include/math.h

root/include/math.h
/*      $NetBSD: math.h,v 1.72 2024/09/09 15:06:29 riastradh Exp $      */

/*
 * ====================================================
 * 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.
 * ====================================================
 */

/*
 * @(#)fdlibm.h 5.1 93/09/24
 */

#ifndef _MATH_H_
#define _MATH_H_

#include <sys/cdefs.h>
#include <sys/featuretest.h>

union __float_u {
        unsigned char __dummy[sizeof(float)];
        float __val;
};

union __double_u {
        unsigned char __dummy[sizeof(double)];
        double __val;
};

union __long_double_u {
        unsigned char __dummy[sizeof(long double)];
        long double __val;
};

#include <machine/math.h>               /* may use __float_u, __double_u,
                                           or __long_double_u */
#include <limits.h>                     /* for INT_{MIN,MAX} */

#if (!defined(_ANSI_SOURCE) && !defined(_POSIX_C_SOURCE) && \
    !defined(_XOPEN_SOURCE)) || ((_POSIX_C_SOURCE - 0) >= 200809L || \
     defined(_ISOC99_SOURCE) || (__STDC_VERSION__ - 0) >= 199901L || \
     (__cplusplus - 0) >= 201103L || defined(_NETBSD_SOURCE))
#define __MATH_C99_FEATURES
#endif

#ifdef __MATH_C99_FEATURES
#  if defined(__FLT_EVAL_METHOD__) && (__FLT_EVAL_METHOD__ - 0) == 0
typedef double double_t;
typedef float float_t;
#  elif (__FLT_EVAL_METHOD__ - 0) == 1
typedef double double_t;
typedef double float_t;
#  elif (__FLT_EVAL_METHOD__ - 0) == 2
typedef long double double_t;
typedef long double float_t;
#  endif
#endif

#ifdef __HAVE_LONG_DOUBLE
#define __fpmacro_unary_floating(__name, __arg0)                        \
        /* LINTED */                                                    \
        ((sizeof (__arg0) == sizeof (float))                            \
        ?       __ ## __name ## f (__arg0)                              \
        : (sizeof (__arg0) == sizeof (double))                          \
        ?       __ ## __name ## d (__arg0)                              \
        :       __ ## __name ## l (__arg0))
#else
#define __fpmacro_unary_floating(__name, __arg0)                        \
        /* LINTED */                                                    \
        ((sizeof (__arg0) == sizeof (float))                            \
        ?       __ ## __name ## f (__arg0)                              \
        :       __ ## __name ## d (__arg0))
#endif /* __HAVE_LONG_DOUBLE */

/*
 * ANSI/POSIX
 */
/* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */
#if __GNUC_PREREQ__(3, 3)
#define HUGE_VAL        __builtin_huge_val()
#else
extern const union __double_u __infinity;
#define HUGE_VAL        __infinity.__val
#endif

/*
 * ISO C99
 */
#if defined(__MATH_C99_FEATURES) || \
    (_POSIX_C_SOURCE - 0) >= 200112L || (_XOPEN_SOURCE  - 0) >= 600
/* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */
#if __GNUC_PREREQ__(3, 3)
#define HUGE_VALF       __builtin_huge_valf()
#define HUGE_VALL       __builtin_huge_vall()
#else
extern const union __float_u __infinityf;
#define HUGE_VALF       __infinityf.__val

extern const union __long_double_u __infinityl;
#define HUGE_VALL       __infinityl.__val
#endif

/* 7.12#4 INFINITY */
#if defined(__INFINITY)
#define INFINITY        __INFINITY      /* float constant which overflows */
#elif __GNUC_PREREQ__(3, 3)
#define INFINITY        __builtin_inff()
#else
#define INFINITY        HUGE_VALF       /* positive infinity */
#endif /* __INFINITY */

/* 7.12#5 NAN: a quiet NaN, if supported */
#ifdef __HAVE_NANF
#if __GNUC_PREREQ__(3,3)
#define NAN     __builtin_nanf("")
#else
extern const union __float_u __nanf;
#define NAN             __nanf.__val
#endif
#endif /* __HAVE_NANF */

/* 7.12#6 number classification macros */
#define FP_INFINITE     0x00
#define FP_NAN          0x01
#define FP_NORMAL       0x02
#define FP_SUBNORMAL    0x03
#define FP_ZERO         0x04
/* NetBSD extensions */
#define _FP_LOMD        0x80            /* range for machine-specific classes */
#define _FP_HIMD        0xff

