364 lines
11 KiB
C
364 lines
11 KiB
C
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/* @(#)fdlibm.h 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* CYGNUS LOCAL: Include files. */
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#include <math.h>
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#include <machine/ieeefp.h>
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/* CYGNUS LOCAL: Default to XOPEN_MODE. */
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#define _XOPEN_MODE
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/* Most routines need to check whether a float is finite, infinite, or not a
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number, and many need to know whether the result of an operation will
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overflow. These conditions depend on whether the largest exponent is
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used for NaNs & infinities, or whether it's used for finite numbers. The
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macros below wrap up that kind of information:
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FLT_UWORD_IS_FINITE(X)
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True if a positive float with bitmask X is finite.
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FLT_UWORD_IS_NAN(X)
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True if a positive float with bitmask X is not a number.
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FLT_UWORD_IS_INFINITE(X)
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True if a positive float with bitmask X is +infinity.
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FLT_UWORD_MAX
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The bitmask of FLT_MAX.
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FLT_UWORD_HALF_MAX
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The bitmask of FLT_MAX/2.
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FLT_UWORD_EXP_MAX
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The bitmask of the largest finite exponent (129 if the largest
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exponent is used for finite numbers, 128 otherwise).
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FLT_UWORD_LOG_MAX
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The bitmask of log(FLT_MAX), rounded down. This value is the largest
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input that can be passed to exp() without producing overflow.
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FLT_UWORD_LOG_2MAX
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The bitmask of log(2*FLT_MAX), rounded down. This value is the
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largest input than can be passed to cosh() without producing
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overflow.
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FLT_LARGEST_EXP
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The largest biased exponent that can be used for finite numbers
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(255 if the largest exponent is used for finite numbers, 254
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otherwise) */
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#ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL
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#define FLT_UWORD_IS_FINITE(x) 1
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#define FLT_UWORD_IS_NAN(x) 0
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#define FLT_UWORD_IS_INFINITE(x) 0
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#define FLT_UWORD_MAX 0x7fffffff
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#define FLT_UWORD_EXP_MAX 0x43010000
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#define FLT_UWORD_LOG_MAX 0x42b2d4fc
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#define FLT_UWORD_LOG_2MAX 0x42b437e0
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#define HUGE ((float)0X1.FFFFFEP128)
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#else
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#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L)
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#define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L)
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#define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L)
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#define FLT_UWORD_MAX 0x7f7fffff
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#define FLT_UWORD_EXP_MAX 0x43000000
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#define FLT_UWORD_LOG_MAX 0x42b17217
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#define FLT_UWORD_LOG_2MAX 0x42b2d4fc
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#define HUGE ((float)3.40282346638528860e+38)
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#endif
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#define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1<<23))
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#define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23)
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/* Many routines check for zero and subnormal numbers. Such things depend
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on whether the target supports denormals or not:
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FLT_UWORD_IS_ZERO(X)
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True if a positive float with bitmask X is +0. Without denormals,
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any float with a zero exponent is a +0 representation. With
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denormals, the only +0 representation is a 0 bitmask.
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FLT_UWORD_IS_SUBNORMAL(X)
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True if a non-zero positive float with bitmask X is subnormal.
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(Routines should check for zeros first.)
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FLT_UWORD_MIN
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The bitmask of the smallest float above +0. Call this number
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REAL_FLT_MIN...
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FLT_UWORD_EXP_MIN
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The bitmask of the float representation of REAL_FLT_MIN's exponent.
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FLT_UWORD_LOG_MIN
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The bitmask of |log(REAL_FLT_MIN)|, rounding down.
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FLT_SMALLEST_EXP
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REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported,
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-22 if they are).
