diff options
Diffstat (limited to 'contrib/perl5/lib/Math/Complex.pm')
| -rw-r--r-- | contrib/perl5/lib/Math/Complex.pm | 188 |
1 files changed, 132 insertions, 56 deletions
diff --git a/contrib/perl5/lib/Math/Complex.pm b/contrib/perl5/lib/Math/Complex.pm index 5b69039..1a47f4a 100644 --- a/contrib/perl5/lib/Math/Complex.pm +++ b/contrib/perl5/lib/Math/Complex.pm @@ -8,9 +8,10 @@ require Exporter; package Math::Complex; +use 5.005_64; use strict; -use vars qw($VERSION @ISA @EXPORT %EXPORT_TAGS); +our($VERSION, @ISA, @EXPORT, %EXPORT_TAGS); my ( $i, $ip2, %logn ); @@ -65,9 +66,10 @@ use overload # Package "privates" # -my $package = 'Math::Complex'; # Package name -my $display = 'cartesian'; # Default display format -my $eps = 1e-14; # Epsilon +my $package = 'Math::Complex'; # Package name +my %DISPLAY_FORMAT = ('style' => 'cartesian', + 'polar_pretty_print' => 1); +my $eps = 1e-14; # Epsilon # # Object attributes (internal): @@ -160,7 +162,7 @@ sub new { &make } # For backward compatibility only. # sub cplx { my ($re, $im) = @_; - return $package->make($re, defined $im ? $im : 0); + return __PACKAGE__->make($re, defined $im ? $im : 0); } # @@ -171,7 +173,7 @@ sub cplx { # sub cplxe { my ($rho, $theta) = @_; - return $package->emake($rho, defined $theta ? $theta : 0); + return __PACKAGE__->emake($rho, defined $theta ? $theta : 0); } # @@ -179,21 +181,21 @@ sub cplxe { # # The number defined as pi = 180 degrees # -use constant pi => 4 * CORE::atan2(1, 1); +sub pi () { 4 * CORE::atan2(1, 1) } # # pit2 # # The full circle # -use constant pit2 => 2 * pi; +sub pit2 () { 2 * pi } # # pip2 # # The quarter circle # -use constant pip2 => pi / 2; +sub pip2 () { pi / 2 } # # deg1 @@ -201,14 +203,14 @@ use constant pip2 => pi / 2; # One degree in radians, used in stringify_polar. # -use constant deg1 => pi / 180; +sub deg1 () { pi / 180 } # # uplog10 # # Used in log10(). # -use constant uplog10 => 1 / CORE::log(10); +sub uplog10 () { 1 / CORE::log(10) } # # i @@ -835,7 +837,7 @@ sub acos { my $u = CORE::atan2(CORE::sqrt(1-$beta*$beta), $beta); my $v = CORE::log($alpha + CORE::sqrt($alpha*$alpha-1)); $v = -$v if $y > 0 || ($y == 0 && $x < -1); - return $package->make($u, $v); + return __PACKAGE__->make($u, $v); } # @@ -857,7 +859,7 @@ sub asin { my $u = CORE::atan2($beta, CORE::sqrt(1-$beta*$beta)); my $v = -CORE::log($alpha + CORE::sqrt($alpha*$alpha-1)); $v = -$v if $y > 0 || ($y == 0 && $x < -1); - return $package->make($u, $v); + return __PACKAGE__->make($u, $v); } # @@ -1153,34 +1155,53 @@ sub atan2 { # display_format # ->display_format # -# Set (fetch if no argument) display format for all complex numbers that +# Set (get if no argument) the display format for all complex numbers that # don't happen to have overridden it via ->display_format # -# When called as a method, this actually sets the display format for +# When called as an object method, this actually sets the display format for # the current object. # # Valid object formats are 'c' and 'p' for cartesian and polar. The first # letter is used actually, so the type can be fully spelled out for clarity. # sub display_format { - my $self = shift; - my $format = undef; + my $self = shift; + my %display_format = %DISPLAY_FORMAT; - if (ref $self) { # Called as a method - $format = shift; - } else { # Regular procedure call - $format = $self; - undef $self; + if (ref $self) { # Called as an object method + if (exists $self->{display_format}) { + my %obj = %{$self->{display_format}}; + @display_format{keys %obj} = values %obj; + } + if (@_ == 1) { + $display_format{style} = shift; + } else { + my %new = @_; + @display_format{keys %new} = values %new; + } + } else { # Called as a class method + if (@_ = 1) { + $display_format{style} = $self; + } else { + my %new = @_; + @display_format{keys %new} = values %new; + } + undef $self; } if (defined $self) { - return defined $self->{display} ? $self->{display} : $display - unless defined $format; - return $self->{display} = $format; + $self->{display_format} = { %display_format }; + return + wantarray ? + %{$self->{display_format}} : + $self->{display_format}->{style}; } - return $display unless defined $format; - return $display = $format; + %DISPLAY_FORMAT = %display_format; + return + wantarray ? + %DISPLAY_FORMAT : + $DISPLAY_FORMAT{style}; } # @@ -1195,12 +1216,12 @@ sub display_format { # sub stringify { my ($z) = shift; - my $format; - $format = $display; - $format = $z->{display} if defined $z->{display}; + my $style = $z->display_format; + + $style = $DISPLAY_FORMAT{style} unless defined $style; - return $z->stringify_polar if $format =~ /^p/i; + return $z->stringify_polar if $style =~ /^p/i; return $z->stringify_cartesian; } @@ -1220,17 +1241,27 @@ sub stringify_cartesian { if int(CORE::abs($y)) != int(CORE::abs($y) + $eps); $re = "$x" if CORE::abs($x) >= $eps; - if ($y == 1) { $im = 'i' } - elsif ($y == -1) { $im = '-i' } - elsif (CORE::abs($y) >= $eps) { $im = $y . "i" } + + my %format = $z->display_format; + my $format = $format{format}; + + if ($y == 1) { $im = 'i' } + elsif ($y == -1) { $im = '-i' } + elsif (CORE::abs($y) >= $eps) { + $im = (defined $format ? sprintf($format, $y) : $y) . "i"; + } my $str = ''; - $str = $re if defined $re; - $str .= "+$im" if defined $im; - $str =~ s/\+-/-/; - $str =~ s/^\+//; - $str =~ s/([-+])1i/$1i/; # Not redundant with the above 1/-1 tests. - $str = '0' unless $str; + $str = defined $format ? sprintf($format, $re) : $re + if defined $re; + if (defined $im) { + if ($y < 0) { + $str .= $im; + } elsif ($y > 0) { + $str .= "+" if defined $re; + $str .= $im; + } + } return $str; } @@ -1277,6 +1308,8 @@ sub stringify_polar { return '[0,0]' if $r <= $eps; + my %format = $z->display_format; + my $nt = $t / pit2; $nt = ($nt - int($nt)) * pit2; $nt += pit2 if $nt < 0; # Range [0, 2pi] @@ -1299,7 +1332,7 @@ sub stringify_polar { $nt -= pit2 if $nt > pi; - if (CORE::abs($nt) >= deg1) { + if ($format{polar_pretty_print} && CORE::abs($nt) >= deg1) { my ($n, $k, $kpi); for ($k = 1, $kpi = pi; $k < 10; $k++, $kpi += pi) { @@ -1328,12 +1361,19 @@ sub stringify_polar { if ($theta !~ m(^-?\d*pi/\d+$) and int(CORE::abs($theta)) != int(CORE::abs($theta) + $eps)); + my $format = $format{format}; + if (defined $format) { + $r = sprintf($format, $r); + $theta = sprintf($format, $theta); + } + return "\[$r,$theta\]"; } 1; __END__ +=pod =head1 NAME Math::Complex - complex numbers and associated mathematical functions @@ -1617,9 +1657,9 @@ It is possible to write: $x = cplxe(-3, pi/4); -but that will be silently converted into C<[3,-3pi/4]>, since the modulus -must be non-negative (it represents the distance to the origin in the complex -plane). +but that will be silently converted into C<[3,-3pi/4]>, since the +modulus must be non-negative (it represents the distance to the origin +in the complex plane). It is also possible to have a complex number as either argument of either the C<make> or C<emake>: the appropriate component of @@ -1631,31 +1671,67 @@ the argument will be used. =head1 STRINGIFICATION When printed, a