=encoding utf8

=head1 NAME

std/math/roman - Roman numeral formatter for ZuzuScript.

=head1 SYNOPSIS

  from std/math/roman import roman;

  say( roman( 2026 ) );   # MMXXVI
  say( roman( 0 ) );      # N
  say( roman( 1.6 ) );    # IS·
  say( roman( 0.5 ) );    # S

=head1 IMPLEMENTATION SUPPORT

This module is supported by all implementations of ZuzuScript.

=head1 DESCRIPTION

This module exports a single pure-Zuzu helper, C<roman>, which
formats numbers using Roman numerals with twelfth fractions.

=head1 EXPORTS

=head2 Functions

=over

=item * C<< roman(Number n) >>

Parameters: C<n> is the number to render. Returns: C<String>. Formats
C<n> as a Roman numeral, returning C<N> for zero.

Whole numbers from 1 to 3999 are formatted with standard Roman
numeral subtractive notation.

Non-integers are rounded to the nearest twelfth. The fractional
part is appended using ancient twelfth marks:

  1/12  => ·
  2/12  => :
  3/12  => ∴
  4/12  => ∷
  5/12  => ⁙
  6/12  => S
  7/12  => S·
  8/12  => S:
  9/12  => S∴
  10/12 => S∷
  11/12 => S⁙

For values whose rounded twelfth part is exactly 12/12, the carry
is applied to the integer Roman numeral part.

=back

=head1 COPYRIGHT AND LICENCE

B<< std/math/roman >> is copyright Toby Inkster.

It is free software; you may redistribute it and/or modify it under
the terms of either the Artistic License 1.0 or the GNU General Public
License version 2.

=cut

function _roman_integer ( Number n ) {
	if ( n < 1 or n > 3999 ) {
		die "Roman integer part must be between 1 and 3999";
	}
	let values := [ 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1 ];
	let numerals := [ "M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I" ];
	let out := "";
	let rem := n;
	let i := 0;

	while ( i < values.length() ) {
		let value := values[i];
		while ( rem >= value ) {
			out _= numerals[i];
			rem -= value;
		}
		i++;
	}

	return out;
}

function _twelfth_marker ( Number twelfths ) {
	if ( twelfths = 0 ) {
		return "";
	}
	if ( twelfths = 1 ) {
		return "·";
	}
	if ( twelfths = 2 ) {
		return":";
	}
	if ( twelfths = 3 ) {
		return "∴";
	}
	if ( twelfths = 4 ) {
		return "∷";
	}
	if ( twelfths = 5 ) {
		return "⁙";
	}
	if ( twelfths = 6 ) {
		return "S";
	}
	if ( twelfths = 7 ) {
		return "S·";
	}
	if ( twelfths = 8 ) {
		return "S:";
	}
	if ( twelfths = 9 ) {
		return "S∴";
	}
	if ( twelfths = 10 ) {
		return "S∷";
	}
	if ( twelfths = 11 ) {
		return "S⁙";
	}
	die "Invalid twelfth marker";
}

function roman ( Number n ) {
	let sign := "";
	let magnitude := n;
	if ( magnitude < 0 ) {
		sign := "-";
		magnitude := abs(magnitude);
	}
	let rounded_twelfths := round( magnitude * 12 );
	let whole := int( rounded_twelfths / 12 );
	let frac := rounded_twelfths mod 12;
	if ( whole = 0 and frac = 0 ) {
		return sign _ "N";
	}
	let whole_text := "";
	if ( whole > 0 ) {
		whole_text := _roman_integer(whole);
	}
	if ( frac = 0 ) {
		return sign _ whole_text;
	}
	if ( whole = 0 ) {
		return sign _ _twelfth_marker(frac);
	}

	return sign _ whole_text _ _twelfth_marker(frac);
}
