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use strlcpy & strlcat (#74) * refactor checkpubkeyperms() with safe BSD functions fix gcc8 warnings ``` svr-authpubkey.c: In function 'checkpubkeyperms': svr-authpubkey.c:427:2: warning: 'strncat' specified bound 5 equals source length [-Wstringop-overflow=] strncat(filename, "/.ssh", 5); /* strlen("/.ssh") == 5 */ ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~ svr-authpubkey.c:433:2: warning: 'strncat' specified bound 16 equals source length [-Wstringop-overflow=] strncat(filename, "/authorized_keys", 16); ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ``` see https://www.sudo.ws/todd/papers/strlcpy.html * restore strlcpy in xstrdup see original https://cvsweb.openbsd.org/cgi-bin/cvsweb/src/usr.bin/ssh/xmalloc.c?rev=1.16
author François Perrad <francois.perrad@gadz.org>
date Wed, 20 Mar 2019 15:09:19 +0100
parents 6dba84798cd5
children
line wrap: on
line source

/* 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.
 */
#include "tomcrypt.h"

/**
  @file ltc_ecc_fp_mulmod.c
  ECC Crypto, Tom St Denis
*/

#if defined(LTC_MECC) && defined(LTC_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 */
   int        lock;           /* flag to indicate cache eviction permitted (0) or not (1) */
} 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 },
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   { 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, return -1 if no hole found */
static int _find_hole(void)
{
   unsigned x;
   int      y, z;
   for (z = -1, y = INT_MAX, x = 0; x < FP_ENTRIES; x++) {
       if (fp_cache[x].lru_count < y && fp_cache[x].lock == 0) {
          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 (z >= 0 && 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
  Computes kA*A + kB*B = C using Shamir's Trick
  @param A        First point to multiply
  @param kA       What to multiple A by
  @param B        Second point to multiply
  @param kB       What to multiple B by
  @param C        [out] Destination point (can overlap with A or B)
  @param modulus  Modulus for curve
  @return CRYPT_OK on success
*/
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(&ltc_ecc_fp_lock);
      /* find point */
      idx1 = _find_base(A);

      /* no entry? */
      if (idx1 == -1) {
         /* find hole and add it */
         if ((idx1 = _find_hole()) >= 0) {
            if ((err = _add_entry(idx1, A)) != CRYPT_OK) {
               goto LBL_ERR;
            }
         }
      }
      if (idx1 != -1) {
         /* increment LRU */
         ++(fp_cache[idx1].lru_count);
      }

      /* find point */
      idx2 = _find_base(B);

      /* no entry? */
      if (idx2 == -1) {
         /* find hole and add it */
         if ((idx2 = _find_hole()) >= 0) {
            if ((err = _add_entry(idx2, B)) != CRYPT_OK) {
               goto LBL_ERR;
            }
         }
      }
      if (idx2 != -1) {
         /* increment LRU */
         ++(fp_cache[idx2].lru_count);
      }

      /* if it's 2 build the LUT, if it's higher just use the LUT */
      if (idx1 >= 0 && 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 (idx2 >= 0 && 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 (idx1 >=0 && idx2 >= 0 && 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(&ltc_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(&ltc_ecc_fp_lock);
      /* find point */
      idx = _find_base(G);

      /* no entry? */
      if (idx == -1) {
         /* find hole and add it */
         idx = _find_hole();

         if (idx >= 0) {
            if ((err = _add_entry(idx, G)) != CRYPT_OK) {
               goto LBL_ERR;
            }
         }
      }
      if (idx != -1) {
         /* increment LRU */
         ++(fp_cache[idx].lru_count);
      }


      /* if it's 2 build the LUT, if it's higher just use the LUT */
      if (idx >= 0 && 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 (idx >= 0 && 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(&ltc_ecc_fp_lock);
    if (mp != NULL) {
       mp_montgomery_free(mp);
    }
    if (mu != NULL) {
       mp_clear(mu);
    }
    return err;
}

/* helper function for freeing the cache ... must be called with the cache mutex locked */
static void _ltc_ecc_fp_free_cache(void)
{
   unsigned x, y;
   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;
         fp_cache[x].lock = 0;
      }
   }
}

/** Free the Fixed Point cache */
void ltc_ecc_fp_free(void)
{
   LTC_MUTEX_LOCK(&ltc_ecc_fp_lock);
   _ltc_ecc_fp_free_cache();
   LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
}

