MultiMedia/mad/fixed.h

   1 /*
   2  * mad - MPEG audio decoder
   3  * Copyright (C) 2000-2001 Robert Leslie
   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  * $Id$
  20  */
  21
  22 # ifndef LIBMAD_FIXED_H
  23 # define LIBMAD_FIXED_H
  24
  25 # if SIZEOF_INT >= 4
  26 typedef   signed int mad_fixed_t;
  27
  28 typedef   signed int mad_fixed64hi_t;
  29 typedef unsigned int mad_fixed64lo_t;
  30 # else
  31 typedef   signed long mad_fixed_t;
  32
  33 typedef   signed long mad_fixed64hi_t;
  34 typedef unsigned long mad_fixed64lo_t;
  35 # endif
  36
  37 /*
  38  * Fixed-point format: 0xABBBBBBB
  39  * A == whole part      (sign + 3 bits)
  40  * B == fractional part (28 bits)
  41  *
  42  * Values are signed two's complement, so the effective range is:
  43  * 0x80000000 to 0x7fffffff
  44  *       -8.0 to +7.9999999962747097015380859375
  45  *
  46  * The smallest representable value is:
  47  * 0x00000001 == 0.0000000037252902984619140625 (i.e. about 3.725e-9)
  48  *
  49  * 28 bits of fractional accuracy represent about
  50  * 8.6 digits of decimal accuracy.
  51  *
  52  * Fixed-point numbers can be added or subtracted as normal
  53  * integers, but multiplication requires shifting the 64-bit result
  54  * from 56 fractional bits back to 28 (and rounding.)
  55  *
  56  * Changing the definition of MAD_F_FRACBITS is only partially
  57  * supported, and must be done with care.
  58  */
  59
  60 # define MAD_F_FRACBITS         28
  61
  62 # if MAD_F_FRACBITS == 28
  63 #  define MAD_F(x)              ((mad_fixed_t) (x##L))
  64 # else
  65 #  if MAD_F_FRACBITS < 28
  66 #   warning "MAD_F_FRACBITS < 28"
  67 #   define MAD_F(x)             ((mad_fixed_t)  \
  68                                  (((x##L) +  \
  69                                    (1L << (28 - MAD_F_FRACBITS - 1))) >>  \
  70                                   (28 - MAD_F_FRACBITS)))
  71 #  elif MAD_F_FRACBITS > 28
  72 #   error "MAD_F_FRACBITS > 28 not currently supported"
  73 #   define MAD_F(x)             ((mad_fixed_t)  \
  74                                  ((x##L) << (MAD_F_FRACBITS - 28)))
  75 #  endif
  76 # endif
  77
  78 # define MAD_F_MIN              ((mad_fixed_t) -0x80000000L)
  79 # define MAD_F_MAX              ((mad_fixed_t) +0x7fffffffL)
  80
  81 # define MAD_F_ONE              MAD_F(0x10000000)
  82
  83 # define mad_f_tofixed(x)       ((mad_fixed_t)  \
  84                                  ((x) * (double) (1L << MAD_F_FRACBITS) + 0.5))
  85 # define mad_f_todouble(x)      ((double)  \
  86                                  ((x) / (double) (1L << MAD_F_FRACBITS)))
  87
  88 # define mad_f_intpart(x)       ((x) >> MAD_F_FRACBITS)
  89 # define mad_f_fracpart(x)      ((x) & ((1L << MAD_F_FRACBITS) - 1))
  90                                 /* (x should be positive) */
  91
  92 # define mad_f_fromint(x)       ((x) << MAD_F_FRACBITS)
  93
  94 # define mad_f_add(x, y)        ((x) + (y))
  95 # define mad_f_sub(x, y)        ((x) - (y))
  96
  97 # if defined(FPM_64BIT)
  98
  99 /*
 100  * This version should be the most accurate if 64-bit (long long) types are
 101  * supported by the compiler, although it may not be the most efficient.
 102  */
 103 #  if defined(OPT_ACCURACY)
 104 #   define mad_f_mul(x, y)  \
 105     ((mad_fixed_t)  \
 106      ((((signed long long) (x) * (y)) +  \
 107        (1L << (MAD_F_SCALEBITS - 1))) >> MAD_F_SCALEBITS))
 108 #  else
 109 #   define mad_f_mul(x, y)  \
 110     ((mad_fixed_t) (((signed long long) (x) * (y)) >> MAD_F_SCALEBITS))
 111 #  endif
 112
 113 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 114
 115 /* --- Intel --------------------------------------------------------------- */
 116
 117 # elif defined(FPM_INTEL)
 118
 119 /*
 120  * This Intel version is fast and accurate; the disposition of the least
 121  * significant bit depends on OPT_ACCURACY via mad_f_scale64().
