libmad/fixed.h

   1 /*
   2  * libmad - MPEG audio decoder library
   3  * Copyright (C) 2000-2003 Underbit Technologies, Inc.
   4  *
   5  * This program is free software; you can redistribute it and/or modify
   6  * it under the terms of the GNU General Public License as published by
   7  * the Free Software Foundation; either version 2 of the License, or
   8  * (at your option) any later version.
   9  *
  10  * This program is distributed in the hope that it will be useful,
  11  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13  * GNU General Public License for more details.
  14  *
  15  * You should have received a copy of the GNU General Public License
  16  * along with this program; if not, write to the Free Software
  17  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  18  *
  19  */
  20
  21 # ifndef LIBMAD_FIXED_H
  22 # define LIBMAD_FIXED_H
  23
  24 #include <gctypes.h>
  25
  26 # if SIZEOF_INT >= 4
  27 typedef s32 mad_fixed_t;
  28
  29 typedef s32 mad_fixed64hi_t;
  30 typedef u32 mad_fixed64lo_t;
  31 # else
  32 typedef s32 mad_fixed_t;
  33
  34 typedef s32 mad_fixed64hi_t;
  35 typedef u32 mad_fixed64lo_t;
  36 # endif
  37
  38 # if defined(_MSC_VER)
  39 #  define mad_fixed64_t  signed __int64
  40 # elif 1 || defined(__GNUC__)
  41 #  define mad_fixed64_t  signed long long
  42 # endif
  43
  44 # if defined(FPM_FLOAT)
  45 typedef double mad_sample_t;
  46 # else
  47 typedef mad_fixed_t mad_sample_t;
  48 # endif
  49
  50 /*
  51  * Fixed-point format: 0xABBBBBBB
  52  * A == whole part      (sign + 3 bits)
  53  * B == fractional part (28 bits)
  54  *
  55  * Values are signed two's complement, so the effective range is:
  56  * 0x80000000 to 0x7fffffff
  57  *       -8.0 to +7.9999999962747097015380859375
  58  *
  59  * The smallest representable value is:
  60  * 0x00000001 == 0.0000000037252902984619140625 (i.e. about 3.725e-9)
  61  *
  62  * 28 bits of fractional accuracy represent about
  63  * 8.6 digits of decimal accuracy.
  64  *
  65  * Fixed-point numbers can be added or subtracted as normal
  66  * integers, but multiplication requires shifting the 64-bit result
  67  * from 56 fractional bits back to 28 (and rounding.)
  68  *
  69  * Changing the definition of MAD_F_FRACBITS is only partially
  70  * supported, and must be done with care.
  71  */
  72
  73 # define MAD_F_FRACBITS         28
  74
  75 # if MAD_F_FRACBITS == 28
  76 #  define MAD_F(x)              ((mad_fixed_t) (x##L))
  77 # else
  78 #  if MAD_F_FRACBITS < 28
  79 #   warning "MAD_F_FRACBITS < 28"
  80 #   define MAD_F(x)             ((mad_fixed_t)  \
  81                                  (((x##L) +  \
  82                                    (1L << (28 - MAD_F_FRACBITS - 1))) >>  \
  83                                   (28 - MAD_F_FRACBITS)))
  84 #  elif MAD_F_FRACBITS > 28
  85 #   error "MAD_F_FRACBITS > 28 not currently supported"
  86 #   define MAD_F(x)             ((mad_fixed_t)  \
  87                                  ((x##L) << (MAD_F_FRACBITS - 28)))
  88 #  endif
  89 # endif
  90
  91 # define MAD_F_MIN              ((mad_fixed_t) -0x80000000L)
  92 # define MAD_F_MAX              ((mad_fixed_t) +0x7fffffffL)
  93
  94 # define MAD_F_ONE              MAD_F(0x10000000)
  95
  96 # define mad_f_tofixed(x)       ((mad_fixed_t)  \
  97                                  ((x) * (double) (1L << MAD_F_FRACBITS) + 0.5))
  98 # define mad_f_todouble(x)      ((double)  \
  99                                  ((x) / (double) (1L << MAD_F_FRACBITS)))
 100
 101 # define mad_f_intpart(x)       ((x) >> MAD_F_FRACBITS)
 102 # define mad_f_fracpart(x)      ((x) & ((1L << MAD_F_FRACBITS) - 1))
 103                                 /* (x should be positive) */
 104
 105 # define mad_f_fromint(x)       ((x) << MAD_F_FRACBITS)
 106
 107 # define mad_f_add(x, y)        ((x) + (y))
 108 # define mad_f_sub(x, y)        ((x) - (y))
 109
 110 # if defined(FPM_FLOAT)
 111 #  error "FPM_FLOAT not yet supported"
 112
 113 #  undef MAD_F
 114 #  define MAD_F(x)              mad_f_todouble(x)
 115
 116 #  define mad_f_mul(x, y)       ((x) * (y))
 117 #  define mad_f_scale64
 118
 119 #  undef ASO_ZEROCHECK
 120
 121 # elif defined(FPM_64BIT)
 122
 123 /*
 124  * This version should be the most accurate if 64-bit types are supported by
 125  * the compiler, although it may not be the most efficient.
