418 lines
12 KiB
C
418 lines
12 KiB
C
|
|
/* @(#)fdlibm.h 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
/* REDHAT LOCAL: Include files. */
|
|
#include <math.h>
|
|
#include <sys/types.h>
|
|
#include <machine/ieeefp.h>
|
|
|
|
/* REDHAT LOCAL: Default to XOPEN_MODE. */
|
|
#define _XOPEN_MODE
|
|
|
|
/* Most routines need to check whether a float is finite, infinite, or not a
|
|
number, and many need to know whether the result of an operation will
|
|
overflow. These conditions depend on whether the largest exponent is
|
|
used for NaNs & infinities, or whether it's used for finite numbers. The
|
|
macros below wrap up that kind of information:
|
|
|
|
FLT_UWORD_IS_FINITE(X)
|
|
True if a positive float with bitmask X is finite.
|
|
|
|
FLT_UWORD_IS_NAN(X)
|
|
True if a positive float with bitmask X is not a number.
|
|
|
|
FLT_UWORD_IS_INFINITE(X)
|
|
True if a positive float with bitmask X is +infinity.
|
|
|
|
FLT_UWORD_MAX
|
|
The bitmask of FLT_MAX.
|
|
|
|
FLT_UWORD_HALF_MAX
|
|
The bitmask of FLT_MAX/2.
|
|
|
|
FLT_UWORD_EXP_MAX
|
|
The bitmask of the largest finite exponent (129 if the largest
|
|
exponent is used for finite numbers, 128 otherwise).
|
|
|
|
FLT_UWORD_LOG_MAX
|
|
The bitmask of log(FLT_MAX), rounded down. This value is the largest
|
|
input that can be passed to exp() without producing overflow.
|
|
|
|
FLT_UWORD_LOG_2MAX
|
|
The bitmask of log(2*FLT_MAX), rounded down. This value is the
|
|
largest input than can be passed to cosh() without producing
|
|
overflow.
|
|
|
|
FLT_LARGEST_EXP
|
|
The largest biased exponent that can be used for finite numbers
|
|
(255 if the largest exponent is used for finite numbers, 254
|
|
otherwise) */
|
|
|
|
#ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL
|
|
#define FLT_UWORD_IS_FINITE(x) 1
|
|
#define FLT_UWORD_IS_NAN(x) 0
|
|
#define FLT_UWORD_IS_INFINITE(x) 0
|
|
#define FLT_UWORD_MAX 0x7fffffff
|
|
#define FLT_UWORD_EXP_MAX 0x43010000
|
|
#define FLT_UWORD_LOG_MAX 0x42b2d4fc
|
|
#define FLT_UWORD_LOG_2MAX 0x42b437e0
|
|
#define HUGE ((float)0X1.FFFFFEP128)
|
|
#else
|
|
#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L)
|
|
#define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L)
|
|
#define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L)
|
|
#define FLT_UWORD_MAX 0x7f7fffffL
|
|
#define FLT_UWORD_EXP_MAX 0x43000000
|
|
#define FLT_UWORD_LOG_MAX 0x42b17217
|
|
#define FLT_UWORD_LOG_2MAX 0x42b2d4fc
|
|
#define HUGE ((float)3.40282346638528860e+38)
|
|
#endif
|
|
#define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1L<<23))
|
|
#define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23)
|
|
|
|
/* Many routines check for zero and subnormal numbers. Such things depend
|
|
on whether the target supports denormals or not:
|
|
|
|
FLT_UWORD_IS_ZERO(X)
|
|
True if a positive float with bitmask X is +0. Without denormals,
|
|
any float with a zero exponent is a +0 representation. With
|
|
denormals, the only +0 representation is a 0 bitmask.
|
|
|
|
FLT_UWORD_IS_SUBNORMAL(X)
|
|
True if a non-zero positive float with bitmask X is subnormal.
|
|
(Routines should check for zeros first.)
|
|
|
|
FLT_UWORD_MIN
|
|
The bitmask of the smallest float above +0. Call this number
|
|
REAL_FLT_MIN...
|
|
|
|
FLT_UWORD_EXP_MIN
|
|
The bitmask of the float representation of REAL_FLT_MIN's exponent.
|
|
|
|
FLT_UWORD_LOG_MIN
|
|
The bitmask of |log(REAL_FLT_MIN)|, rounding down.
