java.lang.Object
- org.apache.commons.math.util.MathUtils

```
public final class MathUtils
extends java.lang.Object
```
Some useful additions to the built-in functions in Math.

Version:

$Revision: 1073472 $ $Date: 2011-02-22 20:49:07 +0100 (mar. 22 févr. 2011) $

Nested Class Summary

Nested Classes
Modifier and Type Class Description

static class MathUtils.OrderDirection
Specification of ordering direction.

Field Summary

Fields
Modifier and Type	Field	Description
`static double`	`EPSILON`	Smallest positive number such that 1 - EPSILON is not numerically equal to 1.
`static double`	`SAFE_MIN`	Safe minimum, such that 1 / SAFE_MIN does not overflow.
`static double`	`TWO_PI`	2 π.

Method Summary

All Methods Static Methods Concrete Methods Deprecated Methods
Modifier and Type	Method	Description
`static int`	`addAndCheck(int x, int y)`	Add two integers, checking for overflow.
`static long`	`addAndCheck(long a, long b)`	Add two long integers, checking for overflow.
`static long`	`binomialCoefficient(int n, int k)`	Returns an exact representation of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set.
`static double`	`binomialCoefficientDouble(int n, int k)`	Returns a `double` representation of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set.
`static double`	`binomialCoefficientLog(int n, int k)`	Returns the natural `log` of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set.
`static void`	`checkOrder(double[] val)`	Checks that the given array is sorted in strictly increasing order.
`static void`	`checkOrder(double[] val, int dir, boolean strict)`	Deprecated. as of 2.2 (please use the new `checkOrder` method).
`static void`	`checkOrder(double[] val, MathUtils.OrderDirection dir, boolean strict)`	Checks that the given array is sorted.
`static int`	`compareTo(double x, double y, double eps)`	Compares two numbers given some amount of allowed error.
`static double`	`cosh(double x)`	Returns the hyperbolic cosine of x.
`static double`	`distance(double[] p1, double[] p2)`	Calculates the L₂ (Euclidean) distance between two points.
`static double`	`distance(int[] p1, int[] p2)`	Calculates the L₂ (Euclidean) distance between two points.
`static double`	`distance1(double[] p1, double[] p2)`	Calculates the L₁ (sum of abs) distance between two points.
`static int`	`distance1(int[] p1, int[] p2)`	Calculates the L₁ (sum of abs) distance between two points.
`static double`	`distanceInf(double[] p1, double[] p2)`	Calculates the L_∞ (max of abs) distance between two points.
`static int`	`distanceInf(int[] p1, int[] p2)`	Calculates the L_∞ (max of abs) distance between two points.
`static boolean`	`equals(double[] x, double[] y)`	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by `equals(double,double)`.
`static boolean`	`equals(double x, double y)`	Returns true iff both arguments are NaN or neither is NaN and they are equal
`static boolean`	`equals(double x, double y, double eps)`	Returns true if both arguments are equal or within the range of allowed error (inclusive).
`static boolean`	`equals(double x, double y, int maxUlps)`	Returns true if both arguments are equal or within the range of allowed error (inclusive).
`static boolean`	`equals(float[] x, float[] y)`	Deprecated. as of 2.2 this method considers that `NaN == NaN`.
`static boolean`	`equals(float x, float y)`	Deprecated. as of 2.2 his method considers that `NaN == NaN`.
`static boolean`	`equals(float x, float y, float eps)`	Returns true if both arguments are equal or within the range of allowed error (inclusive).
`static boolean`	`equals(float x, float y, int maxUlps)`	Returns true if both arguments are equal or within the range of allowed error (inclusive).
`static boolean`	`equalsIncludingNaN(double[] x, double[] y)`	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by `equalsIncludingNaN(double,double)`.
`static boolean`	`equalsIncludingNaN(double x, double y)`	Returns true if both arguments are NaN or neither is NaN and they are equal as defined by `equals(x, y, 1)`.
`static boolean`	`equalsIncludingNaN(double x, double y, double eps)`	Returns true if both arguments are NaN or are equal or within the range of allowed error (inclusive).
`static boolean`	`equalsIncludingNaN(double x, double y, int maxUlps)`	Returns true if both arguments are NaN or if they are equal as defined by `equals(x, y, maxUlps`.
`static boolean`	`equalsIncludingNaN(float[] x, float[] y)`	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by `equalsIncludingNaN(float,float)`.
`static boolean`	`equalsIncludingNaN(float x, float y)`	Returns true if both arguments are NaN or neither is NaN and they are equal as defined by `equals(x, y, 1)`.
`static boolean`	`equalsIncludingNaN(float x, float y, float eps)`	Returns true if both arguments are NaN or are equal or within the range of allowed error (inclusive).