/** Add a point to the cache and initialize the LUT
  @param g        The point to add
  @param modulus  Modulus for curve
  @param lock     Flag to indicate if this entry should be locked into the cache or not
  @return CRYPT_OK on success
*/
int
ltc_ecc_fp_add_point(ecc_point *g, void *modulus, int lock)
{
   int idx;
   int err;
   void *mp = NULL;
   void *mu = NULL;

   LTC_MUTEX_LOCK(&ltc_ecc_fp_lock);
   if ((idx = _find_base(g)) >= 0) {
      /* it is already in the cache ... just check that the LUT is initialized */
      if(fp_cache[idx].lru_count >= 2) {
         LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
         return CRYPT_OK;
      }
   }

   if(idx == -1 && (idx = _find_hole()) == -1) {
      err = CRYPT_BUFFER_OVERFLOW;
      goto LBL_ERR;
   }
   if ((err = _add_entry(idx, g)) != CRYPT_OK) {
      goto LBL_ERR;
   }
   /* 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;
   }
   fp_cache[idx].lru_count = 2;
   fp_cache[idx].lock = lock;
LBL_ERR:
   LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
   if (mp != NULL) {
      mp_montgomery_free(mp);
   }
   if (mu != NULL) {
      mp_clear(mu);
   }
   return err;
}

/** Prevent/permit the FP cache from being updated
    @param flag        If flag is 0, remove cache lock (unlock), otherwise lock it
*/
void ltc_ecc_fp_tablelock(int lock)
{
   int i;

   LTC_MUTEX_LOCK(&ltc_ecc_fp_lock);
   for (i = 0; i < FP_ENTRIES; i++) {
      fp_cache[i].lock = lock;
   }
   LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
}

/** Export the current cache as a binary packet
    @param out      [out] pointer to malloc'ed space containing the packet
    @param outlen   [out] size of exported packet
    @return CRYPT_OK if successful
*/
int ltc_ecc_fp_save_state(unsigned char **out, unsigned long *outlen)
{
   ltc_asn1_list *cache_entry;
   unsigned int   i, j, k;
   unsigned long  fp_entries, fp_lut, num_entries;
   int            err;

   LTC_ARGCHK(out    != NULL);
   LTC_ARGCHK(outlen != NULL);

   fp_entries  = FP_ENTRIES;
   fp_lut      = FP_LUT;
   num_entries = 0;

   LTC_MUTEX_LOCK(&ltc_ecc_fp_lock);
   /*
    * build the list;
      Cache DEFINITIONS ::=
      BEGIN
       CacheDump ::= SEQUENCE {
         numEntries    SHORTINTEGER,
         maxEntries    SHORTINTEGER,
         numLUT        SHORTINTEGER,
         cache         SEQUENCE OF INTEGER
       }
      END
    *
    */
   /*
    * The cache itself is a point (3 INTEGERS),
    * the LUT as pairs of INTEGERS (2 * 1<<FP_LUT),
    * and the mu INTEGER
    */
   cache_entry = XCALLOC(FP_ENTRIES*(2*(1U<<FP_LUT)+4)+3, sizeof(ltc_asn1_list));
   if (cache_entry == NULL)
      return CRYPT_MEM;
   j = 1;   /* handle the zero'th element later */

   LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_SHORT_INTEGER, &fp_entries, 1);
   LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_SHORT_INTEGER, &fp_lut, 1);

   for (i = 0; i < FP_ENTRIES; i++) {
      /*
       * do not save empty entries, or entries that have not yet had the lut built
       */
      if (fp_cache[i].g == NULL || fp_cache[i].lru_count < 2) {
         continue;
      }
      num_entries++;
      LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].g->x, 1);
      LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].g->y, 1);
      LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].g->z, 1);
      for (k = 0; k < (1U<<FP_LUT); k++) {
         LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].LUT[k]->x, 1);
         LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].LUT[k]->y, 1);
      }
      LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_INTEGER, fp_cache[i].mu, 1);
   }
   LTC_SET_ASN1(cache_entry, j++, LTC_ASN1_EOL, 0, 0);

