# Class Math

• `java.lang.Object`
• `java.lang.Math`

`public final class Math`
`extends Object`

Helper class containing useful mathematical functions and constants.

Note that angles are specified in radians. Conversion functions are provided for your convenience.

Since:
1.0

## Field Summary

`static double`
`E`
The most accurate approximation to the mathematical constant e: `2.718281828459045`.
`static double`
`PI`
The most accurate approximation to the mathematical constant pi: `3.141592653589793`.

## Method Summary

`static double`
`IEEEremainder(double x, double y)`
Get the IEEE 754 floating point remainder on two numbers.
`static double`
`abs(double d)`
Take the absolute value of the argument.
`static float`
`abs(float f)`
Take the absolute value of the argument.
`static int`
`abs(int i)`
Take the absolute value of the argument.
`static long`
`abs(long l)`
Take the absolute value of the argument.
`static double`
`acos(double a)`
The trigonometric function arccos.
`static double`
`asin(double a)`
The trigonometric function arcsin.
`static double`
`atan(double a)`
The trigonometric function arcsin.
`static double`
`atan2(double y, double x)`
A special version of the trigonometric function arctan, for converting rectangular coordinates (x, y) to polar (r, theta).
`static double`
`cbrt(double a)`
Take a cube root.
`static double`
`ceil(double a)`
Take the nearest integer that is that is greater than or equal to the argument.
`static double`
`cos(double a)`
The trigonometric function cos.
`static double`
`cosh(double a)`
Returns the hyperbolic cosine of the given value.
`static double`
`exp(double a)`
Take ea.
`static double`
`expm1(double a)`
Returns `ea - 1. `
`static double`
`floor(double a)`
Take the nearest integer that is that is less than or equal to the argument.
`static double`
`hypot(double a, double b)`
Returns the hypotenuse, `a2 + b2`, without intermediate overflow or underflow.
`static double`
`log(double a)`
Take ln(a) (the natural log).
`static double`
`log10(double a)`
Returns the base 10 logarithm of the supplied value.
`static double`
`log1p(double a)`
Returns the natural logarithm resulting from the sum of the argument, `a` and 1.
`static double`
`max(double a, double b)`
Return whichever argument is larger.
`static float`
`max(float a, float b)`
Return whichever argument is larger.
`static int`
`max(int a, int b)`
Return whichever argument is larger.
`static long`
`max(long a, long b)`
Return whichever argument is larger.
`static double`
`min(double a, double b)`
Return whichever argument is smaller.
`static float`
`min(float a, float b)`
Return whichever argument is smaller.
`static int`
`min(int a, int b)`
Return whichever argument is smaller.
`static long`
`min(long a, long b)`
Return whichever argument is smaller.
`static double`
`pow(double a, double b)`
Raise a number to a power.
`static double`
`random()`
Get a random number.
`static double`
`rint(double a)`
Take the nearest integer to the argument.
`static long`
`round(double a)`
Take the nearest long to the argument.
`static int`
`round(float a)`
Take the nearest integer to the argument.
`static double`
`signum(double a)`
Returns the sign of the argument as follows:
• If `a` is greater than zero, the result is 1.0.
• If `a` is less than zero, the result is -1.0.
• If `a` is `NaN`, the result is `NaN`.
`static float`
`signum(float a)`
Returns the sign of the argument as follows:
• If `a` is greater than zero, the result is 1.0f.
• If `a` is less than zero, the result is -1.0f.
• If `a` is `NaN`, the result is `NaN`.
`static double`
`sin(double a)`
The trigonometric function sin.
`static double`
`sinh(double a)`
Returns the hyperbolic sine of the given value.
`static double`
`sqrt(double a)`
Take a square root.
`static double`
`tan(double a)`
The trigonometric function tan.
`static double`
`tanh(double a)`
Returns the hyperbolic tangent of the given value.
`static double`
`toDegrees(double rads)`
`static double`
`toRadians(double degrees)`
`static double`
`ulp(double d)`
Return the ulp for the given double argument.
`static float`
`ulp(float f)`
Return the ulp for the given float argument.

