Package org.apfloat.internal

Class LongKaratsubaConvolutionStrategy

java.lang.Object

org.apfloat.internal.LongBaseMath

org.apfloat.internal.LongMediumConvolutionStrategy

org.apfloat.internal.LongKaratsubaConvolutionStrategy

All Implemented Interfaces:

Serializable, ConvolutionStrategy

public class LongKaratsubaConvolutionStrategy
extends LongMediumConvolutionStrategy

Convolution strategy using the Karatsuba algorithm. The complexity of the algorithm is O(n^{log(3)/log(2)}) as the operands are split to two and multiplied using three multiplications (and five additions / subtractions). This splitting is done recursively until some cut-off point where the basic O(n²) algorithm is applied. The Karatsuba algorithm is faster than the basic O(n²) multiplication algorithm for medium size numbers larger than some certain size. For very large numbers, the transform-based convolution algorithms are faster.

Since:

1.4

Version:

1.4

Author:

Mikko Tommila

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final int	CUTOFF_POINT	Cut-off point for Karatsuba / basic convolution.

Constructor Summary

Constructors

Constructor	Description
LongKaratsubaConvolutionStrategy(int radix)	Creates a convolution strategy using the specified radix.

Method Summary

Modifier and Type	Method	Description
DataStorage	convolute(DataStorage x, DataStorage y, long resultSize)	Convolutes the two sets of data.

Methods inherited from class org.apfloat.internal.LongBaseMath

baseAdd, baseDivide, baseMultiplyAdd, baseSubtract

Methods inherited from class java.lang.Object

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

Field Details

CUTOFF_POINT

public static final int CUTOFF_POINT

Cut-off point for Karatsuba / basic convolution.

Convolutions where the shorter number is at most this long are calculated using the basic O(n²) algorithm i.e. super.convolute().

See Also:

• Constant Field Values

Constructor Details

LongKaratsubaConvolutionStrategy

public LongKaratsubaConvolutionStrategy(int radix)

Creates a convolution strategy using the specified radix.

Parameters:

radix - The radix that will be used.

Method Details

convolute

public DataStorage convolute(DataStorage x,
 DataStorage y,
 long resultSize)
                      throws ApfloatRuntimeException

Description copied from interface: ConvolutionStrategy

Convolutes the two sets of data.

Specified by:

convolute in interface ConvolutionStrategy

Overrides:

convolute in class LongMediumConvolutionStrategy

Parameters:

x - First data set.

y - Second data set.

resultSize - Number of elements needed in the result data.

Returns:

The convolved data.

Throws:

ApfloatRuntimeException