1024 }, { 5, 58, 1024 }, { 6, 59, 1024 }, { 5, 60, 1024 }, { 6, 61, 1024 }, { 6, 62, 1024 }, { 7, 63, 1024 }, + { 2, 64, 1024 }, { 3, 65, 1024 }, { 3, 66, 1024 }, { 4, 67, 1024 }, { 3, 68, 1024 }, { 4, 69, 1024 }, { 4, 70, 1024 }, { 5, 71, 1024 }, + { 3, 72, 1024 }, { 4, 73, 1024 }, { 4, 74, 1024 }, { 5, 75, 1024 }, { 4, 76, 1024 }, { 5, 77, 1024 }, { 5, 78, 1024 }, { 6, 79, 1024 }, + { 3, 80, 1024 }, { 4, 81, 1024 }, { 4, 82, 1024 }, { 5, 83, 1024 }, { 4, 84, 1024 }, { 5, 85, 1024 }, { 5, 86, 1024 }, { 6, 87, 1024 }, + { 4, 88, 1024 }, { 5, 89, 1024 }, { 5, 90, 1024 }, { 6, 91, 1024 }, { 5, 92, 1024 }, { 6, 93, 1024 }, { 6, 94, 1024 }, { 7, 95, 1024 }, + { 3, 96, 1024 }, { 4, 97, 1024 }, { 4, 98, 1024 }, { 5, 99, 1024 }, { 4, 100, 1024 }, { 5, 101, 1024 }, { 5, 102, 1024 }, { 6, 103, 1024 }, + { 4, 104, 1024 }, { 5, 105, 1024 }, { 5, 106, 1024 }, { 6, 107, 1024 }, { 5, 108, 1024 }, { 6, 109, 1024 }, { 6, 110, 1024 }, { 7, 111, 1024 }, + { 4, 112, 1024 }, { 5, 113, 1024 }, { 5, 114, 1024 }, { 6, 115, 1024 }, { 5, 116, 1024 }, { 6, 117, 1024 }, { 6, 118, 1024 }, { 7, 119, 1024 }, + { 5, 120, 1024 }, { 6, 121, 1024 }, { 6, 122, 1024 }, { 7, 123, 1024 }, { 6, 124, 1024 }, { 7, 125, 1024 }, { 7, 126, 1024 }, { 8, 127, 1024 }, + { 2, 128, 1024 }, { 3, 129, 1024 }, { 3, 130, 1024 }, { 4, 131, 1024 }, { 3, 132, 1024 }, { 4, 133, 1024 }, { 4, 134, 1024 }, { 5, 135, 1024 }, + { 3, 136, 1024 }, { 4, 137, 1024 }, { 4, 138, 1024 }, { 5, 139, 1024 }, { 4, 140, 1024 }, { 5, 141, 1024 }, { 5, 142, 1024 }, { 6, 143, 1024 }, + { 3, 144, 1024 }, { 4, 145, 1024 }, { 4, 146, 1024 }, { 5, 147, 1024 }, { 4, 148, 1024 }, { 5, 149, 1024 }, { 5, 150, 1024 }, { 6, 151, 1024 }, + { 4, 152, 1024 }, { 5, 153, 1024 }, { 5, 154, 1024 }, { 6, 155, 1024 }, { 5, 156, 1024 }, { 6, 157, 1024 }, { 6, 158, 1024 }, { 7, 159, 1024 }, + { 3, 160, 1024 }, { 4, 161, 1024 }, { 4, 162, 1024 }, { 5, 163, 1024 }, { 4, 164, 1024 }, { 5, 165, 1024 }, { 5, 166, 1024 }, { 6, 167, 1024 }, + { 4, 168, 1024 }, { 5, 169, 1024 }, { 5, 170, 1024 }, { 6, 171, 1024 }, { 5, 172, 1024 }, { 6, 173, 1024 }, { 6, 174, 1024 }, { 7, 175, 1024 }, + { 4, 176, 1024 }, { 5, 177, 1024 }, { 5, 178, 1024 }, { 6, 179, 1024 }, { 5, 180, 1024 }, { 6, 181, 1024 }, { 6, 182, 1024 }, { 7, 183, 1024 }, + { 5, 184, 1024 }, { 6, 185, 1024 }, { 6, 186, 1024 }, { 7, 187, 1024 }, { 6, 188, 1024 }, { 7, 189, 1024 }, { 7, 190, 1024 }, { 8, 191, 1024 }, + { 3, 192, 1024 }, { 4, 193, 1024 }, { 4, 194, 1024 }, { 5, 195, 1024 }, { 4, 196, 1024 }, { 5, 197, 1024 }, { 5, 198, 1024 }, { 6, 199, 1024 }, + { 4, 200, 1024 }, { 5, 201, 1024 }, { 5, 202, 1024 }, { 6, 203, 1024 }, { 5, 204, 1024 }, { 6, 205, 1024 }, { 6, 206, 1024 }, { 7, 207, 1024 }, + { 4, 208, 1024 }, { 5, 209, 1024 }, { 5, 210, 1024 }, { 6, 211, 1024 }, { 5, 212, 1024 }, { 6, 213, 1024 }, { 6, 214, 1024 }, { 7, 215, 1024 }, + { 5, 216, 1024 }, { 6, 217, 1024 }, { 6, 218, 1024 }, { 7, 219, 1024 }, { 6, 220, 1024 }, { 7, 221, 1024 }, { 7, 222, 1024 }, { 8, 223, 1024 }, + { 4, 224, 1024 }, { 5, 225, 1024 }, { 5, 226, 1024 }, { 6, 227, 1024 }, { 5, 228, 1024 }, { 6, 229, 1024 }, { 6, 230, 1024 }, { 7, 231, 1024 }, + { 5, 232, 1024 }, { 6, 233, 1024 }, { 6, 234, 1024 }, { 7, 235, 1024 }, { 6, 236, 1024 }, { 7, 237, 1024 }, { 7, 238, 1024 }, { 8, 239, 1024 }, + { 5, 240, 1024 }, { 6, 241, 1024 }, { 6, 242, 1024 }, { 7, 243, 1024 }, { 6, 244, 1024 }, { 7, 245, 1024 }, { 7, 246, 1024 }, { 8, 247, 1024 }, + { 6, 248, 1024 }, { 7, 249, 1024 }, { 7, 250, 1024 }, { 8, 251, 1024 }, { 7, 252, 1024 }, { 8, 253, 1024 }, { 8, 254, 1024 }, { 9, 255, 1024 }, + { 2, 256, 1024 }, { 3, 257, 1024 }, { 3, 258, 1024 }, { 4, 259, 1024 }, { 3, 260, 1024 }, { 4, 261, 1024 }, { 4, 262, 1024 }, { 5, 263, 1024 }, + { 3, 264, 1024 }, { 4, 265, 1024 }, { 4, 266, 1024 }, { 5, 267, 1024 }, { 4, 268, 1024 }, { 5, 269, 1024 }, { 5, 270, 1024 }, { 6, 271, 1024 }, + { 3, 272, 1024 }, { 4, 273, 1024 }, { 4, 274, 1024 }, { 5, 275, 1024 }, { 4, 276, 1024 }, { 5, 277, 1024 }, { 5, 278, 1024 }, { 6, 279, 1024 }, + { 4, 280, 1024 }, { 5, 281, 1024 }, { 5, 282, 1024 }, { 6, 283, 1024 }, { 5, 284, 1024 }, { 6, 285, 1024 }, { 6, 286, 1024 }, { 7, 287, 1024 }, + { 3, 288, 1024 }, { 4, 289, 1024 }, { 4, 290, 1024 }, { 5, 291, 1024 }, { 4, 292, 1024 }, { 5, 293, 1024 }, { 5, 294, 1024 }, { 6, 295, 1024 }, + { 4, 296, 1024 }, { 5, 297, 1024 }, { 5, 298, 1024 }, { 6, 299, 1024 }, { 5, 300, 1024 }, { 6, 301, 1024 }, { 6, 302, 1024 }, { 7, 303, 1024 }, + { 4, 304, 1024 }, { 5, 305, 1024 }, { 5, 306, 1024 }, { 6, 307, 1024 }, { 5, 308, 1024 }, { 6, 309, 1024 }, { 6, 310, 1024 }, { 7, 311, 1024 }, + { 5, 312, 1024 }, { 6, 313, 1024 }, { 6, 314, 1024 }, { 7, 315, 1024 }, { 6, 316, 1024 }, { 7, 317, 1024 }, { 7, 318, 1024 }, { 8, 319, 1024 }, + { 3, 320, 1024 }, { 4, 321, 1024 }, { 4, 322, 1024 }, { 5, 323, 1024 }, { 4, 324, 1024 }, { 5, 325, 1024 }, { 5, 326, 1024 }, { 6, 327, 1024 }, + { 4, 328, 1024 }, { 5, 329, 1024 }, { 5, 330, 1024 }, { 6, 331, 1024 }, { 5, 332, 1024 }, { 6, 333, 1024 }, { 6, 334, 1024 }, { 7, 335, 1024 }, + { 4, 336, 1024 }, { 5, 337, 1024 }, { 5, 338, 1024 }, { 6, 339, 1024 }, { 5, 340, 1024 }, { 6, 341, 1024 }, { 6, 342, 1024 }, { 7, 343, 1024 }, + { 5, 344, 1024 }, { 6, 345, 1024 }, { 6, 346, 1024 }, { 7, 347, 1024 }, { 6, 348, 1024 }, { 7, 349, 1024 }, { 7, 350, 1024 }, { 8, 351, 1024 }, + { 4, 352, 1024 }, { 5, 353, 1024 }, { 5, 354, 1024 }, { 6, 355, 1024 }, { 5, 356, 1024 }, { 6, 357, 1024 }, { 6, 358, 1024 }, { 7, 359, 1024 }, + { 5, 360, 1024 }, { 6, 361, 1024 }, { 6, 362, 1024 }, { 7, 363, 1024 }, { 6, 364, 1024 }, { 7, 365, 1024 }, { 7, 366, 1024 }, { 8, 367, 1024 }, + { 5, 368, 1024 }, { 6, 369, 1024 }, { 6, 370, 1024 }, { 7, 371, 1024 }, { 6, 372, 1024 }, { 7, 373, 1024 }, { 7, 374, 1024 }, { 8, 375, 1024 }, + { 6, 376, 1024 }, { 7, 377, 1024 }, { 7, 378, 1024 }, { 8, 379, 1024 }, { 7, 380, 1024 }, { 8, 381, 1024 }, { 8, 382, 1024 }, { 9, 383, 1024 }, + { 3, 384, 1024 }, { 4, 385, 1024 }, { 4, 386, 1024 }, { 5, 387, 1024 }, { 4, 388, 1024 }, { 5, 389, 1024 }, { 5, 390, 1024 }, { 6, 391, 1024 }, + { 4, 392, 1024 }, { 5, 393, 1024 }, { 5, 394, 1024 }, { 6, 395, 1024 }, { 5, 396, 1024 }, { 6, 397, 1024 }, { 6, 398, 1024 }, { 7, 399, 1024 }, + { 4, 400, 1024 }, { 5, 401, 1024 }, { 5, 402, 1024 }, { 6, 403, 1024 }, { 5, 404, 1024 }, { 6, 405, 1024 }, { 6, 406, 1024 }, { 7, 407, 1024 }, + { 5, 408, 1024 }, { 6, 409, 1024 }, { 6, 410, 1024 }, { 7, 411, 1024 }, { 6, 412, 1024 }, { 7, 413, 1024 }, { 7, 414, 1024 }, { 8, 415, 1024 }, + { 4, 416, 1024 }, { 5, 417, 1024 }, { 5, 418, 1024 }, { 6, 419, 1024 }, { 5, 420, 1024 }, { 6, 421, 1024 }, { 6, 422, 1024 }, { 7, 423, 1024 }, + { 5, 424, 1024 }, { 6, 425, 1024 }, { 6, 426, 1024 }, { 7, 427, 1024 }, { 6, 428, 1024 }, { 7, 429, 1024 }, { 7, 430, 1024 }, { 8, 431, 1024 }, + { 5, 432, 1024 }, { 6, 433, 1024 }, { 6, 434, 1024 }, { 7, 435, 1024 }, { 6, 436, 1024 }, { 7, 437, 1024 }, { 7, 438, 1024 }, { 8, 439, 1024 }, + { 6, 440, 1024 }, { 7, 441, 1024 }, { 7, 442, 1024 }, { 8, 443, 1024 }, { 7, 444, 1024 }, { 8, 445, 1024 }, { 8, 446, 1024 }, { 9, 447, 1024 }, + { 4, 448, 1024 }, { 5, 449, 1024 }, { 5, 450, 1024 }, { 6, 451, 1024 }, { 5, 452, 1024 }, { 6, 453, 1024 }, { 6, 454, 1024 }, { 7, 455, 1024 }, + { 5, 456, 1024 }, { 6, 457, 1024 }, { 6, 458, 1024 }, { 7, 459, 1024 }, { 6, 460, 1024 }, { 7, 461, 1024 }, { 7, 462, 1024 }, { 8, 463, 1024 }, + { 5, 464, 1024 }, { 6, 465, 1024 }, { 6, 466, 1024 }, { 7, 467, 1024 }, { 6, 468, 1024 }, { 7, 469, 1024 }, { 7, 470, 1024 }, { 8, 471, 1024 }, + { 6, 472, 1024 }, { 7, 473, 1024 }, { 7, 474, 1024 }, { 8, 475, 1024 }, { 7, 476, 1024 }, { 8, 477, 1024 }, { 8, 478, 1024 }, { 9, 479, 1024 }, + { 5, 480, 1024 }, { 6, 481, 1024 }, { 6, 482, 1024 }, { 7, 483, 1024 }, { 6, 484, 1024 }, { 7, 485, 1024 }, { 7, 486, 1024 }, { 8, 487, 1024 }, + { 6, 488, 1024 }, { 7, 489, 1024 }, { 7, 490, 1024 }, { 8, 491, 1024 }, { 7, 492, 1024 }, { 8, 493, 1024 }, { 8, 494, 1024 }, { 9, 495, 1024 }, + { 6, 496, 1024 }, { 7, 497, 1024 }, { 7, 498, 1024 }, { 8, 499, 1024 }, { 7, 500, 1024 }, { 8, 501, 1024 }, { 8, 502, 1024 }, { 9, 503, 1024 }, + { 7, 504, 1024 }, { 8, 505, 1024 }, { 8, 506, 1024 }, { 9, 507, 1024 }, { 8, 508, 1024 }, { 9, 509, 1024 }, { 9, 510, 1024 }, { 10, 511, 1024 }, + { 2, 512, 1024 }, { 3, 513, 1024 }, { 3, 514, 1024 }, { 4, 515, 1024 }, { 3, 516, 1024 }, { 4, 517, 1024 }, { 4, 518, 1024 }, { 5, 519, 1024 }, + { 3, 520, 1024 }, { 4, 521, 1024 }, { 4, 522, 1024 }, { 5, 523, 1024 }, { 4, 524, 1024 }, { 5, 525, 1024 }, { 5, 526, 1024 }, { 6, 527, 1024 }, + { 3, 528, 1024 }, { 4, 529, 1024 }, { 4, 530, 1024 }, { 5, 531, 1024 }, { 4, 532, 1024 }, { 5, 533, 1024 }, { 5, 534, 1024 }, { 6, 535, 1024 }, + { 4, 536, 1024 }, { 5, 537, 1024 }, { 5, 538, 1024 }, { 6, 539, 1024 }, { 5, 540, 1024 }, { 6, 541, 1024 }, { 6, 542, 1024 }, { 7, 543, 1024 }, + { 3, 544, 1024 }, { 4, 545, 1024 }, { 4, 546, 1024 }, { 5, 547, 1024 }, { 4, 548, 1024 }, { 5, 549, 1024 }, { 5, 550, 1024 }, { 6, 551, 1024 }, + { 4, 552, 1024 }, { 5, 553, 1024 }, { 5, 554, 1024 }, { 6, 555, 1024 }, { 5, 556, 1024 }, { 6, 557, 1024 }, { 6, 558, 1024 }, { 7, 559, 1024 }, + { 4, 560, 1024 }, { 5, 561, 1024 }, { 5, 562, 1024 }, { 6, 563, 1024 }, { 5, 564, 1024 }, { 6, 565, 1024 }, { 6, 566, 1024 }, { 7, 567, 1024 }, + { 5, 568, 1024 }, { 6, 569, 1024 }, { 6, 570, 1024 }, { 7, 571, 1024 }, { 6, 572, 1024 }, { 7, 573, 1024 }, { 7, 574, 1024 }, { 8, 575, 1024 }, + { 3, 576, 1024 }, { 4, 577, 1024 }, { 4, 578, 1024 }, { 5, 579, 1024 }, { 4, 580, 1024 }, { 5, 581, 1024 }, { 5, 582, 1024 }, { 6, 583, 1024 }, + { 4, 584, 1024 }, { 5, 585, 1024 }, { 5, 586, 1024 }, { 6, 587, 1024 }, { 5, 588, 1024 }, { 6, 589, 1024 }, { 6, 590, 1024 }, { 7, 591, 1024 }, + { 4, 592, 1024 }, { 5, 593, 1024 }, { 5, 594, 1024 }, { 6, 595, 1024 }, { 5, 596, 1024 }, { 6, 597, 1024 }, { 6, 598, 1024 }, { 7, 599, 1024 }, + { 5, 600, 1024 }, { 6, 601, 1024 }, { 6, 602, 1024 }, { 7, 603, 1024 }, { 6, 604, 1024 }, { 7, 605, 1024 }, { 7, 606, 1024 }, { 8, 607, 1024 }, + { 4, 608, 1024 }, { 5, 609, 1024 }, { 5, 610, 1024 }, { 6, 611, 1024 }, { 5, 612, 1024 }, { 6, 613, 1024 }, { 6, 614, 1024 }, { 7, 615, 1024 }, + { 5, 616, 1024 }, { 6, 617, 1024 }, { 6, 618, 1024 }, { 7, 619, 1024 }, { 6, 620, 1024 }, { 7, 621, 1024 }, { 7, 622, 1024 }, { 8, 623, 1024 }, + { 5, 624, 1024 }, { 6, 625, 1024 }, { 6, 626, 1024 }, { 7, 627, 1024 }, { 6, 628, 1024 }, { 7, 629, 1024 }, { 7, 630, 1024 }, { 8, 631, 1024 }, + { 6, 632, 1024 }, { 7, 633, 1024 }, { 7, 634, 1024 }, { 8, 635, 1024 }, { 7, 636, 1024 }, { 8, 637, 1024 }, { 8, 638, 1024 }, { 9, 639, 1024 }, + { 3, 640, 1024 }, { 4, 641, 1024 }, { 4, 642, 1024 }, { 5, 643, 1024 }, { 4, 644, 1024 }, { 5, 645, 1024 }, { 5, 646, 1024 }, { 6, 647, 1024 }, + { 4, 648, 1024 }, { 5, 649, 1024 }, { 5, 650, 1024 }, { 6, 651, 1024 }, { 5, 652, 1024 }, { 6, 653, 1024 }, { 6, 654, 1024 }, { 7, 655, 1024 }, + { 4, 656, 1024 }, { 5, 657, 1024 }, { 5, 658, 1024 }, { 6, 659, 1024 }, { 5, 660, 1024 }, { 6, 661, 1024 }, { 6, 662, 1024 }, { 7, 663, 1024 }, + { 5, 664, 1024 }, { 6, 665, 1024 }, { 6, 666, 1024 }, { 7, 667, 1024 }, { 6, 668, 1024 }, { 7, 669, 1024 }, { 7, 670, 1024 }, { 8, 671, 1024 }, + { 4, 672, 1024 }, { 5, 673, 1024 }, { 5, 674, 1024 }, { 6, 675, 1024 }, { 5, 676, 1024 }, { 6, 677, 1024 }, { 6, 678, 1024 }, { 7, 679, 1024 }, + { 5, 680, 1024 }, { 6, 681, 1024 }, { 6, 682, 1024 }, { 7, 683, 1024 }, { 6, 684, 1024 }, { 7, 685, 1024 }, { 7, 686, 1024 }, { 8, 687, 1024 }, + { 5, 688, 1024 }, { 6, 689, 1024 }, { 6, 690, 1024 }, { 7, 691, 1024 }, { 6, 692, 1024 }, { 7, 693, 1024 }, { 7, 694, 1024 }, { 8, 695, 1024 }, + { 6, 696, 1024 }, { 7, 697, 1024 }, { 7, 698, 1024 }, { 8, 699, 1024 }, { 7, 700, 1024 }, { 8, 701, 1024 }, { 8, 702, 1024 }, { 9, 703, 1024 }, + { 4, 704, 1024 }, { 5, 705, 1024 }, { 5, 706, 1024 }, { 6, 707, 1024 }, { 5, 708, 1024 }, { 6, 709, 1024 }, { 6, 710, 1024 }, { 7, 711, 1024 }, + { 5, 712, 1024 }, { 6, 713, 1024 }, { 6, 714, 1024 }, { 7, 715, 1024 }, { 6, 716, 1024 }, { 7, 717, 1024 }, { 7, 718, 1024 }, { 8, 719, 1024 }, + { 5, 720, 1024 }, { 6, 721, 1024 }, { 6, 722, 1024 }, { 7, 723, 1024 }, { 6, 724, 1024 }, { 7, 725, 1024 }, { 7, 726, 1024 }, { 8, 727, 1024 }, + { 6, 728, 1024 }, { 7, 729, 1024 }, { 7, 730, 1024 }, { 8, 731, 1024 }, { 7, 732, 1024 }, { 8, 733, 1024 }, { 8, 734, 1024 }, { 9, 735, 1024 }, + { 5, 736, 1024 }, { 6, 737, 1024 }, { 6, 738, 1024 }, { 7, 739, 1024 }, { 6, 740, 1024 }, { 7, 741, 1024 }, { 7, 742, 1024 }, { 8, 743, 1024 }, + { 6, 744, 1024 }, { 7, 745, 1024 }, { 7, 746, 1024 }, { 8, 747, 1024 }, { 7, 748, 1024 }, { 8, 749, 1024 }, { 8, 750, 1024 }, { 9, 751, 1024 }, + { 6, 752, 1024 }, { 7, 753, 1024 }, { 7, 754, 1024 }, { 8, 755, 1024 }, { 7, 756, 1024 }, { 8, 757, 1024 }, { 8, 758, 1024 }, { 9, 759, 1024 }, + { 7, 760, 1024 }, { 8, 761, 1024 }, { 8, 762, 1024 }, { 9, 763, 1024 }, { 8, 764, 1024 }, { 9, 765, 1024 }, { 9, 766, 1024 }, { 10, 767, 1024 }, + { 3, 768, 1024 }, { 4, 769, 1024 }, { 4, 770, 1024 }, { 5, 771, 1024 }, { 4, 772, 1024 }, { 5, 773, 1024 }, { 5, 774, 1024 }, { 6, 775, 1024 }, + { 4, 776, 1024 }, { 5, 777, 1024 }, { 5, 778, 1024 }, { 6, 779, 1024 }, { 5, 780, 1024 }, { 6, 781, 1024 }, { 6, 782, 1024 }, { 7, 783, 1024 }, + { 4, 784, 1024 }, { 5, 785, 1024 }, { 5, 786, 1024 }, { 6, 787, 1024 }, { 5, 788, 1024 }, { 6, 789, 1024 }, { 6, 790, 1024 }, { 7, 791, 1024 }, + { 5, 792, 1024 }, { 6, 793, 1024 }, { 6, 794, 1024 }, { 7, 795, 1024 }, { 6, 796, 1024 }, { 7, 797, 1024 }, { 7, 798, 1024 }, { 8, 799, 