### Methods inherited from class java.lang.Object

`clone`, `equals`, `extends Object> getClass`, `finalize`, `hashCode`, `notify`, `notifyAll`, `toString`, `wait`, `wait`, `wait`

## Field Details

### E

`public static final double E`
The most accurate approximation to the mathematical constant e: `2.718281828459045`. Used in natural log and exp.
Field Value:
2.0

### PI

`public static final double PI`
The most accurate approximation to the mathematical constant pi: `3.141592653589793`. This is the ratio of a circle's diameter to its circumference.
Field Value:
3.0

## Method Details

### IEEEremainder

```public static double IEEEremainder(double x,
double y)```
Get the IEEE 754 floating point remainder on two numbers. This is the value of `x - y * n`, where n is the closest double to `x / y` (ties go to the even n); for a zero remainder, the sign is that of `x`. If either argument is NaN, the first argument is infinite, or the second argument is zero, the result is NaN; if x is finite but y is infinite, the result is x. This is accurate within the limits of doubles.
Parameters:
`x` - the dividend (the top half)
`y` - the divisor (the bottom half)
Returns:
the IEEE 754-defined floating point remainder of x/y

### abs

`public static double abs(double d)`
Take the absolute value of the argument. (Absolute value means make it positive.) This is equivalent, but faster than, calling ```Double.longBitsToDouble(Double.doubleToLongBits(a) << 1) >>> 1);```.
Parameters:
`d` - the number to take the absolute value of
Returns:
the absolute value

### abs

`public static float abs(float f)`
Take the absolute value of the argument. (Absolute value means make it positive.)

This is equivalent, but faster than, calling `Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))`.

Parameters:
`f` - the number to take the absolute value of
Returns:
the absolute value

### abs

`public static int abs(int i)`
Take the absolute value of the argument. (Absolute value means make it positive.)

Note that the the largest negative value (Integer.MIN_VALUE) cannot be made positive. In this case, because of the rules of negation in a computer, MIN_VALUE is what will be returned. This is a negative value. You have been warned.

Parameters:
`i` - the number to take the absolute value of
Returns:
the absolute value

### abs

`public static long abs(long l)`
Take the absolute value of the argument. (Absolute value means make it positive.)

Note that the the largest negative value (Long.MIN_VALUE) cannot be made positive. In this case, because of the rules of negation in a computer, MIN_VALUE is what will be returned. This is a negative value. You have been warned.

Parameters:
`l` - the number to take the absolute value of
Returns:
the absolute value

### acos

`public static double acos(double a)`
The trigonometric function arccos. The range of angles returned is 0 to pi radians (0 to 180 degrees). If the argument is NaN or its absolute value is beyond 1, the result is NaN. This is accurate within 1 ulp, and is semi-monotonic.
Parameters:
`a` - the cos to turn back into an angle
Returns:
arccos(a)

### asin

`public static double asin(double a)`
The trigonometric function arcsin. The range of angles returned is -pi/2 to pi/2 radians (-90 to 90 degrees). If the argument is NaN or its absolute value is beyond 1, the result is NaN; and the arcsine of 0 retains its sign. This is accurate within 1 ulp, and is semi-monotonic.
Parameters:
`a` - the sin to turn back into an angle
Returns:
arcsin(a)

### atan

`public static double atan(double a)`
The trigonometric function arcsin. The range of angles returned is -pi/2 to pi/2 radians (-90 to 90 degrees). If the argument is NaN, the result is NaN; and the arctangent of 0 retains its sign. This is accurate within 1 ulp, and is semi-monotonic.
Parameters:
`a` - the tan to turn back into an angle
Returns:
arcsin(a)

### atan2

```public static double atan2(double y,
double x)```
A special version of the trigonometric function arctan, for converting rectangular coordinates (x, y) to polar (r, theta). This computes the arctangent of x/y in the range of -pi to pi radians (-180 to 180 degrees). Special cases:
• If either argument is NaN, 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.

This is accurate within 2 ulps, and is semi-monotonic. To get r, use sqrt(x*x+y*y).

Parameters:
`y` - the y position
`x` - the x position
Returns:
theta in the conversion of (x, y) to (r, theta)

### cbrt

`public static double cbrt(double a)`
Take a cube root. If the argument is `NaN`, an infinity or zero, then the original value is returned. The returned result is within 1 ulp of the exact result. For a finite value, `x`, the cube root of `-x` is equal to the negation of the cube root of `x`.

