Perl is no longer in base. Long live the port!

4 files changed, 0 insertions, 3262 deletions

diff --git a/contrib/perl5/lib/Math/BigFloat.pm b/contrib/perl5/lib/Math/BigFloat.pm
deleted file mode 100644
index 1eefac2..0000000
--- a/contrib/perl5/lib/Math/BigFloat.pm
+++ /dev/null
@@ -1,398 +0,0 @@
-package Math::BigFloat;
-
-use Math::BigInt;
-
-use Exporter;  # just for use to be happy
-@ISA = (Exporter);
-$VERSION = '0.02';
-
-use overload
-'+'	=>	sub {new Math::BigFloat &fadd},
-'-'	=>	sub {new Math::BigFloat
-		       $_[2]? fsub($_[1],${$_[0]}) : fsub(${$_[0]},$_[1])},
-'<=>'	=>	sub {$_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])},
-'cmp'	=>	sub {$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])},
-'*'	=>	sub {new Math::BigFloat &fmul},
-'/'	=>	sub {new Math::BigFloat
-		       $_[2]? scalar fdiv($_[1],${$_[0]}) :
-			 scalar fdiv(${$_[0]},$_[1])},
-'%'	=>	sub {new Math::BigFloat
-		       $_[2]? scalar fmod($_[1],${$_[0]}) :
-			 scalar fmod(${$_[0]},$_[1])},
-'neg'	=>	sub {new Math::BigFloat &fneg},
-'abs'	=>	sub {new Math::BigFloat &fabs},
-
-qw(
-""	stringify
-0+	numify)			# Order of arguments unsignificant
-;
-
-sub new {
-  my ($class) = shift;
-  my ($foo) = fnorm(shift);
-  bless \$foo, $class;
-}
-
-sub numify { 0 + "${$_[0]}" }	# Not needed, additional overhead
-				# comparing to direct compilation based on
-				# stringify
-sub stringify {
-    my $n = ${$_[0]};
-
-    my $minus = ($n =~ s/^([+-])// && $1 eq '-');
-    $n =~ s/E//;
-
-    $n =~ s/([-+]\d+)$//;
-
-    my $e = $1;
-    my $ln = length($n);
-
-    if ( defined $e )
-    {
-        if ($e > 0) {
-        $n .= "0" x $e . '.';
-        } elsif (abs($e) < $ln) {
-        substr($n, $ln + $e, 0) = '.';
-        } else {
-        $n = '.' . ("0" x (abs($e) - $ln)) . $n;
-        }
-    }
-    $n = "-$n" if $minus;
-
-    # 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/;
-
-    return $n;
-}
-
-$div_scale = 40;
-
-# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
-
-$rnd_mode = 'even';
-
-sub fadd; sub fsub; sub fmul; sub fdiv;
-sub fneg; sub fabs; sub fcmp;
-sub fround; sub ffround;
-sub fnorm; sub fsqrt;
-
-# Convert a number to canonical string form.
-#   Takes something that looks like a number and converts it to
-#   the form /^[+-]\d+E[+-]\d+$/.
-sub fnorm { #(string) return fnum_str
-    local($_) = @_;
-    s/\s+//g;                               # strip white space
-    no warnings;	# $4 and $5 below might legitimately be undefined
-    if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') {
-	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6));
-    } else {
-	'NaN';
-    }
-}
-
-# normalize number -- for internal use
-sub norm { #(mantissa, exponent) return fnum_str
-    local($_, $exp) = @_;
-	$exp = 0 unless defined $exp;
-    if ($_ eq 'NaN') {
-	'NaN';
-    } else {
-	s/^([+-])0+/$1/;                        # strip leading zeros
-	if (length($_) == 1) {
-	    '+0E+0';
-	} else {
-	    $exp += length($1) if (s/(0+)$//);  # strip trailing zeros
-	    sprintf("%sE%+ld", $_, $exp);
-	}
-    }
-}
-
-# negation
-sub fneg { #(fnum_str) return fnum_str
-    local($_) = fnorm($_[$[]);
-    vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
-    s/^H/N/;
-    $_;
-}
-
-# absolute value
-sub fabs { #(fnum_str) return fnum_str
-    local($_) = fnorm($_[$[]);
-    s/^-/+/;		                       # mash sign
-    $_;
-}
-
-# multiplication
-sub fmul { #(fnum_str, fnum_str) return fnum_str
-    local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
-    if ($x eq 'NaN' || $y eq 'NaN') {
-	'NaN';
-    } else {
-	local($xm,$xe) = split('E',$x);
-	local($ym,$ye) = split('E',$y);
-	&norm(Math::BigInt::bmul($xm,$ym),$xe+$ye);
-    }
-}
-
-# addition
-sub fadd { #(fnum_str, fnum_str) return fnum_str
-    local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
-    if ($x eq 'NaN' || $y eq 'NaN') {
-	'NaN';
-    } else {
-	local($xm,$xe) = split('E',$x);
-	local($ym,$ye) = split('E',$y);
-	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
-	&norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye);
-    }
-}
-
-# subtraction
-sub fsub { #(fnum_str, fnum_str) return fnum_str
-    fadd($_[$[],fneg($_[$[+1]));
-}
-
-# division
-#   args are dividend, divisor, scale (optional)
-#   result has at most max(scale, length(dividend), length(divisor)) digits
-sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
-{
-    local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]);
-    if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') {
-	'NaN';
-    } else {
-	local($xm,$xe) = split('E',$x);
-	local($ym,$ye) = split('E',$y);
-	$scale = $div_scale if (!$scale);
-	$scale = length($xm)-1 if (length($xm)-1 > $scale);
-	$scale = length($ym)-1 if (length($ym)-1 > $scale);
-	$scale = $scale + length($ym) - length($xm);
-	&norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym),
-		    Math::BigInt::babs($ym)),
-	    $xe-$ye-$scale);
-    }
-}
-
-# modular division
-#   args are dividend, divisor
-sub fmod #(fnum_str, fnum_str) return fnum_str
-{
-    local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
-    if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') {
-	'NaN';
-    } else {
-	local($xm,$xe) = split('E',$x);
-	local($ym,$ye) = split('E',$y);
-	if ( $xe < $ye )
-	{
-		$ym .= ('0' x ($ye-$xe));
-	}
-	else
-	{
-		$xm .= ('0' x ($xe-$ye));
-	}
-	&norm(Math::BigInt::bmod($xm,$ym));
-    }
-}
-# round int $q based on fraction $r/$base using $rnd_mode
-sub round { #(int_str, int_str, int_str) return int_str
-    local($q,$r,$base) = @_;
-    if ($q eq 'NaN' || $r eq 'NaN') {
-	'NaN';
-    } elsif ($rnd_mode eq 'trunc') {
-	$q;                         # just truncate
-    } else {
-	local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base);
-	if ( $cmp < 0 ||
-		 ($cmp == 0 &&                                          (
-		   ($rnd_mode eq 'zero'                            ) ||
-		   ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) ||
-		   ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) ||
-		   ($rnd_mode eq 'even' && $q =~ /[24680]$/        ) ||
-		   ($rnd_mode eq 'odd'  && $q =~ /[13579]$/        )    )
-		  )
-		) {
-	    $q;                     # round down
-	} else {
-	    Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
-				    # round up
-	}
-    }
-}
-
-# round the mantissa of $x to $scale digits
-sub fround { #(fnum_str, scale) return fnum_str
-    local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
-    if ($x eq 'NaN' || $scale <= 0) {
-	$x;
-    } else {
-	local($xm,$xe) = split('E',$x);
-	if (length($xm)-1 <= $scale) {
-	    $x;
-	} else {
-	    &norm(&round(substr($xm,$[,$scale+1),
-			 "+0".substr($xm,$[+$scale+1),"+1"."0" x length(substr($xm,$[+$scale+1))),
-		  $xe+length($xm)-$scale-1);
-	}
-    }
-}
-
-# round $x at the 10 to the $scale digit place
-sub ffround { #(fnum_str, scale) return fnum_str
-    local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
-    if ($x eq 'NaN') {
-	'NaN';
-    } else {
-	local($xm,$xe) = split('E',$x);
-	if ($xe >= $scale) {
-	    $x;
-	} else {
-	    $xe = length($xm)+$xe-$scale;
-	    if ($xe < 1) {
-		'+0E+0';
-	    } elsif ($xe == 1) {
-		# The first substr preserves the sign, passing a non-
-		# normalized "-0" to &round when rounding -0.006 (for
-		# example), purely so &round won't lose the sign.
