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/***************************************************************************
* __________ __ ___.
* Open \______ \ ____ ____ | | _\_ |__ _______ ___
* Source | _// _ \_/ ___\| |/ /| __ \ / _ \ \/ /
* Jukebox | | ( <_> ) \___| < | \_\ ( <_> > < <
* Firmware |____|_ /\____/ \___ >__|_ \|___ /\____/__/\_ \
* \/ \/ \/ \/ \/
* $Id$
*
* Copyright (C) 2006 Jens Arnold
*
* Fixed point library for plugins
*
* 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 (at your option) any later version.
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY
* KIND, either express or implied.
*
****************************************************************************/
#include <inttypes.h>
#include "fixedpoint.h"
/* Inverse gain of circular cordic rotation in s0.31 format. */
static const long cordic_circular_gain = 0xb2458939; /* 0.607252929 */
/* Table of values of atan(2^-i) in 0.32 format fractions of pi where pi = 0xffffffff / 2 */
static const unsigned long atan_table[] = {
0x1fffffff, /* +0.785398163 (or pi/4) */
0x12e4051d, /* +0.463647609 */
0x09fb385b, /* +0.244978663 */
0x051111d4, /* +0.124354995 */
0x028b0d43, /* +0.062418810 */
0x0145d7e1, /* +0.031239833 */
0x00a2f61e, /* +0.015623729 */
0x00517c55, /* +0.007812341 */
0x0028be53, /* +0.003906230 */
0x00145f2e, /* +0.001953123 */
0x000a2f98, /* +0.000976562 */
0x000517cc, /* +0.000488281 */
0x00028be6, /* +0.000244141 */
0x000145f3, /* +0.000122070 */
0x0000a2f9, /* +0.000061035 */
0x0000517c, /* +0.000030518 */
0x000028be, /* +0.000015259 */
0x0000145f, /* +0.000007629 */
0x00000a2f, /* +0.000003815 */
0x00000517, /* +0.000001907 */
0x0000028b, /* +0.000000954 */
0x00000145, /* +0.000000477 */
0x000000a2, /* +0.000000238 */
0x00000051, /* +0.000000119 */
0x00000028, /* +0.000000060 */
0x00000014, /* +0.000000030 */
0x0000000a, /* +0.000000015 */
0x00000005, /* +0.000000007 */
0x00000002, /* +0.000000004 */
0x00000001, /* +0.000000002 */
0x00000000, /* +0.000000001 */
0x00000000, /* +0.000000000 */
};
/* Precalculated sine and cosine * 16384 (2^14) (fixed point 18.14) */
static const short sin_table[91] =
{
0, 285, 571, 857, 1142, 1427, 1712, 1996, 2280, 2563,
2845, 3126, 3406, 3685, 3963, 4240, 4516, 4790, 5062, 5334,
5603, 5871, 6137, 6401, 6663, 6924, 7182, 7438, 7691, 7943,
8191, 8438, 8682, 8923, 9161, 9397, 9630, 9860, 10086, 10310,
10531, 10748, 10963, 11173, 11381, 11585, 11785, 11982, 12175, 12365,
12550, 12732, 12910, 13084, 13254, 13420, 13582, 13740, 13894, 14043,
14188, 14329, 14466, 14598, 14725, 14848, 14967, 15081, 15190, 15295,
15395, 15491, 15582, 15668, 15749, 15825, 15897, 15964, 16025, 16082,
16135, 16182, 16224, 16261, 16294, 16321, 16344, 16361, 16374, 16381,
16384
};
/**
* Implements sin and cos using CORDIC rotation.
*
* @param phase has range from 0 to 0xffffffff, representing 0 and
* 2*pi respectively.
* @param cos return address for cos
* @return sin of phase, value is a signed value from LONG_MIN to LONG_MAX,
* representing -1 and 1 respectively.
