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 #include <inttypes.h>
  28
  29 #ifndef BIT_N
  30 #define BIT_N(n) (1U << (n))
  31 #endif
  32
  33 /** TAKEN FROM ORIGINAL fixedpoint.h */
  34 /* Inverse gain of circular cordic rotation in s0.31 format. */
  35 static const long cordic_circular_gain = 0xb2458939; /* 0.607252929 */
  36
  37 /* Table of values of atan(2^-i) in 0.32 format fractions of pi where pi = 0xffffffff / 2 */
  38 static const unsigned long atan_table[] = {
  39     0x1fffffff, /* +0.785398163 (or pi/4) */
  40     0x12e4051d, /* +0.463647609 */
  41     0x09fb385b, /* +0.244978663 */
  42     0x051111d4, /* +0.124354995 */
  43     0x028b0d43, /* +0.062418810 */
  44     0x0145d7e1, /* +0.031239833 */
  45     0x00a2f61e, /* +0.015623729 */
  46     0x00517c55, /* +0.007812341 */
  47     0x0028be53, /* +0.003906230 */
  48     0x00145f2e, /* +0.001953123 */
  49     0x000a2f98, /* +0.000976562 */
  50     0x000517cc, /* +0.000488281 */
  51     0x00028be6, /* +0.000244141 */
  52     0x000145f3, /* +0.000122070 */
  53     0x0000a2f9, /* +0.000061035 */
  54     0x0000517c, /* +0.000030518 */
  55     0x000028be, /* +0.000015259 */
  56     0x0000145f, /* +0.000007629 */
  57     0x00000a2f, /* +0.000003815 */
  58     0x00000517, /* +0.000001907 */
  59     0x0000028b, /* +0.000000954 */
  60     0x00000145, /* +0.000000477 */
  61     0x000000a2, /* +0.000000238 */
  62     0x00000051, /* +0.000000119 */
  63     0x00000028, /* +0.000000060 */
  64     0x00000014, /* +0.000000030 */
  65     0x0000000a, /* +0.000000015 */
  66     0x00000005, /* +0.000000007 */
  67     0x00000002, /* +0.000000004 */
  68     0x00000001, /* +0.000000002 */
  69     0x00000000, /* +0.000000001 */
  70     0x00000000, /* +0.000000000 */
  71 };
  72
  73 /* Precalculated sine and cosine * 16384 (2^14) (fixed point 18.14) */
  74 static const short sin_table[91] =
  75 {
  76         0,   285,   571,   857,  1142,  1427,  1712,  1996,  2280,  2563,
  77      2845,  3126,  3406,  3685,  3963,  4240,  4516,  4790,  5062,  5334,
  78      5603,  5871,  6137,  6401,  6663,  6924,  7182,  7438,  7691,  7943,
  79      8191,  8438,  8682,  8923,  9161,  9397,  9630,  9860, 10086, 10310,
  80     10531, 10748, 10963, 11173, 11381, 11585, 11785, 11982, 12175, 12365,
  81     12550, 12732, 12910, 13084, 13254, 13420, 13582, 13740, 13894, 14043,
  82     14188, 14329, 14466, 14598, 14725, 14848, 14967, 15081, 15190, 15295,
  83     15395, 15491, 15582, 15668, 15749, 15825, 15897, 15964, 16025, 16082,
  84     16135, 16182, 16224, 16261, 16294, 16321, 16344, 16361, 16374, 16381,
  85     16384
  86 };
  87
  88 /**
  89  * Implements sin and cos using CORDIC rotation.
  90  *
  91  * @param phase has range from 0 to 0xffffffff, representing 0 and
  92  *        2*pi respectively.
  93  * @param cos return address for cos
  94  * @return sin of phase, value is a signed value from LONG_MIN to LONG_MAX,
  95  *         representing -1 and 1 respectively.
