apps/fixedpoint.c

   1 /***************************************************************************
   2  *             __________               __   ___.
   3  *   Open      \______   \ ____   ____ |  | _\_ |__   _______  ___
   4  *   Source     |       _//  _ \_/ ___\|  |/ /| __ \ /  _ \  \/  /
   5  *   Jukebox    |    |   (  <_> )  \___|    < | \_\ (  <_> > <  <
   6  *   Firmware   |____|_  /\____/ \___  >__|_ \|___  /\____/__/\_ \
   7  *                     \/            \/     \/    \/            \/
   8  * $Id: fixedpoint.c -1   $
   9  *
  10  * Copyright (C) 2006 Jens Arnold
  11  *
  12  * Fixed point library for plugins
  13  *
  14  * This program is free software; you can redistribute it and/or
  15  * modify it under the terms of the GNU General Public License
  16  * as published by the Free Software Foundation; either version 2
  17  * of the License, or (at your option) any later version.
  18  *
  19  * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY
  20  * KIND, either express or implied.
  21  *
  22  ****************************************************************************/
  23
  24 #include "fixedpoint.h"
  25 #include <stdlib.h>
  26 #include <stdbool.h>
  27
  28 #ifndef BIT_N
  29 #define BIT_N(n) (1U << (n))
  30 #endif
  31
  32 /** TAKEN FROM ORIGINAL fixedpoint.h */
  33 /* Inverse gain of circular cordic rotation in s0.31 format. */
  34 static const long cordic_circular_gain = 0xb2458939; /* 0.607252929 */
  35
  36 /* Table of values of atan(2^-i) in 0.32 format fractions of pi where pi = 0xffffffff / 2 */
  37 static const unsigned long atan_table[] = {
  38     0x1fffffff, /* +0.785398163 (or pi/4) */
  39     0x12e4051d, /* +0.463647609 */
  40     0x09fb385b, /* +0.244978663 */
  41     0x051111d4, /* +0.124354995 */
  42     0x028b0d43, /* +0.062418810 */
  43     0x0145d7e1, /* +0.031239833 */
  44     0x00a2f61e, /* +0.015623729 */
  45     0x00517c55, /* +0.007812341 */
  46     0x0028be53, /* +0.003906230 */
  47     0x00145f2e, /* +0.001953123 */
  48     0x000a2f98, /* +0.000976562 */
  49     0x000517cc, /* +0.000488281 */
  50     0x00028be6, /* +0.000244141 */
  51     0x000145f3, /* +0.000122070 */
  52     0x0000a2f9, /* +0.000061035 */
  53     0x0000517c, /* +0.000030518 */
  54     0x000028be, /* +0.000015259 */
  55     0x0000145f, /* +0.000007629 */
  56     0x00000a2f, /* +0.000003815 */
  57     0x00000517, /* +0.000001907 */
  58     0x0000028b, /* +0.000000954 */
  59     0x00000145, /* +0.000000477 */
  60     0x000000a2, /* +0.000000238 */
  61     0x00000051, /* +0.000000119 */
  62     0x00000028, /* +0.000000060 */
  63     0x00000014, /* +0.000000030 */
  64     0x0000000a, /* +0.000000015 */
  65     0x00000005, /* +0.000000007 */
  66     0x00000002, /* +0.000000004 */
  67     0x00000001, /* +0.000000002 */
  68     0x00000000, /* +0.000000001 */
  69     0x00000000, /* +0.000000000 */
  70 };
  71
  72 /* Precalculated sine and cosine * 16384 (2^14) (fixed point 18.14) */
  73 static const short sin_table[91] =
  74 {
  75         0,   285,   571,   857,  1142,  1427,  1712,  1996,  2280,  2563,
  76      2845,  3126,  3406,  3685,  3963,  4240,  4516,  4790,  5062,  5334,
  77      5603,  5871,  6137,  6401,  6663,  6924,  7182,  7438,  7691,  7943,
  78      8191,  8438,  8682,  8923,  9161,  9397,  9630,  9860, 10086, 10310,
  79     10531, 10748, 10963, 11173, 11381, 11585, 11785, 11982, 12175, 12365,
  80     12550, 12732, 12910, 13084, 13254, 13420, 13582, 13740, 13894, 14043,
  81     14188, 14329, 14466, 14598, 14725, 14848, 14967, 15081, 15190, 15295,
  82     15395, 15491, 15582, 15668, 15749, 15825, 15897, 15964, 16025, 16082,
  83     16135, 16182, 16224, 16261, 16294, 16321, 16344, 16361, 16374, 16381,
  84     16384
  85 };
  86
  87 /**
  88  * Implements sin and cos using CORDIC rotation.