`static boolean`	`equalsIncludingNaN(float x, float y, int maxUlps)`	Returns true if both arguments are NaN or if they are equal as defined by `equals(x, y, maxUlps)`.
`static long`	`factorial(int n)`	Returns n!.
`static double`	`factorialDouble(int n)`	Returns n!.
`static double`	`factorialLog(int n)`	Returns the natural logarithm of n!.
`static int`	`gcd(int p, int q)`	Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations.
`static long`	`gcd(long p, long q)`	Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations.
`static int`	`hash(double value)`	Returns an integer hash code representing the given double value.
`static int`	`hash(double[] value)`	Returns an integer hash code representing the given double array.
`static byte`	`indicator(byte x)`	For a byte value x, this method returns (byte)(+1) if x >= 0 and (byte)(-1) if x < 0.
`static double`	`indicator(double x)`	For a double precision value x, this method returns +1.0 if x >= 0 and -1.0 if x < 0.
`static float`	`indicator(float x)`	For a float value x, this method returns +1.0F if x >= 0 and -1.0F if x < 0.
`static int`	`indicator(int x)`	For an int value x, this method returns +1 if x >= 0 and -1 if x < 0.
`static long`	`indicator(long x)`	For a long value x, this method returns +1L if x >= 0 and -1L if x < 0.
`static short`	`indicator(short x)`	For a short value x, this method returns (short)(+1) if x >= 0 and (short)(-1) if x < 0.
`static int`	`lcm(int a, int b)`	Returns the least common multiple of the absolute value of two numbers, using the formula `lcm(a,b) = (a / gcd(a,b)) * b`.
`static long`	`lcm(long a, long b)`	Returns the least common multiple of the absolute value of two numbers, using the formula `lcm(a,b) = (a / gcd(a,b)) * b`.
`static double`	`log(double base, double x)`	Returns the logarithm for base `b` of `x`.
`static int`	`mulAndCheck(int x, int y)`	Multiply two integers, checking for overflow.
`static long`	`mulAndCheck(long a, long b)`	Multiply two long integers, checking for overflow.
`static double`	`nextAfter(double d, double direction)`	Deprecated. as of 2.2, replaced by `FastMath.nextAfter(double, double)` which handles Infinities differently, and returns direction if d and direction compare equal.
`static double`	`normalizeAngle(double a, double center)`	Normalize an angle in a 2&pi wide interval around a center value.
`static double[]`	`normalizeArray(double[] values, double normalizedSum)`	Normalizes an array to make it sum to a specified value.
`static int`	`pow(int k, int e)`	Raise an int to an int power.
`static int`	`pow(int k, long e)`	Raise an int to a long power.
`static long`	`pow(long k, int e)`	Raise a long to an int power.
`static long`	`pow(long k, long e)`	Raise a long to a long power.
`static java.math.BigInteger`	`pow(java.math.BigInteger k, int e)`	Raise a BigInteger to an int power.
`static java.math.BigInteger`	`pow(java.math.BigInteger k, long e)`	Raise a BigInteger to a long power.
`static java.math.BigInteger`	`pow(java.math.BigInteger k, java.math.BigInteger e)`	Raise a BigInteger to a BigInteger power.
`static double`	`round(double x, int scale)`	Round the given value to the specified number of decimal places.
`static double`	`round(double x, int scale, int roundingMethod)`	Round the given value to the specified number of decimal places.
`static float`	`round(float x, int scale)`	Round the given value to the specified number of decimal places.
`static float`	`round(float x, int scale, int roundingMethod)`	Round the given value to the specified number of decimal places.
`static double`	`safeNorm(double[] v)`	Returns the Cartesian norm (2-norm), handling both overflow and underflow.
`static double`	`scalb(double d, int scaleFactor)`	Deprecated. as of 2.2, replaced by `FastMath.scalb(double, int)`
`static byte`	`sign(byte x)`	Returns the sign for byte value `x`.
`static double`	`sign(double x)`	Returns the sign for double precision `x`.
`static float`	`sign(float x)`	Returns the sign for float value `x`.
`static int`	`sign(int x)`	Returns the sign for int value `x`.
`static long`	`sign(long x)`	Returns the sign for long value `x`.
`static short`	`sign(short x)`	Returns the sign for short value `x`.
`static double`	`sinh(double x)`	Returns the hyperbolic sine of x.
`static int`	`subAndCheck(int x, int y)`	Subtract two integers, checking for overflow.
`static long`	`subAndCheck(long a, long b)`	Subtract two long integers, checking for overflow.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail
- EPSILON
```
public static final double EPSILON
```
  Smallest positive number such that 1 - EPSILON is not numerically equal to 1.
  
  See Also:
  
  Constant Field Values
- SAFE_MIN
```
public static final double SAFE_MIN
```
  Safe minimum, such that 1 / SAFE_MIN does not overflow.
  In IEEE 754 arithmetic, this is also the smallest normalized number 2^-1022.
  
  See Also:
  
  Constant Field Values
- TWO_PI
```
public static final double TWO_PI
```
  2 π.
  
