a36c8f1db3
git-svn-id: svn://svn.rockbox.org/rockbox/trunk@17353 a1c6a512-1295-4272-9138-f99709370657
235 lines
7.4 KiB
C
235 lines
7.4 KiB
C
/***************************************************************************
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* __________ __ ___.
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* Open \______ \ ____ ____ | | _\_ |__ _______ ___
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* Source | _// _ \_/ ___\| |/ /| __ \ / _ \ \/ /
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* Jukebox | | ( <_> ) \___| < | \_\ ( <_> > < <
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* Firmware |____|_ /\____/ \___ >__|_ \|___ /\____/__/\_ \
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* \/ \/ \/ \/ \/
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* $Id$
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*
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* Copyright (C) 2006 Jens Arnold
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*
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* Fixed point library for plugins
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*
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* All files in this archive are subject to the GNU General Public License.
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* See the file COPYING in the source tree root for full license agreement.
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*
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* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY
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* KIND, either express or implied.
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*
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****************************************************************************/
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#include <inttypes.h>
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#include "fixedpoint.h"
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/* Inverse gain of circular cordic rotation in s0.31 format. */
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static const long cordic_circular_gain = 0xb2458939; /* 0.607252929 */
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/* Table of values of atan(2^-i) in 0.32 format fractions of pi where pi = 0xffffffff / 2 */
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static const unsigned long atan_table[] = {
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0x1fffffff, /* +0.785398163 (or pi/4) */
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0x12e4051d, /* +0.463647609 */
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0x09fb385b, /* +0.244978663 */
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0x051111d4, /* +0.124354995 */
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0x028b0d43, /* +0.062418810 */
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0x0145d7e1, /* +0.031239833 */
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0x00a2f61e, /* +0.015623729 */
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0x00517c55, /* +0.007812341 */
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0x0028be53, /* +0.003906230 */
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0x00145f2e, /* +0.001953123 */
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0x000a2f98, /* +0.000976562 */
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0x000517cc, /* +0.000488281 */
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0x00028be6, /* +0.000244141 */
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0x000145f3, /* +0.000122070 */
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0x0000a2f9, /* +0.000061035 */
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0x0000517c, /* +0.000030518 */
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0x000028be, /* +0.000015259 */
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0x0000145f, /* +0.000007629 */
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0x00000a2f, /* +0.000003815 */
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0x00000517, /* +0.000001907 */
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0x0000028b, /* +0.000000954 */
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0x00000145, /* +0.000000477 */
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0x000000a2, /* +0.000000238 */
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0x00000051, /* +0.000000119 */
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0x00000028, /* +0.000000060 */
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0x00000014, /* +0.000000030 */
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0x0000000a, /* +0.000000015 */
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0x00000005, /* +0.000000007 */
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0x00000002, /* +0.000000004 */
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0x00000001, /* +0.000000002 */
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0x00000000, /* +0.000000001 */
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0x00000000, /* +0.000000000 */
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};
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/* Precalculated sine and cosine * 16384 (2^14) (fixed point 18.14) */
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static const short sin_table[91] =
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{
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0, 285, 571, 857, 1142, 1427, 1712, 1996, 2280, 2563,
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2845, 3126, 3406, 3685, 3963, 4240, 4516, 4790, 5062, 5334,
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5603, 5871, 6137, 6401, 6663, 6924, 7182, 7438, 7691, 7943,
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8191, 8438, 8682, 8923, 9161, 9397, 9630, 9860, 10086, 10310,
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10531, 10748, 10963, 11173, 11381, 11585, 11785, 11982, 12175, 12365,
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12550, 12732, 12910, 13084, 13254, 13420, 13582, 13740, 13894, 14043,
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14188, 14329, 14466, 14598, 14725, 14848, 14967, 15081, 15190, 15295,
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15395, 15491, 15582, 15668, 15749, 15825, 15897, 15964, 16025, 16082,
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16135, 16182, 16224, 16261, 16294, 16321, 16344, 16361, 16374, 16381,
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16384
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};
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/**
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* Implements sin and cos using CORDIC rotation.
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*
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* @param phase has range from 0 to 0xffffffff, representing 0 and
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* 2*pi respectively.
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* @param cos return address for cos
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* @return sin of phase, value is a signed value from LONG_MIN to LONG_MAX,
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* representing -1 and 1 respectively.