 122  */
 123 #  define MAD_F_MLX(hi, lo, x, y)  \
 124     asm ("imull %3"  \
 125          : "=a" (lo), "=d" (hi)  \
 126          : "%a" (x), "rm" (y)  \
 127          : "cc")
 128
 129 #  if defined(OPT_ACCURACY)
 130 /*
 131  * This gives best accuracy but is not very fast.
 132  */
 133 #   define MAD_F_MLA(hi, lo, x, y)  \
 134     ({ mad_fixed64hi_t __hi;  \
 135        mad_fixed64lo_t __lo;  \
 136        MAD_F_MLX(__hi, __lo, (x), (y));  \
 137        asm ("addl %2,%0\n\t"  \
 138             "adcl %3,%1"  \
 139             : "=rm" (lo), "=rm" (hi)  \
 140             : "r" (__lo), "r" (__hi), "0" (lo), "1" (hi)  \
 141             : "cc");  \
 142     })
 143 #  endif  /* OPT_ACCURACY */
 144
 145 #  if defined(OPT_ACCURACY)
 146 /*
 147  * Surprisingly, this is faster than SHRD followed by ADC.
 148  */
 149 #   define mad_f_scale64(hi, lo)  \
 150     ({ mad_fixed64hi_t __hi_;  \
 151        mad_fixed64lo_t __lo_;  \
 152        mad_fixed_t __result;  \
 153        asm ("addl %4,%2\n\t"  \
 154             "adcl %5,%3"  \
 155             : "=rm" (__lo_), "=rm" (__hi_)  \
 156             : "0" (lo), "1" (hi),  \
 157               "ir" (1L << (MAD_F_SCALEBITS - 1)), "ir" (0)  \
 158             : "cc");  \
 159        asm ("shrdl %3,%2,%1"  \
 160             : "=rm" (__result)  \
 161             : "0" (__lo_), "r" (__hi_), "I" (MAD_F_SCALEBITS)  \
 162             : "cc");  \
 163        __result;  \
 164     })
 165 #  else
 166 #   define mad_f_scale64(hi, lo)  \
 167     ({ mad_fixed_t __result;  \
 168        asm ("shrdl %3,%2,%1"  \
 169             : "=rm" (__result)  \
 170             : "0" (lo), "r" (hi), "I" (MAD_F_SCALEBITS)  \
 171             : "cc");  \
 172        __result;  \
 173     })
 174 #  endif  /* OPT_ACCURACY */
 175
 176 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 177
 178 /* --- ARM ----------------------------------------------------------------- */
 179
 180 # elif defined(FPM_ARM)
 181
 182 /*
 183  * This ARM V4 version is as accurate as FPM_64BIT but much faster. The
 184  * least significant bit is properly rounded at no CPU cycle cost!
 185  */
 186 # if 1
 187 /*
 188  * There's a bug somewhere, possibly in the compiler, that sometimes makes
 189  * this necessary instead of the default implementation via MAD_F_MLX and
 190  * mad_f_scale64. It may be related to the use (or lack) of
 191  * -finline-functions and/or -fstrength-reduce.
 192  *
 193  * This is also apparently faster than MAD_F_MLX/mad_f_scale64.
 194  */
 195 #  define mad_f_mul(x, y)  \
 196     ({ mad_fixed64hi_t __hi;  \
 197        mad_fixed64lo_t __lo;  \
 198        mad_fixed_t __result;  \
 199        asm ("smull      %0, %1, %3, %4\n\t"  \
 200             "movs       %0, %0, lsr %5\n\t"  \
 201             "adc        %2, %0, %1, lsl %6"  \
 202             : "=&r" (__lo), "=&r" (__hi), "=r" (__result)  \
 203             : "%r" (x), "r" (y),  \
 204               "M" (MAD_F_SCALEBITS), "M" (32 - MAD_F_SCALEBITS)  \
 205             : "cc");  \
 206        __result;  \
 207     })
 208 # endif
 209
 210 #  define MAD_F_MLX(hi, lo, x, y)  \
 211     asm ("smull %0, %1, %2, %3"  \
 212          : "=&r" (lo), "=&r" (hi)  \
 213          : "%r" (x), "r" (y))
 214
 215 #  define MAD_F_MLA(hi, lo, x, y)  \
 216     asm ("smlal %0, %1, %2, %3"  \
 217          : "+r" (lo), "+r" (hi)  \
 218          : "%r" (x), "r" (y))
 219
 220 #  define mad_f_scale64(hi, lo)  \
 221     ({ mad_fixed_t __result;  \
 222        asm ("movs       %0, %1, lsr %3\n\t"  \
 223             "adc        %0, %0, %2, lsl %4"  \
 224             : "=r" (__result)  \
 225             : "r" (lo), "r" (hi),  \
 226               "M" (MAD_F_SCALEBITS), "M" (32 - MAD_F_SCALEBITS)  \
 227             : "cc");  \
 228        __result;  \
 229     })
 230
 231 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 232
 233 /* --- MIPS ---------------------------------------------------------------- */
 234
 235 # elif defined(FPM_MIPS)
 236
 237 /*
 238  * This MIPS version is fast and accurate; the disposition of the least
 239  * significant bit depends on OPT_ACCURACY via mad_f_scale64().
 240  */
 241 #  define MAD_F_MLX(hi, lo, x, y)  \
 242     asm ("mult  %2,%3"  \
 243          : "=l" (lo), "=h" (hi)  \
 244          : "%r" (x), "r" (y))
 245
 246 # if defined(HAVE_MADD_ASM)
 247 #  define MAD_F_MLA(hi, lo, x, y)  \
 248     asm ("madd  %2,%3"  \
 249          : "+l" (lo), "+h" (hi)  \
 250          : "%r" (x), "r" (y))
 251 # elif defined(HAVE_MADD16_ASM)
 252 /*
 253  * This loses significant accuracy due to the 16-bit integer limit in the
 254  * multiply/accumulate instruction.
 255  */
 256 #  define MAD_F_ML0(hi, lo, x, y)  \
 257     asm ("mult  %2,%3"  \
 258          : "=l" (lo), "=h" (hi)  \
 259          : "%r" ((x) >> 12), "r" ((y) >> 16))
 260 #  define MAD_F_MLA(hi, lo, x, y)  \
 261     asm ("madd16        %2,%3"  \
 262          : "+l" (lo), "+h" (hi)  \
 263          : "%r" ((x) >> 12), "r" ((y) >> 16))
 264 #  define MAD_F_MLZ(hi, lo)  ((mad_fixed_t) (lo))
 265 # endif
 266
 267 # if defined(OPT_SPEED)
 268 #  define mad_f_scale64(hi, lo)  \
 269     ((mad_fixed_t) ((hi) << (32 - MAD_F_SCALEBITS)))
 270 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 271 # endif
 272
 273 /* --- SPARC --------------------------------------------------------------- */
 274
 275 # elif defined(FPM_SPARC)
 276
 277 /*
 278  * This SPARC V8 version is fast and accurate; the disposition of the least
 279  * significant bit depends on OPT_ACCURACY via mad_f_scale64().
 280  */
 281 #  define MAD_F_MLX(hi, lo, x, y)  \
 282     asm ("smul %2, %3, %0\n\t"  \
 283          "rd %%y, %1"  \
 284          : "=r" (lo), "=r" (hi)  \
 285          : "%r" (x), "rI" (y))
 286
 287 /* --- PowerPC ------------------------------------------------------------- */
 288
 289 # elif defined(FPM_PPC)
 290
 291 /*
 292  * This PowerPC version is tuned for the 4xx embedded processors. It is
 293  * effectively a tuned version of FPM_64BIT. It is a little faster and just
 294  * as accurate. The disposition of the least significant bit depends on
 295  * OPT_ACCURACY via mad_f_scale64().
 296  */
 297 #  define MAD_F_MLX(hi, lo, x, y)  \
 298     asm ("mulhw %1, %2, %3\n\t"  \
 299          "mullw %0, %2, %3"  \
 300          : "=&r" (lo), "=&r" (hi)  \
 301          : "%r" (x), "r" (y))
 302
 303 #  define MAD_F_MLA(hi, lo, x, y)  \
 304     ({ mad_fixed64hi_t __hi;  \
 305        mad_fixed64lo_t __lo;  \
 306        MAD_F_MLX(__hi, __lo, (x), (y));  \
 307        asm ("addc %0, %2, %3\n\t"  \
 308             "adde %1, %4, %5"  \
 309             : "=r" (lo), "=r" (hi)  \
 310             : "%r" (__lo), "0" (lo), "%r" (__hi), "1" (hi));  \
 311     })
 312
 313 #  if defined(OPT_ACCURACY)
 314 /*
 315  * This is accurate and ~2 - 2.5 times slower than the unrounded version.
 316  *
 317  * The __volatile__ improves the generated code by another 5% (fewer spills
 318  * to memory); eventually they should be removed.
 319  */
 320 #   define mad_f_scale64(hi, lo)  \
 321     ({ mad_fixed_t __result;  \
 322        mad_fixed64hi_t __hi_;  \
 323        mad_fixed64lo_t __lo_;  \
 324        asm __volatile__ ("addc %0, %2, %4\n\t"  \
 325                          "addze %1, %3"  \
 326             : "=r" (__lo_), "=r" (__hi_)  \
 327             : "r" (lo), "r" (hi), "r" (1 << (MAD_F_SCALEBITS - 1)));  \
 328        asm __volatile__ ("rlwinm %0, %2,32-%3,0,%3-1\n\t"  \
 329                          "rlwimi %0, %1,32-%3,%3,31"  \
 330             : "=&r" (__result)  \
 331             : "r" (__lo_), "r" (__hi_), "I" (MAD_F_SCALEBITS));  \
 332             __result;  \
 333     })
 334 #  else
 335 #   define mad_f_scale64(hi, lo)  \
 336     ({ mad_fixed_t __result;  \
 337        asm ("rlwinm %0, %2,32-%3,0,%3-1\n\t"  \
 338             "rlwimi %0, %1,32-%3,%3,31"  \
 339             : "=r" (__result)  \
 340             : "r" (lo), "r" (hi), "I" (MAD_F_SCALEBITS));  \
 341             __result;  \
 342     })
 343 #  endif  /* OPT_ACCURACY */
 344
 345 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 346
 347 /* --- Default ------------------------------------------------------------- */
 348
 349 # elif defined(FPM_DEFAULT)
 350
 351 /*
 352  * This version is the most portable but it loses significant accuracy.
 353  * Furthermore, accuracy is biased against the second argument, so care
 354  * should be taken when ordering operands.
 355  *
 356  * The scale factors are constant as this is not used with SSO.
 357  *
 358  * Pre-rounding is required to stay within the limits of compliance.
 359  */
 360 #  define mad_f_mul(x, y)       ((((x) + (1L << 11)) >> 12) *  \
 361                                  (((y) + (1L << 15)) >> 16))
 362
 363 /* ------------------------------------------------------------------------- */
 364
 365 # else
 366 #  error "no FPM selected"
 367 # endif
 368
 369 /* default implementations */
 370
 371 # if !defined(mad_f_mul)
 372 #  define mad_f_mul(x, y)  \
 373     ({ mad_fixed64hi_t __hi;  \
 374        mad_fixed64lo_t __lo;  \
 375        MAD_F_MLX(__hi, __lo, (x), (y));  \
 376        mad_f_scale64(__hi, __lo);  \
 377     })
 378 # endif
 379
 380 # if !defined(MAD_F_MLA)
 381 #  define MAD_F_ML0(hi, lo, x, y)       ((lo)  = mad_f_mul((x), (y)))
 382 #  define MAD_F_MLA(hi, lo, x, y)       ((lo) += mad_f_mul((x), (y)))
 383 #  define MAD_F_MLZ(hi, lo)             ((void) (hi), (mad_fixed_t) (lo))
 384 # endif
 385
 386 # if !defined(MAD_F_ML0)
 387 #  define MAD_F_ML0(hi, lo, x, y)       MAD_F_MLX((hi), (lo), (x), (y))
 388 # endif
 389
 390 # if !defined(MAD_F_MLZ)
 391 #  define MAD_F_MLZ(hi, lo)             mad_f_scale64((hi), (lo))
 392 # endif
 393
 394 # if !defined(mad_f_scale64)
 395 #  if defined(OPT_ACCURACY)
 396 #   define mad_f_scale64(hi, lo)  \
 397     ((((mad_fixed_t)  \
 398        (((hi) << (32 - (MAD_F_SCALEBITS - 1))) |  \
 399         ((lo) >> (MAD_F_SCALEBITS - 1)))) + 1) >> 1)
 400 #  else
 401 #   define mad_f_scale64(hi, lo)  \
 402     ((mad_fixed_t)  \
 403      (((hi) << (32 - MAD_F_SCALEBITS)) |  \
 404       ((lo) >> MAD_F_SCALEBITS)))
 405 #  endif
 406 #  define MAD_F_SCALEBITS  MAD_F_FRACBITS
 407 # endif
 408
 409 /* miscellaneous C routines */
 410
 411 mad_fixed_t mad_f_abs(mad_fixed_t);
 412
 413 # endif