libc/include/math.h - android_bionic - Gitiles

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

 /*
  * Originally based on fdlibm.h 5.1 via FreeBSD.
  */

 #pragma once

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

 __BEGIN_DECLS

 /* C11. */

 typedef double __double_t;
 typedef __double_t double_t;
 typedef float __float_t;
 typedef __float_t float_t;

 #define HUGE_VAL __builtin_huge_val()
 #define HUGE_VALF __builtin_huge_valf()
 #define HUGE_VALL __builtin_huge_vall()

 #define INFINITY __builtin_inff()

 #define NAN __builtin_nanf("")

 #define FP_INFINITE 0x01
 #define FP_NAN 0x02
 #define FP_NORMAL 0x04
 #define FP_SUBNORMAL 0x08
 #define FP_ZERO 0x10

 #if defined(__FP_FAST_FMA)
 #define FP_FAST_FMA 1
 #endif
 #if defined(__FP_FAST_FMAF)
 #define FP_FAST_FMAF 1
 #endif
 #if defined(__FP_FAST_FMAL)
 #define FP_FAST_FMAL 1
 #endif

 #define FP_ILOGB0 (-INT_MAX)
 #define FP_ILOGBNAN INT_MAX

 #define MATH_ERRNO 1
 #define MATH_ERREXCEPT 2
 #define math_errhandling MATH_ERREXCEPT

 #define fpclassify(x) __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)

 #define isfinite(x) __builtin_isfinite(x)

 #define isinf(x) __builtin_isinf(x)

 #define isnan(x) __builtin_isnan(x)

 #define isnormal(x) __builtin_isnormal(x)

 #define signbit(x) \
     ((sizeof(x) == sizeof(float)) ? __builtin_signbitf(x) \
     : (sizeof(x) == sizeof(double)) ? __builtin_signbit(x) \
     : __builtin_signbitl(x))

 double acos(double __x);
 float acosf(float __x);
 long double acosl(long double __x) __RENAME_LDBL(acos, 3, 21);

 double asin(double __x);
 float asinf(float __x);
 long double asinl(long double __x) __RENAME_LDBL(asin, 3, 21);

 double atan(double __x);
 float atanf(float __x);
 long double atanl(long double __x) __RENAME_LDBL(atan, 3, 21);

 double atan2(double __y, double __x);
 float atan2f(float __y, float __x);
 long double atan2l(long double __y, long double __x) __RENAME_LDBL(atan2, 3, 21);

 double cos(double __x);
 float cosf(float __x);
 long double cosl(long double __x) __RENAME_LDBL(cos, 3, 21);

 double sin(double __x);
 float sinf(float __x);
 long double sinl(long double __x) __RENAME_LDBL(sin, 3, 21);

 double tan(double __x);
 float tanf(float __x);
 long double tanl(long double __x) __RENAME_LDBL(tan, 3, 21);

 double acosh(double __x);
 float acoshf(float __x);
 long double acoshl(long double __x) __RENAME_LDBL(acosh, 3, 21);

 double asinh(double __x);
 float asinhf(float __x);
 long double asinhl(long double __x) __RENAME_LDBL(asinh, 3, 21);

 double atanh(double __x);
 float atanhf(float __x);
 long double atanhl(long double __x) __RENAME_LDBL(atanh, 3, 21);

 double cosh(double __x);
 float coshf(float __x);
 long double coshl(long double __x) __RENAME_LDBL(cosh, 3, 21);

 double sinh(double __x);
 float sinhf(float __x);
 long double sinhl(long double __x) __RENAME_LDBL(sinh, 3, 21);

 double tanh(double __x);
 float tanhf(float __x);
 long double tanhl(long double __x) __RENAME_LDBL(tanh, 3, 21);

 double exp(double __x);
 float expf(float __x);
 long double expl(long double __x) __RENAME_LDBL(exp, 3, 21);

 double exp2(double __x);
 float exp2f(float __x);
 long double exp2l(long double __x) __RENAME_LDBL(exp2, 3, 21);

 double expm1(double __x);
 float expm1f(float __x);
 long double expm1l(long double __x) __RENAME_LDBL(expm1, 3, 21);

 double frexp(double __x, int* _Nonnull __exponent);
 float frexpf(float __x, int* _Nonnull __exponent);
 long double frexpl(long double __x, int* _Nonnull __exponent) __RENAME_LDBL(frexp, 3, 21);

 int ilogb(double __x) __attribute_const__;
 int ilogbf(float __x) __attribute_const__;
 int ilogbl(long double __x) __RENAME_LDBL(ilogb, 3, 3) __attribute_const__;

 double ldexp(double __x, int __exponent);
 float ldexpf(float __x, int __exponent);
 long double ldexpl(long double __x, int __exponent) __RENAME_LDBL(ldexp, 3, 3);

 double log(double __x);
 float logf(float __x);
 long double logl(long double __x) __RENAME_LDBL(log, 3, 21);

 double log10(double __x);
 float log10f(float __x);
 long double log10l(long double __x) __RENAME_LDBL(log10, 3, 21);

 double log1p(double __x);
 float log1pf(float __x);
 long double log1pl(long double __x) __RENAME_LDBL(log1p, 3, 21);

 double log2(double __x) __INTRODUCED_IN(18);
 float log2f(float __x) __INTRODUCED_IN(18);
 long double log2l(long double __x) __RENAME_LDBL(log2, 18, 18);

 double logb(double __x);
 float logbf(float __x);
 long double logbl(long double __x) __RENAME_LDBL(logb, 3, 18);

 double modf(double __x, double* _Nonnull __integral_part);
 float modff(float __x, float* _Nonnull __integral_part);
 long double modfl(long double __x, long double* _Nonnull __integral_part) __RENAME_LDBL(modf, 3, 21);

 double scalbn(double __x, int __exponent);
 float scalbnf(float __x, int __exponent);
 long double scalbnl(long double __x, int __exponent) __RENAME_LDBL(scalbn, 3, 3);

 /* TODO: once the NDK only supports >= 18, use __RENAME_LDBL here too. */
 double scalbln(double __x, long __exponent) __INTRODUCED_IN_X86_NO_GUARD_FOR_NDK(18);
 float scalblnf(float __x, long __exponent) __INTRODUCED_IN_X86_NO_GUARD_FOR_NDK(18);
 long double scalblnl(long double __x, long __exponent) __INTRODUCED_IN_X86_NO_GUARD_FOR_NDK(18);

 double cbrt(double __x);
 float cbrtf(float __x);
 long double cbrtl(long double __x) __RENAME_LDBL(cbrt, 3, 21);

 double fabs(double __x) __attribute_const__;
 float fabsf(float __x) __attribute_const__;
 long double fabsl(long double __x) __RENAME_LDBL(fabs, 3, 3) __attribute_const__;

 double hypot(double __x, double __y);
 float hypotf(float __x, float __y);
 long double hypotl(long double __x, long double __y) __RENAME_LDBL(hypot, 3, 21);

 double pow(double __x, double __y);
 float powf(float __x, float __y);
 long double powl(long double __x, long double __y) __RENAME_LDBL(pow, 3, 21);

 double sqrt(double __x);
 float sqrtf(float __x);
 long double sqrtl(long double __x) __RENAME_LDBL(sqrt, 3, 21);

 double erf(double __x);
 float erff(float __x);
 long double erfl(long double __x) __RENAME_LDBL(erf, 3, 21);

 double erfc(double __x);
 float erfcf(float __x);
 long double erfcl(long double __x) __RENAME_LDBL(erfc, 3, 21);

 double lgamma(double __x);
 float lgammaf(float __x);
 long double lgammal(long double __x) __RENAME_LDBL(lgamma, 3, 21);

 double tgamma(double __x);
 float tgammaf(float __x);
 long double tgammal(long double __x) __RENAME_LDBL(tgamma, 3, 21);

 double ceil(double __x);
 float ceilf(float __x);
 long double ceill(long double __x) __RENAME_LDBL(ceil, 3, 3);

 double floor(double __x);
 float floorf(float __x);
 long double floorl(long double __x) __RENAME_LDBL(floor, 3, 3);

 double nearbyint(double __x);
 float nearbyintf(float __x);
 long double nearbyintl(long double __x) __RENAME_LDBL(nearbyint, 3, 21);

 double rint(double __x);
 float rintf(float __x);
 long double rintl(long double __x) __RENAME_LDBL(rint, 3, 21);

 long lrint(double __x);
 long lrintf(float __x);
 long lrintl(long double __x) __RENAME_LDBL(lrint, 3, 21);

 long long llrint(double __x);
 long long llrintf(float __x);
 long long llrintl(long double __x) __RENAME_LDBL(llrint, 3, 21);

 double round(double __x);
 float roundf(float __x);
 long double roundl(long double __x) __RENAME_LDBL(roundl, 3, 3);

 long lround(double __x);
 long lroundf(float __x);
 long lroundl(long double __x) __RENAME_LDBL(lround, 3, 3);

 long long llround(double __x);
 long long llroundf(float __x);
 long long llroundl(long double __x) __RENAME_LDBL(llround, 3, 3);

 double trunc(double __x);
 float truncf(float __x);
 long double truncl(long double __x) __RENAME_LDBL(trunc, 3, 3);

 double fmod(double __x, double __y);
 float fmodf(float __x, float __y);
 long double fmodl(long double __x, long double __y) __RENAME_LDBL(fmod, 3, 21);

 double remainder(double __x, double __y);
 float remainderf(float __x, float __y);
 long double remainderl(long double __x, long double __y) __RENAME_LDBL(remainder, 3, 21);

 double remquo(double __x, double __y, int* _Nonnull __quotient_bits);
 float remquof(float __x, float __y, int* _Nonnull __quotient_bits);
 long double remquol(long double __x, long double __y, int* _Nonnull __quotient_bits) __RENAME_LDBL(remquo, 3, 21);

 double copysign(double __value, double __sign) __attribute_const__;
 float copysignf(float __value, float __sign) __attribute_const__;
 long double copysignl(long double __value, long double __sign) __RENAME_LDBL(copysign, 3, 3) __attribute_const__;

 double nan(const char* _Nonnull __kind) __attribute_const__;
 float nanf(const char* _Nonnull __kind) __attribute_const__;
 long double nanl(const char* _Nonnull __kind) __RENAME_LDBL(nan, 13, 13) __attribute_const__;

 double nextafter(double __x, double __y);
 float nextafterf(float __x, float __y);
 long double nextafterl(long double __x, long double __y) __RENAME_LDBL_NO_GUARD_FOR_NDK(nextafter, 3, 21);

 double nexttoward(double __x, long double __y) __INTRODUCED_IN_NO_GUARD_FOR_NDK(18);
 float nexttowardf(float __x, long double __y);
 long double nexttowardl(long double __x, long double __y) __RENAME_LDBL_NO_GUARD_FOR_NDK(nexttoward, 18, 18);

 double fdim(double __x, double __y);
 float fdimf(float __x, float __y);
 long double fdiml(long double __x, long double __y) __RENAME_LDBL(fdim, 3, 3);

 double fmax(double __x, double __y) __attribute_const__;
 float fmaxf(float __x, float __y) __attribute_const__;
 long double fmaxl(long double __x, long double __y) __RENAME_LDBL(fmax, 3, 3) __attribute_const__;

 double fmin(double __x, double __y) __attribute_const__;
 float fminf(float __x, float __y) __attribute_const__;
 long double fminl(long double __x, long double __y) __RENAME_LDBL(fmin, 3, 3) __attribute_const__;

 double fma(double __x, double __y, double __z);
 float fmaf(float __x, float __y, float __z);
 long double fmal(long double __x, long double __y, long double __z) __RENAME_LDBL_NO_GUARD_FOR_NDK(fma, 3, 21);

 #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))

 /*
  * https://code.google.com/p/android/issues/detail?id=271629
  * To be fully compliant with C++, we need to not define these (C doesn't
  * specify them either). Exposing these means that isinf and isnan will have a
  * return type of int in C++ rather than bool like they're supposed to be.
  *
  * GNU libstdc++ 4.9 isn't able to handle a standard compliant C library. Its
  * <cmath> will `#undef isnan` from math.h and only adds the function overloads
  * to the std namespace, making it impossible to use both <cmath> (which gets
  * included by a lot of other standard headers) and ::isnan.
  */
 int (isinf)(double __x) __attribute_const__ __INTRODUCED_IN(21);
 int (isnan)(double __x) __attribute_const__;

 /* POSIX extensions. */

 extern int signgam;

 double j0(double __x);
 double j1(double __x);
 double jn(int __n, double __x);
 double y0(double __x);
 double y1(double __x);
 double yn(int __n, double __x);

 #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)

 /* BSD extensions. */

 #if defined(__USE_BSD)
 #define HUGE MAXFLOAT
 #endif

 /* Extensions in both BSD and GNU. */

 #if defined(__USE_BSD) || defined(__USE_GNU)
 double gamma(double __x);
 double scalb(double __x, double __exponent);
 double drem(double __x, double __y);
 int finite(double __x) __attribute_const__;
 int isnanf(float __x) __attribute_const__;
 double gamma_r(double __x, int* _Nonnull __sign);
 double lgamma_r(double __x, int* _Nonnull __sign);
 double significand(double __x);
 long double lgammal_r(long double __x, int* _Nonnull __sign) __INTRODUCED_IN(23);
 long double significandl(long double __x) __INTRODUCED_IN(21);
 float dremf(float __x, float __y);
 int finitef(float __x) __attribute_const__;
 float gammaf(float __x);
 float j0f(float __x);
 float j1f(float __x);
 float jnf(int __n, float __x);
 float scalbf(float __x, float __exponent);
 float y0f(float __x);
 float y1f(float __x);
 float ynf(int __n, float __x);
 float gammaf_r(float __x, int* _Nonnull __sign);
 float lgammaf_r(float __x, int* _Nonnull __sign);
 float significandf(float __x);
 void sincos(double __x, double* _Nonnull __sin, double* _Nonnull __cos);
 void sincosf(float __x, float* _Nonnull __sin, float* _Nonnull __cos);
 void sincosl(long double __x, long double* _Nonnull __sin, long double* _Nonnull __cos);
 #endif

 /* GNU extensions. */

 #if defined(__USE_GNU)
 #define M_El            2.718281828459045235360287471352662498L /* e */
 #define M_LOG2El        1.442695040888963407359924681001892137L /* log 2e */
 #define M_LOG10El       0.434294481903251827651128918916605082L /* log 10e */
 #define M_LN2l          0.693147180559945309417232121458176568L /* log e2 */
 #define M_LN10l         2.302585092994045684017991454684364208L /* log e10 */
 #define M_PIl           3.141592653589793238462643383279502884L /* pi */
 #define M_PI_2l         1.570796326794896619231321691639751442L /* pi/2 */
 #define M_PI_4l         0.785398163397448309615660845819875721L /* pi/4 */
 #define M_1_PIl         0.318309886183790671537767526745028724L /* 1/pi */
 #define M_2_PIl         0.636619772367581343075535053490057448L /* 2/pi */
 #define M_2_SQRTPIl     1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 #define M_SQRT2l        1.414213562373095048801688724209698079L /* sqrt(2) */
 #define M_SQRT1_2l      0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 #endif

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

	/*
	* Originally based on fdlibm.h 5.1 via FreeBSD.
	*/

	#pragma once

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

	__BEGIN_DECLS

	/* C11. */

	typedef double __double_t;
	typedef __double_t double_t;
	typedef float __float_t;
	typedef __float_t float_t;

	#define HUGE_VAL __builtin_huge_val()
	#define HUGE_VALF __builtin_huge_valf()
	#define HUGE_VALL __builtin_huge_vall()

	#define INFINITY __builtin_inff()

	#define NAN __builtin_nanf("")

	#define FP_INFINITE 0x01
	#define FP_NAN 0x02
	#define FP_NORMAL 0x04
	#define FP_SUBNORMAL 0x08
	#define FP_ZERO 0x10

	#if defined(__FP_FAST_FMA)
	#define FP_FAST_FMA 1
	#endif
	#if defined(__FP_FAST_FMAF)
	#define FP_FAST_FMAF 1
	#endif
	#if defined(__FP_FAST_FMAL)
	#define FP_FAST_FMAL 1
	#endif

	#define FP_ILOGB0 (-INT_MAX)
	#define FP_ILOGBNAN INT_MAX

	#define MATH_ERRNO 1
	#define MATH_ERREXCEPT 2
	#define math_errhandling MATH_ERREXCEPT

	#define fpclassify(x) __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)

	#define isfinite(x) __builtin_isfinite(x)

	#define isinf(x) __builtin_isinf(x)

	#define isnan(x) __builtin_isnan(x)

	#define isnormal(x) __builtin_isnormal(x)

	#define signbit(x) \
	((sizeof(x) == sizeof(float)) ? __builtin_signbitf(x) \
	: (sizeof(x) == sizeof(double)) ? __builtin_signbit(x) \
	: __builtin_signbitl(x))

	double acos(double __x);
	float acosf(float __x);
	long double acosl(long double __x) __RENAME_LDBL(acos, 3, 21);

	double asin(double __x);
	float asinf(float __x);
	long double asinl(long double __x) __RENAME_LDBL(asin, 3, 21);

	double atan(double __x);
	float atanf(float __x);
	long double atanl(long double __x) __RENAME_LDBL(atan, 3, 21);

	double atan2(double __y, double __x);
	float atan2f(float __y, float __x);
	long double atan2l(long double __y, long double __x) __RENAME_LDBL(atan2, 3, 21);

	double cos(double __x);
	float cosf(float __x);
	long double cosl(long double __x) __RENAME_LDBL(cos, 3, 21);

	double sin(double __x);
	float sinf(float __x);
	long double sinl(long double __x) __RENAME_LDBL(sin, 3, 21);

	double tan(double __x);
	float tanf(float __x);
	long double tanl(long double __x) __RENAME_LDBL(tan, 3, 21);

	double acosh(double __x);
	float acoshf(float __x);
	long double acoshl(long double __x) __RENAME_LDBL(acosh, 3, 21);

	double asinh(double __x);
	float asinhf(float __x);
	long double asinhl(long double __x) __RENAME_LDBL(asinh, 3, 21);

	double atanh(double __x);
	float atanhf(float __x);
	long double atanhl(long double __x) __RENAME_LDBL(atanh, 3, 21);

	double cosh(double __x);
	float coshf(float __x);
	long double coshl(long double __x) __RENAME_LDBL(cosh, 3, 21);

	double sinh(double __x);
	float sinhf(float __x);
	long double sinhl(long double __x) __RENAME_LDBL(sinh, 3, 21);

	double tanh(double __x);
	float tanhf(float __x);
	long double tanhl(long double __x) __RENAME_LDBL(tanh, 3, 21);

	double exp(double __x);
	float expf(float __x);
	long double expl(long double __x) __RENAME_LDBL(exp, 3, 21);

	double exp2(double __x);
	float exp2f(float __x);
	long double exp2l(long double __x) __RENAME_LDBL(exp2, 3, 21);

	double expm1(double __x);
	float expm1f(float __x);
	long double expm1l(long double __x) __RENAME_LDBL(expm1, 3, 21);

	double frexp(double __x, int* _Nonnull __exponent);
	float frexpf(float __x, int* _Nonnull __exponent);
	long double frexpl(long double __x, int* _Nonnull __exponent) __RENAME_LDBL(frexp, 3, 21);

	int ilogb(double __x) __attribute_const__;
	int ilogbf(float __x) __attribute_const__;
	int ilogbl(long double __x) __RENAME_LDBL(ilogb, 3, 3) __attribute_const__;

	double ldexp(double __x, int __exponent);
	float ldexpf(float __x, int __exponent);
	long double ldexpl(long double __x, int __exponent) __RENAME_LDBL(ldexp, 3, 3);

	double log(double __x);
	float logf(float __x);
	long double logl(long double __x) __RENAME_LDBL(log, 3, 21);

	double log10(double __x);
	float log10f(float __x);
	long double log10l(long double __x) __RENAME_LDBL(log10, 3, 21);

	double log1p(double __x);
	float log1pf(float __x);
	long double log1pl(long double __x) __RENAME_LDBL(log1p, 3, 21);

	double log2(double __x) __INTRODUCED_IN(18);
	float log2f(float __x) __INTRODUCED_IN(18);
	long double log2l(long double __x) __RENAME_LDBL(log2, 18, 18);

	double logb(double __x);
	float logbf(float __x);
	long double logbl(long double __x) __RENAME_LDBL(logb, 3, 18);

	double modf(double __x, double* _Nonnull __integral_part);
	float modff(float __x, float* _Nonnull __integral_part);
	long double modfl(long double __x, long double* _Nonnull __integral_part) __RENAME_LDBL(modf, 3, 21);

	double scalbn(double __x, int __exponent);
	float scalbnf(float __x, int __exponent);
	long double scalbnl(long double __x, int __exponent) __RENAME_LDBL(scalbn, 3, 3);

	/* TODO: once the NDK only supports >= 18, use __RENAME_LDBL here too. */
	double scalbln(double __x, long __exponent) __INTRODUCED_IN_X86_NO_GUARD_FOR_NDK(18);
	float scalblnf(float __x, long __exponent) __INTRODUCED_IN_X86_NO_GUARD_FOR_NDK(18);
	long double scalblnl(long double __x, long __exponent) __INTRODUCED_IN_X86_NO_GUARD_FOR_NDK(18);

	double cbrt(double __x);
	float cbrtf(float __x);
	long double cbrtl(long double __x) __RENAME_LDBL(cbrt, 3, 21);

	double fabs(double __x) __attribute_const__;
	float fabsf(float __x) __attribute_const__;
	long double fabsl(long double __x) __RENAME_LDBL(fabs, 3, 3) __attribute_const__;

	double hypot(double __x, double __y);
	float hypotf(float __x, float __y);
	long double hypotl(long double __x, long double __y) __RENAME_LDBL(hypot, 3, 21);

	double pow(double __x, double __y);
	float powf(float __x, float __y);
	long double powl(long double __x, long double __y) __RENAME_LDBL(pow, 3, 21);

	double sqrt(double __x);
	float sqrtf(float __x);
	long double sqrtl(long double __x) __RENAME_LDBL(sqrt, 3, 21);

	double erf(double __x);
	float erff(float __x);
	long double erfl(long double __x) __RENAME_LDBL(erf, 3, 21);

	double erfc(double __x);
	float erfcf(float __x);
	long double erfcl(long double __x) __RENAME_LDBL(erfc, 3, 21);

	double lgamma(double __x);
	float lgammaf(float __x);
	long double lgammal(long double __x) __RENAME_LDBL(lgamma, 3, 21);

	double tgamma(double __x);
	float tgammaf(float __x);
	long double tgammal(long double __x) __RENAME_LDBL(tgamma, 3, 21);

	double ceil(double __x);
	float ceilf(float __x);
	long double ceill(long double __x) __RENAME_LDBL(ceil, 3, 3);

	double floor(double __x);
	float floorf(float __x);
	long double floorl(long double __x) __RENAME_LDBL(floor, 3, 3);

	double nearbyint(double __x);
	float nearbyintf(float __x);
	long double nearbyintl(long double __x) __RENAME_LDBL(nearbyint, 3, 21);

	double rint(double __x);
	float rintf(float __x);
	long double rintl(long double __x) __RENAME_LDBL(rint, 3, 21);

	long lrint(double __x);
	long lrintf(float __x);
	long lrintl(long double __x) __RENAME_LDBL(lrint, 3, 21);

	long long llrint(double __x);
	long long llrintf(float __x);
	long long llrintl(long double __x) __RENAME_LDBL(llrint, 3, 21);

	double round(double __x);
	float roundf(float __x);
	long double roundl(long double __x) __RENAME_LDBL(roundl, 3, 3);

	long lround(double __x);
	long lroundf(float __x);
	long lroundl(long double __x) __RENAME_LDBL(lround, 3, 3);

	long long llround(double __x);
	long long llroundf(float __x);
	long long llroundl(long double __x) __RENAME_LDBL(llround, 3, 3);

	double trunc(double __x);
	float truncf(float __x);
	long double truncl(long double __x) __RENAME_LDBL(trunc, 3, 3);

	double fmod(double __x, double __y);
	float fmodf(float __x, float __y);
	long double fmodl(long double __x, long double __y) __RENAME_LDBL(fmod, 3, 21);

	double remainder(double __x, double __y);
	float remainderf(float __x, float __y);
	long double remainderl(long double __x, long double __y) __RENAME_LDBL(remainder, 3, 21);

	double remquo(double __x, double __y, int* _Nonnull __quotient_bits);
	float remquof(float __x, float __y, int* _Nonnull __quotient_bits);
	long double remquol(long double __x, long double __y, int* _Nonnull __quotient_bits) __RENAME_LDBL(remquo, 3, 21);

	double copysign(double __value, double __sign) __attribute_const__;
	float copysignf(float __value, float __sign) __attribute_const__;
	long double copysignl(long double __value, long double __sign) __RENAME_LDBL(copysign, 3, 3) __attribute_const__;

	double nan(const char* _Nonnull __kind) __attribute_const__;
	float nanf(const char* _Nonnull __kind) __attribute_const__;
	long double nanl(const char* _Nonnull __kind) __RENAME_LDBL(nan, 13, 13) __attribute_const__;

	double nextafter(double __x, double __y);
	float nextafterf(float __x, float __y);
	long double nextafterl(long double __x, long double __y) __RENAME_LDBL_NO_GUARD_FOR_NDK(nextafter, 3, 21);

	double nexttoward(double __x, long double __y) __INTRODUCED_IN_NO_GUARD_FOR_NDK(18);
	float nexttowardf(float __x, long double __y);
	long double nexttowardl(long double __x, long double __y) __RENAME_LDBL_NO_GUARD_FOR_NDK(nexttoward, 18, 18);

	double fdim(double __x, double __y);
	float fdimf(float __x, float __y);
	long double fdiml(long double __x, long double __y) __RENAME_LDBL(fdim, 3, 3);

	double fmax(double __x, double __y) __attribute_const__;
	float fmaxf(float __x, float __y) __attribute_const__;
	long double fmaxl(long double __x, long double __y) __RENAME_LDBL(fmax, 3, 3) __attribute_const__;

	double fmin(double __x, double __y) __attribute_const__;
	float fminf(float __x, float __y) __attribute_const__;
	long double fminl(long double __x, long double __y) __RENAME_LDBL(fmin, 3, 3) __attribute_const__;

	double fma(double __x, double __y, double __z);
	float fmaf(float __x, float __y, float __z);
	long double fmal(long double __x, long double __y, long double __z) __RENAME_LDBL_NO_GUARD_FOR_NDK(fma, 3, 21);

	#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))

	/*
	* https://code.google.com/p/android/issues/detail?id=271629
	* To be fully compliant with C++, we need to not define these (C doesn't
	* specify them either). Exposing these means that isinf and isnan will have a
	* return type of int in C++ rather than bool like they're supposed to be.
	*
	* GNU libstdc++ 4.9 isn't able to handle a standard compliant C library. Its
	* <cmath> will `#undef isnan` from math.h and only adds the function overloads
	* to the std namespace, making it impossible to use both <cmath> (which gets
	* included by a lot of other standard headers) and ::isnan.
	*/
	int (isinf)(double __x) __attribute_const__ __INTRODUCED_IN(21);
	int (isnan)(double __x) __attribute_const__;

	/* POSIX extensions. */

	extern int signgam;

	double j0(double __x);
	double j1(double __x);
	double jn(int __n, double __x);
	double y0(double __x);
	double y1(double __x);
	double yn(int __n, double __x);

	#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)

	/* BSD extensions. */

	#if defined(__USE_BSD)
	#define HUGE MAXFLOAT
	#endif

	/* Extensions in both BSD and GNU. */

	#if defined(__USE_BSD) \|\| defined(__USE_GNU)
	double gamma(double __x);
	double scalb(double __x, double __exponent);
	double drem(double __x, double __y);
	int finite(double __x) __attribute_const__;
	int isnanf(float __x) __attribute_const__;
	double gamma_r(double __x, int* _Nonnull __sign);
	double lgamma_r(double __x, int* _Nonnull __sign);
	double significand(double __x);
	long double lgammal_r(long double __x, int* _Nonnull __sign) __INTRODUCED_IN(23);
	long double significandl(long double __x) __INTRODUCED_IN(21);
	float dremf(float __x, float __y);
	int finitef(float __x) __attribute_const__;
	float gammaf(float __x);
	float j0f(float __x);
	float j1f(float __x);
	float jnf(int __n, float __x);
	float scalbf(float __x, float __exponent);
	float y0f(float __x);
	float y1f(float __x);
	float ynf(int __n, float __x);
	float gammaf_r(float __x, int* _Nonnull __sign);
	float lgammaf_r(float __x, int* _Nonnull __sign);
	float significandf(float __x);
	void sincos(double __x, double* _Nonnull __sin, double* _Nonnull __cos);
	void sincosf(float __x, float* _Nonnull __sin, float* _Nonnull __cos);
	void sincosl(long double __x, long double* _Nonnull __sin, long double* _Nonnull __cos);
	#endif

	/* GNU extensions. */

	#if defined(__USE_GNU)
	#define M_El 2.718281828459045235360287471352662498L /* e */
	#define M_LOG2El 1.442695040888963407359924681001892137L /* log 2e */
	#define M_LOG10El 0.434294481903251827651128918916605082L /* log 10e */
	#define M_LN2l 0.693147180559945309417232121458176568L /* log e2 */
	#define M_LN10l 2.302585092994045684017991454684364208L /* log e10 */
	#define M_PIl 3.141592653589793238462643383279502884L /* pi */
	#define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
	#define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
	#define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
	#define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
	#define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
	#define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
	#define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
	#endif

	__END_DECLS