<math.h>: Mathematics

Defines
#define	M_E   2.7182818284590452354
#define	M_LOG2E   1.4426950408889634074
#define	M_LOG10E   0.43429448190325182765
#define	M_LN2   0.69314718055994530942
#define	M_LN10   2.30258509299404568402
#define	M_PI   3.14159265358979323846
#define	M_PI_2   1.57079632679489661923
#define	M_PI_4   0.78539816339744830962
#define	M_1_PI   0.31830988618379067154
#define	M_2_PI   0.63661977236758134308
#define	M_2_SQRTPI   1.12837916709551257390
#define	M_SQRT2   1.41421356237309504880
#define	M_SQRT1_2   0.70710678118654752440
#define	NAN   __builtin_nan("")
#define	INFINITY   __builtin_inf()
#define	cosf   cos
#define	sinf   sin
#define	tanf   tan
#define	fabsf   fabs
#define	fmodf   fmod
#define	sqrtf   sqrt
#define	cbrtf   cbrt
#define	hypotf   hypot
#define	squaref   square
#define	floorf   floor
#define	ceilf   ceil
#define	frexpf   frexp
#define	ldexpf   ldexp
#define	expf   exp
#define	coshf   cosh
#define	sinhf   sinh
#define	tanhf   tanh
#define	acosf   acos
#define	asinf   asin
#define	atanf   atan
#define	atan2f   atan2
#define	logf   log
#define	log10f   log10
#define	powf   pow
#define	isnanf   isnan
#define	isinff   isinf
#define	isfinitef   isfinite
#define	copysignf   copysign
#define	signbitf   signbit
#define	fdimf   fdim
#define	fmaf   fma
#define	fmaxf   fmax
#define	fminf   fmin
#define	truncf   trunc
#define	roundf   round
#define	lroundf   lround
#define	lrintf   lrint
Functions
double	cos (double __x)
double	sin (double __x)
double	tan (double __x)
double	fabs (double __x)
double	fmod (double __x, double __y)
double	modf (double __x, double *__iptr)
float	modff (float __x, float *__iptr)
double	sqrt (double __x)
double	cbrt (double __x)
double	hypot (double __x, double __y)
double	square (double __x)
double	floor (double __x)
double	ceil (double __x)
double	frexp (double __x, int *__pexp)
double	ldexp (double __x, int __exp)
double	exp (double __x)
double	cosh (double __x)
double	sinh (double __x)
double	tanh (double __x)
double	acos (double __x)
double	asin (double __x)
double	atan (double __x)
double	atan2 (double __y, double __x)
double	log (double __x)
double	log10 (double __x)
double	pow (double __x, double __y)
int	isnan (double __x)
int	isinf (double __x)
static int	isfinite (double __x)
static double	copysign (double __x, double __y)
int	signbit (double __x)
double	fdim (double __x, double __y)
double	fma (double __x, double __y, double __z)
double	fmax (double __x, double __y)
double	fmin (double __x, double __y)
double	trunc (double __x)
double	round (double __x)
long	lround (double __x)
long	lrint (double __x)

---

Detailed Description

 #include <math.h> 

This header file declares basic mathematics constants and functions.

Notes:

• In order to access the functions delcared herein, it is usually also required to additionally link against the library libm.a. See also the related FAQ entry.
• Math functions do not raise exceptions and do not change the errno variable. Therefore the majority of them are declared with const attribute, for better optimization by GCC.

---

Define Documentation

#define acosf   acos

The alias for acos().

#define asinf   asin

The alias for asin().

#define atan2f   atan2

The alias for atan2().

#define atanf   atan

The alias for atan().

#define cbrtf   cbrt

The alias for cbrt().

#define ceilf   ceil

The alias for ceil().

#define copysignf   copysign

The alias for copysign().

#define cosf   cos

The alias for cos().

#define coshf   cosh

The alias for cosh().

#define expf   exp

The alias for exp().

#define fabsf   fabs

The alias for fabs().

#define fdimf   fdim

The alias for fdim().

#define floorf   floor

The alias for floor().

#define fmaf   fma

The alias for fma().

#define fmaxf   fmax

The alias for fmax().

#define fminf   fmin

The alias for fmin().

#define fmodf   fmod

The alias for fmod().

#define frexpf   frexp

The alias for frexp().

#define hypotf   hypot

The alias for hypot().

#define INFINITY   __builtin_inf()

INFINITY constant.

#define isfinitef   isfinite

The alias for isfinite().

#define isinff   isinf

The alias for isinf().

#define isnanf   isnan

The alias for isnan().

#define ldexpf   ldexp

The alias for ldexp().

#define log10f   log10

The alias for log10().

#define logf   log

The alias for log().

#define lrintf   lrint

The alias for lrint().

#define lroundf   lround

The alias for lround().

#define M_1_PI   0.31830988618379067154

The constant 1/pi.

#define M_2_PI   0.63661977236758134308

The constant 2/pi.

#define M_2_SQRTPI   1.12837916709551257390

The constant 2/sqrt(pi).

#define M_E   2.7182818284590452354

The constant e.

#define M_LN10   2.30258509299404568402

The natural logarithm of the 10.

#define M_LN2   0.69314718055994530942

The natural logarithm of the 2.

#define M_LOG10E   0.43429448190325182765

The logarithm of the e to base 10.

#define M_LOG2E   1.4426950408889634074

The logarithm of the e to base 2.

#define M_PI   3.14159265358979323846

The constant pi.

#define M_PI_2   1.57079632679489661923

The constant pi/2.

#define M_PI_4   0.78539816339744830962

The constant pi/4.

#define M_SQRT1_2   0.70710678118654752440

The constant 1/sqrt(2).

#define M_SQRT2   1.41421356237309504880

The square root of 2.

#define NAN   __builtin_nan("")

NAN constant.

#define powf   pow

The alias for pow().

#define roundf   round

The alias for round().

#define signbitf   signbit

The alias for signbit().

#define sinf   sin

The alias for sin().

#define sinhf   sinh

The alias for sinh().

#define sqrtf   sqrt

The alias for sqrt().

#define squaref   square

The alias for square().

#define tanf   tan

The alias for tan().

#define tanhf   tanh

The alias for tanh().

#define truncf   trunc

The alias for trunc().

---

Function Documentation

double acos

(

double

__x

)

The acos() function computes the principal value of the arc cosine of __x. The returned value is in the range [0, pi] radians. A domain error occurs for arguments not in the range [-1, +1].

double asin

(

double

__x

)

The asin() function computes the principal value of the arc sine of __x. The returned value is in the range [-pi/2, pi/2] radians. A domain error occurs for arguments not in the range [-1, +1].

double atan

(

double

__x

)

The atan() function computes the principal value of the arc tangent of __x. The returned value is in the range [-pi/2, pi/2] radians.

double atan2	(	double	__y,
		double	__x
	)

The atan2() function computes the principal value of the arc tangent of __y / __x, using the signs of both arguments to determine the quadrant of the return value. The returned value is in the range [-pi, +pi] radians.

double cbrt

(

double

__x

)

The cbrt() function returns the cube root of __x.

double ceil

(

double

__x

)

The ceil() function returns the smallest integral value greater than or equal to __x, expressed as a floating-point number.

static double copysign	(	double	__x,
		double	__y
	)		[static]

The copysign() function returns __x but with the sign of __y. They work even if __x or __y are NaN or zero.

double cos

(

double

__x

)

The cos() function returns the cosine of __x, measured in radians.

double cosh

(

double

__x

)

The cosh() function returns the hyperbolic cosine of __x.

double exp

(

double

__x

)

The exp() function returns the exponential value of __x.

double fabs

(

double

__x

)

The fabs() function computes the absolute value of a floating-point number __x.

double fdim	(	double	__x,
		double	__y
	)

The fdim() function returns max(__x - __y, 0). If __x or __y or both are NaN, NaN is returned.

double floor

(

double

__x

)

The floor() function returns the largest integral value less than or equal to __x, expressed as a floating-point number.

double fma	(	double	__x,
		double	__y,
		double	__z
	)

The fma() function performs floating-point multiply-add. This is the operation (__x * __y) + __z, but the intermediate result is not rounded to the destination type. This can sometimes improve the precision of a calculation.

double fmax	(	double	__x,
		double	__y
	)

The fmax() function returns the greater of the two values __x and __y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

double fmin	(	double	__x,
		double	__y
	)

The fmin() function returns the lesser of the two values __x and __y. If an argument is NaN, the other argument is returned. If both arguments are NaN, NaN is returned.

double fmod	(	double	__x,
		double	__y
	)

The function fmod() returns the floating-point remainder of __x / __y.

double frexp	(	double	__x,
		int *	__pexp
	)

The frexp() function breaks a floating-point number into a normalized fraction and an integral power of 2. It stores the integer in the int object pointed to by __pexp.

