PLEAC-Perl 教程 - Numbers (Perl进阶者极力推荐)

转载 于 2008-04-25 12:40:00 发布 · 840 阅读 · 0
文章标签：

#numbers #perl #math #permissions #random #integer

本文介绍了一系列数值操作的方法，包括检查字符串是否为有效数字、比较浮点数、四舍五入、二进制与十进制转换等。此外还涉及了矩阵运算、复数运算及特殊数值如罗马数字和随机数的生成。

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2. Numbers

Checking Whether a String Is a Valid Number

#-----------------------------
if ($string =~ /PATTERN/) {
    # is a number
} else {
    # is not
}
#-----------------------------
warn "has nondigits"        if     //D/;
warn "not a natural number" unless /^/d+$/;             # rejects -3
warn "not an integer"       unless /^-?/d+$/;           # rejects +3
warn "not an integer"       unless /^[+-]?/d+$/;
warn "not a decimal number" unless /^-?/d+/.?/d*$/;     # rejects .2
warn "not a decimal number" unless /^-?(?:/d+(?:/./d*)?|/./d+)$/;
warn "not a C float"
       unless /^([+-]?)(?=/d|/./d)/d*(/./d*)?([Ee]([+-]?/d+))?$/;
#-----------------------------
sub getnum {
    use POSIX qw(strtod);
    my $str = shift;
    $str =~ s/^/s+//;
    $str =~ s//s+$//;
    $! = 0;
    my($num, $unparsed) = strtod($str);
    if (($str eq '') || ($unparsed != 0) || $!) {
        return;
    } else {
        return $num;
    } 
} 

sub is_numeric { defined scalar &getnum } 
#-----------------------------

Comparing Floating-Point Numbers

#-----------------------------
# equal(NUM1, NUM2, ACCURACY) : returns true if NUM1 and NUM2 are
# equal to ACCURACY number of decimal places

sub equal {
    my ($A, $B, $dp) = @_;

    return sprintf("%.${dp}g", $A) eq sprintf("%.${dp}g", $B);
  }
#-----------------------------
$wage = 536;                # $5.36/hour
$week = 40 * $wage;         # $214.40
printf("One week's wage is: /$%.2f/n", $week/100);
#
#One week's wage is: $214.40
#-----------------------------

Rounding Floating-Point Numbers

#-----------------------------
$rounded = sprintf("%FORMATf", $unrounded);
#-----------------------------
$a = 0.255;
$b = sprintf("%.2f", $a);
print "Unrounded: $a/nRounded: $b/n";
printf "Unrounded: $a/nRounded: %.2f/n", $a;

# Unrounded: 0.255
# 
# Rounded: 0.26
# 
# Unrounded: 0.255
# 
# Rounded: 0.26
#-----------------------------
use POSIX;
print "number/tint/tfloor/tceil/n";
@a = ( 3.3 , 3.5 , 3.7, -3.3 );
foreach (@a) {
    printf( "%.1f/t%.1f/t%.1f/t%.1f/n", 
        $_, int($_), floor($_), ceil($_) );
}

# number  int     floor   ceil
# 
#  3.3     3.0     3.0     4.0
# 
#  3.5     3.0     3.0     4.0
# 
#  3.7     3.0     3.0     4.0
# 
# -3.3    -3.0    -4.0    -3.0
#-----------------------------

Converting Between Binary and Decimal

#-----------------------------
sub dec2bin {
    my $str = unpack("B32", pack("N", shift));
    $str =~ s/^0+(?=/d)//;   # otherwise you'll get leading zeros
    return $str;
}
#-----------------------------
sub bin2dec {
    return unpack("N", pack("B32", substr("0" x 32 . shift, -32)));
}
#-----------------------------
$num = bin2dec('0110110');  # $num is 54
$binstr = dec2bin(54);      # $binstr is 110110
#-----------------------------

Operating on a Series of Integers

#-----------------------------
foreach ($X .. $Y) {
    # $_ is set to every integer from X to Y, inclusive
}

foreach $i ($X .. $Y) {
    # $i is set to every integer from X to Y, inclusive
    }

for ($i = $X; $i <= $Y; $i++) {
    # $i is set to every integer from X to Y, inclusive
}

for ($i = $X; $i <= $Y; $i += 7) {
    # $i is set to every integer from X to Y, stepsize = 7
}
#-----------------------------
print "Infancy is: ";
foreach (0 .. 2) {
    print "$_ ";
}
print "/n";

print "Toddling is: ";
foreach $i (3 .. 4) {
    print "$i ";
}
print "/n";

print "Childhood is: ";
for ($i = 5; $i <= 12; $i++) {
    print "$i ";
}
print "/n";