1024 }, + { 4, 800, 1024 }, { 5, 801, 1024 }, { 5, 802, 1024 }, { 6, 803, 1024 }, { 5, 804, 1024 }, { 6, 805, 1024 }, { 6, 806, 1024 }, { 7, 807, 1024 }, + { 5, 808, 1024 }, { 6, 809, 1024 }, { 6, 810, 1024 }, { 7, 811, 1024 }, { 6, 812, 1024 }, { 7, 813, 1024 }, { 7, 814, 1024 }, { 8, 815, 1024 }, + { 5, 816, 1024 }, { 6, 817, 1024 }, { 6, 818, 1024 }, { 7, 819, 1024 }, { 6, 820, 1024 }, { 7, 821, 1024 }, { 7, 822, 1024 }, { 8, 823, 1024 }, + { 6, 824, 1024 }, { 7, 825, 1024 }, { 7, 826, 1024 }, { 8, 827, 1024 }, { 7, 828, 1024 }, { 8, 829, 1024 }, { 8, 830, 1024 }, { 9, 831, 1024 }, + { 4, 832, 1024 }, { 5, 833, 1024 }, { 5, 834, 1024 }, { 6, 835, 1024 }, { 5, 836, 1024 }, { 6, 837, 1024 }, { 6, 838, 1024 }, { 7, 839, 1024 }, + { 5, 840, 1024 }, { 6, 841, 1024 }, { 6, 842, 1024 }, { 7, 843, 1024 }, { 6, 844, 1024 }, { 7, 845, 1024 }, { 7, 846, 1024 }, { 8, 847, 1024 }, + { 5, 848, 1024 }, { 6, 849, 1024 }, { 6, 850, 1024 }, { 7, 851, 1024 }, { 6, 852, 1024 }, { 7, 853, 1024 }, { 7, 854, 1024 }, { 8, 855, 1024 }, + { 6, 856, 1024 }, { 7, 857, 1024 }, { 7, 858, 1024 }, { 8, 859, 1024 }, { 7, 860, 1024 }, { 8, 861, 1024 }, { 8, 862, 1024 }, { 9, 863, 1024 }, + { 5, 864, 1024 }, { 6, 865, 1024 }, { 6, 866, 1024 }, { 7, 867, 1024 }, { 6, 868, 1024 }, { 7, 869, 1024 }, { 7, 870, 1024 }, { 8, 871, 1024 }, + { 6, 872, 1024 }, { 7, 873, 1024 }, { 7, 874, 1024 }, { 8, 875, 1024 }, { 7, 876, 1024 }, { 8, 877, 1024 }, { 8, 878, 1024 }, { 9, 879, 1024 }, + { 6, 880, 1024 }, { 7, 881, 1024 }, { 7, 882, 1024 }, { 8, 883, 1024 }, { 7, 884, 1024 }, { 8, 885, 1024 }, { 8, 886, 1024 }, { 9, 887, 1024 }, + { 7, 888, 1024 }, { 8, 889, 1024 }, { 8, 890, 1024 }, { 9, 891, 1024 }, { 8, 892, 1024 }, { 9, 893, 1024 }, { 9, 894, 1024 }, { 10, 895, 1024 }, + { 4, 896, 1024 }, { 5, 897, 1024 }, { 5, 898, 1024 }, { 6, 899, 1024 }, { 5, 900, 1024 }, { 6, 901, 1024 }, { 6, 902, 1024 }, { 7, 903, 1024 }, + { 5, 904, 1024 }, { 6, 905, 1024 }, { 6, 906, 1024 }, { 7, 907, 1024 }, { 6, 908, 1024 }, { 7, 909, 1024 }, { 7, 910, 1024 }, { 8, 911, 1024 }, + { 5, 912, 1024 }, { 6, 913, 1024 }, { 6, 914, 1024 }, { 7, 915, 1024 }, { 6, 916, 1024 }, { 7, 917, 1024 }, { 7, 918, 1024 }, { 8, 919, 1024 }, + { 6, 920, 1024 }, { 7, 921, 1024 }, { 7, 922, 1024 }, { 8, 923, 1024 }, { 7, 924, 1024 }, { 8, 925, 1024 }, { 8, 926, 1024 }, { 9, 927, 1024 }, + { 5, 928, 1024 }, { 6, 929, 1024 }, { 6, 930, 1024 }, { 7, 931, 1024 }, { 6, 932, 1024 }, { 7, 933, 1024 }, { 7, 934, 1024 }, { 8, 935, 1024 }, + { 6, 936, 1024 }, { 7, 937, 1024 }, { 7, 938, 1024 }, { 8, 939, 1024 }, { 7, 940, 1024 }, { 8, 941, 1024 }, { 8, 942, 1024 }, { 9, 943, 1024 }, + { 6, 944, 1024 }, { 7, 945, 1024 }, { 7, 946, 1024 }, { 8, 947, 1024 }, { 7, 948, 1024 }, { 8, 949, 1024 }, { 8, 950, 1024 }, { 9, 951, 1024 }, + { 7, 952, 1024 }, { 8, 953, 1024 }, { 8, 954, 1024 }, { 9, 955, 1024 }, { 8, 956, 1024 }, { 9, 957, 1024 }, { 9, 958, 1024 }, { 10, 959, 1024 }, + { 5, 960, 1024 }, { 6, 961, 1024 }, { 6, 962, 1024 }, { 7, 963, 1024 }, { 6, 964, 1024 }, { 7, 965, 1024 }, { 7, 966, 1024 }, { 8, 967, 1024 }, + { 6, 968, 1024 }, { 7, 969, 1024 }, { 7, 970, 1024 }, { 8, 971, 1024 }, { 7, 972, 1024 }, { 8, 973, 1024 }, { 8, 974, 1024 }, { 9, 975, 1024 }, + { 6, 976, 1024 }, { 7, 977, 1024 }, { 7, 978, 1024 }, { 8, 979, 1024 }, { 7, 980, 1024 }, { 8, 981, 1024 }, { 8, 982, 1024 }, { 9, 983, 1024 }, + { 7, 984, 1024 }, { 8, 985, 1024 }, { 8, 986, 1024 }, { 9, 987, 1024 }, { 8, 988, 1024 }, { 9, 989, 1024 }, { 9, 990, 1024 }, { 10, 991, 1024 }, + { 6, 992, 1024 }, { 7, 993, 1024 }, { 7, 994, 1024 }, { 8, 995, 1024 }, { 7, 996, 1024 }, { 8, 997, 1024 }, { 8, 998, 1024 }, { 9, 999, 1024 }, + { 7, 1000, 1024 }, { 8, 1001, 1024 }, { 8, 1002, 1024 }, { 9, 1003, 1024 }, { 8, 1004, 1024 }, { 9, 1005, 1024 }, { 9, 1006, 1024 }, { 10, 1007, 1024 }, + { 7, 1008, 1024 }, { 8, 1009, 1024 }, { 8, 1010, 1024 }, { 9, 1011, 1024 }, { 8, 1012, 1024 }, { 9, 1013, 1024 }, { 9, 1014, 1024 }, { 10, 1015, 1024 }, + { 8, 1016, 1024 }, { 9, 1017, 1024 }, { 9, 1018, 1024 }, { 10, 1019, 1024 }, { 9, 1020, 1024 }, { 10, 1021, 1024 }, { 10, 1022, 1024 }, { 11, 1023, 1024 }, +#if FP_LUT > 11 + { 1, 0, 0 }, { 2, 1, 2048 }, { 2, 2, 2048 }, { 3, 3, 2048 }, { 2, 4, 2048 }, { 3, 5, 2048 }, { 3, 6, 2048 }, { 4, 7, 2048 }, + { 2, 8, 2048 }, { 3, 9, 2048 }, { 3, 10, 2048 }, { 4, 11, 2048 }, { 3, 12, 2048 }, { 4, 13, 2048 }, { 4, 14, 2048 }, { 5, 15, 2048 }, + { 2, 16, 2048 }, { 3, 17, 2048 }, { 3, 18, 2048 }, { 4, 19, 2048 }, { 3, 20, 2048 }, { 4, 21, 2048 }, { 4, 22, 2048 }, { 5, 23, 2048 }, + { 3, 24, 2048 }, { 4, 25, 2048 }, { 4, 26, 2048 }, { 5, 27, 2048 }, { 4, 28, 2048 }, { 5, 29, 2048 }, { 5, 30, 2048 }, { 6, 31, 2048 }, + { 2, 32, 2048 }, { 3, 33, 2048 }, { 3, 34, 2048 }, { 4, 35, 2048 }, { 3, 36, 2048 }, { 4, 37, 2048 }, { 4, 38, 2048 }, { 5, 39, 2048 }, + { 3, 40, 2048 }, { 4, 41, 2048 }, { 4, 42, 2048 }, { 5, 43, 2048 }, { 4, 44, 2048 }, { 5, 45, 2048 }, { 5, 46, 2048 }, { 6, 47, 2048 }, + { 3, 48, 2048 }, { 4, 49, 2048 }, { 4, 50, 2048 }, { 5, 51, 2048 }, { 4, 52, 2048 }, { 5, 53, 2048 }, { 5, 54, 2048 }, { 6, 55, 2048 }, + { 4, 56, 2048 }, { 5, 57, 2048 }, { 5, 58, 2048 }, { 6, 59, 2048 }, { 5, 60, 2048 }, { 6, 61, 2048 }, { 6, 62, 2048 }, { 7, 63, 2048 }, + { 2, 64, 2048 }, { 3, 65, 2048 }, { 3, 66, 2048 }, { 4, 67, 2048 }, { 3, 68, 2048 }, { 4, 69, 2048 }, { 4, 70, 2048 }, { 5, 71, 2048 }, + { 3, 72, 2048 }, { 4, 73, 2048 }, { 4, 74, 2048 }, { 5, 75, 2048 }, { 4, 76, 2048 }, { 5, 77, 2048 }, { 5, 78, 2048 }, { 6, 79, 2048 }, + { 3, 80, 2048 }, { 4, 81, 2048 }, { 4, 82, 2048 }, { 5, 83, 2048 }, { 4, 84, 2048 }, { 5, 85, 2048 }, { 5, 86, 2048 }, { 6, 87, 2048 }, + { 4, 88, 2048 }, { 5, 89, 2048 }, { 5, 90, 2048 }, { 6, 91, 2048 }, { 5, 92, 2048 }, { 6, 93, 2048 }, { 6, 94, 2048 }, { 7, 95, 2048 }, + { 3, 96, 2048 }, { 4, 97, 2048 }, { 4, 98, 2048 }, { 5, 99, 2048 }, { 4, 100, 2048 }, { 5, 101, 2048 }, { 5, 102, 2048 }, { 6, 103, 2048 }, + { 4, 104, 2048 }, { 5, 105, 2048 }, { 5, 106, 2048 }, { 6, 107, 2048 }, { 5, 108, 2048 }, { 6, 109, 2048 }, { 6, 110, 2048 }, { 7, 111, 2048 }, + { 4, 112, 2048 }, { 5, 113, 2048 }, { 5, 114, 2048 }, { 6, 115, 2048 }, { 5, 116, 2048 }, { 6, 117, 2048 }, { 6, 118, 2048 }, { 7, 119, 2048 }, + { 5, 120, 2048 }, { 6, 121, 2048 }, { 6, 122, 2048 }, { 7, 123, 2048 }, { 6, 124, 2048 }, { 7, 125, 2048 }, { 7, 126, 2048 }, { 8, 127, 2048 }, + { 2, 128, 2048 }, { 3, 129, 2048 }, { 3, 130, 2048 }, { 4, 131, 2048 }, { 3, 132, 2048 }, { 4, 133, 2048 }, { 4, 134, 2048 }, { 5, 135, 2048 }, + { 3, 136, 2048 }, { 4, 137, 2048 }, { 4, 138, 2048 }, { 5, 139, 2048 }, { 4, 140, 2048 }, { 5, 141, 2048 }, { 5, 142, 2048 }, { 6, 143, 2048 }, + { 3, 144, 2048 }, { 4, 145, 2048 }, { 4, 146, 2048 }, { 5, 147, 2048 }, { 4, 148, 2048 }, { 5, 149, 2048 }, { 5, 150, 2048 }, { 6, 151, 2048 }, + { 4, 152, 2048 }, { 5, 153, 2048 }, { 5, 154, 2048 }, { 6, 155, 2048 }, { 5, 156, 2048 }, { 6, 157, 2048 }, { 6, 158, 2048 }, { 7, 159, 2048 }, + { 3, 160, 2048 }, { 4, 161, 2048 }, { 4, 162, 2048 }, { 5, 163, 2048 }, { 4, 164, 2048 }, { 5, 165, 2048 }, { 5, 166, 2048 }, { 6, 167, 2048 }, + { 4, 168, 2048 }, { 5, 169, 2048 }, { 5, 170, 2048 }, { 6, 171, 2048 }, { 5, 172, 2048 }, { 6, 173, 2048 }, { 6, 174, 2048 }, { 7, 175, 2048 }, + { 4, 176, 2048 }, { 5, 177, 2048 }, { 5, 178, 2048 }, { 6, 179, 2048 }, { 5, 180, 2048 }, { 6, 181, 2048 }, { 6, 182, 2048 }, { 7, 183, 2048 }, + { 5, 184, 2048 }, { 6, 185, 2048 }, { 6, 186, 2048 }, { 7, 187, 2048 }, { 6, 188, 2048 }, { 7, 189, 2048 }, { 7, 190, 2048 }, { 8, 191, 2048 }, + { 3, 192, 2048 }, { 4, 193, 2048 }, { 4, 194, 2048 }, { 5, 195, 2048 }, { 4, 196, 2048 }, { 5, 197, 2048 }, { 5, 198, 2048 }, { 6, 199, 2048 }, + { 4, 200, 2048 }, { 5, 201, 2048 }, { 5, 202, 2048 }, { 6, 203, 2048 }, { 5, 204, 2048 }, { 6, 205, 2048 }, { 6, 206, 2048 }, { 7, 207, 2048 }, + { 4, 208, 2048 }, { 5, 209, 2048 }, { 5, 210, 2048 }, { 6, 211, 2048 }, { 5, 212, 2048 }, { 6, 213, 2048 }, { 6, 214, 2048 }, { 7, 215, 2048 }, + { 5, 216, 2048 }, { 6, 217, 2048 }, { 6, 218, 2048 }, { 7, 219, 2048 }, { 6, 220, 2048 }, { 7, 221, 2048 }, { 7, 222, 2048 }, { 8, 223, 2048 }, + { 4, 224, 2048 }, { 5, 225, 2048 }, { 5, 226, 2048 }, { 6, 227, 2048 }, { 5, 228, 2048 }, { 6, 229, 2048 }, { 6, 230, 2048 }, { 7, 231, 2048 }, + { 5, 232, 2048 }, { 6, 233, 2048 }, { 6, 234, 2048 }, { 7, 235, 2048 }, { 6, 236, 2048 }, { 7, 237, 2048 }, { 7, 238, 2048 }, { 8, 239, 2048 }, + { 5, 240, 2048 }, { 6, 241, 2048 }, { 6, 242, 2048 }, { 7, 243, 2048 }, { 6, 244, 2048 }, { 7, 245, 2048 }, { 7, 246, 2048 }, { 8, 247, 2048 }, + { 6, 248, 2048 }, { 7, 249, 2048 }, { 7, 250, 2048 }, { 8, 251, 2048 }, { 7, 252, 2048 }, { 8, 253, 2048 }, { 8, 254, 2048 }, { 9, 255, 2048 }, + { 2, 256, 2048 }, { 3, 257, 2048 }, { 3, 258, 2048 }, { 4, 259, 2048 }, { 3, 260, 2048 }, { 4, 261, 2048 }, { 4, 262, 2048 }, { 5, 263, 2048 }, + { 3, 264, 2048 }, { 4, 265, 2048 }, { 4, 266, 2048 }, { 5, 267, 2048 }, { 4, 268, 2048 }, { 5, 269, 2048 }, { 5, 270, 2048 }, { 6, 271, 2048 }, + { 3, 272, 2048 }, { 4, 273, 2048 }, { 4, 274, 2048 }, { 5, 275, 2048 }, { 4, 276, 2048 }, { 5, 277, 2048 }, { 5, 278, 2048 }, { 6, 279, 2048 }, + { 4, 280, 2048 }, { 5, 281, 2048 }, { 5, 282, 2048 }, { 6, 283, 2048 }, { 5, 284, 2048 }, { 6, 285, 2048 }, { 6, 286, 2048 }, { 7, 287, 2048 }, + { 3, 288, 2048 }, { 4, 289, 2048 }, { 4, 290, 2048 }, { 5, 291, 2048 }, { 4, 292, 2048 }, { 5, 293, 2048 }, { 5, 294, 2048 }, { 6, 295, 2048 }, + { 4, 296, 2048 }, { 5, 297, 2048 }, { 5, 298, 2048 }, { 6, 299, 2048 }, { 5, 300, 2048 }, { 6, 301, 2048 }, { 6, 302, 2048 }, { 7, 303, 2048 }, + { 4, 304, 2048 }, { 5, 305, 2048 }, { 5, 306, 2048 }, { 6, 307, 2048 }, { 5, 308, 2048 }, { 6, 309, 2048 }, { 6, 310, 2048 }, { 7, 311, 2048 }, + { 5, 312, 2048 }, { 6, 313, 2048 }, { 6, 314, 2048 }, { 7, 315, 2048 }, { 6, 316, 2048 }, { 7, 317, 2048 }, { 7, 318, 2048 }, { 8, 319, 2048 }, + { 3, 320, 2048 }, { 4, 321, 2048 }, { 4, 322, 2048 }, { 5, 323, 2048 }, { 4, 324, 2048 }, { 5, 325, 2048 }, { 5, 326, 2048 }, { 6, 327, 2048 }, + { 4, 328, 2048 }, { 5, 329, 2048 }, { 5, 330, 2048 }, { 6, 331, 2048 }, { 5, 332, 2048 }, { 6, 333, 2048 }, { 6, 334, 2048 }, { 7, 335, 2048 }, + { 4, 336, 2048 }, { 5, 337, 2048 }, { 5, 338, 2048 }, { 6, 339, 2048 }, { 5, 340, 2048 }, { 6, 341, 2048 }, { 6, 342, 2048 }, { 7, 343, 2048 }, + { 5, 344, 2048 }, { 6, 345, 2048 }, { 6, 346, 2048 }, { 7, 347, 2048 }, { 6, 348, 2048 }, { 7, 349, 2048 }, { 7, 350, 2048 }, { 8, 351, 2048 }, + { 4, 352, 2048 }, { 5, 353, 2048 }, { 5, 354, 2048 }, { 6, 355, 2048 }, { 5, 356, 2048 }, { 6, 357, 2048 }, { 6, 358, 2048 }, { 7, 359, 2048 }, + { 5, 360, 2048 }, { 6, 361, 2048 }, { 6, 362, 2048 }, { 7, 363, 2048 }, { 6, 364, 2048 }, { 7, 365, 2048 }, { 7, 366, 2048 }, { 8, 367, 2048 }, + { 5, 368, 2048 }, { 6, 369, 2048 }, { 6, 370, 2048 }, { 7, 371, 2048 }, { 6, 372, 2048 }, { 7, 373, 2048 }, { 7, 374, 2048 }, { 8, 375, 2048 }, + { 6, 376, 2048 }, { 7, 377, 2048 }, { 7, 378, 2048 }, { 8, 379, 2048 }, { 7, 380, 2048 }, { 8, 381, 2048 }, { 8, 382, 2048 }, { 9, 383, 2048 }, + { 3, 384, 2048 }, { 4, 385, 2048 }, { 4, 386, 2048 }, { 5, 387, 2048 }, { 4, 388, 2048 }, { 5, 389, 2048 }, { 5, 390, 2048 }, { 6, 391, 2048 }, + { 4, 392, 2048 }, { 5, 393, 2048 }, { 5, 394, 2048 }, { 6, 395, 2048 }, { 5, 396, 2048 }, { 6, 397, 2048 }, { 6, 398, 2048 }, { 7, 399, 2048 }, + { 4, 400, 2048 }, { 5, 401, 2048 }, { 5, 402, 2048 }, { 6, 403, 2048 }, { 5, 404, 2048 }, { 6, 405, 2048 }, { 6, 406, 2048 }, { 7, 407, 2048 }, + { 5, 408, 2048 }, { 6, 409, 2048 }, { 6, 410, 2048 }, { 7, 411, 2048 }, { 6, 412, 2048 }, { 7, 413, 2048 }, { 7, 414, 2048 }, { 8, 415, 2048 }, + { 4, 416, 2048 }, { 5, 417, 2048 }, { 5, 418, 2048 }, { 6, 419, 2048 }, { 5, 420, 2048 }, { 6, 421, 2048 }, { 6, 422, 2048 }, { 7, 423, 2048 }, + { 5, 424, 2048 }, { 6, 425, 2048 }, { 6, 426, 2048 }, { 7, 427, 2048 }, { 6, 428, 2048 }, { 7, 429, 2048 }, { 7, 430, 2048 }, { 8, 431, 2048 }, + { 5, 432, 2048 }, { 6, 433, 2048 }, { 6, 434, 2048 }, { 7, 435, 2048 }, { 6, 436, 2048 }, { 7, 437, 2048 }, { 7, 438, 2048 }, { 8, 439, 2048 }, + { 6, 440, 2048 }, { 7, 441, 2048 }, { 7, 442, 2048 }, { 8, 443, 2048 }, { 7, 444, 2048 }, { 8, 445, 2048 }, { 8, 446, 2048 }, { 9, 447, 2048 }, + { 4, 448, 2048 }, { 5, 449, 2048 }, { 5, 450, 2048 }, { 6, 451, 2048 }, { 5, 452, 2048 }, { 6, 453, 2048 }, { 6, 454, 2048 }, { 7, 455, 2048 }, + { 5, 456, 2048 }, { 6, 457, 2048 }, { 6, 458, 2048 }, { 7, 459, 2048 }, { 6, 460, 2048 }, { 7, 461, 2048 }, { 7, 462, 2048 }, { 8, 463, 2048 }, + { 5, 464, 2048 }, { 6, 465, 2048 }, { 6, 466, 2048 }, { 7, 467, 2048 }, { 6, 468, 2048 }, { 7, 469, 2048 }, { 7, 470, 2048 }, { 8, 471, 2048 }, + { 6, 472, 2048 }, { 7, 473, 2048 }, { 7, 474, 2048 }, { 8, 475, 2048 }, { 7, 476, 2048 }, { 8, 477, 2048 }, { 8, 478, 2048 }, { 9, 479, 2048 }, + { 5, 480, 2048 }, { 6, 481, 2048 }, { 6, 482, 2048 }, { 7, 483, 2048 }, { 6, 484, 2048 }, { 7, 485, 2048 }, { 7, 486, 2048 }, { 8, 487, 2048 }, + { 6, 488, 2048 }, { 7, 489, 2048 }, { 7, 490, 2048 }, { 8, 491, 2048 }, { 7, 492, 2048 }, { 8, 493, 2048 }, { 8, 494, 2048 }, { 9, 495, 2048 }, + { 6, 496, 2048 }, { 7, 497, 2048 }, { 7, 498, 2048 }, { 8, 499, 2048 }, { 7, 500, 2048 }, { 8, 501, 2048 }, { 8, 502, 2048 }, { 9, 503, 2048 }, + { 7, 504, 2048 }, { 8, 505, 2048 }, { 8, 506, 2048 }, { 9, 507, 2048 }, { 8, 508, 2048 }, { 9, 509, 2048 }, { 9, 510, 2048 }, { 10, 511, 2048 }, + { 2, 512, 2048 }, { 3, 513, 2048 }, { 3, 514, 2048 }, { 4, 515, 2048 }, { 3, 516, 2048 }, { 4, 517, 2048 }, { 4, 518, 2048 }, { 5, 519, 2048 }, + { 3, 520, 2048 }, { 4, 521, 2048 }, { 4, 522, 2048 }, { 5, 523, 2048 }, { 4, 524, 2048 }, { 5, 525, 2048 }, { 5, 526, 2048 }, { 6, 527, 2048 }, + { 3, 528, 2048 }, { 4, 529, 2048 }, { 4, 530, 2048 }, { 5, 531, 2048 }, { 4, 532, 2048 }, { 5, 533, 2048 }, { 5, 534, 2048 }, { 6, 535, 2048 }, + { 4, 536, 2048 }, { 5, 537, 2048 }, { 5, 538, 2048 }, { 6, 539, 2048 }, { 5, 540, 2048 }, { 6, 541, 2048 }, { 6, 542, 2048 }, { 7, 543, 2048 }, + { 3, 544, 2048 }, { 4, 545, 2048 }, { 4, 546, 2048 }, { 5, 547, 2048 }, { 4, 548, 2048 }, { 5, 549, 2048 }, { 5, 550, 2048 }, { 6, 551, 2048 }, + { 4, 552, 2048 }, { 5, 553, 2048 }, { 5, 554, 2048 }, { 6, 555, 2048 }, { 5, 556, 2048 }, { 6, 557, 2048 }, { 6, 558, 2048 }, { 7, 559, 2048 }, + { 4, 560, 2048 }, { 5, 561, 2048 }, { 5, 562, 2048 }, { 6, 563, 2048 }, { 5, 564, 2048 }, { 6, 565, 2048 }, { 6, 566, 2048 }, { 7, 567, 2048 }, + { 5, 568, 2048 }, { 6, 569, 2048 }, { 6, 570, 2048 }, { 7, 571, 2048 }, { 6, 572, 2048 }, { 7, 573, 2048 }, { 7, 574, 2048 }, { 8, 575, 2048 }, + { 3, 576, 2048 }, { 4, 577, 2048 }, { 4, 578, 2048 }, { 5, 579, 2048 }, { 4, 580, 2048 }, { 5, 581, 2048 }, { 5, 582, 2048 }, { 6, 583, 2048 }, + { 4, 584, 2048 }, { 5, 585, 2048 }, { 5, 586, 2048 }, { 6, 587, 2048 }, { 5, 588, 2048 }, { 6, 589, 2048 }, { 6, 590, 2048 }, { 7, 591, 2048 }, + { 4, 592, 2048 }, { 5, 593, 2048 }, { 5, 594, 2048 }, { 6, 595, 2048 }, { 5, 596, 2048 }, { 6, 597, 2048 }, { 6, 598, 2048 }, { 7, 599, 2048 }, + { 5, 600, 2048 }, { 6, 601, 2048 }, { 6, 602, 2048 }, { 7, 603, 2048 }, { 6, 604, 2048 }, { 7, 605, 2048 }, { 7, 606, 2048 }, { 8, 607, 2048 }, + { 4, 608, 2048 }, { 5, 609, 2048 }, { 5, 610, 2048 }, { 6, 611, 2048 }, { 5, 612, 2048 }, { 6, 613, 2048 }, { 6, 614, 2048 }, { 7, 615, 2048 }, + { 5, 616, 2048 }, { 6, 617, 2048 }, { 6, 618, 2048 }, { 7, 619, 2048 }, { 6, 620, 2048 }, { 7, 621, 2048 }, { 7, 622, 2048 }, { 8, 623, 2048 }, + { 5, 624, 2048 }, { 6, 625, 2048 }, { 6, 626, 2048 }, { 7, 627, 2048 }, { 6, 628, 2048 }, { 7, 629, 2048 }, { 7, 630, 2048 }, { 8, 631, 2048 }, + { 6, 632, 2048 }, { 7, 633, 2048 }, { 7, 634, 2048 }, { 8, 635, 2048 }, { 7, 636, 2048 }, { 8, 637, 2048 }, { 8, 638, 2048 }, { 9, 639, 2048 }, + { 3, 640, 2048 }, { 4, 641, 2048 }, { 4, 642, 2048 }, { 5, 643, 2048 }, { 4, 644, 2048 }, { 5, 645, 2048 }, { 5, 646, 2048 }, { 6, 647, 2048 }, + { 4, 648, 2048 }, { 5, 649, 2048 }, { 5, 650, 2048 }, { 6, 651, 2048 }, { 5, 652, 2048 }, { 6, 653, 2048 }, { 6, 654, 2048 }, { 7, 655, 2048 }, + { 4, 656, 2048 }, { 5, 657, 2048 }, { 5, 658, 2048 }, { 6, 659, 2048 }, { 5, 660, 2048 }, { 6, 661, 2048 }, { 6, 662, 2048 }, { 7, 663, 2048 }, + { 5, 664, 2048 }, { 6, 665, 2048 }, { 6, 666, 2048 }, { 7, 667, 2048 }, { 6, 668, 2048 }, { 7, 669, 2048 }, { 7, 670, 2048 }, { 8, 671, 2048 }, + { 4, 672, 2048 }, { 5, 673, 2048 }, { 5, 674, 2048 }, { 6, 675, 2048 }, { 5, 676, 2048 }, { 6, 677, 2048 }, { 6, 678, 2048 }, { 7, 679, 2048 }, + { 5, 680, 2048 }, { 6, 681, 2048 }, { 6, 682, 2048 }, { 7, 683, 2048 }, { 6, 684, 2048 }, { 7, 685, 2048 }, { 7, 686, 2048 }, { 8, 687, 2048 }, + { 5, 688, 2048 }, { 6, 689, 2048 }, { 6, 690, 2048 }, { 7, 691, 2048 }, { 6, 692, 2048 }, { 7, 693, 2048 }, { 7, 694, 2048 }, { 8, 695, 2048 }, + { 6, 696, 2048 }, { 7, 697, 2048 }, { 7, 698, 2048 }, { 8, 699, 2048 }, { 7, 700, 2048 }, { 8, 701, 2048 }, { 8, 702, 2048 }, { 9, 703, 2048 }, + { 4, 704, 2048 }, { 5, 705, 2048 }, { 5, 706, 2048 }, { 6, 707, 2048 }, { 5, 708, 2048 }, { 6, 709, 2048 }, { 6, 710, 2048 }, { 7, 711, 2048 }, + { 5, 712, 2048 }, { 6, 713, 2048 }, { 6, 714, 2048 }, { 7, 715, 2048 }, { 6, 716, 2048 }, { 7, 717, 2048 }, { 7, 718, 2048 }, { 8, 719, 2048 }, + { 5, 720, 2048 }, { 6, 721, 2048 }, { 6, 722, 2048 }, { 7, 723, 2048 }, { 6, 724, 2048 }, { 7, 725, 2048 }, { 7, 726, 2048 }, { 8, 727, 2048 }, + { 6, 728, 2048 }, { 7, 729, 2048 }, { 7, 730, 2048 }, { 8, 731, 2048 }, { 7, 732, 2048 }, { 8, 733, 2048 }, { 8, 734, 2048 }, { 9, 735, 2048 }, + { 5, 736, 2048 }, { 6, 737, 2048 }, { 6, 738, 2048 }, { 7, 739, 2048 }, { 6, 740, 2048 }, { 7, 741, 2048 }, { 7, 742, 2048 }, { 8, 743, 2048 }, + { 6, 744, 2048 }, { 7, 745, 2048 }, { 7, 746, 2048 }, { 8, 747, 2048 }, { 7, 748, 2048 }, { 8, 749, 2048 }, { 8, 750, 2048 }, { 9, 751, 2048 }, + { 6, 752, 2048 }, { 7, 753, 2048 }, { 7, 754, 2048 }, { 8, 755, 2048 }, { 7, 756, 2048 }, { 8, 757, 2048 }, { 8, 758, 2048 }, { 9, 759, 2048 }, + { 7, 760, 2048 }, { 8, 761, 2048 }, { 8, 762, 2048 }, { 9, 763, 2048 }, { 8, 764, 2048 }, { 9, 765, 2048 }, { 9, 766, 2048 }, { 10, 767, 2048 }, + { 3, 768, 2048 }, { 4, 769, 2048 }, { 4, 770, 2048 }, { 5, 771, 2048 }, { 4, 772, 2048 }, { 5, 773, 2048 }, { 5, 774, 2048 }, { 6, 775, 2048 }, + { 4, 776, 2048 }, { 5, 777, 2048 }, { 5, 778, 2048 }, { 6, 779, 2048 }, { 5, 780, 2048 }, { 6, 781, 2048 }, { 6, 782, 2048 }, { 7, 783, 2048 }, + { 4, 784, 2048 }, { 5, 785, 2048 }, { 5, 786, 2048 }, { 6, 787, 2048 }, { 5, 788, 2048 }, { 6, 789, 2048 }, { 6, 790, 2048 }, { 7, 791, 2048 }, + { 5, 792, 2048 }, { 6, 793, 2048 }, { 6, 794, 2048 }, { 7, 795, 2048 }, { 6, 796, 2048 }, { 7, 797, 2048 }, { 7, 798, 2048 }, { 8, 799, 2048 }, + { 4, 800, 2048 }, { 5, 801, 2048 }, { 5, 802, 2048 }, { 6, 803, 2048 }, { 5, 804, 2048 }, { 6, 805, 2048 }, { 6, 806, 2048 }, { 7, 807, 2048 }, + { 5, 808, 2048 }, { 6, 809, 2048 }, { 6, 810, 2048 }, { 7, 811, 2048 }, { 6, 812, 2048 }, { 7, 813, 2048 }, { 7, 814, 2048 }, { 8, 815, 2048 }, + { 5, 816, 2048 }, { 6, 817, 2048 }, { 6, 818, 2048 }, { 7, 819, 2048 }, { 6, 820, 2048 }, { 7, 821, 2048 }, { 7, 822, 2048 }, { 8, 823, 2048 }, + { 6, 824, 2048 }, { 7, 825, 2048 }, { 7, 826, 2048 }, { 8, 827, 2048 }, { 7, 828, 2048 }, { 8, 829, 2048 }, { 8, 830, 2048 }, { 9, 831, 2048 }, + { 4, 832, 2048 }, { 5, 833, 2048 }, { 5, 834, 2048 }, { 6, 835, 2048 }, { 5, 836, 2048 }, { 6, 837, 2048 }, { 6, 838, 2048 }, { 7, 839, 2048 }, + { 5, 840, 2048 }, { 6, 841, 2048 }, { 6, 842, 2048 }, { 7, 843, 2048 }, { 6, 844, 2048 }, { 7, 845, 2048 }, { 7, 846, 2048 }, { 8, 847, 2048 }, + { 5, 848, 2048 }, { 6, 849, 2048 }, { 6, 850, 2048 }, { 7, 851, 2048 }, { 6, 852, 2048 }, { 7, 853, 2048 }, { 7, 854, 2048 }, { 8, 855, 2048 }, + { 6, 856, 2048 }, { 7, 857, 2048 }, { 7, 858, 2048 }, { 8, 859, 2048 }, { 7, 860, 2048 }, { 8, 861, 2048 }, { 8, 862, 2048 }, { 9, 863, 2048 }, + { 5, 864, 2048 }, { 6, 865, 2048 }, { 6, 866, 2048 }, { 7, 867, 2048 }, { 6, 868, 2048 }, { 7, 869, 2048 }, { 7, 870, 2048 }, { 8, 871, 2048 }, + { 6, 872, 2048 }, { 7, 873, 2048 }, { 7, 874, 2048 }, { 8, 875, 2048 }, { 7, 876, 2048 }, { 8, 877, 2048 }, { 8, 878, 2048 }, { 9, 879, 2048 }, + { 6, 880, 2048 }, { 7, 881, 2048 }, { 7, 882, 2048 }, { 8, 883, 2048 }, { 7, 884, 2048 }, { 8, 885, 2048 }, { 8, 886, 2048 }, { 9, 887, 2048 }, + { 7, 888, 2048 }, { 8, 889, 2048 }, { 8, 890, 2048 }, { 9, 891, 2048 }, { 8, 892, 2048 }, { 9, 893, 2048 }, { 9, 894, 2048 }, { 10, 895, 2048 }, + { 4, 896, 2048 }, { 5, 897, 2048 }, { 5, 898, 2048 }, { 6, 899, 2048 }, { 5, 900, 2048 }, { 6, 901, 2048 }, { 6, 902, 2048 }, { 7, 903, 2048 }, + { 5, 904, 2048 }, { 6, 905, 2048 }, { 6, 906, 2048 }, { 7, 907, 2048 }, { 6, 908, 2048 }, { 7, 909, 2048 }, { 7, 910, 2048 }, { 8, 911, 2048 }, + { 5, 912, 2048 }, { 6, 913, 2048 }, { 6, 914, 2048 }, { 7, 915, 2048 }, { 6, 916, 2048 }, { 7, 917, 2048 }, { 7, 918, 2048 }, { 8, 919, 2048 }, + { 6, 920, 2048 }, { 7, 921, 2048 }, { 7, 922, 2048 }, { 8, 923, 2048 }, { 7, 924, 2048 }, { 8, 925, 2048 }, { 8, 926, 2048 }, { 9, 927, 2048 }, + { 5, 928, 2048 }, { 6, 929, 2048 }, { 6, 930, 2048 }, { 7, 931, 2048 }, { 6, 932, 2048 }, { 7, 933, 2048 }, { 7, 934, 2048 }, { 8, 935, 2048 }, + { 6, 936, 2048 }, { 7, 937, 2048 }, { 7, 938, 2048 }, { 8, 939, 2048 }, { 7, 940, 2048 }, { 8, 941, 2048 }, { 8, 942, 2048 }, { 9, 943, 2048 }, + { 6, 944, 2048 }, { 7, 945, 2048 }, { 7, 946, 2048 }, { 8, 947, 2048 }, { 7, 948, 2048 }, { 8, 949, 2048 }, { 8, 950, 2048 }, { 9, 951, 2048 }, + { 7, 952, 2048 }, { 8, 953, 2048 }, { 8, 954, 2048 }, { 9, 955, 2048 }, { 8, 956, 2048 }, { 9, 957, 2048 }, { 9, 958, 2048 }, { 10, 959, 2048 }, + { 5, 960, 2048 }, { 6, 961, 2048 }, { 6, 962, 2048 }, { 7, 963, 2048 }, { 6, 964, 2048 }, { 7, 965, 2048 }, { 7, 966, 2048 }, { 8, 967, 2048 }, + { 6, 968, 2048 }, { 7, 969, 2048 }, { 7, 970, 2048 }, { 8, 971, 2048 }, { 7, 972, 2048 }, { 8, 973, 2048 }, { 8, 974, 2048 }, { 9, 975, 2048 }, + { 6, 976, 2048 }, { 7, 977, 2048 }, { 7, 978, 2048 }, { 8, 979, 2048 }, { 7, 980, 2048 }, { 8, 981, 2048 }, { 8, 982, 2048 }, { 9, 983, 2048 }, + { 7, 984, 2048 }, { 8, 985, 2048 }, { 8, 986, 2048 }, { 9, 987, 2048 }, { 8, 988, 2048 }, { 9, 989, 2048 }, { 9, 990, 2048 }, { 10, 991, 2048 }, + { 6, 992, 2048 }, { 7, 993, 2048 }, { 7, 994, 2048 }, { 8, 995, 2048 }, { 7, 996, 2048 }, { 8, 997, 2048 }, { 8, 998, 2048 }, { 9, 999, 2048 }, + { 7, 1000, 2048 }, { 8, 1001, 2048 }, { 8, 1002, 2048 }, { 9, 1003, 2048 }, { 8, 1004, 2048 }, { 9, 1005, 2048 }, { 9, 1006, 2048 }, { 10, 1007, 2048 }, + { 7, 1008, 2048 }, { 8, 1009, 2048 }, { 8, 1010, 2048 }, { 9, 1011, 2048 }, { 8, 1012, 2048 }, { 9, 1013, 2048 }, { 9, 1014, 2048 }, { 10, 1015, 2048 }, + { 8, 1016, 2048 }, { 9, 1017, 2048 }, { 9, 1018, 2048 }, { 10, 1019, 2048 }, { 9, 1020, 2048 }, { 10, 1021, 2048 }, { 10, 1022, 2048 }, { 11, 1023, 2048 }, + { 2, 1024, 2048 }, { 3, 1025, 2048 }, { 3, 1026, 2048 }, { 4, 1027, 2048 }, { 3, 1028, 2048 }, { 4, 1029, 2048 }, { 4, 1030, 2048 }, { 5, 1031, 2048 }, + { 3, 1032, 2048 }, { 4, 1033, 2048 }, { 4, 1034, 2048 }, { 5, 1035, 2048 }, { 4, 1036, 2048 }, { 5, 1037, 2048 }, { 5, 1038, 2048 }, { 6, 1039, 2048 }, + { 3, 1040, 2048 }, { 4, 1041, 2048 }, { 4, 1042, 2048 }, { 5, 1043, 2048 }, { 4, 1044, 2048 }, { 5, 1045, 2048 }, { 5, 1046, 2048 }, { 6, 1047, 2048 }, + { 4, 1048, 2048 }, { 5, 1049, 2048 }, { 5, 1050, 2048 }, { 6, 1051, 2048 }, { 5, 1052, 2048 }, { 6, 1053, 2048 }, { 6, 1054, 2048 }, { 7, 1055, 2048 }, + { 3, 1056, 2048 }, { 4, 1057, 2048 }, { 4, 1058, 2048 }, { 5, 1059, 2048 }, { 4, 1060, 2048 }, { 5, 1061, 2048 }, { 5, 1062, 2048 }, { 6, 1063, 2048 }, + { 4, 1064, 2048 }, { 5, 1065, 2048 }, { 5, 1066, 2048 }, { 6, 1067, 2048 }, { 5, 1068, 2048 }, { 6, 1069, 2048 }, { 6, 1070, 2048 }, { 7, 1071, 2048 }, + { 4, 1072, 2048 }, { 5, 1073, 2048 }, { 5, 1074, 2048 }, { 6, 1075, 2048 }, { 5, 1076, 2048 }, { 6, 1077, 2048 }, { 6, 1078, 2048 }, { 7, 1079, 2048 }, + { 5, 1080, 2048 }, { 6, 1081, 2048 }, { 6, 1082, 2048 }, { 7, 1083, 2048 }, { 6, 1084, 2048 }, { 7, 1085, 2048 }, { 7, 1086, 2048 }, { 8, 1087, 2048 }, + { 3, 1088, 2048 }, { 4, 1089, 2048 }, { 4, 1090, 2048 }, { 5, 1091, 2048 }, { 4, 1092, 2048 }, { 5, 1093, 2048 }, { 5, 1094, 2048 }, { 6, 1095, 2048 }, + { 4, 1096, 2048 }, { 5, 1097, 2048 }, { 5, 1098, 2048 }, { 6, 1099, 2048 }, { 5, 1100, 2048 }, { 6, 1101, 2048 }, { 6, 1102, 2048 }, { 7, 1103, 2048 }, + { 4, 1104, 2048 }, { 5, 1105, 2048 }, { 5, 1106, 2048 }, { 6, 1107, 2048 }, { 5, 1108, 2048 }, { 6, 1109, 2048 }, { 6, 1110, 2048 }, { 7, 1111, 2048 }, + { 5, 1112, 2048 }, { 6, 1113, 2048 }, { 6, 1114, 2048 }, { 7, 1115, 2048 }, { 6, 1116, 2048 }, { 7, 1117, 2048 }, { 7, 1118, 2048 }, { 8, 1119, 2048 }, + { 4, 1120, 2048 }, { 5, 1121, 2048 }, { 5, 1122, 2048 }, { 6, 1123, 2048 }, { 5, 1124, 2048 }, { 6, 1125, 2048 }, { 6, 1126, 2048 }, { 7, 1127, 2048 }, + { 5, 1128, 2048 }, { 6, 1129, 2048 }, { 6, 1130, 2048 }, { 7, 1131, 2048 }, { 6, 1132, 2048 }, { 7, 1133, 2048 }, { 7, 1134, 2048 }, { 8, 1135, 2048 }, + { 5, 1136, 2048 }, { 6, 1137, 2048 }, { 6, 1138, 2048 }, { 7, 1139, 2048 }, { 6, 1140, 2048 }, { 7, 1141, 2048 }, { 7, 1142, 2048 }, { 8, 1143, 2048 }, + { 6, 1144, 2048 }, { 7, 1145, 2048 }, { 7, 1146, 2048 }, { 8, 1147, 2048 }, { 7, 1148, 2048 }, { 8, 1149, 2048 }, { 8, 1150, 2048 }, { 9, 1151, 2048 }, + { 3, 1152, 2048 }, { 4, 1153, 2048 }, { 4, 1154, 2048 }, { 5, 1155, 2048 }, { 4, 1156, 2048 }, { 5, 1157, 2048 }, { 5, 1158, 2048 }, { 6, 1159, 2048 }, + { 4, 1160, 2048 }, { 5, 1161, 2048 }, { 5, 1162, 2048 }, { 6, 1163, 2048 }, { 5, 1164, 2048 }, { 6, 1165, 2048 }, { 6, 1166, 2048 }, { 7, 1167, 2048 }, + { 4, 1168, 2048 }, { 5, 1169, 2048 }, { 5, 1170, 2048 }, { 6, 1171, 2048 }, { 5, 1172, 2048 }, { 6, 1173, 2048 }, { 6, 1174, 2048 }, { 7, 1175, 2048 }, + { 5, 1176, 2048 }, { 6, 1177, 2048 }, { 6, 1178, 2048 }, { 7, 1179, 2048 }, { 6, 1180, 2048 }, { 7, 1181, 2048 }, { 7, 1182, 2048 }, { 8, 1183, 2048 }, + { 4, 1184, 2048 }, { 5, 1185, 2048 }, { 5, 1186, 2048 }, { 6, 1187, 2048 }, { 5, 1188, 2048 }, { 6, 1189, 2048 }, { 6, 1190, 2048 }, { 7, 1191, 2048 }, + { 5, 1192, 2048 }, { 6, 1193, 2048 }, { 6, 1194, 2048 }, { 7, 1195, 2048 }, { 6, 1196, 2048 }, { 7, 1197, 2048 }, { 7, 1198, 2048 }, { 8, 1199, 2048 }, + { 5, 1200, 2048 }, { 6, 1201, 2048 }, { 6, 1202, 2048 }, { 7, 1203, 2048 }, { 6, 1204, 2048 }, { 7, 1205, 2048 }, { 7, 1206, 2048 }, { 8, 1207, 2048 }, + { 6, 1208, 2048 }, { 7, 1209, 2048 }, { 7, 1210, 2048 }, { 8, 1211, 2048 }, { 7, 1212, 2048 }, { 8, 1213, 2048 }, { 8, 1214, 2048 }, { 9, 1215, 2048 }, + { 4, 1216, 2048 }, { 5, 1217, 2048 }, { 5, 1218, 2048 }, { 6, 1219, 2048 }, { 5, 1220, 2048 }, { 6, 1221, 2048 }, { 6, 1222, 2048 }, { 7, 1223, 2048 }, + { 5, 1224, 2048 }, { 6, 1225, 2048 }, { 6, 1226, 2048 }, { 7, 1227, 2048 }, { 6, 1228, 2048 }, { 7, 1229, 2048 }, { 7, 1230, 2048 }, { 8, 1231, 2048 }, + { 5, 1232, 2048 }, { 6, 1233, 2048 }, { 6, 1234, 2048 }, { 7, 1235, 2048 }, { 6, 1236, 2048 }, { 7, 1237, 2048 }, { 7, 1238, 2048 }, { 8, 1239, 2048 }, + { 6, 1240, 2048 }, { 7, 1241, 2048 }, { 7, 1242, 2048 }, { 8, 1243, 2048 }, { 7, 1244, 2048 }, { 8, 1245, 2048 }, { 8, 1246, 2048 }, { 9, 1247, 2048 }, + { 5, 1248, 2048 }, { 6, 1249, 2048 }, { 6, 1250, 2048 }, { 7, 1251, 2048 }, { 6, 1252, 2048 }, { 7, 1253, 2048 }, { 7, 1254, 2048 }, { 8, 1255, 2048 }, + { 6, 1256, 2048 }, { 7, 1257, 2048 }, { 7, 1258, 2048 }, { 8, 1259, 2048 }, { 7, 1260, 2048 }, { 8, 1261, 2048 }, { 8, 1262, 2048 }, { 9, 1263, 2048 }, + { 6, 1264, 2048 }, { 7, 1265, 2048 }, { 7, 1266, 2048 }, { 8, 1267, 2048 }, { 7, 1268, 2048 }, { 8, 1269, 2048 }, { 8, 1270, 2048 }, { 9, 1271, 2048 }, + { 7, 1272, 2048 }, { 8, 1273, 2048 }, { 8, 1274, 2048 }, { 9, 1275, 2048 }, { 8, 1276, 2048 }, { 9, 1277, 2048 }, { 9, 1278, 2048 }, { 10, 1279, 2048 }, + { 3, 1280, 2048 }, { 4, 1281, 2048 }, { 4, 1282, 2048 }, { 5, 1283, 2048 }, { 4, 1284, 2048 }, { 5, 1285, 2048 }, { 5, 1286, 2048 }, { 6, 1287, 2048 }, + { 4, 1288, 2048 }, { 5, 1289, 2048 }, { 5, 1290, 2048 }, { 6, 1291, 2048 }, { 5, 1292, 2048 }, { 6, 1293, 2048 }, { 6, 1294, 2048 }, { 7, 1295, 2048 }, + { 4, 1296, 2048 }, { 5, 1297, 2048 }, { 5, 1298, 2048 }, { 6, 1299, 2048 }, { 5, 1300, 2048 }, { 6, 1301, 2048 }, { 6, 1302, 2048 }, { 7, 1303, 2048 }, + { 5, 1304, 2048 }, { 6, 1305, 2048 }, { 6, 1306, 2048 }, { 7, 1307, 2048 }, { 6, 1308, 2048 }, { 7, 1309, 2048 }, { 7, 1310, 2048 }, { 8, 1311, 2048 }, + { 4, 1312, 2048 }, { 5, 1313, 2048 }, { 5, 1314, 2048 }, { 6, 1315, 2048 }, { 5, 1316, 2048 }, { 6, 1317, 2048 }, { 6, 1318, 2048 }, { 7, 1319, 2048 }, + { 5, 1320, 2048 }, { 6, 1321, 2048 }, { 6, 1322, 2048 }, { 7, 1323, 2048 }, { 6, 1324, 2048 }, { 7, 1325, 2048 }, { 7, 1326, 2048 }, { 8, 1327, 2048 }, + { 5, 1328, 2048 }, { 6, 1329, 2048 }, { 6, 1330, 2048 }, { 7, 1331, 2048 }, { 6, 1332, 2048 }, { 7, 1333, 2048 }, { 7, 1334, 2048 }, { 8, 1335, 2048 }, + { 6, 1336, 2048 }, { 7, 1337, 2048 }, { 7, 1338, 2048 }, { 8, 1339, 2048 }, { 7, 1340, 2048 }, { 8, 1341, 2048 }, { 8, 1342, 2048 }, { 9, 1343, 2048 }, + { 4, 1344, 2048 }, { 5, 1345, 2048 }, { 5, 1346, 2048 }, { 6, 1347, 2048 }, { 5, 1348, 2048 }, { 6, 1349, 2048 }, { 6, 1350, 2048 }, { 7, 1351, 2048 }, + { 5, 1352, 2048 }, { 6, 1353, 2048 }, { 6, 1354, 2048 }, { 7, 1355, 2048 }, { 6, 1356, 2048 }, { 7, 1357, 2048 }, { 7, 1358, 2048 }, { 8, 1359, 2048 }, + { 5, 1360, 2048 }, { 6, 1361, 2048 }, { 6, 1362, 2048 }, { 7, 1363, 2048 }, { 6, 1364, 2048 }, { 7, 1365, 2048 }, { 7, 1366, 2048 }, { 8, 1367, 2048 }, + { 6, 1368, 2048 }, { 7, 1369, 2048 }, { 7, 1370, 2048 }, { 8, 1371, 2048 }, { 7, 1372, 2048 }, { 8, 1373, 2048 }, { 8, 1374, 2048 }, { 9, 1375, 2048 }, + { 5, 1376, 2048 }, { 6, 1377, 2048 }, { 6, 1378, 2048 }, { 7, 1379, 2048 }, { 6, 1380, 2048 }, { 7, 1381, 2048 }, { 7, 1382, 2048 }, { 8, 1383, 2048 }, + { 6, 1384, 2048 }, { 7, 1385, 2048 }, { 7, 1386, 2048 }, { 8, 1387, 2048 }, { 7, 1388, 2048 }, { 8, 1389, 2048 }, { 8, 1390, 2048 }, { 9, 1391, 2048 }, + { 6, 1392, 2048 }, { 7, 1393, 2048 }, { 7, 1394, 2048 }, { 8, 1395, 2048 }, { 7, 1396, 2048 }, { 8, 1397, 2048 }, { 8, 1398, 2048 }, { 9, 1399, 2048 }, + { 7, 1400, 2048 }, { 8, 1401, 2048 }, { 8, 1402, 2048 }, { 9, 1403, 2048 }, { 8, 1404, 2048 }, { 9, 1405, 2048 }, { 9, 1406, 2048 }, { 10, 1407, 2048 }, + { 4, 1408, 2048 }, { 5, 1409, 2048 }, { 5, 1410, 2048 }, { 6, 1411, 2048 }, { 5, 1412, 2048 }, { 6, 1413, 2048 }, { 6, 1414, 2048 }, { 7, 1415, 2048 }, + { 5, 1416, 2048 }, { 6, 1417, 2048 }, { 6, 1418, 2048 }, { 7, 1419, 2048 }, { 6, 1420, 2048 }, { 7, 1421, 2048 }, { 7, 1422, 2048 }, { 8, 1423, 2048 }, + { 5, 1424, 2048 }, { 6, 1425, 2048 }, { 6, 1426, 2048 }, { 7, 1427, 2048 }, { 6, 1428, 2048 }, { 7, 1429, 2048 }, { 7, 1430, 2048 }, { 8, 1431, 2048 }, + { 6, 1432, 2048 }, { 7, 1433, 2048 }, { 7, 1434, 2048 }, { 8, 1435, 2048 }, { 7, 1436, 2048 }, { 8, 1437, 2048 }, { 8, 1438, 2048 }, { 9, 1439, 2048 }, + { 5, 1440, 2048 }, { 6, 1441, 2048 }, { 6, 1442, 2048 }, { 7, 1443, 2048 }, { 6, 1444, 2048 }, { 7, 1445, 2048 }, { 7, 1446, 2048 }, { 8, 1447, 2048 }, + { 6, 1448, 2048 }, { 7, 1449, 2048 }, { 7, 1450, 2048 }, { 8, 1451, 2048 }, { 7, 1452, 2048 }, { 8, 1453, 2048 }, { 8, 1454, 2048 }, { 9, 1455, 2048 }, + { 6, 1456, 2048 }, { 7, 1457, 2048 }, { 7, 1458, 2048 }, { 8, 1459, 2048 }, { 7, 1460, 2048 }, { 8, 1461, 2048 }, { 8, 1462, 2048 }, { 9, 1463, 2048 }, + { 7, 1464, 2048 }, { 8, 1465, 2048 }, { 8, 1466, 2048 }, { 9, 1467, 2048 }, { 8, 1468, 2048 }, { 9, 1469, 2048 }, { 9, 1470, 2048 }, { 10, 1471, 2048 }, + { 5, 1472, 2048 }, { 6, 1473, 2048 }, { 6, 1474, 2048 }, { 7, 1475, 2048 }, { 6, 1476, 2048 }, { 7, 1477, 2048 }, { 7, 1478, 2048 }, { 8, 1479, 2048 }, + { 6, 1480, 2048 }, { 7, 1481, 2048 }, { 7, 1482, 2048 }, { 8, 1483, 2048 }, { 7, 1484, 2048 }, { 8, 1485, 2048 }, { 8, 1486, 2048 }, { 9, 1487, 2048 }, + { 6, 1488, 2048 }, { 7, 1489, 2048 }, { 7, 1490, 2048 }, { 8, 1491, 2048 }, { 7, 1492, 2048 }, { 8, 1493, 2048 }, { 8, 1494, 2048 }, { 9, 1495, 2048 }, + { 7, 1496, 2048 }, { 8, 1497, 2048 }, { 8, 1498, 2048 }, { 9, 1499, 2048 }, { 8, 1500, 2048 }, { 9, 1501, 2048 }, { 9, 1502, 2048 }, { 10, 1503, 2048 }, + { 6, 1504, 2048 }, { 7, 1505, 2048 }, { 7, 1506, 2048 }, { 8, 1507, 2048 }, { 7, 1508, 2048 }, { 8, 1509, 2048 }, { 8, 1510, 2048 }, { 9, 1511, 2048 }, + { 7, 1512, 2048 }, { 8, 1513, 2048 }, { 8, 1514, 2048 }, { 9, 1515, 2048 }, { 8, 1516, 2048 }, { 9, 1517, 2048 }, { 9, 1518, 2048 }, { 10, 1519, 2048 }, + { 7, 1520, 2048 }, { 8, 1521, 2048 }, { 8, 1522, 2048 }, { 9, 1523, 2048 }, { 8, 1524, 2048 }, { 9, 1525, 2048 }, { 9, 1526, 2048 }, { 10, 1527, 2048 }, + { 8, 1528, 2048 }, { 9, 1529, 2048 }, { 9, 1530, 2048 }, { 10, 1531, 2048 }, { 9, 1532, 2048 }, { 10, 1533, 2048 }, { 10, 1534, 2048 }, { 11, 1535, 2048 }, + { 3, 1536, 2048 }, { 4, 1537, 2048 }, { 4, 1538, 2048 }, { 5, 1539, 2048 }, { 4, 1540, 2048 }, { 5, 1541, 2048 }, { 5, 1542, 2048 }, { 6, 1543, 2048 }, + { 4, 1544, 2048 }, { 5, 1545, 2048 }, { 5, 1546, 2048 }, { 6, 1547, 2048 }, { 5, 1548, 2048 }, { 6, 1549, 2048 }, { 6, 1550, 2048 }, { 7, 1551, 2048 }, + { 4, 1552, 2048 }, { 5, 1553, 2048 }, { 5, 1554, 2048 }, { 6, 1555, 2048 }, { 5, 1556, 2048 }, { 6, 1557, 2048 }, { 6, 1558, 2048 }, { 7, 1559, 2048 }, + { 5, 1560, 2048 }, { 6, 1561, 2048 }, { 6, 1562, 2048 }, { 7, 1563, 2048 }, { 6, 1564, 2048 }, { 7, 1565, 2048 }, { 7, 1566, 2048 }, { 8, 1567, 2048 }, + { 4, 1568, 2048 }, { 5, 1569, 2048 }, { 5, 1570, 2048 }, { 6, 1571, 2048 }, { 5, 1572, 2048 }, { 6, 1573, 2048 }, { 6, 1574, 2048 }, { 7, 1575, 2048 }, + { 5, 1576, 2048 }, { 6, 1577, 2048 }, { 6, 1578, 2048 }, { 7, 1579, 2048 }, { 6, 1580, 2048 }, { 7, 1581, 2048 }, { 7, 1582, 2048 }, { 8, 1583, 2048 }, + { 5, 1584, 2048 }, { 6, 1585, 2048 }, { 6, 1586, 2048 }, { 7, 1587, 2048 }, { 6, 1588, 2048 }, { 7, 1589, 2048 }, { 7, 1590, 2048 }, { 8, 1591, 2048 }, + { 6, 1592, 2048 }, { 7, 1593, 2048 }, { 7, 1594, 2048 }, { 8, 1595, 2048 }, { 7, 1596, 2048 }, { 8, 1597, 2048 }, { 8, 1598, 2048 }, { 9, 1599, 2048 }, + { 4, 1600, 2048 }, { 5, 1601, 2048 }, { 5, 1602, 2048 }, { 6, 1603, 2048 }, { 5, 1604, 2048 }, { 6, 1605, 2048 }, { 6, 1606, 2048 }, { 7, 1607, 2048 }, + { 5, 1608, 2048 }, { 6, 1609, 2048 }, { 6, 1610, 2048 }, { 7, 1611, 2048 }, { 6, 1612, 2048 }, { 7, 1613, 2048 }, { 7, 1614, 2048 }, { 8, 1615, 2048 }, + { 5, 1616, 2048 }, { 6, 1617, 2048 }, { 6, 1618, 2048 }, { 7, 1619, 2048 }, { 6, 1620, 2048 }, { 7, 1621, 2048 }, { 7, 1622, 2048 }, { 8, 1623, 2048 }, + { 6, 1624, 2048 }, { 7, 1625, 2048 }, { 7, 1626, 2048 }, { 8, 1627, 2048 }, { 7, 1628, 2048 }, { 8, 1629, 2048 }, { 8, 1630, 2048 }, { 9, 1631, 2048 }, + { 5, 1632, 2048 }, { 6, 1633, 2048 }, { 6, 1634, 2048 }, { 7, 1635, 2048 }, { 6, 1636, 2048 }, { 7, 1637, 2048 }, { 7, 1638, 2048 }, { 8, 1639, 2048 }, + { 6, 1640, 2048 }, { 7, 1641, 2048 }, { 7, 1642, 2048 }, { 8, 1643, 2048 }, { 7, 1644, 2048 }, { 8, 1645, 2048 }, { 8, 1646, 2048 }, { 9, 1647, 2048 }, + { 6, 1648, 2048 }, { 7, 1649, 2048 }, { 7, 1650, 2048 }, { 8, 1651, 2048 }, { 7, 1652, 2048 }, { 8, 1653, 2048 }, { 8, 1654, 2048 }, { 9, 1655, 2048 }, + { 7, 1656, 2048 }, { 8, 1657, 2048 }, { 8, 1658, 2048 }, { 9, 1659, 2048 }, { 8, 1660, 2048 }, { 9, 1661, 2048 }, { 9, 1662, 2048 }, { 10, 1663, 2048 }, + { 4, 1664, 2048 }, { 5, 1665, 2048 }, { 5, 1666, 2048 }, { 6, 1667, 2048 }, { 5, 1668, 2048 }, { 6, 1669, 2048 }, { 6, 1670, 2048 }, { 7, 1671, 2048 }, + { 5, 1672, 2048 }, { 6, 1673, 2048 }, { 6, 1674, 2048 }, { 7, 1675, 2048 }, { 6, 1676, 2048 }, { 7, 1677, 2048 }, { 7, 1678, 2048 }, { 8, 1679, 2048 }, + { 5, 1680, 2048 }, { 6, 1681, 2048 }, { 6, 1682, 2048 }, { 7, 1683, 2048 }, { 6, 1684, 2048 }, { 7, 1685, 2048 }, { 7, 1686, 2048 }, { 8, 1687, 2048 }, + { 6, 1688, 2048 }, { 7, 1689, 2048 }, { 7, 1690, 2048 }, { 8, 1691, 2048 }, { 7, 1692, 2048 }, { 8, 1693, 2048 }, { 8, 1694, 2048 }, { 9, 1695, 2048 }, + { 5, 1696, 2048 }, { 6, 1697, 2048 }, { 6, 1698, 2048 }, { 7, 1699, 2048 }, { 6, 1700, 2048 }, { 7, 1701, 2048 }, { 7, 1702, 2048 }, { 8, 1703, 2048 }, + { 6, 1704, 2048 }, { 7, 1705, 2048 }, { 7, 1706, 2048 }, { 8, 1707, 2048 }, { 7, 1708, 2048 }, { 8, 1709, 2048 }, { 8, 1710, 2048 }, { 9, 1711, 2048 }, + { 6, 1712, 2048 }, { 7, 1713, 2048 }, { 7, 1714, 2048 }, { 8, 1715, 2048 }, { 7, 1716, 2048 }, { 8, 1717, 2048 }, { 8, 1718, 2048 }, { 9, 1719, 2048 }, + { 7, 1720, 2048 }, { 8, 1721, 2048 }, { 8, 1722, 2048 }, { 9, 1723, 2048 }, { 8, 1724, 2048 }, { 9, 1725, 2048 }, { 9, 1726, 2048 }, { 10, 1727, 2048 }, + { 5, 1728, 2048 }, { 6, 1729, 2048 }, { 6, 1730, 2048 }, { 7, 1731, 2048 }, { 6, 1732, 2048 }, { 7, 1733, 2048 }, { 7, 1734, 2048 }, { 8, 1735, 2048 }, + { 6, 1736, 2048 }, { 7, 1737, 2048 }, { 7, 1738, 2048 }, { 8, 1739, 2048 }, { 7, 1740, 2048 }, { 8, 1741, 2048 }, { 8, 1742, 2048 }, { 9, 1743, 2048 }, + { 6, 1744, 2048 }, { 7, 1745, 2048 }, { 7, 1746, 2048 }, { 8, 1747, 2048 }, { 7, 1748, 2048 }, { 8, 1749, 2048 }, { 8, 1750, 2048 }, { 9, 1751, 2048 }, + { 7, 1752, 2048 }, { 8, 1753, 2048 }, { 8, 1754, 2048 }, { 9, 1755, 2048 }, { 8, 1756, 2048 }, { 9, 1757, 2048 }, { 9, 1758, 2048 }, { 10, 1759, 2048 }, + { 6, 1760, 2048 }, { 7, 1761, 2048 }, { 7, 1762, 2048 }, { 8, 1763, 2048 }, { 7, 1764, 2048 }, { 8, 1765, 2048 }, { 8, 1766, 2048 }, { 9, 1767, 2048 }, + { 7, 1768, 2048 }, { 8, 1769, 2048 }, { 8, 1770, 2048 }, { 9, 1771, 2048 }, { 8, 1772, 2048 }, { 9, 1773, 2048 }, { 9, 1774, 2048 }, { 10, 1775, 2048 }, + { 7, 1776, 2048 }, { 8, 1777, 2048 }, { 8, 1778, 2048 }, { 9, 1779, 2048 }, { 8, 1780, 2048 }, { 9, 1781, 2048 }, { 9, 1782, 2048 }, { 10, 1783, 2048 }, + { 8, 1784, 2048 }, { 9, 1785, 2048 }, { 9, 1786, 2048 }, { 10, 1787, 2048 }, { 9, 1788, 2048 }, { 10, 1789, 2048 }, { 10, 1790, 2048 }, { 11, 1791, 2048 }, + { 4, 1792, 2048 }, { 5, 1793, 2048 }, { 5, 1794, 2048 }, { 6, 1795, 2048 }, { 5, 1796, 2048 }, { 6, 1797, 2048 }, { 6, 1798, 2048 }, { 7, 1799, 2048 }, + { 5, 1800, 2048 }, { 6, 1801, 2048 }, { 6, 1802, 2048 }, { 7, 1803, 2048 }, { 6, 1804, 2048 }, { 7, 1805, 2048 }, { 7, 1806, 2048 }, { 8, 1807, 2048 }, + { 5, 1808, 2048 }, { 6, 1809, 2048 }, { 6, 1810, 2048 }, { 7, 1811, 2048 }, { 6, 1812, 2048 }, { 7, 1813, 2048 }, { 7, 1814, 2048 }, { 8, 1815, 2048 }, + { 6, 1816, 2048 }, { 7, 1817, 2048 }, { 7, 1818, 2048 }, { 8, 1819, 2048 }, { 7, 1820, 2048 }, { 8, 1821, 2048 }, { 8, 1822, 2048 }, { 9, 1823, 2048 }, + { 5, 1824, 2048 }, { 6, 1825, 2048 }, { 6, 1826, 2048 }, { 7, 1827, 2048 }, { 6, 1828, 2048 }, { 7, 1829, 2048 }, { 7, 1830, 2048 }, { 8, 1831, 2048 }, + { 6, 1832, 2048 }, { 7, 1833, 2048 }, { 7, 1834, 2048 }, { 8, 1835, 2048 }, { 7, 1836, 2048 }, { 8, 1837, 2048 }, { 8, 1838, 2048 }, { 9, 1839, 2048 }, + { 6, 1840, 2048 }, { 7, 1841, 2048 }, { 7, 1842, 2048 }, { 8, 1843, 2048 }, { 7, 1844, 2048 }, { 8, 1845, 2048 }, { 8, 1846, 2048 }, { 9, 1847, 2048 }, + { 7, 1848, 2048 }, { 8, 1849, 2048 }, { 8, 1850, 2048 }, { 9, 1851, 2048 }, { 8, 1852, 2048 }, { 9, 1853, 2048 }, { 9, 1854, 2048 }, { 10, 1855, 2048 }, + { 5, 1856, 2048 }, { 6, 1857, 2048 }, { 6, 1858, 2048 }, { 7, 1859, 2048 }, { 6, 1860, 2048 }, { 7, 1861, 2048 }, { 7, 1862, 2048 }, { 8, 1863, 2048 }, + { 6, 1864, 2048 }, { 7, 1865, 2048 }, { 7, 1866, 2048 }, { 8, 1867, 2048 }, { 7, 1868, 2048 }, { 8, 1869, 2048 }, { 8, 1870, 2048 }, { 9, 1871, 2048 }, + { 6, 1872, 2048 }, { 7, 1873, 2048 }, { 7, 1874, 2048 }, { 8, 1875, 2048 }, { 7, 1876, 2048 }, { 8, 1877, 2048 }, { 8, 1878, 2048 }, { 9, 1879, 2048 }, + { 7, 1880, 2048 }, { 8, 1881, 2048 }, { 8, 1882, 2048 }, { 9, 1883, 2048 }, { 8, 1884, 2048 }, { 9, 1885, 2048 }, { 9, 1886, 2048 }, { 10, 1887, 2048 }, + { 6, 1888, 2048 }, { 7, 1889, 2048 }, { 7, 1890, 2048 }, { 8, 1891, 2048 }, { 7, 1892, 2048 }, { 8, 1893, 2048 }, { 8, 1894, 2048 }, { 9, 1895, 2048 }, + { 7, 1896, 2048 }, { 8, 1897, 2048 }, { 8, 1898, 2048 }, { 9, 1899, 2048 }, { 8, 1900, 2048 }, { 9, 1901, 2048 }, { 9, 1902, 2048 }, { 10, 1903, 2048 }, + { 7, 1904, 2048 }, { 8, 1905, 2048 }, { 8, 1906, 2048 }, { 9, 1907, 2048 }, { 8, 1908, 2048 }, { 9, 1909, 2048 }, { 9, 1910, 2048 }, { 10, 1911, 2048 }, + { 8, 1912, 2048 }, { 9, 1913, 2048 }, { 9, 1914, 2048 }, { 10, 1915, 2048 }, { 9, 1916, 2048 }, { 10, 1917, 2048 }, { 10, 1918, 2048 }, { 11, 1919, 2048 }, + { 5, 1920, 2048 }, { 6, 1921, 2048 }, { 6, 1922, 2048 }, { 7, 1923, 2048 }, { 6, 1924, 2048 }, { 7, 1925, 2048 }, { 7, 1926, 2048 }, { 8, 1927, 2048 }, + { 6, 1928, 2048 }, { 7, 1929, 2048 }, { 7, 1930, 2048 }, { 8, 1931, 2048 }, { 7, 1932, 2048 }, { 8, 1933, 2048 }, { 8, 1934, 2048 }, { 9, 1935, 2048 }, + { 6, 1936, 2048 }, { 7, 1937, 2048 }, { 7, 1938, 2048 }, { 8, 1939, 2048 }, { 7, 1940, 2048 }, { 8, 1941, 2048 }, { 8, 1942, 2048 }, { 9, 1943, 2048 }, + { 7, 1944, 2048 }, { 8, 1945, 2048 }, { 8, 1946, 2048 }, { 9, 1947, 2048 }, { 8, 1948, 2048 }, { 9, 1949, 2048 }, { 9, 1950, 2048 }, { 10, 1951, 2048 }, + { 6, 1952, 2048 }, { 7, 1953, 2048 }, { 7, 1954, 2048 }, { 8, 1955, 2048 }, { 7, 1956, 2048 }, { 8, 1957, 2048 }, { 8, 1958, 2048 }, { 9, 1959, 2048 }, + { 7, 1960, 2048 }, { 8, 1961, 2048 }, { 8, 1962, 2048 }, { 9, 1963, 2048 }, { 8, 1964, 2048 }, { 9, 1965, 2048 }, { 9, 1966, 2048 }, { 10, 1967, 2048 }, + { 7, 1968, 2048 }, { 8, 1969, 2048 }, { 8, 1970, 2048 }, { 9, 1971, 2048 }, { 8, 1972, 2048 }, { 9, 1973, 2048 }, { 9, 1974, 2048 }, { 10, 1975, 2048 }, + { 8, 1976, 2048 }, { 9, 1977, 2048 }, { 9, 1978, 2048 }, { 10, 1979, 2048 }, { 9, 1980, 2048 }, { 10, 1981, 2048 }, { 10, 1982, 2048 }, { 11, 1983, 2048 }, + { 6, 1984, 2048 }, { 7, 1985, 2048 }, { 7, 1986, 2048 }, { 8, 1987, 2048 }, { 7, 1988, 2048 }, { 8, 1989, 2048 }, { 8, 1990, 2048 }, { 9, 1991, 2048 }, + { 7, 1992, 2048 }, { 8, 1993, 2048 }, { 8, 1994, 2048 }, { 9, 1995, 2048 }, { 8, 1996, 2048 }, { 9, 1997, 2048 }, { 9, 1998, 2048 }, { 10, 1999, 2048 }, + { 7, 2000, 2048 }, { 8, 2001, 2048 }, { 8, 2002, 2048 }, { 9, 2003, 2048 }, { 8, 2004, 2048 }, { 9, 2005, 2048 }, { 9, 2006, 2048 }, { 10, 2007, 2048 }, + { 8, 2008, 2048 }, { 9, 2009, 2048 }, { 9, 2010, 2048 }, { 10, 2011, 2048 }, { 9, 2012, 2048 }, { 10, 2013, 2048 }, { 10, 2014, 2048 }, { 11, 2015, 2048 }, + { 7, 2016, 2048 }, { 8, 2017, 2048 }, { 8, 2018, 2048 }, { 9, 2019, 2048 }, { 8, 2020, 2048 }, { 9, 2021, 2048 }, { 9, 2022, 2048 }, { 10, 2023, 2048 }, + { 8, 2024, 2048 }, { 9, 2025, 2048 }, { 9, 2026, 2048 }, { 10, 2027, 2048 }, { 9, 2028, 2048 }, { 10, 2029, 2048 }, { 10, 2030, 2048 }, { 11, 2031, 2048 }, + { 8, 2032, 2048 }, { 9, 2033, 2048 }, { 9, 2034, 2048 }, { 10, 2035, 2048 }, { 9, 2036, 2048 }, { 10, 2037, 2048 }, { 10, 2038, 2048 }, { 11, 2039, 2048 }, + { 9, 2040, 2048 }, { 10, 2041, 2048 }, { 10, 2042, 2048 }, { 11, 2043, 2048 }, { 10, 2044, 2048 }, { 11, 2045, 2048 }, { 11, 2046, 2048 }, { 12, 2047, 2048 }, +#endif +#endif +#endif +#endif +#endif +#endif +}; + +/* find a hole and free as required */ +static int find_hole(void) +{ + unsigned x; + int y, z; + for (z = 0, y = INT_MAX, x = 0; x < FP_ENTRIES; x++) { + if (fp_cache[x].lru_count < y) { + z = x; + y = fp_cache[x].lru_count; + } + } + + /* decrease all */ + for (x = 0; x < FP_ENTRIES; x++) { + if (fp_cache[x].lru_count > 3) { + --(fp_cache[x].lru_count); + } + } + + /* free entry z */ + if (fp_cache[z].g) { + if (fp_cache[z].mu != NULL) { + mp_clear(fp_cache[z].mu); + fp_cache[z].mu = NULL; + } + ltc_ecc_del_point(fp_cache[z].g); + fp_cache[z].g = NULL; + for (x = 0; x < (1U<<FP_LUT); x++) { + ltc_ecc_del_point(fp_cache[z].LUT[x]); + fp_cache[z].LUT[x] = NULL; + } + fp_cache[z].lru_count = 0; + } + return z; +} + +/* determine if a base is already in the cache and if so, where */ +static int find_base(ecc_point *g) +{ + int x; + for (x = 0; x < FP_ENTRIES; x++) { + if (fp_cache[x].g != NULL && + mp_cmp(fp_cache[x].g->x, g->x) == LTC_MP_EQ && + mp_cmp(fp_cache[x].g->y, g->y) == LTC_MP_EQ && + mp_cmp(fp_cache[x].g->z, g->z) == LTC_MP_EQ) { + break; + } + } + if (x == FP_ENTRIES) { + x = -1; + } + return x; +} + +/* add a new base to the cache */ +static int add_entry(int idx, ecc_point *g) +{ + unsigned x, y; + + /* allocate base and LUT */ + fp_cache[idx].g = ltc_ecc_new_point(); + if (fp_cache[idx].g == NULL) { + return CRYPT_MEM; + } + + /* copy x and y */ + if ((mp_copy(g->x, fp_cache[idx].g->x) != CRYPT_OK) || + (mp_copy(g->y, fp_cache[idx].g->y) != CRYPT_OK) || + (mp_copy(g->z, fp_cache[idx].g->z) != CRYPT_OK)) { + ltc_ecc_del_point(fp_cache[idx].g); + fp_cache[idx].g = NULL; + return CRYPT_MEM; + } + + for (x = 0; x < (1U<<FP_LUT); x++) { + fp_cache[idx].LUT[x] = ltc_ecc_new_point(); + if (fp_cache[idx].LUT[x] == NULL) { + for (y = 0; y < x; y++) { + ltc_ecc_del_point(fp_cache[idx].LUT[y]); + fp_cache[idx].LUT[y] = NULL; + } + ltc_ecc_del_point(fp_cache[idx].g); + fp_cache[idx].g = NULL; + fp_cache[idx].lru_count = 0; + return CRYPT_MEM; + } + } + + fp_cache[idx].lru_count = 0; + return CRYPT_OK; +} + +/* build the LUT by spacing the bits of the input by #modulus/FP_LUT bits apart + * + * The algorithm builds patterns in increasing bit order by first making all + * single bit input patterns, then all two bit input patterns and so on + */ +static int build_lut(int idx, void *modulus, void *mp, void *mu) +{ + unsigned x, y, err, bitlen, lut_gap; + void *tmp; + + tmp = NULL; + + /* sanity check to make sure lut_order table is of correct size, should compile out to a NOP if true */ + if ((sizeof(lut_orders) / sizeof(lut_orders[0])) < (1U<<FP_LUT)) { + err = CRYPT_INVALID_ARG; + goto DONE; + } + + /* get bitlen and round up to next multiple of FP_LUT */ + bitlen = mp_unsigned_bin_size(modulus) << 3; + x = bitlen % FP_LUT; + if (x) { + bitlen += FP_LUT - x; + } + lut_gap = bitlen / FP_LUT; + + /* init the mu */ + if ((err = mp_init_copy(&fp_cache[idx].mu, mu)) != CRYPT_OK) { + goto ERR; + } + + /* copy base */ + if ((mp_mulmod(fp_cache[idx].g->x, mu, modulus, fp_cache[idx].LUT[1]->x) != CRYPT_OK) || + (mp_mulmod(fp_cache[idx].g->y, mu, modulus, fp_cache[idx].LUT[1]->y) != CRYPT_OK) || + (mp_mulmod(fp_cache[idx].g->z, mu, modulus, fp_cache[idx].LUT[1]->z) != CRYPT_OK)) { goto ERR; } + + /* make all single bit entries */ + for (x = 1; x < FP_LUT; x++) { + if ((mp_copy(fp_cache[idx].LUT[1<<(x-1)]->x, fp_cache[idx].LUT[1<<x]->x) != CRYPT_OK) || + (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->y, fp_cache[idx].LUT[1<<x]->y) != CRYPT_OK) || + (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->z, fp_cache[idx].LUT[1<<x]->z) != CRYPT_OK)) { goto ERR; } + + /* now double it bitlen/FP_LUT times */ + for (y = 0; y < lut_gap; y++) { + if ((err = ltc_mp.ecc_ptdbl(fp_cache[idx].LUT[1<<x], fp_cache[idx].LUT[1<<x], modulus, mp)) != CRYPT_OK) { + goto ERR; + } + } + } + + /* now make all entries in increase order of hamming weight */ + for (x = 2; x <= FP_LUT; x++) { + for (y = 0; y < (1UL<<FP_LUT); y++) { + if (lut_orders[y].ham != (int)x) continue; + + /* perform the add */ + if ((err = ltc_mp.ecc_ptadd(fp_cache[idx].LUT[lut_orders[y].terma], fp_cache[idx].LUT[lut_orders[y].termb], + fp_cache[idx].LUT[y], modulus, mp)) != CRYPT_OK) { + goto ERR; + } + } + } + + /* now map all entries back to affine space to make point addition faster */ + if ((err = mp_init(&tmp)) != CRYPT_OK) { goto ERR; } + for (x = 1; x < (1UL<<FP_LUT); x++) { + /* convert z to normal from montgomery */ + if ((err = mp_montgomery_reduce(fp_cache[idx].LUT[x]->z, modulus, mp)) != CRYPT_OK) { goto ERR; } + + /* invert it */ + if ((err = mp_invmod(fp_cache[idx].LUT[x]->z, modulus, fp_cache[idx].LUT[x]->z)) != CRYPT_OK) { goto ERR; } + + /* now square it */ + if ((err = mp_sqrmod(fp_cache[idx].LUT[x]->z, modulus, tmp)) != CRYPT_OK) { goto ERR; } + + /* fix x */ + if ((err = mp_mulmod(fp_cache[idx].LUT[x]->x, tmp, modulus, fp_cache[idx].LUT[x]->x)) != CRYPT_OK) { goto ERR; } + + /* get 1/z^3 */ + if ((err = mp_mulmod(tmp, fp_cache[idx].LUT[x]->z, modulus, tmp)) != CRYPT_OK) { goto ERR; } + + /* fix y */ + if ((err = mp_mulmod(fp_cache[idx].LUT[x]->y, tmp, modulus, fp_cache[idx].LUT[x]->y)) != CRYPT_OK) { goto ERR; } + + /* free z */ + mp_clear(fp_cache[idx].LUT[x]->z); + fp_cache[idx].LUT[x]->z = NULL; + } + mp_clear(tmp); + + return CRYPT_OK; +ERR: + err = CRYPT_MEM; +DONE: + for (y = 0; y < (1U<<FP_LUT); y++) { + ltc_ecc_del_point(fp_cache[idx].LUT[y]); + fp_cache[idx].LUT[y] = NULL; + } + ltc_ecc_del_point(fp_cache[idx].g); + fp_cache[idx].g = NULL; + fp_cache[idx].lru_count = 0; + if (fp_cache[idx].mu != NULL) { + mp_clear(fp_cache[idx].mu); + fp_cache[idx].mu = NULL; + } + if (tmp != NULL) { + mp_clear(tmp); + } + return err; +} + +/* perform a fixed point ECC mulmod */ +static int accel_fp_mul(int idx, void *k, ecc_point *R, void *modulus, void *mp, int map) +{ + unsigned char kb[128]; + int x; + unsigned y, z, err, bitlen, bitpos, lut_gap, first; + void *tk, *order; + + /* if it's smaller than modulus we fine */ + if (mp_unsigned_bin_size(k) > mp_unsigned_bin_size(modulus)) { + /* find order */ + y = mp_unsigned_bin_size(modulus); + for (x = 0; ltc_ecc_sets[x].size; x++) { + if (y <= (unsigned)ltc_ecc_sets[x].size) break; + } + + /* back off if we are on the 521 bit curve */ + if (y == 66) --x; + + if ((err = mp_init(&order)) != CRYPT_OK) { + return err; + } + if ((err = mp_read_radix(order, ltc_ecc_sets[x].order, 16)) != CRYPT_OK) { + mp_clear(&order); + return err; + } + + /* k must be less than modulus */ + if (mp_cmp(k, order) != LTC_MP_LT) { + if ((err = mp_init(&tk)) != CRYPT_OK) { + mp_clear(order); + return err; + } + if ((err = mp_mod(k, order, tk)) != CRYPT_OK) { + mp_clear(tk); + mp_clear(order); + return err; + } + } else { + tk = k; + } + mp_clear(order); + } else { + tk = k; + } + + /* get bitlen and round up to next multiple of FP_LUT */ + bitlen = mp_unsigned_bin_size(modulus) << 3; + x = bitlen % FP_LUT; + if (x) { + bitlen += FP_LUT - x; + } + lut_gap = bitlen / FP_LUT; + + /* get the k value */ + if (mp_unsigned_bin_size(tk) > (sizeof(kb) - 2)) { + if (tk != k) { + mp_clear(tk); + } + return CRYPT_BUFFER_OVERFLOW; + } + + /* store k */ + zeromem(kb, sizeof(kb)); + if ((err = mp_to_unsigned_bin(tk, kb)) != CRYPT_OK) { + if (tk != k) { + mp_clear(tk); + } + return err; + } + + /* let's reverse kb so it's little endian */ + x = 0; + y = mp_unsigned_bin_size(tk) - 1; + if (tk != k) { + mp_clear(tk); + } + while ((unsigned)x < y) { + z = kb[x]; kb[x] = kb[y]; kb[y] = z; + ++x; --y; + } + + /* at this point we can start, yipee */ + first = 1; + for (x = lut_gap-1; x >= 0; x--) { + /* extract FP_LUT bits from kb spread out by lut_gap bits and offset by x bits from the start */ + bitpos = x; + for (y = z = 0; y < FP_LUT; y++) { + z |= ((kb[bitpos>>3] >> (bitpos&7)) & 1) << y; + bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid the mult in each loop */ + } + + /* double if not first */ + if (!first) { + if ((err = ltc_mp.ecc_ptdbl(R, R, modulus, mp)) != CRYPT_OK) { + return err; + } + } + + /* add if not first, otherwise copy */ + if (!first && z) { + if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx].LUT[z], R, modulus, mp)) != CRYPT_OK) { + return err; + } + } else if (z) { + if ((mp_copy(fp_cache[idx].LUT[z]->x, R->x) != CRYPT_OK) || + (mp_copy(fp_cache[idx].LUT[z]->y, R->y) != CRYPT_OK) || + (mp_copy(fp_cache[idx].mu, R->z) != CRYPT_OK)) { return CRYPT_MEM; } + first = 0; + } + } + z = 0; + zeromem(kb, sizeof(kb)); + /* map R back from projective space */ + if (map) { + err = ltc_ecc_map(R, modulus, mp); + } else { + err = CRYPT_OK; + } + return err; +} + +#ifdef LTC_ECC_SHAMIR +/* perform a fixed point ECC mulmod */ +static int accel_fp_mul2add(int idx1, int idx2, + void *kA, void *kB, + ecc_point *R, void *modulus, void *mp) +{ + unsigned char kb[2][128]; + int x; + unsigned y, z, err, bitlen, bitpos, lut_gap, first, zA, zB; + void *tka, *tkb, *order; + + /* if it's smaller than modulus we fine */ + if (mp_unsigned_bin_size(kA) > mp_unsigned_bin_size(modulus)) { + /* find order */ + y = mp_unsigned_bin_size(modulus); + for (x = 0; ltc_ecc_sets[x].size; x++) { + if (y <= (unsigned)ltc_ecc_sets[x].size) break; + } + + /* back off if we are on the 521 bit curve */ + if (y == 66) --x; + + if ((err = mp_init(&order)) != CRYPT_OK) { + return err; + } + if ((err = mp_read_radix(order, ltc_ecc_sets[x].order, 16)) != CRYPT_OK) { + mp_clear(&order); + return err; + } + + /* kA must be less than modulus */ + if (mp_cmp(kA, order) != LTC_MP_LT) { + if ((err = mp_init(&tka)) != CRYPT_OK) { + mp_clear(order); + return err; + } + if ((err = mp_mod(kA, order, tka)) != CRYPT_OK) { + mp_clear(tka); + mp_clear(order); + return err; + } + } else { + tka = kA; + } + mp_clear(order); + } else { + tka = kA; + } + + /* if it's smaller than modulus we fine */ + if (mp_unsigned_bin_size(kB) > mp_unsigned_bin_size(modulus)) { + /* find order */ + y = mp_unsigned_bin_size(modulus); + for (x = 0; ltc_ecc_sets[x].size; x++) { + if (y <= (unsigned)ltc_ecc_sets[x].size) break; + } + + /* back off if we are on the 521 bit curve */ + if (y == 66) --x; + + if ((err = mp_init(&order)) != CRYPT_OK) { + return err; + } + if ((err = mp_read_radix(order, ltc_ecc_sets[x].order, 16)) != CRYPT_OK) { + mp_clear(&order); + return err; + } + + /* kB must be less than modulus */ + if (mp_cmp(kB, order) != LTC_MP_LT) { + if ((err = mp_init(&tkb)) != CRYPT_OK) { + mp_clear(order); + return err; + } + if ((err = mp_mod(kB, order, tkb)) != CRYPT_OK) { + mp_clear(tkb); + mp_clear(order); + return err; + } + } else { + tkb = kB; + } + mp_clear(order); + } else { + tkb = kB; + } + + /* get bitlen and round up to next multiple of FP_LUT */ + bitlen = mp_unsigned_bin_size(modulus) << 3; + x = bitlen % FP_LUT; + if (x) { + bitlen += FP_LUT - x; + } + lut_gap = bitlen / FP_LUT; + + /* get the k value */ + if ((mp_unsigned_bin_size(tka) > (sizeof(kb[0]) - 2)) || (mp_unsigned_bin_size(tkb) > (sizeof(kb[0]) - 2)) ) { + if (tka != kA) { + mp_clear(tka); + } + if (tkb != kB) { + mp_clear(tkb); + } + return CRYPT_BUFFER_OVERFLOW; + } + + /* store k */ + zeromem(kb, sizeof(kb)); + if ((err = mp_to_unsigned_bin(tka, kb[0])) != CRYPT_OK) { + if (tka != kA) { + mp_clear(tka); + } + if (tkb != kB) { + mp_clear(tkb); + } + return err; + } + + /* let's reverse kb so it's little endian */ + x = 0; + y = mp_unsigned_bin_size(tka) - 1; + if (tka != kA) { + mp_clear(tka); + } + while ((unsigned)x < y) { + z = kb[0][x]; kb[0][x] = kb[0][y]; kb[0][y] = z; + ++x; --y; + } + + /* store b */ + if ((err = mp_to_unsigned_bin(tkb, kb[1])) != CRYPT_OK) { + if (tkb != kB) { + mp_clear(tkb); + } + return err; + } + + x = 0; + y = mp_unsigned_bin_size(tkb) - 1; + if (tkb != kB) { + mp_clear(tkb); + } + while ((unsigned)x < y) { + z = kb[1][x]; kb[1][x] = kb[1][y]; kb[1][y] = z; + ++x; --y; + } + + /* at this point we can start, yipee */ + first = 1; + for (x = lut_gap-1; x >= 0; x--) { + /* extract FP_LUT bits from kb spread out by lut_gap bits and offset by x bits from the start */ + bitpos = x; + for (y = zA = zB = 0; y < FP_LUT; y++) { + zA |= ((kb[0][bitpos>>3] >> (bitpos&7)) & 1) << y; + zB |= ((kb[1][bitpos>>3] >> (bitpos&7)) & 1) << y; + bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid the mult in each loop */ + } + + /* double if not first */ + if (!first) { + if ((err = ltc_mp.ecc_ptdbl(R, R, modulus, mp)) != CRYPT_OK) { + return err; + } + } + + /* add if not first, otherwise copy */ + if (!first) { + if (zA) { + if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx1].LUT[zA], R, modulus, mp)) != CRYPT_OK) { + return err; + } + } + if (zB) { + if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx2].LUT[zB], R, modulus, mp)) != CRYPT_OK) { + return err; + } + } + } else { + if (zA) { + if ((mp_copy(fp_cache[idx1].LUT[zA]->x, R->x) != CRYPT_OK) || + (mp_copy(fp_cache[idx1].LUT[zA]->y, R->y) != CRYPT_OK) || + (mp_copy(fp_cache[idx1].mu, R->z) != CRYPT_OK)) { return CRYPT_MEM; } + first = 0; + } + if (zB && first == 0) { + if (zB) { + if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx2].LUT[zB], R, modulus, mp)) != CRYPT_OK) { + return err; + } + } + } else if (zB && first == 1) { + if ((mp_copy(fp_cache[idx2].LUT[zB]->x, R->x) != CRYPT_OK) || + (mp_copy(fp_cache[idx2].LUT[zB]->y, R->y) != CRYPT_OK) || + (mp_copy(fp_cache[idx2].mu, R->z) != CRYPT_OK)) { return CRYPT_MEM; } + first = 0; + } + } + } + zeromem(kb, sizeof(kb)); + return ltc_ecc_map(R, modulus, mp); +} + +/** ECC Fixed Point mulmod global + @param k The multiplicand + @param G Base point to multiply + @param R [out] Destination of product + @param modulus The modulus for the curve + @param map [boolean] If non-zero maps the point back to affine co-ordinates, otherwise it's left in jacobian-montgomery form + @return CRYPT_OK if successful +*/ +int ltc_ecc_fp_mul2add(ecc_point *A, void *kA, + ecc_point *B, void *kB, + ecc_point *C, void *modulus) +{ + int idx1, idx2, err; + void *mp, *mu; + + mp = NULL; + mu = NULL; + LTC_MUTEX_LOCK(<c_ecc_fp_lock); + /* find point */ + idx1 = find_base(A); + + /* no entry? */ + if (idx1 == -1) { + /* find hole and add it */ + idx1 = find_hole(); + + if ((err = add_entry(idx1, A)) != CRYPT_OK) { + goto LBL_ERR; + } + } + + /* increment LRU */ + ++(fp_cache[idx1].lru_count); + + /* find point */ + idx2 = find_base(B); + + /* no entry? */ + if (idx2 == -1) { + /* find hole and add it */ + idx2 = find_hole(); + + if ((err = add_entry(idx2, B)) != CRYPT_OK) { + goto LBL_ERR; + } + } + + /* increment LRU */ + ++(fp_cache[idx2].lru_count); + + /* if it's 2 build the LUT, if it's higher just use the LUT */ + if (fp_cache[idx1].lru_count == 2) { + /* compute mp */ + if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; } + + /* compute mu */ + if ((err = mp_init(&mu)) != CRYPT_OK) { + goto LBL_ERR; + } + if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) { + goto LBL_ERR; + } + + /* build the LUT */ + if ((err = build_lut(idx1, modulus, mp, mu)) != CRYPT_OK) { + goto LBL_ERR;; + } + } + + /* if it's 2 build the LUT, if it's higher just use the LUT */ + if (fp_cache[idx2].lru_count == 2) { + if (mp == NULL) { + /* compute mp */ + if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; } + + /* compute mu */ + if ((err = mp_init(&mu)) != CRYPT_OK) { + goto LBL_ERR; + } + if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) { + goto LBL_ERR; + } + } + + /* build the LUT */ + if ((err = build_lut(idx2, modulus, mp, mu)) != CRYPT_OK) { + goto LBL_ERR;; + } + } + + + if (fp_cache[idx1].lru_count >= 2 && fp_cache[idx2].lru_count >= 2) { + if (mp == NULL) { + /* compute mp */ + if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; } + } + err = accel_fp_mul2add(idx1, idx2, kA, kB, C, modulus, mp); + } else { + err = ltc_ecc_mul2add(A, kA, B, kB, C, modulus); + } +LBL_ERR: + LTC_MUTEX_UNLOCK(<c_ecc_fp_lock); + if (mp != NULL) { + mp_montgomery_free(mp); + } + if (mu != NULL) { + mp_clear(mu); + } + return err; +} +#endif + +/** ECC Fixed Point mulmod global + @param k The multiplicand + @param G Base point to multiply + @param R [out] Destination of product + @param modulus The modulus for the curve + @param map [boolean] If non-zero maps the point back to affine co-ordinates, otherwise it's left in jacobian-montgomery form + @return CRYPT_OK if successful +*/ +int ltc_ecc_fp_mulmod(void *k, ecc_point *G, ecc_point *R, void *modulus, int map) +{ + int idx, err; + void *mp, *mu; + + mp = NULL; + mu = NULL; + LTC_MUTEX_LOCK(<c_ecc_fp_lock); + /* find point */ + idx = find_base(G); + + /* no entry? */ + if (idx == -1) { + /* find hole and add it */ + idx = find_hole(); + + if ((err = add_entry(idx, G)) != CRYPT_OK) { + goto LBL_ERR; + } + } + + /* increment LRU */ + ++(fp_cache[idx].lru_count); + + /* if it's 2 build the LUT, if it's higher just use the LUT */ + if (fp_cache[idx].lru_count == 2) { + /* compute mp */ + if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; } + + /* compute mu */ + if ((err = mp_init(&mu)) != CRYPT_OK) { + goto LBL_ERR; + } + if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) { + goto LBL_ERR; + } + + /* build the LUT */ + if ((err = build_lut(idx, modulus, mp, mu)) != CRYPT_OK) { + goto LBL_ERR;; + } + } + + if (fp_cache[idx].lru_count >= 2) { + if (mp == NULL) { + /* compute mp */ + if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; } + } + err = accel_fp_mul(idx, k, R, modulus, mp, map); + } else { + err = ltc_ecc_mulmod(k, G, R, modulus, map); + } +LBL_ERR: + LTC_MUTEX_UNLOCK(<c_ecc_fp_lock); + if (mp != NULL) { + mp_montgomery_free(mp); + } + if (mu != NULL) { + mp_clear(mu); + } + return err; +} + +/** Free the Fixed Point tables */ +void ltc_ecc_fp_free(void) +{ + unsigned x, y; + LTC_MUTEX_LOCK(<c_ecc_fp_lock); + for (x = 0; x < FP_ENTRIES; x++) { + if (fp_cache[x].g != NULL) { + for (y = 0; y < (1U<<FP_LUT); y++) { + ltc_ecc_del_point(fp_cache[x].LUT[y]); + fp_cache[x].LUT[y] = NULL; + } + ltc_ecc_del_point(fp_cache[x].g); + fp_cache[x].g = NULL; + if (fp_cache[x].mu != NULL) { + mp_clear(fp_cache[x].mu); + fp_cache[x].mu = NULL; + } + fp_cache[x].lru_count = 0; + } + } + LTC_MUTEX_UNLOCK(<c_ecc_fp_lock); +} + +#endif + + +/* $Source: /cvs/libtom/libtomcrypt/src/math/fp/ltc_ecc_fp_mulmod.c,v $ */ +/* $Revision: 1.27 $ */ +/* $Date: 2006/12/03 00:39:56 $ */ + diff --git a/libtomcrypt/src/math/gmp_desc.c b/libtomcrypt/src/math/gmp_desc.c new file mode 100644 index 0000000..66c279e --- /dev/null +++ b/libtomcrypt/src/math/gmp_desc.c @@ -0,0 +1,478 @@ +/* LibTomCrypt, modular cryptographic library -- Tom St Denis + * + * LibTomCrypt is a library that provides various cryptographic + * algorithms in a highly modular and flexible manner. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com + */ + +#define DESC_DEF_ONLY +#include "tomcrypt.h" + +#ifdef GMP_DESC + +#include <stdio.h> +#include <gmp.h> + +static int init(void **a) +{ + LTC_ARGCHK(a != NULL); + + *a = XCALLOC(1, sizeof(__mpz_struct)); + if (*a == NULL) { + return CRYPT_MEM; + } + mpz_init(((__mpz_struct *)*a)); + return CRYPT_OK; +} + +static void deinit(void *a) +{ + LTC_ARGCHKVD(a != NULL); + mpz_clear(a); + XFREE(a); +} + +static int neg(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_neg(b, a); + return CRYPT_OK; +} + +static int copy(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_set(b, a); + return CRYPT_OK; +} + +static int init_copy(void **a, void *b) +{ + if (init(a) != CRYPT_OK) { + return CRYPT_MEM; + } + return copy(b, *a); +} + +/* ---- trivial ---- */ +static int set_int(void *a, unsigned long b) +{ + LTC_ARGCHK(a != NULL); + mpz_set_ui(((__mpz_struct *)a), b); + return CRYPT_OK; +} + +static unsigned long get_int(void *a) +{ + LTC_ARGCHK(a != NULL); + return mpz_get_ui(a); +} + +static unsigned long get_digit(void *a, int n) +{ + LTC_ARGCHK(a != NULL); + return mpz_getlimbn(a, n); +} + +static int get_digit_count(void *a) +{ + LTC_ARGCHK(a != NULL); + return mpz_size(a); +} + +static int compare(void *a, void *b) +{ + int ret; + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + ret = mpz_cmp(a, b); + if (ret < 0) { + return LTC_MP_LT; + } else if (ret > 0) { + return LTC_MP_GT; + } else { + return LTC_MP_EQ; + } +} + +static int compare_d(void *a, unsigned long b) +{ + int ret; + LTC_ARGCHK(a != NULL); + ret = mpz_cmp_ui(((__mpz_struct *)a), b); + if (ret < 0) { + return LTC_MP_LT; + } else if (ret > 0) { + return LTC_MP_GT; + } else { + return LTC_MP_EQ; + } +} + +static int count_bits(void *a) +{ + LTC_ARGCHK(a != NULL); + return mpz_sizeinbase(a, 2); +} + +static int count_lsb_bits(void *a) +{ + LTC_ARGCHK(a != NULL); + return mpz_scan1(a, 0); +} + + +static int twoexpt(void *a, int n) +{ + LTC_ARGCHK(a != NULL); + mpz_set_ui(a, 0); + mpz_setbit(a, n); + return CRYPT_OK; +} + +/* ---- conversions ---- */ + +/* read ascii string */ +static int read_radix(void *a, const char *b, int radix) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_set_str(a, b, radix); + return CRYPT_OK; +} + +/* write one */ +static int write_radix(void *a, char *b, int radix) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_get_str(b, radix, a); + return CRYPT_OK; +} + +/* get size as unsigned char string */ +static unsigned long unsigned_size(void *a) +{ + unsigned long t; + LTC_ARGCHK(a != NULL); + t = mpz_sizeinbase(a, 2); + if (mpz_cmp_ui(((__mpz_struct *)a), 0) == 0) return 0; + return (t>>3) + ((t&7)?1:0); +} + +/* store */ +static int unsigned_write(void *a, unsigned char *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_export(b, NULL, 1, 1, 1, 0, ((__mpz_struct*)a)); + return CRYPT_OK; +} + +/* read */ +static int unsigned_read(void *a, unsigned char *b, unsigned long len) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_import(a, len, 1, 1, 1, 0, b); + return CRYPT_OK; +} + +/* add */ +static int add(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_add(c, a, b); + return CRYPT_OK; +} + +static int addi(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + mpz_add_ui(c, a, b); + return CRYPT_OK; +} + +/* sub */ +static int sub(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_sub(c, a, b); + return CRYPT_OK; +} + +static int subi(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + mpz_sub_ui(c, a, b); + return CRYPT_OK; +} + +/* mul */ +static int mul(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_mul(c, a, b); + return CRYPT_OK; +} + +static int muli(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + mpz_mul_ui(c, a, b); + return CRYPT_OK; +} + +/* sqr */ +static int sqr(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_mul(b, a, a); + return CRYPT_OK; +} + +/* div */ +static int divide(void *a, void *b, void *c, void *d) +{ + mpz_t tmp; + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + if (c != NULL) { + mpz_init(tmp); + mpz_divexact(tmp, a, b); + } + if (d != NULL) { + mpz_mod(d, a, b); + } + if (c != NULL) { + mpz_set(c, tmp); + mpz_clear(tmp); + } + return CRYPT_OK; +} + +static int div_2(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_divexact_ui(b, a, 2); + return CRYPT_OK; +} + +/* modi */ +static int modi(void *a, unsigned long b, unsigned long *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + + *c = mpz_fdiv_ui(a, b); + return CRYPT_OK; +} + +/* gcd */ +static int gcd(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_gcd(c, a, b); + return CRYPT_OK; +} + +/* lcm */ +static int lcm(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_lcm(c, a, b); + return CRYPT_OK; +} + +static int mulmod(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + LTC_ARGCHK(d != NULL); + mpz_mul(d, a, b); + mpz_mod(d, d, c); + return CRYPT_OK; +} + +static int sqrmod(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_mul(c, a, a); + mpz_mod(c, c, b); + return CRYPT_OK; +} + +/* invmod */ +static int invmod(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_invert(c, a, b); + return CRYPT_OK; +} + +/* setup */ +static int montgomery_setup(void *a, void **b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + *b = (void *)1; + return CRYPT_OK; +} + +/* get normalization value */ +static int montgomery_normalization(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + mpz_set_ui(a, 1); + return CRYPT_OK; +} + +/* reduce */ +static int montgomery_reduce(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + mpz_mod(a, a, b); + return CRYPT_OK; +} + +/* clean up */ +static void montgomery_deinit(void *a) +{ +} + +static int exptmod(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + LTC_ARGCHK(d != NULL); + mpz_powm(d, a, b, c); + return CRYPT_OK; +} + +static int isprime(void *a, int *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + *b = mpz_probab_prime_p(a, 8) > 0 ? LTC_MP_YES : LTC_MP_NO; + return CRYPT_OK; +} + +const ltc_math_descriptor gmp_desc = { + "GNU MP", + sizeof(mp_limb_t) * CHAR_BIT - GMP_NAIL_BITS, + + &init, + &init_copy, + &deinit, + + &neg, + ©, + + &set_int, + &get_int, + &get_digit, + &get_digit_count, + &compare, + &compare_d, + &count_bits, + &count_lsb_bits, + &twoexpt, + + &read_radix, + &write_radix, + &unsigned_size, + &unsigned_write, + &unsigned_read, + + &add, + &addi, + &sub, + &subi, + &mul, + &muli, + &sqr, + ÷, + &div_2, + &modi, + &gcd, + &lcm, + + &mulmod, + &sqrmod, + &invmod, + + &montgomery_setup, + &montgomery_normalization, + &montgomery_reduce, + &montgomery_deinit, + + &exptmod, + &isprime, + +#ifdef MECC +#ifdef MECC_FP + <c_ecc_fp_mulmod, +#else + <c_ecc_mulmod, +#endif /* MECC_FP */ + <c_ecc_projective_add_point, + <c_ecc_projective_dbl_point, + <c_ecc_map, +#ifdef LTC_ECC_SHAMIR +#ifdef MECC_FP + <c_ecc_fp_mul2add, +#else + <c_ecc_mul2add, +#endif /* MECC_FP */ +#else + NULL, +#endif /* LTC_ECC_SHAMIR */ +#else + NULL, NULL, NULL, NULL, NULL +#endif /* MECC */ + +#ifdef MRSA + &rsa_make_key, + &rsa_exptmod, +#else + NULL, NULL +#endif + +}; + + +#endif + +/* $Source: /cvs/libtom/libtomcrypt/src/math/gmp_desc.c,v $ */ +/* $Revision: 1.14 $ */ +/* $Date: 2006/12/03 00:39:56 $ */ diff --git a/libtomcrypt/src/math/ltm_desc.c b/libtomcrypt/src/math/ltm_desc.c new file mode 100644 index 0000000..07fdd5a --- /dev/null +++ b/libtomcrypt/src/math/ltm_desc.c @@ -0,0 +1,483 @@ +/* LibTomCrypt, modular cryptographic library -- Tom St Denis + * + * LibTomCrypt is a library that provides various cryptographic + * algorithms in a highly modular and flexible manner. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com + */ + +#define DESC_DEF_ONLY +#include "tomcrypt.h" + +#ifdef LTM_DESC + +#include <tommath.h> + +static const struct { + int mpi_code, ltc_code; +} mpi_to_ltc_codes[] = { + { MP_OKAY , CRYPT_OK}, + { MP_MEM , CRYPT_MEM}, + { MP_VAL , CRYPT_INVALID_ARG}, +}; + +/** + Convert a MPI error to a LTC error (Possibly the most powerful function ever! Oh wait... no) + @param err The error to convert + @return The equivalent LTC error code or CRYPT_ERROR if none found +*/ +static int mpi_to_ltc_error(int err) +{ + int x; + + for (x = 0; x < (int)(sizeof(mpi_to_ltc_codes)/sizeof(mpi_to_ltc_codes[0])); x++) { + if (err == mpi_to_ltc_codes[x].mpi_code) { + return mpi_to_ltc_codes[x].ltc_code; + } + } + return CRYPT_ERROR; +} + +static int init(void **a) +{ + int err; + + LTC_ARGCHK(a != NULL); + + *a = XCALLOC(1, sizeof(mp_int)); + if (*a == NULL) { + return CRYPT_MEM; + } + + if ((err = mpi_to_ltc_error(mp_init(*a))) != CRYPT_OK) { + XFREE(*a); + } + return err; +} + +static void deinit(void *a) +{ + LTC_ARGCHKVD(a != NULL); + mp_clear(a); + XFREE(a); +} + +static int neg(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_neg(a, b)); +} + +static int copy(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_copy(a, b)); +} + +static int init_copy(void **a, void *b) +{ + if (init(a) != CRYPT_OK) { + return CRYPT_MEM; + } + return copy(b, *a); +} + +/* ---- trivial ---- */ +static int set_int(void *a, unsigned long b) +{ + LTC_ARGCHK(a != NULL); + return mpi_to_ltc_error(mp_set_int(a, b)); +} + +static unsigned long get_int(void *a) +{ + LTC_ARGCHK(a != NULL); + return mp_get_int(a); +} + +static unsigned long get_digit(void *a, int n) +{ + mp_int *A; + LTC_ARGCHK(a != NULL); + A = a; + return (n >= A->used || n < 0) ? 0 : A->dp[n]; +} + +static int get_digit_count(void *a) +{ + mp_int *A; + LTC_ARGCHK(a != NULL); + A = a; + return A->used; +} + +static int compare(void *a, void *b) +{ + int ret; + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + ret = mp_cmp(a, b); + switch (ret) { + case MP_LT: return LTC_MP_LT; + case MP_EQ: return LTC_MP_EQ; + case MP_GT: return LTC_MP_GT; + } + return 0; +} + +static int compare_d(void *a, unsigned long b) +{ + int ret; + LTC_ARGCHK(a != NULL); + ret = mp_cmp_d(a, b); + switch (ret) { + case MP_LT: return LTC_MP_LT; + case MP_EQ: return LTC_MP_EQ; + case MP_GT: return LTC_MP_GT; + } + return 0; +} + +static int count_bits(void *a) +{ + LTC_ARGCHK(a != NULL); + return mp_count_bits(a); +} + +static int count_lsb_bits(void *a) +{ + LTC_ARGCHK(a != NULL); + return mp_cnt_lsb(a); +} + + +static int twoexpt(void *a, int n) +{ + LTC_ARGCHK(a != NULL); + return mpi_to_ltc_error(mp_2expt(a, n)); +} + +/* ---- conversions ---- */ + +/* read ascii string */ +static int read_radix(void *a, const char *b, int radix) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_read_radix(a, b, radix)); +} + +/* write one */ +static int write_radix(void *a, char *b, int radix) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_toradix(a, b, radix)); +} + +/* get size as unsigned char string */ +static unsigned long unsigned_size(void *a) +{ + LTC_ARGCHK(a != NULL); + return mp_unsigned_bin_size(a); +} + +/* store */ +static int unsigned_write(void *a, unsigned char *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_to_unsigned_bin(a, b)); +} + +/* read */ +static int unsigned_read(void *a, unsigned char *b, unsigned long len) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_read_unsigned_bin(a, b, len)); +} + +/* add */ +static int add(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_add(a, b, c)); +} + +static int addi(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_add_d(a, b, c)); +} + +/* sub */ +static int sub(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_sub(a, b, c)); +} + +static int subi(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_sub_d(a, b, c)); +} + +/* mul */ +static int mul(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_mul(a, b, c)); +} + +static int muli(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_mul_d(a, b, c)); +} + +/* sqr */ +static int sqr(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_sqr(a, b)); +} + +/* div */ +static int divide(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_div(a, b, c, d)); +} + +static int div_2(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_div_2(a, b)); +} + +/* modi */ +static int modi(void *a, unsigned long b, unsigned long *c) +{ + mp_digit tmp; + int err; + + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + + if ((err = mpi_to_ltc_error(mp_mod_d(a, b, &tmp))) != CRYPT_OK) { + return err; + } + *c = tmp; + return CRYPT_OK; +} + +/* gcd */ +static int gcd(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_gcd(a, b, c)); +} + +/* lcm */ +static int lcm(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_lcm(a, b, c)); +} + +static int mulmod(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + LTC_ARGCHK(d != NULL); + return mpi_to_ltc_error(mp_mulmod(a,b,c,d)); +} + +static int sqrmod(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_sqrmod(a,b,c)); +} + +/* invmod */ +static int invmod(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_invmod(a, b, c)); +} + +/* setup */ +static int montgomery_setup(void *a, void **b) +{ + int err; + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + *b = XCALLOC(1, sizeof(mp_digit)); + if (*b == NULL) { + return CRYPT_MEM; + } + if ((err = mpi_to_ltc_error(mp_montgomery_setup(a, (mp_digit *)*b))) != CRYPT_OK) { + XFREE(*b); + } + return err; +} + +/* get normalization value */ +static int montgomery_normalization(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return mpi_to_ltc_error(mp_montgomery_calc_normalization(a, b)); +} + +/* reduce */ +static int montgomery_reduce(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return mpi_to_ltc_error(mp_montgomery_reduce(a, b, *((mp_digit *)c))); +} + +/* clean up */ +static void montgomery_deinit(void *a) +{ + XFREE(a); +} + +static int exptmod(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + LTC_ARGCHK(d != NULL); + return mpi_to_ltc_error(mp_exptmod(a,b,c,d)); +} + +static int isprime(void *a, int *b) +{ + int err; + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + err = mpi_to_ltc_error(mp_prime_is_prime(a, 8, b)); + *b = (*b == MP_YES) ? LTC_MP_YES : LTC_MP_NO; + return err; +} + +const ltc_math_descriptor ltm_desc = { + + "LibTomMath", + (int)DIGIT_BIT, + + &init, + &init_copy, + &deinit, + + &neg, + ©, + + &set_int, + &get_int, + &get_digit, + &get_digit_count, + &compare, + &compare_d, + &count_bits, + &count_lsb_bits, + &twoexpt, + + &read_radix, + &write_radix, + &unsigned_size, + &unsigned_write, + &unsigned_read, + + &add, + &addi, + &sub, + &subi, + &mul, + &muli, + &sqr, + ÷, + &div_2, + &modi, + &gcd, + &lcm, + + &mulmod, + &sqrmod, + &invmod, + + &montgomery_setup, + &montgomery_normalization, + &montgomery_reduce, + &montgomery_deinit, + + &exptmod, + &isprime, + +#ifdef MECC +#ifdef MECC_FP + <c_ecc_fp_mulmod, +#else + <c_ecc_mulmod, +#endif + <c_ecc_projective_add_point, + <c_ecc_projective_dbl_point, + <c_ecc_map, +#ifdef LTC_ECC_SHAMIR +#ifdef MECC_FP + <c_ecc_fp_mul2add, +#else + <c_ecc_mul2add, +#endif /* MECC_FP */ +#else + NULL, +#endif /* LTC_ECC_SHAMIR */ +#else + NULL, NULL, NULL, NULL, NULL, +#endif /* MECC */ + +#ifdef MRSA + &rsa_make_key, + &rsa_exptmod, +#else + NULL, NULL +#endif +}; + + +#endif + +/* $Source: /cvs/libtom/libtomcrypt/src/math/ltm_desc.c,v $ */ +/* $Revision: 1.29 $ */ +/* $Date: 2006/12/03 00:39:56 $ */ diff --git a/libtomcrypt/src/math/multi.c b/libtomcrypt/src/math/multi.c new file mode 100644 index 0000000..8ee4d79 --- /dev/null +++ b/libtomcrypt/src/math/multi.c @@ -0,0 +1,61 @@ +/* LibTomCrypt, modular cryptographic library -- Tom St Denis + * + * LibTomCrypt is a library that provides various cryptographic + * algorithms in a highly modular and flexible manner. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com + */ +#include "tomcrypt.h" + +#ifdef MPI +#include <stdarg.h> + +int ltc_init_multi(void **a, ...) +{ + void **cur = a; + int np = 0; + va_list args; + + va_start(args, a); + while (cur != NULL) { + if (mp_init(cur) != CRYPT_OK) { + /* failed */ + va_list clean_list; + + va_start(clean_list, a); + cur = a; + while (np--) { + mp_clear(*cur); + cur = va_arg(clean_list, void**); + } + va_end(clean_list); + return CRYPT_MEM; + } + ++np; + cur = va_arg(args, void**); + } + va_end(args); + return CRYPT_OK; +} + +void ltc_deinit_multi(void *a, ...) +{ + void *cur = a; + va_list args; + + va_start(args, a); + while (cur != NULL) { + mp_clear(cur); + cur = va_arg(args, void *); + } + va_end(args); +} + +#endif + +/* $Source: /cvs/libtom/libtomcrypt/src/math/multi.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/03/31 14:15:35 $ */ diff --git a/libtomcrypt/src/math/rand_prime.c b/libtomcrypt/src/math/rand_prime.c new file mode 100644 index 0000000..05477fe --- /dev/null +++ b/libtomcrypt/src/math/rand_prime.c @@ -0,0 +1,87 @@ +/* LibTomCrypt, modular cryptographic library -- Tom St Denis + * + * LibTomCrypt is a library that provides various cryptographic + * algorithms in a highly modular and flexible manner. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com + */ +#include "tomcrypt.h" + +/** + @file rand_prime.c + Generate a random prime, Tom St Denis +*/ + +#define USE_BBS 1 + +int rand_prime(void *N, long len, prng_state *prng, int wprng) +{ + int err, res, type; + unsigned char *buf; + + LTC_ARGCHK(N != NULL); + + /* get type */ + if (len < 0) { + type = USE_BBS; + len = -len; + } else { + type = 0; + } + + /* allow sizes between 2 and 512 bytes for a prime size */ + if (len < 2 || len > 512) { + return CRYPT_INVALID_PRIME_SIZE; + } + + /* valid PRNG? Better be! */ + if ((err = prng_is_valid(wprng)) != CRYPT_OK) { + return err; + } + + /* allocate buffer to work with */ + buf = XCALLOC(1, len); + if (buf == NULL) { + return CRYPT_MEM; + } + + do { + /* generate value */ + if (prng_descriptor[wprng].read(buf, len, prng) != (unsigned long)len) { + XFREE(buf); + return CRYPT_ERROR_READPRNG; + } + + /* munge bits */ + buf[0] |= 0x80 | 0x40; + buf[len-1] |= 0x01 | ((type & USE_BBS) ? 0x02 : 0x00); + + /* load value */ + if ((err = mp_read_unsigned_bin(N, buf, len)) != CRYPT_OK) { + XFREE(buf); + return err; + } + + /* test */ + if ((err = mp_prime_is_prime(N, 8, &res)) != CRYPT_OK) { + XFREE(buf); + return err; + } + } while (res == LTC_MP_NO); + +#ifdef LTC_CLEAN_STACK + zeromem(buf, len); +#endif + + XFREE(buf); + return CRYPT_OK; +} + + + +/* $Source: /cvs/libtom/libtomcrypt/src/math/rand_prime.c,v $ */ +/* $Revision: 1.6 $ */ +/* $Date: 2006/03/31 14:15:35 $ */ diff --git a/libtomcrypt/src/math/tfm_desc.c b/libtomcrypt/src/math/tfm_desc.c new file mode 100644 index 0000000..023756d --- /dev/null +++ b/libtomcrypt/src/math/tfm_desc.c @@ -0,0 +1,777 @@ +/* LibTomCrypt, modular cryptographic library -- Tom St Denis + * + * LibTomCrypt is a library that provides various cryptographic + * algorithms in a highly modular and flexible manner. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com + */ + +#define DESC_DEF_ONLY +#include "tomcrypt.h" + +#ifdef TFM_DESC + +#include <tfm.h> + +static const struct { + int tfm_code, ltc_code; +} tfm_to_ltc_codes[] = { + { FP_OKAY , CRYPT_OK}, + { FP_MEM , CRYPT_MEM}, + { FP_VAL , CRYPT_INVALID_ARG}, +}; + +/** + Convert a tfm error to a LTC error (Possibly the most powerful function ever! Oh wait... no) + @param err The error to convert + @return The equivalent LTC error code or CRYPT_ERROR if none found +*/ +static int tfm_to_ltc_error(int err) +{ + int x; + + for (x = 0; x < (int)(sizeof(tfm_to_ltc_codes)/sizeof(tfm_to_ltc_codes[0])); x++) { + if (err == tfm_to_ltc_codes[x].tfm_code) { + return tfm_to_ltc_codes[x].ltc_code; + } + } + return CRYPT_ERROR; +} + +static int init(void **a) +{ + LTC_ARGCHK(a != NULL); + + *a = XCALLOC(1, sizeof(fp_int)); + if (*a == NULL) { + return CRYPT_MEM; + } + fp_init(*a); + return CRYPT_OK; +} + +static void deinit(void *a) +{ + LTC_ARGCHKVD(a != NULL); + XFREE(a); +} + +static int neg(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + fp_neg(((fp_int*)a), ((fp_int*)b)); + return CRYPT_OK; +} + +static int copy(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + fp_copy(a, b); + return CRYPT_OK; +} + +static int init_copy(void **a, void *b) +{ + if (init(a) != CRYPT_OK) { + return CRYPT_MEM; + } + return copy(b, *a); +} + +/* ---- trivial ---- */ +static int set_int(void *a, unsigned long b) +{ + LTC_ARGCHK(a != NULL); + fp_set(a, b); + return CRYPT_OK; +} + +static unsigned long get_int(void *a) +{ + fp_int *A; + LTC_ARGCHK(a != NULL); + A = a; + return A->used > 0 ? A->dp[0] : 0; +} + +static unsigned long get_digit(void *a, int n) +{ + fp_int *A; + LTC_ARGCHK(a != NULL); + A = a; + return (n >= A->used || n < 0) ? 