For a square root, use `sqrt`. For other roots, use `pow(a, 1 / rootNumber)`.

Parameters:
`a` - the numeric argument
Returns:
the cube root of the argument
Since:
1.5

### ceil

`public static double ceil(double a)`
Take the nearest integer that is that is greater than or equal to the argument. If the argument is NaN, infinite, or zero, the result is the same; if the argument is between -1 and 0, the result is negative zero. Note that `Math.ceil(x) == -Math.floor(-x)`.
Parameters:
`a` - the value to act upon
Returns:
the nearest integer >= `a`

### cos

`public static double cos(double a)`
The trigonometric function cos. The cosine of NaN or infinity is NaN. This is accurate within 1 ulp, and is semi-monotonic.
Parameters:
`a` - the angle (in radians)
Returns:
cos(a)

### cosh

`public static double cosh(double a)`
Returns the hyperbolic cosine of the given value. For a value, `x`, the hyperbolic cosine is ```(ex + e-x)/2``` with `e` being Euler's number. The returned result is within 2.5 ulps of the exact result.

If the supplied value is `NaN`, then the original value is returned. For either infinity, positive infinity is returned. The hyperbolic cosine of zero is 1.0.

Parameters:
`a` - the numeric argument
Returns:
the hyperbolic cosine of `a`.
Since:
1.5

### exp

`public static double exp(double a)`
Take ea. The opposite of `log()`. If the argument is NaN, the result is NaN; if the argument is positive infinity, the result is positive infinity; and if the argument is negative infinity, the result is positive zero. This is accurate within 1 ulp, and is semi-monotonic.
Parameters:
`a` - the number to raise to the power
Returns:
the number raised to the power of e

### expm1

`public static double expm1(double a)`
Returns ```ea - 1. For values close to 0, the result of ````expm1(a) + 1` tend to be much closer to the exact result than simply `exp(x)`. The result is within 1 ulp of the exact result, and results are semi-monotonic. For finite inputs, the returned value is greater than or equal to -1.0. Once a result enters within half a ulp of this limit, the limit is returned.

For `NaN`, positive infinity and zero, the original value is returned. Negative infinity returns a result of -1.0 (the limit).

Parameters:
`a` - the numeric argument
Returns:
`ea - 1`
Since:
1.5

### floor

`public static double floor(double a)`
Take the nearest integer that is that is less than or equal to the argument. If the argument is NaN, infinite, or zero, the result is the same. Note that `Math.ceil(x) == -Math.floor(-x)`.
Parameters:
`a` - the value to act upon
Returns:
the nearest integer <= `a`

### hypot

```public static double hypot(double a,
double b)```
Returns the hypotenuse, `a2 + b2`, without intermediate overflow or underflow. The returned result is within 1 ulp of the exact result. If one parameter is held constant, then the result in the other parameter is semi-monotonic.

If either of the arguments is an infinity, then the returned result is positive infinity. Otherwise, if either argument is `NaN`, then `NaN` is returned.

Parameters:
`a` - the first parameter.
`b` - the second parameter.
Returns:
the hypotenuse matching the supplied parameters.
Since:
1.5

### log

`public static double log(double a)`
Take ln(a) (the natural log). The opposite of `exp()`. If the argument is NaN or negative, the result is NaN; if the argument is positive infinity, the result is positive infinity; and if the argument is either zero, the result is negative infinity. This is accurate within 1 ulp, and is semi-monotonic.

Note that the way to get logb(a) is to do this: `ln(a) / ln(b)`.

Parameters:
`a` - the number to take the natural log of
Returns:
the natural log of `a`

### log10

`public static double log10(double a)`
Returns the base 10 logarithm of the supplied value. The returned result is within 1 ulp of the exact result, and the results are semi-monotonic.

Arguments of either `NaN` or less than zero return `NaN`. An argument of positive infinity returns positive infinity. Negative infinity is returned if either positive or negative zero is supplied. Where the argument is the result of `10n`, then `n` is returned.

Parameters:
`a` - the numeric argument.
Returns:
the base 10 logarithm of `a`.
Since:
1.5

### log1p

`public static double log1p(double a)`
Returns the natural logarithm resulting from the sum of the argument, `a` and 1. For values close to 0, the result of `log1p(a)` tend to be much closer to the exact result than simply `log(1.0+a)`. The returned result is within 1 ulp of the exact result, and the results are semi-monotonic.

Arguments of either `NaN` or less than -1 return `NaN`. An argument of positive infinity or zero returns the original argument. Negative infinity is returned from an argument of -1.

Parameters:
`a` - the numeric argument.
Returns:
the natural logarithm of `a` + 1.
Since:
1.5

### max

