Summary: Constants | Methods | Inherited Methods | [Expand All]

public final class

Math

extends Object

java.lang.Object
↳	java.lang.Math

Class Overview

The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point Math methods is measured in terms of ulps, units in the last place. For a given floating-point format, an ulp of a specific real number value is the distance between the two floating-point values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floating-point number nearest the exact result; such a method is correctly rounded. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded. Instead, for the Math class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be semi-monotonic: whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.

Summary

Constants
double	E	The `double` value that is closer than any other to e, the base of the natural logarithms.
double	PI	The `double` value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.

Public Methods
static double	IEEEremainder(double f1, double f2) Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard.
static long	abs(long a) Returns the absolute value of a `long` value.
static int	abs(int a) Returns the absolute value of an `int` value.
static float	abs(float a) Returns the absolute value of a `float` value.
static double	abs(double a) Returns the absolute value of a `double` value.
static double	acos(double a) Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi.
static double	asin(double a) Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2.
static double	atan(double a) Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2.
static double	atan2(double y, double x) Returns the angle theta from the conversion of rectangular coordinates (`x`, `y`) to polar coordinates (r, theta).
static double	cbrt(double a) Returns the cube root of a `double` value.
static double	ceil(double a) Returns the smallest (closest to negative infinity) `double` value that is greater than or equal to the argument and is equal to a mathematical integer.
static double	cos(double a) Returns the trigonometric cosine of an angle.
static double	cosh(double x) Returns the hyperbolic cosine of a `double` value.
static double	exp(double a) Returns Euler's number e raised to the power of a `double` value.
static double	expm1(double x) Returns e^x -1.
static double	floor(double a) Returns the largest (closest to positive infinity) `double` value that is less than or equal to the argument and is equal to a mathematical integer.
static double	hypot(double x, double y) Returns sqrt(x² +y²) without intermediate overflow or underflow.
static double	log(double a) Returns the natural logarithm (base e) of a `double` value.
static double	log10(double a) Returns the base 10 logarithm of a `double` value.
static double	log1p(double x) Returns the natural logarithm of the sum of the argument and 1.
static int	max(int a, int b) Returns the greater of two `int` values.
static double	max(double a, double b) Returns the greater of two `double` values.
static long	max(long a, long b) Returns the greater of two `long` values.
static float	max(float a, float b) Returns the greater of two `float` values.
static float	min(float a, float b) Returns the smaller of two `float` values.
static int	min(int a, int b) Returns the smaller of two `int` values.
static long	min(long a, long b) Returns the smaller of two `long` values.
static double	min(double a, double b) Returns the smaller of two `double` values.
static double	pow(double a, double b) Returns the value of the first argument raised to the power of the second argument.
static double	rint(double a) Returns the `double` value that is closest in value to the argument and is equal to a mathematical integer.
static int	round(float a) Returns the closest `int` to the argument.
static long	round(double a) Returns the closest `long` to the argument.
static double	signum(double d) Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.
static float	signum(float f) Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.
static double	sin(double a) Returns the trigonometric sine of an angle.
static double	sinh(double x) Returns the hyperbolic sine of a `double` value.
static double	sqrt(double a) Returns the correctly rounded positive square root of a `double` value.
static double	tan(double a) Returns the trigonometric tangent of an angle.
static double	tanh(double x) Returns the hyperbolic tangent of a `double` value.
static double	toDegrees(double angrad) Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
static double	toRadians(double angdeg) Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
static double	ulp(double d) Returns the size of an ulp of the argument.
static float	ulp(float f) Returns the size of an ulp of the argument.

[Expand]

Inherited Methods

From class java.lang.Object

boolean	equals(Object obj) Indicates whether some other object is "equal to" this one.
final Class<?>	getClass() Returns the runtime class of an object.
int	hashCode() Returns a hash code value for the object.
final void	notify() Wakes up a single thread that is waiting on this object's monitor.
final void	notifyAll() Wakes up all threads that are waiting on this object's monitor.
String	toString() Returns a string representation of the object.
final void	wait(long timeout, int nanos) Causes current thread to wait until another thread invokes the `notify()` method or the `notifyAll()` method for this object, or some other thread interrupts the current thread, or a certain amount of real time has elapsed.
final void	wait(long timeout) Causes current thread to wait until either another thread invokes the `notify()` method or the `notifyAll()` method for this object, or a specified amount of time has elapsed.
final void	wait() Causes current thread to wait until another thread invokes the `notify()` method or the `notifyAll()` method for this object.