/* 7.12#7 fast fma(3) feature test macros */
#if __GNUC_PREREQ__(4, 4)
#  ifdef __FP_FAST_FMA
#    define     FP_FAST_FMA     1
#  endif
#  ifdef __FP_FAST_FMAF
#    define     FP_FAST_FMAF    1
#  endif
#  ifdef __FP_FAST_FMAL
#    define     FP_FAST_FMAL    1
#  endif
#endif

/* 7.12#8 ilogb exceptional input result value macros */
#define FP_ILOGB0       INT_MIN
#define FP_ILOGBNAN     INT_MAX

/* 7.12#9 error handling (__math_errhandling from machine/math.h) */
#define MATH_ERRNO              1
#define MATH_ERREXCEPT          2
#ifdef __vax__                  /* XXX !__HAVE_FENV */
#define math_errhandling        MATH_ERRNO
#else
#define math_errhandling        MATH_ERREXCEPT
#endif

#endif /* C99 || _XOPEN_SOURCE >= 600 */

/*
 * XOPEN/SVID
 */
#if defined(_XOPEN_SOURCE) || defined(_NETBSD_SOURCE)
#define M_E             2.7182818284590452354   /* e */
#define M_LOG2E         1.4426950408889634074   /* log 2e */
#define M_LOG10E        0.43429448190325182765  /* log 10e */
#define M_LN2           0.69314718055994530942  /* log e2 */
#define M_LN10          2.30258509299404568402  /* log e10 */
#define M_PI            3.14159265358979323846  /* pi */
#define M_PI_2          1.57079632679489661923  /* pi/2 */
#define M_PI_4          0.78539816339744830962  /* pi/4 */
#define M_1_PI          0.31830988618379067154  /* 1/pi */
#define M_2_PI          0.63661977236758134308  /* 2/pi */
#define M_2_SQRTPI      1.12837916709551257390  /* 2/sqrt(pi) */
#define M_SQRT2         1.41421356237309504880  /* sqrt(2) */
#define M_SQRT1_2       0.70710678118654752440  /* 1/sqrt(2) */

#define MAXFLOAT        ((float)3.40282346638528860e+38)
extern int signgam;
#endif /* _XOPEN_SOURCE || _NETBSD_SOURCE */

#if defined(_NETBSD_SOURCE)
enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};

#define _LIB_VERSION_TYPE enum fdversion
#define _LIB_VERSION _fdlib_version

/* if global variable _LIB_VERSION is not desirable, one may
 * change the following to be a constant by:
 *      #define _LIB_VERSION_TYPE const enum version
 * In that case, after one initializes the value _LIB_VERSION (see
 * s_lib_version.c) during compile time, it cannot be modified
 * in the middle of a program
 */
extern  _LIB_VERSION_TYPE  _LIB_VERSION;

#define _IEEE_  fdlibm_ieee
#define _SVID_  fdlibm_svid
#define _XOPEN_ fdlibm_xopen
#define _POSIX_ fdlibm_posix

#ifndef __cplusplus
struct exception {
        int type;
        const char *name;
        double arg1;
        double arg2;
        double retval;
};
#endif

#define HUGE            MAXFLOAT

/*
 * 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

#define DOMAIN          1
#define SING            2
#define OVERFLOW        3
#define UNDERFLOW       4
#define TLOSS           5
#define PLOSS           6

#endif /* _NETBSD_SOURCE */

__BEGIN_DECLS
/*
 * ANSI/POSIX
 */
double  acos(double);
double  asin(double);
double  atan(double);
double  atan2(double, double);
double  cos(double);
double  sin(double);
double  tan(double);

double  cosh(double);
double  sinh(double);
double  tanh(double);

double  exp(double);
double  exp2(double);
double  frexp(double, int *);
double  ldexp(double, int);
double  log(double);
double  log2(double);
double  log10(double);
double  modf(double, double *);

double  pow(double, double);
double  sqrt(double);

double  ceil(double);
double  fabs(double);
double  floor(double);
double  fmod(double, double);

#if defined(__MATH_C99_FEATURES) || defined(_XOPEN_SOURCE)
double  erf(double);
double  erfc(double);
double  hypot(double, double);
#endif

#if defined(_XOPEN_SOURCE) || defined(_NETBSD_SOURCE)
int     finite(double);
double  gamma(double);
double  j0(double);
double  j1(double);
double  jn(int, double);
double  y0(double);
double  y1(double);
double  yn(int, double);

#if (_XOPEN_SOURCE - 0) >= 500 || defined(_NETBSD_SOURCE)
double  scalb(double, double);
#endif /* (_XOPEN_SOURCE - 0) >= 500 || defined(_NETBSD_SOURCE)*/
#endif /* _XOPEN_SOURCE || _NETBSD_SOURCE */