```public static double max(double a,
double b)```
Return whichever argument is larger. If either argument is NaN, the result is NaN, and when comparing 0 and -0, 0 is always larger.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the larger of the two numbers

### max

```public static float max(float a,
float b)```
Return whichever argument is larger. If either argument is NaN, the result is NaN, and when comparing 0 and -0, 0 is always larger.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the larger of the two numbers

### max

```public static int max(int a,
int b)```
Return whichever argument is larger.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the larger of the two numbers

### max

```public static long max(long a,
long b)```
Return whichever argument is larger.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the larger of the two numbers

### min

```public static double min(double a,
double b)```
Return whichever argument is smaller. If either argument is NaN, the result is NaN, and when comparing 0 and -0, -0 is always smaller.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the smaller of the two numbers

### min

```public static float min(float a,
float b)```
Return whichever argument is smaller. If either argument is NaN, the result is NaN, and when comparing 0 and -0, -0 is always smaller.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the smaller of the two numbers

### min

```public static int min(int a,
int b)```
Return whichever argument is smaller.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the smaller of the two numbers

### min

```public static long min(long a,
long b)```
Return whichever argument is smaller.
Parameters:
`a` - the first number
`b` - a second number
Returns:
the smaller of the two numbers

### pow

```public static double pow(double a,
double b)```
Raise a number to a power. 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 less than zero and the second argument is a finite even integer, then 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 first argument is less than zero and the second argument is a finite odd integer, then 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 first argument is finite and less than zero and 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 a fixed point of the method `ceil(double)` or, equivalently, a fixed point of the method `floor(double)`. 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.) This is accurate within 1 ulp, and is semi-monotonic.

Parameters:
`a` - the number to raise
`b` - the power to raise it to
Returns:
ab

### random

`public static double random()`
Get a random number. This behaves like Random.nextDouble(), seeded by System.currentTimeMillis() when first called. In other words, the number is from a pseudorandom sequence, and lies in the range [+0.0, 1.0). This random sequence is only used by this method, and is threadsafe, although you may want your own random number generator if it is shared among threads.
Returns:
a random number

### rint

`public static double rint(double a)`
Take the nearest integer to the argument. If it is exactly between two integers, the even integer is taken. If the argument is NaN, infinite, or zero, the result is the same.
Parameters:
`a` - the value to act upon
Returns:
the nearest integer to `a`

### round

`public static long round(double a)`
Take the nearest long to the argument. This is equivalent to `(long) Math.floor(a + 0.5)`. If the argument is NaN, the result is 0; otherwise if the argument is outside the range of long, the result will be Long.MIN_VALUE or Long.MAX_VALUE, as appropriate.
Parameters:
`a` - the argument to round
Returns:
the nearest long to the argument

### round

`public static int round(float a)`
Take the nearest integer to the argument. This is equivalent to `(int) Math.floor(a + 0.5f)`. If the argument is NaN, the result is 0; otherwise if the argument is outside the range of int, the result will be Integer.MIN_VALUE or Integer.MAX_VALUE, as appropriate.
Parameters:
`a` - the argument to round
Returns:
the nearest integer to the argument

### signum

`public static double signum(double a)`
Returns the sign of the argument as follows:
• If `a` is greater than zero, the result is 1.0.
• If `a` is less than zero, the result is -1.0.
• If `a` is `NaN`, the result is `NaN`.
• If `a` is positive or negative zero, the result is the same.
Parameters:
`a` - the numeric argument.
Returns:
the sign of the argument.
Since:
1.5.

