fixed.h
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- /*
- * libmad - MPEG audio decoder library
- * Copyright (C) 2000-2003 Underbit Technologies, Inc.
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 2 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
- *
- * $Id: fixed.h,v 1.1 2003/08/31 18:59:46 gabest Exp $
- */
- # ifndef LIBMAD_FIXED_H
- # define LIBMAD_FIXED_H
- # if SIZEOF_INT >= 4
- typedef signed int mad_fixed_t;
- typedef signed int mad_fixed64hi_t;
- typedef unsigned int mad_fixed64lo_t;
- # else
- typedef signed long mad_fixed_t;
- typedef signed long mad_fixed64hi_t;
- typedef unsigned long mad_fixed64lo_t;
- # endif
- # if defined(_MSC_VER)
- # define mad_fixed64_t signed __int64
- # elif 1 || defined(__GNUC__)
- # define mad_fixed64_t signed long long
- # endif
- # if defined(FPM_FLOAT)
- typedef double mad_sample_t;
- # else
- typedef mad_fixed_t mad_sample_t;
- # endif
- /*
- * Fixed-point format: 0xABBBBBBB
- * A == whole part (sign + 3 bits)
- * B == fractional part (28 bits)
- *
- * Values are signed two's complement, so the effective range is:
- * 0x80000000 to 0x7fffffff
- * -8.0 to +7.9999999962747097015380859375
- *
- * The smallest representable value is:
- * 0x00000001 == 0.0000000037252902984619140625 (i.e. about 3.725e-9)
- *
- * 28 bits of fractional accuracy represent about
- * 8.6 digits of decimal accuracy.
- *
- * Fixed-point numbers can be added or subtracted as normal
- * integers, but multiplication requires shifting the 64-bit result
- * from 56 fractional bits back to 28 (and rounding.)
- *
- * Changing the definition of MAD_F_FRACBITS is only partially
- * supported, and must be done with care.
- */
- # define MAD_F_FRACBITS 28
- # if MAD_F_FRACBITS == 28
- # define MAD_F(x) ((mad_fixed_t) (x##L))
- # else
- # if MAD_F_FRACBITS < 28
- # warning "MAD_F_FRACBITS < 28"
- # define MAD_F(x) ((mad_fixed_t)
- (((x##L) +
- (1L << (28 - MAD_F_FRACBITS - 1))) >>
- (28 - MAD_F_FRACBITS)))
- # elif MAD_F_FRACBITS > 28
- # error "MAD_F_FRACBITS > 28 not currently supported"
- # define MAD_F(x) ((mad_fixed_t)
- ((x##L) << (MAD_F_FRACBITS - 28)))
- # endif
- # endif
- # define MAD_F_MIN ((mad_fixed_t) -0x80000000L)
- # define MAD_F_MAX ((mad_fixed_t) +0x7fffffffL)
- # define MAD_F_ONE MAD_F(0x10000000)
- # define mad_f_tofixed(x) ((mad_fixed_t)
- ((x) * (double) (1L << MAD_F_FRACBITS) + 0.5))
- # define mad_f_todouble(x) ((double)
- ((x) / (double) (1L << MAD_F_FRACBITS)))
- # define mad_f_intpart(x) ((x) >> MAD_F_FRACBITS)
- # define mad_f_fracpart(x) ((x) & ((1L << MAD_F_FRACBITS) - 1))
- /* (x should be positive) */
- # define mad_f_fromint(x) ((x) << MAD_F_FRACBITS)
- # define mad_f_add(x, y) ((x) + (y))
- # define mad_f_sub(x, y) ((x) - (y))
- # if defined(FPM_FLOAT)
- # error "FPM_FLOAT not yet supported"
- # undef MAD_F
- # define MAD_F(x) mad_f_todouble(x)
- # define mad_f_mul(x, y) ((x) * (y))
- # define mad_f_scale64
- # undef ASO_ZEROCHECK
- # elif defined(FPM_64BIT)
- /*
- * This version should be the most accurate if 64-bit types are supported by
- * the compiler, although it may not be the most efficient.