 126  */
 127 #  if defined(OPT_ACCURACY)
 128 #   define mad_f_mul(x, y)  \
 129     ((mad_fixed_t)  \
 130      ((((mad_fixed64_t) (x) * (y)) +  \
 131        (1L << (MAD_F_SCALEBITS - 1))) >> MAD_F_SCALEBITS))
 132 #  else
 133 #   define mad_f_mul(x, y)  \
 134     ((mad_fixed_t) (((mad_fixed64_t) (x) * (y)) >> MAD_F_SCALEBITS))
 135 #  endif
 136
 137 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 138
 139 /* --- Intel --------------------------------------------------------------- */
 140
 141 # elif defined(FPM_INTEL)
 142
 143 #  if defined(_MSC_VER)
 144 #   pragma warning(push)
 145 #   pragma warning(disable: 4035)  /* no return value */
 146 static __forceinline
 147 mad_fixed_t mad_f_mul_inline(mad_fixed_t x, mad_fixed_t y)
 148 {
 149   enum {
 150     fracbits = MAD_F_FRACBITS
 151   };
 152
 153   __asm {
 154     mov eax, x
 155     imul y
 156     shrd eax, edx, fracbits
 157   }
 158
 159   /* implicit return of eax */
 160 }
 161 #   pragma warning(pop)
 162
 163 #   define mad_f_mul            mad_f_mul_inline
 164 #   define mad_f_scale64
 165 #  else
 166 /*
 167  * This Intel version is fast and accurate; the disposition of the least
 168  * significant bit depends on OPT_ACCURACY via mad_f_scale64().
 169  */
 170 #   define MAD_F_MLX(hi, lo, x, y)  \
 171     asm ("imull %3"  \
 172          : "=a" (lo), "=d" (hi)  \
 173          : "%a" (x), "rm" (y)  \
 174          : "cc")
 175
 176 #   if defined(OPT_ACCURACY)
 177 /*
 178  * This gives best accuracy but is not very fast.
 179  */
 180 #    define MAD_F_MLA(hi, lo, x, y)  \
 181     ({ mad_fixed64hi_t __hi;  \
 182        mad_fixed64lo_t __lo;  \
 183        MAD_F_MLX(__hi, __lo, (x), (y));  \
 184        asm ("addl %2,%0\n\t"  \
 185             "adcl %3,%1"  \
 186             : "=rm" (lo), "=rm" (hi)  \
 187             : "r" (__lo), "r" (__hi), "0" (lo), "1" (hi)  \
 188             : "cc");  \
 189     })
 190 #   endif  /* OPT_ACCURACY */
 191
 192 #   if defined(OPT_ACCURACY)
 193 /*
 194  * Surprisingly, this is faster than SHRD followed by ADC.
