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/* @(#)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.

 * ====================================================

 */

/* CYGNUS LOCAL: Include files.  */

#include <math.h>

#include <machine/ieeefp.h>

/* CYGNUS 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 0x7f7fffff

#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-(1<<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__

#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>.  */

extern double logb __P((double));

#ifdef _SCALB_INT

extern double scalb __P((double, int));

#else

extern double scalb __P((double, double));

#endif

extern double significand __P((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.  */

extern float logbf __P((float));

#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

/* 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)