0 : A->dp[n]; +} + +static int get_digit_count(void *a) +{ + fp_int *A; + LTC_ARGCHK(a != NULL); + A = a; + return A->used; +} + +static int compare(void *a, void *b) +{ + int ret; + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + ret = fp_cmp(a, b); + switch (ret) { + case FP_LT: return LTC_MP_LT; + case FP_EQ: return LTC_MP_EQ; + case FP_GT: return LTC_MP_GT; + } + return 0; +} + +static int compare_d(void *a, unsigned long b) +{ + int ret; + LTC_ARGCHK(a != NULL); + ret = fp_cmp_d(a, b); + switch (ret) { + case FP_LT: return LTC_MP_LT; + case FP_EQ: return LTC_MP_EQ; + case FP_GT: return LTC_MP_GT; + } + return 0; +} + +static int count_bits(void *a) +{ + LTC_ARGCHK(a != NULL); + return fp_count_bits(a); +} + +static int count_lsb_bits(void *a) +{ + LTC_ARGCHK(a != NULL); + return fp_cnt_lsb(a); +} + +static int twoexpt(void *a, int n) +{ + LTC_ARGCHK(a != NULL); + fp_2expt(a, n); + return CRYPT_OK; +} + +/* ---- conversions ---- */ + +/* read ascii string */ +static int read_radix(void *a, const char *b, int radix) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return tfm_to_ltc_error(fp_read_radix(a, (char *)b, radix)); +} + +/* write one */ +static int write_radix(void *a, char *b, int radix) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return tfm_to_ltc_error(fp_toradix(a, b, radix)); +} + +/* get size as unsigned char string */ +static unsigned long unsigned_size(void *a) +{ + LTC_ARGCHK(a != NULL); + return fp_unsigned_bin_size(a); +} + +/* store */ +static int unsigned_write(void *a, unsigned char *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + fp_to_unsigned_bin(a, b); + return CRYPT_OK; +} + +/* read */ +static int unsigned_read(void *a, unsigned char *b, unsigned long len) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + fp_read_unsigned_bin(a, b, len); + return CRYPT_OK; +} + +/* add */ +static int add(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + fp_add(a, b, c); + return CRYPT_OK; +} + +static int addi(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + fp_add_d(a, b, c); + return CRYPT_OK; +} + +/* sub */ +static int sub(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + fp_sub(a, b, c); + return CRYPT_OK; +} + +static int subi(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + fp_sub_d(a, b, c); + return CRYPT_OK; +} + +/* mul */ +static int mul(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + fp_mul(a, b, c); + return CRYPT_OK; +} + +static int muli(void *a, unsigned long b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + fp_mul_d(a, b, c); + return CRYPT_OK; +} + +/* sqr */ +static int sqr(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + fp_sqr(a, b); + return CRYPT_OK; +} + +/* div */ +static int divide(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + return tfm_to_ltc_error(fp_div(a, b, c, d)); +} + +static int div_2(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + fp_div_2(a, b); + return CRYPT_OK; +} + +/* modi */ +static int modi(void *a, unsigned long b, unsigned long *c) +{ + fp_digit tmp; + int err; + + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(c != NULL); + + if ((err = tfm_to_ltc_error(fp_mod_d(a, b, &tmp))) != CRYPT_OK) { + return err; + } + *c = tmp; + return CRYPT_OK; +} + +/* gcd */ +static int gcd(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + fp_gcd(a, b, c); + return CRYPT_OK; +} + +/* lcm */ +static int lcm(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + fp_lcm(a, b, c); + return CRYPT_OK; +} + +static int mulmod(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + LTC_ARGCHK(d != NULL); + return tfm_to_ltc_error(fp_mulmod(a,b,c,d)); +} + +static int sqrmod(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return tfm_to_ltc_error(fp_sqrmod(a,b,c)); +} + +/* invmod */ +static int invmod(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + return tfm_to_ltc_error(fp_invmod(a, b, c)); +} + +/* setup */ +static int montgomery_setup(void *a, void **b) +{ + int err; + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + *b = XCALLOC(1, sizeof(fp_digit)); + if (*b == NULL) { + return CRYPT_MEM; + } + if ((err = tfm_to_ltc_error(fp_montgomery_setup(a, (fp_digit *)*b))) != CRYPT_OK) { + XFREE(*b); + } + return err; +} + +/* get normalization value */ +static int montgomery_normalization(void *a, void *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + fp_montgomery_calc_normalization(a, b); + return CRYPT_OK; +} + +/* reduce */ +static int montgomery_reduce(void *a, void *b, void *c) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + fp_montgomery_reduce(a, b, *((fp_digit *)c)); + return CRYPT_OK; +} + +/* clean up */ +static void montgomery_deinit(void *a) +{ + XFREE(a); +} + +static int exptmod(void *a, void *b, void *c, void *d) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + LTC_ARGCHK(c != NULL); + LTC_ARGCHK(d != NULL); + return tfm_to_ltc_error(fp_exptmod(a,b,c,d)); +} + +static int isprime(void *a, int *b) +{ + LTC_ARGCHK(a != NULL); + LTC_ARGCHK(b != NULL); + *b = (fp_isprime(a) == FP_YES) ? LTC_MP_YES : LTC_MP_NO; + return CRYPT_OK; +} + +#if defined(MECC) && defined(MECC_ACCEL) + +static int tfm_ecc_projective_dbl_point(ecc_point *P, ecc_point *R, void *modulus, void *Mp) +{ + fp_int t1, t2; + fp_digit mp; + + LTC_ARGCHK(P != NULL); + LTC_ARGCHK(R != NULL); + LTC_ARGCHK(modulus != NULL); + LTC_ARGCHK(Mp != NULL); + + mp = *((fp_digit*)Mp); + + fp_init(&t1); + fp_init(&t2); + + if (P != R) { + fp_copy(P->x, R->x); + fp_copy(P->y, R->y); + fp_copy(P->z, R->z); + } + + /* t1 = Z * Z */ + fp_sqr(R->z, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + /* Z = Y * Z */ + fp_mul(R->z, R->y, R->z); + fp_montgomery_reduce(R->z, modulus, mp); + /* Z = 2Z */ + fp_add(R->z, R->z, R->z); + if (fp_cmp(R->z, modulus) != FP_LT) { + fp_sub(R->z, modulus, R->z); + } + + /* &t2 = X - T1 */ + fp_sub(R->x, &t1, &t2); + if (fp_cmp_d(&t2, 0) == FP_LT) { + fp_add(&t2, modulus, &t2); + } + /* T1 = X + T1 */ + fp_add(&t1, R->x, &t1); + if (fp_cmp(&t1, modulus) != FP_LT) { + fp_sub(&t1, modulus, &t1); + } + /* T2 = T1 * T2 */ + fp_mul(&t1, &t2, &t2); + fp_montgomery_reduce(&t2, modulus, mp); + /* T1 = 2T2 */ + fp_add(&t2, &t2, &t1); + if (fp_cmp(&t1, modulus) != FP_LT) { + fp_sub(&t1, modulus, &t1); + } + /* T1 = T1 + T2 */ + fp_add(&t1, &t2, &t1); + if (fp_cmp(&t1, modulus) != FP_LT) { + fp_sub(&t1, modulus, &t1); + } + + /* Y = 2Y */ + fp_add(R->y, R->y, R->y); + if (fp_cmp(R->y, modulus) != FP_LT) { + fp_sub(R->y, modulus, R->y); + } + /* Y = Y * Y */ + fp_sqr(R->y, R->y); + fp_montgomery_reduce(R->y, modulus, mp); + /* T2 = Y * Y */ + fp_sqr(R->y, &t2); + fp_montgomery_reduce(&t2, modulus, mp); + /* T2 = T2/2 */ + if (fp_isodd(&t2)) { + fp_add(&t2, modulus, &t2); + } + fp_div_2(&t2, &t2); + /* Y = Y * X */ + fp_mul(R->y, R->x, R->y); + fp_montgomery_reduce(R->y, modulus, mp); + + /* X = T1 * T1 */ + fp_sqr(&t1, R->x); + fp_montgomery_reduce(R->x, modulus, mp); + /* X = X - Y */ + fp_sub(R->x, R->y, R->x); + if (fp_cmp_d(R->x, 0) == FP_LT) { + fp_add(R->x, modulus, R->x); + } + /* X = X - Y */ + fp_sub(R->x, R->y, R->x); + if (fp_cmp_d(R->x, 0) == FP_LT) { + fp_add(R->x, modulus, R->x); + } + + /* Y = Y - X */ + fp_sub(R->y, R->x, R->y); + if (fp_cmp_d(R->y, 0) == FP_LT) { + fp_add(R->y, modulus, R->y); + } + /* Y = Y * T1 */ + fp_mul(R->y, &t1, R->y); + fp_montgomery_reduce(R->y, modulus, mp); + /* Y = Y - T2 */ + fp_sub(R->y, &t2, R->y); + if (fp_cmp_d(R->y, 0) == FP_LT) { + fp_add(R->y, modulus, R->y); + } + + return CRYPT_OK; +} + +/** + Add two ECC points + @param P The point to add + @param Q The point to add + @param R [out] The destination of the double + @param modulus The modulus of the field the ECC curve is in + @param mp The "b" value from montgomery_setup() + @return CRYPT_OK on success +*/ +static int tfm_ecc_projective_add_point(ecc_point *P, ecc_point *Q, ecc_point *R, void *modulus, void *Mp) +{ + fp_int t1, t2, x, y, z; + fp_digit mp; + + LTC_ARGCHK(P != NULL); + LTC_ARGCHK(Q != NULL); + LTC_ARGCHK(R != NULL); + LTC_ARGCHK(modulus != NULL); + LTC_ARGCHK(Mp != NULL); + + mp = *((fp_digit*)Mp); + + fp_init(&t1); + fp_init(&t2); + fp_init(&x); + fp_init(&y); + fp_init(&z); + + /* should we dbl instead? */ + fp_sub(modulus, Q->y, &t1); + if ( (fp_cmp(P->x, Q->x) == FP_EQ) && + (Q->z != NULL && fp_cmp(P->z, Q->z) == FP_EQ) && + (fp_cmp(P->y, Q->y) == FP_EQ || fp_cmp(P->y, &t1) == FP_EQ)) { + return tfm_ecc_projective_dbl_point(P, R, modulus, Mp); + } + + fp_copy(P->x, &x); + fp_copy(P->y, &y); + fp_copy(P->z, &z); + + /* if Z is one then these are no-operations */ + if (Q->z != NULL) { + /* T1 = Z' * Z' */ + fp_sqr(Q->z, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + /* X = X * T1 */ + fp_mul(&t1, &x, &x); + fp_montgomery_reduce(&x, modulus, mp); + /* T1 = Z' * T1 */ + fp_mul(Q->z, &t1, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + /* Y = Y * T1 */ + fp_mul(&t1, &y, &y); + fp_montgomery_reduce(&y, modulus, mp); + } + + /* T1 = Z*Z */ + fp_sqr(&z, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + /* T2 = X' * T1 */ + fp_mul(Q->x, &t1, &t2); + fp_montgomery_reduce(&t2, modulus, mp); + /* T1 = Z * T1 */ + fp_mul(&z, &t1, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + /* T1 = Y' * T1 */ + fp_mul(Q->y, &t1, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + + /* Y = Y - T1 */ + fp_sub(&y, &t1, &y); + if (fp_cmp_d(&y, 0) == FP_LT) { + fp_add(&y, modulus, &y); + } + /* T1 = 2T1 */ + fp_add(&t1, &t1, &t1); + if (fp_cmp(&t1, modulus) != FP_LT) { + fp_sub(&t1, modulus, &t1); + } + /* T1 = Y + T1 */ + fp_add(&t1, &y, &t1); + if (fp_cmp(&t1, modulus) != FP_LT) { + fp_sub(&t1, modulus, &t1); + } + /* X = X - T2 */ + fp_sub(&x, &t2, &x); + if (fp_cmp_d(&x, 0) == FP_LT) { + fp_add(&x, modulus, &x); + } + /* T2 = 2T2 */ + fp_add(&t2, &t2, &t2); + if (fp_cmp(&t2, modulus) != FP_LT) { + fp_sub(&t2, modulus, &t2); + } + /* T2 = X + T2 */ + fp_add(&t2, &x, &t2); + if (fp_cmp(&t2, modulus) != FP_LT) { + fp_sub(&t2, modulus, &t2); + } + + /* if Z' != 1 */ + if (Q->z != NULL) { + /* Z = Z * Z' */ + fp_mul(&z, Q->z, &z); + fp_montgomery_reduce(&z, modulus, mp); + } + + /* Z = Z * X */ + fp_mul(&z, &x, &z); + fp_montgomery_reduce(&z, modulus, mp); + + /* T1 = T1 * X */ + fp_mul(&t1, &x, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + /* X = X * X */ + fp_sqr(&x, &x); + fp_montgomery_reduce(&x, modulus, mp); + /* T2 = T2 * x */ + fp_mul(&t2, &x, &t2); + fp_montgomery_reduce(&t2, modulus, mp); + /* T1 = T1 * X */ + fp_mul(&t1, &x, &t1); + fp_montgomery_reduce(&t1, modulus, mp); + + /* X = Y*Y */ + fp_sqr(&y, &x); + fp_montgomery_reduce(&x, modulus, mp); + /* X = X - T2 */ + fp_sub(&x, &t2, &x); + if (fp_cmp_d(&x, 0) == FP_LT) { + fp_add(&x, modulus, &x); + } + + /* T2 = T2 - X */ + fp_sub(&t2, &x, &t2); + if (fp_cmp_d(&t2, 0) == FP_LT) { + fp_add(&t2, modulus, &t2); + } + /* T2 = T2 - X */ + fp_sub(&t2, &x, &t2); + if (fp_cmp_d(&t2, 0) == FP_LT) { + fp_add(&t2, modulus, &t2); + } + /* T2 = T2 * Y */ + fp_mul(&t2, &y, &t2); + fp_montgomery_reduce(&t2, modulus, mp); + /* Y = T2 - T1 */ + fp_sub(&t2, &t1, &y); + if (fp_cmp_d(&y, 0) == FP_LT) { + fp_add(&y, modulus, &y); + } + /* Y = Y/2 */ + if (fp_isodd(&y)) { + fp_add(&y, modulus, &y); + } + fp_div_2(&y, &y); + + fp_copy(&x, R->x); + fp_copy(&y, R->y); + fp_copy(&z, R->z); + + return CRYPT_OK; +} + + +#endif + +const ltc_math_descriptor tfm_desc = { + + "TomsFastMath", + (int)DIGIT_BIT, + + &init, + &init_copy, + &deinit, + + &neg, + ©, + + &set_int, + &get_int, + &get_digit, + &get_digit_count, + &compare, + &compare_d, + &count_bits, + &count_lsb_bits, + &twoexpt, + + &read_radix, + &write_radix, + &unsigned_size, + &unsigned_write, + &unsigned_read, + + &add, + &addi, + &sub, + &subi, + &mul, + &muli, + &sqr, + ÷, + &div_2, + &modi, + &gcd, + &lcm, + + &mulmod, + &sqrmod, + &invmod, + + &montgomery_setup, + &montgomery_normalization, + &montgomery_reduce, + &montgomery_deinit, + + &exptmod, + &isprime, + +#ifdef MECC +#ifdef MECC_FP + <c_ecc_fp_mulmod, +#else + <c_ecc_mulmod, +#endif /* MECC_FP */ +#ifdef MECC_ACCEL + &tfm_ecc_projective_add_point, + &tfm_ecc_projective_dbl_point, +#else + <c_ecc_projective_add_point, + <c_ecc_projective_dbl_point, +#endif /* MECC_ACCEL */ + <c_ecc_map, +#ifdef LTC_ECC_SHAMIR +#ifdef MECC_FP + <c_ecc_fp_mul2add, +#else + <c_ecc_mul2add, +#endif /* MECC_FP */ +#else + NULL, +#endif /* LTC_ECC_SHAMIR */ +#else + NULL, NULL, NULL, NULL, NULL, +#endif /* MECC */ + +#ifdef MRSA + &rsa_make_key, + &rsa_exptmod, +#else + NULL, NULL +#endif + +}; + + +#endif + +/* $Source: /cvs/libtom/libtomcrypt/src/math/tfm_desc.c,v $ */ +/* $Revision: 1.26 $ */ +/* $Date: 2006/12/03 00:39:56 $ */ |