apps/fixedpoint.c

   1 /***************************************************************************
   2  *             __________               __   ___.
   3  *   Open      \______   \ ____   ____ |  | _\_ |__   _______  ___
   4  *   Source     |       _//  _ \_/ ___\|  |/ /| __ \ /  _ \  \/  /
   5  *   Jukebox    |    |   (  <_> )  \___|    < | \_\ (  <_> > <  <
   6  *   Firmware   |____|_  /\____/ \___  >__|_ \|___  /\____/__/\_ \
   7  *                     \/            \/     \/    \/            \/
   8  * $Id$
   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.
 156  */
 157 long fp_sqrt(long x, unsigned int fracbits)
 158 {
 159     unsigned long xfp, b;
 160     int n = 8; /* iteration limit (should terminate earlier) */
 161
 162     if (x <= 0)
 163         return 0; /* no sqrt(neg), or just sqrt(0) = 0 */
 164
 165     /* Increase working precision by one bit */
 166     xfp = x << 1;
 167     fracbits++;
 168
 169     /* Get the midpoint between fracbits index and the highest bit index */
 170     b = ((sizeof(xfp)*8-1) - __builtin_clzl(xfp) + fracbits) >> 1;
 171     b = BIT_N(b);
 172
 173     do
 174     {
 175         unsigned long c = b;
 176         b = (fp_div(xfp, b, fracbits) + b) >> 1;
 177         if (c == b) break;
 178     }
 179     while (n-- > 0);
 180
 181     return b >> 1;
 182 }
 183
 184 /* Accurate int sqrt with only elementary operations.
 185  * Snagged from:
 186  *   http://www.devmaster.net/articles/fixed-point-optimizations/ */
 187 unsigned long isqrt(unsigned long x)
 188 {
 189     /* Adding CLZ could optimize this further */
 190     unsigned long g = 0;
 191     int bshift = 15;
 192     unsigned long b = 1ul << bshift;
 193
 194     do
 195     {
 196         unsigned long temp = (g + g + b) << bshift;
 197
 198         if (x > temp)
 199         {
 200             g += b;
 201             x -= temp;
 202         }
 203
 204         b >>= 1;
 205     }
 206     while (bshift--);
 207
 208     return g;
 209 }
 210 #endif  /* PLUGIN or CODEC */
 211
 212
 213 #if defined(PLUGIN)
 214 /**
 215  * Fixed point sinus using a lookup table
 216  * don't forget to divide the result by 16384 to get the actual sinus value
 217  * @param val sinus argument in degree
 218  * @return sin(val)*16384
 219  */
 220 long fp14_sin(int val)
 221 {
 222     val = (val+360)%360;
 223     if (val < 181)
 224     {
 225         if (val < 91)/* phase 0-90 degree */
 226             return (long)sin_table[val];
 227         else/* phase 91-180 degree */
 228             return (long)sin_table[180-val];
 229     }
 230     else
 231     {
 232         if (val < 271)/* phase 181-270 degree */
 233             return -(long)sin_table[val-180];
 234         else/* phase 270-359 degree */
 235             return -(long)sin_table[360-val];
 236     }
 237     return 0;
 238 }
 239
 240 /**
 241  * Fixed point cosinus using a lookup table
 242  * don't forget to divide the result by 16384 to get the actual cosinus value
 243  * @param val sinus argument in degree
 244  * @return cos(val)*16384
 245  */
 246 long fp14_cos(int val)
 247 {
 248     val = (val+360)%360;
 249     if (val < 181)
 250     {
 251         if (val < 91)/* phase 0-90 degree */
 252             return (long)sin_table[90-val];
 253         else/* phase 91-180 degree */
 254             return -(long)sin_table[val-90];
 255     }
 256     else
 257     {
 258         if (val < 271)/* phase 181-270 degree */
 259             return -(long)sin_table[270-val];
 260         else/* phase 270-359 degree */
 261             return (long)sin_table[val-270];
 262     }
 263     return 0;
 264 }
 265
 266 /**
 267  * Fixed-point natural log
 268  * taken from http://www.quinapalus.com/efunc.html
 269  *  "The code assumes integers are at least 32 bits long. The (positive)
 270  *   argument and the result of the function are both expressed as fixed-point
 271  *   values with 16 fractional bits, although intermediates are kept with 28
 272  *   bits of precision to avoid loss of accuracy during shifts."