-		&norm(&round(substr($xm,$[,1).'0',
-		      "+0".substr($xm,$[+1),
-		      "+1"."0" x length(substr($xm,$[+1))), $scale);
-	    } else {
-		&norm(&round(substr($xm,$[,$xe),
-		      "+0".substr($xm,$[+$xe),
-		      "+1"."0" x length(substr($xm,$[+$xe))), $scale);
-	    }
-	}
-    }
-}
-
-# compare 2 values returns one of undef, <0, =0, >0
-#   returns undef if either or both input value are not numbers
-sub fcmp #(fnum_str, fnum_str) return cond_code
-{
-    local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1]));
-    if ($x eq "NaN" || $y eq "NaN") {
-	undef;
-    } else {
-	local($xm,$xe,$ym,$ye) = split('E', $x."E$y");
-	if ($xm eq '+0' || $ym eq '+0') {
-	    return $xm <=> $ym;
-	}
-	if ( $xe < $ye )	# adjust the exponents to be equal
-	{
-		$ym .= '0' x ($ye - $xe);
-		$ye = $xe;
-	}
-	elsif ( $ye < $xe )	# same here
-	{
-		$xm .= '0' x ($xe - $ye);
-		$xe = $ye;
-	}
-	return Math::BigInt::cmp($xm,$ym);
-    }
-}
-
-# square root by Newtons method.
-sub fsqrt { #(fnum_str[, scale]) return fnum_str
-    local($x, $scale) = (fnorm($_[$[]), $_[$[+1]);
-    if ($x eq 'NaN' || $x =~ /^-/) {
-	'NaN';
-    } elsif ($x eq '+0E+0') {
-	'+0E+0';
-    } else {
-	local($xm, $xe) = split('E',$x);
-	$scale = $div_scale if (!$scale);
-	$scale = length($xm)-1 if ($scale < length($xm)-1);
-	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
-	while ($gs < 2*$scale) {
-	    $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5");
-	    $gs *= 2;
-	}
-	new Math::BigFloat &fround($guess, $scale);
-    }
-}
-
-1;
-__END__
-
-=head1 NAME
-
-Math::BigFloat - Arbitrary length float math package
-
-=head1 SYNOPSIS
-
-  use Math::BigFloat;
-  $f = Math::BigFloat->new($string);
-
-  $f->fadd(NSTR) return NSTR            addition
-  $f->fsub(NSTR) return NSTR            subtraction
-  $f->fmul(NSTR) return NSTR            multiplication
-  $f->fdiv(NSTR[,SCALE]) returns NSTR   division to SCALE places
-  $f->fmod(NSTR) returns NSTR           modular remainder
-  $f->fneg() return NSTR                negation
-  $f->fabs() return NSTR                absolute value
-  $f->fcmp(NSTR) return CODE            compare undef,<0,=0,>0
-  $f->fround(SCALE) return NSTR         round to SCALE digits
-  $f->ffround(SCALE) return NSTR        round at SCALEth place
-  $f->fnorm() return (NSTR)             normalize
-  $f->fsqrt([SCALE]) return NSTR        sqrt to SCALE places
-
-=head1 DESCRIPTION
-
-All basic math operations are overloaded if you declare your big
-floats as
-
-    $float = new Math::BigFloat "2.123123123123123123123123123123123";
-
-=over 2
-
-=item number format
-
-canonical strings have the form /[+-]\d+E[+-]\d+/ .  Input values can
-have embedded whitespace.
-
-=item Error returns 'NaN'
-
-An input parameter was "Not a Number" or divide by zero or sqrt of
-negative number.
-
-=item Division is computed to
-
-C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))>
-digits by default.
-Also used for default sqrt scale.
-
-=item Rounding is performed
-
-according to the value of
-C<$Math::BigFloat::rnd_mode>:
-
-  trunc     truncate the value
-  zero      round towards 0
-  +inf      round towards +infinity (round up)
-  -inf      round towards -infinity (round down)
-  even      round to the nearest, .5 to the even digit
-  odd       round to the nearest, .5 to the odd digit
-
-The default is C<even> rounding.
-
-=back
-
-=head1 BUGS
-
-The current version of this module is a preliminary version of the
-real thing that is currently (as of perl5.002) under development.
-
-The printf subroutine does not use the value of
-C<$Math::BigFloat::rnd_mode> when rounding values for printing.
-Consequently, the way to print rounded values is
-to specify the number of digits both as an
-argument to C<ffround> and in the C<%f> printf string,
-as follows:
-
-  printf "%.3f\n", $bigfloat->ffround(-3);
-
-=head1 AUTHOR
-
-Mark Biggar
-Patches by John Peacock Apr 2001
-=cut
diff --git a/contrib/perl5/lib/Math/BigInt.pm b/contrib/perl5/lib/Math/BigInt.pm
deleted file mode 100644
index 066577d..0000000
--- a/contrib/perl5/lib/Math/BigInt.pm
+++ /dev/null
@@ -1,519 +0,0 @@
-package Math::BigInt;
-$VERSION='0.01';
-
-use overload
-'+'	=>	sub {new Math::BigInt &badd},
-'-'	=>	sub {new Math::BigInt
-		       $_[2]? bsub($_[1],${$_[0]}) : bsub(${$_[0]},$_[1])},
-'<=>'	=>	sub {$_[2]? bcmp($_[1],${$_[0]}) : bcmp(${$_[0]},$_[1])},
-'cmp'	=>	sub {$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])},
-'*'	=>	sub {new Math::BigInt &bmul},
-'/'	=>	sub {new Math::BigInt 
-		       $_[2]? scalar bdiv($_[1],${$_[0]}) :
-			 scalar bdiv(${$_[0]},$_[1])},
-'%'	=>	sub {new Math::BigInt
-		       $_[2]? bmod($_[1],${$_[0]}) : bmod(${$_[0]},$_[1])},
-'**'	=>	sub {new Math::BigInt
-		       $_[2]? bpow($_[1],${$_[0]}) : bpow(${$_[0]},$_[1])},
-'neg'	=>	sub {new Math::BigInt &bneg},
-'abs'	=>	sub {new Math::BigInt &babs},
-'<<'	=>	sub {new Math::BigInt
-		       $_[2]? blsft($_[1],${$_[0]}) : blsft(${$_[0]},$_[1])},
-'>>'	=>	sub {new Math::BigInt
-		       $_[2]? brsft($_[1],${$_[0]}) : brsft(${$_[0]},$_[1])},
-'&'	=>	sub {new Math::BigInt &band},
-'|'	=>	sub {new Math::BigInt &bior},
-'^'	=>	sub {new Math::BigInt &bxor},
-'~'	=>	sub {new Math::BigInt &bnot},
-
-qw(
-""	stringify
-0+	numify)			# Order of arguments unsignificant
-;
-
-$NaNOK=1;
-
-sub new {
-  my($class) = shift;
-  my($foo) = bnorm(shift);
-  die "Not a number initialized to Math::BigInt" if !$NaNOK && $foo eq "NaN";
-  bless \$foo, $class;
-}
-sub stringify { "${$_[0]}" }
-sub numify { 0 + "${$_[0]}" }	# Not needed, additional overhead
-				# comparing to direct compilation based on
-				# stringify
-sub import {
-  shift;
-  return unless @_;
-  die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
-  overload::constant integer => sub {Math::BigInt->new(shift)};
-}
-
-$zero = 0;
-
-# overcome a floating point problem on certain osnames (posix-bc, os390)
-BEGIN {
-    my $x = 100000.0;
-    my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0;
-}
-
-# normalize string form of number.   Strip leading zeros.  Strip any
-#   white space and add a sign, if missing.