  Since:
  
  2.1
  
  See Also:
  
  Constant Field Values

Method Detail

addAndCheck
```
public static int addAndCheck(int x,
                              int y)
```
Add two integers, checking for overflow.

Parameters:

x - an addend

y - an addend

Returns:

the sum x+y

Throws:

java.lang.ArithmeticException - if the result can not be represented as an int

Since:

1.1

addAndCheck
```
public static long addAndCheck(long a,
                               long b)
```
Add two long integers, checking for overflow.

Parameters:

a - an addend

b - an addend

Returns:

the sum a+b

Throws:

java.lang.ArithmeticException - if the result can not be represented as an long

Since:

1.2

binomialCoefficient
```
public static long binomialCoefficient(int n,
                                       int k)
```
Returns an exact representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.
Preconditions:
- 0 <= k <= n (otherwise IllegalArgumentException is thrown)
- The result is small enough to fit into a long. The largest value of n for which all coefficients are < Long.MAX_VALUE is 66. If the computed value exceeds Long.MAX_VALUE an ArithMeticException is thrown.
Parameters:

n - the size of the set

k - the size of the subsets to be counted

Returns:

n choose k

Throws:

java.lang.IllegalArgumentException - if preconditions are not met.

java.lang.ArithmeticException - if the result is too large to be represented by a long integer.

binomialCoefficientDouble
```
public static double binomialCoefficientDouble(int n,
                                               int k)
```
Returns a double representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.
Preconditions:
- 0 <= k <= n (otherwise IllegalArgumentException is thrown)
- The result is small enough to fit into a double. The largest value of n for which all coefficients are < Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned
Parameters:

n - the size of the set

k - the size of the subsets to be counted

Returns:

n choose k

Throws:

java.lang.IllegalArgumentException - if preconditions are not met.

binomialCoefficientLog
```
public static double binomialCoefficientLog(int n,
                                            int k)
```
Returns the natural log of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.
Preconditions:
- 0 <= k <= n (otherwise IllegalArgumentException is thrown)
Parameters:

n - the size of the set

k - the size of the subsets to be counted

Returns:

n choose k

Throws:

java.lang.IllegalArgumentException - if preconditions are not met.

compareTo
```
public static int compareTo(double x,
                            double y,
                            double eps)
```
Compares two numbers given some amount of allowed error.
Parameters:

x - the first number

y - the second number

eps - the amount of error to allow when checking for equality

Returns:
- 0 if equals(x, y, eps)
- < 0 if !equals(x, y, eps) && x < y
- > 0 if !equals(x, y, eps) && x > y

cosh
```
public static double cosh(double x)
```
Returns the hyperbolic cosine of x.

Parameters:

x - double value for which to find the hyperbolic cosine

Returns:

hyperbolic cosine of x

equals
```
@Deprecated
public static boolean equals(float x,
                             float y)
```
Deprecated.
as of 2.2 his method considers that NaN == NaN. In release 3.0, the semantics will change in order to comply with IEEE754 where it is specified that NaN != NaN. New methods have been added for those cases wher the old semantics is useful (see e.g. equalsIncludingNaN.

Returns true iff they are strictly equal.

Parameters:

x - first value

y - second value

Returns:

true if the values are equal.

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(float x,
                                         float y)
```
Returns true if both arguments are NaN or neither is NaN and they are equal as defined by equals(x, y, 1).

Parameters:

x - first value

y - second value

Returns:

true if the values are equal or both are NaN.

Since:

2.2

equals
```
public static boolean equals(float x,
                             float y,
                             float eps)
```
Returns true if both arguments are equal or within the range of allowed error (inclusive).

Parameters:

x - first value

y - second value

eps - the amount of absolute error to allow.

Returns:

true if the values are equal or within range of each other.

Since:

2.2

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(float x,
                                         float y,
                                         float eps)
```
Returns true if both arguments are NaN or are equal or within the range of allowed error (inclusive).

Parameters:

x - first value

y - second value

eps - the amount of absolute error to allow.

Returns:

true if the values are equal or within range of each other, or both are NaN.

Since:

2.2

equals
```
public static boolean equals(float x,
                             float y,
                             int maxUlps)
```
Returns true if both arguments are equal or within the range of allowed error (inclusive). Two float numbers are considered equal if there are (maxUlps - 1) (or fewer) floating point numbers between them, i.e. two adjacent floating point numbers are considered equal. Adapted from Bruce Dawson

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if there are fewer than maxUlps floating point values between x and y.

