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Diffstat (limited to 'lib/MDK/Common/Math.pm')
-rw-r--r-- | lib/MDK/Common/Math.pm | 197 |
1 files changed, 197 insertions, 0 deletions
diff --git a/lib/MDK/Common/Math.pm b/lib/MDK/Common/Math.pm new file mode 100644 index 0000000..5ed9a61 --- /dev/null +++ b/lib/MDK/Common/Math.pm @@ -0,0 +1,197 @@ +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 Exporter; +our @ISA = qw(Exporter); +our @EXPORT_OK = qw($PI even odd sqr sign round round_up round_down divide min max or_ and_ sum product factorial); +our %EXPORT_TAGS = (all => [ @EXPORT_OK ]); + + +our $PRECISION = 10; +our $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; |