apps/eq.c

   1 /***************************************************************************
   2  *             __________               __   ___.
   3  *   Open      \______   \ ____   ____ |  | _\_ |__   _______  ___
   4  *   Source     |       _//  _ \_/ ___\|  |/ /| __ \ /  _ \  \/  /
   5  *   Jukebox    |    |   (  <_> )  \___|    < | \_\ (  <_> > <  <
   6  *   Firmware   |____|_  /\____/ \___  >__|_ \|___  /\____/__/\_ \
   7  *                     \/            \/     \/    \/            \/
   8  * $Id$
   9  *
  10  * Copyright (C) 2006-2007 Thom Johansen
  11  *
  12  * This program is free software; you can redistribute it and/or
  13  * modify it under the terms of the GNU General Public License
  14  * as published by the Free Software Foundation; either version 2
  15  * of the License, or (at your option) any later version.
  16  *
  17  * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY
  18  * KIND, either express or implied.
  19  *
  20  ****************************************************************************/
  21
  22 #include <inttypes.h>
  23 #include "config.h"
  24 #include "dsp.h"
  25 #include "eq.h"
  26 #include "replaygain.h"
  27
  28 /* Inverse gain of circular cordic rotation in s0.31 format. */
  29 static const long cordic_circular_gain = 0xb2458939; /* 0.607252929 */
  30
  31 /* Table of values of atan(2^-i) in 0.32 format fractions of pi where pi = 0xffffffff / 2 */
  32 static const unsigned long atan_table[] = {
  33     0x1fffffff, /* +0.785398163 (or pi/4) */
  34     0x12e4051d, /* +0.463647609 */
  35     0x09fb385b, /* +0.244978663 */
  36     0x051111d4, /* +0.124354995 */
  37     0x028b0d43, /* +0.062418810 */
  38     0x0145d7e1, /* +0.031239833 */
  39     0x00a2f61e, /* +0.015623729 */
  40     0x00517c55, /* +0.007812341 */
  41     0x0028be53, /* +0.003906230 */
  42     0x00145f2e, /* +0.001953123 */
  43     0x000a2f98, /* +0.000976562 */
  44     0x000517cc, /* +0.000488281 */
  45     0x00028be6, /* +0.000244141 */
  46     0x000145f3, /* +0.000122070 */
  47     0x0000a2f9, /* +0.000061035 */
  48     0x0000517c, /* +0.000030518 */
  49     0x000028be, /* +0.000015259 */
  50     0x0000145f, /* +0.000007629 */
  51     0x00000a2f, /* +0.000003815 */
  52     0x00000517, /* +0.000001907 */
  53     0x0000028b, /* +0.000000954 */
  54     0x00000145, /* +0.000000477 */
  55     0x000000a2, /* +0.000000238 */
  56     0x00000051, /* +0.000000119 */
  57     0x00000028, /* +0.000000060 */
  58     0x00000014, /* +0.000000030 */
  59     0x0000000a, /* +0.000000015 */
  60     0x00000005, /* +0.000000007 */
  61     0x00000002, /* +0.000000004 */
  62     0x00000001, /* +0.000000002 */
  63     0x00000000, /* +0.000000001 */
  64     0x00000000, /* +0.000000000 */
  65 };
  66
  67 /**
  68  * Implements sin and cos using CORDIC rotation.
  69  *
  70  * @param phase has range from 0 to 0xffffffff, representing 0 and
  71  *        2*pi respectively.
  72  * @param cos return address for cos
  73  * @return sin of phase, value is a signed value from LONG_MIN to LONG_MAX,
  74  *         representing -1 and 1 respectively.