Since:

2.2

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(float x,
                                         float y,
                                         int maxUlps)
```
Returns true if both arguments are NaN or if they are equal as defined by equals(x, y, maxUlps).

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if both arguments are NaN or if there are less than maxUlps floating point values between x and y.

Since:

2.2

equals
```
@Deprecated
public static boolean equals(float[] x,
                             float[] y)
```
Deprecated.
as of 2.2 this method considers that NaN == NaN. In release 3.0, the semantics will change in order to comply with IEEE754 where it is specified that NaN != NaN. New methods have been added for those cases where the old semantics is useful (see e.g. equalsIncludingNaN.

Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by equals(float,float).

Parameters:

x - first array

y - second array

Returns:

true if the values are both null or have same dimension and equal elements.

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(float[] x,
                                         float[] y)
```
Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by equalsIncludingNaN(float,float).

Parameters:

x - first array

y - second array

Returns:

true if the values are both null or have same dimension and equal elements

Since:

2.2

equals
```
public static boolean equals(double x,
                             double y)
```
Returns true iff both arguments are NaN or neither is NaN and they are equal
This method considers that NaN == NaN. In release 3.0, the semantics will change in order to comply with IEEE754 where it is specified that NaN != NaN. New methods have been added for those cases where the old semantics (w.r.t. NaN) is useful (see e.g. equalsIncludingNaN.

Parameters:

x - first value

y - second value

Returns:

true if the values are equal.

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(double x,
                                         double y)
```
Returns true if both arguments are NaN or neither is NaN and they are equal as defined by equals(x, y, 1).

Parameters:

x - first value

y - second value

Returns:

true if the values are equal or both are NaN.

Since:

2.2

equals
```
public static boolean equals(double x,
                             double y,
                             double eps)
```
Returns true if both arguments are equal or within the range of allowed error (inclusive).
Two NaNs are considered equals, as are two infinities with same sign.

This method considers that NaN == NaN. In release 3.0, the semantics will change in order to comply with IEEE754 where it is specified that NaN != NaN. New methods have been added for those cases where the old semantics (w.r.t. NaN) is useful (see e.g. equalsIncludingNaN.

Parameters:

x - first value

y - second value

eps - the amount of absolute error to allow.

Returns:

true if the values are equal or within range of each other.

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(double x,
                                         double y,
                                         double eps)
```
Returns true if both arguments are NaN or are equal or within the range of allowed error (inclusive).

Parameters:

x - first value

y - second value

eps - the amount of absolute error to allow.

Returns:

true if the values are equal or within range of each other, or both are NaN.

Since:

2.2

equals
```
public static boolean equals(double x,
                             double y,
                             int maxUlps)
```
Returns true if both arguments are equal or within the range of allowed error (inclusive). Two float numbers are considered equal if there are (maxUlps - 1) (or fewer) floating point numbers between them, i.e. two adjacent floating point numbers are considered equal. Adapted from Bruce Dawson
This method considers that NaN == NaN. In release 3.0, the semantics will change in order to comply with IEEE754 where it is specified that NaN != NaN. New methods have been added for those cases where the old semantics (w.r.t. NaN) is useful (see e.g. equalsIncludingNaN.

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if there are fewer than maxUlps floating point values between x and y.

