/*
* The ManaPlus Client
* Copyright (C) 2009 The Mana World Development Team
* Copyright (C) 2009-2010 The Mana Developers
* Copyright (C) 2011-2015 The ManaPlus Developers
*
* This file is part of The ManaPlus Client.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef UTILS_MATHUTILS_H
#define UTILS_MATHUTILS_H
#include <string>
#include <cmath>
#include "localconsts.h"
static constexpr const uint16_t crc_table[256] =
{
0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50a5, 0x60c6, 0x70e7,
0x8108, 0x9129, 0xa14a, 0xb16b, 0xc18c, 0xd1ad, 0xe1ce, 0xf1ef,
0x1231, 0x0210, 0x3273, 0x2252, 0x52b5, 0x4294, 0x72f7, 0x62d6,
0x9339, 0x8318, 0xb37b, 0xa35a, 0xd3bd, 0xc39c, 0xf3ff, 0xe3de,
0x2462, 0x3443, 0x0420, 0x1401, 0x64e6, 0x74c7, 0x44a4, 0x5485,
0xa56a, 0xb54b, 0x8528, 0x9509, 0xe5ee, 0xf5cf, 0xc5ac, 0xd58d,
0x3653, 0x2672, 0x1611, 0x0630, 0x76d7, 0x66f6, 0x5695, 0x46b4,
0xb75b, 0xa77a, 0x9719, 0x8738, 0xf7df, 0xe7fe, 0xd79d, 0xc7bc,
0x48c4, 0x58e5, 0x6886, 0x78a7, 0x0840, 0x1861, 0x2802, 0x3823,
0xc9cc, 0xd9ed, 0xe98e, 0xf9af, 0x8948, 0x9969, 0xa90a, 0xb92b,
0x5af5, 0x4ad4, 0x7ab7, 0x6a96, 0x1a71, 0x0a50, 0x3a33, 0x2a12,
0xdbfd, 0xcbdc, 0xfbbf, 0xeb9e, 0x9b79, 0x8b58, 0xbb3b, 0xab1a,
0x6ca6, 0x7c87, 0x4ce4, 0x5cc5, 0x2c22, 0x3c03, 0x0c60, 0x1c41,
0xedae, 0xfd8f, 0xcdec, 0xddcd, 0xad2a, 0xbd0b, 0x8d68, 0x9d49,
0x7e97, 0x6eb6, 0x5ed5, 0x4ef4, 0x3e13, 0x2e32, 0x1e51, 0x0e70,
0xff9f, 0xefbe, 0xdfdd, 0xcffc, 0xbf1b, 0xaf3a, 0x9f59, 0x8f78,
0x9188, 0x81a9, 0xb1ca, 0xa1eb, 0xd10c, 0xc12d, 0xf14e, 0xe16f,
0x1080, 0x00a1, 0x30c2, 0x20e3, 0x5004, 0x4025, 0x7046, 0x6067,
0x83b9, 0x9398, 0xa3fb, 0xb3da, 0xc33d, 0xd31c, 0xe37f, 0xf35e,
0x02b1, 0x1290, 0x22f3, 0x32d2, 0x4235, 0x5214, 0x6277, 0x7256,
0xb5ea, 0xa5cb, 0x95a8, 0x8589, 0xf56e, 0xe54f, 0xd52c, 0xc50d,
0x34e2, 0x24c3, 0x14a0, 0x0481, 0x7466, 0x6447, 0x5424, 0x4405,
0xa7db, 0xb7fa, 0x8799, 0x97b8, 0xe75f, 0xf77e, 0xc71d, 0xd73c,
0x26d3, 0x36f2, 0x0691, 0x16b0, 0x6657, 0x7676, 0x4615, 0x5634,
0xd94c, 0xc96d, 0xf90e, 0xe92f, 0x99c8, 0x89e9, 0xb98a, 0xa9ab,
0x5844, 0x4865, 0x7806, 0x6827, 0x18c0, 0x08e1, 0x3882, 0x28a3,
0xcb7d, 0xdb5c, 0xeb3f, 0xfb1e, 0x8bf9, 0x9bd8, 0xabbb, 0xbb9a,
0x4a75, 0x5a54, 0x6a37, 0x7a16, 0x0af1, 0x1ad0, 0x2ab3, 0x3a92,
0xfd2e, 0xed0f, 0xdd6c, 0xcd4d, 0xbdaa, 0xad8b, 0x9de8, 0x8dc9,
0x7c26, 0x6c07, 0x5c64, 0x4c45, 0x3ca2, 0x2c83, 0x1ce0, 0x0cc1,
0xef1f, 0xff3e, 0xcf5d, 0xdf7c, 0xaf9b, 0xbfba, 0x8fd9, 0x9ff8,
0x6e17, 0x7e36, 0x4e55, 0x5e74, 0x2e93, 0x3eb2, 0x0ed1, 0x1ef0
};
static constexpr const uint8_t square_roots[1000] =
{
0, 1, 1, 1, 2, 2, 2, 2, 2, 3,
3, 3, 3, 3, 3, 3, 4, 4, 4, 4,
4, 4, 4, 4, 4, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16, 17,
17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
17, 17, 17, 17, 18, 18, 18, 18, 18, 18,
18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
18, 19, 19, 19, 19, 19, 19, 19, 19, 19,
19, 19, 19, 19, 19, 19, 19, 19, 19, 19,
19, 19, 19, 19, 19, 19, 19, 19, 19, 19,
19, 19, 19, 19, 19, 19, 19, 19, 19, 19,
20, 20, 20, 20, 20, 20, 20, 20, 20, 20,
20, 20, 20, 20, 20, 20, 20, 20, 20, 20,
20, 20, 20, 20, 20, 20, 20, 20, 20, 20,
20, 20, 20, 20, 20, 20, 20, 20, 20, 20,
20, 21, 21, 21, 21, 21, 21, 21, 21, 21,
21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
21, 21, 21, 21, 22, 22, 22, 22, 22, 22,
22, 22, 22, 22, 22, 22, 22, 22, 22, 22,
22, 22, 22, 22, 22, 22, 22, 22, 22, 22,
22, 22, 22, 22, 22, 22, 22, 22, 22, 22,
