thomasegense / bigmathfast

Java implementation of math utils for large numbers. Fast factoring + inverse Euler Totient etc.

bigmathfast

Java implementation of mathematical functions for large numbers. The implementation uses some of the fastests algorithms know. See benchmark tests below.

Factorization

For numbers less than 22 digits the PollardRho algoritm is used. For numbers larger than 22 digits the algorithm will use ECM/Siqs.

The ECM/Siqs implementation is the same algorithm decribed here and by same auhor: https://www.alpertron.com.ar/ECM.HTM

Factorization time depends on the size of the second largest primefactor. If the second largest primefactor has over 45 digits the factorization can take many days. See the benchmark tests below.

Usage:

BigMathFast.factorize(BigInteger b)

Euler Totient (phi) and inverse Euler Totient (invphi)

The inverse euler totient uses the algorithm described by Hansraj Gupta: https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a81_22.pdf

Usage:

BigMathFast.inverseEulerTotient(BigInteger b)

BigMathFast.eulerTotient(BigInteger b)

Rationalize - approximate a BigDecimal with a fraction.

Finds the best rational approximation to a BigDecimal. Precision up to 10000 digits. Can take maximum denominator value or maximum number of digits in denominator as input.

BigMathFast.PI constant has the first 5400 digits of PI

Usage:

FareyRationalApproxmation.fareyApproxWithMaxDenom(BigMathFast.PI, new BigInteger("999"));

Will return 355/113

FareyRationalApproxmation.fareyApproxWithMaxDenom(BigMathFast.PI, 5); //Maximum denominator will be 99999

Will return 312689/99532

Maven

Add these two blocks to your .m2/settings.xml

profiles>
    <profile>
      <id>github</id>
      <repositories>
        <repository>
          <id>central</id>
          <url>https://repo1.maven.org/maven2</url>
          <releases><enabled>true</enabled></releases>
          <snapshots><enabled>true</enabled></snapshots>
        </repository>
        <repository>
          <id>github</id>
          <name>GitHub OWNER Apache Maven Packages</name>
          <url>https://maven.pkg.github.com/thomasegense/bigmathfast</url>
        </repository>
      </repositories>
    </profile>
  </profiles>

<server>
    <id>github</id>
    <username>username</username>
    <password>password or token</password>
  </server>

Binary release

Download the stand alone jar:

https://github.com/thomasegense/bigmathfast/releases/download/v1.0/bigmathfast-1.0-jar-with-dependencies.jar

Main method to try the factorization:

java -cp bigmathfast-1.0-jar-with-dependencies.jar dk.teg.bigmathfast.BigMathFast 5519446392203102380014492878452138579184343772913786312128

Factorization benchmark for worst case numbers (*)

Number of digits	bigmathfast(ECM)	Math Wolfram	PARI
30	80 millis
40	290 millis
50	1.2 sec
60	4,7 sec		10.6 sec
70	25 sec	21 minutes	55 sec
80	6 minuntes 30 sec	12 hour 30 minutes	16 minutes
90	1 hours 16 minutes	6 days 16 hours	3 hours 37 minutes

(*) Numbers from benchmark table:

30 digits 147275865199119510385557165977 = 26573469154506 * 554221446747557

40 digits: 1468859383233401953850079471177142403357 = 4344062700916566703 * 33813033659101719361

50 digits: 8924060181263144762913076834769824195165519271249 = 1580680038114991309325617 * 5645709420045157326539297

60 digits: 57006543036882955477733064155963100765859988504898777062311 = 135153797414605589804898502907 * 421790168884462740869075554373

70 digits: 2008366610044614145105509426936481148630631765118331491742083502567441 = 229 * 13296624793876881897048465625547 * 659577900793976541082703745871501207

80 digits: 93035149443954345347665179408833277091909532522394543659489519897196854705698057 = 9365079368113765900517013922746586856483 * 9934261717067827536371100301835771377379

90 digits: 235619162309580984868967318620943039846576548536713751373304739395055583551615448989006587 = 477116622855714229032892479353541386967943093 * 493839767936224340101985740267792644210443759