  89  *
  90  * @param phase has range from 0 to 0xffffffff, representing 0 and
  91  *        2*pi respectively.
  92  * @param cos return address for cos
  93  * @return sin of phase, value is a signed value from LONG_MIN to LONG_MAX,
  94  *         representing -1 and 1 respectively.
  95  */
  96 long fsincos(unsigned long phase, long *cos)
  97 {
  98     int32_t x, x1, y, y1;
  99     unsigned long z, z1;
 100     int i;
 101
 102     /* Setup initial vector */
 103     x = cordic_circular_gain;
 104     y = 0;
 105     z = phase;
 106
 107     /* The phase has to be somewhere between 0..pi for this to work right */
 108     if (z < 0xffffffff / 4) {
 109         /* z in first quadrant, z += pi/2 to correct */
 110         x = -x;
 111         z += 0xffffffff / 4;
 112     } else if (z < 3 * (0xffffffff / 4)) {
 113         /* z in third quadrant, z -= pi/2 to correct */
 114         z -= 0xffffffff / 4;
 115     } else {
 116         /* z in fourth quadrant, z -= 3pi/2 to correct */
 117         x = -x;
 118         z -= 3 * (0xffffffff / 4);
 119     }
 120
 121     /* Each iteration adds roughly 1-bit of extra precision */
 122     for (i = 0; i < 31; i++) {
 123         x1 = x >> i;
 124         y1 = y >> i;
 125         z1 = atan_table[i];
 126
 127         /* Decided which direction to rotate vector. Pivot point is pi/2 */
 128         if (z >= 0xffffffff / 4) {
 129             x -= y1;
 130             y += x1;
 131             z -= z1;
 132         } else {
 133             x += y1;
 134             y -= x1;
 135             z += z1;
 136         }
 137     }
 138
 139     if (cos)
 140         *cos = x;
 141
 142     return y;
 143 }
 144
 145 /**
 146  * Fixed point square root via Newton-Raphson.
 147  * @param x square root argument.
 148  * @param fracbits specifies number of fractional bits in argument.
 149  * @return Square root of argument in same fixed point format as input.
 150  *
 151  * This routine has been modified to run longer for greater precision,
 152  * but cuts calculation short if the answer is reached sooner.  In
 153  * general, the closer x is to 1, the quicker the calculation.
 154  */
 155 long fsqrt(long x, unsigned int fracbits)
 156 {
 157     long b = x/2 + BIT_N(fracbits); /* initial approximation */
 158     long c;
 159     unsigned n;
 160     const unsigned iterations = 8;
 161
 162     for (n = 0; n < iterations; ++n)
 163     {
 164         c = DIV64(x, b, fracbits);
 165         if (c == b) break;
 166         b = (b + c)/2;
 167     }
 168
 169     return b;
 170 }
 171
 172 /**
 173  * Fixed point sinus using a lookup table
 174  * don't forget to divide the result by 16384 to get the actual sinus value
 175  * @param val sinus argument in degree
 176  * @return sin(val)*16384
 177  */
 178 long sin_int(int val)
 179 {
 180     val = (val+360)%360;
 181     if (val < 181)
 182     {
 183         if (val < 91)/* phase 0-90 degree */
 184             return (long)sin_table[val];
 185         else/* phase 91-180 degree */
 186             return (long)sin_table[180-val];
 187     }
 188     else
 189     {
 190         if (val < 271)/* phase 181-270 degree */
 191             return -(long)sin_table[val-180];
 192         else/* phase 270-359 degree */
 193             return -(long)sin_table[360-val];
 194     }
 195     return 0;
 196 }
 197
 198 /**
 199  * Fixed point cosinus using a lookup table
 200  * don't forget to divide the result by 16384 to get the actual cosinus value
 201  * @param val sinus argument in degree
 202  * @return cos(val)*16384
 203  */
 204 long cos_int(int val)
 205 {
 206     val = (val+360)%360;
 207     if (val < 181)
 208     {
 209         if (val < 91)/* phase 0-90 degree */
 210             return (long)sin_table[90-val];
 211         else/* phase 91-180 degree */
 212             return -(long)sin_table[val-90];
 213     }
 214     else
 215     {
 216         if (val < 271)/* phase 181-270 degree */
 217             return -(long)sin_table[270-val];
 218         else/* phase 270-359 degree */
 219             return (long)sin_table[val-270];
 220     }
 221     return 0;
 222 }
 223
 224 /**
 225  * Fixed-point natural log
 226  * taken from http://www.quinapalus.com/efunc.html
 227  *  "The code assumes integers are at least 32 bits long. The (positive)
 228  *   argument and the result of the function are both expressed as fixed-point
 229  *   values with 16 fractional bits, although intermediates are kept with 28
 230  *   bits of precision to avoid loss of accuracy during shifts."
