/*
* ====================================================
* 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.
* ====================================================
*/
/*
* from: @(#)fdlibm.h 5.1 93/09/24
* $NetBSD: math_private.h,v 1.23 2016/09/19 22:05:05 christos Exp $
*/
#ifndef _MATH_PRIVATE_H_
#define _MATH_PRIVATE_H_
#include <sys/types.h>
/* The original fdlibm 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. */
/* A union which permits us to convert between a double and two 32 bit
ints. */
/*
* The ARM ports are little endian except for the FPA word order which is
* big endian.
*/
#if (BYTE_ORDER == BIG_ENDIAN) || (defined(__arm__) && !defined(__VFP_FP__))
typedef union
{
double value;
struct
{
u_int32_t msw;
u_int32_t lsw;
} parts;
struct {
u_int64_t w;
} xparts;
} ieee_double_shape_type;
#endif
#if (BYTE_ORDER == LITTLE_ENDIAN) && \
!(defined(__arm__) && !defined(__VFP_FP__))
typedef union
{
double value;
struct
{
u_int32_t lsw;
u_int32_t msw;
} parts;
struct {
u_int64_t w;
} xparts;
} 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 (/*CONSTCOND*/0)
/* Get a 64-bit int from a double. */
#define EXTRACT_WORD64(ix,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix) = ew_u.xparts.w; \
} while (/*CONSTCOND*/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 (/*CONSTCOND*/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 (/*CONSTCOND*/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 (/*CONSTCOND*/0)
/* Set a double from a 64-bit int. */
#define INSERT_WORD64(d,ix) \
do { \
ieee_double_shape_type iw_u; \
iw_u.xparts.w = (ix); \
(d) = iw_u.value; \
} while (/*CONSTCOND*/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 (/*CONSTCOND*/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 (/*CONSTCOND*/0)
/* A union which permits us to convert between a float and a 32 bit
int. */
typedef union
{
float value;
u_int32_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 (/*CONSTCOND*/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 (/*CONSTCOND*/0)
/*
* Attempt to get strict C99 semantics for assignment with non-C99 compilers.
*/
#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval))
#else
#define STRICT_ASSIGN(type, lval, rval) do { \
volatile type __lval; \
\
if (sizeof(type) >= sizeof(long double)) \
(lval) = (rval); \
else { \
__lval = (rval); \
(lval) = __lval; \
} \
} while (/*CONSTCOND*/0)
#endif
#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])
/*
* Inline functions that can be used to construct complex values.
*
* The C99 standard intends x+I*y to be used for this, but x+I*y is
* currently unusable in general since gcc introduces many overflow,
* underflow, sign and efficiency bugs by rewriting I*y as
* (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
* In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
* to -0.0+I*0.0.
*
* The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL()
* to construct complex values. Compilers that conform to the C99
* standard require the following functions to avoid the above issues.
*/
#ifndef CMPLXF
static __inline float complex
CMPLXF(float x, float y)
{
float_complex z;
REAL_PART(z) = x;
IMAG_PART(z) = y;
return (z.z);
}
#endif
#ifndef CMPLX
static __inline double complex
CMPLX(double x, double y)
{
double_complex z;
REAL_PART(z) = x;
IMAG_PART(z) = y;
return (z.z);
}
#endif
#ifndef CMPLXL
static __inline long double complex
CMPLXL(long double x, long double y)
{
long_double_complex z;
REAL_PART(z) = x;
IMAG_PART(z) = y;
return (z.z);
}
#endif
#endif /* _COMPLEX_H */
/* 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_lgamma __P((double));
extern double __ieee754_gamma __P((double));
extern double __ieee754_log10 __P((double));
extern double __ieee754_log2 __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*));
extern double __ieee754_scalb __P((double,double));
/* 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*));
/* 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_lgammaf __P((float));
extern float __ieee754_gammaf __P((float));
extern float __ieee754_log10f __P((float));
extern float __ieee754_log2f __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*));
extern float __ieee754_scalbf __P((float,float));
/* 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*));
/* ieee style elementary long double functions */
extern long double __ieee754_fmodl(long double, long double);
extern long double __ieee754_sqrtl(long double);
/*
* TRUNC() is a macro that sets the trailing 27 bits in the mantissa of an
* IEEE double variable to zero. It must be expression-like for syntactic
* reasons, and we implement this expression using an inline function
* instead of a pure macro to avoid depending on the gcc feature of
* statement-expressions.
*/
#define TRUNC(d) (_b_trunc(&(d)))
static __inline void
_b_trunc(volatile double *_dp)
{
uint32_t _lw;
GET_LOW_WORD(_lw, *_dp);
SET_LOW_WORD(*_dp, _lw & 0xf8000000);
}
struct Double {
double a;
double b;
};
/*
* Functions internal to the math package, yet not static.
*/
double __exp__D(double, double);
struct Double __log__D(double);
#endif /* _MATH_PRIVATE_H_ */