summaryrefslogtreecommitdiffstats
path: root/MDK/Common/Math.pm
blob: 5ed9a616bd3e3861396015d8e69e08cd8d3054ac (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
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;