- */
- # if defined(OPT_ACCURACY)
- # define mad_f_mul(x, y)
- ((mad_fixed_t)
- ((((mad_fixed64_t) (x) * (y)) +
- (1L << (MAD_F_SCALEBITS - 1))) >> MAD_F_SCALEBITS))
- # else
- # define mad_f_mul(x, y)
- ((mad_fixed_t) (((mad_fixed64_t) (x) * (y)) >> MAD_F_SCALEBITS))
- # endif
- # define MAD_F_SCALEBITS MAD_F_FRACBITS
- /* --- Intel --------------------------------------------------------------- */
- # elif defined(FPM_INTEL)
- # if defined(_MSC_VER)
- # pragma warning(push)
- # pragma warning(disable: 4035) /* no return value */
- static __forceinline
- mad_fixed_t mad_f_mul_inline(mad_fixed_t x, mad_fixed_t y)
- {
- enum {
- fracbits = MAD_F_FRACBITS
- };
- __asm {
- mov eax, x
- imul y
- shrd eax, edx, fracbits
- }
- /* implicit return of eax */
- }
- # pragma warning(pop)
- # define mad_f_mul mad_f_mul_inline
- # define mad_f_scale64
- # else
- /*
- * This Intel version is fast and accurate; the disposition of the least
- * significant bit depends on OPT_ACCURACY via mad_f_scale64().
- */
- # define MAD_F_MLX(hi, lo, x, y)
- asm ("imull %3"
- : "=a" (lo), "=d" (hi)
- : "%a" (x), "rm" (y)
- : "cc")
- # if defined(OPT_ACCURACY)
- /*
- * This gives best accuracy but is not very fast.
- */
- # define MAD_F_MLA(hi, lo, x, y)
- ({ mad_fixed64hi_t __hi;
- mad_fixed64lo_t __lo;
- MAD_F_MLX(__hi, __lo, (x), (y));
- asm ("addl %2,%0nt"
- "adcl %3,%1"
- : "=rm" (lo), "=rm" (hi)
- : "r" (__lo), "r" (__hi), "0" (lo), "1" (hi)
- : "cc");
- })
- # endif /* OPT_ACCURACY */
- # if defined(OPT_ACCURACY)
- /*
- * Surprisingly, this is faster than SHRD followed by ADC.
- */
- # define mad_f_scale64(hi, lo)
- ({ mad_fixed64hi_t __hi_;
- mad_fixed64lo_t __lo_;
- mad_fixed_t __result;
- asm ("addl %4,%2nt"
- "adcl %5,%3"
- : "=rm" (__lo_), "=rm" (__hi_)
- : "0" (lo), "1" (hi),
- "ir" (1L << (MAD_F_SCALEBITS - 1)), "ir" (0)
- : "cc");
- asm ("shrdl %3,%2,%1"
- : "=rm" (__result)
- : "0" (__lo_), "r" (__hi_), "I" (MAD_F_SCALEBITS)
- : "cc");
- __result;
- })
- # else
- # define mad_f_scale64(hi, lo)
- ({ mad_fixed_t __result;
- asm ("shrdl %3,%2,%1"
- : "=rm" (__result)
- : "0" (lo), "r" (hi), "I" (MAD_F_SCALEBITS)
- : "cc");
- __result;
- })
- # endif /* OPT_ACCURACY */
- # define MAD_F_SCALEBITS MAD_F_FRACBITS
- # endif
- /* --- ARM ----------------------------------------------------------------- */
- # elif defined(FPM_ARM)
- /*
- * This ARM V4 version is as accurate as FPM_64BIT but much faster. The
- * least significant bit is properly rounded at no CPU cycle cost!
- */
- # if 1
- /*
- * This is faster than the default implementation via MAD_F_MLX() and
- * mad_f_scale64().
