Class SixStepFNTStrategy

• All Implemented Interfaces:
Parallelizable, NTTStrategy
Direct Known Subclasses:
ColumnSixStepFNTStrategy

public class SixStepFNTStrategy
extends AbstractStepFNTStrategy
Fast Number Theoretic Transform that uses a "six-step" algorithm to calculate a long transform more efficiently on cache-based memory architectures.

When the data to be transformed is considered to be an n1 x n2 matrix of data, instead of a linear array, the six steps are as follows:

1. Transpose the matrix.
2. Transform the rows.
3. Transpose the matrix.
4. Multiply each matrix element by wi j (where w is the n:th root of unity).
5. Transform the rows.
6. Transpose the matrix.

In a convolution algorithm the last transposition step can be omitted to increase performance, as well as the first transposition step in the inverse transform. The convolution's element-by-element multiplication is not sensitive to the order in which the elements are. Also scrambling the data can be omitted.

All access to this class must be externally synchronized.

Since:
1.7.0
Version:
1.9.0
Author:
Mikko Tommila
• Field Summary

Fields
Modifier and Type Field Description
protected MatrixStrategy matrixStrategy
The matrix strategy.
• Fields inherited from class org.apfloat.internal.AbstractStepFNTStrategy

stepStrategy
• Constructor Summary

Constructors
Constructor Description
SixStepFNTStrategy()
Default constructor.
• Method Summary

Modifier and Type Method Description
protected void inverseTransform​(DataStorage dataStorage, int n1, int n2, long length, long totalTransformLength, int modulus)
Inverse transform the data in steps.
protected void multiplyElements​(ArrayAccess arrayAccess, int rows, int columns, long length, long totalTransformLength, boolean isInverse, int modulus)
Multiply each matrix element by a power of the n:th root of unity.
protected void postTransform​(ArrayAccess arrayAccess)
Finish processing the data after the (inverse) transform.
protected void preTransform​(ArrayAccess arrayAccess)
Prepare the data for the (inverse) transform.
protected void transform​(DataStorage dataStorage, int n1, int n2, long length, int modulus)
Transform the data in steps.
protected void transformFirst​(ArrayAccess arrayAccess, int length, int count, boolean isInverse, int modulus)
The first transform of the rows (or columns) of the data matrix.
protected void transformSecond​(ArrayAccess arrayAccess, int length, int count, boolean isInverse, int modulus)
The second transform of the rows (or columns) of the data matrix.
protected void transposeFinal​(ArrayAccess arrayAccess, int n1, int n2, boolean isInverse)
The final transpose of the forward transform, or the initial transpose of the inverse transform.
protected void transposeInitial​(ArrayAccess arrayAccess, int n1, int n2, boolean isInverse)
The initial transpose of the forward transform, or the final transpose of the inverse transform, to transpose the columns of the matrix to be rows.
protected void transposeMiddle​(ArrayAccess arrayAccess, int n1, int n2, boolean isInverse)
The second transpose of either the forward or inverse transform.
• Field Detail

• matrixStrategy

protected MatrixStrategy matrixStrategy
The matrix strategy.
• Constructor Detail

• SixStepFNTStrategy

public SixStepFNTStrategy()
Default constructor.
• Method Detail

• preTransform

protected void preTransform​(ArrayAccess arrayAccess)
Prepare the data for the (inverse) transform.
Parameters:
arrayAccess - The data to prepare.
• transposeInitial

protected void transposeInitial​(ArrayAccess arrayAccess,
int n1,
int n2,
boolean isInverse)
The initial transpose of the forward transform, or the final transpose of the inverse transform, to transpose the columns of the matrix to be rows. This step is needed in the six-step algorithm but is omitted in the four-step algorithm.
Parameters:
arrayAccess - Accessor to the matrix data. This data will be transposed.
n1 - Number of rows in the matrix.
n2 - Number of columns in the matrix.
isInverse - true if an inverse transform is performed, false if a forward transform is performed.
• transposeMiddle

protected void transposeMiddle​(ArrayAccess arrayAccess,
int n1,
int n2,
boolean isInverse)
The second transpose of either the forward or inverse transform. Normally this step is always required as the four-step algorithm only transforms columns of the matrix and the six-step algorithm transforms only rows.
Parameters:
arrayAccess - Accessor to the matrix data. This data will be transposed.
n1 - Number of rows in the matrix.
n2 - Number of columns in the matrix.
isInverse - true if an inverse transform is performed, false if a forward transform is performed.
• transposeFinal

protected void transposeFinal​(ArrayAccess arrayAccess,
int n1,
int n2,
boolean isInverse)
The final transpose of the forward transform, or the initial transpose of the inverse transform. By default this method does nothing as the step is always unnecessary when the data is only needed for convolution.
Parameters:
arrayAccess - Accessor to the matrix data.
n1 - Number of rows in the matrix.
n2 - Number of columns in the matrix.
isInverse - true if an inverse transform is performed, false if a forward transform is performed.
• transformFirst

protected void transformFirst​(ArrayAccess arrayAccess,
int length,
int count,
boolean isInverse,
int modulus)
The first transform of the rows (or columns) of the data matrix. In the default implementation the rows are transformed because in the forward transform the matrix is transposed first. In the inverse transform the matrix is initially in transposed form as it was left like that by the forward transform.

By default the row transforms permute the data, leaving it in the correct order so the element-by-element multiplication is simpler.

Parameters:
arrayAccess - The memory array to split and transform.
length - Length of one transform (one row physically, by default).
count - Number of transforms.
isInverse - true if an inverse transform is performed, false if a forward transform is performed.
modulus - Index of the modulus.
• transformSecond

protected void transformSecond​(ArrayAccess arrayAccess,
int length,
int count,
boolean isInverse,
int modulus)
The second transform of the rows (or columns) of the data matrix. In the default implementation the rows are transformed because in the forward transform the matrix is transposed first. In the inverse transform the matrix is initially in transposed form as it was left like that by the forward transform.

By default the row transforms do not permute the data, leaving it in scrambled order, as this does not matter when the data is only used for convolution.

Parameters:
arrayAccess - The memory array to split to rows and to transform.
length - Length of one transform (one row).
count - Number of rows.
isInverse - true if an inverse transform is performed, false if a forward transform is performed.
modulus - Index of the modulus.
• multiplyElements

protected void multiplyElements​(ArrayAccess arrayAccess,
int rows,
int columns,
long length,
long totalTransformLength,
boolean isInverse,
int modulus)
Multiply each matrix element by a power of the n:th root of unity.
Parameters:
arrayAccess - The memory array to multiply.
rows - The number of rows in the arrayAccess to multiply.
columns - The number of columns in the matrix (= n2).
length - The length of data in the matrix being transformed.
totalTransformLength - The total transform length, for the scaling factor. Used only for the inverse case.
isInverse - If the multiplication is done for the inverse transform or not.
modulus - Index of the modulus.
• postTransform

protected void postTransform​(ArrayAccess arrayAccess)
Finish processing the data after the (inverse) transform.
Parameters:
arrayAccess - The data to finish.