*/
long fsincos(unsigned long phase, long *cos)
{
int32_t x, x1, y, y1;
unsigned long z, z1;
int i;
/* Setup initial vector */
x = cordic_circular_gain;
y = 0;
z = phase;
/* The phase has to be somewhere between 0..pi for this to work right */
if (z < 0xffffffff / 4) {
/* z in first quadrant, z += pi/2 to correct */
x = -x;
z += 0xffffffff / 4;
} else if (z < 3 * (0xffffffff / 4)) {
/* z in third quadrant, z -= pi/2 to correct */
z -= 0xffffffff / 4;
} else {
/* z in fourth quadrant, z -= 3pi/2 to correct */
x = -x;
z -= 3 * (0xffffffff / 4);
}
/* Each iteration adds roughly 1-bit of extra precision */
for (i = 0; i < 31; i++) {
x1 = x >> i;
y1 = y >> i;
z1 = atan_table[i];
/* Decided which direction to rotate vector. Pivot point is pi/2 */
if (z >= 0xffffffff / 4) {
x -= y1;
y += x1;
z -= z1;
} else {
x += y1;
y -= x1;
z += z1;
}
}
if (cos)
*cos = x;
return y;
}
/**
* Fixed point square root via Newton-Raphson.
* @param a square root argument.
* @param fracbits specifies number of fractional bits in argument.
* @return Square root of argument in same fixed point format as input.
*/
long fsqrt(long a, unsigned int fracbits)
{
long b = a/2 + (1 << fracbits); /* initial approximation */
unsigned n;
const unsigned iterations = 4;
for (n = 0; n < iterations; ++n)
b = (b + (long)(((long long)(a) << fracbits)/b))/2;
return b;
}
/**
* Fixed point sinus using a lookup table
* don't forget to divide the result by 16384 to get the actual sinus value
* @param val sinus argument in degree
* @return sin(val)*16384
*/
long sin_int(int val)
{
val = (val+360)%360;
if (val < 181)
{
if (val < 91)/* phase 0-90 degree */
return (long)sin_table[val];
else/* phase 91-180 degree */
return (long)sin_table[180-val];
}
else
{
if (val < 271)/* phase 181-270 degree */
return -(long)sin_table[val-180];
else/* phase 270-359 degree */
return -(long)sin_table[360-val];
}
return 0;
}
/**
* Fixed point cosinus using a lookup table
* don't forget to divide the result by 16384 to get the actual cosinus value
* @param val sinus argument in degree
* @return cos(val)*16384
*/
long cos_int(int val)
{
val = (val+360)%360;
if (val < 181)
{
if (val < 91)/* phase 0-90 degree */
return (long)sin_table[90-val];
else/* phase 91-180 degree */
return -(long)sin_table[val-90];
}
else
{
if (val < 271)/* phase 181-270 degree */
return -(long)sin_table[270-val];
else/* phase 270-359 degree */
return (long)sin_table[val-270];
}
return 0;
}
/**
* Fixed-point natural log
* taken from http://www.quinapalus.com/efunc.html
* "The code assumes integers are at least 32 bits long. The (positive)
* argument and the result of the function are both expressed as fixed-point
* values with 16 fractional bits, although intermediates are kept with 28
* bits of precision to avoid loss of accuracy during shifts."
*/
long flog(int x) {
long t,y;
y=0xa65af;
if(x<0x00008000) x<<=16, y-=0xb1721;
if(x<0x00800000) x<<= 8, y-=0x58b91;
if(x<0x08000000) x<<= 4, y-=0x2c5c8;
if(x<0x20000000) x<<= 2, y-=0x162e4;
if(x<0x40000000) x<<= 1, y-=0x0b172;
t=x+(x>>1); if((t&0x80000000)==0) x=t,y-=0x067cd;
t=x+(x>>2); if((t&0x80000000)==0) x=t,y-=0x03920;
t=x+(x>>3); if((t&0x80000000)==0) x=t,y-=0x01e27;
t=x+(x>>4); if((t&0x80000000)==0) x=t,y-=0x00f85;
t=x+(x>>5); if((t&0x80000000)==0) x=t,y-=0x007e1;
t=x+(x>>6); if((t&0x80000000)==0) x=t,y-=0x003f8;
t=x+(x>>7); if((t&0x80000000)==0) x=t,y-=0x001fe;
x=0x80000000-x;
y-=x>>15;
return y;
}
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