 195  */
 196 #    define mad_f_scale64(hi, lo)  \
 197     ({ mad_fixed64hi_t __hi_;  \
 198        mad_fixed64lo_t __lo_;  \
 199        mad_fixed_t __result;  \
 200        asm ("addl %4,%2\n\t"  \
 201             "adcl %5,%3"  \
 202             : "=rm" (__lo_), "=rm" (__hi_)  \
 203             : "0" (lo), "1" (hi),  \
 204               "ir" (1L << (MAD_F_SCALEBITS - 1)), "ir" (0)  \
 205             : "cc");  \
 206        asm ("shrdl %3,%2,%1"  \
 207             : "=rm" (__result)  \
 208             : "0" (__lo_), "r" (__hi_), "I" (MAD_F_SCALEBITS)  \
 209             : "cc");  \
 210        __result;  \
 211     })
 212 #    else
 213 #    define mad_f_scale64(hi, lo)  \
 214     ({ mad_fixed_t __result;  \
 215        asm ("shrdl %3,%2,%1"  \
 216             : "=rm" (__result)  \
 217             : "0" (lo), "r" (hi), "I" (MAD_F_SCALEBITS)  \
 218             : "cc");  \
 219        __result;  \
 220     })
 221 #   endif  /* OPT_ACCURACY */
 222
 223 #   define MAD_F_SCALEBITS  MAD_F_FRACBITS
 224 #  endif
 225
 226 /* --- ARM ----------------------------------------------------------------- */
 227
 228 # elif defined(FPM_ARM)
 229
 230 /*
 231  * This ARM V4 version is as accurate as FPM_64BIT but much faster. The
 232  * least significant bit is properly rounded at no CPU cycle cost!
 233  */
 234 # if 1
 235 /*
 236  * This is faster than the default implementation via MAD_F_MLX() and
 237  * mad_f_scale64().
 238  */
 239 #  define mad_f_mul(x, y)  \
 240     ({ mad_fixed64hi_t __hi;  \
 241        mad_fixed64lo_t __lo;  \
 242        mad_fixed_t __result;  \
 243        asm ("smull      %0, %1, %3, %4\n\t"  \
 244             "movs       %0, %0, lsr %5\n\t"  \
 245             "adc        %2, %0, %1, lsl %6"  \
 246             : "=&r" (__lo), "=&r" (__hi), "=r" (__result)  \
 247             : "%r" (x), "r" (y),  \
 248               "M" (MAD_F_SCALEBITS), "M" (32 - MAD_F_SCALEBITS)  \
 249             : "cc");  \
 250        __result;  \
 251     })
 252 # endif
 253
 254 #  define MAD_F_MLX(hi, lo, x, y)  \
 255     asm ("smull %0, %1, %2, %3"  \
 256          : "=&r" (lo), "=&r" (hi)  \
 257          : "%r" (x), "r" (y))
 258
 259 #  define MAD_F_MLA(hi, lo, x, y)  \
 260     asm ("smlal %0, %1, %2, %3"  \
 261          : "+r" (lo), "+r" (hi)  \
 262          : "%r" (x), "r" (y))
 263
 264 #  define MAD_F_MLN(hi, lo)  \
 265     asm ("rsbs  %0, %2, #0\n\t"  \
 266          "rsc   %1, %3, #0"  \
 267          : "=r" (lo), "=r" (hi)  \
 268          : "0" (lo), "1" (hi)  \
 269          : "cc")
 270
 271 #  define mad_f_scale64(hi, lo)  \
 272     ({ mad_fixed_t __result;  \
 273        asm ("movs       %0, %1, lsr %3\n\t"  \
 274             "adc        %0, %0, %2, lsl %4"  \
 275             : "=&r" (__result)  \
 276             : "r" (lo), "r" (hi),  \
 277               "M" (MAD_F_SCALEBITS), "M" (32 - MAD_F_SCALEBITS)  \
 278             : "cc");  \
 279        __result;  \
 280     })
 281
 282 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 283
 284 /* --- MIPS ---------------------------------------------------------------- */
 285
 286 # elif defined(FPM_MIPS)
 287
 288 /*
 289  * This MIPS version is fast and accurate; the disposition of the least
 290  * significant bit depends on OPT_ACCURACY via mad_f_scale64().