  96  */
  97 long fp_sincos(unsigned long phase, long *cos)
  98 {
  99     int32_t x, x1, y, y1;
 100     unsigned long z, z1;
 101     int i;
 102
 103     /* Setup initial vector */
 104     x = cordic_circular_gain;
 105     y = 0;
 106     z = phase;
 107
 108     /* The phase has to be somewhere between 0..pi for this to work right */
 109     if (z < 0xffffffff / 4) {
 110         /* z in first quadrant, z += pi/2 to correct */
 111         x = -x;
 112         z += 0xffffffff / 4;
 113     } else if (z < 3 * (0xffffffff / 4)) {
 114         /* z in third quadrant, z -= pi/2 to correct */
 115         z -= 0xffffffff / 4;
 116     } else {
 117         /* z in fourth quadrant, z -= 3pi/2 to correct */
 118         x = -x;
 119         z -= 3 * (0xffffffff / 4);
 120     }
 121
 122     /* Each iteration adds roughly 1-bit of extra precision */
 123     for (i = 0; i < 31; i++) {
 124         x1 = x >> i;
 125         y1 = y >> i;
 126         z1 = atan_table[i];
 127
 128         /* Decided which direction to rotate vector. Pivot point is pi/2 */
 129         if (z >= 0xffffffff / 4) {
 130             x -= y1;
 131             y += x1;
 132             z -= z1;
 133         } else {
 134             x += y1;
 135             y -= x1;
 136             z += z1;
 137         }
 138     }
 139
 140     if (cos)
 141         *cos = x;
 142
 143     return y;
 144 }
 145
 146
 147 #if defined(PLUGIN) || defined(CODEC)
 148 /**
 149  * Fixed point square root via Newton-Raphson.
 150  * @param x square root argument.
 151  * @param fracbits specifies number of fractional bits in argument.
 152  * @return Square root of argument in same fixed point format as input.
 153  *
 154  * This routine has been modified to run longer for greater precision,
 155  * but cuts calculation short if the answer is reached sooner.  In
 156  * general, the closer x is to 1, the quicker the calculation.
 157  */
 158 long fp_sqrt(long x, unsigned int fracbits)
 159 {
 160     long b = x/2 + BIT_N(fracbits); /* initial approximation */
 161     long c;
 162     unsigned n;
 163     const unsigned iterations = 8;
 164
 165     for (n = 0; n < iterations; ++n)
 166     {
 167         c = fp_div(x, b, fracbits);
 168         if (c == b) break;
 169         b = (b + c)/2;
 170     }
 171
 172     return b;
 173 }
 174 #endif  /* PLUGIN or CODEC */
 175
 176
 177 #if defined(PLUGIN)
 178 /**
 179  * Fixed point sinus using a lookup table
 180  * don't forget to divide the result by 16384 to get the actual sinus value
 181  * @param val sinus argument in degree
 182  * @return sin(val)*16384
 183  */
 184 long fp14_sin(int val)
 185 {
 186     val = (val+360)%360;
 187     if (val < 181)
 188     {
 189         if (val < 91)/* phase 0-90 degree */
 190             return (long)sin_table[val];
 191         else/* phase 91-180 degree */
 192             return (long)sin_table[180-val];
 193     }
 194     else
 195     {
 196         if (val < 271)/* phase 181-270 degree */
 197             return -(long)sin_table[val-180];
 198         else/* phase 270-359 degree */
 199             return -(long)sin_table[360-val];
 200     }
 201     return 0;
 202 }
 203
 204 /**
 205  * Fixed point cosinus using a lookup table
 206  * don't forget to divide the result by 16384 to get the actual cosinus value
 207  * @param val sinus argument in degree
 208  * @return cos(val)*16384
 209  */
 210 long fp14_cos(int val)
 211 {
 212     val = (val+360)%360;
 213     if (val < 181)
 214     {
 215         if (val < 91)/* phase 0-90 degree */
 216             return (long)sin_table[90-val];
 217         else/* phase 91-180 degree */
 218             return -(long)sin_table[val-90];
 219     }
 220     else
 221     {
 222         if (val < 271)/* phase 181-270 degree */
 223             return -(long)sin_table[270-val];
 224         else/* phase 270-359 degree */
 225             return (long)sin_table[val-270];
 226     }
 227     return 0;
 228 }
 229
 230 /**
 231  * Fixed-point natural log
 232  * taken from http://www.quinapalus.com/efunc.html
 233  *  "The code assumes integers are at least 32 bits long. The (positive)
 234  *   argument and the result of the function are both expressed as fixed-point
 235  *   values with 16 fractional bits, although intermediates are kept with 28
 236  *   bits of precision to avoid loss of accuracy during shifts."
