D.2 The math.h Module

#include <math.h>

This module defines a collection of standard mathematical functions, which use floating-point values, and associated constants.

Constants

double M_PI

An approximation for the value of $π$ .

double M_PI_2

The value of $π$ divided by 2.

double M_PI_4

The value of $π$ divided by 4.

double M_E

The value $e$ , which is the base of the natural logarithms.

Functions

Power Functions

double sqrt(double x);

Computes and returns the square root of x.

double pow(double x, double y);

Computes and returns the power

x^{y}

double cbrt(double x);

Computes and returns the cube root of x.

double hypot(double x, double y);

Computes and returns the hypotenuse of a right-angled triangle with sides of length

x

and

y

Trigonometric Functions

double sin(double x);

Computes and returns the sine of an angle given in radians.

double cos(double x);

Computes and returns the cosine of an angle given in radians.

double tan(double x);

Computes and returns the tangent of an angle given in radians.

double asin(double x);

Computes and returns the angle with the given sine.

double acos(double x);

Computes and returns the angle with the given cosine.

double atan(double x);

Computes and returns the angle with the given tangent.

double atan2(double y, double x);

Computes and returns the angle with the given tangent,

y / x

Rounding and Remainder Functions

double ceil(double x);

Returns the smallest integer

\geq x

(as a floating-point value).

double floor(double x);

Returns the largest integer

\leq x

(as a floating-point value).

double trunc(double x);

Rounds

x

toward zero.

double round(double x);

Rounds

x

to the nearest integer, away from zero.

Exponential and Logarithmic Functions

double log(double x);

double log10(double x);

double log2(double x);

double exp(double x);

double exp2(double x);

Absolute Functions

double fabs(double x);

Detailed Description

Computes and returns the square root of x.

Parameters:

x: The numerical value for which the square root is to be computed.

Returns:: The square root of x.

Computes and returns the power

x^{y}

. If

x > 0

, y can be any value. If x is zero, y must be

> 0

. If

x < 0

, y must be an integer.

Parameters:

x: The numerical value of the base that raised to a power.
y: The numerical value of the exponent to which the based is raised.

Returns:: The value of $x^{y}$ .

Computes and returns the cube root of x.

Parameters:

x: The numerical value whose cubic root is computed.

Returns:: The cube root of x or $\sqrt[3]{x}$ .

Computes and returns the hypotenuse of a right-angled triangle with sides of length

x

and

y

Parameters:

x, y: The numerical values corresponding to the legs of a right-angled triangle for which the hypotenuse is computed.

Returns:: The square root of $(x^{2} + y^{2})$ .

Computes and returns the sine of an angle given in radians.

Parameters:

x: An angle in radians.

Returns:: The sine of the argument.

Computes and returns the cosine of an angle given in radians.

Parameters:

x: An angle in radians.

Returns:: The cosine of the argument.

Computes and returns the tangent of an angle given in radians.

Parameters:

x: An angle in radians.

Returns:: The tangent of the argument.

Computes and returns the angle with the given sine.

Parameters:

x: A floating-point value between -1 and 1.

Returns:: The arc sine of the argument in radians; the value is in the range $[- π / 2 � π / 2]$ .

Computes and returns the angle with the given cosine.

Parameters:

x: A floating-point value between -1 and 1.

Returns:: The arc cosine of the argument in radians; the value is in the range $[0 � π]$ .

Computes and returns the angle with the given tangent.

Parameters:

x: A floating-point value.

Returns:: The arc tangent of the argument in radians; the value is in the range $[- π / 2 � π / 2]$ .

Computes and returns the angle with the given tangent,

y / x

. The signs of the two arguments are used to determine the quadrant of the result. If x can equal zero, or if it is necessary to distinguish "northwest" from "southeast" and "northeast" from "southwest", use this function instead of atan(y/x).

Parameters:

x, y: Two floating-point values.

Returns:: The angle, in radians, in the range $[- π � π]$ .

Returns the smallest integer

\geq x

(as a floating-point value).

Parameters:

x: The floating-point value to round up.

Returns:: The smallest integral value that is not less than $x$ (as a floating-point value).

Returns the largest integer

\leq x

(as a floating-point value).

Parameters:

x: The floating-point value to round down.

Returns:: The largest integral value less than or equal to $x$ (as a floating-point value).

Rounds

x

toward zero.

Parameters:

x: The floating-point value to truncate.

Returns:: The nearest integer value that is not larger in magnitude than $x$ (as a floating-point value).

Rounds

x

to the nearest integer, away from zero.

Parameters:

x: The floating-point value to round.

Returns:: The value of $x$ rounded to the nearest integer (as a floating-point value).

Parameters:

x

Parameters:

x

Parameters:

x

Parameters:

x

Parameters:

x

Parameters:

x

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