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*/
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#ifdef _FLT_NO_DENORMALS
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#define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L)
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#define FLT_UWORD_IS_SUBNORMAL(x) 0
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#define FLT_UWORD_MIN 0x00800000
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#define FLT_UWORD_EXP_MIN 0x42fc0000
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#define FLT_UWORD_LOG_MIN 0x42aeac50
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#define FLT_SMALLEST_EXP 1
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#else
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#define FLT_UWORD_IS_ZERO(x) ((x)==0)
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#define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L)
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#define FLT_UWORD_MIN 0x00000001
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#define FLT_UWORD_EXP_MIN 0x43160000
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#define FLT_UWORD_LOG_MIN 0x42cff1b5
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#define FLT_SMALLEST_EXP -22
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#endif
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#ifdef __STDC__
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#define __P(p) p
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#else
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#define __P(p) ()
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#endif
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/*
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* set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
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* (one may replace the following line by "#include <values.h>")
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*/
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#define X_TLOSS 1.41484755040568800000e+16
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/* Functions that are not documented, and are not in <math.h>. */
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extern double logb __P((double));
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#ifdef _SCALB_INT
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extern double scalb __P((double, int));
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#else
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extern double scalb __P((double, double));
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#endif
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extern double significand __P((double));
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/* ieee style elementary functions */
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extern double __ieee754_sqrt __P((double));
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extern double __ieee754_acos __P((double));
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extern double __ieee754_acosh __P((double));
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extern double __ieee754_log __P((double));
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extern double __ieee754_atanh __P((double));
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extern double __ieee754_asin __P((double));
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extern double __ieee754_atan2 __P((double,double));
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extern double __ieee754_exp __P((double));
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extern double __ieee754_cosh __P((double));
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extern double __ieee754_fmod __P((double,double));
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extern double __ieee754_pow __P((double,double));
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extern double __ieee754_lgamma_r __P((double,int *));
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extern double __ieee754_gamma_r __P((double,int *));
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extern double __ieee754_log10 __P((double));
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extern double __ieee754_sinh __P((double));
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extern double __ieee754_hypot __P((double,double));
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extern double __ieee754_j0 __P((double));
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extern double __ieee754_j1 __P((double));
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extern double __ieee754_y0 __P((double));
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extern double __ieee754_y1 __P((double));
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extern double __ieee754_jn __P((int,double));
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extern double __ieee754_yn __P((int,double));
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extern double __ieee754_remainder __P((double,double));
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extern __int32_t __ieee754_rem_pio2 __P((double,double*));
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#ifdef _SCALB_INT
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extern double __ieee754_scalb __P((double,int));
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#else
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extern double __ieee754_scalb __P((double,double));
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#endif
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/* fdlibm kernel function */
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extern double __kernel_standard __P((double,double,int));
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extern double __kernel_sin __P((double,double,int));
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extern double __kernel_cos __P((double,double));
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extern double __kernel_tan __P((double,double,int));
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extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const __int32_t*));
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/* Undocumented float functions. */
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extern float logbf __P((float));
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#ifdef _SCALB_INT
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extern float scalbf __P((float, int));
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#else
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extern float scalbf __P((float, float));
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#endif
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extern float significandf __P((float));
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/* ieee style elementary float functions */
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extern float __ieee754_sqrtf __P((float));
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extern float __ieee754_acosf __P((float));
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extern float __ieee754_acoshf __P((float));
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extern float __ieee754_logf __P((float));
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extern float __ieee754_atanhf __P((float));
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extern float __ieee754_asinf __P((float));
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extern float __ieee754_atan2f __P((float,float));
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extern float __ieee754_expf __P((float));
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extern float __ieee754_coshf __P((float));
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extern float __ieee754_fmodf __P((float,float));
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extern float __ieee754_powf __P((float,float));
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extern float __ieee754_lgammaf_r __P((float,int *));
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extern float __ieee754_gammaf_r __P((float,int *));
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extern float __ieee754_log10f __P((float));
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extern float __ieee754_sinhf __P((float));
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extern float __ieee754_hypotf __P((float,float));
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extern float __ieee754_j0f __P((float));
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extern float __ieee754_j1f __P((float));
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extern float __ieee754_y0f __P((float));
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extern float __ieee754_y1f __P((float));
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extern float __ieee754_jnf __P((int,float));
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extern float __ieee754_ynf __P((int,float));
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extern float __ieee754_remainderf __P((float,float));
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extern __int32_t __ieee754_rem_pio2f __P((float,float*));
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#ifdef _SCALB_INT
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extern float __ieee754_scalbf __P((float,int));
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#else
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extern float __ieee754_scalbf __P((float,float));
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#endif
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/* float versions of fdlibm kernel functions */
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extern float __kernel_sinf __P((float,float,int));
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extern float __kernel_cosf __P((float,float));
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extern float __kernel_tanf __P((float,float,int));
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extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __int32_t*));
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/* The original code used statements like
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n0 = ((*(int*)&one)>>29)^1; * index of high word *
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ix0 = *(n0+(int*)&x); * high word of x *
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ix1 = *((1-n0)+(int*)&x); * low word of x *
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to dig two 32 bit words out of the 64 bit IEEE floating point
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value. That is non-ANSI, and, moreover, the gcc instruction
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scheduler gets it wrong. We instead use the following macros.