Constants

public static final double E

The double value that is closer than any other to e, the base of the natural logarithms.

Constant Value: 2.718281828459045

public static final double PI

The double value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.

Constant Value: 3.141592653589793

Public Methods

public static double IEEEremainder (double f1, double f2)

Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to f1 - f2 × n, where n is the mathematical integer closest to the exact mathematical value of the quotient f1/f2, and if two mathematical integers are equally close to f1/f2, then n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:

If either argument is NaN, or the first argument is infinite, or the second argument is positive zero or negative zero, then the result is NaN.
If the first argument is finite and the second argument is infinite, then the result is the same as the first argument.

Parameters

f1	the dividend.
f2	the divisor.

Returns

the remainder when f1 is divided by f2.

public static long abs (long a)

Returns the absolute value of a long value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

Note that if the argument is equal to the value of MIN_VALUE, the most negative representable long value, the result is that same value, which is negative.

Parameters

a	the argument whose absolute value is to be determined

Returns

the absolute value of the argument.

public static int abs (int a)

Returns the absolute value of an int value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

Note that if the argument is equal to the value of MIN_VALUE, the most negative representable int value, the result is that same value, which is negative.

Parameters

a	the argument whose absolute value is to be determined

Returns

the absolute value of the argument.

public static float abs (float a)

Returns the absolute value of a float value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:

If the argument is positive zero or negative zero, the result is positive zero.
If the argument is infinite, the result is positive infinity.
If the argument is NaN, the result is NaN.

In other words, the result is the same as the value of the expression:

Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))

Parameters

a	the argument whose absolute value is to be determined

Returns

the absolute value of the argument.

public static double abs (double a)

Returns the absolute value of a double value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:

If the argument is positive zero or negative zero, the result is positive zero.
If the argument is infinite, the result is positive infinity.
If the argument is NaN, the result is NaN.

In other words, the result is the same as the value of the expression:

Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)

Parameters

a	the argument whose absolute value is to be determined

Returns

the absolute value of the argument.

public static double acos (double a)

Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi. Special case:

If the argument is NaN or its absolute value is greater than 1, then the result is NaN.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	the value whose arc cosine is to be returned.

Returns

the arc cosine of the argument.

public static double asin (double a)

Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:

If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	the value whose arc sine is to be returned.

Returns

the arc sine of the argument.

public static double atan (double a)

Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:

If the argument is NaN, then the result is NaN.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	the value whose arc tangent is to be returned.

Returns

the arc tangent of the argument.

public static double atan2 (double y, double x)

Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta). This method computes the phase theta by computing an arc tangent of y/x in the range of -pi to pi. Special cases:

If either argument is NaN, then the result is NaN.
If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.
If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is positive infinity, then the result is negative zero.
If the first argument is positive zero and the second argument is negative, or the first argument is positive and finite and the second argument is negative infinity, then the result is the double value closest to pi.
If the first argument is negative zero and the second argument is negative, or the first argument is negative and finite and the second argument is negative infinity, then the result is the double value closest to -pi.
If the first argument is positive and the second argument is positive zero or negative zero, or the first argument is positive infinity and the second argument is finite, then the result is the double value closest to pi/2.
If the first argument is negative and the second argument is positive zero or negative zero, or the first argument is negative infinity and the second argument is finite, then the result is the double value closest to -pi/2.
If both arguments are positive infinity, then the result is the double value closest to pi/4.
If the first argument is positive infinity and the second argument is negative infinity, then the result is the double value closest to 3*pi/4.
If the first argument is negative infinity and the second argument is positive infinity, then the result is the double value closest to -pi/4.
If both arguments are negative infinity, then the result is the double value closest to -3*pi/4.

The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.

Parameters

y	the ordinate coordinate
x	the abscissa coordinate

Returns

the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.

public static double cbrt (double a)

Returns the cube root of a double value. For positive finite x, cbrt(-x) == -cbrt(x); that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases:

If the argument is NaN, then the result is NaN.
If the argument is infinite, then the result is an infinity with the same sign as the argument.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result.

Parameters

a	a value.

Returns

the cube root of a.

public static double ceil (double a)

Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:

If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
If the argument value is less than zero but greater than -1.0, then the result is negative zero.

Note that the value of Math.ceil(x) is exactly the value of -Math.floor(-x).

Parameters

a	a value.