# Infancy is: 0 1 2 
# 
# Toddling is: 3 4 
# 
# Childhood is: 5 6 7 8 9 10 11 12 
#-----------------------------

Working with Roman Numerals

#-----------------------------
use Roman;
$roman = roman($arabic);                        # convert to roman numerals
$arabic = arabic($roman) if isroman($roman);    # convert from roman numerals
#-----------------------------
use Roman;
$roman_fifteen = roman(15);                         # "xv"
print "Roman for fifteen is $roman_fifteen/n";
$arabic_fifteen = arabic($roman_fifteen);
print "Converted back, $roman_fifteen is $arabic_fifteen/n";

Roman for fifteen is xv

Converted back, xv is 15
#-----------------------------

Generating Random Numbers

#-----------------------------
$random = int( rand( $Y-$X+1 ) ) + $X;
#-----------------------------
$random = int( rand(51)) + 25;
print "$random/n";
#-----------------------------
$elt = $array[ rand @array ];
#-----------------------------
@chars = ( "A" .. "Z", "a" .. "z", 0 .. 9, qw(! @ $ % ^ & *) );
$password = join("", @chars[ map { rand @chars } ( 1 .. 8 ) ]);
#-----------------------------

Generating Different Random Numbers

#-----------------------------
srand EXPR;
#-----------------------------
srand( <STDIN> );
#-----------------------------

Making Numbers Even More Random

#-----------------------------
use Math::TrulyRandom;
$random = truly_random_value();

use Math::Random;
$random = random_uniform();
#-----------------------------

Generating Biased Random Numbers

#-----------------------------
sub gaussian_rand {
    my ($u1, $u2);  # uniformly distributed random numbers
    my $w;          # variance, then a weight
    my ($g1, $g2);  # gaussian-distributed numbers

    do {
        $u1 = 2 * rand() - 1;
        $u2 = 2 * rand() - 1;
        $w = $u1*$u1 + $u2*$u2;
    } while ( $w >= 1 );

    $w = sqrt( (-2 * log($w))  / $w );
    $g2 = $u1 * $w;
    $g1 = $u2 * $w;
    # return both if wanted, else just one
    return wantarray ? ($g1, $g2) : $g1;
}
#-----------------------------
# weight_to_dist: takes a hash mapping key to weight and returns
# a hash mapping key to probability
sub weight_to_dist {
    my %weights = @_;
    my %dist    = ();
    my $total   = 0;
    my ($key, $weight);
    local $_;

    foreach (values %weights) {
        $total += $_;
    }

    while ( ($key, $weight) = each %weights ) {
        $dist{$key} = $weight/$total;
    }

    return %dist;
}

# weighted_rand: takes a hash mapping key to probability, and
# returns the corresponding element
sub weighted_rand {
    my %dist = @_;
    my ($key, $weight);

    while (1) {                     # to avoid floating point inaccuracies
        my $rand = rand;
        while ( ($key, $weight) = each %dist ) {
            return $key if ($rand -= $weight) < 0;
        }
    }
}
#-----------------------------
# gaussian_rand as above
$mean = 25;
$sdev = 2;
$salary = gaussian_rand() * $sdev + $mean;
printf("You have been hired at /$%.2f/n", $salary);
#-----------------------------

Doing Trigonometry in Degrees, not Radians

#-----------------------------
BEGIN {
    use constant PI => 3.14159265358979;

    sub deg2rad {
        my $degrees = shift;
        return ($degrees / 180) * PI;
    }

    sub rad2deg {
        my $radians = shift;
        return ($radians / PI) * 180;
    }
}
#-----------------------------
use Math::Trig;

$radians = deg2rad($degrees);
$degrees = rad2deg($radians);
#-----------------------------
# deg2rad and rad2deg defined either as above or from Math::Trig
sub degree_sine {
    my $degrees = shift;
    my $radians = deg2rad($degrees);
    my $result = sin($radians);

    return $result;
}
#-----------------------------

Calculating More Trigonometric Functions

#-----------------------------
sub tan {
    my $theta = shift;

    return sin($theta)/cos($theta);
}
#-----------------------------
use POSIX;

$y = acos(3.7);
#-----------------------------
use Math::Trig;

$y = acos(3.7);
#-----------------------------
eval {
    $y = tan($pi/2);
} or return undef;
#-----------------------------