 273  */
 274
 275 long fp16_log(int x) {
 276     long t,y;
 277
 278     y=0xa65af;
 279     if(x<0x00008000) x<<=16,              y-=0xb1721;
 280     if(x<0x00800000) x<<= 8,              y-=0x58b91;
 281     if(x<0x08000000) x<<= 4,              y-=0x2c5c8;
 282     if(x<0x20000000) x<<= 2,              y-=0x162e4;
 283     if(x<0x40000000) x<<= 1,              y-=0x0b172;
 284     t=x+(x>>1); if((t&0x80000000)==0) x=t,y-=0x067cd;
 285     t=x+(x>>2); if((t&0x80000000)==0) x=t,y-=0x03920;
 286     t=x+(x>>3); if((t&0x80000000)==0) x=t,y-=0x01e27;
 287     t=x+(x>>4); if((t&0x80000000)==0) x=t,y-=0x00f85;
 288     t=x+(x>>5); if((t&0x80000000)==0) x=t,y-=0x007e1;
 289     t=x+(x>>6); if((t&0x80000000)==0) x=t,y-=0x003f8;
 290     t=x+(x>>7); if((t&0x80000000)==0) x=t,y-=0x001fe;
 291     x=0x80000000-x;
 292     y-=x>>15;
 293     return y;
 294 }
 295
 296 /**
 297  * Fixed-point exponential
 298  * taken from http://www.quinapalus.com/efunc.html
 299  *  "The code assumes integers are at least 32 bits long. The (non-negative)
 300  *   argument and the result of the function are both expressed as fixed-point
 301  *   values with 16 fractional bits. Notice that after 11 steps of the
 302  *   algorithm the constants involved become such that the code is simply
 303  *   doing a multiplication: this is explained in the note below.
 304  *   The extension to negative arguments is left as an exercise."
 305  */
 306 long fp16_exp(int x)
 307 {
 308     int t,y;
 309
 310     y=0x00010000;
 311     t=x-0x58b91; if(t>=0) x=t,y<<=8;
 312     t=x-0x2c5c8; if(t>=0) x=t,y<<=4;
 313     t=x-0x162e4; if(t>=0) x=t,y<<=2;
 314     t=x-0x0b172; if(t>=0) x=t,y<<=1;
 315     t=x-0x067cd; if(t>=0) x=t,y+=y>>1;
 316     t=x-0x03920; if(t>=0) x=t,y+=y>>2;
 317     t=x-0x01e27; if(t>=0) x=t,y+=y>>3;
 318     t=x-0x00f85; if(t>=0) x=t,y+=y>>4;
 319     t=x-0x007e1; if(t>=0) x=t,y+=y>>5;
 320     t=x-0x003f8; if(t>=0) x=t,y+=y>>6;
 321     t=x-0x001fe; if(t>=0) x=t,y+=y>>7;
 322     if(x&0x100)               y+=y>>8;
 323     if(x&0x080)               y+=y>>9;
 324     if(x&0x040)               y+=y>>10;
 325     if(x&0x020)               y+=y>>11;
 326     if(x&0x010)               y+=y>>12;
 327     if(x&0x008)               y+=y>>13;
 328     if(x&0x004)               y+=y>>14;
 329     if(x&0x002)               y+=y>>15;
 330     if(x&0x001)               y+=y>>16;
 331     return y;
 332 }
 333 #endif /* PLUGIN */
 334
 335
 336 #if (!defined(PLUGIN) && !defined(CODEC))
 337 /** MODIFIED FROM replaygain.c */
 338
 339 #define FP_MUL_FRAC(x, y) fp_mul(x, y, fracbits)
 340 #define FP_DIV_FRAC(x, y) fp_div(x, y, fracbits)
 341
 342 /* constants in fixed point format, 28 fractional bits */
 343 #define FP28_LN2        (186065279L)    /* ln(2)        */
 344 #define FP28_LN2_INV    (387270501L)    /* 1/ln(2)      */
 345 #define FP28_EXP_ZERO   (44739243L)     /* 1/6          */
 346 #define FP28_EXP_ONE    (-745654L)      /* -1/360       */
 347 #define FP28_EXP_TWO    (12428L)        /* 1/21600      */
 348 #define FP28_LN10       (618095479L)    /* ln(10)       */
 349 #define FP28_LOG10OF2   (80807124L)     /* log10(2)     */
 350
 351 #define TOL_BITS         2              /* log calculation tolerance */
 352
 353
 354 /* The fpexp10 fixed point math routine is based
 355  * on oMathFP by Dan Carter (http://orbisstudios.com).
