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Code covered by the BSD License  

Highlights from
Variable Precision Integer Arithmetic

  • demo_vpi
  • base2vpi(B,base) bin2vpi: converts an integer in an arbitrary base into vpi (decimal) form
  • bin2vpi(B) bin2vpi: converts a binary representation of an integer into vpi (decimal) form
  • binomfactors(n,k) binomfactors: list all factors of the binomial coefficient nchoosek(n,k)
  • catdigits(N,M) catdigits: concatenates the digits of N and M into an aggregate number
  • createPrimesList createPrimesList - For users of older matlab releases, this function will generate a compatible _primeslist_ file
  • factorialfactors(n) factorialfactors: efficient computation of the prime factors of factorial(n)
  • fibonacci(n) fibonacci: vpi tool to efficiently compute the n'th Fibonacci number and the n'th Lucas number
  • getprimeslist loads the primeslist file, and decompresses it, returning the list of primes up to 2^26
  • ispalindrome(N) ispalindrome: test if the number N (vpi or numeric, or a digit string as a vector) is a palindrome
  • iszero(INT) vpi/iszero: test to see if a numeric object is zero
  • legendresymbol(a,p) legendresymbol: computes the legendre symbol (a/p) for prime p
  • lineardiophantine(A,B,C) lineardiophantine: solve the linear Diophantine equation, A*x + B*y = C
  • mersenne(p) mersenne: identify whether 2^p-1 is a Mersenne prime, using the Lucas-Lehmer test
  • minv(a,p)
  • modfibonacci(n,modulus) fibonacci: compute the n'th Fibonacci number and the n'th Lucas number, all modulo a given value
  • modrank(A,p) modrank: compute the rank of an integer array, modulo p
  • modroot(a,p)
  • modsolve(A,rhs,p)
  • nextprime(N,direction,kprimes) nextprime: finds the next larger prime number directly above (or below) N
  • numberOfPartitions(N) numberOfPartitions: compute the number of partitions of the positive integer n
  • powermod(a,d,n) vpi/powermod: Compute mod(a^d,n)
  • quadraticresidues(N) quadraticresidues: returns a list of the possible quadratic residues of the integer N
  • quotient(numerator,denominato... quotient: divides two integers, computing a quotient and remainder
  • subfactorial(N) subfactorial: The subfactorial of an integer (or integers) N, known as !N
  • totient(N) vpi/totient: the number of positive integers less than N that are coprime to N
  • vpi(N) vpi: Creator function for a variable precision integer
  • View all files
from Variable Precision Integer Arithmetic by John D'Errico
Arithmetic with integers of fully arbitrary size. Arrays and vectors of vpi numbers are supported.

getprimeslist 
function primeslist = getprimeslist
% loads the primeslist file, and decompresses it, returning the list of primes up to 2^26
% usage: primeslist = getprimeslist
%
% see also: createprimeslist, primes
%
% Author: John D'Errico
% e-mail: woodchips@rochester.rr.com
% Release: 1.0
% Release date: 7/22/09

% load the compressed form
load _primeslist_

% these are uint8 numbers, where I simply stored
% difference between consecutive primes as a uint8.
% this works, since the largest such difference was
% never more than 220 up to that point.
% The act of decompressing the list takes no more
% than a double and a cumsum.
primeslist = cumsum([2,double(primeslist)]);

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