 291  */
 292 #  define MAD_F_MLX(hi, lo, x, y)  \
 293     asm ("mult  %2,%3"  \
 294          : "=l" (lo), "=h" (hi)  \
 295          : "%r" (x), "r" (y))
 296
 297 # if defined(HAVE_MADD_ASM)
 298 #  define MAD_F_MLA(hi, lo, x, y)  \
 299     asm ("madd  %2,%3"  \
 300          : "+l" (lo), "+h" (hi)  \
 301          : "%r" (x), "r" (y))
 302 # elif defined(HAVE_MADD16_ASM)
 303 /*
 304  * This loses significant accuracy due to the 16-bit integer limit in the
 305  * multiply/accumulate instruction.
 306  */
 307 #  define MAD_F_ML0(hi, lo, x, y)  \
 308     asm ("mult  %2,%3"  \
 309          : "=l" (lo), "=h" (hi)  \
 310          : "%r" ((x) >> 12), "r" ((y) >> 16))
 311 #  define MAD_F_MLA(hi, lo, x, y)  \
 312     asm ("madd16        %2,%3"  \
 313          : "+l" (lo), "+h" (hi)  \
 314          : "%r" ((x) >> 12), "r" ((y) >> 16))
 315 #  define MAD_F_MLZ(hi, lo)  ((mad_fixed_t) (lo))
 316 # endif
 317
 318 # if defined(OPT_SPEED)
 319 #  define mad_f_scale64(hi, lo)  \
 320     ((mad_fixed_t) ((hi) << (32 - MAD_F_SCALEBITS)))
 321 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 322 # endif
 323
 324 /* --- SPARC --------------------------------------------------------------- */
 325
 326 # elif defined(FPM_SPARC)
 327
 328 /*
 329  * This SPARC V8 version is fast and accurate; the disposition of the least
 330  * significant bit depends on OPT_ACCURACY via mad_f_scale64().
 331  */
 332 #  define MAD_F_MLX(hi, lo, x, y)  \
 333     asm ("smul %2, %3, %0\n\t"  \
 334          "rd %%y, %1"  \
 335          : "=r" (lo), "=r" (hi)  \
 336          : "%r" (x), "rI" (y))
 337
 338 /* --- PowerPC ------------------------------------------------------------- */
 339
 340 # elif defined(FPM_PPC)
 341
 342 /*
 343  * This PowerPC version is fast and accurate; the disposition of the least
 344  * significant bit depends on OPT_ACCURACY via mad_f_scale64().
 345  */
 346 #  define MAD_F_MLX(hi, lo, x, y)  \
 347     do {  \
 348       asm ("mullw %0,%1,%2"  \
 349            : "=r" (lo)  \
 350            : "%r" (x), "r" (y));  \
 351       asm ("mulhw %0,%1,%2"  \
 352            : "=r" (hi)  \
 353            : "%r" (x), "r" (y));  \
 354     }  \
 355     while (0)
 356
 357 #  if defined(OPT_ACCURACY)
 358 /*
 359  * This gives best accuracy but is not very fast.
 360  */
 361 #   define MAD_F_MLA(hi, lo, x, y)  \
 362     ({ mad_fixed64hi_t __hi;  \
 363        mad_fixed64lo_t __lo;  \
 364        MAD_F_MLX(__hi, __lo, (x), (y));  \
 365        asm ("addc %0,%2,%3\n\t"  \
 366             "adde %1,%4,%5"  \
 367             : "=r" (lo), "=r" (hi)  \
 368             : "%r" (lo), "r" (__lo),  \
 369               "%r" (hi), "r" (__hi)  \
 370             : "xer");  \
 371     })
 372 #  endif
 373
 374 #  if defined(OPT_ACCURACY)
 375 /*
 376  * This is slower than the truncating version below it.
