/*************************************************************************** * __________ __ ___. * Open \______ \ ____ ____ | | _\_ |__ _______ ___ * Source | _// _ \_/ ___\| |/ /| __ \ / _ \ \/ / * Jukebox | | ( <_> ) \___| < | \_\ ( <_> > < < * Firmware |____|_ /\____/ \___ >__|_ \|___ /\____/__/\_ \ * \/ \/ \/ \/ \/ * * 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 #include #include #include #define ULONG_BITS (sizeof (unsigned long)*CHAR_BIT) /** 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; } /* Accurate sqrt with only elementary operations. * Snagged from: * http://www.devmaster.net/articles/fixed-point-optimizations/ * * Extension to fractions and initial estimate improvement by jethead71 */ long fp_sqrt(long x, unsigned int fracbits) { if (x <= 0) { return 0; /* no sqrt(neg), or just sqrt(0) = 0 */ } unsigned long g = 0; unsigned long e = x; int intwidth = ULONG_BITS - fracbits; int bshift = __builtin_clzl(e); if (bshift >= intwidth) { bshift = -1; } else { bshift = (intwidth - bshift - 1) >> 1; } unsigned long b = 1ul << (bshift + fracbits); /* integer part */ while (e && bshift >= 0) { unsigned long t = ((g << 1) | b) << bshift--; if (e >= t) { g |= b; e -= t; } b >>= 1; } /* fractional part */ while (e && b) { unsigned long t = (g << 1) | b; unsigned long c = e; /* detect carry */ e <<= 1; if (e < c || e >= t) { g |= b; e -= t; } b >>= 1; } #if 0 /* round up if the next bit would be a '1' */ if (e) { unsigned long c = e; /* detect carry */ e <<= 1; if (e < c || e >= ((g << 1) | 1)) { g++; } } #endif return g; } /* raise an integer to an integer power */ long ipow(long x, long y) { /* y[k] = bit k of y, 0 or 1; k=0...n; n=|_ lg(y) _| * * x^y = x^(y[0]*2^0 + y[1]*2^1 + ... + y[n]*2^n) * = x^(y[0]*2^0) * x^(y[1]*2^1) * ... * x^(y[n]*2^n) */ long a = 1; if (y < 0 && x != -1) { a = 0; /* would be < 1 or +inf if x == 0 */ } else { while (y) { if (y & 1) a *= x; y /= 2; x *= x; } } return a; } /** * 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) { int t; int 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; int y = 0x00010000; if (x < 0) x += 0xb1721, y >>= 16; 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; y += ((y >> 8) * x) >> 8; return y; } /** 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. */ 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); } /** FIXED POINT LOG10 * Return log10(x) as FP integer. Argument is FP integer. */ 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)); } /** 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); }