 231  */
 232
 233 long flog(int x) {
 234     long t,y;
 235
 236     y=0xa65af;
 237     if(x<0x00008000) x<<=16,              y-=0xb1721;
 238     if(x<0x00800000) x<<= 8,              y-=0x58b91;
 239     if(x<0x08000000) x<<= 4,              y-=0x2c5c8;
 240     if(x<0x20000000) x<<= 2,              y-=0x162e4;
 241     if(x<0x40000000) x<<= 1,              y-=0x0b172;
 242     t=x+(x>>1); if((t&0x80000000)==0) x=t,y-=0x067cd;
 243     t=x+(x>>2); if((t&0x80000000)==0) x=t,y-=0x03920;
 244     t=x+(x>>3); if((t&0x80000000)==0) x=t,y-=0x01e27;
 245     t=x+(x>>4); if((t&0x80000000)==0) x=t,y-=0x00f85;
 246     t=x+(x>>5); if((t&0x80000000)==0) x=t,y-=0x007e1;
 247     t=x+(x>>6); if((t&0x80000000)==0) x=t,y-=0x003f8;
 248     t=x+(x>>7); if((t&0x80000000)==0) x=t,y-=0x001fe;
 249     x=0x80000000-x;
 250     y-=x>>15;
 251     return y;
 252 }
 253
 254 /** MODIFIED FROM replaygain.c */
 255 /* These math routines have 64-bit internal precision to avoid overflows.
 256  * Arguments and return values are 32-bit (long) precision.
 257  */
 258
 259 #define FP_MUL64(x, y) (((x) * (y)) >> (fracbits))
 260 #define FP_DIV64(x, y) (((x) << (fracbits)) / (y))
 261
 262 static long long fp_exp10(long long x, unsigned int fracbits);
 263 static long long fp_log10(long long n, unsigned int fracbits);
 264
 265 /* constants in fixed point format, 28 fractional bits */
 266 #define FP28_LN2        (186065279LL)   /* ln(2)        */
 267 #define FP28_LN2_INV    (387270501LL)   /* 1/ln(2)      */
 268 #define FP28_EXP_ZERO   (44739243LL)    /* 1/6          */
 269 #define FP28_EXP_ONE    (-745654LL)     /* -1/360       */
 270 #define FP28_EXP_TWO    (12428LL)       /* 1/21600      */
 271 #define FP28_LN10       (618095479LL)   /* ln(10)       */
 272 #define FP28_LOG10OF2   (80807124LL)    /* log10(2)     */
 273
 274 #define TOL_BITS         2              /* log calculation tolerance */
 275
 276
 277 /* The fpexp10 fixed point math routine is based
 278  * on oMathFP by Dan Carter (http://orbisstudios.com).
 279  */
 280
 281 /** FIXED POINT EXP10
 282  * Return 10^x as FP integer.  Argument is FP integer.