- */
- # define mad_f_mul(x, y)
- ({ mad_fixed64hi_t __hi;
- mad_fixed64lo_t __lo;
- mad_fixed_t __result;
- asm ("smull %0, %1, %3, %4nt"
- "movs %0, %0, lsr %5nt"
- "adc %2, %0, %1, lsl %6"
- : "=&r" (__lo), "=&r" (__hi), "=r" (__result)
- : "%r" (x), "r" (y),
- "M" (MAD_F_SCALEBITS), "M" (32 - MAD_F_SCALEBITS)
- : "cc");
- __result;
- })
- # endif
- # define MAD_F_MLX(hi, lo, x, y)
- asm ("smull %0, %1, %2, %3"
- : "=&r" (lo), "=&r" (hi)
- : "%r" (x), "r" (y))
- # define MAD_F_MLA(hi, lo, x, y)
- asm ("smlal %0, %1, %2, %3"
- : "+r" (lo), "+r" (hi)
- : "%r" (x), "r" (y))
- # define MAD_F_MLN(hi, lo)
- asm ("rsbs %0, %2, #0nt"
- "rsc %1, %3, #0"
- : "=r" (lo), "=r" (hi)
- : "0" (lo), "1" (hi)
- : "cc")
- # define mad_f_scale64(hi, lo)
- ({ mad_fixed_t __result;
- asm ("movs %0, %1, lsr %3nt"
- "adc %0, %0, %2, lsl %4"
- : "=&r" (__result)
- : "r" (lo), "r" (hi),
- "M" (MAD_F_SCALEBITS), "M" (32 - MAD_F_SCALEBITS)
- : "cc");
- __result;
- })
- # define MAD_F_SCALEBITS MAD_F_FRACBITS
- /* --- MIPS ---------------------------------------------------------------- */
- # elif defined(FPM_MIPS)
- /*
- * This MIPS version is fast and accurate; the disposition of the least
- * significant bit depends on OPT_ACCURACY via mad_f_scale64().
- */
- # define MAD_F_MLX(hi, lo, x, y)
- asm ("mult %2,%3"
- : "=l" (lo), "=h" (hi)
- : "%r" (x), "r" (y))
- # if defined(HAVE_MADD_ASM)
- # define MAD_F_MLA(hi, lo, x, y)
- asm ("madd %2,%3"
- : "+l" (lo), "+h" (hi)
- : "%r" (x), "r" (y))
- # elif defined(HAVE_MADD16_ASM)
- /*
- * This loses significant accuracy due to the 16-bit integer limit in the
- * multiply/accumulate instruction.
- */
- # define MAD_F_ML0(hi, lo, x, y)
- asm ("mult %2,%3"
- : "=l" (lo), "=h" (hi)
- : "%r" ((x) >> 12), "r" ((y) >> 16))
- # define MAD_F_MLA(hi, lo, x, y)
- asm ("madd16 %2,%3"
- : "+l" (lo), "+h" (hi)
- : "%r" ((x) >> 12), "r" ((y) >> 16))
- # define MAD_F_MLZ(hi, lo) ((mad_fixed_t) (lo))
- # endif
- # if defined(OPT_SPEED)
- # define mad_f_scale64(hi, lo)
- ((mad_fixed_t) ((hi) << (32 - MAD_F_SCALEBITS)))
- # define MAD_F_SCALEBITS MAD_F_FRACBITS
- # endif
- /* --- SPARC --------------------------------------------------------------- */
- # elif defined(FPM_SPARC)
- /*
- * This SPARC V8 version is fast and accurate; the disposition of the least
- * significant bit depends on OPT_ACCURACY via mad_f_scale64().
- */
- # define MAD_F_MLX(hi, lo, x, y)
- asm ("smul %2, %3, %0nt"
- "rd %%y, %1"
- : "=r" (lo), "=r" (hi)
- : "%r" (x), "rI" (y))
- /* --- PowerPC ------------------------------------------------------------- */
- # elif defined(FPM_PPC)
- /*
- * This PowerPC version is fast and accurate; the disposition of the least
- * significant bit depends on OPT_ACCURACY via mad_f_scale64().
- */
- # define MAD_F_MLX(hi, lo, x, y)
- do {
- asm ("mullw %0,%1,%2"
- : "=r" (lo)
- : "%r" (x), "r" (y));
- asm ("mulhw %0,%1,%2"
- : "=r" (hi)
- : "%r" (x), "r" (y));
- }
- while (0)
- # if defined(OPT_ACCURACY)
- /*
- * This gives best accuracy but is not very fast.
- */
- # define MAD_F_MLA(hi, lo, x, y)
- ({ mad_fixed64hi_t __hi;
- mad_fixed64lo_t __lo;
- MAD_F_MLX(__hi, __lo, (x), (y));
- asm ("addc %0,%2,%3nt"
- "adde %1,%4,%5"
- : "=r" (lo), "=r" (hi)
- : "%r" (lo), "r" (__lo),
- "%r" (hi), "r" (__hi)
- : "xer");
- })
- # endif
- # if defined(OPT_ACCURACY)
- /*
- * This is slower than the truncating version below it.
- */
- # define mad_f_scale64(hi, lo)
- ({ mad_fixed_t __result, __round;
- asm ("rotrwi %0,%1,%2"
- : "=r" (__result)
- : "r" (lo), "i" (MAD_F_SCALEBITS));
- asm ("extrwi %0,%1,1,0"
- : "=r" (__round)
- : "r" (__result));
- asm ("insrwi %0,%1,%2,0"
- : "+r" (__result)
- : "r" (hi), "i" (MAD_F_SCALEBITS));
- asm ("add %0,%1,%2"
- : "=r" (__result)
- : "%r" (__result), "r" (__round));
- __result;
- })
- # else
- # define mad_f_scale64(hi, lo)
- ({ mad_fixed_t __result;
- asm ("rotrwi %0,%1,%2"
- : "=r" (__result)
- : "r" (lo), "i" (MAD_F_SCALEBITS));
- asm ("insrwi %0,%1,%2,0"
- : "+r" (__result)
- : "r" (hi), "i" (MAD_F_SCALEBITS));
- __result;
- })
- # endif
- # define MAD_F_SCALEBITS MAD_F_FRACBITS
- /* --- Default ------------------------------------------------------------- */
- # elif defined(FPM_DEFAULT)
- /*
- * This version is the most portable but it loses significant accuracy.
- * Furthermore, accuracy is biased against the second argument, so care
- * should be taken when ordering operands.
- *
- * The scale factors are constant as this is not used with SSO.
- *
- * Pre-rounding is required to stay within the limits of compliance.
- */
- # if defined(OPT_SPEED)
- # define mad_f_mul(x, y) (((x) >> 12) * ((y) >> 16))
- # else
- # define mad_f_mul(x, y) ((((x) + (1L << 11)) >> 12) *
- (((y) + (1L << 15)) >> 16))
- # endif
- /* ------------------------------------------------------------------------- */
- # else
- # error "no FPM selected"
- # endif
- /* default implementations */
- # if !defined(mad_f_mul)
- # define mad_f_mul(x, y)
- ({ register mad_fixed64hi_t __hi;
- register mad_fixed64lo_t __lo;
- MAD_F_MLX(__hi, __lo, (x), (y));
- mad_f_scale64(__hi, __lo);
- })
- # endif
- # if !defined(MAD_F_MLA)
- # define MAD_F_ML0(hi, lo, x, y) ((lo) = mad_f_mul((x), (y)))
- # define MAD_F_MLA(hi, lo, x, y) ((lo) += mad_f_mul((x), (y)))
- # define MAD_F_MLN(hi, lo) ((lo) = -(lo))
- # define MAD_F_MLZ(hi, lo) ((void) (hi), (mad_fixed_t) (lo))
- # endif
- # if !defined(MAD_F_ML0)
- # define MAD_F_ML0(hi, lo, x, y) MAD_F_MLX((hi), (lo), (x), (y))
- # endif
- # if !defined(MAD_F_MLN)
- # define MAD_F_MLN(hi, lo) ((hi) = ((lo) = -(lo)) ? ~(hi) : -(hi))
- # endif
- # if !defined(MAD_F_MLZ)
- # define MAD_F_MLZ(hi, lo) mad_f_scale64((hi), (lo))
- # endif
- # if !defined(mad_f_scale64)
- # if defined(OPT_ACCURACY)
- # define mad_f_scale64(hi, lo)
- ((((mad_fixed_t)
- (((hi) << (32 - (MAD_F_SCALEBITS - 1))) |
- ((lo) >> (MAD_F_SCALEBITS - 1)))) + 1) >> 1)
- # else
- # define mad_f_scale64(hi, lo)
- ((mad_fixed_t)
- (((hi) << (32 - MAD_F_SCALEBITS)) |
- ((lo) >> MAD_F_SCALEBITS)))
- # endif
- # define MAD_F_SCALEBITS MAD_F_FRACBITS
- # endif
- /* C routines */
- mad_fixed_t mad_f_abs(mad_fixed_t);
- mad_fixed_t mad_f_div(mad_fixed_t, mad_fixed_t);
- # endif