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(double x,
                                         double y,
                                         int maxUlps)
```
Returns true if both arguments are NaN or if they are equal as defined by equals(x, y, maxUlps.

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if both arguments are NaN or if there are less than maxUlps floating point values between x and y.

Since:

2.2

equals
```
public static boolean equals(double[] x,
                             double[] y)
```
Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by equals(double,double).
This method considers that NaN == NaN. In release 3.0, the semantics will change in order to comply with IEEE754 where it is specified that NaN != NaN. New methods have been added for those cases wher the old semantics is useful (see e.g. equalsIncludingNaN.

Parameters:

x - first array

y - second array

Returns:

true if the values are both null or have same dimension and equal elements.

equalsIncludingNaN
```
public static boolean equalsIncludingNaN(double[] x,
                                         double[] y)
```
Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by equalsIncludingNaN(double,double).

Parameters:

x - first array

y - second array

Returns:

true if the values are both null or have same dimension and equal elements

Since:

2.2

factorial
```
public static long factorial(int n)
```
Returns n!. Shorthand for n Factorial, the product of the numbers 1,...,n.
Preconditions:
- n >= 0 (otherwise IllegalArgumentException is thrown)
- The result is small enough to fit into a long. The largest value of n for which n! < Long.MAX_VALUE is 20. If the computed value exceeds Long.MAX_VALUE an ArithMeticException is thrown.
Parameters:

n - argument

Returns:

n!

Throws:

java.lang.ArithmeticException - if the result is too large to be represented by a long integer.

java.lang.IllegalArgumentException - if n < 0

factorialDouble
```
public static double factorialDouble(int n)
```
Returns n!. Shorthand for n Factorial, the product of the numbers 1,...,n as a double.
Preconditions:
- n >= 0 (otherwise IllegalArgumentException is thrown)
- The result is small enough to fit into a double. The largest value of n for which n! < Double.MAX_VALUE is 170. If the computed value exceeds Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned
Parameters:

n - argument

Returns:

n!

Throws:

java.lang.IllegalArgumentException - if n < 0

factorialLog
```
public static double factorialLog(int n)
```
Returns the natural logarithm of n!.
Preconditions:
- n >= 0 (otherwise IllegalArgumentException is thrown)
Parameters:

n - argument

Returns:

n!

Throws:

java.lang.IllegalArgumentException - if preconditions are not met.

gcd
```
public static int gcd(int p,
                      int q)
```
Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef Stein (1961).
Special cases:
- The invocations gcd(Integer.MIN_VALUE, Integer.MIN_VALUE), gcd(Integer.MIN_VALUE, 0) and gcd(0, Integer.MIN_VALUE) throw an ArithmeticException, because the result would be 2^31, which is too large for an int value.
- The result of gcd(x, x), gcd(0, x) and gcd(x, 0) is the absolute value of x, except for the special cases above.
- The invocation gcd(0, 0) is the only one which returns 0.
Parameters:

p - any number

q - any number

Returns:

the greatest common divisor, never negative

Throws:

java.lang.ArithmeticException - if the result cannot be represented as a nonnegative int value

Since:

1.1

gcd
```
public static long gcd(long p,
                       long q)
```
Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef Stein (1961).
Special cases:
- The invocations gcd(Long.MIN_VALUE, Long.MIN_VALUE), gcd(Long.MIN_VALUE, 0L) and gcd(0L, Long.MIN_VALUE) throw an ArithmeticException, because the result would be 2^63, which is too large for a long value.
- The result of gcd(x, x), gcd(0L, x) and gcd(x, 0L) is the absolute value of x, except for the special cases above.
- The invocation gcd(0L, 0L) is the only one which returns 0L.
Parameters:

p - any number

q - any number

Returns:

the greatest common divisor, never negative

Throws:

java.lang.ArithmeticException - if the result cannot be represented as a nonnegative long value

Since:

2.1

hash
```
public static int hash(double value)
```
Returns an integer hash code representing the given double value.

Parameters:

value - the value to be hashed

Returns:

the hash code

hash
```
public static int hash(double[] value)
```
Returns an integer hash code representing the given double array.

Parameters:

value - the value to be hashed (may be null)

Returns:

the hash code

Since:

1.2

indicator
```
public static byte indicator(byte x)
```
For a byte value x, this method returns (byte)(+1) if x >= 0 and (byte)(-1) if x < 0.

Parameters:

x - the value, a byte

Returns:

(byte)(+1) or (byte)(-1), depending on the sign of x

indicator
```
public static double indicator(double x)
```
For a double precision value x, this method returns +1.0 if x >= 0 and -1.0 if x < 0. Returns NaN if x is NaN.

Parameters:

x - the value, a double

Returns:

+1.0 or -1.0, depending on the sign of x

indicator
```
public static float indicator(float x)
```
For a float value x, this method returns +1.0F if x >= 0 and -1.0F if x < 0. Returns NaN if x is NaN.

Parameters:

x - the value, a float

Returns:

+1.0F or -1.0F, depending on the sign of x

indicator
```
public static int indicator(int x)
```
For an int value x, this method returns +1 if x >= 0 and -1 if x < 0.

Parameters:

x - the value, an int

Returns:

+1 or -1, depending on the sign of x

indicator
```
public static long indicator(long x)
```
For a long value x, this method returns +1L if x >= 0 and -1L if x < 0.

Parameters:

x - the value, a long

Returns:

+1L or -1L, depending on the sign of x

indicator
```
public static short indicator(short x)
```
For a short value x, this method returns (short)(+1) if x >= 0 and (short)(-1) if x < 0.

Parameters:

x - the value, a short