complex number is usually shown under its cartesian -form I<a+bi>, but there are legitimate cases where the polar format +style I<a+bi>, but there are legitimate cases where the polar style I<[r,t]> is more appropriate. -By calling the routine C<Math::Complex::display_format> and supplying either -C<"polar"> or C<"cartesian">, you override the default display format, -which is C<"cartesian">. Not supplying any argument returns the current -setting. +By calling the class method C<Math::Complex::display_format> and +supplying either C<"polar"> or C<"cartesian"> as an argument, you +override the default display style, which is C<"cartesian">. Not +supplying any argument returns the current settings. This default can be overridden on a per-number basis by calling the C<display_format> method instead. As before, not supplying any argument -returns the current display format for this number. Otherwise whatever you -specify will be the new display format for I<this> particular number. +returns the current display style for this number. Otherwise whatever you +specify will be the new display style for I<this> particular number. For instance: use Math::Complex; Math::Complex::display_format('polar'); - $j = ((root(1, 3))[1]; - print "j = $j\n"; # Prints "j = [1,2pi/3] + $j = (root(1, 3))[1]; + print "j = $j\n"; # Prints "j = [1,2pi/3]" $j->display_format('cartesian'); print "j = $j\n"; # Prints "j = -0.5+0.866025403784439i" -The polar format attempts to emphasize arguments like I<k*pi/n> -(where I<n> is a positive integer and I<k> an integer within [-9,+9]). +The polar style attempts to emphasize arguments like I<k*pi/n> +(where I<n> is a positive integer and I<k> an integer within [-9,+9]), +this is called I<polar pretty-printing>. + +=head2 CHANGED IN PERL 5.6 + +The C<display_format> class method and the corresponding +C<display_format> object method can now be called using +a parameter hash instead of just a one parameter. + +The old display format style, which can have values C<"cartesian"> or +C<"polar">, can be changed using the C<"style"> parameter. (The one +parameter calling convention also still works.) + +There are two new display parameters. + +The first one is C<"format">, which is a sprintf()-style format +string to be used for both parts of the complex number(s). The +default is C<undef>, which corresponds usually (this is somewhat +system-dependent) to C<"%.15g">. You can revert to the default by +setting the format string to C<undef>. + + # the $j from the above example + + $j->display_format('format' => '%.5f'); + print "j = $j\n"; # Prints "j = -0.50000+0.86603i" + $j->display_format('format' => '%.6f'); + print "j = $j\n"; # Prints "j = -0.5+0.86603i" + +Notice that this affects also the return values of the +C<display_format> methods: in list context the whole parameter hash +will be returned, as opposed to only the style parameter value. If +you want to know the whole truth for a complex number, you must call +both the class method and the object method: + +The second new display parameter is C<"polar_pretty_print">, which can +be set to true or false, the default being true. See the previous +section for what this means. =head1 USAGE @@ -1746,7 +1822,7 @@ Whatever it is, it does not manifest itself anywhere else where Perl runs. =head1 AUTHORS -Raphael Manfredi <F<Raphael_Manfredi@grenoble.hp.com>> and +Raphael Manfredi <F<Raphael_Manfredi@pobox.com>> and Jarkko Hietaniemi <F<jhi@iki.fi>>. Extensive patches by Daniel S. Lewart <F<d-lewart@uiuc.edu>>. |