Returns

the smallest (closest to negative infinity) floating-point value that is greater than or equal to the argument and is equal to a mathematical integer.

public static double cos (double a)

Returns the trigonometric cosine of an angle. Special cases:

If the argument is NaN or an infinity, then the result is NaN.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	an angle, in radians.

Returns

the cosine of the argument.

public static double cosh (double x)

Returns the hyperbolic cosine of a double value. The hyperbolic cosine of x is defined to be (e^x + e^-x)/2 where e is Euler's number.

Special cases:

If the argument is NaN, then the result is NaN.
If the argument is infinite, then the result is positive infinity.
If the argument is zero, then the result is 1.0.

The computed result must be within 2.5 ulps of the exact result.

Parameters

x	The number whose hyperbolic cosine is to be returned.

Returns

The hyperbolic cosine of x.

public static double exp (double a)

Returns Euler's number e raised to the power of a double value. Special cases:

If the argument is NaN, the result is NaN.
If the argument is positive infinity, then the result is positive infinity.
If the argument is negative infinity, then the result is positive zero.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	the exponent to raise e to.

Returns

the value e^a, where e is the base of the natural logarithms.

public static double expm1 (double x)

Returns e^x -1. Note that for values of x near 0, the exact sum of expm1(x) + 1 is much closer to the true result of e^x than exp(x).

Special cases:

If the argument is NaN, the result is NaN.
If the argument is positive infinity, then the result is positive infinity.
If the argument is negative infinity, then the result is -1.0.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. The result of expm1 for any finite input must be greater than or equal to -1.0. Note that once the exact result of e^x - 1 is within 1/2 ulp of the limit value -1, -1.0 should be returned.

Parameters

x	the exponent to raise e to in the computation of e^x -1.

Returns

the value e^x - 1.

public static double floor (double a)

Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:

If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.

Parameters

a	a value.

Returns

the largest (closest to positive infinity) floating-point value that less than or equal to the argument and is equal to a mathematical integer.

public static double hypot (double x, double y)

Returns sqrt(x² +y²) without intermediate overflow or underflow.

Special cases:

If either argument is infinite, then the result is positive infinity.
If either argument is NaN and neither argument is infinite, then the result is NaN.

The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.

Parameters

x	a value
y	a value

Returns

sqrt(x² +y²) without intermediate overflow or underflow

public static double log (double a)

Returns the natural logarithm (base e) of a double value. Special cases:

If the argument is NaN or less than zero, then the result is NaN.
If the argument is positive infinity, then the result is positive infinity.
If the argument is positive zero or negative zero, then the result is negative infinity.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	a value

Returns

the value ln a, the natural logarithm of a.

public static double log10 (double a)

Returns the base 10 logarithm of a double value. Special cases:

If the argument is NaN or less than zero, then the result is NaN.
If the argument is positive infinity, then the result is positive infinity.
If the argument is positive zero or negative zero, then the result is negative infinity.
If the argument is equal to 10ⁿ for integer n, then the result is n.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	a value

Returns

the base 10 logarithm of a.

public static double log1p (double x)

Returns the natural logarithm of the sum of the argument and 1. Note that for small values x, the result of log1p(x) is much closer to the true result of ln(1 + x) than the floating-point evaluation of log(1.0+x).

Special cases:

If the argument is NaN or less than -1, then the result is NaN.
If the argument is positive infinity, then the result is positive infinity.
If the argument is negative one, then the result is negative infinity.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

x	a value

Returns

the value ln(x + 1), the natural log of x + 1

public static int max (int a, int b)

Returns the greater of two int values. That is, the result is the argument closer to the value of MAX_VALUE. If the arguments have the same value, the result is that same value.

Parameters

a	an argument.
b	another argument.

Returns

the larger of a and b.

public static double max (double a, double b)

Returns the greater of two double values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.

Parameters

a	an argument.
b	another argument.

Returns

the larger of a and b.

public static long max (long a, long b)

Returns the greater of two long values. That is, the result is the argument closer to the value of MAX_VALUE. If the arguments have the same value, the result is that same value.

Parameters

a	an argument.
b	another argument.

Returns

the larger of a and b.

public static float max (float a, float b)

Returns the greater of two float values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.

Parameters

a	an argument.
b	another argument.

Returns

the larger of a and b.

public static float min (float a, float b)

Returns the smaller of two float values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.

Parameters

a	an argument.
b	another argument.

Returns

the smaller of a and b.

public static int min (int a, int b)

Returns the smaller of two int values. That is, the result the argument closer to the value of MIN_VALUE. If the arguments have the same value, the result is that same value.