-# Strings that are not numbers result the value 'NaN'.
-
-sub bnorm { #(num_str) return num_str
-    local($_) = @_;
-    s/\s+//g;                           # strip white space
-    if (s/^([+-]?)0*(\d+)$/$1$2/) {     # test if number
-	substr($_,$[,0) = '+' unless $1; # Add missing sign
-	s/^-0/+0/;
-	$_;
-    } else {
-	'NaN';
-    }
-}
-
-# Convert a number from string format to internal base 100000 format.
-#   Assumes normalized value as input.
-sub internal { #(num_str) return int_num_array
-    local($d) = @_;
-    ($is,$il) = (substr($d,$[,1),length($d)-2);
-    substr($d,$[,1) = '';
-    ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
-}
-
-# Convert a number from internal base 100000 format to string format.
-#   This routine scribbles all over input array.
-sub external { #(int_num_array) return num_str
-    $es = shift;
-    grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_);   # zero pad
-    &bnorm(join('', $es, reverse(@_)));    # reverse concat and normalize
-}
-
-# Negate input value.
-sub bneg { #(num_str) return num_str
-    local($_) = &bnorm(@_);
-    return $_ if $_ eq '+0' or $_ eq 'NaN';
-    vec($_,0,8) ^= ord('+') ^ ord('-');
-    $_;
-}
-
-# Returns the absolute value of the input.
-sub babs { #(num_str) return num_str
-    &abs(&bnorm(@_));
-}
-
-sub abs { # post-normalized abs for internal use
-    local($_) = @_;
-    s/^-/+/;
-    $_;
-}
-
-# Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
-sub bcmp { #(num_str, num_str) return cond_code
-    local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
-    if ($x eq 'NaN') {
-	undef;
-    } elsif ($y eq 'NaN') {
-	undef;
-    } else {
-	&cmp($x,$y) <=> 0;
-    }
-}
-
-sub cmp { # post-normalized compare for internal use
-    local($cx, $cy) = @_;
-    
-    return 0 if ($cx eq $cy);
-
-    local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
-    local($ld);
-
-    if ($sx eq '+') {
-      return  1 if ($sy eq '-' || $cy eq '+0');
-      $ld = length($cx) - length($cy);
-      return $ld if ($ld);
-      return $cx cmp $cy;
-    } else { # $sx eq '-'
-      return -1 if ($sy eq '+');
-      $ld = length($cy) - length($cx);
-      return $ld if ($ld);
-      return $cy cmp $cx;
-    }
-}
-
-sub badd { #(num_str, num_str) return num_str
-    local(*x, *y); ($x, $y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
-    if ($x eq 'NaN') {
-	'NaN';
-    } elsif ($y eq 'NaN') {
-	'NaN';
-    } else {
-	@x = &internal($x);             # convert to internal form
-	@y = &internal($y);
-	local($sx, $sy) = (shift @x, shift @y); # get signs
-	if ($sx eq $sy) {
-	    &external($sx, &add(*x, *y)); # if same sign add
-	} else {
-	    ($x, $y) = (&abs($x),&abs($y)); # make abs
-	    if (&cmp($y,$x) > 0) {
-		&external($sy, &sub(*y, *x));
-	    } else {
-		&external($sx, &sub(*x, *y));
-	    }
-	}
-    }
-}
-
-sub bsub { #(num_str, num_str) return num_str
-    &badd($_[$[],&bneg($_[$[+1]));    
-}
-
-# GCD -- Euclids algorithm Knuth Vol 2 pg 296
-sub bgcd { #(num_str, num_str) return num_str
-    local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
-    if ($x eq 'NaN' || $y eq 'NaN') {
-	'NaN';
-    } else {
-	($x, $y) = ($y,&bmod($x,$y)) while $y ne '+0';
-	$x;
-    }
-}
-
-# routine to add two base 1e5 numbers
-#   stolen from Knuth Vol 2 Algorithm A pg 231
-#   there are separate routines to add and sub as per Kunth pg 233
-sub add { #(int_num_array, int_num_array) return int_num_array
-    local(*x, *y) = @_;
-    $car = 0;
-    for $x (@x) {
-	last unless @y || $car;
-	$x -= 1e5 if $car = (($x += (@y ? shift(@y) : 0) + $car) >= 1e5) ? 1 : 0;
-    }
-    for $y (@y) {
-	last unless $car;
-	$y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
-    }
-    (@x, @y, $car);
-}
-
-# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
-sub sub { #(int_num_array, int_num_array) return int_num_array
-    local(*sx, *sy) = @_;
-    $bar = 0;
-    for $sx (@sx) {
-	last unless @sy || $bar;
-	$sx += 1e5 if $bar = (($sx -= (@sy ? shift(@sy) : 0) + $bar) < 0);
-    }
-    @sx;
-}
-
-# multiply two numbers -- stolen from Knuth Vol 2 pg 233
-sub bmul { #(num_str, num_str) return num_str
-    local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
-    if ($x eq 'NaN') {
-	'NaN';
-    } elsif ($y eq 'NaN') {
-	'NaN';
-    } else {
-	@x = &internal($x);
-	@y = &internal($y);
-	&external(&mul(*x,*y));
-    }
-}
-
-# multiply two numbers in internal representation
-# destroys the arguments, supposes that two arguments are different
-sub mul { #(*int_num_array, *int_num_array) return int_num_array
-    local(*x, *y) = (shift, shift);
-    local($signr) = (shift @x ne shift @y) ? '-' : '+';
-    @prod = ();
-    for $x (@x) {
-      ($car, $cty) = (0, $[);
-      for $y (@y) {
-	$prod = $x * $y + ($prod[$cty] || 0) + $car;
-        if ($use_mult) {
-	$prod[$cty++] =
-	  $prod - ($car = int($prod * 1e-5)) * 1e5;
-        }
-        else {
-	$prod[$cty++] =
-	  $prod - ($car = int($prod / 1e5)) * 1e5;
-        }
-      }
-      $prod[$cty] += $car if $car;
-      $x = shift @prod;
-    }
-    ($signr, @x, @prod);
-}
-
-# modulus
-sub bmod { #(num_str, num_str) return num_str
-    (&bdiv(@_))[$[+1];
-}
-
-sub bdiv { #(dividend: num_str, divisor: num_str) return num_str
-    local (*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
-    return wantarray ? ('NaN','NaN') : 'NaN'
-	if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
-    return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
-    @x = &internal($x); @y = &internal($y);
-    $srem = $y[$[];
-    $sr = (shift @x ne shift @y) ? '-' : '+';
-    $car = $bar = $prd = 0;
-    if (($dd = int(1e5/($y[$#y]+1))) != 1) {
-	for $x (@x) {
-	    $x = $x * $dd + $car;
-            if ($use_mult) {
-	    $x -= ($car = int($x * 1e-5)) * 1e5;
-            }
-            else {
-	    $x -= ($car = int($x / 1e5)) * 1e5;
-            }
-	}
-	push(@x, $car); $car = 0;
-	for $y (@y) {
-	    $y = $y * $dd + $car;
-            if ($use_mult) {
-	    $y -= ($car = int($y * 1e-5)) * 1e5;
-            }
-            else {
-	    $y -= ($car = int($y / 1e5)) * 1e5;
-            }
-	}
-    }
-    else {
-	push(@x, 0);
-    }
-    @q = (); ($v2,$v1) = @y[-2,-1];
-    $v2 = 0 unless $v2;
