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authorMaurus Cuelenaere <mcuelenaere@gmail.com>2009-07-04 12:26:45 +0000
committerMaurus Cuelenaere <mcuelenaere@gmail.com>2009-07-04 12:26:45 +0000
commit4710a3280025b0ba8ffb6e8183578a5df48257fa (patch)
tree3dd82b90ab668c18109d0885cd3114449efaddf1 /apps/fixedpoint.c
parent69c73e8bd6c8c6ac79c6538cb0ad4686b9d1d920 (diff)
downloadrockbox-4710a3280025b0ba8ffb6e8183578a5df48257fa.tar.gz
rockbox-4710a3280025b0ba8ffb6e8183578a5df48257fa.zip
Consolidate all fixed point math routines in one library (FS#10400) by Jeffrey Goode
git-svn-id: svn://svn.rockbox.org/rockbox/trunk@21633 a1c6a512-1295-4272-9138-f99709370657
Diffstat (limited to 'apps/fixedpoint.c')
-rw-r--r--apps/fixedpoint.c440
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diff --git a/apps/fixedpoint.c b/apps/fixedpoint.c
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+/***************************************************************************
+ * __________ __ ___.
+ * Open \______ \ ____ ____ | | _\_ |__ _______ ___
+ * Source | _// _ \_/ ___\| |/ /| __ \ / _ \ \/ /
+ * Jukebox | | ( <_> ) \___| < | \_\ ( <_> > < <
+ * Firmware |____|_ /\____/ \___ >__|_ \|___ /\____/__/\_ \
+ * \/ \/ \/ \/ \/
+ * $Id: fixedpoint.c -1 $
+ *
+ * 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>
+
+#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 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 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. In
+ * general, the closer x is to 1, the quicker the calculation.
+ */
+long fsqrt(long x, unsigned int fracbits)
+{
+ long b = x/2 + BIT_N(fracbits); /* initial approximation */
+ long c;
+ unsigned n;
+ const unsigned iterations = 8;
+
+ for (n = 0; n < iterations; ++n)
+ {
+ c = DIV64(x, b, fracbits);
+ if (c == b) break;
+ b = (b + c)/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;
+}
+
+/** MODIFIED FROM replaygain.c */
+/* These math routines have 64-bit internal precision to avoid overflows.
+ * Arguments and return values are 32-bit (long) precision.
+ */
+
+#define FP_MUL64(x, y) (((x) * (y)) >> (fracbits))
+#define FP_DIV64(x, y) (((x) << (fracbits)) / (y))
+
+static long long fp_exp10(long long x, unsigned int fracbits);
+static long long fp_log10(long long n, unsigned int fracbits);
+
+/* constants in fixed point format, 28 fractional bits */
+#define FP28_LN2 (186065279LL) /* ln(2) */
+#define FP28_LN2_INV (387270501LL) /* 1/ln(2) */
+#define FP28_EXP_ZERO (44739243LL) /* 1/6 */
+#define FP28_EXP_ONE (-745654LL) /* -1/360 */
+#define FP28_EXP_TWO (12428LL) /* 1/21600 */
+#define FP28_LN10 (618095479LL) /* ln(10) */
+#define FP28_LOG10OF2 (80807124LL) /* 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 long fp_exp10(long long x, unsigned int fracbits)
+{
+ long long k;
+ long long z;
+ long long R;
+ long long xp;
+
+ /* scale constants */
+ const long long fp_one = (1 << fracbits);
+ const long long fp_half = (1 << (fracbits - 1));
+ const long long fp_two = (2 << fracbits);
+ const long long fp_mask = (fp_one - 1);
+ const long long fp_ln2_inv = (FP28_LN2_INV >> (28 - fracbits));
+ const long long fp_ln2 = (FP28_LN2 >> (28 - fracbits));
+ const long long fp_ln10 = (FP28_LN10 >> (28 - fracbits));
+ const long long fp_exp_zero = (FP28_EXP_ZERO >> (28 - fracbits));
+ const long long fp_exp_one = (FP28_EXP_ONE >> (28 - fracbits));
+ const long 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_MUL64(x, fp_ln10);
+
+ /* calculate exp(x) */
+ k = (FP_MUL64(abs(x), fp_ln2_inv) + fp_half) & ~fp_mask;
+
+ if (x < 0)
+ {
+ k = -k;
+ }
+
+ x -= FP_MUL64(k, fp_ln2);
+ z = FP_MUL64(x, x);
+ R = fp_two + FP_MUL64(z, fp_exp_zero + FP_MUL64(z, fp_exp_one
+ + FP_MUL64(z, fp_exp_two)));
+ xp = fp_one + FP_DIV64(FP_MUL64(fp_two, x), R - x);
+
+ if (k < 0)
+ {
+ k = fp_one >> (-k >> fracbits);
+ }
+ else
+ {
+ k = fp_one << (k >> fracbits);
+ }
+
+ return FP_MUL64(k, xp);
+}
+
+
+/** FIXED POINT LOG10
+ * Return log10(x) as FP integer. Argument is FP integer.
+ */
+static long long fp_log10(long long n, unsigned int fracbits)
+{
+ /* Calculate log2 of argument */
+
+ long long log2, frac;
+ const long long fp_one = (1 << fracbits);
+ const long 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_MUL64(n, n);
+ if (n >= fp_two)
+ {
+ n >>= 1;
+ log2 += frac;
+ }
+ }
+
+ /* convert log2 to log10 */
+ return FP_MUL64(log2, (FP28_LOG10OF2 >> (28 - fracbits)));
+}
+
+
+/** CONVERT FACTOR TO DECIBELS */
+long fp_decibels(unsigned long factor, unsigned int fracbits)
+{
+ long long decibels;
+ long long f = (long long)factor;
+ bool neg;
+
+ /* keep factor in signed long range */
+ if (f >= (1LL << 31))
+ f = (1LL << 31) - 1;
+
+ /* decibels = 20 * log10(factor) */
+ decibels = FP_MUL64((20LL << fracbits), fp_log10(f, fracbits));
+
+ /* keep result in signed long range */
+ if ((neg = (decibels < 0)))
+ decibels = -decibels;
+ if (decibels >= (1LL << 31))
+ return neg ? FP_NEGINF : FP_INF;
+
+ return neg ? (long)-decibels : (long)decibels;
+}
+
+
+/** CONVERT DECIBELS TO FACTOR */
+long fp_factor(long decibels, unsigned int fracbits)
+{
+ bool neg;
+ long long factor;
+ long long db = (long long)decibels;
+
+ /* if decibels is 0, factor is 1 */
+ if (db == 0)
+ return (1L << fracbits);
+
+ /* calculate for positive decibels only */
+ if ((neg = (db < 0)))
+ db = -db;
+
+ /* factor = 10 ^ (decibels / 20) */
+ factor = fp_exp10(FP_DIV64(db, (20LL << fracbits)), fracbits);
+
+ /* keep result in signed long range, return 0 if very small */
+ if (factor >= (1LL << 31))
+ {
+ if (neg)
+ return 0;
+ else
+ return FP_INF;
+ }
+
+ /* if negative argument, factor is 1 / result */
+ if (neg)
+ factor = FP_DIV64((1LL << fracbits), factor);
+
+ return (long)factor;
+}