Taking Logarithms

#-----------------------------
$log_e = log(VALUE);
#-----------------------------
use POSIX qw(log10);
$log_10 = log10(VALUE);
#-----------------------------
sub log_base {
    my ($base, $value) = @_;
    return log($value)/log($base);
}
#-----------------------------
# log_base defined as above
$answer = log_base(10, 10_000);
print "log10(10,000) = $answer/n";
# log10(10,000) = 4
#-----------------------------
use Math::Complex;
printf "log2(1024) = %lf/n", logn(1024, 2); # watch out for argument order!
# log2(1024) = 10.000000
#-----------------------------

Multiplying Matrices

#-----------------------------
use PDL;
# $a and $b are both pdl objects
$c = $a * $b;
#-----------------------------
sub mmult {
    my ($m1,$m2) = @_;
    my ($m1rows,$m1cols) = matdim($m1);
    my ($m2rows,$m2cols) = matdim($m2);

    unless ($m1cols == $m2rows) {  # raise exception
        die "IndexError: matrices don't match: $m1cols != $m2rows";
    }

    my $result = [];
    my ($i, $j, $k);

    for $i (range($m1rows)) {
        for $j (range($m2cols)) {
            for $k (range($m1cols)) {
                $result->[$i][$j] += $m1->[$i][$k] * $m2->[$k][$j];
            }
        }
    }
    return $result;
}

sub range { 0 .. ($_[0] - 1) }

sub veclen {
    my $ary_ref = $_[0];
    my $type = ref $ary_ref;
    if ($type ne "ARRAY") { die "$type is bad array ref for $ary_ref" }
    return scalar(@$ary_ref);
}

sub matdim {
    my $matrix = $_[0];
    my $rows = veclen($matrix);
    my $cols = veclen($matrix->[0]);
    return ($rows, $cols);
}
#-----------------------------
use PDL;

$a = pdl [
    [ 3, 2, 3 ],
    [ 5, 9, 8 ],
];

$b = pdl [
    [ 4, 7 ],
    [ 9, 3 ],
    [ 8, 1 ],
];

$c = $a x $b;  # x overload
#-----------------------------
# mmult() and other subroutines as above

$x = [
       [ 3, 2, 3 ],
       [ 5, 9, 8 ],
];

$y = [
       [ 4, 7 ],
       [ 9, 3 ],
       [ 8, 1 ],
];

$z = mmult($x, $y);
#-----------------------------

Using Complex Numbers

#-----------------------------
# $c = $a * $b manually
$c_real = ( $a_real * $b_real ) - ( $a_imaginary * $b_imaginary );
$c_imaginary = ( $a_real * $b_imaginary ) + ( $b_real * $a_imaginary );
#-----------------------------
# $c = $a * $b using Math::Complex
use Math::Complex;
$c = $a * $b;
#-----------------------------
$a_real = 3; $a_imaginary = 5;              # 3 + 5i;
$b_real = 2; $b_imaginary = -2;             # 2 - 2i;
$c_real = ( $a_real * $b_real ) - ( $a_imaginary * $b_imaginary );
$c_imaginary = ( $a_real * $b_imaginary ) + ( $b_real * $a_imaginary );
print "c = ${c_real}+${c_imaginary}i/n";

c = 16+4i
#-----------------------------
use Math::Complex;
$a = Math::Complex->new(3,5);               # or Math::Complex->new(3,5);
$b = Math::Complex->new(2,-2);
$c = $a * $b;
print "c = $c/n";

c = 16+4i
#-----------------------------
use Math::Complex;
$c = cplx(3,5) * cplx(2,-2);                # easier on the eye
$d = 3 + 4*i;                               # 3 + 4i
printf "sqrt($d) = %s/n", sqrt($d);

# sqrt(3+4i) = 2+i
#-----------------------------

Converting Between Octal and Hexadecimal

#-----------------------------
$number = hex($hexadecimal);         # hexadecimal
$number = oct($octal);               # octal
#-----------------------------
print "Gimme a number in decimal, octal, or hex: ";
$num = <STDIN>;
chomp $num;
exit unless defined $num;
$num = oct($num) if $num =~ /^0/; # does both oct and hex
printf "%d %x %o/n", $num, $num, $num;
#-----------------------------
print "Enter file permission in octal: ";
$permissions = <STDIN>;
die "Exiting .../n" unless defined $permissions;
chomp $permissions;
$permissions = oct($permissions);   # permissions always octal
print "The decimal value is $permissions/n";
#-----------------------------