-    while ($#x > $#y) {
-	($u2,$u1,$u0) = @x[-3..-1];
-	$u2 = 0 unless $u2;
-	$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
-	--$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
-	if ($q) {
-	    ($car, $bar) = (0,0);
-	    for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
-		$prd = $q * $y[$y] + $car;
-                if ($use_mult) {
-		$prd -= ($car = int($prd * 1e-5)) * 1e5;
-                }
-                else {
-		$prd -= ($car = int($prd / 1e5)) * 1e5;
-                }
-		$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
-	    }
-	    if ($x[$#x] < $car + $bar) {
-		$car = 0; --$q;
-		for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
-		    $x[$x] -= 1e5
-			if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
-		}
-	    }   
-	}
-	pop(@x); unshift(@q, $q);
-    }
-    if (wantarray) {
-	@d = ();
-	if ($dd != 1) {
-	    $car = 0;
-	    for $x (reverse @x) {
-		$prd = $car * 1e5 + $x;
-		$car = $prd - ($tmp = int($prd / $dd)) * $dd;
-		unshift(@d, $tmp);
-	    }
-	}
-	else {
-	    @d = @x;
-	}
-	(&external($sr, @q), &external($srem, @d, $zero));
-    } else {
-	&external($sr, @q);
-    }
-}
-
-# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
-sub bpow { #(num_str, num_str) return num_str
-    local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
-    if ($x eq 'NaN') {
-	'NaN';
-    } elsif ($y eq 'NaN') {
-	'NaN';
-    } elsif ($x eq '+1') {
-	'+1';
-    } elsif ($x eq '-1') {
-	&bmod($x,2) ? '-1': '+1';
-    } elsif ($y =~ /^-/) {
-	'NaN';
-    } elsif ($x eq '+0' && $y eq '+0') {
-	'NaN';
-    } else {
-	@x = &internal($x);
-	local(@pow2)=@x;
-	local(@pow)=&internal("+1");
-	local($y1,$res,@tmp1,@tmp2)=(1); # need tmp to send to mul
-	while ($y ne '+0') {
-	  ($y,$res)=&bdiv($y,2);
-	  if ($res ne '+0') {@tmp=@pow2; @pow=&mul(*pow,*tmp);}
-	  if ($y ne '+0') {@tmp=@pow2;@pow2=&mul(*pow2,*tmp);}
-	}
-	&external(@pow);
-    }
-}
-
-# compute x << y, y >= 0
-sub blsft { #(num_str, num_str) return num_str
-    &bmul($_[$[], &bpow(2, $_[$[+1]));
-}
-
-# compute x >> y, y >= 0
-sub brsft { #(num_str, num_str) return num_str
-    &bdiv($_[$[], &bpow(2, $_[$[+1]));
-}
-
-# compute x & y
-sub band { #(num_str, num_str) return num_str
-    local($x,$y,$r,$m,$xr,$yr) = (&bnorm($_[$[]),&bnorm($_[$[+1]),0,1);
-    if ($x eq 'NaN' || $y eq 'NaN') {
-	'NaN';
-    } else {
-	while ($x ne '+0' && $y ne '+0') {
-	    ($x, $xr) = &bdiv($x, 0x10000);
-	    ($y, $yr) = &bdiv($y, 0x10000);
-	    $r = &badd(&bmul(int $xr & $yr, $m), $r);
-	    $m = &bmul($m, 0x10000);
-	}
-	$r;
-    }
-}
-
-# compute x | y
-sub bior { #(num_str, num_str) return num_str
-    local($x,$y,$r,$m,$xr,$yr) = (&bnorm($_[$[]),&bnorm($_[$[+1]),0,1);
-    if ($x eq 'NaN' || $y eq 'NaN') {
-	'NaN';
-    } else {
-	while ($x ne '+0' || $y ne '+0') {
-	    ($x, $xr) = &bdiv($x, 0x10000);
-	    ($y, $yr) = &bdiv($y, 0x10000);
-	    $r = &badd(&bmul(int $xr | $yr, $m), $r);
-	    $m = &bmul($m, 0x10000);
-	}
-	$r;
-    }
-}
-
-# compute x ^ y
-sub bxor { #(num_str, num_str) return num_str
-    local($x,$y,$r,$m,$xr,$yr) = (&bnorm($_[$[]),&bnorm($_[$[+1]),0,1);
-    if ($x eq 'NaN' || $y eq 'NaN') {
-	'NaN';
-    } else {
-	while ($x ne '+0' || $y ne '+0') {
-	    ($x, $xr) = &bdiv($x, 0x10000);
-	    ($y, $yr) = &bdiv($y, 0x10000);
-	    $r = &badd(&bmul(int $xr ^ $yr, $m), $r);
-	    $m = &bmul($m, 0x10000);
-	}
-	$r;
-    }
-}
-
-# represent ~x as twos-complement number
-sub bnot { #(num_str) return num_str
-    &bsub(-1,$_[$[]);
-}
-
-1;
-__END__
-
-=head1 NAME
-
-Math::BigInt - Arbitrary size integer math package
-
-=head1 SYNOPSIS
-
-  use Math::BigInt;
-  $i = Math::BigInt->new($string);
-
-  $i->bneg return BINT               negation
-  $i->babs return BINT               absolute value
-  $i->bcmp(BINT) return CODE         compare numbers (undef,<0,=0,>0)
-  $i->badd(BINT) return BINT         addition
-  $i->bsub(BINT) return BINT         subtraction
-  $i->bmul(BINT) return BINT         multiplication
-  $i->bdiv(BINT) return (BINT,BINT)  division (quo,rem) just quo if scalar
-  $i->bmod(BINT) return BINT         modulus
-  $i->bgcd(BINT) return BINT         greatest common divisor
-  $i->bnorm return BINT              normalization
-  $i->blsft(BINT) return BINT        left shift
-  $i->brsft(BINT) return (BINT,BINT) right shift (quo,rem) just quo if scalar
-  $i->band(BINT) return BINT         bit-wise and
-  $i->bior(BINT) return BINT         bit-wise inclusive or
-  $i->bxor(BINT) return BINT         bit-wise exclusive or
-  $i->bnot return BINT               bit-wise not
-
-=head1 DESCRIPTION
-
-All basic math operations are overloaded if you declare your big
-integers as
-
-  $i = new Math::BigInt '123 456 789 123 456 789';
-
-
-=over 2
-
-=item Canonical notation
-
-Big integer value are strings of the form C</^[+-]\d+$/> with leading
-zeros suppressed.
-
-=item Input
-
-Input values to these routines may be strings of the form
-C</^\s*[+-]?[\d\s]+$/>.
-
-=item Output
-
-Output values always always in canonical form
-
-=back
-
-Actual math is done in an internal format consisting of an array
-whose first element is the sign (/^[+-]$/) and whose remaining 
-elements are base 100000 digits with the least significant digit first.
-The string 'NaN' is used to represent the result when input arguments 
-are not numbers, as well as the result of dividing by zero.
-
-=head1 EXAMPLES
-
-   '+0'                            canonical zero value
-   '   -123 123 123'               canonical value '-123123123'
-   '1 23 456 7890'                 canonical value '+1234567890'
-
-
-=head1 Autocreating constants
-
-After C<use Math::BigInt ':constant'> all the integer decimal constants
-in the given scope are converted to C<Math::BigInt>.  This conversion
-happens at compile time.
-
-In particular
-
-  perl -MMath::BigInt=:constant -e 'print 2**100'
-
-print the integer value of C<2**100>.  Note that without conversion of 
-constants the expression 2**100 will be calculated as floating point number.
-
-=head1 BUGS
-
-The current version of this module is a preliminary version of the
-real thing that is currently (as of perl5.002) under development.
-
-=head1 AUTHOR
-
-Mark Biggar, overloaded interface by Ilya Zakharevich.