 283  */
 284 static long long fp_exp10(long long x, unsigned int fracbits)
 285 {
 286     long long k;
 287     long long z;
 288     long long R;
 289     long long xp;
 290
 291     /* scale constants */
 292     const long long fp_one      = (1 << fracbits);
 293     const long long fp_half     = (1 << (fracbits - 1));
 294     const long long fp_two      = (2 << fracbits);
 295     const long long fp_mask     = (fp_one - 1);
 296     const long long fp_ln2_inv  = (FP28_LN2_INV     >> (28 - fracbits));
 297     const long long fp_ln2      = (FP28_LN2         >> (28 - fracbits));
 298     const long long fp_ln10     = (FP28_LN10        >> (28 - fracbits));
 299     const long long fp_exp_zero = (FP28_EXP_ZERO    >> (28 - fracbits));
 300     const long long fp_exp_one  = (FP28_EXP_ONE     >> (28 - fracbits));
 301     const long long fp_exp_two  = (FP28_EXP_TWO     >> (28 - fracbits));
 302
 303     /* exp(0) = 1 */
 304     if (x == 0)
 305     {
 306         return fp_one;
 307     }
 308
 309     /* convert from base 10 to base e */
 310     x = FP_MUL64(x, fp_ln10);
 311
 312     /* calculate exp(x) */
 313     k = (FP_MUL64(abs(x), fp_ln2_inv) + fp_half) & ~fp_mask;
 314
 315     if (x < 0)
 316     {
 317         k = -k;
 318     }
 319
 320     x -= FP_MUL64(k, fp_ln2);
 321     z = FP_MUL64(x, x);
 322     R = fp_two + FP_MUL64(z, fp_exp_zero + FP_MUL64(z, fp_exp_one
 323         + FP_MUL64(z, fp_exp_two)));
 324     xp = fp_one + FP_DIV64(FP_MUL64(fp_two, x), R - x);
 325
 326     if (k < 0)
 327     {
 328         k = fp_one >> (-k >> fracbits);
 329     }
 330     else
 331     {
 332         k = fp_one << (k >> fracbits);
 333     }
 334
 335     return FP_MUL64(k, xp);
 336 }
 337
 338
 339 /** FIXED POINT LOG10
 340  * Return log10(x) as FP integer.  Argument is FP integer.
 341  */
 342 static long long fp_log10(long long n, unsigned int fracbits)
 343 {
 344     /* Calculate log2 of argument */
 345
 346     long long log2, frac;
 347     const long long fp_one  = (1 << fracbits);
 348     const long long fp_two  = (2 << fracbits);
 349     const long tolerance    = (1 << ((fracbits / 2) + 2));
 350
 351     if (n <=0) return FP_NEGINF;
 352     log2 = 0;
 353
 354     /* integer part */
 355     while (n < fp_one)
 356     {
 357         log2 -= fp_one;
 358         n <<= 1;
 359     }
 360     while (n >= fp_two)
 361     {
 362         log2 += fp_one;
 363         n >>= 1;
 364     }
 365
 366     /* fractional part */
 367     frac = fp_one;
 368     while (frac > tolerance)
 369     {
 370         frac >>= 1;
 371         n = FP_MUL64(n, n);
 372         if (n >= fp_two)
 373         {
 374             n >>= 1;
 375             log2 += frac;
 376         }
 377     }
 378
 379     /* convert log2 to log10 */
 380     return FP_MUL64(log2, (FP28_LOG10OF2 >> (28 - fracbits)));
 381 }
 382
 383
 384 /** CONVERT FACTOR TO DECIBELS */
 385 long fp_decibels(unsigned long factor, unsigned int fracbits)
 386 {
 387     long long decibels;
 388     long long f = (long long)factor;
 389     bool neg;
 390
 391     /* keep factor in signed long range */
 392     if (f >= (1LL << 31))
 393         f = (1LL << 31) - 1;
 394
 395     /* decibels = 20 * log10(factor) */
 396     decibels = FP_MUL64((20LL << fracbits), fp_log10(f, fracbits));
 397
 398     /* keep result in signed long range */
 399     if ((neg = (decibels < 0)))
 400         decibels = -decibels;
 401     if (decibels >= (1LL << 31))
 402         return neg ? FP_NEGINF : FP_INF;
 403
 404     return neg ? (long)-decibels : (long)decibels;
 405 }
 406
 407
 408 /** CONVERT DECIBELS TO FACTOR */
 409 long fp_factor(long decibels, unsigned int fracbits)
 410 {
 411     bool neg;
 412     long long factor;
 413     long long db = (long long)decibels;
 414
 415     /* if decibels is 0, factor is 1 */
 416     if (db == 0)
 417         return (1L << fracbits);
 418
 419     /* calculate for positive decibels only */
 420     if ((neg = (db < 0)))
 421         db = -db;
 422
 423     /* factor = 10 ^ (decibels / 20) */
 424     factor = fp_exp10(FP_DIV64(db, (20LL << fracbits)), fracbits);
 425
 426     /* keep result in signed long range, return 0 if very small */
 427     if (factor >= (1LL << 31))
 428     {
 429         if (neg)
 430             return 0;
 431         else
 432             return FP_INF;
 433     }
 434
 435     /* if negative argument, factor is 1 / result */
 436     if (neg)
 437         factor = FP_DIV64((1LL << fracbits), factor);
 438
 439     return (long)factor;
 440 }