| /*************************************************************************** |
| * __________ __ ___. |
| * 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; |
| } |