/*
* ====================================================
* 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
* $FreeBSD: src/lib/msun/src/math.h,v 1.61 2005/04/16 21:12:47 das Exp $
*/
#ifndef _MATH_H_
#define _MATH_H_
#include <sys/cdefs.h>
#include <sys/types.h>
#include <limits.h>
#define __pure2
/*
* ANSI/POSIX
*/
extern const union __infinity_un {
unsigned char __uc[8];
double __ud;
} __infinity;
extern const union __nan_un {
unsigned char __uc[sizeof(float)];
float __uf;
} __nan;
/* #if __GNUC_PREREQ__(3, 3) || (defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 800) */
#if 1
#define __MATH_BUILTIN_CONSTANTS
#endif
/* #if __GNUC_PREREQ__(3, 0) && !defined(__INTEL_COMPILER) */
#if 1
#define __MATH_BUILTIN_RELOPS
#endif
/* #ifdef __MATH_BUILTIN_CONSTANTS */
#if 1
#define HUGE_VAL __builtin_huge_val()
#else
#define HUGE_VAL (__infinity.__ud)
#endif
/* #if __ISO_C_VISIBLE >= 1999 */
#if 0
#define FP_ILOGB0 (-__INT_MAX)
#define FP_ILOGBNAN __INT_MAX
#else
#define FP_ILOGB0 (-INT_MAX)
#define FP_ILOGBNAN INT_MAX
#endif
#ifdef __MATH_BUILTIN_CONSTANTS
#define HUGE_VALF __builtin_huge_valf()
#define HUGE_VALL __builtin_huge_vall()
#define INFINITY __builtin_inf()
#define NAN __builtin_nan("")
#else
#define HUGE_VALF (float)HUGE_VAL
#define HUGE_VALL (long double)HUGE_VAL
#define INFINITY HUGE_VALF
#define NAN (__nan.__uf)
#endif /* __MATH_BUILTIN_CONSTANTS */
#define MATH_ERRNO 1
#define MATH_ERREXCEPT 2
#define math_errhandling MATH_ERREXCEPT
/* XXX We need a <machine/math.h>. */
#if defined(__ia64__) || defined(__sparc64__)
#define FP_FAST_FMA
#endif
#ifdef __ia64__
#define FP_FAST_FMAL
#endif
#define FP_FAST_FMAF
/* Symbolic constants to classify floating point numbers. */
#define FP_INFINITE 0x01
#define FP_NAN 0x02
#define FP_NORMAL 0x04
#define FP_SUBNORMAL 0x08
#define FP_ZERO 0x10
#define fpclassify(x) \
((sizeof (x) == sizeof (float)) ? __fpclassifyf(x) \
: (sizeof (x) == sizeof (double)) ? __fpclassifyd(x) \
: __fpclassifyl(x))
#define isfinite(x) \
((sizeof (x) == sizeof (float)) ? __isfinitef(x) \
: (sizeof (x) == sizeof (double)) ? __isfinite(x) \
: __isfinitel(x))
#define isinf(x) \
((sizeof (x) == sizeof (float)) ? __isinff(x) \
: (sizeof (x) == sizeof (double)) ? __isinf(x) \
: __isinfl(x))
#define isnan(x) \
((sizeof (x) == sizeof (float)) ? isnanf(x) \
: (sizeof (x) == sizeof (double)) ? isnan(x) \
: __isnanl(x))
#define isnormal(x) \
((sizeof (x) == sizeof (float)) ? __isnormalf(x) \
: (sizeof (x) == sizeof (double)) ? __isnormal(x) \
: __isnormall(x))
#ifdef __MATH_BUILTIN_RELOPS
#define isgreater(x, y) __builtin_isgreater((x), (y))
#define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y))
#define isless(x, y) __builtin_isless((x), (y))
#define islessequal(x, y) __builtin_islessequal((x), (y))
#define islessgreater(x, y) __builtin_islessgreater((x), (y))
#define isunordered(x, y) __builtin_isunordered((x), (y))
#else
#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)))
#define isunordered(x, y) (isnan(x) || isnan(y))
#endif /* __MATH_BUILTIN_RELOPS */
#define signbit(x) \
((sizeof (x) == sizeof (float)) ? __signbitf(x) \
: (sizeof (x) == sizeof (double)) ? __signbit(x) \
: __signbitl(x))
#if 0
typedef __double_t double_t;
typedef __float_t float_t;
#endif
/* #endif */ /* __ISO_C_VISIBLE >= 1999 */
/*
* XOPEN/SVID
*/
/* #if __BSD_VISIBLE || __XSI_VISIBLE */
#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 */ /* __BSD_VISIBLE || __XSI_VISIBLE */
#if __BSD_VISIBLE
#if 0
/* Old value from 4.4BSD-Lite math.h; this is probably better. */
#define HUGE HUGE_VAL
#else
#define HUGE MAXFLOAT
#endif
#endif /* __BSD_VISIBLE */
/*
* Most of these functions depend on the rounding mode and have the side
* effect of raising floating-point exceptions, so they are not declared
* as __pure2. In C99, FENV_ACCESS affects the purity of these functions.
*/
__BEGIN_DECLS
/*
* ANSI/POSIX
*/
int __fpclassifyd(double) __NDK_FPABI_MATH__ __pure2;
int __fpclassifyf(float) __NDK_FPABI_MATH__ __pure2;
int __fpclassifyl(long double) __NDK_FPABI_MATH__ __pure2;
int __isfinitef(float) __NDK_FPABI_MATH__ __pure2;
int __isfinite(double) __NDK_FPABI_MATH__ __pure2;
int __isfinitel(long double) __NDK_FPABI_MATH__ __pure2;
int __isinff(float) __NDK_FPABI_MATH__ __pure2;
int __isinf(double) __NDK_FPABI_MATH__ __pure2;
int __isinfl(long double) __NDK_FPABI_MATH__ __pure2;
int __isnanl(long double) __NDK_FPABI_MATH__ __pure2;
int __isnormalf(float) __NDK_FPABI_MATH__ __pure2;
int __isnormal(double) __NDK_FPABI_MATH__ __pure2;
int __isnormall(long double) __NDK_FPABI_MATH__ __pure2;
int __signbit(double) __NDK_FPABI_MATH__ __pure2;
int __signbitf(float) __NDK_FPABI_MATH__ __pure2;
int __signbitl(long double) __NDK_FPABI_MATH__ __pure2;
double acos(double) __NDK_FPABI_MATH__;
double asin(double) __NDK_FPABI_MATH__;
double atan(double) __NDK_FPABI_MATH__;
double atan2(double, double) __NDK_FPABI_MATH__;
double cos(double) __NDK_FPABI_MATH__;
double sin(double) __NDK_FPABI_MATH__;
double tan(double) __NDK_FPABI_MATH__;
double cosh(double) __NDK_FPABI_MATH__;
double sinh(double) __NDK_FPABI_MATH__;
double tanh(double) __NDK_FPABI_MATH__;
double exp(double) __NDK_FPABI_MATH__;
double frexp(double, int *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
double ldexp(double, int) __NDK_FPABI_MATH__;
double log(double) __NDK_FPABI_MATH__;
double log10(double) __NDK_FPABI_MATH__;
double modf(double, double *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
double pow(double, double) __NDK_FPABI_MATH__;
double sqrt(double) __NDK_FPABI_MATH__;
double ceil(double) __NDK_FPABI_MATH__;
double fabs(double) __NDK_FPABI_MATH__ __pure2;
double floor(double) __NDK_FPABI_MATH__;
double fmod(double, double) __NDK_FPABI_MATH__;
/*
* These functions are not in C90.
*/
/* #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */
double acosh(double) __NDK_FPABI_MATH__;
double asinh(double) __NDK_FPABI_MATH__;
double atanh(double) __NDK_FPABI_MATH__;
double cbrt(double) __NDK_FPABI_MATH__;
double erf(double) __NDK_FPABI_MATH__;
double erfc(double) __NDK_FPABI_MATH__;
double exp2(double) __NDK_FPABI_MATH__;
double expm1(double) __NDK_FPABI_MATH__;
double fma(double, double, double) __NDK_FPABI_MATH__;
double hypot(double, double) __NDK_FPABI_MATH__;
int ilogb(double) __NDK_FPABI_MATH__ __pure2;
/* int (isinf)(double) __NDK_FPABI_MATH__ __pure2; */
int (isnan)(double) __NDK_FPABI_MATH__ __pure2;
double lgamma(double) __NDK_FPABI_MATH__;
long long llrint(double) __NDK_FPABI_MATH__;
long long llround(double) __NDK_FPABI_MATH__;
double log1p(double) __NDK_FPABI_MATH__;
double logb(double) __NDK_FPABI_MATH__;
long lrint(double) __NDK_FPABI_MATH__;
long lround(double) __NDK_FPABI_MATH__;
double nextafter(double, double) __NDK_FPABI_MATH__;
double remainder(double, double) __NDK_FPABI_MATH__;
double remquo(double, double, int *) __NDK_FPABI_MATH__;
double rint(double) __NDK_FPABI_MATH__;
/* #endif */ /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */
/* #if __BSD_VISIBLE || __XSI_VISIBLE */
double j0(double) __NDK_FPABI_MATH__;
double j1(double) __NDK_FPABI_MATH__;
double jn(int, double) __NDK_FPABI_MATH__;
double scalb(double, double) __NDK_FPABI_MATH__;
double y0(double) __NDK_FPABI_MATH__;
double y1(double) __NDK_FPABI_MATH__;
double yn(int, double) __NDK_FPABI_MATH__;
/* #if __XSI_VISIBLE <= 500 || __BSD_VISIBLE */
double gamma(double) __NDK_FPABI_MATH__;
/* #endif */
/* #endif */ /* __BSD_VISIBLE || __XSI_VISIBLE */
/* #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 */
double copysign(double, double) __NDK_FPABI_MATH__ __pure2;
double fdim(double, double) __NDK_FPABI_MATH__;
double fmax(double, double) __NDK_FPABI_MATH__ __pure2;
double fmin(double, double) __NDK_FPABI_MATH__ __pure2;
double nearbyint(double) __NDK_FPABI_MATH__;
double round(double) __NDK_FPABI_MATH__;
double scalbln(double, long) __NDK_FPABI_MATH__;
double scalbn(double, int) __NDK_FPABI_MATH__;
double tgamma(double) __NDK_FPABI_MATH__;
double trunc(double) __NDK_FPABI_MATH__;
/* #endif */
/*
* BSD math library entry points
*/
/* #if __BSD_VISIBLE */
double drem(double, double) __NDK_FPABI_MATH__;
int finite(double) __NDK_FPABI_MATH__ __pure2;
int isnanf(float) __NDK_FPABI_MATH__ __pure2;
/*
* 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 *) __NDK_FPABI_MATH__;
double lgamma_r(double, int *) __NDK_FPABI_MATH__;
/*
* IEEE Test Vector
*/
double significand(double) __NDK_FPABI_MATH__;
/* #endif */ /* __BSD_VISIBLE */
/* float versions of ANSI/POSIX functions */
/*#if __ISO_C_VISIBLE >= 1999 */
float acosf(float) __NDK_FPABI_MATH__;
float asinf(float) __NDK_FPABI_MATH__;
float atanf(float) __NDK_FPABI_MATH__;
float atan2f(float, float) __NDK_FPABI_MATH__;
float cosf(float) __NDK_FPABI_MATH__;
float sinf(float) __NDK_FPABI_MATH__;
float tanf(float) __NDK_FPABI_MATH__;
float coshf(float) __NDK_FPABI_MATH__;
float sinhf(float) __NDK_FPABI_MATH__;
float tanhf(float) __NDK_FPABI_MATH__;
float exp2f(float) __NDK_FPABI_MATH__;
float expf(float) __NDK_FPABI_MATH__;
float expm1f(float) __NDK_FPABI_MATH__;
float frexpf(float, int *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
int ilogbf(float) __NDK_FPABI_MATH__ __pure2;
float ldexpf(float, int) __NDK_FPABI_MATH__;
float log10f(float) __NDK_FPABI_MATH__;
float log1pf(float) __NDK_FPABI_MATH__;
float logf(float) __NDK_FPABI_MATH__;
float modff(float, float *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
float powf(float, float) __NDK_FPABI_MATH__;
float sqrtf(float) __NDK_FPABI_MATH__;
float ceilf(float) __NDK_FPABI_MATH__;
float fabsf(float) __NDK_FPABI_MATH__ __pure2;
float floorf(float) __NDK_FPABI_MATH__;
float fmodf(float, float) __NDK_FPABI_MATH__;
float roundf(float) __NDK_FPABI_MATH__;
float erff(float) __NDK_FPABI_MATH__;
float erfcf(float) __NDK_FPABI_MATH__;
float hypotf(float, float) __NDK_FPABI_MATH__;
float lgammaf(float) __NDK_FPABI_MATH__;
float acoshf(float) __NDK_FPABI_MATH__;
float asinhf(float) __NDK_FPABI_MATH__;
float atanhf(float) __NDK_FPABI_MATH__;
float cbrtf(float) __NDK_FPABI_MATH__;
float logbf(float) __NDK_FPABI_MATH__;
float copysignf(float, float) __NDK_FPABI_MATH__ __pure2;
long long llrintf(float) __NDK_FPABI_MATH__;
long long llroundf(float) __NDK_FPABI_MATH__;
long lrintf(float) __NDK_FPABI_MATH__;
long lroundf(float) __NDK_FPABI_MATH__;
float nearbyintf(float) __NDK_FPABI_MATH__;
float nextafterf(float, float) __NDK_FPABI_MATH__;
float remainderf(float, float) __NDK_FPABI_MATH__;
float remquof(float, float, int *) __NDK_FPABI_MATH__;
float rintf(float) __NDK_FPABI_MATH__;
float scalblnf(float, long) __NDK_FPABI_MATH__;
float scalbnf(float, int) __NDK_FPABI_MATH__;
float truncf(float) __NDK_FPABI_MATH__;
float fdimf(float, float) __NDK_FPABI_MATH__;
float fmaf(float, float, float) __NDK_FPABI_MATH__;
float fmaxf(float, float) __NDK_FPABI_MATH__ __pure2;
float fminf(float, float) __NDK_FPABI_MATH__ __pure2;
/* #endif */
/*
* float versions of BSD math library entry points
*/
/* #if __BSD_VISIBLE */
float dremf(float, float) __NDK_FPABI_MATH__;
int finitef(float) __NDK_FPABI_MATH__ __pure2;
float gammaf(float) __NDK_FPABI_MATH__;
float j0f(float) __NDK_FPABI_MATH__;
float j1f(float) __NDK_FPABI_MATH__;
float jnf(int, float) __NDK_FPABI_MATH__;
float scalbf(float, float) __NDK_FPABI_MATH__;
float y0f(float) __NDK_FPABI_MATH__;
float y1f(float) __NDK_FPABI_MATH__;
float ynf(int, float) __NDK_FPABI_MATH__;
/*
* 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 *) __NDK_FPABI_MATH__;
float lgammaf_r(float, int *) __NDK_FPABI_MATH__;
/*
* float version of IEEE Test Vector
*/
float significandf(float) __NDK_FPABI_MATH__;
/* #endif */ /* __BSD_VISIBLE */
/*
* long double versions of ISO/POSIX math functions
*/
/* #if __ISO_C_VISIBLE >= 1999 */
#if 0
long double acoshl(long double) __NDK_FPABI_MATH__;
long double acosl(long double) __NDK_FPABI_MATH__;
long double asinhl(long double) __NDK_FPABI_MATH__;
long double asinl(long double) __NDK_FPABI_MATH__;
long double atan2l(long double, long double) __NDK_FPABI_MATH__;
long double atanhl(long double) __NDK_FPABI_MATH__;
long double atanl(long double) __NDK_FPABI_MATH__;
long double cbrtl(long double) __NDK_FPABI_MATH__;
#endif
long double ceill(long double) __NDK_FPABI_MATH__;
long double copysignl(long double, long double) __NDK_FPABI_MATH__ __pure2;
#if 0
long double coshl(long double) __NDK_FPABI_MATH__;
long double cosl(long double) __NDK_FPABI_MATH__;
long double erfcl(long double) __NDK_FPABI_MATH__;
long double erfl(long double) __NDK_FPABI_MATH__;
long double exp2l(long double) __NDK_FPABI_MATH__;
long double expl(long double) __NDK_FPABI_MATH__;
long double expm1l(long double) __NDK_FPABI_MATH__;
#endif
long double fabsl(long double) __NDK_FPABI_MATH__ __pure2;
long double fdiml(long double, long double) __NDK_FPABI_MATH__;
long double floorl(long double) __NDK_FPABI_MATH__;
long double fmal(long double, long double, long double) __NDK_FPABI_MATH__;
long double fmaxl(long double, long double) __NDK_FPABI_MATH__ __pure2;
long double fminl(long double, long double) __NDK_FPABI_MATH__ __pure2;
#if 0
long double fmodl(long double, long double) __NDK_FPABI_MATH__;
#endif
long double frexpl(long double value, int *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
#if 0
long double hypotl(long double, long double) __NDK_FPABI_MATH__;
#endif
int ilogbl(long double) __NDK_FPABI_MATH__ __pure2;
long double ldexpl(long double, int) __NDK_FPABI_MATH__;
#if 0
long double lgammal(long double) __NDK_FPABI_MATH__;
long long llrintl(long double) __NDK_FPABI_MATH__;
#endif
long long llroundl(long double) __NDK_FPABI_MATH__;
#if 0
long double log10l(long double) __NDK_FPABI_MATH__;
long double log1pl(long double) __NDK_FPABI_MATH__;
long double log2l(long double) __NDK_FPABI_MATH__;
long double logbl(long double) __NDK_FPABI_MATH__;
long double logl(long double) __NDK_FPABI_MATH__;
long lrintl(long double) __NDK_FPABI_MATH__;
#endif
long lroundl(long double) __NDK_FPABI_MATH__;
#if 0
long double modfl(long double, long double *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
long double nanl(const char *) __NDK_FPABI_MATH__ __pure2;
long double nearbyintl(long double) __NDK_FPABI_MATH__;
#endif
long double nextafterl(long double, long double) __NDK_FPABI_MATH__;
double nexttoward(double, long double) __NDK_FPABI_MATH__;
float nexttowardf(float, long double) __NDK_FPABI_MATH__;
long double nexttowardl(long double, long double) __NDK_FPABI_MATH__;
#if 0
long double powl(long double, long double) __NDK_FPABI_MATH__;
long double remainderl(long double, long double) __NDK_FPABI_MATH__;
long double remquol(long double, long double, int *) __NDK_FPABI_MATH__;
long double rintl(long double) __NDK_FPABI_MATH__;
#endif
long double roundl(long double) __NDK_FPABI_MATH__;
long double scalblnl(long double, long) __NDK_FPABI_MATH__;
long double scalbnl(long double, int) __NDK_FPABI_MATH__;
#if 0
long double sinhl(long double) __NDK_FPABI_MATH__;
long double sinl(long double) __NDK_FPABI_MATH__;
long double sqrtl(long double) __NDK_FPABI_MATH__;
long double tanhl(long double) __NDK_FPABI_MATH__;
long double tanl(long double) __NDK_FPABI_MATH__;
long double tgammal(long double) __NDK_FPABI_MATH__;
#endif
long double truncl(long double) __NDK_FPABI_MATH__;
/* BIONIC: GLibc compatibility - required by the ARM toolchain */
#ifdef _GNU_SOURCE
void sincos(double x, double *sin, double *cos) __NDK_FPABI_MATH__;
void sincosf(float x, float *sin, float *cos) __NDK_FPABI_MATH__;
void sincosl(long double x, long double *sin, long double *cos) __NDK_FPABI_MATH__;
#endif
/* builtin version of all the above math functions are annotated too */
double __builtin_acos(double) __NDK_FPABI_MATH__;
double __builtin_asin(double) __NDK_FPABI_MATH__;
double __builtin_atan(double) __NDK_FPABI_MATH__;
double __builtin_atan2(double, double) __NDK_FPABI_MATH__;
double __builtin_cos(double) __NDK_FPABI_MATH__;
double __builtin_sin(double) __NDK_FPABI_MATH__;
double __builtin_tan(double) __NDK_FPABI_MATH__;
double __builtin_cosh(double) __NDK_FPABI_MATH__;
double __builtin_sinh(double) __NDK_FPABI_MATH__;
double __builtin_tanh(double) __NDK_FPABI_MATH__;
double __builtin_exp(double) __NDK_FPABI_MATH__;
double __builtin_frexp(double, int *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
double __builtin_ldexp(double, int) __NDK_FPABI_MATH__;
double __builtin_log(double) __NDK_FPABI_MATH__;
double __builtin_log10(double) __NDK_FPABI_MATH__;
double __builtin_modf(double, double *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
double __builtin_pow(double, double) __NDK_FPABI_MATH__;
double __builtin_sqrt(double) __NDK_FPABI_MATH__;
double __builtin_ceil(double) __NDK_FPABI_MATH__;
double __builtin_fabs(double) __NDK_FPABI_MATH__ __pure2;
double __builtin_floor(double) __NDK_FPABI_MATH__;
double __builtin_fmod(double, double) __NDK_FPABI_MATH__;
double __builtin_acosh(double) __NDK_FPABI_MATH__;
double __builtin_asinh(double) __NDK_FPABI_MATH__;
double __builtin_atanh(double) __NDK_FPABI_MATH__;
double __builtin_cbrt(double) __NDK_FPABI_MATH__;
double __builtin_erf(double) __NDK_FPABI_MATH__;
double __builtin_erfc(double) __NDK_FPABI_MATH__;
double __builtin_exp2(double) __NDK_FPABI_MATH__;
double __builtin_expm1(double) __NDK_FPABI_MATH__;
double __builtin_fma(double, double, double) __NDK_FPABI_MATH__;
double __builtin_hypot(double, double) __NDK_FPABI_MATH__;
int __builtin_ilogb(double) __NDK_FPABI_MATH__ __pure2;
/* int __builtin_isinf(double) __NDK_FPABI_MATH__ __pure2; */
#if !defined(__clang__) || __clang_major__ > 3 || (__clang_major__ == 3 && __clang_minor__ >= 6)
int __builtin_isnan(double) __NDK_FPABI_MATH__ __pure2;
#else
/* clang < 3.5 has faulty prototype for __builtin_isnan */
#endif
double __builtin_lgamma(double) __NDK_FPABI_MATH__;
long long __builtin_llrint(double) __NDK_FPABI_MATH__;
long long __builtin_llround(double) __NDK_FPABI_MATH__;
double __builtin_log1p(double) __NDK_FPABI_MATH__;
double __builtin_logb(double) __NDK_FPABI_MATH__;
long __builtin_lrint(double) __NDK_FPABI_MATH__;
long __builtin_lround(double) __NDK_FPABI_MATH__;
double __builtin_nextafter(double, double) __NDK_FPABI_MATH__;
double __builtin_remainder(double, double) __NDK_FPABI_MATH__;
double __builtin_remquo(double, double, int *) __NDK_FPABI_MATH__;
double __builtin_rint(double) __NDK_FPABI_MATH__;
double __builtin_j0(double) __NDK_FPABI_MATH__;
double __builtin_j1(double) __NDK_FPABI_MATH__;
double __builtin_jn(int, double) __NDK_FPABI_MATH__;
double __builtin_scalb(double, double) __NDK_FPABI_MATH__;
double __builtin_y0(double) __NDK_FPABI_MATH__;
double __builtin_y1(double) __NDK_FPABI_MATH__;
double __builtin_yn(int, double) __NDK_FPABI_MATH__;
double __builtin_gamma(double) __NDK_FPABI_MATH__;
double __builtin_copysign(double, double) __NDK_FPABI_MATH__ __pure2;
double __builtin_fdim(double, double) __NDK_FPABI_MATH__;
double __builtin_fmax(double, double) __NDK_FPABI_MATH__ __pure2;
double __builtin_fmin(double, double) __NDK_FPABI_MATH__ __pure2;
double __builtin_nearbyint(double) __NDK_FPABI_MATH__;
double __builtin_round(double) __NDK_FPABI_MATH__;
double __builtin_scalbln(double, long) __NDK_FPABI_MATH__;
double __builtin_scalbn(double, int) __NDK_FPABI_MATH__;
double __builtin_tgamma(double) __NDK_FPABI_MATH__;
double __builtin_trunc(double) __NDK_FPABI_MATH__;
double __builtin_drem(double, double) __NDK_FPABI_MATH__;
int __builtin_finite(double) __NDK_FPABI_MATH__ __pure2;
int __builtin_isnanf(float) __NDK_FPABI_MATH__ __pure2;
double __builtin_gamma_r(double, int *) __NDK_FPABI_MATH__;
double __builtin_lgamma_r(double, int *) __NDK_FPABI_MATH__;
double __builtin_significand(double) __NDK_FPABI_MATH__;
float __builtin_acosf(float) __NDK_FPABI_MATH__;
float __builtin_asinf(float) __NDK_FPABI_MATH__;
float __builtin_atanf(float) __NDK_FPABI_MATH__;
float __builtin_atan2f(float, float) __NDK_FPABI_MATH__;
float __builtin_cosf(float) __NDK_FPABI_MATH__;
float __builtin_sinf(float) __NDK_FPABI_MATH__;
float __builtin_tanf(float) __NDK_FPABI_MATH__;
float __builtin_coshf(float) __NDK_FPABI_MATH__;
float __builtin_sinhf(float) __NDK_FPABI_MATH__;
float __builtin_tanhf(float) __NDK_FPABI_MATH__;
float __builtin_exp2f(float) __NDK_FPABI_MATH__;
float __builtin_expf(float) __NDK_FPABI_MATH__;
float __builtin_expm1f(float) __NDK_FPABI_MATH__;
float __builtin_frexpf(float, int *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
int __builtin_ilogbf(float) __NDK_FPABI_MATH__ __pure2;
float __builtin_ldexpf(float, int) __NDK_FPABI_MATH__;
float __builtin_log10f(float) __NDK_FPABI_MATH__;
float __builtin_log1pf(float) __NDK_FPABI_MATH__;
float __builtin_logf(float) __NDK_FPABI_MATH__;
float __builtin_modff(float, float *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
float __builtin_powf(float, float) __NDK_FPABI_MATH__;
float __builtin_sqrtf(float) __NDK_FPABI_MATH__;
float __builtin_ceilf(float) __NDK_FPABI_MATH__;
float __builtin_fabsf(float) __NDK_FPABI_MATH__ __pure2;
float __builtin_floorf(float) __NDK_FPABI_MATH__;
float __builtin_fmodf(float, float) __NDK_FPABI_MATH__;
float __builtin_roundf(float) __NDK_FPABI_MATH__;
float __builtin_erff(float) __NDK_FPABI_MATH__;
float __builtin_erfcf(float) __NDK_FPABI_MATH__;
float __builtin_hypotf(float, float) __NDK_FPABI_MATH__;
float __builtin_lgammaf(float) __NDK_FPABI_MATH__;
float __builtin_acoshf(float) __NDK_FPABI_MATH__;
float __builtin_asinhf(float) __NDK_FPABI_MATH__;
float __builtin_atanhf(float) __NDK_FPABI_MATH__;
float __builtin_cbrtf(float) __NDK_FPABI_MATH__;
float __builtin_logbf(float) __NDK_FPABI_MATH__;
float __builtin_copysignf(float, float) __NDK_FPABI_MATH__ __pure2;
long long __builtin_llrintf(float) __NDK_FPABI_MATH__;
long long __builtin_llroundf(float) __NDK_FPABI_MATH__;
long __builtin_lrintf(float) __NDK_FPABI_MATH__;
long __builtin_lroundf(float) __NDK_FPABI_MATH__;
float __builtin_nearbyintf(float) __NDK_FPABI_MATH__;
float __builtin_nextafterf(float, float) __NDK_FPABI_MATH__;
float __builtin_remainderf(float, float) __NDK_FPABI_MATH__;
float __builtin_remquof(float, float, int *) __NDK_FPABI_MATH__;
float __builtin_rintf(float) __NDK_FPABI_MATH__;
float __builtin_scalblnf(float, long) __NDK_FPABI_MATH__;
float __builtin_scalbnf(float, int) __NDK_FPABI_MATH__;
float __builtin_truncf(float) __NDK_FPABI_MATH__;
float __builtin_fdimf(float, float) __NDK_FPABI_MATH__;
float __builtin_fmaf(float, float, float) __NDK_FPABI_MATH__;
float __builtin_fmaxf(float, float) __NDK_FPABI_MATH__ __pure2;
float __builtin_fminf(float, float) __NDK_FPABI_MATH__ __pure2;
float __builtin_dremf(float, float) __NDK_FPABI_MATH__;
int __builtin_finitef(float) __NDK_FPABI_MATH__ __pure2;
float __builtin_gammaf(float) __NDK_FPABI_MATH__;
float __builtin_j0f(float) __NDK_FPABI_MATH__;
float __builtin_j1f(float) __NDK_FPABI_MATH__;
float __builtin_jnf(int, float) __NDK_FPABI_MATH__;
float __builtin_scalbf(float, float) __NDK_FPABI_MATH__;
float __builtin_y0f(float) __NDK_FPABI_MATH__;
float __builtin_y1f(float) __NDK_FPABI_MATH__;
float __builtin_ynf(int, float) __NDK_FPABI_MATH__;
float __builtin_gammaf_r(float, int *) __NDK_FPABI_MATH__;
float __builtin_lgammaf_r(float, int *) __NDK_FPABI_MATH__;
float __builtin_significandf(float) __NDK_FPABI_MATH__;
long double __builtin_acoshl(long double) __NDK_FPABI_MATH__;
long double __builtin_acosl(long double) __NDK_FPABI_MATH__;
long double __builtin_asinhl(long double) __NDK_FPABI_MATH__;
long double __builtin_asinl(long double) __NDK_FPABI_MATH__;
long double __builtin_atan2l(long double, long double) __NDK_FPABI_MATH__;
long double __builtin_atanhl(long double) __NDK_FPABI_MATH__;
long double __builtin_atanl(long double) __NDK_FPABI_MATH__;
long double __builtin_cbrtl(long double) __NDK_FPABI_MATH__;
long double __builtin_ceill(long double) __NDK_FPABI_MATH__;
long double __builtin_copysignl(long double, long double) __NDK_FPABI_MATH__ __pure2;