-
-=cut
diff --git a/contrib/perl5/lib/Math/Complex.pm b/contrib/perl5/lib/Math/Complex.pm
deleted file mode 100644
index 9812513..0000000
--- a/contrib/perl5/lib/Math/Complex.pm
+++ /dev/null
@@ -1,1889 +0,0 @@
-#
-# Complex numbers and associated mathematical functions
-# -- Raphael Manfredi	Since Sep 1996
-# -- Jarkko Hietaniemi	Since Mar 1997
-# -- Daniel S. Lewart	Since Sep 1997
-#
-
-package Math::Complex;
-
-our($VERSION, @ISA, @EXPORT, %EXPORT_TAGS, $Inf);
-
-$VERSION = 1.31;
-
-BEGIN {
-    unless ($^O eq 'unicosmk') {
-        my $e = $!;
-	# We do want an arithmetic overflow, Inf INF inf Infinity:.
-        undef $Inf unless eval <<'EOE' and $Inf =~ /^inf(?:inity)?$/i;
-	  local $SIG{FPE} = sub {die};
-	  my $t = CORE::exp 30;
-	  $Inf = CORE::exp $t;
-EOE
-	if (!defined $Inf) {		# Try a different method
-	  undef $Inf unless eval <<'EOE' and $Inf =~ /^inf(?:inity)?$/i;
-	    local $SIG{FPE} = sub {die};
-	    my $t = 1;
-	    $Inf = $t + "1e99999999999999999999999999999999";
-EOE
-	}
-        $! = $e; # Clear ERANGE.
-    }
-    $Inf = "Inf" if !defined $Inf || !($Inf > 0); # Desperation.
-}
-
-use strict;
-
-my $i;
-my %LOGN;
-
-require Exporter;
-
-@ISA = qw(Exporter);
-
-my @trig = qw(
-	      pi
-	      tan
-	      csc cosec sec cot cotan
-	      asin acos atan
-	      acsc acosec asec acot acotan
-	      sinh cosh tanh
-	      csch cosech sech coth cotanh
-	      asinh acosh atanh
-	      acsch acosech asech acoth acotanh
-	     );
-
-@EXPORT = (qw(
-	     i Re Im rho theta arg
-	     sqrt log ln
-	     log10 logn cbrt root
-	     cplx cplxe
-	     ),
-	   @trig);
-
-%EXPORT_TAGS = (
-    'trig' => [@trig],
-);
-
-use overload
-	'+'	=> \&plus,
-	'-'	=> \&minus,
-	'*'	=> \&multiply,
-	'/'	=> \&divide,
-	'**'	=> \&power,
-	'=='	=> \&numeq,
-	'<=>'	=> \&spaceship,
-	'neg'	=> \&negate,
-	'~'	=> \&conjugate,
-	'abs'	=> \&abs,
-	'sqrt'	=> \&sqrt,
-	'exp'	=> \&exp,
-	'log'	=> \&log,
-	'sin'	=> \&sin,
-	'cos'	=> \&cos,
-	'tan'	=> \&tan,
-	'atan2'	=> \&atan2,
-	qw("" stringify);
-
-#
-# Package "privates"
-#
-
-my %DISPLAY_FORMAT = ('style' => 'cartesian',
-		      'polar_pretty_print' => 1);
-my $eps            = 1e-14;		# Epsilon
-
-#
-# Object attributes (internal):
-#	cartesian	[real, imaginary] -- cartesian form
-#	polar		[rho, theta] -- polar form
-#	c_dirty		cartesian form not up-to-date
-#	p_dirty		polar form not up-to-date
-#	display		display format (package's global when not set)
-#
-
-# Die on bad *make() arguments.
-
-sub _cannot_make {
-    die "@{[(caller(1))[3]]}: Cannot take $_[0] of $_[1].\n";
-}
-
-#
-# ->make
-#
-# Create a new complex number (cartesian form)
-#
-sub make {
-	my $self = bless {}, shift;
-	my ($re, $im) = @_;
-	my $rre = ref $re;
-	if ( $rre ) {
-	    if ( $rre eq ref $self ) {
-		$re = Re($re);
-	    } else {
-		_cannot_make("real part", $rre);
-	    }
-	}
-	my $rim = ref $im;
-	if ( $rim ) {
-	    if ( $rim eq ref $self ) {
-		$im = Im($im);
-	    } else {
-		_cannot_make("imaginary part", $rim);
-	    }
-	}
-	$self->{'cartesian'} = [ $re, $im ];
-	$self->{c_dirty} = 0;
-	$self->{p_dirty} = 1;
-	$self->display_format('cartesian');
-	return $self;
-}
-
-#
-# ->emake
-#
-# Create a new complex number (exponential form)
-#
-sub emake {
-	my $self = bless {}, shift;
-	my ($rho, $theta) = @_;
-	my $rrh = ref $rho;
-	if ( $rrh ) {
-	    if ( $rrh eq ref $self ) {
-		$rho = rho($rho);
-	    } else {
-		_cannot_make("rho", $rrh);
-	    }
-	}
-	my $rth = ref $theta;
-	if ( $rth ) {
-	    if ( $rth eq ref $self ) {
-		$theta = theta($theta);
-	    } else {
-		_cannot_make("theta", $rth);
-	    }
-	}
-	if ($rho < 0) {
-	    $rho   = -$rho;
-	    $theta = ($theta <= 0) ? $theta + pi() : $theta - pi();
-	}
-	$self->{'polar'} = [$rho, $theta];
-	$self->{p_dirty} = 0;
-	$self->{c_dirty} = 1;
-	$self->display_format('polar');
-	return $self;
-}
-
-sub new { &make }		# For backward compatibility only.
-
-#
-# cplx
-#
-# Creates a complex number from a (re, im) tuple.
-# This avoids the burden of writing Math::Complex->make(re, im).
-#
-sub cplx {
-	my ($re, $im) = @_;
-	return __PACKAGE__->make($re, defined $im ? $im : 0);
-}
-
-#
-# cplxe
-#
-# Creates a complex number from a (rho, theta) tuple.
-# This avoids the burden of writing Math::Complex->emake(rho, theta).
-#
-sub cplxe {
-	my ($rho, $theta) = @_;
-	return __PACKAGE__->emake($rho, defined $theta ? $theta : 0);
-}
-
-#
-# pi
-#
-# The number defined as pi = 180 degrees
-#
-sub pi () { 4 * CORE::atan2(1, 1) }
-
-#
-# pit2
-#
-# The full circle
-#
-sub pit2 () { 2 * pi }
-
-#
-# pip2
-#
-# The quarter circle
-#
-sub pip2 () { pi / 2 }
-
-#
-# deg1
-#
-# One degree in radians, used in stringify_polar.
-#
-
-sub deg1 () { pi / 180 }
-
-#
-# uplog10
-#
-# Used in log10().
-#
-sub uplog10 () { 1 / CORE::log(10) }
-
-#
-# i
-#
-# The number defined as i*i = -1;
-#
-sub i () {
-        return $i if ($i);
-	$i = bless {};
-	$i->{'cartesian'} = [0, 1];
-	$i->{'polar'}     = [1, pip2];
-	$i->{c_dirty} = 0;
-	$i->{p_dirty} = 0;
-	return $i;
-}
-
-#
-# ip2
-#
-# Half of i.
-#
-sub ip2 () { i / 2 }
-
-#
-# Attribute access/set routines
-#
-
-sub cartesian {$_[0]->{c_dirty} ?
-		   $_[0]->update_cartesian : $_[0]->{'cartesian'}}
-sub polar     {$_[0]->{p_dirty} ?
-		   $_[0]->update_polar : $_[0]->{'polar'}}
-
-sub set_cartesian { $_[0]->{p_dirty}++; $_[0]->{'cartesian'} = $_[1] }
-sub set_polar     { $_[0]->{c_dirty}++; $_[0]->{'polar'} = $_[1] }
-
-#
-# ->update_cartesian
-#
-# Recompute and return the cartesian form, given accurate polar form.
