TinyEcm64_MontSqr (org.matheclipse:matheclipse-gpl 3.0.0 API)

java.lang.Object
- de.tilman_neumann.jml.factor.FactorAlgorithm
- - de.tilman_neumann.jml.factor.ecm.TinyEcm64_MontSqr

```
public class TinyEcm64_MontSqr
extends FactorAlgorithm
```
A port of Ben Buhrow's tinyecm.c (https://www.mersenneforum.org/showpost.php?p=521028&postcount=84) an ECM implementation for unsigned 64 bit integers. So far it works for inputs up to 62 bit, albeit not as fast as the C original. The (lack of an) assembler instruction to multiply two 64 bit integers seems to make a big impact here... This variant uses a special implementation for Montgomery squares. Not a very impressing improvement...

Author:

Tilman Neumann

Nested Class Summary

Nested Classes
Modifier and Type Class Description

static class TinyEcm64_MontSqr.EcmResult

Field Summary
- Fields inherited from class de.tilman_neumann.jml.factor.FactorAlgorithm
  DEFAULT, NUM_PRIMES_FOR_31_BIT_TDIV, tdivLimit

Constructor Summary

Constructors
Constructor Description

TinyEcm64_MontSqr()

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`BigInteger`	`findSingleFactor(BigInteger N)`	Find a single factor of the given N, which is composite and odd.
`String`	`getName()`
`static void`	`main(String[] args)`
`static long`	`montMul64(long a, long b, long N, long Nhat)`	Montgomery multiplication of a*b mod n.
`static long`	`montSqr64(long a, long N, long Nhat)`	Montgomery square of a mod n.

Methods inherited from class de.tilman_neumann.jml.factor.FactorAlgorithm
factor, factor, searchFactors

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

- Constructor Detail
  - TinyEcm64_MontSqr
```
public TinyEcm64_MontSqr()
```
- Method Detail
  - getName
```
public String getName()
```
    Specified by:
    
    getName in class FactorAlgorithm
    
    Returns:
    
    The name of the algorithm, possibly including important parameters.
  - montMul64
```
public static long montMul64(long a,
                             long b,
                             long N,
                             long Nhat)
```
    Montgomery multiplication of a*b mod n. ("mulredcx" in Yafu)
    
    Parameters:
    
    a -
    
    b -
    
    N -
    
    Nhat - complement of N mod 2^64
    
    Returns:
    
    Montgomery multiplication of a*b mod n
  - montSqr64
```
public static long montSqr64(long a,
                             long N,
                             long Nhat)
```
    Montgomery square of a mod n.
    
    Parameters:
    
    a -
    
    N -
    
    Nhat - complement of N mod 2^64
    
    Returns:
    
    Montgomery square of a mod n
  - findSingleFactor
```
public BigInteger findSingleFactor(BigInteger N)
```
    Description copied from class: FactorAlgorithm
    
    Find a single factor of the given N, which is composite and odd.
    
    Specified by:
    
    findSingleFactor in class FactorAlgorithm
    
    Returns:
    
    factor
  - main
```
public static void main(String[] args)
```