Parameters

a	an argument.
b	another argument.

Returns

the smaller of a and b.

public static long min (long a, long b)

Returns the smaller of two long values. That is, the result is the argument closer to the value of MIN_VALUE. If the arguments have the same value, the result is that same value.

Parameters

a	an argument.
b	another argument.

Returns

the smaller of a and b.

public static double min (double a, double b)

Returns the smaller of two double values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.

Parameters

a	an argument.
b	another argument.

Returns

the smaller of a and b.

public static double pow (double a, double b)

Returns the value of the first argument raised to the power of the second argument. Special cases:

If the second argument is positive or negative zero, then the result is 1.0.
If the second argument is 1.0, then the result is the same as the first argument.
If the second argument is NaN, then the result is NaN.
If the first argument is NaN and the second argument is nonzero, then the result is NaN.
If
- the absolute value of the first argument is greater than 1 and the second argument is positive infinity, or
- the absolute value of the first argument is less than 1 and the second argument is negative infinity,
then the result is positive infinity.
If
- the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
- the absolute value of the first argument is less than 1 and the second argument is positive infinity,
then the result is positive zero.
If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is NaN.
If
- the first argument is positive zero and the second argument is greater than zero, or
- the first argument is positive infinity and the second argument is less than zero,
then the result is positive zero.
If
- the first argument is positive zero and the second argument is less than zero, or
- the first argument is positive infinity and the second argument is greater than zero,
then the result is positive infinity.
If
- the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
- the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
then the result is positive zero.
If
- the first argument is negative zero and the second argument is a positive finite odd integer, or
- the first argument is negative infinity and the second argument is a negative finite odd integer,
then the result is negative zero.
If
- the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
- the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
then the result is positive infinity.
If
- the first argument is negative zero and the second argument is a negative finite odd integer, or
- the first argument is negative infinity and the second argument is a positive finite odd integer,
then the result is negative infinity.
If the first argument is finite and less than zero
- if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
- if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
- if the second argument is finite and not an integer, then the result is NaN.
If both arguments are integers, then the result is exactly equal to the mathematical result of raising the first argument to the power of the second argument if that result can in fact be represented exactly as a double value.

(In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil or, equivalently, a fixed point of the method floor. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	the base.
b	the exponent.

Returns

the value a^b.

public static double rint (double a)

Returns the double value that is closest in value to the argument and is equal to a mathematical integer. If two double values that are mathematical integers are equally close, the result is the integer value that is even. Special cases:

If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.

Parameters

a	a `double` value.

Returns

the closest floating-point value to a that is equal to a mathematical integer.

public static int round (float a)

Returns the closest int to the argument. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to type int. In other words, the result is equal to the value of the expression:

(int)Math.floor(a + 0.5f)

Special cases:

If the argument is NaN, the result is 0.
If the argument is negative infinity or any value less than or equal to the value of Integer.MIN_VALUE, the result is equal to the value of Integer.MIN_VALUE.
If the argument is positive infinity or any value greater than or equal to the value of Integer.MAX_VALUE, the result is equal to the value of Integer.MAX_VALUE.

Parameters

a	a floating-point value to be rounded to an integer.

Returns

the value of the argument rounded to the nearest int value.

public static long round (double a)

Returns the closest long to the argument. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to type long. In other words, the result is equal to the value of the expression:

(long)Math.floor(a + 0.5d)

Special cases:

If the argument is NaN, the result is 0.
If the argument is negative infinity or any value less than or equal to the value of Long.MIN_VALUE, the result is equal to the value of Long.MIN_VALUE.
If the argument is positive infinity or any value greater than or equal to the value of Long.MAX_VALUE, the result is equal to the value of Long.MAX_VALUE.

Parameters

a	a floating-point value to be rounded to a `long`.

Returns

the value of the argument rounded to the nearest long value.

public static double signum (double d)

Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.

Special Cases:

If the argument is NaN, then the result is NaN.
If the argument is positive zero or negative zero, then the result is the same as the argument.

Parameters

d	the floating-point value whose signum is to be returned

Returns

the signum function of the argument

public static float signum (float f)

Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.

Special Cases:

If the argument is NaN, then the result is NaN.
If the argument is positive zero or negative zero, then the result is the same as the argument.

Parameters

f	the floating-point value whose signum is to be returned

Returns

the signum function of the argument

public static double sin (double a)

Returns the trigonometric sine of an angle. Special cases:

If the argument is NaN or an infinity, then the result is NaN.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	an angle, in radians.

Returns

the sine of the argument.

public static double sinh (double x)

Returns the hyperbolic sine of a double value. The hyperbolic sine of x is defined to be (e^x - e^-x)/2 where e is Euler's number.

Special cases:

If the argument is NaN, then the result is NaN.
If the argument is infinite, then the result is an infinity with the same sign as the argument.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 2.5 ulps of the exact result.

Parameters

x	The number whose hyperbolic sine is to be returned.

Returns

The hyperbolic sine of x.

public static double sqrt (double a)

Returns the correctly rounded positive square root of a double value. Special cases:

If the argument is NaN or less than zero, then the result is NaN.
If the argument is positive infinity, then the result is positive infinity.
If the argument is positive zero or negative zero, then the result is the same as the argument.

Otherwise, the result is the double value closest to the true mathematical square root of the argument value.

Parameters

a	a value.

Returns

the positive square root of a. If the argument is NaN or less than zero, the result is NaN.

public static double tan (double a)

Returns the trigonometric tangent of an angle. Special cases:

If the argument is NaN or an infinity, then the result is NaN.
If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters

a	an angle, in radians.

Returns

the tangent of the argument.

public static double tanh (double x)

Returns the hyperbolic tangent of a double value. The hyperbolic tangent of x is defined to be (e^x - e^-x)/(e^x + e^-x), in other words, sinh(x)/cosh(x). Note that the absolute value of the exact tanh is always less than 1.

Special cases:

If the argument is NaN, then the result is NaN.
If the argument is zero, then the result is a zero with the same sign as the argument.
If the argument is positive infinity, then the result is +1.0.
If the argument is negative infinity, then the result is -1.0.

The computed result must be within 2.5 ulps of the exact result. The result of tanh for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±1.0 should be returned.

Parameters

x	The number whose hyperbolic tangent is to be returned.

Returns

The hyperbolic tangent of x.

public static double toDegrees (double angrad)

Converts an angle measured in radians to an approximately equivalent angle measured in degrees. The conversion from radians to degrees is generally inexact; users should not expect cos(toRadians(90.0)) to exactly equal 0.0.

Parameters

angrad	an angle, in radians

Returns

the measurement of the angle angrad in degrees.

public static double toRadians (double angdeg)

Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.

Parameters

angdeg	an angle, in degrees

Returns

the measurement of the angle angdeg in radians.

public static double ulp (double d)

Returns the size of an ulp of the argument. An ulp of a double value is the positive distance between this floating-point value and the double value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

Special Cases:

If the argument is NaN, then the result is NaN.
If the argument is positive or negative infinity, then the result is positive infinity.
If the argument is positive or negative zero, then the result is Double.MIN_VALUE.
If the argument is ±Double.MAX_VALUE, then the result is equal to 2⁹⁷¹.

Parameters

d	the floating-point value whose ulp is to be returned

Returns

the size of an ulp of the argument

public static float ulp (float f)

Returns the size of an ulp of the argument. An ulp of a float value is the positive distance between this floating-point value and the float value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

Special Cases:

If the argument is NaN, then the result is NaN.
If the argument is positive or negative infinity, then the result is positive infinity.
If the argument is positive or negative zero, then the result is Float.MIN_VALUE.
If the argument is ±Float.MAX_VALUE, then the result is equal to 2¹⁰⁴.

Parameters

f	the floating-point value whose ulp is to be returned

Returns

the size of an ulp of the argument

Interfaces

Classes

Annotations

Exceptions

Errors

Math

Class Overview

Summary

Constants

public static final double E

public static final double PI

Public Methods

public static double IEEEremainder (double f1, double f2)

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public static long abs (long a)

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public static int abs (int a)

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public static float abs (float a)

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public static double abs (double a)

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public static double acos (double a)

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public static double asin (double a)

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public static double atan (double a)

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public static double atan2 (double y, double x)

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public static double cbrt (double a)

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public static double ceil (double a)

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public static double cos (double a)

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public static double cosh (double x)

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public static double exp (double a)

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public static double expm1 (double x)

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public static double floor (double a)

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public static double hypot (double x, double y)

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public static double log (double a)

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public static double log10 (double a)

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public static double log1p (double x)

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public static int max (int a, int b)

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public static double max (double a, double b)

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public static long max (long a, long b)

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