/*
 * ISO C99
 */
#if defined(__MATH_C99_FEATURES) || (_XOPEN_SOURCE - 0) >= 500
double  acosh(double);
double  asinh(double);
double  atanh(double);
double  cbrt(double);
double  expm1(double);
int     ilogb(double);
double  log1p(double);
double  logb(double);
double  nextafter(double, double);
double  remainder(double, double);
double  rint(double);
#endif

#if defined(__MATH_C99_FEATURES) || (_XOPEN_SOURCE - 0) >= 600 || \
    (_POSIX_C_SOURCE - 0) >= 200112L
/* 7.12.3.1 int fpclassify(real-floating x) */
#define fpclassify(__x) __fpmacro_unary_floating(fpclassify, __x)

/* 7.12.3.2 int isfinite(real-floating x) */
#define isfinite(__x)   __fpmacro_unary_floating(isfinite, __x)

/* 7.12.3.5 int isnormal(real-floating x) */
#define isnormal(__x)   (fpclassify(__x) == FP_NORMAL)

/* 7.12.3.6 int signbit(real-floating x) */
#define signbit(__x)    __fpmacro_unary_floating(signbit, __x)

/* 7.12.4 trigonometric */

float   acosf(float);
float   asinf(float);
float   atanf(float);
float   atan2f(float, float);
float   cosf(float);
float   sinf(float);
float   tanf(float);

long double     acosl(long double);
long double     asinl(long double);
long double     atanl(long double);
long double     atan2l(long double, long double);
long double     cosl(long double);
long double     sinl(long double);
long double     tanl(long double);

/* 7.12.5 hyperbolic */

float   acoshf(float);
float   asinhf(float);
float   atanhf(float);
float   coshf(float);
float   sinhf(float);
float   tanhf(float);
long double     acoshl(long double);
long double     asinhl(long double);
long double     atanhl(long double);
long double     coshl(long double);
long double     sinhl(long double);
long double     tanhl(long double);

/* 7.12.6 exp / log */
double  scalbn(double, int);
double  scalbln(double, long);

float   expf(float);
float   exp2f(float);
float   expm1f(float);
float   frexpf(float, int *);
int     ilogbf(float);
float   ldexpf(float, int);
float   logf(float);
float   log2f(float);
float   log10f(float);
float   log1pf(float);
float   logbf(float);
float   modff(float, float *);
float   scalbnf(float, int);
float   scalblnf(float, long);

long double     expl(long double);
long double     exp2l(long double);
long double     expm1l(long double);
long double     frexpl(long double, int *);
int             ilogbl(long double);
long double     ldexpl(long double, int);
long double     logl(long double);
long double     log2l(long double);
long double     log10l(long double);
long double     log1pl(long double);
long double     logbl(long double);
long double     modfl(long double, long double *);
long double     scalbnl(long double, int);
long double     scalblnl(long double, long);


/* 7.12.7 power / absolute */

float   cbrtf(float);
float   fabsf(float);
float   hypotf(float, float);
float   powf(float, float);
float   sqrtf(float);
long double     cbrtl(long double);
long double     fabsl(long double);
long double     hypotl(long double, long double);
long double     powl(long double, long double);
long double     sqrtl(long double);

/* 7.12.8 error / gamma */

double  lgamma(double);
double  tgamma(double);
float   erff(float);
float   erfcf(float);
float   lgammaf(float);
float   tgammaf(float);
long double     erfl(long double);
long double     erfcl(long double);
long double     lgammal(long double);
long double     tgammal(long double);

/* 7.12.9 nearest integer */

/* LONGLONG */
long long int   llrint(double);
long int        lround(double);
/* LONGLONG */
long long int   llround(double);
long int        lrint(double);
double  round(double);
double  trunc(double);

float   ceilf(float);
float   floorf(float);
/* LONGLONG */
long long int   llrintf(float);
long int        lroundf(float);
/* LONGLONG */
long long int   llroundf(float);
long int        lrintf(float);
float   rintf(float);
float   roundf(float);
float   truncf(float);
long double     ceill(long double);
long double     floorl(long double);
/* LONGLONG */
long long int   llrintl(long double);
long int        lroundl(long double);
/* LONGLONG */
long long int   llroundl(long double);
long int        lrintl(long double);
long double     rintl(long double);
long double     roundl(long double);
long double     truncl(long double);

/* 7.12.10 remainder */

float   fmodf(float, float);
float   remainderf(float, float);
long double     fmodl(long double, long double);
long double     remainderl(long double, long double);

/* 7.12.10.3 The remquo functions */
double  remquo(double, double, int *);
float   remquof(float, float, int *);
long double     remquol(long double, long double, int *);

