IntegersZp64 (rings 2.5.7 API)

java.lang.Object
- cc.redberry.rings.IntegersZp64

All Implemented Interfaces:

Serializable
```
public final class IntegersZp64
extends Object
implements Serializable
```
Zp ring over machine numbers which provides fast modular arithmetic.

Since:

1.0

See Also:

FastDivision, Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`cc.redberry.libdivide4j.FastDivision.Magic`	`magic` magic
`cc.redberry.libdivide4j.FastDivision.Magic`	`magic32MulMod` magic
`long`	`modulus` the modulus
`boolean`	`modulusFits32` whether modulus less then 2^32 (if so, faster mulmod available)

Constructor Summary

Constructors
Constructor and Description
`IntegersZp64(long modulus)` Creates the ring.
`IntegersZp64(long modulus, cc.redberry.libdivide4j.FastDivision.Magic magic, cc.redberry.libdivide4j.FastDivision.Magic magic32MulMod, boolean modulusFits32)`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`long`	`add(long a, long b)` Add mod operation
`IntegersZp`	`asGenericRing()` Converts this to a generic ring over big integers
`void`	`buildCachedReciprocals()` builds a table of cached reciprocals
`long`	`divide(long a, long b)` Subtract mod operation
`boolean`	`equals(Object o)`
`long`	`factorial(int value)` Gives value!
`int`	`hashCode()`
`boolean`	`isPerfectPower()` Returns whether the modulus is a perfect power
`long`	`modulus(BigInteger val)` Returns `val % this.modulus`
`long`	`modulus(long val)` Returns `val % this.modulus`
`void`	`modulus(long[] data)` Inplace sets elements of `data` to `data % this.modulus`
`long`	`multiply(long a, long b)` Multiply mod operation
`long`	`negate(long val)` Negate mod operation
`long`	`perfectPowerBase()` Returns `base` if `modulus == base^exponent`, and `-1` otherwisec
`IntegersZp64`	`perfectPowerBaseDomain()` Returns ring for `perfectPowerBase()` or `this` if modulus is not a perfect power
`long`	`perfectPowerExponent()` Returns `exponent` if `modulus == base^exponent`, and `-1` otherwisec
`long`	`powMod(long base, long exponent)` Returns `base` in a power of non-negative `e` modulo `magic.modulus`
`long`	`randomElement()` Returns a random element from this ring
`long`	`randomElement(org.apache.commons.math3.random.RandomGenerator rnd)` Returns a random element from this ring
`long`	`randomNonZeroElement(org.apache.commons.math3.random.RandomGenerator rnd)` Returns a random non zero element from this ring
`long`	`reciprocal(long val)` Returns modular inverse of `val`
`long`	`subtract(long a, long b)` Subtract mod operation
`long`	`symmetricForm(long value)` to symmetric modulus
`String`	`toString()`

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

- Field Detail
  - modulus
```
public final long modulus
```
    the modulus
  - magic
```
public final cc.redberry.libdivide4j.FastDivision.Magic magic
```
    magic
  - magic32MulMod
```
public final cc.redberry.libdivide4j.FastDivision.Magic magic32MulMod
```
    magic
  - modulusFits32
```
public final boolean modulusFits32
```
    whether modulus less then 2^32 (if so, faster mulmod available)
- Constructor Detail
  - IntegersZp64
```
public IntegersZp64(long modulus,
                    cc.redberry.libdivide4j.FastDivision.Magic magic,
                    cc.redberry.libdivide4j.FastDivision.Magic magic32MulMod,
                    boolean modulusFits32)
```
  - IntegersZp64
```
public IntegersZp64(long modulus)
```
    Creates the ring.
    
    Parameters:
    
    modulus - the modulus
- Method Detail
  - modulus
```
public long modulus(long val)
```
    Returns val % this.modulus
  - modulus
```
public long modulus(BigInteger val)
```
    Returns val % this.modulus
  - modulus
```
public void modulus(long[] data)
```
    Inplace sets elements of data to data % this.modulus
  - multiply
```
public long multiply(long a,
                     long b)
```
    Multiply mod operation
  - add
```
public long add(long a,
                long b)
```
    Add mod operation
  - subtract
```
public long subtract(long a,
                     long b)
```
    Subtract mod operation
  - divide
```
public long divide(long a,
                   long b)
```
    Subtract mod operation
  - buildCachedReciprocals
```
public void buildCachedReciprocals()
```
    builds a table of cached reciprocals
  - reciprocal
```
public long reciprocal(long val)
```
    Returns modular inverse of val
  - negate
```
public long negate(long val)
```
    Negate mod operation
  - symmetricForm
```
public long symmetricForm(long value)
```
    to symmetric modulus
  - asGenericRing
```
public IntegersZp asGenericRing()
```
    Converts this to a generic ring over big integers
    
    Returns:
    
    generic ring
  - powMod
```
public long powMod(long base,
                   long exponent)
```
    Returns base in a power of non-negative e modulo magic.modulus
    
    Parameters:
    
    base - the base
    
    exponent - the non-negative exponent
    
    Returns:
    
    base in a power of e
  - randomElement
```
public long randomElement(org.apache.commons.math3.random.RandomGenerator rnd)
```
    Returns a random element from this ring
    
    Parameters:
    
    rnd - the source of randomness
    
    Returns:
    
    random element from this ring
  - randomElement
```
public long randomElement()
```
    Returns a random element from this ring
    
    Returns:
    
    random element from this ring
  - randomNonZeroElement
```
public long randomNonZeroElement(org.apache.commons.math3.random.RandomGenerator rnd)
```
    Returns a random non zero element from this ring
    
    Parameters:
    
    rnd - the source of randomness
    
    Returns:
    
    random non zero element from this ring
  - factorial
```
public long factorial(int value)
```
    Gives value!
    
    Parameters:
    
    value - the number
    
    Returns:
    
    value!
  - isPerfectPower
```
public boolean isPerfectPower()
```
    Returns whether the modulus is a perfect power
    
    Returns:
    
    whether the modulus is a perfect power
  - perfectPowerBase
```
public long perfectPowerBase()
```
    Returns base if modulus == base^exponent, and -1 otherwisec
    
    Returns:
    
    base if modulus == base^exponent, and -1 otherwisec
  - perfectPowerExponent
```
public long perfectPowerExponent()
```
    Returns exponent if modulus == base^exponent, and -1 otherwisec
    
    Returns:
    
    exponent if modulus == base^exponent, and -1 otherwisec
  - perfectPowerBaseDomain
```
public IntegersZp64 perfectPowerBaseDomain()
```
    Returns ring for perfectPowerBase() or this if modulus is not a perfect power
    
    Returns:
    
    ring for perfectPowerBase() or this if modulus is not a perfect power
  - equals
```
public boolean equals(Object o)
```
    Overrides:
    
    equals in class Object
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class Object

Class IntegersZp64

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

modulus

magic

magic32MulMod

modulusFits32

Constructor Detail

IntegersZp64

IntegersZp64

Method Detail

modulus

modulus

modulus

multiply

add

subtract

divide

buildCachedReciprocals

reciprocal

negate

symmetricForm

asGenericRing

powMod

randomElement

randomElement

randomNonZeroElement

factorial

isPerfectPower

perfectPowerBase

perfectPowerExponent

perfectPowerBaseDomain

equals

toString

hashCode