long double __builtin_coshl(long double) __NDK_FPABI_MATH__;
long double __builtin_cosl(long double) __NDK_FPABI_MATH__;
long double __builtin_erfcl(long double) __NDK_FPABI_MATH__;
long double __builtin_erfl(long double) __NDK_FPABI_MATH__;
long double __builtin_exp2l(long double) __NDK_FPABI_MATH__;
long double __builtin_expl(long double) __NDK_FPABI_MATH__;
long double __builtin_expm1l(long double) __NDK_FPABI_MATH__;
long double __builtin_fabsl(long double) __NDK_FPABI_MATH__ __pure2;
long double __builtin_fdiml(long double, long double) __NDK_FPABI_MATH__;
long double __builtin_floorl(long double) __NDK_FPABI_MATH__;
long double __builtin_fmal(long double, long double, long double) __NDK_FPABI_MATH__;
long double __builtin_fmaxl(long double, long double) __NDK_FPABI_MATH__ __pure2;
long double __builtin_fminl(long double, long double) __NDK_FPABI_MATH__ __pure2;
long double __builtin_fmodl(long double, long double) __NDK_FPABI_MATH__;
long double __builtin_frexpl(long double value, int *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
long double __builtin_hypotl(long double, long double) __NDK_FPABI_MATH__;
int __builtin_ilogbl(long double) __NDK_FPABI_MATH__ __pure2;
long double __builtin_ldexpl(long double, int) __NDK_FPABI_MATH__;
long double __builtin_lgammal(long double) __NDK_FPABI_MATH__;
long long __builtin_llrintl(long double) __NDK_FPABI_MATH__;
long long __builtin_llroundl(long double) __NDK_FPABI_MATH__;
long double __builtin_log10l(long double) __NDK_FPABI_MATH__;
long double __builtin_log1pl(long double) __NDK_FPABI_MATH__;
long double __builtin_log2l(long double) __NDK_FPABI_MATH__;
long double __builtin_logbl(long double) __NDK_FPABI_MATH__;
long double __builtin_logl(long double) __NDK_FPABI_MATH__;
long __builtin_lrintl(long double) __NDK_FPABI_MATH__;
long __builtin_lroundl(long double) __NDK_FPABI_MATH__;
long double __builtin_modfl(long double, long double *) __NDK_FPABI_MATH__; /* fundamentally !__pure2 */
long double __builtin_nanl(const char *) __NDK_FPABI_MATH__ __pure2;
long double __builtin_nearbyintl(long double) __NDK_FPABI_MATH__;
long double __builtin_nextafterl(long double, long double) __NDK_FPABI_MATH__;
#if !defined(__clang__) || __clang_major__ > 3 || (__clang_major__ == 3 && __clang_minor__ >= 4)
double __builtin_nexttoward(double, long double) __NDK_FPABI_MATH__;
float __builtin_nexttowardf(float, long double) __NDK_FPABI_MATH__;
#else
/* clang < 3.4 */
double __builtin_nexttoward(double, double) __NDK_FPABI_MATH__;
float __builtin_nexttowardf(float, float) __NDK_FPABI_MATH__;
#endif
long double __builtin_nexttowardl(long double, long double) __NDK_FPABI_MATH__;
long double __builtin_powl(long double, long double) __NDK_FPABI_MATH__;
long double __builtin_remainderl(long double, long double) __NDK_FPABI_MATH__;
long double __builtin_remquol(long double, long double, int *) __NDK_FPABI_MATH__;
long double __builtin_rintl(long double) __NDK_FPABI_MATH__;
long double __builtin_roundl(long double) __NDK_FPABI_MATH__;
long double __builtin_scalblnl(long double, long) __NDK_FPABI_MATH__;
long double __builtin_scalbnl(long double, int) __NDK_FPABI_MATH__;
long double __builtin_sinhl(long double) __NDK_FPABI_MATH__;
long double __builtin_sinl(long double) __NDK_FPABI_MATH__;
long double __builtin_sqrtl(long double) __NDK_FPABI_MATH__;
long double __builtin_tanhl(long double) __NDK_FPABI_MATH__;
long double __builtin_tanl(long double) __NDK_FPABI_MATH__;
long double __builtin_tgammal(long double) __NDK_FPABI_MATH__;
long double __builtin_truncl(long double) __NDK_FPABI_MATH__;
__END_DECLS
#endif /* !_MATH_H_ */