|
|
|
|
FLT_SMALLEST_EXP
|
|
REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported,
|
|
-22 if they are).
|
|
*/
|
|
|
|
#ifdef _FLT_NO_DENORMALS
|
|
#define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L)
|
|
#define FLT_UWORD_IS_SUBNORMAL(x) 0
|
|
#define FLT_UWORD_MIN 0x00800000
|
|
#define FLT_UWORD_EXP_MIN 0x42fc0000
|
|
#define FLT_UWORD_LOG_MIN 0x42aeac50
|
|
#define FLT_SMALLEST_EXP 1
|
|
#else
|
|
#define FLT_UWORD_IS_ZERO(x) ((x)==0)
|
|
#define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L)
|
|
#define FLT_UWORD_MIN 0x00000001
|
|
#define FLT_UWORD_EXP_MIN 0x43160000
|
|
#define FLT_UWORD_LOG_MIN 0x42cff1b5
|
|
#define FLT_SMALLEST_EXP -22
|
|
#endif
|
|
|
|
#ifdef __STDC__
|
|
#undef __P
|
|
#define __P(p) p
|
|
#else
|
|
#define __P(p) ()
|
|
#endif
|
|
|
|
/*
|
|
* set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
|
|
* (one may replace the following line by "#include <values.h>")
|
|
*/
|
|
|
|
#define X_TLOSS 1.41484755040568800000e+16
|
|
|
|
/* Functions that are not documented, and are not in <math.h>. */
|
|
|
|
#ifdef _SCALB_INT
|
|
extern double scalb __P((double, int));
|
|
#else
|
|
extern double scalb __P((double, double));
|
|
#endif
|
|
extern double significand __P((double));
|
|
|
|
extern long double __ieee754_hypotl __P((long double, long double));
|
|
|
|
/* ieee style elementary functions */
|
|
extern double __ieee754_sqrt __P((double));
|
|
extern double __ieee754_acos __P((double));
|
|
extern double __ieee754_acosh __P((double));
|
|
extern double __ieee754_log __P((double));
|
|
extern double __ieee754_atanh __P((double));
|
|
extern double __ieee754_asin __P((double));
|
|
extern double __ieee754_atan2 __P((double,double));
|
|
extern double __ieee754_exp __P((double));
|
|
extern double __ieee754_cosh __P((double));
|
|
extern double __ieee754_fmod __P((double,double));
|
|
extern double __ieee754_pow __P((double,double));
|
|
extern double __ieee754_lgamma_r __P((double,int *));
|
|
extern double __ieee754_gamma_r __P((double,int *));
|
|
extern double __ieee754_log10 __P((double));
|
|
extern double __ieee754_sinh __P((double));
|
|
extern double __ieee754_hypot __P((double,double));
|
|
extern double __ieee754_j0 __P((double));
|
|
extern double __ieee754_j1 __P((double));
|
|
extern double __ieee754_y0 __P((double));
|
|
extern double __ieee754_y1 __P((double));
|
|
extern double __ieee754_jn __P((int,double));
|
|
extern double __ieee754_yn __P((int,double));
|
|
extern double __ieee754_remainder __P((double,double));
|
|
extern __int32_t __ieee754_rem_pio2 __P((double,double*));
|
|
#ifdef _SCALB_INT
|
|
extern double __ieee754_scalb __P((double,int));
|
|
#else
|
|
extern double __ieee754_scalb __P((double,double));
|
|
#endif
|
|
|
|
/* fdlibm kernel function */
|
|
extern double __kernel_standard __P((double,double,int));
|
|
extern double __kernel_sin __P((double,double,int));
|
|
extern double __kernel_cos __P((double,double));
|
|
extern double __kernel_tan __P((double,double,int));
|
|
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const __int32_t*));
|
|
|
|
/* Undocumented float functions. */
|
|
#ifdef _SCALB_INT
|
|
extern float scalbf __P((float, int));
|
|
#else
|
|
extern float scalbf __P((float, float));