 237  */
 238
 239 long fp16_log(int x) {
 240     long t,y;
 241
 242     y=0xa65af;
 243     if(x<0x00008000) x<<=16,              y-=0xb1721;
 244     if(x<0x00800000) x<<= 8,              y-=0x58b91;
 245     if(x<0x08000000) x<<= 4,              y-=0x2c5c8;
 246     if(x<0x20000000) x<<= 2,              y-=0x162e4;
 247     if(x<0x40000000) x<<= 1,              y-=0x0b172;
 248     t=x+(x>>1); if((t&0x80000000)==0) x=t,y-=0x067cd;
 249     t=x+(x>>2); if((t&0x80000000)==0) x=t,y-=0x03920;
 250     t=x+(x>>3); if((t&0x80000000)==0) x=t,y-=0x01e27;
 251     t=x+(x>>4); if((t&0x80000000)==0) x=t,y-=0x00f85;
 252     t=x+(x>>5); if((t&0x80000000)==0) x=t,y-=0x007e1;
 253     t=x+(x>>6); if((t&0x80000000)==0) x=t,y-=0x003f8;
 254     t=x+(x>>7); if((t&0x80000000)==0) x=t,y-=0x001fe;
 255     x=0x80000000-x;
 256     y-=x>>15;
 257     return y;
 258 }
 259 #endif /* PLUGIN */
 260
 261
 262 #if (!defined(PLUGIN) && !defined(CODEC))
 263 /** MODIFIED FROM replaygain.c */
 264 /* These math routines have 64-bit internal precision to avoid overflows.
 265  * Arguments and return values are 32-bit (long) precision.
 266  */
 267
 268 #define FP_MUL64(x, y) (((x) * (y)) >> (fracbits))
 269 #define FP_DIV64(x, y) (((x) << (fracbits)) / (y))
 270
 271 static long long fp_exp10(long long x, unsigned int fracbits);
 272 /* static long long fp_log10(long long n, unsigned int fracbits); */
 273
 274 /* constants in fixed point format, 28 fractional bits */
 275 #define FP28_LN2        (186065279LL)   /* ln(2)        */
 276 #define FP28_LN2_INV    (387270501LL)   /* 1/ln(2)      */
 277 #define FP28_EXP_ZERO   (44739243LL)    /* 1/6          */
 278 #define FP28_EXP_ONE    (-745654LL)     /* -1/360       */
 279 #define FP28_EXP_TWO    (12428LL)       /* 1/21600      */
 280 #define FP28_LN10       (618095479LL)   /* ln(10)       */
 281 #define FP28_LOG10OF2   (80807124LL)    /* log10(2)     */
 282
 283 #define TOL_BITS         2              /* log calculation tolerance */
 284
 285
 286 /* The fpexp10 fixed point math routine is based
 287  * on oMathFP by Dan Carter (http://orbisstudios.com).
 288  */
 289
 290 /** FIXED POINT EXP10
 291  * Return 10^x as FP integer.  Argument is FP integer.
 292  */
 293 static long long fp_exp10(long long x, unsigned int fracbits)
 294 {
 295     long long k;
 296     long long z;
 297     long long R;
 298     long long xp;
 299
 300     /* scale constants */
 301     const long long fp_one      = (1 << fracbits);
 302     const long long fp_half     = (1 << (fracbits - 1));
 303     const long long fp_two      = (2 << fracbits);
 304     const long long fp_mask     = (fp_one - 1);
 305     const long long fp_ln2_inv  = (FP28_LN2_INV     >> (28 - fracbits));
 306     const long long fp_ln2      = (FP28_LN2         >> (28 - fracbits));
 307     const long long fp_ln10     = (FP28_LN10        >> (28 - fracbits));
 308     const long long fp_exp_zero = (FP28_EXP_ZERO    >> (28 - fracbits));
 309     const long long fp_exp_one  = (FP28_EXP_ONE     >> (28 - fracbits));
 310     const long long fp_exp_two  = (FP28_EXP_TWO     >> (28 - fracbits));
 311
 312     /* exp(0) = 1 */
 313     if (x == 0)
 314     {
 315         return fp_one;
 316     }
 317
 318     /* convert from base 10 to base e */
 319     x = FP_MUL64(x, fp_ln10);
 320
 321     /* calculate exp(x) */
 322     k = (FP_MUL64(abs(x), fp_ln2_inv) + fp_half) & ~fp_mask;
 323
 324     if (x < 0)
 325     {
 326         k = -k;
 327     }
 328
 329     x -= FP_MUL64(k, fp_ln2);
 330     z = FP_MUL64(x, x);
 331     R = fp_two + FP_MUL64(z, fp_exp_zero + FP_MUL64(z, fp_exp_one
 332         + FP_MUL64(z, fp_exp_two)));
 333     xp = fp_one + FP_DIV64(FP_MUL64(fp_two, x), R - x);
 334
 335     if (k < 0)
 336     {
 337         k = fp_one >> (-k >> fracbits);
 338     }
 339     else
 340     {
 341         k = fp_one << (k >> fracbits);
 342     }
 343
 344     return FP_MUL64(k, xp);
 345 }
 346
 347
 348 #if 0   /* useful code, but not currently used */
 349 /** FIXED POINT LOG10
 350  * Return log10(x) as FP integer.  Argument is FP integer.
