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rockbox/apps/fixedpoint.c

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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 "fixedpoint.h"
#include <stdlib.h>
#include <stdbool.h>
#include <inttypes.h>
#ifndef BIT_N
#define BIT_N(n) (1U << (n))
#endif
/** TAKEN FROM ORIGINAL 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 fp_sincos(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;
}
#if defined(PLUGIN) || defined(CODEC)
/**
* Fixed point square root via Newton-Raphson.
* @param x square root argument.
* @param fracbits specifies number of fractional bits in argument.
* @return Square root of argument in same fixed point format as input.
*
* This routine has been modified to run longer for greater precision,
* but cuts calculation short if the answer is reached sooner.
*/
long fp_sqrt(long x, unsigned int fracbits)
{
unsigned long xfp, b;
int n = 8; /* iteration limit (should terminate earlier) */
if (x <= 0)
return 0; /* no sqrt(neg), or just sqrt(0) = 0 */
/* Increase working precision by one bit */
xfp = x << 1;
fracbits++;
/* Get the midpoint between fracbits index and the highest bit index */
b = ((sizeof(xfp)*8-1) - __builtin_clzl(xfp) + fracbits) >> 1;
b = BIT_N(b);
do
{
unsigned long c = b;
b = (fp_div(xfp, b, fracbits) + b) >> 1;
if (c == b) break;
}
while (n-- > 0);
return b >> 1;
}
/* Accurate int sqrt with only elementary operations.
* Snagged from:
* http://www.devmaster.net/articles/fixed-point-optimizations/ */
unsigned long isqrt(unsigned long x)
{
/* Adding CLZ could optimize this further */
unsigned long g = 0;
int bshift = 15;
unsigned long b = 1ul << bshift;
do
{
unsigned long temp = (g + g + b) << bshift;
if (x > temp)
{
g += b;
x -= temp;
}
b >>= 1;
}
while (bshift--);
return g;
}
#endif /* PLUGIN or CODEC */
#if defined(PLUGIN)
/**
* 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 fp14_sin(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 fp14_cos(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 fp16_log(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;
}
/**
* Fixed-point exponential
* taken from http://www.quinapalus.com/efunc.html
* "The code assumes integers are at least 32 bits long. The (non-negative)
* argument and the result of the function are both expressed as fixed-point
* values with 16 fractional bits. Notice that after 11 steps of the
* algorithm the constants involved become such that the code is simply
* doing a multiplication: this is explained in the note below.
* The extension to negative arguments is left as an exercise."
*/
long fp16_exp(int x)
{
int t,y;
y=0x00010000;
t=x-0x58b91; if(t>=0) x=t,y<<=8;
t=x-0x2c5c8; if(t>=0) x=t,y<<=4;
t=x-0x162e4; if(t>=0) x=t,y<<=2;
t=x-0x0b172; if(t>=0) x=t,y<<=1;
t=x-0x067cd; if(t>=0) x=t,y+=y>>1;
t=x-0x03920; if(t>=0) x=t,y+=y>>2;
t=x-0x01e27; if(t>=0) x=t,y+=y>>3;
t=x-0x00f85; if(t>=0) x=t,y+=y>>4;
t=x-0x007e1; if(t>=0) x=t,y+=y>>5;
t=x-0x003f8; if(t>=0) x=t,y+=y>>6;
t=x-0x001fe; if(t>=0) x=t,y+=y>>7;
if(x&0x100) y+=y>>8;
if(x&0x080) y+=y>>9;
if(x&0x040) y+=y>>10;
if(x&0x020) y+=y>>11;
if(x&0x010) y+=y>>12;
if(x&0x008) y+=y>>13;
if(x&0x004) y+=y>>14;
if(x&0x002) y+=y>>15;
if(x&0x001) y+=y>>16;
return y;
}
#endif /* PLUGIN */
#if (!defined(PLUGIN) && !defined(CODEC))
/** MODIFIED FROM replaygain.c */
#define FP_MUL_FRAC(x, y) fp_mul(x, y, fracbits)
#define FP_DIV_FRAC(x, y) fp_div(x, y, fracbits)
/* constants in fixed point format, 28 fractional bits */
#define FP28_LN2 (186065279L) /* ln(2) */
#define FP28_LN2_INV (387270501L) /* 1/ln(2) */
#define FP28_EXP_ZERO (44739243L) /* 1/6 */
#define FP28_EXP_ONE (-745654L) /* -1/360 */
#define FP28_EXP_TWO (12428L) /* 1/21600 */
#define FP28_LN10 (618095479L) /* ln(10) */
#define FP28_LOG10OF2 (80807124L) /* log10(2) */
#define TOL_BITS 2 /* log calculation tolerance */
/* The fpexp10 fixed point math routine is based
* on oMathFP by Dan Carter (http://orbisstudios.com).
