# Perl Weekly Challenge 167: too much math!

It is sad that, after more than two years of me doing Raku, I still don’t have any production code project to work on. Therefore, in order to keep my coding and Raku-ing (is that a term?) knowdledge, I try to solve every Perl Weekly Challenge tasks.

In the following, the assigned tasks for Challenge 167.

and for the sake of some Perl 5, let’s do some stuff also in PostgreSQL Pl/Perl:
Last, the solutions in PostgreSQL PL/PgSQL:

## PWC 167 - Task 1

Compute all cyclic primes within the rage of three digits. A cyclic prime is a number that is prime and has its digits, permutated towards left, that provide also all prime numbers.

``````sub is-circular-prime( Int \$prime )
{
return False if ! \$prime.is-prime;

my @digits = \$prime.comb;
my \$found = True;
for 1 ..^ @digits.elems {
return False if ! ( |@digits[ \$_ .. * - 1], |@digits[ 0 .. \$_ - 1 ] ).join.Int.is-prime;
}

return True;
}

sub MAIN() {
(100 .. 999).grep( { is-circular-prime( \$_ ) } ).join( "\n" ).say;
}

``````

All the work is done clearly from the `is-circular-prime` function, that checks if the input number is prime, and then computes the permutations by moving digits towards left and re-inserting the extracted digits on the end. As soon as a non-prime number is detected, the function stops.

## PWC 167 - Task 2

An implementation of the Gamma Function, quite complex to me!

``````my @coeffs = <
1.000000000000000174663
5716.400188274341379136
-14815.30426768413909044
14291.49277657478554025
-6348.160217641458813289
1301.608286058321874105
-108.1767053514369634679
2.605696505611755827729
-0.7423452510201416151527e-2
0.5384136432509564062961e-7
-0.4023533141268236372067e-8
>;

sub gamma( \$z )
{
if ( \$z < 0.5 ) {
pi / sin( pi * \$z ) / gamma( \$z - 1 );
}
else {
sqrt( 2 * pi )
* ( \$z + 9 - 0.5) ** ( \$z  - 0.5)
* exp( -1 * ( \$z + 9 - 0.5))
* [+] @coeffs Z* 1, |map 1 / (\$z + * ) , 0 .. *;
}

}

sub MAIN( Int \$value ) {
gamma( \$value ).say;
}

``````

I have to say that is not something I can re-implement easily, and I have to search online about possible implementations trying to understand how to implement it.

## PWC 167 - Task 1 in PostgreSQL PL/Perl

Pretty much the same implementation of Raku, done with anonymous subroutines:

``````CREATE OR REPLACE FUNCTION
RETURNS SETOF int
AS \$CODE\$

# utility function to check if a number is prime
my \$is_prime = sub {
my (\$num) = @_;
for ( 2 .. \$num - 1 ) {
return 0 if ( \$num % \$_ == 0 );
}

return 1;
};

# get all the permutations
my \$compute_permutations = sub {
my (\$num) = @_;
my @perms;
my @digits = split //, \$num;

for ( 0 .. \$#digits  ) {
push @perms, join( '',        @digits[ \$_ .. \$#digits ], @digits[ 0 .. \$_ - 1 ] );
}

return @perms;
};

# check if the given number is a
# cyclic prime
my \$is_cyclic_prime = sub {
my (\$value) = @_;

return 0 unless( \$is_prime->( \$value ) );
for (\$compute_permutations->( \$value ) ) {
return 0 unless( \$is_prime->( \$_ ) );
}

return 1;
};

for ( 100 .. 999 ) {
return_next( \$_ ) if \$is_cyclic_prime->( \$_ );
}

return undef;

\$CODE\$
LANGUAGE plperl;

``````

## PWC 167 - Task 2 in PostgreSQL PL/Perl

A translation of what the Raku version does:

``````CREATE OR REPLACE FUNCTION
RETURNS numeric
AS \$CODE\$

my @coeffs = qw/
1.000000000000000174663
5716.400188274341379136
-14815.30426768413909044
14291.49277657478554025
-6348.160217641458813289
1301.608286058321874105
-108.1767053514369634679
2.605696505611755827729
-0.7423452510201416151527e-2
0.5384136432509564062961e-7
-0.4023533141268236372067e-8
/;

my \$sum_coeffs = 0;
\$sum_coeffs += \$_ for ( @coeffs );

my \$gamma = sub {
my (\$z) = @_;
my \$pi = 3.1415;

if ( \$z < 0.5 ) {
\$pi / sin( \$pi * \$z ) / gamma( \$z - 1 );
}
else {
sqrt( 2 * \$pi )
* ( \$z + 9 - 0.5) ** ( \$z  - 0.5)
* exp( -1 * ( \$z + 9 - 0.5))
*  do {
my (\$sum, \$i) = (shift(@coeffs), 0);
\$sum += \$_ / (\$z + \$i++) for @coeffs;
\$sum;
};
}

};

return \$gamma->( \$_ );

\$CODE\$
LANGUAGE plperl;

``````

## PWC 167 - Task 1 in PostgreSQL PL/PgSQL

not implemented

``````
``````

## PWC 167 - Task 2 in PostgreSQL PL/PgSQL

not implemented

``````
``````

The article Perl Weekly Challenge 167: too much math! has been posted by Luca Ferrari on May 30, 2022