|
|
#endif
|
|
extern float significandf __P((float));
|
|
|
|
/* ieee style elementary float functions */
|
|
extern float __ieee754_sqrtf __P((float));
|
|
extern float __ieee754_acosf __P((float));
|
|
extern float __ieee754_acoshf __P((float));
|
|
extern float __ieee754_logf __P((float));
|
|
extern float __ieee754_atanhf __P((float));
|
|
extern float __ieee754_asinf __P((float));
|
|
extern float __ieee754_atan2f __P((float,float));
|
|
extern float __ieee754_expf __P((float));
|
|
extern float __ieee754_coshf __P((float));
|
|
extern float __ieee754_fmodf __P((float,float));
|
|
extern float __ieee754_powf __P((float,float));
|
|
extern float __ieee754_lgammaf_r __P((float,int *));
|
|
extern float __ieee754_gammaf_r __P((float,int *));
|
|
extern float __ieee754_log10f __P((float));
|
|
extern float __ieee754_sinhf __P((float));
|
|
extern float __ieee754_hypotf __P((float,float));
|
|
extern float __ieee754_j0f __P((float));
|
|
extern float __ieee754_j1f __P((float));
|
|
extern float __ieee754_y0f __P((float));
|
|
extern float __ieee754_y1f __P((float));
|
|
extern float __ieee754_jnf __P((int,float));
|
|
extern float __ieee754_ynf __P((int,float));
|
|
extern float __ieee754_remainderf __P((float,float));
|
|
extern __int32_t __ieee754_rem_pio2f __P((float,float*));
|
|
#ifdef _SCALB_INT
|
|
extern float __ieee754_scalbf __P((float,int));
|
|
#else
|
|
extern float __ieee754_scalbf __P((float,float));
|
|
#endif
|
|
|
|
#if !__OBSOLETE_MATH
|
|
/* The new math code does not provide separate wrapper function
|
|
for error handling, so the extern symbol is called directly.
|
|
This is valid as long as there are no namespace issues (the
|
|
extern symbol is reserved whenever the caller is reserved)
|
|
and there are no observable error handling side effects. */
|
|
# define __ieee754_expf(x) expf(x)
|
|
# define __ieee754_logf(x) logf(x)
|
|
# define __ieee754_powf(x,y) powf(x,y)
|
|
#endif
|
|
|
|
/* float versions of fdlibm kernel functions */
|
|
extern float __kernel_sinf __P((float,float,int));
|
|
extern float __kernel_cosf __P((float,float));
|
|
extern float __kernel_tanf __P((float,float,int));
|
|
extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __int32_t*));
|
|
|
|
/* The original code used statements like
|
|
n0 = ((*(int*)&one)>>29)^1; * index of high word *
|
|
ix0 = *(n0+(int*)&x); * high word of x *
|
|
ix1 = *((1-n0)+(int*)&x); * low word of x *
|
|
to dig two 32 bit words out of the 64 bit IEEE floating point
|
|
value. That is non-ANSI, and, moreover, the gcc instruction
|
|
scheduler gets it wrong. We instead use the following macros.
|
|
Unlike the original code, we determine the endianness at compile
|
|
time, not at run time; I don't see much benefit to selecting
|
|
endianness at run time. */
|
|
|
|
#ifndef __IEEE_BIG_ENDIAN
|
|
#ifndef __IEEE_LITTLE_ENDIAN
|
|
#error Must define endianness
|
|
#endif
|
|
#endif
|
|
|
|
/* A union which permits us to convert between a double and two 32 bit
|
|
ints. */
|
|
|
|
#ifdef __IEEE_BIG_ENDIAN
|
|
|
|
typedef union
|
|
{
|
|
double value;
|
|
struct
|
|
{
|
|
__uint32_t msw;
|
|
__uint32_t lsw;
|
|
} parts;
|
|
} ieee_double_shape_type;
|
|
|
|
#endif
|
|
|
|
#ifdef __IEEE_LITTLE_ENDIAN
|
|
|
|
