cern.jet.math.tfloat

Class FloatArithmetic

java.lang.Object

cern.jet.math.tfloat.FloatConstants

cern.jet.math.tfloat.FloatArithmetic

public class FloatArithmetic
extends FloatConstants

Arithmetic functions.

Method Summary

Modifier and Type	Method and Description
static float	binomial(float n, long k) Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
static float	binomial(long n, long k) Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
static long	ceil(float value) Returns the smallest long >= value.
static float	chbevl(float x, float[] coef, int N) Evaluates the series of Chebyshev polynomials Ti at argument x/2.
static float	factorial(int k) Instantly returns the factorial k!.
static long	floor(float value) Returns the largest long <= value.
static float	log(float base, float value) Returns logbasevalue.
static float	log10(float value) Returns log10value.
static float	log2(float value) Returns log2value.
static float	logFactorial(int k) Returns log(k!).
static long	longFactorial(int k) Instantly returns the factorial k!.
static float	stirlingCorrection(int k) Returns the StirlingCorrection.

Methods inherited from class java.lang.Object

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

Method Detail

binomial

public static float binomial(float n,
                             long k)

Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k". The binomial coefficient is defined as (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).

• k<0: 0.
• k==0: 1.
• k==1: n.
• else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).

Returns:

the binomial coefficient.

binomial

public static float binomial(long n,
                             long k)

Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k". The binomial coefficient is defined as

• k<0: 0.
• k==0 || k==n: 1.
• k==1 || k==n-1: n.
• else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).

Returns:

the binomial coefficient.

ceil

public static long ceil(float value)

Returns the smallest long >= value.

Examples: 1.0 -> 1, 1.2 -> 2, 1.9 -> 2. This method is safer than using (long) Math.ceil(value), because of possible rounding error.

chbevl

public static float chbevl(float x,
                           float[] coef,
                           int N)
                    throws java.lang.ArithmeticException

Evaluates the series of Chebyshev polynomials Ti at argument x/2. The series is given by

        N-1
         - '
  y  =   >   coef[i] T (x/2)
         -            i
        i=0
 

Coefficients are stored in reverse order, i.e. the zero order term is last in the array. Note N is the number of coefficients, not the order.

If coefficients are for the interval a to b, x must have been transformed to x -> 2(2x - b - a)/(b-a) before entering the routine. This maps x from (a, b) to (-1, 1), over which the Chebyshev polynomials are defined.

If the coefficients are for the inverted interval, in which (a, b) is mapped to (1/b, 1/a), the transformation required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity, this becomes x -> 4a/x - 1.

SPEED:

Taking advantage of the recurrence properties of the Chebyshev polynomials, the routine requires one more addition per loop than evaluating a nested polynomial of the same degree.

Parameters:

x - argument to the polynomial.

coef - the coefficients of the polynomial.

N - the number of coefficients.

Throws:

java.lang.ArithmeticException

factorial

public static float factorial(int k)

Instantly returns the factorial k!.

Parameters:

k - must hold k >= 0.

floor

public static long floor(float value)

Returns the largest long <= value.

Examples: 1.0 -> 1, 1.2 -> 1, 1.9 -> 1

2.0 -> 2, 2.2 -> 2, 2.9 -> 2

This method is safer than using (long) Math.floor(value), because of possible rounding error.

log

public static float log(float base,
                        float value)

Returns log_basevalue.

log10

public static float log10(float value)

Returns log₁₀value.

log2

public static float log2(float value)

Returns log₂value.

logFactorial

public static float logFactorial(int k)

Returns log(k!). Tries to avoid overflows. For k<30 simply looks up a table in O(1). For k>=30 uses stirlings approximation.

Parameters:

k - must hold k >= 0.

longFactorial

public static long longFactorial(int k)
                          throws java.lang.IllegalArgumentException

Instantly returns the factorial k!.

Parameters:

k - must hold k >= 0 && k < 21.

Throws:

java.lang.IllegalArgumentException

stirlingCorrection

public static float stirlingCorrection(int k)

Returns the StirlingCorrection.

Correction term of the Stirling approximation for log(k!) (series in 1/k, or table values for small k) with int parameter k.

log k! = (k + 1/2)log(k + 1) - (k + 1) + (1/2)log(2Pi) + stirlingCorrection(k + 1)

log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + stirlingCorrection(k)