-#
-sub update_cartesian {
-	my $self = shift;
-	my ($r, $t) = @{$self->{'polar'}};
-	$self->{c_dirty} = 0;
-	return $self->{'cartesian'} = [$r * CORE::cos($t), $r * CORE::sin($t)];
-}
-
-#
-#
-# ->update_polar
-#
-# Recompute and return the polar form, given accurate cartesian form.
-#
-sub update_polar {
-	my $self = shift;
-	my ($x, $y) = @{$self->{'cartesian'}};
-	$self->{p_dirty} = 0;
-	return $self->{'polar'} = [0, 0] if $x == 0 && $y == 0;
-	return $self->{'polar'} = [CORE::sqrt($x*$x + $y*$y),
-				   CORE::atan2($y, $x)];
-}
-
-#
-# (plus)
-#
-# Computes z1+z2.
-#
-sub plus {
-	my ($z1, $z2, $regular) = @_;
-	my ($re1, $im1) = @{$z1->cartesian};
-	$z2 = cplx($z2) unless ref $z2;
-	my ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
-	unless (defined $regular) {
-		$z1->set_cartesian([$re1 + $re2, $im1 + $im2]);
-		return $z1;
-	}
-	return (ref $z1)->make($re1 + $re2, $im1 + $im2);
-}
-
-#
-# (minus)
-#
-# Computes z1-z2.
-#
-sub minus {
-	my ($z1, $z2, $inverted) = @_;
-	my ($re1, $im1) = @{$z1->cartesian};
-	$z2 = cplx($z2) unless ref $z2;
-	my ($re2, $im2) = @{$z2->cartesian};
-	unless (defined $inverted) {
-		$z1->set_cartesian([$re1 - $re2, $im1 - $im2]);
-		return $z1;
-	}
-	return $inverted ?
-		(ref $z1)->make($re2 - $re1, $im2 - $im1) :
-		(ref $z1)->make($re1 - $re2, $im1 - $im2);
-
-}
-
-#
-# (multiply)
-#
-# Computes z1*z2.
-#
-sub multiply {
-        my ($z1, $z2, $regular) = @_;
-	if ($z1->{p_dirty} == 0 and ref $z2 and $z2->{p_dirty} == 0) {
-	    # if both polar better use polar to avoid rounding errors
-	    my ($r1, $t1) = @{$z1->polar};
-	    my ($r2, $t2) = @{$z2->polar};
-	    my $t = $t1 + $t2;
-	    if    ($t >   pi()) { $t -= pit2 }
-	    elsif ($t <= -pi()) { $t += pit2 }
-	    unless (defined $regular) {
-		$z1->set_polar([$r1 * $r2, $t]);
-		return $z1;
-	    }
-	    return (ref $z1)->emake($r1 * $r2, $t);
-	} else {
-	    my ($x1, $y1) = @{$z1->cartesian};
-	    if (ref $z2) {
-		my ($x2, $y2) = @{$z2->cartesian};
-		return (ref $z1)->make($x1*$x2-$y1*$y2, $x1*$y2+$y1*$x2);
-	    } else {
-		return (ref $z1)->make($x1*$z2, $y1*$z2);
-	    }
-	}
-}
-
-#
-# _divbyzero
-#
-# Die on division by zero.
-#
-sub _divbyzero {
-    my $mess = "$_[0]: Division by zero.\n";
-
-    if (defined $_[1]) {
-	$mess .= "(Because in the definition of $_[0], the divisor ";
-	$mess .= "$_[1] " unless ("$_[1]" eq '0');
-	$mess .= "is 0)\n";
-    }
-
-    my @up = caller(1);
-
-    $mess .= "Died at $up[1] line $up[2].\n";
-
-    die $mess;
-}
-
-#
-# (divide)
-#
-# Computes z1/z2.
-#
-sub divide {
-	my ($z1, $z2, $inverted) = @_;
-	if ($z1->{p_dirty} == 0 and ref $z2 and $z2->{p_dirty} == 0) {
-	    # if both polar better use polar to avoid rounding errors
-	    my ($r1, $t1) = @{$z1->polar};
-	    my ($r2, $t2) = @{$z2->polar};
-	    my $t;
-	    if ($inverted) {
-		_divbyzero "$z2/0" if ($r1 == 0);
-		$t = $t2 - $t1;
-		if    ($t >   pi()) { $t -= pit2 }
-		elsif ($t <= -pi()) { $t += pit2 }
-		return (ref $z1)->emake($r2 / $r1, $t);
-	    } else {
-		_divbyzero "$z1/0" if ($r2 == 0);
-		$t = $t1 - $t2;
-		if    ($t >   pi()) { $t -= pit2 }
-		elsif ($t <= -pi()) { $t += pit2 }
-		return (ref $z1)->emake($r1 / $r2, $t);
-	    }
-	} else {
-	    my ($d, $x2, $y2);
-	    if ($inverted) {
-		($x2, $y2) = @{$z1->cartesian};
-		$d = $x2*$x2 + $y2*$y2;
-		_divbyzero "$z2/0" if $d == 0;
-		return (ref $z1)->make(($x2*$z2)/$d, -($y2*$z2)/$d);
-	    } else {
-		my ($x1, $y1) = @{$z1->cartesian};
-		if (ref $z2) {
-		    ($x2, $y2) = @{$z2->cartesian};
-		    $d = $x2*$x2 + $y2*$y2;
-		    _divbyzero "$z1/0" if $d == 0;
-		    my $u = ($x1*$x2 + $y1*$y2)/$d;
-		    my $v = ($y1*$x2 - $x1*$y2)/$d;
-		    return (ref $z1)->make($u, $v);
-		} else {
-		    _divbyzero "$z1/0" if $z2 == 0;
-		    return (ref $z1)->make($x1/$z2, $y1/$z2);
-		}
-	    }
-	}
-}
-
-#
-# (power)
-#
-# Computes z1**z2 = exp(z2 * log z1)).
-#
-sub power {
-	my ($z1, $z2, $inverted) = @_;
-	if ($inverted) {
-	    return 1 if $z1 == 0 || $z2 == 1;
-	    return 0 if $z2 == 0 && Re($z1) > 0;
-	} else {
-	    return 1 if $z2 == 0 || $z1 == 1;
-	    return 0 if $z1 == 0 && Re($z2) > 0;
-	}
-	my $w = $inverted ? &exp($z1 * &log($z2))
-	                  : &exp($z2 * &log($z1));
-	# If both arguments cartesian, return cartesian, else polar.
-	return $z1->{c_dirty} == 0 &&
-	       (not ref $z2 or $z2->{c_dirty} == 0) ?
-	       cplx(@{$w->cartesian}) : $w;
-}
-
-#
-# (spaceship)
-#
-# Computes z1 <=> z2.
-# Sorts on the real part first, then on the imaginary part. Thus 2-4i < 3+8i.
-#
-sub spaceship {
-	my ($z1, $z2, $inverted) = @_;
-	my ($re1, $im1) = ref $z1 ? @{$z1->cartesian} : ($z1, 0);
-	my ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
-	my $sgn = $inverted ? -1 : 1;
-	return $sgn * ($re1 <=> $re2) if $re1 != $re2;
-	return $sgn * ($im1 <=> $im2);
-}
-
-#
-# (numeq)
-#
-# Computes z1 == z2.
-#
-# (Required in addition to spaceship() because of NaNs.)
-sub numeq {
-	my ($z1, $z2, $inverted) = @_;
-	my ($re1, $im1) = ref $z1 ? @{$z1->cartesian} : ($z1, 0);
-	my ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
-	return $re1 == $re2 && $im1 == $im2 ? 1 : 0;
-}
-
-#
-# (negate)
-#
-# Computes -z.
