JSci.maths
Class ExtraMath

java.lang.Object
  JSci.maths.AbstractMath
      JSci.maths.ExtraMath

public final class ExtraMath
extends AbstractMath

The extra math library. Provides extra functions not in java.lang.Math class. This class cannot be subclassed or instantiated because all methods are static.

Method Summary

static double	acosh(double x) Returns the inverse hyperbolic cosine of a double value.
static double	acoth(double x) Returns the inverse hyperbolic cotangent of a double value.
static double	acsch(double x) Returns the inverse hyperbolic cosecant of a double value.
static double	asech(double x) Returns the inverse hyperbolic secant of a double value.
static double	asinh(double x) Returns the inverse hyperbolic sine of a double value.
static double	atanh(double x) Returns the inverse hyperbolic tangent of a double value.
static double	binomial(double n, double k) Returns the binomial coefficient (n k).
static int	binomial(int n, int k) Returns the binomial coefficient (n k).
static double	cosh(double x) Returns the hyperbolic cosine of a double.
static double	coth(double x) Returns the hyperbolic cotangent of a double value.
static double	csch(double x) Returns the hyperbolic cosecant of a double value.
static double	factorial(double x) Returns the factorial.
static double	hypot(double x, double y) Returns sqrt(x2+y2).
static double	log10(double x) Returns the base 10 logarithm of a double.
static double	logFactorial(double x) Returns the natural logarithm of the factorial.
static int	pow(int a, int b) Returns ab.
static int	pow2(int a) Returns 2a.
static double	random(double min, double max) Returns a random number within a specified range.
static double	round(double x, int significant) Rounds a number to so many significant figures.
static double	sech(double x) Returns the hyperbolic secant of a double value.
static int	sign(double x) Returns the sign of a number.
static double	sinh(double x) Returns the hyperbolic sine of a double.
static double	tanh(double x) Returns the hyperbolic tangent of a double.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

round

public static double round(double x,
                           int significant)

Rounds a number to so many significant figures.

Parameters:

x - a number to be rounded.

significant - number of significant figures to round to.

random

public static double random(double min,
                            double max)

Returns a random number within a specified range.

sign

public static int sign(double x)

Returns the sign of a number.

Returns:

1 if x>0.0, -1 if x<0.0, else 0.

hypot

public static double hypot(double x,
                           double y)

Returns sqrt(x²+y²).

pow

public static int pow(int a,
                      int b)

Returns a^b.

Parameters:

a - an integer.

b - a positive integer.

pow2

public static int pow2(int a)

Returns 2^a.

Parameters:

a - a positive integer.

factorial

public static double factorial(double x)

Returns the factorial. (Wrapper for the gamma function).

Parameters:

x - a double.

See Also:

SpecialMath.gamma(double)

logFactorial

public static double logFactorial(double x)

Returns the natural logarithm of the factorial. (Wrapper for the log gamma function).

Parameters:

x - a double.

See Also:

SpecialMath.logGamma(double)

binomial

public static int binomial(int n,
                           int k)

Returns the binomial coefficient (n k). Uses Pascal's recursion formula.

Parameters:

n - an integer.

k - an integer.

PlanetMath references:

PascalsRule

binomial

public static double binomial(double n,
                              double k)

Returns the binomial coefficient (n k). Uses gamma functions.

Parameters:

n - a double.

k - a double.

PlanetMath references:

BinomialCoefficient

log10

public static double log10(double x)

Returns the base 10 logarithm of a double.

Parameters:

x - a double.

sinh

public static double sinh(double x)

Returns the hyperbolic sine of a double.

Parameters:

x - a double.

cosh

public static double cosh(double x)

Returns the hyperbolic cosine of a double.

Parameters:

x - a double.

tanh

public static double tanh(double x)

Returns the hyperbolic tangent of a double.

Parameters:

x - a double.

coth

public static double coth(double x)

Returns the hyperbolic cotangent of a double value.

The identity is:

coth(x) = (e^x + e^-x)/(e^x - e^-x), in other words, cosh(x)/sinh(x).

