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