  75  */
  76 static long fsincos(unsigned long phase, long *cos) {
  77     int32_t x, x1, y, y1;
  78     unsigned long z, z1;
  79     int i;
  80
  81     /* Setup initial vector */
  82     x = cordic_circular_gain;
  83     y = 0;
  84     z = phase;
  85
  86     /* The phase has to be somewhere between 0..pi for this to work right */
  87     if (z < 0xffffffff / 4) {
  88         /* z in first quadrant, z += pi/2 to correct */
  89         x = -x;
  90         z += 0xffffffff / 4;
  91     } else if (z < 3 * (0xffffffff / 4)) {
  92         /* z in third quadrant, z -= pi/2 to correct */
  93         z -= 0xffffffff / 4;
  94     } else {
  95         /* z in fourth quadrant, z -= 3pi/2 to correct */
  96         x = -x;
  97         z -= 3 * (0xffffffff / 4);
  98     }
  99
 100     /* Each iteration adds roughly 1-bit of extra precision */
 101     for (i = 0; i < 31; i++) {
 102         x1 = x >> i;
 103         y1 = y >> i;
 104         z1 = atan_table[i];
 105
 106         /* Decided which direction to rotate vector. Pivot point is pi/2 */
 107         if (z >= 0xffffffff / 4) {
 108             x -= y1;
 109             y += x1;
 110             z -= z1;
 111         } else {
 112             x += y1;
 113             y -= x1;
 114             z += z1;
 115         }
 116     }
 117
 118     *cos = x;
 119
 120     return y;
 121 }
 122
 123 /**
 124  * Calculate first order shelving filter. Filter is not directly usable by the
 125  * eq_filter() function.
 126  * @param cutoff shelf midpoint frequency. See eq_pk_coefs for format.
 127  * @param A decibel value multiplied by ten, describing gain/attenuation of
 128  * shelf. Max value is 24 dB.
 129  * @param low true for low-shelf filter, false for high-shelf filter.
 130  * @param c pointer to coefficient storage. Coefficients are s4.27 format.
 131  */
 132 void filter_shelf_coefs(unsigned long cutoff, long A, bool low, int32_t *c)
 133 {
 134     long sin, cos;
 135     int32_t b0, b1, a0, a1; /* s3.28 */
 136     const long g = get_replaygain_int(A*5) << 4; /* 10^(db/40), s3.28 */
 137
 138     sin = fsincos(cutoff/2, &cos);
 139     if (low) {
 140         const int32_t sin_div_g = DIV64(sin, g, 25);
 141         cos >>= 3;
 142         b0 = FRACMUL(sin, g) + cos;   /* 0.25 .. 4.10 */
 143         b1 = FRACMUL(sin, g) - cos;   /* -1 .. 3.98 */
 144         a0 = sin_div_g + cos;         /* 0.25 .. 4.10 */
 145         a1 = sin_div_g - cos;         /* -1 .. 3.98 */
 146     } else {
 147         const int32_t cos_div_g = DIV64(cos, g, 25);
 148         sin >>= 3;
 149         b0 = sin + FRACMUL(cos, g);   /* 0.25 .. 4.10 */
 150         b1 = sin - FRACMUL(cos, g);   /* -3.98 .. 1 */
 151         a0 = sin + cos_div_g;         /* 0.25 .. 4.10 */
 152         a1 = sin - cos_div_g;         /* -3.98 .. 1 */
 153     }
 154
 155     const int32_t rcp_a0 = DIV64(1, a0, 57); /* 0.24 .. 3.98, s2.29 */
 156     *c++ = FRACMUL_SHL(b0, rcp_a0, 1);       /* 0.063 .. 15.85 */
 157     *c++ = FRACMUL_SHL(b1, rcp_a0, 1);       /* -15.85 .. 15.85 */
 158     *c++ = -FRACMUL_SHL(a1, rcp_a0, 1);      /* -1 .. 1 */
 159 }
 160
 161 #ifdef HAVE_SW_TONE_CONTROLS
 162 /**
 163  * Calculate second order section filter consisting of one low-shelf and one
 164  * high-shelf section.
 165  * @param cutoff_low low-shelf midpoint frequency. See eq_pk_coefs for format.
 166  * @param cutoff_high high-shelf midpoint frequency.
 167  * @param A_low decibel value multiplied by ten, describing gain/attenuation of
 168  * low-shelf part. Max value is 24 dB.
 169  * @param A_high decibel value multiplied by ten, describing gain/attenuation of
 170  * high-shelf part. Max value is 24 dB.
 171  * @param A decibel value multiplied by ten, describing additional overall gain.
 172  * @param c pointer to coefficient storage. Coefficients are s4.27 format.
 173  */
 174 void filter_bishelf_coefs(unsigned long cutoff_low, unsigned long cutoff_high,
 175                           long A_low, long A_high, long A, int32_t *c)
 176 {
 177     const long g = get_replaygain_int(A*10) << 7; /* 10^(db/20), s0.31 */
 178     int32_t c_ls[3], c_hs[3];
 179
 180     filter_shelf_coefs(cutoff_low, A_low, true, c_ls);
 181     filter_shelf_coefs(cutoff_high, A_high, false, c_hs);
 182     c_ls[0] = FRACMUL(g, c_ls[0]);
 183     c_ls[1] = FRACMUL(g, c_ls[1]);
 184
 185     /* now we cascade the two first order filters to one second order filter
 186      * which can be used by eq_filter(). these resulting coefficients have a
 187      * really wide numerical range, so we use a fixed point format which will
 188      * work for the selected cutoff frequencies (in dsp.c) only.
 189      */
 190     const int32_t b0 = c_ls[0], b1 = c_ls[1], b2 = c_hs[0], b3 = c_hs[1];
 191     const int32_t a0 = c_ls[2], a1 = c_hs[2];
 192     *c++ = FRACMUL_SHL(b0, b2, 4);
 193     *c++ = FRACMUL_SHL(b0, b3, 4) + FRACMUL_SHL(b1, b2, 4);
 194     *c++ = FRACMUL_SHL(b1, b3, 4);
 195     *c++ = a0 + a1;
 196     *c++ = -FRACMUL_SHL(a0, a1, 4);
 197 }
 198 #endif
 199
 200 /* Coef calculation taken from Audio-EQ-Cookbook.txt by Robert Bristow-Johnson.
 201  * Slightly faster calculation can be done by deriving forms which use tan()
 202  * instead of cos() and sin(), but the latter are far easier to use when doing
 203  * fixed point math, and performance is not a big point in the calculation part.
 204  * All the 'a' filter coefficients are negated so we can use only additions
 205  * in the filtering equation.
 206  */
 207
 208 /**
 209  * Calculate second order section peaking filter coefficients.
 210  * @param cutoff a value from 0 to 0x80000000, where 0 represents 0 Hz and
 211  * 0x80000000 represents the Nyquist frequency (samplerate/2).
 212  * @param Q Q factor value multiplied by ten. Lower bound is artificially set
 213  * at 0.5.
 214  * @param db decibel value multiplied by ten, describing gain/attenuation at
 215  * peak freq. Max value is 24 dB.
 216  * @param c pointer to coefficient storage. Coefficients are s3.28 format.
 217  */
 218 void eq_pk_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
 219 {
 220     long cs;
 221     const long one = 1 << 28; /* s3.28 */
 222     const long A = get_replaygain_int(db*5) << 5; /* 10^(db/40), s2.29 */
 223     const long alpha = fsincos(cutoff, &cs)/(2*Q)*10 >> 1; /* s1.30 */
 224     int32_t a0, a1, a2; /* these are all s3.28 format */
 225     int32_t b0, b1, b2;
 226     const long alphadivA = DIV64(alpha, A, 27);
 227
 228     /* possible numerical ranges are in comments by each coef */
 229     b0 = one + FRACMUL(alpha, A);     /* [1 .. 5] */
 230     b1 = a1 = -2*(cs >> 3);           /* [-2 .. 2] */
 231     b2 = one - FRACMUL(alpha, A);     /* [-3 .. 1] */
 232     a0 = one + alphadivA;             /* [1 .. 5] */
 233     a2 = one - alphadivA;             /* [-3 .. 1] */
 234
 235     /* range of this is roughly [0.2 .. 1], but we'll never hit 1 completely */
 236     const long rcp_a0 = DIV64(1, a0, 59); /* s0.31 */
 237     *c++ = FRACMUL(b0, rcp_a0);         /* [0.25 .. 4] */
 238     *c++ = FRACMUL(b1, rcp_a0);         /* [-2 .. 2] */
 239     *c++ = FRACMUL(b2, rcp_a0);         /* [-2.4 .. 1] */
 240     *c++ = FRACMUL(-a1, rcp_a0);        /* [-2 .. 2] */
 241     *c++ = FRACMUL(-a2, rcp_a0);        /* [-0.6 .. 1] */
 242 }
 243
 244 /**
 245  * Calculate coefficients for lowshelf filter. Parameters are as for
 246  * eq_pk_coefs, but the coefficient format is s5.26 fixed point.
 247  */
 248 void eq_ls_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
 249 {
 250     long cs;
 251     const long one = 1 << 25; /* s6.25 */
 252     const long sqrtA = get_replaygain_int(db*5/2) << 2; /* 10^(db/80), s5.26 */
 253     const long A = FRACMUL_SHL(sqrtA, sqrtA, 8); /* s2.29 */
 254     const long alpha = fsincos(cutoff, &cs)/(2*Q)*10 >> 1; /* s1.30 */
 255     const long ap1 = (A >> 4) + one;
 256     const long am1 = (A >> 4) - one;
 257     const long twosqrtalpha = 2*FRACMUL(sqrtA, alpha);
 258     int32_t a0, a1, a2; /* these are all s6.25 format */
 259     int32_t b0, b1, b2;
 260
 261     /* [0.1 .. 40] */
 262     b0 = FRACMUL_SHL(A, ap1 - FRACMUL(am1, cs) + twosqrtalpha, 2);
 263     /* [-16 .. 63.4] */
 264     b1 = FRACMUL_SHL(A, am1 - FRACMUL(ap1, cs), 3);
 265     /* [0 .. 31.7] */
 266     b2 = FRACMUL_SHL(A, ap1 - FRACMUL(am1, cs) - twosqrtalpha, 2);
 267     /* [0.5 .. 10] */
 268     a0 = ap1 + FRACMUL(am1, cs) + twosqrtalpha;
 269     /* [-16 .. 4] */
 270     a1 = -2*((am1 + FRACMUL(ap1, cs)));
 271     /* [0 .. 8] */
 272     a2 = ap1 + FRACMUL(am1, cs) - twosqrtalpha;
 273
 274     /* [0.1 .. 1.99] */
 275     const long rcp_a0 = DIV64(1, a0, 55);    /* s1.30 */
 276     *c++ = FRACMUL_SHL(b0, rcp_a0, 2);       /* [0.06 .. 15.9] */
 277     *c++ = FRACMUL_SHL(b1, rcp_a0, 2);       /* [-2 .. 31.7] */
 278     *c++ = FRACMUL_SHL(b2, rcp_a0, 2);       /* [0 .. 15.9] */
 279     *c++ = FRACMUL_SHL(-a1, rcp_a0, 2);      /* [-2 .. 2] */
 280     *c++ = FRACMUL_SHL(-a2, rcp_a0, 2);      /* [0 .. 1] */
 281 }
 282
 283 /**
 284  * Calculate coefficients for highshelf filter. Parameters are as for
 285  * eq_pk_coefs, but the coefficient format is s5.26 fixed point.
 286  */
 287 void eq_hs_coefs(unsigned long cutoff, unsigned long Q, long db, int32_t *c)
 288 {
 289     long cs;
 290     const long one = 1 << 25; /* s6.25 */
 291     const long sqrtA = get_replaygain_int(db*5/2) << 2; /* 10^(db/80), s5.26 */
 292     const long A = FRACMUL_SHL(sqrtA, sqrtA, 8); /* s2.29 */
 293     const long alpha = fsincos(cutoff, &cs)/(2*Q)*10 >> 1; /* s1.30 */
 294     const long ap1 = (A >> 4) + one;
 295     const long am1 = (A >> 4) - one;
 296     const long twosqrtalpha = 2*FRACMUL(sqrtA, alpha);
 297     int32_t a0, a1, a2; /* these are all s6.25 format */
 298     int32_t b0, b1, b2;
 299
 300     /* [0.1 .. 40] */
 301     b0 = FRACMUL_SHL(A, ap1 + FRACMUL(am1, cs) + twosqrtalpha, 2);
 302     /* [-63.5 .. 16] */
 303     b1 = -FRACMUL_SHL(A, am1 + FRACMUL(ap1, cs), 3);
 304     /* [0 .. 32] */
 305     b2 = FRACMUL_SHL(A, ap1 + FRACMUL(am1, cs) - twosqrtalpha, 2);
 306     /* [0.5 .. 10] */
 307     a0 = ap1 - FRACMUL(am1, cs) + twosqrtalpha;
 308     /* [-4 .. 16] */
 309     a1 = 2*((am1 - FRACMUL(ap1, cs)));
 310     /* [0 .. 8] */
 311     a2 = ap1 - FRACMUL(am1, cs) - twosqrtalpha;
 312
 313     /* [0.1 .. 1.99] */
 314     const long rcp_a0 = DIV64(1, a0, 55);    /* s1.30 */
 315     *c++ = FRACMUL_SHL(b0, rcp_a0, 2);       /* [0 .. 16] */
 316     *c++ = FRACMUL_SHL(b1, rcp_a0, 2);       /* [-31.7 .. 2] */
 317     *c++ = FRACMUL_SHL(b2, rcp_a0, 2);       /* [0 .. 16] */
 318     *c++ = FRACMUL_SHL(-a1, rcp_a0, 2);      /* [-2 .. 2] */
 319     *c++ = FRACMUL_SHL(-a2, rcp_a0, 2);      /* [0 .. 1] */
 320 }
 321
 322 /* We realise the filters as a second order direct form 1 structure. Direct
 323  * form 1 was chosen because of better numerical properties for fixed point
 324  * implementations.
 325  */
 326
 327 #if (!defined(CPU_COLDFIRE) && !defined(CPU_ARM))
 328 void eq_filter(int32_t **x, struct eqfilter *f, unsigned num,
 329                unsigned channels, unsigned shift)
 330 {
 331     unsigned c, i;
 332     long long acc;
 333
 334     /* Direct form 1 filtering code.
 335        y[n] = b0*x[i] + b1*x[i - 1] + b2*x[i - 2] + a1*y[i - 1] + a2*y[i - 2],
 336        where y[] is output and x[] is input.
 337      */
 338
 339     for (c = 0; c < channels; c++) {
 340         for (i = 0; i < num; i++) {
 341             acc  = (long long) x[c][i] * f->coefs[0];
 342             acc += (long long) f->history[c][0] * f->coefs[1];
 343             acc += (long long) f->history[c][1] * f->coefs[2];
 344             acc += (long long) f->history[c][2] * f->coefs[3];
 345             acc += (long long) f->history[c][3] * f->coefs[4];
 346             f->history[c][1] = f->history[c][0];
 347             f->history[c][0] = x[c][i];
 348             f->history[c][3] = f->history[c][2];
 349             x[c][i] = (acc << shift) >> 32;
 350             f->history[c][2] = x[c][i];
 351         }
 352     }
 353 }
 354 #endif
 355