-#
-sub negate {
-	my ($z) = @_;
-	if ($z->{c_dirty}) {
-		my ($r, $t) = @{$z->polar};
-		$t = ($t <= 0) ? $t + pi : $t - pi;
-		return (ref $z)->emake($r, $t);
-	}
-	my ($re, $im) = @{$z->cartesian};
-	return (ref $z)->make(-$re, -$im);
-}
-
-#
-# (conjugate)
-#
-# Compute complex's conjugate.
-#
-sub conjugate {
-	my ($z) = @_;
-	if ($z->{c_dirty}) {
-		my ($r, $t) = @{$z->polar};
-		return (ref $z)->emake($r, -$t);
-	}
-	my ($re, $im) = @{$z->cartesian};
-	return (ref $z)->make($re, -$im);
-}
-
-#
-# (abs)
-#
-# Compute or set complex's norm (rho).
-#
-sub abs {
-	my ($z, $rho) = @_;
-	unless (ref $z) {
-	    if (@_ == 2) {
-		$_[0] = $_[1];
-	    } else {
-		return CORE::abs($z);
-	    }
-	}
-	if (defined $rho) {
-	    $z->{'polar'} = [ $rho, ${$z->polar}[1] ];
-	    $z->{p_dirty} = 0;
-	    $z->{c_dirty} = 1;
-	    return $rho;
-	} else {
-	    return ${$z->polar}[0];
-	}
-}
-
-sub _theta {
-    my $theta = $_[0];
-
-    if    ($$theta >   pi()) { $$theta -= pit2 }
-    elsif ($$theta <= -pi()) { $$theta += pit2 }
-}
-
-#
-# arg
-#
-# Compute or set complex's argument (theta).
-#
-sub arg {
-	my ($z, $theta) = @_;
-	return $z unless ref $z;
-	if (defined $theta) {
-	    _theta(\$theta);
-	    $z->{'polar'} = [ ${$z->polar}[0], $theta ];
-	    $z->{p_dirty} = 0;
-	    $z->{c_dirty} = 1;
-	} else {
-	    $theta = ${$z->polar}[1];
-	    _theta(\$theta);
-	}
-	return $theta;
-}
-
-#
-# (sqrt)
-#
-# Compute sqrt(z).
-#
-# It is quite tempting to use wantarray here so that in list context
-# sqrt() would return the two solutions.  This, however, would
-# break things like
-#
-#	print "sqrt(z) = ", sqrt($z), "\n";
-#
-# The two values would be printed side by side without no intervening
-# whitespace, quite confusing.
-# Therefore if you want the two solutions use the root().
-#
-sub sqrt {
-	my ($z) = @_;
-	my ($re, $im) = ref $z ? @{$z->cartesian} : ($z, 0);
-	return $re < 0 ? cplx(0, CORE::sqrt(-$re)) : CORE::sqrt($re)
-	    if $im == 0;
-	my ($r, $t) = @{$z->polar};
-	return (ref $z)->emake(CORE::sqrt($r), $t/2);
-}
-
-#
-# cbrt
-#
-# Compute cbrt(z) (cubic root).
-#
-# Why are we not returning three values?  The same answer as for sqrt().
-#
-sub cbrt {
-	my ($z) = @_;
-	return $z < 0 ?
-	    -CORE::exp(CORE::log(-$z)/3) :
-		($z > 0 ? CORE::exp(CORE::log($z)/3): 0)
-	    unless ref $z;
-	my ($r, $t) = @{$z->polar};
-	return 0 if $r == 0;
-	return (ref $z)->emake(CORE::exp(CORE::log($r)/3), $t/3);
-}
-
-#
-# _rootbad
-#
-# Die on bad root.
-#
-sub _rootbad {
-    my $mess = "Root $_[0] illegal, root rank must be positive integer.\n";
-
-    my @up = caller(1);
-
-    $mess .= "Died at $up[1] line $up[2].\n";
-
-    die $mess;
-}
-
-#
-# root
-#
-# Computes all nth root for z, returning an array whose size is n.
-# `n' must be a positive integer.
-#
-# The roots are given by (for k = 0..n-1):
-#
-# z^(1/n) = r^(1/n) (cos ((t+2 k pi)/n) + i sin ((t+2 k pi)/n))
-#
-sub root {
-	my ($z, $n) = @_;
-	_rootbad($n) if ($n < 1 or int($n) != $n);
-	my ($r, $t) = ref $z ?
-	    @{$z->polar} : (CORE::abs($z), $z >= 0 ? 0 : pi);
-	my @root;
-	my $k;
-	my $theta_inc = pit2 / $n;
-	my $rho = $r ** (1/$n);
-	my $theta;
-	my $cartesian = ref $z && $z->{c_dirty} == 0;
-	for ($k = 0, $theta = $t / $n; $k < $n; $k++, $theta += $theta_inc) {
-	    my $w = cplxe($rho, $theta);
-	    # Yes, $cartesian is loop invariant.
-	    push @root, $cartesian ? cplx(@{$w->cartesian}) : $w;
-	}
-	return @root;
-}
-
-#
-# Re
-#
-# Return or set Re(z).
-#
-sub Re {
-	my ($z, $Re) = @_;
-	return $z unless ref $z;
-	if (defined $Re) {
-	    $z->{'cartesian'} = [ $Re, ${$z->cartesian}[1] ];
-	    $z->{c_dirty} = 0;
-	    $z->{p_dirty} = 1;
-	} else {
-	    return ${$z->cartesian}[0];
-	}
-}
-
-#
-# Im
-#
-# Return or set Im(z).
-#
-sub Im {
-	my ($z, $Im) = @_;
-	return 0 unless ref $z;
-	if (defined $Im) {
-	    $z->{'cartesian'} = [ ${$z->cartesian}[0], $Im ];
-	    $z->{c_dirty} = 0;
-	    $z->{p_dirty} = 1;
-	} else {
-	    return ${$z->cartesian}[1];
-	}
-}
-
-#
-# rho
-#
-# Return or set rho(w).
-#
-sub rho {
-    Math::Complex::abs(@_);
-}
-
-#
-# theta
-#
-# Return or set theta(w).
-#
-sub theta {
-    Math::Complex::arg(@_);
-}
-
-#
-# (exp)
-#
-# Computes exp(z).
-#
-sub exp {
-	my ($z) = @_;
-	my ($x, $y) = @{$z->cartesian};
-	return (ref $z)->emake(CORE::exp($x), $y);
-}
-
-#
-# _logofzero
-#
-# Die on logarithm of zero.
-#
-sub _logofzero {
-    my $mess = "$_[0]: Logarithm of zero.\n";
-
-    if (defined $_[1]) {
-	$mess .= "(Because in the definition of $_[0], the argument ";
-	$mess .= "$_[1] " unless ($_[1] eq '0');
-	$mess .= "is 0)\n";
-    }
-
-    my @up = caller(1);
-
-    $mess .= "Died at $up[1] line $up[2].\n";
-
-    die $mess;
-}
-
-#
-# (log)
-#
-# Compute log(z).
-#
-sub log {
-	my ($z) = @_;
-	unless (ref $z) {
-	    _logofzero("log") if $z == 0;
-	    return $z > 0 ? CORE::log($z) : cplx(CORE::log(-$z), pi);
-	}
-	my ($r, $t) = @{$z->polar};
-	_logofzero("log") if $r == 0;
-	if    ($t >   pi()) { $t -= pit2 }
-	elsif ($t <= -pi()) { $t += pit2 }
-	return (ref $z)->make(CORE::log($r), $t);
-}
-
-#
-# ln
-#
-# Alias for log().
-#
-sub ln { Math::Complex::log(@_) }
-
-#
-# log10
-#
-# Compute log10(z).