   LTC_SET_ASN1(cache_entry, 0, LTC_ASN1_SHORT_INTEGER, &num_entries, 1);

   if ((err = der_length_sequence(cache_entry, j, outlen)) != CRYPT_OK) {
      goto save_err;
   }
   if ((*out = XMALLOC(*outlen)) == NULL) {
      err = CRYPT_MEM;
      goto save_err;
   }
   err = der_encode_sequence(cache_entry, j, *out, outlen);
save_err:
   XFREE(cache_entry);
   LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
   return err;
}

/** Import a binary packet into the current cache
    @param in      [in] pointer to packet
    @param inlen   [in] size of packet (bytes)
    @return CRYPT_OK if successful
*/
int ltc_ecc_fp_restore_state(unsigned char *in, unsigned long inlen)
{
   int            err;
   ltc_asn1_list *asn1_list;
   unsigned long  num_entries, fp_entries, fp_lut;
   unsigned long  i, j;
   unsigned int   x;

   LTC_ARGCHK(in != NULL);
   if (inlen == 0) {
      return CRYPT_INVALID_ARG;
   }

   /* zero indecies */
   i         = 0;
   j         = 0;
   asn1_list = NULL;

   LTC_MUTEX_LOCK(&ltc_ecc_fp_lock);
   /*
    * start with an empty cache
    */
   _ltc_ecc_fp_free_cache();

   /*
    * decode the input packet: It consists of a sequence with a few
    * integers (including the FP_ENTRIES and FP_LUT sizes), followed by a
    * SEQUENCE which is the cache itself.
    *
    * use standard decoding for the first part, then flexible for the second
    */
   if((err = der_decode_sequence_multi(in, inlen,
                                       LTC_ASN1_SHORT_INTEGER, 1, &num_entries,
                                       LTC_ASN1_SHORT_INTEGER, 1, &fp_entries,
                                       LTC_ASN1_SHORT_INTEGER, 1, &fp_lut,
                                       LTC_ASN1_EOL,           0, 0)) != CRYPT_OK) {
      goto ERR_OUT;
   }
   if (fp_entries != FP_ENTRIES || fp_lut != FP_LUT || num_entries > fp_entries) {
      err = CRYPT_INVALID_PACKET;
      goto ERR_OUT;
   }
   if ((asn1_list = XCALLOC(3+num_entries*(4+2*(1<<FP_LUT))+1, sizeof(ltc_asn1_list))) == NULL) {
      err = CRYPT_MEM;
      goto ERR_OUT;
   }
   j = 0;
   LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_SHORT_INTEGER, &num_entries, 1);
   LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_SHORT_INTEGER, &fp_entries, 1);
   LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_SHORT_INTEGER, &fp_lut, 1);
   for (i = 0; i < num_entries; i++) {
      if((fp_cache[i].g = ltc_ecc_new_point()) == NULL) {
         err = CRYPT_MEM;
         goto ERR_OUT;
      }
      LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].g->x, 1);
      LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].g->y, 1);
      LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].g->z, 1);
      for (x = 0; x < (1U<<FP_LUT); x++) {
         /* since we don't store z in the cache, don't use ltc_ecc_new_point()
          * (which allocates space for z, only to have to free it later) */
         ecc_point *p = XCALLOC(1, sizeof(*p));

         if (p == NULL) {
            err = CRYPT_MEM;
            goto ERR_OUT;
         }
         fp_cache[i].LUT[x] = p;
         if ((err = mp_init_multi(&p->x, &p->y, NULL)) != CRYPT_OK) {
            goto ERR_OUT;
         }
         p->z = NULL;
         LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, p->x, 1);
         LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, p->y, 1);
      }
      if((err = mp_init(&fp_cache[i].mu)) != CRYPT_OK) {
         goto ERR_OUT;
      }
      LTC_SET_ASN1(asn1_list, j++, LTC_ASN1_INTEGER, fp_cache[i].mu, 1);
      fp_cache[i].lru_count = 3;
      fp_cache[i].lock = 1;
   }

   if ((err = der_decode_sequence(in, inlen, asn1_list, j)) != CRYPT_OK) {
      goto ERR_OUT;
   }
   XFREE(asn1_list);
   LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
   return CRYPT_OK;
ERR_OUT:
   if(asn1_list)
      XFREE(asn1_list);
   _ltc_ecc_fp_free_cache();
   LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
   return err;
}

#endif


/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */