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# <math.h>: Mathematics

## Defines

#define M_PI   3.141592653589793238462643
#define M_SQRT2   1.4142135623730950488016887
#define NAN   __builtin_nan("")
#define INFINITY   __builtin_inf()

## Functions

double cos (double __x)
double fabs (double __x)
double fmod (double __x, double __y)
double modf (double __x, double *__iptr)
double sin (double __x)
double sqrt (double __x)
double tan (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)
double square (double __x)
static double copysign (double __x, double __y)
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)
int signbit (double __x)
double trunc (double __x)
static int isfinite (double __x)
double hypot (double __x, double __y)
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 INFINITY   __builtin_inf()

INFINITY constant.

 #define M_PI   3.141592653589793238462643

The constant `pi`.

 #define M_SQRT2   1.4142135623730950488016887

The square root of 2.

 #define NAN   __builtin_nan("")

NAN constant.

## 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 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.

 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.

The ldexp() function 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.

 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.

Note:
This implementation returns 1 if sign bit is set.

 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.

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