Putting Commas in Numbers

#-----------------------------
sub commify {
    my $text = reverse $_[0];
    $text =~ s/(/d/d/d)(?=/d)(?!/d*/.)/$1,/g;
    return scalar reverse $text;
}
#-----------------------------
# more reasonable web counter :-)
use Math::TrulyRandom;
$hits = truly_random_value();       # negative hits!
$output = "Your web page received $hits accesses last month./n";
print commify($output);
Your web page received -1,740,525,205 accesses last month.
#-----------------------------

Printing Correct Plurals

#-----------------------------
printf "It took %d hour%s/n", $time, $time == 1 ? "" : "s";

printf "%d hour%s %s enough./n", $time, 
        $time == 1 ? ""   : "s",
        $time == 1 ? "is" : "are";
#-----------------------------
printf "It took %d centur%s", $time, $time == 1 ? "y" : "ies";
#-----------------------------
sub noun_plural {
    local $_ = shift;
    # order really matters here!
    s/ss$/sses/                             ||
    s/([psc]h)$/${1}es/                     ||
    s/z$/zes/                               ||
    s/ff$/ffs/                              ||
    s/f$/ves/                               ||
    s/ey$/eys/                              ||
    s/y$/ies/                               ||
    s/ix$/ices/                             ||
    s/([sx])$/$1es/                         ||
    s/$/s/                                  ||
                die "can't get here";
    return $_;
}
*verb_singular = /&noun_plural;   # make function alias
#-----------------------------
use Lingua::EN::Inflect qw(PL classical);
classical(1);               # why isn't this the default?
while (<DATA>) {            # each line in the data
    for (split) {           # each word on the line
        print "One $_, two ", PL($_), "./n";
    }
} 
# plus one more
$_ = 'secretary general';
print "One $_, two ", PL($_), "./n";

#__END__
#fish fly ox 
#species genus phylum 
#cherub radius jockey 
#index matrix mythos
#phenomenon formula 
#-----------------------------
#One fish, two fish.
#
#One fly, two flies.
#
#One ox, two oxen.
#
#One species, two species.
#
#One genus, two genera.
#
#One phylum, two phyla.
#
#One cherub, two cherubim.
#
#One radius, two radii.
#
#One jockey, two jockeys.
#
#One index, two indices.
#
#One matrix, two matrices.
#
#One mythos, two mythoi.
#
#One phenomenon, two phenomena.
#
#One formula, two formulae.
#
#One secretary general, two secretaries general.
#-----------------------------

Program: Calculating Prime Factors

#-----------------------------
#% bigfact 8 9 96 2178
#8          2**3
#
#9          3**2
#
#96         2**5 3
#
#2178       2 3**2 11**2
#-----------------------------
#% bigfact 239322000000000000000000
#+239322000000000000000000 2**19 3 5**18 +39887 
#
#
#% bigfact 25000000000000000000000000
#+25000000000000000000000000 2**24 5**26
#-----------------------------
# download the following standalone program
#!/usr/bin/perl
# bigfact - calculate prime factors
use strict;
use integer;

use vars qw{ $opt_b $opt_d };
use Getopt::Std;

@ARGV && getopts('bd')        or die "usage: $0 [-b] number ...";

load_biglib() if $opt_b;

ARG: foreach my $orig ( @ARGV ) {
    my ($n, $root, %factors, $factor);
    $n = $opt_b ? Math::BigInt->new($orig) : $orig;
    if ($n + 0 ne $n) { # don't use -w for this
        printf STDERR "bignum: %s would become %s/n", $n, $n+0 if $opt_d;
        load_biglib();
        $n = Math::BigInt->new($orig);
    }
    printf "%-10s ", $n;

    # Here $sqi will be the square of $i. We will take advantage
    # of the fact that ($i + 1) ** 2 == $i ** 2 + 2 * $i + 1.
    for (my ($i, $sqi) = (2, 4); $sqi <= $n; $sqi += 2 * $i ++ + 1) {
        while ($n % $i == 0) {
            $n /= $i;
            print STDERR "<$i>" if $opt_d;
            $factors {$i} ++;
        }
    }

    if ($n != 1 && $n != $orig) { $factors{$n}++ }
    if (! %factors) {
        print "PRIME/n";
        next ARG;
    }
    for $factor ( sort { $a <=> $b } keys %factors ) {
            print "$factor";
        if ($factors{$factor} > 1) {
        print "**$factors{$factor}";
        }
        print " ";
    }
    print "/n";
}

# this simulates a use, but at run time
sub load_biglib {
    require Math::BigInt;
    Math::BigInt->import();          #immaterial?
}

#-----------------------------
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