math_private.h

Newlib 嵌入式 C库 标准实现代码

/*
 * ====================================================
 * 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
 * $Id: math_private.h,v 1.3 2003/07/09 17:52:31 aoliva Exp $
 */

#ifndef _MATH_PRIVATE_H_
#define _MATH_PRIVATE_H_

#include <endian.h>
#include <sys/types.h>
#include <machine/weakalias.h>
#include <machine/huge_val.h>

#define INFINITY HUGE_VALF

#define __nan nan
#define __isnan isnan
#define __isinf isinf
#define __copysignf copysignf
#define __copysign copysign
#define __isnanf isnanf
#define __isinff isinff
#define __nanf nanf
#define feraiseexcept(x) /* nothing */
#define __sincos sincos
#define __sincosf sincosf

int __signbitd (double x);
int __signbitf (float x);

/* 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.  */

#if __FLOAT_WORD_ORDER == BIG_ENDIAN

typedef union
{
  double value;
  struct
  {
    u_int32_t msw;
    u_int32_t lsw;
  } parts;
} ieee_double_shape_type;

#endif

#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN

typedef union
{
  double value;
  struct
  {
    u_int32_t lsw;
    u_int32_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;
  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 (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)

#if 0
/* ieee style elementary functions */
extern double __ieee754_sqrt (double);
extern double __ieee754_acos (double);
extern double __ieee754_acosh (double);
extern double __ieee754_log (double);
extern double __ieee754_atanh (double);
extern double __ieee754_asin (double);
extern double __ieee754_atan2 (double,double);
extern double __ieee754_exp (double);
extern double __ieee754_exp2 (double);
extern double __ieee754_exp10 (double);
extern double __ieee754_cosh (double);
extern double __ieee754_fmod (double,double);
extern double __ieee754_pow (double,double);
extern double __ieee754_lgamma_r (double,int *);
extern double __ieee754_gamma_r (double,int *);
extern double __ieee754_lgamma (double);
extern double __ieee754_gamma (double);
extern double __ieee754_log10 (double);
extern double __ieee754_log2 (double);
extern double __ieee754_sinh (double);
extern double __ieee754_hypot (double,double);
extern double __ieee754_j0 (double);
extern double __ieee754_j1 (double);
extern double __ieee754_y0 (double);
extern double __ieee754_y1 (double);
extern double __ieee754_jn (int,double);
extern double __ieee754_yn (int,double);
extern double __ieee754_remainder (double,double);
extern int32_t __ieee754_rem_pio2 (double,double*);
extern double __ieee754_scalb (double,double);
#endif

/* This is necessary because the hardware accelerated version of libm
   does not provide the __ieee754 functions. */
#define __ieee754_sinh   sinh
#define __ieee754_hypot  hypot
#define __ieee754_hypotf hypotf
#define __ieee754_logf   logf
#define __ieee754_log10  log10
#define __ieee754_exp    exp
#define __ieee754_cosh   cosh
#define __ieee754_expf   expf
#define __ieee754_log10f log10f
#define __ieee754_atan2  atan2
#define __ieee754_sqrtf  sqrtf
#define __ieee754_sinhf  sinhf
#define __ieee754_log    log
#define __ieee754_sqrt   sqrt
#define __ieee754_coshf  coshf
#define __ieee754_atan2f atan2f

/* fdlibm kernel function */
extern double __kernel_standard (double,double,int);
extern double __kernel_sin (double,double,int);
extern double __kernel_cos (double,double);
extern double __kernel_tan (double,double,int);
extern int    __kernel_rem_pio2 (double*,double*,int,int,int, const int32_t*);

/* internal functions.  */
extern double __copysign (double x, double __y);


/* ieee style elementary float functions */
extern float __ieee754_sqrtf (float);
extern float __ieee754_acosf (float);
extern float __ieee754_acoshf (float);
extern float __ieee754_logf (float);
extern float __ieee754_atanhf (float);
extern float __ieee754_asinf (float);
extern float __ieee754_atan2f (float,float);
extern float __ieee754_expf (float);
extern float __ieee754_exp2f (float);
extern float __ieee754_exp10f (float);
extern float __ieee754_coshf (float);
extern float __ieee754_fmodf (float,float);
extern float __ieee754_powf (float,float);
extern float __ieee754_lgammaf_r (float,int *);
extern float __ieee754_gammaf_r (float,int *);
extern float __ieee754_lgammaf (float);
extern float __ieee754_gammaf (float);
extern float __ieee754_log10f (float);
extern float __ieee754_log2f (float);
extern float __ieee754_sinhf (float);
extern float __ieee754_hypotf (float,float);
extern float __ieee754_j0f (float);
extern float __ieee754_j1f (float);
extern float __ieee754_y0f (float);
extern float __ieee754_y1f (float);
extern float __ieee754_jnf (int,float);
extern float __ieee754_ynf (int,float);
extern float __ieee754_remainderf (float,float);
extern int32_t __ieee754_rem_pio2f (float,float*);
extern float __ieee754_scalbf (float,float);