Returns:

(short)(+1) or (short)(-1), depending on the sign of x

lcm
```
public static int lcm(int a,
                      int b)
```
Returns the least common multiple of the absolute value of two numbers, using the formula lcm(a,b) = (a / gcd(a,b)) * b.
Special cases:
- The invocations lcm(Integer.MIN_VALUE, n) and lcm(n, Integer.MIN_VALUE), where abs(n) is a power of 2, throw an ArithmeticException, because the result would be 2^31, which is too large for an int value.
- The result of lcm(0, x) and lcm(x, 0) is 0 for any x.
Parameters:

a - any number

b - any number

Returns:

the least common multiple, never negative

Throws:

java.lang.ArithmeticException - if the result cannot be represented as a nonnegative int value

Since:

1.1

lcm
```
public static long lcm(long a,
                       long b)
```
Returns the least common multiple of the absolute value of two numbers, using the formula lcm(a,b) = (a / gcd(a,b)) * b.
Special cases:
- The invocations lcm(Long.MIN_VALUE, n) and lcm(n, Long.MIN_VALUE), where abs(n) is a power of 2, throw an ArithmeticException, because the result would be 2^63, which is too large for an int value.
- The result of lcm(0L, x) and lcm(x, 0L) is 0L for any x.
Parameters:

a - any number

b - any number

Returns:

the least common multiple, never negative

Throws:

java.lang.ArithmeticException - if the result cannot be represented as a nonnegative long value

Since:

2.1

log
```
public static double log(double base,
                         double x)
```
Returns the logarithm for base b of x.

Returns NaN if either argument is negative. If base is 0 and x is positive, 0 is returned. If base is positive and x is 0, Double.NEGATIVE_INFINITY is returned. If both arguments are 0, the result is NaN.
Parameters: base - the base of the logarithm, must be greater than 0 x - argument, must be greater than 0 Returns: the value of the logarithm - the number y such that base^y = x. Since: 1.2







mulAndCheck
public static int mulAndCheck(int x,
                              int y)
Multiply two integers, checking for overflow.

Parameters:
x - a factor
y - a factor
Returns:
the product x*y
Throws:
java.lang.ArithmeticException - if the result can not be represented as an
         int
Since:
1.1








mulAndCheck
public static long mulAndCheck(long a,
                               long b)
Multiply two long integers, checking for overflow.

Parameters:
a - first value
b - second value
Returns:
the product a * b
Throws:
java.lang.ArithmeticException - if the result can not be represented as an
         long
Since:
1.2








nextAfter
@Deprecated
public static double nextAfter(double d,
                               double direction)
Deprecated.
as of 2.2, replaced by FastMath.nextAfter(double, double)
 which handles Infinities differently, and returns direction if d and direction compare equal.

Get the next machine representable number after a number, moving
 in the direction of another number.
 
 If direction is greater than or equal tod,
 the smallest machine representable number strictly greater than
 d is returned; otherwise the largest representable number
 strictly less than d is returned.
 
 If d is NaN or Infinite, it is returned unchanged.

Parameters:
d - base number
direction - (the only important thing is whether
 direction is greater or smaller than d)
Returns:
the next machine representable number in the specified direction
Since:
1.2








scalb
@Deprecated
public static double scalb(double d,
                           int scaleFactor)
Deprecated.
as of 2.2, replaced by FastMath.scalb(double, int)

Scale a number by 2^scaleFactor.
 If d is 0 or NaN or Infinite, it is returned unchanged.

Parameters:
d - base number
scaleFactor - power of two by which d should be multiplied
Returns:
d × 2^scaleFactor
Since:
2.0








normalizeAngle
public static double normalizeAngle(double a,
                                    double center)
Normalize an angle in a 2&pi wide interval around a center value.
 This method has three main uses:
 
   normalize an angle between 0 and 2π:

       a = MathUtils.normalizeAngle(a, FastMath.PI);
   normalize an angle between -π and +π

       a = MathUtils.normalizeAngle(a, 0.0);
   compute the angle between two defining angular positions:

       angle = MathUtils.normalizeAngle(end, start) - start;
 
 Note that due to numerical accuracy and since π cannot be represented
 exactly, the result interval is closed, it cannot be half-closed
 as would be more satisfactory in a purely mathematical view.

Parameters:
a - angle to normalize
center - center of the desired 2π interval for the result
Returns:
a-2kπ with integer k and center-π <= a-2kπ <= center+π
Since:
1.2








normalizeArray
public static double[] normalizeArray(double[] values,
                                      double normalizedSum)
                               throws java.lang.ArithmeticException,
                                      java.lang.IllegalArgumentException
Normalizes an array to make it sum to a specified value.
 Returns the result of the transformation 
    x |-> x * normalizedSum / sum
 
 applied to each non-NaN element x of the input array, where sum is the
 sum of the non-NaN entries in the input array.

 Throws IllegalArgumentException if normalizedSum is infinite
 or NaN and ArithmeticException if the input array contains any infinite elements
 or sums to 0

 Ignores (i.e., copies unchanged to the output array) NaNs in the input array.

Parameters:
values - input array to be normalized
normalizedSum - target sum for the normalized array
Returns:
normalized array
Throws:
java.lang.ArithmeticException - if the input array contains infinite elements or sums to zero
java.lang.IllegalArgumentException - if the target sum is infinite or NaN
Since:
2.1








round
public static double round(double x,
                           int scale)
Round the given value to the specified number of decimal places. The
 value is rounded using the BigDecimal.ROUND_HALF_UP method.

Parameters:
x - the value to round.
