How to resolve the algorithm Miller–Rabin primality test step by step in the Raku programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Miller–Rabin primality test step by step in the Raku programming language
Table of Contents
Problem Statement
The Miller–Rabin primality test or Rabin–Miller primality test is a primality test: an algorithm which determines whether a given number is prime or not. The algorithm, as modified by Michael O. Rabin to avoid the generalized Riemann hypothesis, is a probabilistic algorithm. The pseudocode, from Wikipedia is:
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Miller–Rabin primality test step by step in the Raku programming language
Source code in the raku programming language
# the expmod-function from: http://rosettacode.org/wiki/Modular_exponentiation
sub expmod(Int $a is copy, Int $b is copy, $n) {
my $c = 1;
repeat while $b div= 2 {
($c *= $a) %= $n if $b % 2;
($a *= $a) %= $n;
}
$c;
}
subset PrimeCandidate of Int where { $_ > 2 and $_ % 2 };
my Bool multi sub is_prime(Int $n, Int $k) { return False; }
my Bool multi sub is_prime(2, Int $k) { return True; }
my Bool multi sub is_prime(PrimeCandidate $n, Int $k) {
my Int $d = $n - 1;
my Int $s = 0;
while $d %% 2 {
$d div= 2;
$s++;
}
for (2 ..^ $n).pick($k) -> $a {
my $x = expmod($a, $d, $n);
# one could just write "next if $x == 1 | $n - 1"
# but this takes much more time in current rakudo/nom
next if $x == 1 or $x == $n - 1;
for 1 ..^ $s {
$x = $x ** 2 mod $n;
return False if $x == 1;
last if $x == $n - 1;
}
return False if $x !== $n - 1;
}
return True;
}
say (1..1000).grep({ is_prime($_, 10) }).join(", ");
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