If __x is a normal float point number, the frexp() function returns the value v, such that v has a magnitude in the interval [1/2, 1) or zero, and __x equals v times 2 raised to the power __pexp. If __x is zero, both parts of the result are zero. If __x is not a finite number, the frexp() returns __x as is and stores 0 by __pexp.

Note:

This implementation permits a zero pointer as a directive to skip a storing the exponent.

double hypot	(	double	__x,
		double	__y
	)

The hypot() function returns sqrt(__x*__x + __y*__y). This is the length of the hypotenuse of a right triangle with sides of length __x and __y, or the distance of the point (__x, __y) from the origin. Using this function instead of the direct formula is wise, since the error is much smaller. No underflow with small __x and __y. No overflow if result is in range.

static int isfinite

(

double

__x

)

[static]

The isfinite() function returns a nonzero value if __x is finite: not plus or minus infinity, and not NaN.

int isinf

(

double

__x

)

The function isinf() returns 1 if the argument __x is positive infinity, -1 if __x is negative infinity, and 0 otherwise.

Note:

The GCC 4.3 can replace this function with inline code that returns the 1 value for both infinities (gcc bug #35509).

int isnan

(

double

__x

)

The function isnan() returns 1 if the argument __x represents a "not-a-number" (NaN) object, otherwise 0.

double ldexp	(	double	__x,
		int	__exp
	)

The ldexp() function multiplies a floating-point number by an integral power of 2. It returns the value of __x times 2 raised to the power __exp.

double log

(

double

__x

)

The log() function returns the natural logarithm of argument __x.

double log10

(

double

__x

)

The log10() function returns the logarithm of argument __x to base 10.

long lrint

(

double

__x

)

The lrint() function rounds __x to the nearest integer, rounding the halfway cases to the even integer direction. (That is both 1.5 and 2.5 values are rounded to 2). This function is similar to rint() function, but it differs in type of return value and in that an overflow is possible.

Returns:

The rounded long integer value. If __x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

long lround

(

double

__x

)

The lround() function rounds __x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). This function is similar to round() function, but it differs in type of return value and in that an overflow is possible.

Returns:

The rounded long integer value. If __x is not a finite number or an overflow was, this realization returns the LONG_MIN value (0x80000000).

double modf	(	double	__x,
		double *	__iptr
	)

The modf() function breaks the argument __x into integral and fractional parts, each of which has the same sign as the argument. It stores the integral part as a double in the object pointed to by __iptr.

The modf() function returns the signed fractional part of __x.

Note:

This implementation skips writing by zero pointer. However, the GCC 4.3 can replace this function with inline code that does not permit to use NULL address for the avoiding of storing.

float modff	(	float	__x,
		float *	__iptr
	)

The alias for modf().

double pow	(	double	__x,
		double	__y
	)

The function pow() returns the value of __x to the exponent __y.

double round

(

double

__x

)

The round() function rounds __x to the nearest integer, but rounds halfway cases away from zero (instead of to the nearest even integer). Overflow is impossible.

Returns:

The rounded value. If __x is an integral or infinite, __x itself is returned. If __x is NaN, then NaN is returned.

int signbit

(

double

__x

)

The signbit() function returns a nonzero value if the value of __x has its sign bit set. This is not the same as `__x < 0.0', because IEEE 754 floating point allows zero to be signed. The comparison `-0.0 < 0.0' is false, but `signbit (-0.0)' will return a nonzero value.

double sin

(

double

__x

)

The sin() function returns the sine of __x, measured in radians.

double sinh

(

double

__x

)

The sinh() function returns the hyperbolic sine of __x.

double sqrt

(

double

__x

)

The sqrt() function returns the non-negative square root of __x.

double square

(

double

__x

)

The function square() returns __x * __x.

Note:

This function does not belong to the C standard definition.

double tan

(

double

__x

)

The tan() function returns the tangent of __x, measured in radians.

double tanh

(

double

__x

)

The tanh() function returns the hyperbolic tangent of __x.

double trunc

(

double

__x

)

The trunc() function rounds __x to the nearest integer not larger in absolute value.