public class Arithmetic extends Constants
| Modifier and Type | Field and Description |
|---|---|
protected static double[] |
doubleFactorials |
protected static double[] |
logFactorials |
protected static long[] |
longFactorials |
| Modifier | Constructor and Description |
|---|---|
protected |
Arithmetic()
Makes this class non instantiable, but still let's others inherit from it.
|
| Modifier and Type | Method and Description |
|---|---|
static double |
binomial(double n,
long k)
Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
|
static double |
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(double value)
Returns the smallest
long >= value. |
static double |
chbevl(double x,
double[] coef,
int N)
Evaluates the series of Chebyshev polynomials Ti at argument x/2.
|
static double |
factorial(int k)
Instantly returns the factorial k!.
|
static long |
floor(double value)
Returns the largest
long <= value. |
static double |
log(double base,
double value)
Returns logbasevalue.
|
static double |
log10(double value)
Returns log10value.
|
static double |
log2(double value)
Returns log2value.
|
static double |
logFactorial(int k)
Returns log(k!).
|
static long |
longFactorial(int k)
Instantly returns the factorial k!.
|
static double |
stirlingCorrection(int k)
Returns the StirlingCorrection.
|
protected static final double[] logFactorials
protected static final long[] longFactorials
protected static final double[] doubleFactorials
protected Arithmetic()
public static double binomial(double n,
long k)
public static double binomial(long n,
long k)
public static long ceil(double value)
long >= value.
1.0 -> 1, 1.2 -> 2, 1.9 -> 2.
This method is safer than using (long) Math.ceil(value), because of possible rounding error.public static double chbevl(double x,
double[] coef,
int N)
throws ArithmeticException
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.
x - argument to the polynomial.coef - the coefficients of the polynomial.N - the number of coefficients.ArithmeticExceptionpublic static double factorial(int k)
k - must hold k >= 0.public static long floor(double value)
long <= value.
1.0 -> 1, 1.2 -> 1, 1.9 -> 1 -
2.0 -> 2, 2.2 -> 2, 2.9 -> 2
public static double log(double base,
double value)
public static double log10(double value)
public static double log2(double value)
public static double logFactorial(int k)
k - must hold k >= 0.public static long longFactorial(int k)
throws IllegalArgumentException
k - must hold k >= 0 && k < 21.IllegalArgumentExceptionpublic static double stirlingCorrection(int k)
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)
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