Arithmetic (math-base 1.0.0 API)

java.lang.Object
- math.cern.Arithmetic

public final class Arithmetic
extends Object

Arithmetic functions.

Method Summary

All Methods Static Methods Concrete Methods
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`	`factoPow(int n)` Returns the value of `n!`
`static double`	`factorial(int k)` Instantly returns the factorial `k!`
`static long`	`floor(double value)` Returns the largest `long <= value`.
`static boolean`	`isBadNum(double value)` Checks whether the passed `value` is one of `Double.NaN`, `Double.NEGATIVE_INFINITY` or `Double.POSITIVE_INFINITY`.
`static boolean`	`isProbability(double value)` Checks whether the passed `value` qualifies as a probability, i.e., whether it fulfills `0.0 <= value <= 1.0`.
`static double`	`log(double base, double x)` Returns `log_base(x)`.
`static double`	`log2(double x)` Returns `log₂(x)`.
`static double`	`logFactorial(int k)` Returns `log(k!)`
`static long`	`longFactorial(int k)` Instantly returns the factorial `k!`
`static double`	`round(double x)`
`static double`	`round(double x, int scale)`
`static int`	`roundToIntStochastically(double x)`
`static double`	`stirlingCorrection(int k)` Returns the Stirling correction.

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

- Method Detail
  - binomial
```
public static double binomial(double 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 )
    Parameters:
    
    n - the n in "n choose k"
    
    k - the k in "n choose k"
    
    Returns:
    
    the binomial coefficient
  - binomial
```
public static double 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 )
    Parameters:
    
    n - the n in "n choose k"
    
    k - the k in "n choose k"
    
    Returns:
    
    the binomial coefficient
  - ceil
```
public static long ceil(double 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.
    
    Parameters:
    
    value - the value
    
    Returns:
    
    ceil of the value
  - factorial
```
public static double factorial(int k)
```
    Instantly returns the factorial k!. If k >= 171, Double.POSITIVE_INFINITY is returned.
    
    Parameters:
    
    k - an integer >= 0
    
    Returns:
    
    the factorial of k
  - floor
```
public static long floor(double 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.
    Parameters:
    
    value - the value
    
    Returns:
    
    floor of the value
  - log
```
public static double log(double base,
                         double x)
```
    Returns log_base(x).
    
    Parameters:
    
    base - the base
    
    x - the value
    
    Returns:
    
    log of the value
  - log2
```
public static double log2(double x)
```
    Returns log₂(x).
    
    Parameters:
    
    x - the value
    
    Returns:
    
    log2 of the value
  - logFactorial
```
public static double 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
    
    Returns:
    
    log factorial of k
  - factoPow
```
public static double factoPow(int n)
```
    Returns the value of n!/n^n.
    
    Parameters:
    
    n - an integer >= 0
    
    Returns:
    
    the value of n!/n^n
  - longFactorial
```
public static long longFactorial(int k)
```
    Instantly returns the factorial k!.
    
    Parameters:
    
    k - must hold k >= 0 && k < 21
    
    Returns:
    
    the factorial
  - stirlingCorrection
```
public static double stirlingCorrection(int k)
```
    Returns the Stirling correction.
    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)
 
```
    Parameters:
    
    k - the value
    
    Returns:
    
    Stirling correction for k
  - isBadNum
```
public static boolean isBadNum(double value)
```
    Checks whether the passed value is one of Double.NaN, Double.NEGATIVE_INFINITY or Double.POSITIVE_INFINITY. Returns true if this is the case, otherwise returns false.
    
    Parameters:
    
    value - the double to check
    
    Returns:
    
    true when value is finite and not Double.NaN, false in all other cases
  - isProbability
```
public static boolean isProbability(double value)
```
    Checks whether the passed value qualifies as a probability, i.e., whether it fulfills 0.0 <= value <= 1.0.
    
    Parameters:
    
    value - the double to check
    
    Returns:
    
    true when value lies within [0, 1], otherwise false
  - roundToIntStochastically
```
public static int roundToIntStochastically(double x)
```
  - round
```
public static double round(double x,
                           int scale)
```
  - round
```
public static double round(double x)
```

Class Arithmetic

Method Summary

Methods inherited from class java.lang.Object

Method Detail

binomial

binomial

ceil

factorial

floor

log

log2

logFactorial

factoPow

longFactorial

stirlingCorrection

isBadNum

isProbability

roundToIntStochastically

round

round