scale - the number of digits to the right of the decimal point.
Returns:
the rounded value.
Since:
1.1








round
public static double round(double x,
                           int scale,
                           int roundingMethod)
Round the given value to the specified number of decimal places. The
 value is rounded using the given method which is any method defined in
 BigDecimal.

Parameters:
x - the value to round.
scale - the number of digits to the right of the decimal point.
roundingMethod - the rounding method as defined in
        BigDecimal.
Returns:
the rounded value.
Since:
1.1








round
public static float round(float x,
                          int scale)
Round the given value to the specified number of decimal places. The
 value is rounding using the BigDecimal.ROUND_HALF_UP method.

Parameters:
x - the value to round.
scale - the number of digits to the right of the decimal point.
Returns:
the rounded value.
Since:
1.1








round
public static float round(float x,
                          int scale,
                          int roundingMethod)
Round the given value to the specified number of decimal places. The
 value is rounded using the given method which is any method defined in
 BigDecimal.

Parameters:
x - the value to round.
scale - the number of digits to the right of the decimal point.
roundingMethod - the rounding method as defined in
        BigDecimal.
Returns:
the rounded value.
Since:
1.1








sign
public static byte sign(byte x)
Returns the  sign
 for byte value x.
 
 For a byte value x, this method returns (byte)(+1) if x > 0, (byte)(0) if
 x = 0, and (byte)(-1) if x < 0.

Parameters:
x - the value, a byte
Returns:
(byte)(+1), (byte)(0), or (byte)(-1), depending on the sign of x








sign
public static double sign(double x)
Returns the  sign
 for double precision x.
 
 For a double value x, this method returns
 +1.0 if x > 0, 0.0 if
 x = 0.0, and -1.0 if x < 0.
 Returns NaN if x is NaN.

Parameters:
x - the value, a double
Returns:
+1.0, 0.0, or -1.0, depending on the sign of x








sign
public static float sign(float x)
Returns the  sign
 for float value x.
 
 For a float value x, this method returns +1.0F if x > 0, 0.0F if x =
 0.0F, and -1.0F if x < 0. Returns NaN if x
 is NaN.

Parameters:
x - the value, a float
Returns:
+1.0F, 0.0F, or -1.0F, depending on the sign of x








sign
public static int sign(int x)
Returns the  sign
 for int value x.
 
 For an int value x, this method returns +1 if x > 0, 0 if x = 0, and -1
 if x < 0.

Parameters:
x - the value, an int
Returns:
+1, 0, or -1, depending on the sign of x








sign
public static long sign(long x)
Returns the  sign
 for long value x.
 
 For a long value x, this method returns +1L if x > 0, 0L if x = 0, and
 -1L if x < 0.

Parameters:
x - the value, a long
Returns:
+1L, 0L, or -1L, depending on the sign of x








sign
public static short sign(short x)
Returns the  sign
 for short value x.
 
 For a short value x, this method returns (short)(+1) if x > 0, (short)(0)
 if x = 0, and (short)(-1) if x < 0.

Parameters:
x - the value, a short
Returns:
(short)(+1), (short)(0), or (short)(-1), depending on the sign of
         x








sinh
public static double sinh(double x)
Returns the 
 hyperbolic sine of x.

Parameters:
x - double value for which to find the hyperbolic sine
Returns:
hyperbolic sine of x








subAndCheck
public static int subAndCheck(int x,
                              int y)
Subtract two integers, checking for overflow.

Parameters:
x - the minuend
y - the subtrahend
Returns:
the difference x-y
Throws:
java.lang.ArithmeticException - if the result can not be represented as an
         int
Since:
1.1








subAndCheck
public static long subAndCheck(long a,
                               long b)
Subtract two long integers, checking for overflow.

Parameters:
a - first value
b - second value
Returns:
the difference a-b
Throws:
java.lang.ArithmeticException - if the result can not be represented as an
         long
Since:
1.2








pow
public static int pow(int k,
                      int e)
               throws java.lang.IllegalArgumentException
Raise an int to an int power.

Parameters:
k - number to raise
e - exponent (must be positive or null)
Returns:
k^e
Throws:
java.lang.IllegalArgumentException - if e is negative








pow
public static int pow(int k,
                      long e)
               throws java.lang.IllegalArgumentException
Raise an int to a long power.

Parameters:
k - number to raise
e - exponent (must be positive or null)
Returns:
k^e
Throws:
java.lang.IllegalArgumentException - if e is negative








pow
public static long pow(long k,
                       int e)
                throws java.lang.IllegalArgumentException
Raise a long to an int power.

Parameters:
k - number to raise
e - exponent (must be positive or null)
Returns:
k^e
Throws:
java.lang.IllegalArgumentException - if e is negative








pow
public static long pow(long k,
                       long e)
                throws java.lang.IllegalArgumentException
Raise a long to a long power.

Parameters:
k - number to raise
e - exponent (must be positive or null)
Returns:
k^e
Throws:
java.lang.IllegalArgumentException - if e is negative








pow
public static java.math.BigInteger pow(java.math.BigInteger k,
                                       int e)
                                throws java.lang.IllegalArgumentException
Raise a BigInteger to an int power.

Parameters:
k - number to raise
e - exponent (must be positive or null)
Returns:
k^e
Throws:
java.lang.IllegalArgumentException - if e is negative








pow
public static java.math.BigInteger pow(java.math.BigInteger k,
                                       long e)
                                throws java.lang.IllegalArgumentException
Raise a BigInteger to a long power.

Parameters:
k - number to raise
e - exponent (must be positive or null)
Returns:
k^e
Throws:
java.lang.IllegalArgumentException - if e is negative








pow