*/
/** FIXED POINT EXP10
* Return 10^x as FP integer. Argument is FP integer.
*/
static long fp_exp10(long x, unsigned int fracbits)
{
long k;
long z;
long R;
long xp;
/* scale constants */
const long fp_one = (1 << fracbits);
const long fp_half = (1 << (fracbits - 1));
const long fp_two = (2 << fracbits);
const long fp_mask = (fp_one - 1);
const long fp_ln2_inv = (FP28_LN2_INV >> (28 - fracbits));
const long fp_ln2 = (FP28_LN2 >> (28 - fracbits));
const long fp_ln10 = (FP28_LN10 >> (28 - fracbits));
const long fp_exp_zero = (FP28_EXP_ZERO >> (28 - fracbits));
const long fp_exp_one = (FP28_EXP_ONE >> (28 - fracbits));
const long fp_exp_two = (FP28_EXP_TWO >> (28 - fracbits));
/* exp(0) = 1 */
if (x == 0)
{
return fp_one;
}
/* convert from base 10 to base e */
x = FP_MUL_FRAC(x, fp_ln10);
/* calculate exp(x) */
k = (FP_MUL_FRAC(abs(x), fp_ln2_inv) + fp_half) & ~fp_mask;
if (x < 0)
{
k = -k;
}
x -= FP_MUL_FRAC(k, fp_ln2);
z = FP_MUL_FRAC(x, x);
R = fp_two + FP_MUL_FRAC(z, fp_exp_zero + FP_MUL_FRAC(z, fp_exp_one
+ FP_MUL_FRAC(z, fp_exp_two)));
xp = fp_one + FP_DIV_FRAC(FP_MUL_FRAC(fp_two, x), R - x);
if (k < 0)
{
k = fp_one >> (-k >> fracbits);
}
else
{
k = fp_one << (k >> fracbits);
}
return FP_MUL_FRAC(k, xp);
}
#if 0 /* useful code, but not currently used */
/** FIXED POINT LOG10
* Return log10(x) as FP integer. Argument is FP integer.
*/
static long fp_log10(long n, unsigned int fracbits)
{
/* Calculate log2 of argument */
long log2, frac;
const long fp_one = (1 << fracbits);
const long fp_two = (2 << fracbits);
const long tolerance = (1 << ((fracbits / 2) + 2));
if (n <=0) return FP_NEGINF;
log2 = 0;
/* integer part */
while (n < fp_one)
{
log2 -= fp_one;
n <<= 1;
}
while (n >= fp_two)
{
log2 += fp_one;
n >>= 1;
}
/* fractional part */
frac = fp_one;
while (frac > tolerance)
{
frac >>= 1;
n = FP_MUL_FRAC(n, n);
if (n >= fp_two)
{
n >>= 1;
log2 += frac;
}
}
/* convert log2 to log10 */
return FP_MUL_FRAC(log2, (FP28_LOG10OF2 >> (28 - fracbits)));
}
/** CONVERT FACTOR TO DECIBELS */
long fp_decibels(unsigned long factor, unsigned int fracbits)
{
/* decibels = 20 * log10(factor) */
return FP_MUL_FRAC((20L << fracbits), fp_log10(factor, fracbits));
}
#endif /* unused code */
/** CONVERT DECIBELS TO FACTOR */
long fp_factor(long decibels, unsigned int fracbits)
{
/* factor = 10 ^ (decibels / 20) */
return fp_exp10(FP_DIV_FRAC(decibels, (20L << fracbits)), fracbits);
}
#endif /* !PLUGIN and !CODEC */
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