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package MDK::Common::Math;
=head1 NAME
MDK::Common::Math - miscellaneous math functions
=head1 SYNOPSIS
use MDK::Common::Math qw(:all);
=head1 EXPORTS
=over
=item $PI
the well-known constant
=item even(INT)
=item odd(INT)
is the number even or odd?
=item sqr(FLOAT)
C<sqr(3)> gives C<9>
=item sign(FLOAT)
returns a value in { -1, 0, 1 }
=item round(FLOAT)
C<round(1.2)> gives C<1>, C<round(1.6)> gives C<2>
=item round_up(FLOAT, INT)
returns the number rounded up to the modulo:
C<round_up(11,10)> gives C<20>
=item round_down(FLOAT, INT)
returns the number rounded down to the modulo:
C<round_down(11,10)> gives C<10>
=item divide(INT, INT)
integer division (which is lacking in perl). In array context, also returns the remainder:
C<($a, $b) = divide(10,3)> gives C<$a is 3> and C<$b is 1>
=item min(LIST)
=item max(LIST)
returns the minimum/maximum number in the list
=item or_(LIST)
is there a true value in the list?
=item and_(LIST)
are all values true in the list?
=item sum(LIST)
=item product(LIST)
returns the sum/product of all the element in the list
=item factorial(INT)
C<factorial(4)> gives C<24> (4*3*2)
=back
=head1 OTHER
the following functions are provided, but not exported:
=over
=item factorize(INT)
C<factorize(40)> gives C<([2,3], [5,1])> as S<40 = 2^3 + 5^1>
=item decimal2fraction(FLOAT)
C<decimal2fraction(1.3333333333)> gives C<(4, 3)>
($PRECISION is used to decide which precision to use)
=item poly2(a,b,c)
Solves the a*x2+b*x+c=0 polynomial:
C<poly2(1,0,-1)> gives C<(1, -1)>
=item permutations(n,p)
A(n,p)
=item combinaisons(n,p)
C(n,p)
=back
=head1 SEE ALSO
L<MDK::Common>
=cut
use vars qw(@ISA %EXPORT_TAGS @EXPORT_OK $PRECISION $PI);
@ISA = qw(Exporter);
@EXPORT_OK = qw($PI even odd sqr sign round round_up round_down divide min max or_ and_ sum product factorial);
%EXPORT_TAGS = (all => [ @EXPORT_OK ]);
$PRECISION = 10;
$PI = 3.1415926535897932384626433832795028841972;
sub even { $_[0] % 2 == 0 }
sub odd { $_[0] % 2 == 1 }
sub sqr { $_[0] * $_[0] }
sub sign { $_[0] <=> 0 }
sub round { int($_[0] + 0.5) }
sub round_up { my ($i, $r) = @_; $i = int $i; $i += $r - ($i + $r - 1) % $r - 1 }
sub round_down { my ($i, $r) = @_; $i = int $i; $i -= $i % $r }
sub divide { my $d = int $_[0] / $_[1]; wantarray() ? ($d, $_[0] % $_[1]) : $d }
sub min { my $n = shift; $_ < $n and $n = $_ foreach @_; $n }
sub max { my $n = shift; $_ > $n and $n = $_ foreach @_; $n }
sub or_ { my $n = 0; $n ||= $_ foreach @_; $n }
sub and_ { my $n = 1; $n &&= $_ foreach @_; $n }
sub sum { my $n = 0; $n += $_ foreach @_; $n }
sub product { my $n = 1; $n *= $_ foreach @_; $n }
sub factorize {
my ($n) = @_;
my @r;
$n == 1 and return [ 1, 1 ];
for (my $k = 2; sqr($k) <= $n; $k++) {
my $i = 0;
for ($i = 0; $n % $k == 0; $i++) { $n /= $k }
$i and push @r, [ $k, $i ];
}
$n > 1 and push @r, [ $n, 1 ];
@r;
}
sub decimal2fraction { # ex: 1.33333333 -> (4, 3)
my $n0 = shift;
my $precision = 10 ** -(shift || $PRECISION);
my ($a, $b) = (int $n0, 1);
my ($c, $d) = (1, 0);
my $n = $n0 - int $n0;
my $k;
until (abs($n0 - $a / $c) < $precision) {
$n = 1 / $n;
$k = int $n;
($a, $b) = ($a * $k + $b, $a);
($c, $d) = ($c * $k + $d, $c);
$n -= $k;
}
($a, $c)
}
sub poly2 {
my ($a, $b, $c) = @_;
my $d = ($b**2 - 4 * $a * $c) ** 0.5;
(-$b + $d) / 2 / $a, (-$b - $d) / 2 / $a
}
# A(n,p)
sub permutations {
my ($n, $p) = @_;
my ($r, $i);
for ($r = 1, $i = 0; $i < $p; $i++) {
$r *= $n - $i;
}
$r
}
# C(n,p)
sub combinaisons {
my ($n, $p) = @_;
permutations($n, $p) / factorial($p)
}
sub factorial { permutations($_[0], $_[0]) }
1;
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