#!/Applications/Rakudo/bin/perl6

use Test;

multi infix:<↑> ( Int:D \n, Int:D \m  --> Int:D )
	is equiv(&infix:<**>)
	is assoc<right>
	{ n ** m }

proto infix:<↑↑> ( Int:D \n, Int:D \m --> Int:D )
	is tighter(&infix:<↑>)
	is assoc<right>
	{ * }
multi infix:<↑↑> ( \n,  0 ) { 1 }
multi infix:<↑↑> ( \n,  1 ) { n }
multi infix:<↑↑> ( \n, \m ) { [↑] n xx m }

proto infix:<↑↑↑> ( Int:D \n, Int:D \m --> Int:D )
	is tighter(&infix:<↑↑>)
	is assoc<right>
	{ * }
multi infix:<↑↑↑> ( \n,  0 ) { 1 }
multi infix:<↑↑↑> ( \n,  1 ) { n }
multi infix:<↑↑↑> ( \n, \m ) { [↑↑] n xx m }


multi infix:<↑⁰> ( Int:D \n, Int:D \m --> Int:D ) is assoc<right> { 1 }
multi infix:<↑²> ( Int:D \n, 0        --> Int:D ) is assoc<right> { 1 }
multi infix:<↑²> ( Int:D \n, Int:D \m --> Int:D ) is assoc<right> {
	[↑] n xx m
	}
multi infix:<↑³> ( Int:D \n, 0        --> Int:D ) is assoc<right> { 1 }
multi infix:<↑³> ( Int:D \n, Int:D \m --> Int:D ) is assoc<right> {
	[↑↑] n xx m
	}

# tetration notation
multi prefix:<⁰>  ( Int:D \m --> Int:D ) { 1 }
multi prefix:<²>  ( Int:D \m --> Int:D ) { m ↑↑ 2 }
multi prefix:<³>  ( Int:D \m --> Int:D ) { m ↑↑ 3 }
multi prefix:<⁴>  ( Int:D \m --> Int:D ) { m ↑↑ 4 }

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# Now a bunch of tests
is 2↑0,  1, '2↑0 ==  1';
is 2↑1,  2, '2↑1 ==  2';
is 2↑2,  4, '2↑2 ==  4';
is 2↑3,  8, '2↑3 ==  8';
is 2↑4, 16, '2↑4 == 16';

is 2↑2↑2,      16, '2↑2↑2 == 16';
is 2↑2↑2↑2, 65536, '2↑2↑2↑2 == 65536';

is 2↑⁰0,  1, '2↑⁰0 ==  1';

is 2↑2↑2,      16, '2↑2↑2 == 16';
is 2↑2↑2↑2, 65536, '2↑2↑2↑2 == 65536';

is 2↑↑0,      1, '2↑↑0 ==     1';
is 2↑↑1,      2, '2↑↑1 ==     2';
is 2↑↑2,      4, '2↑↑2 ==     4';
is 2↑↑3,     16, '2↑↑3 ==    16';
is 2↑↑4,  65536, '2↑↑4 == 65536';

is ²2, 2↑↑2, '²2  ==  4';

is 2↑²4,  65536, '2↑²4 == 65536';
is ⁴2,    2↑↑4,  '⁴2   == 65536';
is (2↑↑2)↑↑2, 4↑↑2,  '(2↑↑2)↑↑2   == 4↑↑2';
is ²(²2), (2↑↑2)↑↑2, '²(²2)   == 256';


is 3↑↑2, 27,    '3↑↑2 == 27';
is 3↑²2, 27,    '3↑²2 == 27';
is ²3,   27,    '²3   == 27';

is 3↑↑3, 7625597484987, '3↑↑3 == 7625597484987';
is 3↑²3, 7625597484987, '3↑²3 == 7625597484987';
is ³3,   7625597484987, '³3   == 7625597484987';

is 4↑↑3, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096,
	'4↑↑3 == 1.34078e154';
is 4↑²3, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096,
	'4↑²3 == 1.34078e154';

is 2↑↑↑3, 65536, '2↑↑↑3 == 65536';
is 2↑³3, 65536, '2↑³3 == 65536';