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# Copyright 2012, 2013, 2014 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-PlanePath is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
package Math::PlanePath::SumFractions;
use 5.004;
use strict;
use List::Util 'max';
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
@ISA = ('Math::PlanePath');
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
use Math::NumSeq::BalancedBinary;
# uncomment this to run the ### lines
# use Smart::Comments;
use constant class_x_negative => 0;
use constant class_y_negative => 0;
use constant xy_is_visited => 1;
sub new {
my $self = shift->SUPER::new (@_);
$self->{'seq'} = Math::NumSeq::BalancedBinary->new;
return $self;
}
sub n_to_xy {
my ($self, $n) = @_;
### SumFractions n_to_xy(): $n
if ($n < 1) { return; }
if (is_infinite($n) || $n == 0) { return ($n,$n); }
{
# fractions on straight line ?
my $int = int($n);
if ($n != $int) {
my $frac = $n - $int; # inherit possible BigFloat/BigRat
my ($x1,$y1) = $self->n_to_xy($int);
my ($x2,$y2) = $self->n_to_xy($int+1);
my $dx = $x2-$x1;
my $dy = $y2-$y1;
return ($frac*$dx + $x1, $frac*$dy + $y1);
}
$n = $int;
}
my $d = int((sqrt(8*$n-7) - 1) / 2);
$n -= $d*($d+1)/2 + 1;
### $d
### $n
return _dn_to_xy($d,$n);
}
sub _dn_to_xy {
my ($d,$n) = @_;
if ($n == 0) { return (1,1); }
if ($n == $d) { return (1,$d+1) };
return _rat_sum(_dn_to_xy($d-1,$n),
_dn_to_xy($d-1,$n-1));
}
sub _rat_sum {
my ($x1,$y1, $x2,$y2) = @_;
my $num = $x1*$y2 + $x2*$y1;
my $den = $y1*$y2;
my $gcd = Math::PlanePath::GcdRationals::_gcd($num,$den);
return ($num/$gcd, $den/$gcd);
}
use Math::PlanePath::GcdRationals;
*_gcd = \&Math::PlanePath::GcdRationals::_gcd;
sub xy_to_n {
my ($self, $x, $y) = @_;
### SumFractions xy_to_n(): "$x, $y"
return undef;
$x = round_nearest ($x);
$y = round_nearest ($y);
if ($x < 0 || $y < 0) {
return undef;
}
my $zero = $x * 0 * $y;
if (is_infinite($x)) { return $x; }
if (is_infinite($y)) { return $y; }
my $value = $self->{'seq'}->ith($y) || 0;
### value at y: $value
my $pow = (4+$zero)**$x;
$value *= $pow;
$value += 2*($pow-1)/3;
### mul: sprintf '%#b', $pow
### add: sprintf '%#b', 2*($pow-1)/3
### value: sprintf '%#b', $value
### $value
### value: ref $value && $value->as_bin
return $self->{'seq'}->value_to_i($value);
}
# exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### SumFractions rect_to_n_range(): "$x1,$y1 $x2,$y2"
return (1,10000);
$x1 = round_nearest ($x1);
$y1 = round_nearest ($y1);
$x2 = round_nearest ($x2);
$y2 = round_nearest ($y2);
($x1,$x2) = ($x2,$x1) if $x1 > $x2;
($y1,$y2) = ($y2,$y1) if $y1 > $y2;
if ($x2 < 0 || $y2 < 0) {
### all outside first quadrant ...
return (1, 0);
}
# bottom left into first quadrant
if ($x1 < 0) { $x1 *= 0; }
if ($y1 < 0) { $y1 *= 0; }
return (0,
4**($x2+$y2));
return ($self->xy_to_n($x1,$y1), # bottom left
$self->xy_to_n($x2,$y2)); # top right
}
1;
__END__
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