public static java.math.BigInteger pow(java.math.BigInteger k,
                                       java.math.BigInteger e)
                                throws java.lang.IllegalArgumentException
Raise a BigInteger to a BigInteger power.

Parameters:
k - number to raise
e - exponent (must be positive or null)
Returns:
k^e
Throws:
java.lang.IllegalArgumentException - if e is negative








distance1
public static double distance1(double[] p1,
                               double[] p2)
Calculates the L₁ (sum of abs) distance between two points.

Parameters:
p1 - the first point
p2 - the second point
Returns:
the L₁ distance between the two points








distance1
public static int distance1(int[] p1,
                            int[] p2)
Calculates the L₁ (sum of abs) distance between two points.

Parameters:
p1 - the first point
p2 - the second point
Returns:
the L₁ distance between the two points








distance
public static double distance(double[] p1,
                              double[] p2)
Calculates the L₂ (Euclidean) distance between two points.

Parameters:
p1 - the first point
p2 - the second point
Returns:
the L₂ distance between the two points








distance
public static double distance(int[] p1,
                              int[] p2)
Calculates the L₂ (Euclidean) distance between two points.

Parameters:
p1 - the first point
p2 - the second point
Returns:
the L₂ distance between the two points








distanceInf
public static double distanceInf(double[] p1,
                                 double[] p2)
Calculates the L_∞ (max of abs) distance between two points.

Parameters:
p1 - the first point
p2 - the second point
Returns:
the L_∞ distance between the two points








distanceInf
public static int distanceInf(int[] p1,
                              int[] p2)
Calculates the L_∞ (max of abs) distance between two points.

Parameters:
p1 - the first point
p2 - the second point
Returns:
the L_∞ distance between the two points








checkOrder
public static void checkOrder(double[] val,
                              MathUtils.OrderDirection dir,
                              boolean strict)
Checks that the given array is sorted.

Parameters:
val - Values.
dir - Ordering direction.
strict - Whether the order should be strict.
Throws:
NonMonotonousSequenceException - if the array is not sorted.
Since:
2.2








checkOrder
public static void checkOrder(double[] val)
Checks that the given array is sorted in strictly increasing order.

Parameters:
val - Values.
Throws:
NonMonotonousSequenceException - if the array is not sorted.
Since:
2.2








checkOrder
@Deprecated
public static void checkOrder(double[] val,
                              int dir,
                              boolean strict)
Deprecated.
as of 2.2 (please use the new checkOrder method). To be removed in 3.0.

Checks that the given array is sorted.

Parameters:
val - Values
dir - Order direction (-1 for decreasing, 1 for increasing)
strict - Whether the order should be strict
Throws:
NonMonotonousSequenceException - if the array is not sorted.








safeNorm
public static double safeNorm(double[] v)
Returns the Cartesian norm (2-norm), handling both overflow and underflow.
 Translation of the minpack enorm subroutine.

 The redistribution policy for MINPACK is available here, for convenience, it
 is reproduced below.

 
 
    Minpack Copyright Notice (1999) University of Chicago.
    All rights reserved
 
 
 Redistribution and use in source and binary forms, with or without
 modification, are permitted provided that the following conditions
 are met:
 
  Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.
 Redistributions in binary form must reproduce the above
     copyright notice, this list of conditions and the following
     disclaimer in the documentation and/or other materials provided
     with the distribution.
 The end-user documentation included with the redistribution, if any,
     must include the following acknowledgment:
     This product includes software developed by the University of
           Chicago, as Operator of Argonne National Laboratory.
     Alternately, this acknowledgment may appear in the software itself,
     if and wherever such third-party acknowledgments normally appear.
 WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
     OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
     OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
     OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
     USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
     THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
     UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
     BE CORRECTED.
 LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
     HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
     ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
     INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
     ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
     PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
     SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
     (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
     EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
     POSSIBILITY OF SUCH LOSS OR DAMAGES.
 
 

Parameters:
v - vector of doubles
Returns:
the 2-norm of the vector
Since:
2.2

Class MathUtils

Nested Class Summary

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

EPSILON

SAFE_MIN

TWO_PI

Method Detail

addAndCheck

addAndCheck

binomialCoefficient

binomialCoefficientDouble

binomialCoefficientLog

compareTo

cosh

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

factorial

factorialDouble

factorialLog

gcd

gcd

hash

hash

indicator

indicator

indicator

indicator

indicator

indicator

lcm

lcm

log

mulAndCheck

mulAndCheck

nextAfter

scalb

normalizeAngle

normalizeArray

round

round

round

round

sign

sign

sign

sign

sign

sign

sinh

subAndCheck

subAndCheck

pow

pow

pow

pow

pow

pow

pow

distance1

distance1

distance

distance

distanceInf