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Unlike the original code, we determine the endianness at compile
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time, not at run time; I don't see much benefit to selecting
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endianness at run time. */
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#ifndef __IEEE_BIG_ENDIAN
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#ifndef __IEEE_LITTLE_ENDIAN
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#error Must define endianness
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#endif
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#endif
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/* A union which permits us to convert between a double and two 32 bit
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ints. */
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#ifdef __IEEE_BIG_ENDIAN
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typedef union
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{
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double value;
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struct
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{
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__uint32_t msw;
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__uint32_t lsw;
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} parts;
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} ieee_double_shape_type;
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#endif
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#ifdef __IEEE_LITTLE_ENDIAN
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typedef union
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{
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double value;
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struct
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{
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__uint32_t lsw;
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__uint32_t msw;
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} parts;
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} ieee_double_shape_type;
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#endif
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/* Get two 32 bit ints from a double. */
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#define EXTRACT_WORDS(ix0,ix1,d) \
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do { \
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ieee_double_shape_type ew_u; \
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ew_u.value = (d); \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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} while (0)
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/* Get the more significant 32 bit int from a double. */
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#define GET_HIGH_WORD(i,d) \
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do { \
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ieee_double_shape_type gh_u; \
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gh_u.value = (d); \
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(i) = gh_u.parts.msw; \
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} while (0)
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/* Get the less significant 32 bit int from a double. */
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#define GET_LOW_WORD(i,d) \
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do { \
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ieee_double_shape_type gl_u; \
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gl_u.value = (d); \
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(i) = gl_u.parts.lsw; \
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} while (0)
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/* Set a double from two 32 bit ints. */
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#define INSERT_WORDS(d,ix0,ix1) \
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do { \
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ieee_double_shape_type iw_u; \
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iw_u.parts.msw = (ix0); \
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iw_u.parts.lsw = (ix1); \
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(d) = iw_u.value; \
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} while (0)
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/* Set the more significant 32 bits of a double from an int. */
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#define SET_HIGH_WORD(d,v) \
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do { \
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ieee_double_shape_type sh_u; \
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sh_u.value = (d); \
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sh_u.parts.msw = (v); \
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(d) = sh_u.value; \
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} while (0)
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/* Set the less significant 32 bits of a double from an int. */
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#define SET_LOW_WORD(d,v) \
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do { \
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ieee_double_shape_type sl_u; \
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sl_u.value = (d); \
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sl_u.parts.lsw = (v); \
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(d) = sl_u.value; \
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} while (0)
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/* A union which permits us to convert between a float and a 32 bit
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int. */
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typedef union
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{
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float value;
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__uint32_t word;
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} ieee_float_shape_type;
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/* Get a 32 bit int from a float. */
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#define GET_FLOAT_WORD(i,d) \
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do { \
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ieee_float_shape_type gf_u; \
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gf_u.value = (d); \
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(i) = gf_u.word; \
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} while (0)
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/* Set a float from a 32 bit int. */
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#define SET_FLOAT_WORD(d,i) \
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do { \
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ieee_float_shape_type sf_u; \
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sf_u.word = (i); \
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(d) = sf_u.value; \
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} while (0)
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