/* float versions of fdlibm kernel functions */
extern float __kernel_sinf (float,float,int);
extern float __kernel_cosf (float,float);
extern float __kernel_tanf (float,float,int);
extern int   __kernel_rem_pio2f (float*,float*,int,int,int, const int32_t*);


/* ieee style elementary long double functions */
extern long double __ieee754_sqrtl (long double);
extern long double __ieee754_acosl (long double);
extern long double __ieee754_acoshl (long double);
extern long double __ieee754_logl (long double);
extern long double __ieee754_atanhl (long double);
extern long double __ieee754_asinl (long double);
extern long double __ieee754_atan2l (long double,long double);
extern long double __ieee754_expl (long double);
extern long double __ieee754_exp2l (long double);
extern long double __ieee754_exp10l (long double);
extern long double __ieee754_coshl (long double);
extern long double __ieee754_fmodl (long double,long double);
extern long double __ieee754_powl (long double,long double);
extern long double __ieee754_lgammal_r (long double,int *);
extern long double __ieee754_gammal_r (long double,int *);
extern long double __ieee754_lgammal (long double);
extern long double __ieee754_gammal (long double);
extern long double __ieee754_log10l (long double);
extern long double __ieee754_log2l (long double);
extern long double __ieee754_sinhl (long double);
extern long double __ieee754_hypotl (long double,long double);
extern long double __ieee754_j0l (long double);
extern long double __ieee754_j1l (long double);
extern long double __ieee754_y0l (long double);
extern long double __ieee754_y1l (long double);
extern long double __ieee754_jnl (int,long double);
extern long double __ieee754_ynl (int,long double);
extern long double __ieee754_remainderl (long double,long double);
extern int   __ieee754_rem_pio2l (long double,long double*);
extern long double __ieee754_scalbl (long double,long double);

/* long double versions of fdlibm kernel functions */
extern long double __kernel_sinl (long double,long double,int);
extern long double __kernel_cosl (long double,long double);
extern long double __kernel_tanl (long double,long double,int);
extern void __kernel_sincosl (long double,long double,
			      long double *,long double *, int);
extern int   __kernel_rem_pio2l (long double*,long double*,int,int,
				 int,const int*);

#ifndef NO_LONG_DOUBLE
/* prototypes required to compile the ldbl-96 support without warnings */
extern int __finitel (long double);
extern int __ilogbl (long double);
extern int __isinfl (long double);
extern int __isnanl (long double);
extern long double __atanl (long double);
extern long double __copysignl (long double, long double);
extern long double __expm1l (long double);
extern long double __floorl (long double);
extern long double __frexpl (long double, int *);
extern long double __ldexpl (long double, int);
extern long double __log1pl (long double);
extern long double __nanl (const char *);
extern long double __rintl (long double);
extern long double __scalbnl (long double, int);
extern long double __sqrtl (long double x);
extern long double fabsl (long double x);
extern void __sincosl (long double, long double *, long double *);
extern long double __logbl (long double x);
extern long double __significandl (long double x);
#endif

/* Prototypes for functions of the IBM Accurate Mathematical Library.  */
extern double __exp1 (double __x, double __xx, double __error);
extern double __sin (double __x);
extern double __cos (double __x);
extern int __branred (double __x, double *__a, double *__aa);
extern void __doasin (double __x, double __dx, double __v[]);
extern void __dubsin (double __x, double __dx, double __v[]);
extern void __dubcos (double __x, double __dx, double __v[]);
extern double __halfulp (double __x, double __y);
extern double __sin32 (double __x, double __res, double __res1);
extern double __cos32 (double __x, double __res, double __res1);
extern double __mpsin (double __x, double __dx);
extern double __mpcos (double __x, double __dx);
extern double __mpsin1 (double __x);
extern double __mpcos1 (double __x);
extern double __slowexp (double __x);
extern double __slowpow (double __x, double __y, double __z);
extern void __docos (double __x, double __dx, double __v[]);

#endif /* _MATH_PRIVATE_H_ */