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*/
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long fsincos(unsigned long phase, long *cos)
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{
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int32_t x, x1, y, y1;
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unsigned long z, z1;
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int i;
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/* Setup initial vector */
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x = cordic_circular_gain;
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y = 0;
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z = phase;
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/* The phase has to be somewhere between 0..pi for this to work right */
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if (z < 0xffffffff / 4) {
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/* z in first quadrant, z += pi/2 to correct */
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x = -x;
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z += 0xffffffff / 4;
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} else if (z < 3 * (0xffffffff / 4)) {
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/* z in third quadrant, z -= pi/2 to correct */
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z -= 0xffffffff / 4;
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} else {
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/* z in fourth quadrant, z -= 3pi/2 to correct */
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x = -x;
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z -= 3 * (0xffffffff / 4);
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}
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/* Each iteration adds roughly 1-bit of extra precision */
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for (i = 0; i < 31; i++) {
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x1 = x >> i;
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y1 = y >> i;
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z1 = atan_table[i];
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/* Decided which direction to rotate vector. Pivot point is pi/2 */
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if (z >= 0xffffffff / 4) {
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x -= y1;
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y += x1;
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z -= z1;
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} else {
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x += y1;
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y -= x1;
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z += z1;
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}
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}
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if (cos)
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*cos = x;
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return y;
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}
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/**
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* Fixed point square root via Newton-Raphson.
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* @param a square root argument.
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* @param fracbits specifies number of fractional bits in argument.
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* @return Square root of argument in same fixed point format as input.
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*/
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long fsqrt(long a, unsigned int fracbits)
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{
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long b = a/2 + (1 << fracbits); /* initial approximation */
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unsigned n;
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const unsigned iterations = 4;
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for (n = 0; n < iterations; ++n)
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b = (b + (long)(((long long)(a) << fracbits)/b))/2;
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return b;
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}
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/**
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* Fixed point sinus using a lookup table
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* don't forget to divide the result by 16384 to get the actual sinus value
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* @param val sinus argument in degree
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* @return sin(val)*16384
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*/
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long sin_int(int val)
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{
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val = (val+360)%360;
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if (val < 181)
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{
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if (val < 91)/* phase 0-90 degree */
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return (long)sin_table[val];
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else/* phase 91-180 degree */
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return (long)sin_table[180-val];
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}
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else
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{
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if (val < 271)/* phase 181-270 degree */
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return -(long)sin_table[val-180];
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else/* phase 270-359 degree */
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return -(long)sin_table[360-val];
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}
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return 0;
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}
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/**
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* Fixed point cosinus using a lookup table
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* don't forget to divide the result by 16384 to get the actual cosinus value
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* @param val sinus argument in degree
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* @return cos(val)*16384
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*/
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long cos_int(int val)
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{
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val = (val+360)%360;
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if (val < 181)
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{
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if (val < 91)/* phase 0-90 degree */
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return (long)sin_table[90-val];
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else/* phase 91-180 degree */
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return -(long)sin_table[val-90];
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}
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else
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{
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if (val < 271)/* phase 181-270 degree */
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return -(long)sin_table[270-val];
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else/* phase 270-359 degree */
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return (long)sin_table[val-270];
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}
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return 0;
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}
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/**
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* Fixed-point natural log
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* taken from http://www.quinapalus.com/efunc.html
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* "The code assumes integers are at least 32 bits long. The (positive)
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* argument and the result of the function are both expressed as fixed-point
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* values with 16 fractional bits, although intermediates are kept with 28
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* bits of precision to avoid loss of accuracy during shifts."
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*/
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long flog(int x) {
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long t,y;
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y=0xa65af;
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if(x<0x00008000) x<<=16, y-=0xb1721;
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if(x<0x00800000) x<<= 8, y-=0x58b91;
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if(x<0x08000000) x<<= 4, y-=0x2c5c8;
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if(x<0x20000000) x<<= 2, y-=0x162e4;
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if(x<0x40000000) x<<= 1, y-=0x0b172;
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t=x+(x>>1); if((t&0x80000000)==0) x=t,y-=0x067cd;
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t=x+(x>>2); if((t&0x80000000)==0) x=t,y-=0x03920;
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t=x+(x>>3); if((t&0x80000000)==0) x=t,y-=0x01e27;
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t=x+(x>>4); if((t&0x80000000)==0) x=t,y-=0x00f85;
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t=x+(x>>5); if((t&0x80000000)==0) x=t,y-=0x007e1;
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t=x+(x>>6); if((t&0x80000000)==0) x=t,y-=0x003f8;
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t=x+(x>>7); if((t&0x80000000)==0) x=t,y-=0x001fe;
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x=0x80000000-x;
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y-=x>>15;
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return y;
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}
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