Special cases:

• If the argument is NaN, then the result is NaN.
• If the argument is zero, then the result is an infinity 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.

Parameters:

x - The number whose hyperbolic cotangent is sought

Returns:

The hyperbolic cotangent of x

csch

public static double csch(double x)

Returns the hyperbolic cosecant of a double value.

The identity is:

csch(x) = (2/(e^x - e^-x), in other words, 1/sinh(x).

Special cases:

• If the argument is NaN, then the result is NaN.
• If the argument is zero, then the result is an infinity with the same sign as the argument.
• If the argument is positive infinity, then the result is +0.0.
• If the argument is negative infinity, then the result is -0.0.

Parameters:

x - The number whose hyperbolic cosecant is sought

Returns:

The hyperbolic cosecant of x

sech

public static double sech(double x)

Returns the hyperbolic secant of a double value.

The identity is:

sech(x) = (2/(e^x + e^-x), in other words, 1/cosh(x).

Special cases:

• If the argument is NaN, then the result is NaN.
• If the argument is an infinity (positive or negative), then the result is +0.0.

Parameters:

x - The number whose hyperbolic secant is sought

Returns:

The hyperbolic secant of x

asinh

public static double asinh(double x)

Returns the inverse hyperbolic sine of a double value.

The identity is:

asinh(x) = ln(x + sqrt(x² + 1))

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.

Parameters:

x - The number whose inverse hyperbolic sine is sought

Returns:

The inverse hyperbolic sine of x

acosh

public static double acosh(double x)

Returns the inverse hyperbolic cosine of a double value. Note that cosh(±acosh(x)) = x; this function arbitrarily returns the positive branch.

The identity is:

acosh(x) = ln(x ± sqrt(x² - 1))

Special cases:

• If the argument is NaN or less than one, then the result is NaN.
• If the argument is a positive infinity, then the result is (positive) infinity.
• If the argument is one, then the result is (positive) zero.

Parameters:

x - The number whose inverse hyperbolic cosine is sought

Returns:

The inverse hyperbolic cosine of x

atanh

public static double atanh(double x)

Returns the inverse hyperbolic tangent of a double value.

The identity is:

atanh(x) = (1/2)*ln((1 + x)/(1 - x))

Special cases:

• If the argument is NaN, an infinity, or has a modulus of greater than one, then the result is NaN.
• If the argument is plus or minus one, then the result is 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.

Parameters:

x - A double specifying the value whose inverse hyperbolic tangent is sought

Returns:

A double specifying the inverse hyperbolic tangent of x

acoth

public static double acoth(double x)

Returns the inverse hyperbolic cotangent of a double value.

The identity is:

acoth(x) = (1/2)*ln((x + 1)/(x - 1))

Special cases:

• If the argument is NaN or a modulus of less than one, then the result is NaN.
• If the argument is an infinity, then the result is zero with the same sign as the argument.
• If the argument is plus or minus one, then the result is infinity with the same sign as the argument.

Parameters:

x - The number whose inverse hyperbolic cotangent is sought

Returns:

The inverse hyperbolic cotangent of x

acsch

public static double acsch(double x)

Returns the inverse hyperbolic cosecant of a double value.

The identity is:

acsch(x) = ln((1 - sqrt(1 + x²))/x) for x < 0;

acsch(x) = ln((1 + sqrt(1 + x²))/x) for x > 0.

Special cases:

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

Parameters:

x - The number whose inverse hyperbolic cosecant is sought

Returns:

The inverse hyperbolic cosecant of x

asech

public static double asech(double x)

Returns the inverse hyperbolic secant of a double value. Note that sech(±asech(x)) = x; this function arbitrarily returns the positive branch.

The identity is:

asech(x) = ln((1 + sqrt(1 - x²))/x).

Special cases:

• If the argument is NaN, less than zero, or greater than one, then the result is NaN.
• If the argument is zero, then the result is infinity with the same sign as the argument.

Parameters:

x - The number whose hyperbolic secant is sought

Returns:

The hyperbolic secant of x