 351  */
 352 static long long fp_log10(long long n, unsigned int fracbits)
 353 {
 354     /* Calculate log2 of argument */
 355
 356     long long log2, frac;
 357     const long long fp_one  = (1 << fracbits);
 358     const long long fp_two  = (2 << fracbits);
 359     const long tolerance    = (1 << ((fracbits / 2) + 2));
 360
 361     if (n <=0) return FP_NEGINF;
 362     log2 = 0;
 363
 364     /* integer part */
 365     while (n < fp_one)
 366     {
 367         log2 -= fp_one;
 368         n <<= 1;
 369     }
 370     while (n >= fp_two)
 371     {
 372         log2 += fp_one;
 373         n >>= 1;
 374     }
 375
 376     /* fractional part */
 377     frac = fp_one;
 378     while (frac > tolerance)
 379     {
 380         frac >>= 1;
 381         n = FP_MUL64(n, n);
 382         if (n >= fp_two)
 383         {
 384             n >>= 1;
 385             log2 += frac;
 386         }
 387     }
 388
 389     /* convert log2 to log10 */
 390     return FP_MUL64(log2, (FP28_LOG10OF2 >> (28 - fracbits)));
 391 }
 392
 393
 394 /** CONVERT FACTOR TO DECIBELS */
 395 long fp_decibels(unsigned long factor, unsigned int fracbits)
 396 {
 397     long long decibels;
 398     long long f = (long long)factor;
 399     bool neg;
 400
 401     /* keep factor in signed long range */
 402     if (f >= (1LL << 31))
 403         f = (1LL << 31) - 1;
 404
 405     /* decibels = 20 * log10(factor) */
 406     decibels = FP_MUL64((20LL << fracbits), fp_log10(f, fracbits));
 407
 408     /* keep result in signed long range */
 409     if ((neg = (decibels < 0)))
 410         decibels = -decibels;
 411     if (decibels >= (1LL << 31))
 412         return neg ? FP_NEGINF : FP_INF;
 413
 414     return neg ? (long)-decibels : (long)decibels;
 415 }
 416 #endif  /* unused code */
 417
 418
 419 /** CONVERT DECIBELS TO FACTOR */
 420 long fp_factor(long decibels, unsigned int fracbits)
 421 {
 422     bool neg;
 423     long long factor;
 424     long long db = (long long)decibels;
 425
 426     /* if decibels is 0, factor is 1 */
 427     if (db == 0)
 428         return (1L << fracbits);
 429
 430     /* calculate for positive decibels only */
 431     if ((neg = (db < 0)))
 432         db = -db;
 433
 434     /* factor = 10 ^ (decibels / 20) */
 435     factor = fp_exp10(FP_DIV64(db, (20LL << fracbits)), fracbits);
 436
 437     /* keep result in signed long range, return 0 if very small */
 438     if (factor >= (1LL << 31))
 439     {
 440         if (neg)
 441             return 0;
 442         else
 443             return FP_INF;
 444     }
 445
 446     /* if negative argument, factor is 1 / result */
 447     if (neg)
 448         factor = FP_DIV64((1LL << fracbits), factor);
 449
 450     return (long)factor;
 451 }
 452 #endif  /* !PLUGIN and !CODEC */