 377  */
 378 #   define mad_f_scale64(hi, lo)  \
 379     ({ mad_fixed_t __result, __round;  \
 380        asm ("rotrwi %0,%1,%2"  \
 381             : "=r" (__result)  \
 382             : "r" (lo), "i" (MAD_F_SCALEBITS));  \
 383        asm ("extrwi %0,%1,1,0"  \
 384             : "=r" (__round)  \
 385             : "r" (__result));  \
 386        asm ("insrwi %0,%1,%2,0"  \
 387             : "+r" (__result)  \
 388             : "r" (hi), "i" (MAD_F_SCALEBITS));  \
 389        asm ("add %0,%1,%2"  \
 390             : "=r" (__result)  \
 391             : "%r" (__result), "r" (__round));  \
 392        __result;  \
 393     })
 394 #  else
 395 #   define mad_f_scale64(hi, lo)  \
 396     ({ mad_fixed_t __result;  \
 397        asm ("rotrwi %0,%1,%2"  \
 398             : "=r" (__result)  \
 399             : "r" (lo), "i" (MAD_F_SCALEBITS));  \
 400        asm ("insrwi %0,%1,%2,0"  \
 401             : "+r" (__result)  \
 402             : "r" (hi), "i" (MAD_F_SCALEBITS));  \
 403        __result;  \
 404     })
 405 #  endif
 406
 407 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 408
 409 /* --- Default ------------------------------------------------------------- */
 410
 411 # elif defined(FPM_DEFAULT)
 412
 413 /*
 414  * This version is the most portable but it loses significant accuracy.
 415  * Furthermore, accuracy is biased against the second argument, so care
 416  * should be taken when ordering operands.
 417  *
 418  * The scale factors are constant as this is not used with SSO.
 419  *
 420  * Pre-rounding is required to stay within the limits of compliance.
 421  */
 422 #  if defined(OPT_SPEED)
 423 #   define mad_f_mul(x, y)      (((x) >> 12) * ((y) >> 16))
 424 #  else
 425 #   define mad_f_mul(x, y)      ((((x) + (1L << 11)) >> 12) *  \
 426                                  (((y) + (1L << 15)) >> 16))
 427 #  endif
 428
 429 /* ------------------------------------------------------------------------- */
 430
 431 # else
 432 #  error "no FPM selected"
 433 # endif
 434
 435 /* default implementations */
 436
 437 # if !defined(mad_f_mul)
 438 #  define mad_f_mul(x, y)  \
 439     ({ register mad_fixed64hi_t __hi;  \
 440        register mad_fixed64lo_t __lo;  \
 441        MAD_F_MLX(__hi, __lo, (x), (y));  \
 442        mad_f_scale64(__hi, __lo);  \
 443     })
 444 # endif
 445
 446 # if !defined(MAD_F_MLA)
 447 #  define MAD_F_ML0(hi, lo, x, y)       ((lo)  = mad_f_mul((x), (y)))
 448 #  define MAD_F_MLA(hi, lo, x, y)       ((lo) += mad_f_mul((x), (y)))
 449 #  define MAD_F_MLN(hi, lo)             ((lo)  = -(lo))
 450 #  define MAD_F_MLZ(hi, lo)             ((void) (hi), (mad_fixed_t) (lo))
 451 # endif
 452
 453 # if !defined(MAD_F_ML0)
 454 #  define MAD_F_ML0(hi, lo, x, y)       MAD_F_MLX((hi), (lo), (x), (y))
 455 # endif
 456
 457 # if !defined(MAD_F_MLN)
 458 #  define MAD_F_MLN(hi, lo)             ((hi) = ((lo) = -(lo)) ? ~(hi) : -(hi))
 459 # endif
 460
 461 # if !defined(MAD_F_MLZ)
 462 #  define MAD_F_MLZ(hi, lo)             mad_f_scale64((hi), (lo))
 463 # endif
 464
 465 # if !defined(mad_f_scale64)
 466 #  if defined(OPT_ACCURACY)
 467 #   define mad_f_scale64(hi, lo)  \
 468     ((((mad_fixed_t)  \
 469        (((hi) << (32 - (MAD_F_SCALEBITS - 1))) |  \
 470         ((lo) >> (MAD_F_SCALEBITS - 1)))) + 1) >> 1)
 471 #  else
 472 #   define mad_f_scale64(hi, lo)  \
 473     ((mad_fixed_t)  \
 474      (((hi) << (32 - MAD_F_SCALEBITS)) |  \
 475       ((lo) >> MAD_F_SCALEBITS)))
 476 #  endif
 477 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 478 # endif
 479
 480 /* C routines */
 481
 482 mad_fixed_t mad_f_abs(mad_fixed_t);
 483 mad_fixed_t mad_f_div(mad_fixed_t, mad_fixed_t);
 484
 485 # endif