### signum

`public static float signum(float a)`
Returns the sign of the argument as follows:
• If `a` is greater than zero, the result is 1.0f.
• If `a` is less than zero, the result is -1.0f.
• If `a` is `NaN`, the result is `NaN`.
• If `a` is positive or negative zero, the result is the same.
Parameters:
`a` - the numeric argument.
Returns:
the sign of the argument.
Since:
1.5.

### sin

`public static double sin(double a)`
The trigonometric function sin. The sine of NaN or infinity is NaN, and the sine of 0 retains its sign. This is accurate within 1 ulp, and is semi-monotonic.
Parameters:
`a` - the angle (in radians)
Returns:
sin(a)

### sinh

`public static double sinh(double a)`
Returns the hyperbolic sine of the given value. For a value, `x`, the hyperbolic sine is ```(ex - e-x)/2``` with `e` being Euler's number. The returned result is within 2.5 ulps of the exact result.

If the supplied value is `NaN`, an infinity or a zero, then the original value is returned.

Parameters:
`a` - the numeric argument
Returns:
the hyperbolic sine of `a`.
Since:
1.5

### sqrt

`public static double sqrt(double a)`
Take a square root. If the argument is NaN or negative, the result is NaN; if the argument is positive infinity, the result is positive infinity; and if the result is either zero, the result is the same. This is accurate within the limits of doubles.

For a cube root, use `cbrt`. For other roots, use `pow(a, 1 / rootNumber)`.

Parameters:
`a` - the numeric argument
Returns:
the square root of the argument

### tan

`public static double tan(double a)`
The trigonometric function tan. The tangent of NaN or infinity is NaN, and the tangent of 0 retains its sign. This is accurate within 1 ulp, and is semi-monotonic.
Parameters:
`a` - the angle (in radians)
Returns:
tan(a)

### tanh

`public static double tanh(double a)`
Returns the hyperbolic tangent of the given value. For a value, `x`, the hyperbolic tangent is ```(ex - e-x)/(ex + e-x)``` (i.e. `sinh(a)/cosh(a)`) with `e` being Euler's number. The returned result is within 2.5 ulps of the exact result. The absolute value of the exact result is always less than 1. Computed results are thus less than or equal to 1 for finite arguments, with results within half a ulp of either positive or negative 1 returning the appropriate limit value (i.e. as if the argument was an infinity).

If the supplied value is `NaN` or zero, then the original value is returned. Positive infinity returns +1.0 and negative infinity returns -1.0.

Parameters:
`a` - the numeric argument
Returns:
the hyperbolic tangent of `a`.
Since:
1.5

### toDegrees

`public static double toDegrees(double rads)`
Convert from radians to degrees. The formula for this is degrees = radians * (180/pi); however it is not always exact given the limitations of floating point numbers.
Parameters:
`rads` - an angle in radians
Returns:
the angle in degrees
Since:
1.2

`public static double toRadians(double degrees)`
Convert from degrees to radians. The formula for this is radians = degrees * (pi/180); however it is not always exact given the limitations of floating point numbers.
Parameters:
`degrees` - an angle in degrees
Returns:
Since:
1.2

### ulp

`public static double ulp(double d)`
Return the ulp for the given double argument. The ulp is the difference between the argument and the next larger double. Note that the sign of the double argument is ignored, that is, ulp(x) == ulp(-x). If the argument is a NaN, then NaN is returned. If the argument is an infinity, then +Inf is returned. If the argument is zero (either positive or negative), then `Double.MIN_VALUE` is returned.
Parameters:
`d` - the double whose ulp should be returned
Returns:
the difference between the argument and the next larger double
Since:
1.5

### ulp

`public static float ulp(float f)`
Return the ulp for the given float argument. The ulp is the difference between the argument and the next larger float. Note that the sign of the float argument is ignored, that is, ulp(x) == ulp(-x). If the argument is a NaN, then NaN is returned. If the argument is an infinity, then +Inf is returned. If the argument is zero (either positive or negative), then `Float.MIN_VALUE` is returned.
Parameters:
`f` - the float whose ulp should be returned
Returns:
the difference between the argument and the next larger float
Since:
1.5