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Diffstat (limited to 'apps/fixedpoint.c')
| -rw-r--r-- | apps/fixedpoint.c | 440 |
1 files changed, 440 insertions, 0 deletions
diff --git a/apps/fixedpoint.c b/apps/fixedpoint.c new file mode 100644 index 0000000000..b65070e348 --- /dev/null +++ b/apps/fixedpoint.c @@ -0,0 +1,440 @@ +/*************************************************************************** + * __________ __ ___. + * 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; +} |