 356  */
 357
 358 /** FIXED POINT EXP10
 359  * Return 10^x as FP integer.  Argument is FP integer.
 360  */
 361 static long fp_exp10(long x, unsigned int fracbits)
 362 {
 363     long k;
 364     long z;
 365     long R;
 366     long xp;
 367
 368     /* scale constants */
 369     const long fp_one       = (1 << fracbits);
 370     const long fp_half      = (1 << (fracbits - 1));
 371     const long fp_two       = (2 << fracbits);
 372     const long fp_mask      = (fp_one - 1);
 373     const long fp_ln2_inv   = (FP28_LN2_INV     >> (28 - fracbits));
 374     const long fp_ln2       = (FP28_LN2         >> (28 - fracbits));
 375     const long fp_ln10      = (FP28_LN10        >> (28 - fracbits));
 376     const long fp_exp_zero  = (FP28_EXP_ZERO    >> (28 - fracbits));
 377     const long fp_exp_one   = (FP28_EXP_ONE     >> (28 - fracbits));
 378     const long fp_exp_two   = (FP28_EXP_TWO     >> (28 - fracbits));
 379
 380     /* exp(0) = 1 */
 381     if (x == 0)
 382     {
 383         return fp_one;
 384     }
 385
 386     /* convert from base 10 to base e */
 387     x = FP_MUL_FRAC(x, fp_ln10);
 388
 389     /* calculate exp(x) */
 390     k = (FP_MUL_FRAC(abs(x), fp_ln2_inv) + fp_half) & ~fp_mask;
 391
 392     if (x < 0)
 393     {
 394         k = -k;
 395     }
 396
 397     x -= FP_MUL_FRAC(k, fp_ln2);
 398     z = FP_MUL_FRAC(x, x);
 399     R = fp_two + FP_MUL_FRAC(z, fp_exp_zero + FP_MUL_FRAC(z, fp_exp_one
 400         + FP_MUL_FRAC(z, fp_exp_two)));
 401     xp = fp_one + FP_DIV_FRAC(FP_MUL_FRAC(fp_two, x), R - x);
 402
 403     if (k < 0)
 404     {
 405         k = fp_one >> (-k >> fracbits);
 406     }
 407     else
 408     {
 409         k = fp_one << (k >> fracbits);
 410     }
 411
 412     return FP_MUL_FRAC(k, xp);
 413 }
 414
 415
 416 #if 0   /* useful code, but not currently used */
 417 /** FIXED POINT LOG10
 418  * Return log10(x) as FP integer.  Argument is FP integer.
 419  */
 420 static long fp_log10(long n, unsigned int fracbits)
 421 {
 422     /* Calculate log2 of argument */
 423
 424     long log2, frac;
 425     const long fp_one       = (1 << fracbits);
 426     const long fp_two       = (2 << fracbits);
 427     const long tolerance    = (1 << ((fracbits / 2) + 2));
 428
 429     if (n <=0) return FP_NEGINF;
 430     log2 = 0;
 431
 432     /* integer part */
 433     while (n < fp_one)
 434     {
 435         log2 -= fp_one;
 436         n <<= 1;
 437     }
 438     while (n >= fp_two)
 439     {
 440         log2 += fp_one;
 441         n >>= 1;
 442     }
 443
 444     /* fractional part */
 445     frac = fp_one;
 446     while (frac > tolerance)
 447     {
 448         frac >>= 1;
 449         n = FP_MUL_FRAC(n, n);
 450         if (n >= fp_two)
 451         {
 452             n >>= 1;
 453             log2 += frac;
 454         }
 455     }
 456
 457     /* convert log2 to log10 */
 458     return FP_MUL_FRAC(log2, (FP28_LOG10OF2 >> (28 - fracbits)));
 459 }
 460
 461
 462 /** CONVERT FACTOR TO DECIBELS */
 463 long fp_decibels(unsigned long factor, unsigned int fracbits)
 464 {
 465     /* decibels = 20 * log10(factor) */
 466     return FP_MUL_FRAC((20L << fracbits), fp_log10(factor, fracbits));
 467 }
 468 #endif  /* unused code */
 469
 470
 471 /** CONVERT DECIBELS TO FACTOR */
 472 long fp_factor(long decibels, unsigned int fracbits)
 473 {
 474     /* factor = 10 ^ (decibels / 20) */
 475     return fp_exp10(FP_DIV_FRAC(decibels, (20L << fracbits)), fracbits);
 476 }
 477 #endif  /* !PLUGIN and !CODEC */