/* 7.12.11 manipulation */

double  copysign(double, double);
double  nan(const char *);
double  nearbyint(double);
double  nexttoward(double, long double);
float   copysignf(float, float);
float   nanf(const char *);
float   nearbyintf(float);
float   nextafterf(float, float);
float   nexttowardf(float, long double);
long double     copysignl(long double, long double);
long double     nanl(const char *);
long double     nearbyintl(long double);
long double     nextafterl(long double, long double);
long double     nexttowardl(long double, long double);

/* 7.12.14 comparison */

#define isunordered(x, y)       (isnan(x) || isnan(y))
#define isgreater(x, y)         (!isunordered((x), (y)) && (x) > (y))
#define isgreaterequal(x, y)    (!isunordered((x), (y)) && (x) >= (y))
#define isless(x, y)            (!isunordered((x), (y)) && (x) < (y))
#define islessequal(x, y)       (!isunordered((x), (y)) && (x) <= (y))
#define islessgreater(x, y)     (!isunordered((x), (y)) && \
                                 ((x) > (y) || (y) > (x)))
double  fdim(double, double);
double  fma(double, double, double);
double  fmax(double, double);
double  fmin(double, double);
float   fdimf(float, float);
float   fmaf(float, float, float);
float   fmaxf(float, float);
float   fminf(float, float);
long double fdiml(long double, long double);
long double fmal(long double, long double, long double);
long double fmaxl(long double, long double);
long double fminl(long double, long double);

#endif /* !_ANSI_SOURCE && ... */

#if defined(__MATH_C99_FEATURES) || (_POSIX_C_SOURCE - 0) >= 200112L
/* 7.12.3.3 int isinf(real-floating x) */
#if defined(__isinf) || defined(__HAVE_INLINE___ISINF)
#define isinf(__x)      __isinf(__x)
#else
#define isinf(__x)      __fpmacro_unary_floating(isinf, __x)
#endif

/* 7.12.3.4 int isnan(real-floating x) */
#if defined(__isnan) || defined(__HAVE_INLINE___ISNAN)
#define isnan(__x)      __isnan(__x)
#else
#define isnan(__x)      __fpmacro_unary_floating(isnan, __x)
#endif
#endif /* !_ANSI_SOURCE && ... */

#if defined(_NETBSD_SOURCE)

#ifndef __cplusplus
int     matherr(struct exception *);
#endif

/*
 * IEEE Test Vector
 */
double  significand(double);

/*
 * BSD math library entry points
 */
double  drem(double, double);

void            sincos(double, double *, double *);
void            sincosf(float, float *, float *);
void            sincosl(long double, long double *, long double *);

double          cospi(double);
float           cospif(float);
long double     cospil(long double);

double          sinpi(double);
float           sinpif(float);
long double     sinpil(long double);

double          tanpi(double);
float           tanpif(float);
long double     tanpil(long double);

#endif /* _NETBSD_SOURCE */

#if defined(_NETBSD_SOURCE) || defined(_REENTRANT)
/*
 * Reentrant version of gamma & lgamma; passes signgam back by reference
 * as the second argument; user must allocate space for signgam.
 */
double  gamma_r(double, int *);
double  lgamma_r(double, int *);
long double     lgammal_r(long double, int *);
#endif /* _NETBSD_SOURCE || _REENTRANT */

#if defined(_NETBSD_SOURCE)

/* float versions of ANSI/POSIX functions */

float   gammaf(float);
int     isinff(float);
int     isnanf(float);
int     finitef(float);
float   j0f(float);
float   j1f(float);
float   jnf(int, float);
float   y0f(float);
float   y1f(float);
float   ynf(int, float);

float   scalbf(float, float);

/*
 * float version of IEEE Test Vector
 */
float   significandf(float);

/*
 * float versions of BSD math library entry points
 */
float   dremf(float, float);
#endif /* _NETBSD_SOURCE */

#if defined(_NETBSD_SOURCE) || defined(_REENTRANT)
/*
 * Float versions of reentrant version of gamma & lgamma; passes
 * signgam back by reference as the second argument; user must
 * allocate space for signgam.
 */
float   gammaf_r(float, int *);
float   lgammaf_r(float, int *);
#endif /* !... || _REENTRANT */

/*
 * Library implementation
 */
int     __fpclassifyf(float);
int     __fpclassifyd(double);
int     __isfinitef(float);
int     __isfinited(double);
int     __isinff(float);
int     __isinfd(double);
int     __isnanf(float);
int     __isnand(double);
int     __signbitf(float);
int     __signbitd(double);

#ifdef __HAVE_LONG_DOUBLE
int     __fpclassifyl(long double);
int     __isfinitel(long double);
int     __isinfl(long double);
int     __isnanl(long double);
int     __signbitl(long double);
#endif

__END_DECLS

#endif /* _MATH_H_ */