typedef union
|
|
{
|
|
double value;
|
|
struct
|
|
{
|
|
__uint32_t lsw;
|
|
__uint32_t msw;
|
|
} parts;
|
|
} ieee_double_shape_type;
|
|
|
|
#endif
|
|
|
|
/* Get two 32 bit ints from a double. */
|
|
|
|
#define EXTRACT_WORDS(ix0,ix1,d) \
|
|
do { \
|
|
ieee_double_shape_type ew_u; \
|
|
ew_u.value = (d); \
|
|
(ix0) = ew_u.parts.msw; \
|
|
(ix1) = ew_u.parts.lsw; \
|
|
} while (0)
|
|
|
|
/* Get the more significant 32 bit int from a double. */
|
|
|
|
#define GET_HIGH_WORD(i,d) \
|
|
do { \
|
|
ieee_double_shape_type gh_u; \
|
|
gh_u.value = (d); \
|
|
(i) = gh_u.parts.msw; \
|
|
} while (0)
|
|
|
|
/* Get the less significant 32 bit int from a double. */
|
|
|
|
#define GET_LOW_WORD(i,d) \
|
|
do { \
|
|
ieee_double_shape_type gl_u; \
|
|
gl_u.value = (d); \
|
|
(i) = gl_u.parts.lsw; \
|
|
} while (0)
|
|
|
|
/* Set a double from two 32 bit ints. */
|
|
|
|
#define INSERT_WORDS(d,ix0,ix1) \
|
|
do { \
|
|
ieee_double_shape_type iw_u; \
|
|
iw_u.parts.msw = (ix0); \
|
|
iw_u.parts.lsw = (ix1); \
|
|
(d) = iw_u.value; \
|
|
} while (0)
|
|
|
|
/* Set the more significant 32 bits of a double from an int. */
|
|
|
|
#define SET_HIGH_WORD(d,v) \
|
|
do { \
|
|
ieee_double_shape_type sh_u; \
|
|
sh_u.value = (d); \
|
|
sh_u.parts.msw = (v); \
|
|
(d) = sh_u.value; \
|
|
} while (0)
|
|
|
|
/* Set the less significant 32 bits of a double from an int. */
|
|
|
|
#define SET_LOW_WORD(d,v) \
|
|
do { \
|
|
ieee_double_shape_type sl_u; \
|
|
sl_u.value = (d); \
|
|
sl_u.parts.lsw = (v); \
|
|
(d) = sl_u.value; \
|
|
} while (0)
|
|
|
|
/* A union which permits us to convert between a float and a 32 bit
|
|
int. */
|
|
|
|
typedef union
|
|
{
|
|
float value;
|
|
__uint32_t word;
|
|
} ieee_float_shape_type;
|
|
|
|
/* Get a 32 bit int from a float. */
|
|
|
|
#define GET_FLOAT_WORD(i,d) \
|
|
do { \
|
|
ieee_float_shape_type gf_u; \
|
|
gf_u.value = (d); \
|
|
(i) = gf_u.word; \
|
|
} while (0)
|
|
|
|
/* Set a float from a 32 bit int. */
|
|
|
|
#define SET_FLOAT_WORD(d,i) \
|
|
do { \
|
|
ieee_float_shape_type sf_u; \
|
|
sf_u.word = (i); \
|
|
(d) = sf_u.value; \
|
|
} while (0)
|
|
|
|
/* Macros to avoid undefined behaviour that can arise if the amount
|
|
of a shift is exactly equal to the size of the shifted operand. */
|
|
|
|
#define SAFE_LEFT_SHIFT(op,amt) \
|
|
(((amt) < 8 * sizeof(op)) ? ((op) << (amt)) : 0)
|
|
|
|
#define SAFE_RIGHT_SHIFT(op,amt) \
|
|
(((amt) < 8 * sizeof(op)) ? ((op) >> (amt)) : 0)
|
|
|
|
#ifdef _COMPLEX_H
|
|
|
|
/*
|
|
* Quoting from ISO/IEC 9899:TC2:
|
|
*
|
|
* 6.2.5.13 Types
|
|
* Each complex type has the same representation and alignment requirements as
|
|
* an array type containing exactly two elements of the corresponding real type;
|
|
* the first element is equal to the real part, and the second element to the
|
|
* imaginary part, of the complex number.
|
|
*/
|
|
typedef union {
|
|
float complex z;
|
|
float parts[2];
|
|
} float_complex;
|
|
|
|
typedef union {
|
|
double complex z;
|
|
double parts[2];
|
|
} double_complex;
|
|
|
|
typedef union {
|
|
long double complex z;
|
|
long double parts[2];
|
|
} long_double_complex;
|
|
|
|
#define REAL_PART(z) ((z).parts[0])
|
|
#define IMAG_PART(z) ((z).parts[1])
|
|
|
|
#endif /* _COMPLEX_H */
|
|
|