Package org.apfloat.internal

Class LongModMath

java.lang.Object

org.apfloat.internal.LongElementaryModMath

org.apfloat.internal.LongModMath

Direct Known Subclasses:

LongFactor3NTTStepStrategy, LongNTTConvolutionStepStrategy, LongTableFNT, LongWTables

public class LongModMath
extends LongElementaryModMath

Modulo arithmetic functions for long data.

Version:

1.0

Author:

Mikko Tommila

Constructor Summary

Constructors

Constructor	Description
LongModMath()	Default constructor.

Method Summary

Modifier and Type	Method	Description
final long[]	createWTable(long w, int n)	Create a table of powers of n:th root of unity.
long	getForwardNthRoot(long primitiveRoot, long n)	Get forward n:th root of unity.
long	getInverseNthRoot(long primitiveRoot, long n)	Get inverse n:th root of unity.
final long	modDivide(long a, long b)	Modular division.
final long	modInverse(long a)	Modular inverse, that is 1 / a.
final long	modPow(long a, long n)	Modular power.
final long	negate(long a)	Modular negation.

Methods inherited from class org.apfloat.internal.LongElementaryModMath

getModulus, modAdd, modMultiply, modSubtract, setModulus

Methods inherited from class java.lang.Object

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

Constructor Details

LongModMath

public LongModMath()

Default constructor.

Method Details

createWTable

public final long[] createWTable(long w,
 int n)

Create a table of powers of n:th root of unity.

Parameters:

w - The n:th root of unity modulo the current modulus.

n - The table length (= transform length).

Returns:

Table of table[i]=wi mod m, i = 0, ..., n-1.

getForwardNthRoot

public long getForwardNthRoot(long primitiveRoot,
 long n)

Get forward n:th root of unity. This is w.

Assumes that the modulus is prime.

Parameters:

primitiveRoot - Primitive root of the modulus.

n - The transform length.

Returns:

Forward n:th root of unity.

getInverseNthRoot

public long getInverseNthRoot(long primitiveRoot,
 long n)

Get inverse n:th root of unity. This is w-1.

Assumes that the modulus is prime.

Parameters:

primitiveRoot - Primitive root of the modulus.

n - The transform length.

Returns:

Inverse n:th root of unity.

modInverse

public final long modInverse(long a)

Modular inverse, that is 1 / a. Assumes that the modulus is prime.

Parameters:

a - The operand.

Returns:

a-1 mod m.

modDivide

public final long modDivide(long a,
 long b)

Modular division. Assumes that the modulus is prime.

Parameters:

a - The dividend.

b - The divisor.

Returns:

a*b-1 mod m.

negate

public final long negate(long a)

Modular negation.

Parameters:

a - The argument.

Returns:

-a mod m.

modPow

public final long modPow(long a,
 long n)

Modular power. Assumes that the modulus is prime.

Parameters:

a - The base.

n - The exponent.

Returns:

an mod m.