22, 22, 22, 22, 22, 22, 22, 22, 22, 23,
23, 23, 23, 23, 23, 23, 23, 23, 23, 23,
23, 23, 23, 23, 23, 23, 23, 23, 23, 23,
23, 23, 23, 23, 23, 23, 23, 23, 23, 23,
23, 23, 23, 23, 23, 23, 23, 23, 23, 23,
23, 23, 23, 23, 23, 23, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 25, 25, 25, 25, 25,
25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
25, 25, 25, 25, 25, 25, 26, 26, 26, 26,
26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
26, 26, 26, 26, 26, 26, 26, 26, 26, 27,
27, 27, 27, 27, 27, 27, 27, 27, 27, 27,
27, 27, 27, 27, 27, 27, 27, 27, 27, 27,
27, 27, 27, 27, 27, 27, 27, 27, 27, 27,
27, 27, 27, 27, 27, 27, 27, 27, 27, 27,
27, 27, 27, 27, 27, 27, 27, 27, 27, 27,
27, 27, 27, 27, 28, 28, 28, 28, 28, 28,
28, 28, 28, 28, 28, 28, 28, 28, 28, 28,
28, 28, 28, 28, 28, 28, 28, 28, 28, 28,
28, 28, 28, 28, 28, 28, 28, 28, 28, 28,
28, 28, 28, 28, 28, 28, 28, 28, 28, 28,
28, 28, 28, 28, 28, 28, 28, 28, 28, 28,
28, 29, 29, 29, 29, 29, 29, 29, 29, 29,
29, 29, 29, 29, 29, 29, 29, 29, 29, 29,
29, 29, 29, 29, 29, 29, 29, 29, 29, 29,
29, 29, 29, 29, 29, 29, 29, 29, 29, 29,
29, 29, 29, 29, 29, 29, 29, 29, 29, 29,
29, 29, 29, 29, 29, 29, 29, 29, 29, 29,
30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
30, 31, 31, 31, 31, 31, 31, 31, 31, 31,
31, 31, 31, 31, 31, 31, 31, 31, 31, 31,
31, 31, 31, 31, 31, 31, 31, 31, 31, 31,
31, 31, 31, 31, 31, 31, 31, 31, 31, 31
};
inline uint16_t getCrc16(const std::string &str) A_WARN_UNUSED;
constexpr2 inline float fastInvSqrt(float x) A_WARN_UNUSED;
constexpr2 inline float fastSqrt(const float x) A_WARN_UNUSED;
constexpr inline float weightedAverage(const float n1, const float n2,
const float w) A_WARN_UNUSED;
constexpr inline int roundDouble(const double v) A_WARN_UNUSED;
constexpr2 inline int powerOfTwo(const unsigned int input) A_WARN_UNUSED;
constexpr2 inline int fastSqrtInt(const unsigned int n) A_WARN_UNUSED;
inline uint16_t getCrc16(const std::string &str)
{
size_t f = str.size();
uint16_t crc16 = 0xffff;
while (f != 0)
{
f --;
crc16 = static_cast<uint16_t>(
crc_table[(crc16 ^ (str[f])) & 0xff] ^ (crc16 >> 8));
}
return crc16;
}
/* A very fast function to calculate the approximate inverse square root of a
* floating point value and a helper function that uses it for getting the
* normal squareroot. For an explanation of the inverse squareroot function
* read:
* http://www.math.purdue.edu/~clomont/Math/Papers/2003/InvSqrt.pdf
*
* Unfortunately the original creator of this function seems to be unknown.
*/
constexpr2 inline float fastInvSqrt(float x)
{
union { int i; float x; } tmp = {0U};
const float xhalf = 0.5F * x;
tmp.x = x;
tmp.i = 0x5f375a86 - (tmp.i >> 1);
x = tmp.x;
x = x * (1.5F - xhalf * x * x);
return x;
}
constexpr2 inline float fastSqrt(const float x)
{
return 1.0F / fastInvSqrt(x);
}
constexpr inline float weightedAverage(const float n1, const float n2,
const float w)
{
return w < 0.0F ? n1 : (w > 1.0F ? n2 : w * n2 + (1.0F - w) * n1);
}
constexpr inline int roundDouble(const double v)
{
return (v > 0.0) ? static_cast<int>(v + 0.5) : static_cast<int>(v - 0.5);
}
constexpr2 inline int powerOfTwo(const unsigned int input)
{
unsigned int value = 1;
while (value < input)
value <<= 1;
return value;
}
constexpr2 inline int fastSqrtInt(const unsigned int n)
{
if (n < 1000)
return static_cast<int>(square_roots[n]);
return static_cast<int>(sqrt(n));
}
#endif // UTILS_MATHUTILS_H
