Package org.apache.commons.numbers.core

Class DDMath

java.lang.Object

org.apache.commons.numbers.core.DDMath

public final class DDMath
extends Object

Computes extended precision floating-point operations.

This class supplements the arithmetic operations in the DD class providing greater accuracy at the cost of performance.

Since:

1.2

Method Summary

Modifier and Type	Method	Description
static DD	pow(DD x, int n, long[] exp)	Compute the number x raised to the power n.

Methods inherited from class java.lang.Object

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

Method Details

pow

public static DD pow(DD x,
 int n,
 long[] exp)

Compute the number x raised to the power n.

The value is returned as fractional f and integral 2^exp components.

 (x+xx)^n = (f+ff) * 2^exp
 

The combined fractional part (f, ff) is in the range [0.5, 1).

Special cases:

• If (x, xx) is zero the high part of the fractional part is computed using Math.pow(x, n) and the exponent is 0.
• If n = 0 the fractional part is 0.5 and the exponent is 1.
• If (x, xx) is an exact power of 2 the fractional part is 0.5 and the exponent is the power of 2 minus 1.
• If the result high-part is an exact power of 2 and the low-part has an opposite signed non-zero magnitude then the fraction high-part f will be +/-1 such that the double-double number is in the range [0.5, 1).
• If the argument is not finite then a fractional representation is not possible. In this case the fraction and the scale factor is undefined.

The computed result is within 1 eps of the exact result where eps is 2^-106.

The performance is approximately 4-fold slower than DD.pow(int, long[]).

Parameters:

x - Number.

n - Power.

exp - Result power of two scale factor (integral exponent).

Returns:

Fraction part.

See Also:

• DD.frexp(int[])