-#
-
-sub log10 {
-	return Math::Complex::log($_[0]) * uplog10;
-}
-
-#
-# logn
-#
-# Compute logn(z,n) = log(z) / log(n)
-#
-sub logn {
-	my ($z, $n) = @_;
-	$z = cplx($z, 0) unless ref $z;
-	my $logn = $LOGN{$n};
-	$logn = $LOGN{$n} = CORE::log($n) unless defined $logn;	# Cache log(n)
-	return &log($z) / $logn;
-}
-
-#
-# (cos)
-#
-# Compute cos(z) = (exp(iz) + exp(-iz))/2.
-#
-sub cos {
-	my ($z) = @_;
-	return CORE::cos($z) unless ref $z;
-	my ($x, $y) = @{$z->cartesian};
-	my $ey = CORE::exp($y);
-	my $sx = CORE::sin($x);
-	my $cx = CORE::cos($x);
-	my $ey_1 = $ey ? 1 / $ey : $Inf;
-	return (ref $z)->make($cx * ($ey + $ey_1)/2,
-			      $sx * ($ey_1 - $ey)/2);
-}
-
-#
-# (sin)
-#
-# Compute sin(z) = (exp(iz) - exp(-iz))/2.
-#
-sub sin {
-	my ($z) = @_;
-	return CORE::sin($z) unless ref $z;
-	my ($x, $y) = @{$z->cartesian};
-	my $ey = CORE::exp($y);
-	my $sx = CORE::sin($x);
-	my $cx = CORE::cos($x);
-	my $ey_1 = $ey ? 1 / $ey : $Inf;
-	return (ref $z)->make($sx * ($ey + $ey_1)/2,
-			      $cx * ($ey - $ey_1)/2);
-}
-
-#
-# tan
-#
-# Compute tan(z) = sin(z) / cos(z).
-#
-sub tan {
-	my ($z) = @_;
-	my $cz = &cos($z);
-	_divbyzero "tan($z)", "cos($z)" if $cz == 0;
-	return &sin($z) / $cz;
-}
-
-#
-# sec
-#
-# Computes the secant sec(z) = 1 / cos(z).
-#
-sub sec {
-	my ($z) = @_;
-	my $cz = &cos($z);
-	_divbyzero "sec($z)", "cos($z)" if ($cz == 0);
-	return 1 / $cz;
-}
-
-#
-# csc
-#
-# Computes the cosecant csc(z) = 1 / sin(z).
-#
-sub csc {
-	my ($z) = @_;
-	my $sz = &sin($z);
-	_divbyzero "csc($z)", "sin($z)" if ($sz == 0);
-	return 1 / $sz;
-}
-
-#
-# cosec
-#
-# Alias for csc().
-#
-sub cosec { Math::Complex::csc(@_) }
-
-#
-# cot
-#
-# Computes cot(z) = cos(z) / sin(z).
-#
-sub cot {
-	my ($z) = @_;
-	my $sz = &sin($z);
-	_divbyzero "cot($z)", "sin($z)" if ($sz == 0);
-	return &cos($z) / $sz;
-}
-
-#
-# cotan
-#
-# Alias for cot().
-#
-sub cotan { Math::Complex::cot(@_) }
-
-#
-# acos
-#
-# Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)).
-#
-sub acos {
-	my $z = $_[0];
-	return CORE::atan2(CORE::sqrt(1-$z*$z), $z)
-	    if (! ref $z) && CORE::abs($z) <= 1;
-	$z = cplx($z, 0) unless ref $z;
-	my ($x, $y) = @{$z->cartesian};
-	return 0 if $x == 1 && $y == 0;
-	my $t1 = CORE::sqrt(($x+1)*($x+1) + $y*$y);
-	my $t2 = CORE::sqrt(($x-1)*($x-1) + $y*$y);
-	my $alpha = ($t1 + $t2)/2;
-	my $beta  = ($t1 - $t2)/2;
-	$alpha = 1 if $alpha < 1;
-	if    ($beta >  1) { $beta =  1 }
-	elsif ($beta < -1) { $beta = -1 }
-	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 (ref $z)->make($u, $v);
-}
-
-#
-# asin
-#
-# Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)).
-#
-sub asin {
-	my $z = $_[0];
-	return CORE::atan2($z, CORE::sqrt(1-$z*$z))
-	    if (! ref $z) && CORE::abs($z) <= 1;
-	$z = cplx($z, 0) unless ref $z;
-	my ($x, $y) = @{$z->cartesian};
-	return 0 if $x == 0 && $y == 0;
-	my $t1 = CORE::sqrt(($x+1)*($x+1) + $y*$y);
-	my $t2 = CORE::sqrt(($x-1)*($x-1) + $y*$y);
-	my $alpha = ($t1 + $t2)/2;
-	my $beta  = ($t1 - $t2)/2;
-	$alpha = 1 if $alpha < 1;
-	if    ($beta >  1) { $beta =  1 }
-	elsif ($beta < -1) { $beta = -1 }
-	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 (ref $z)->make($u, $v);
-}
-
-#
-# atan
-#
-# Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)).
-#
-sub atan {
-	my ($z) = @_;
-	return CORE::atan2($z, 1) unless ref $z;
-	my ($x, $y) = ref $z ? @{$z->cartesian} : ($z, 0);
-	return 0 if $x == 0 && $y == 0;
-	_divbyzero "atan(i)"  if ( $z == i);
-	_logofzero "atan(-i)" if (-$z == i); # -i is a bad file test...
-	my $log = &log((i + $z) / (i - $z));
-	return ip2 * $log;
-}
-
-#
-# asec
-#
-# Computes the arc secant asec(z) = acos(1 / z).
-#
-sub asec {
-	my ($z) = @_;
-	_divbyzero "asec($z)", $z if ($z == 0);
-	return acos(1 / $z);
-}
-
-#
-# acsc
-#
-# Computes the arc cosecant acsc(z) = asin(1 / z).
-#
-sub acsc {
-	my ($z) = @_;
-	_divbyzero "acsc($z)", $z if ($z == 0);
-	return asin(1 / $z);
-}
-
-#
-# acosec
-#
-# Alias for acsc().
-#
-sub acosec { Math::Complex::acsc(@_) }
-
-#
-# acot
-#
-# Computes the arc cotangent acot(z) = atan(1 / z)
-#
-sub acot {
-	my ($z) = @_;
-	_divbyzero "acot(0)"  if $z == 0;
-	return ($z >= 0) ? CORE::atan2(1, $z) : CORE::atan2(-1, -$z)
-	    unless ref $z;
-	_divbyzero "acot(i)"  if ($z - i == 0);
-	_logofzero "acot(-i)" if ($z + i == 0);
-	return atan(1 / $z);
-}
-
-#
-# acotan
-#
-# Alias for acot().
-#
-sub acotan { Math::Complex::acot(@_) }
-
-#
-# cosh
-#
-# Computes the hyperbolic cosine cosh(z) = (exp(z) + exp(-z))/2.
-#
-sub cosh {
-	my ($z) = @_;
-	my $ex;
-	unless (ref $z) {
-	    $ex = CORE::exp($z);
-	    return $ex ? ($ex + 1/$ex)/2 : $Inf;
-	}
-	my ($x, $y) = @{$z->cartesian};
-	$ex = CORE::exp($x);
-	my $ex_1 = $ex ? 1 / $ex : $Inf;
-	return (ref $z)->make(CORE::cos($y) * ($ex + $ex_1)/2,
-			      CORE::sin($y) * ($ex - $ex_1)/2);
-}
-
-#
-# sinh
-#
-# Computes the hyperbolic sine sinh(z) = (exp(z) - exp(-z))/2.
-#
-sub sinh {
-	my ($z) = @_;
-	my $ex;
-	unless (ref $z) {
-	    return 0 if $z == 0;
-	    $ex = CORE::exp($z);
-	    return $ex ? ($ex - 1/$ex)/2 : "-$Inf";
-	}
-	my ($x, $y) = @{$z->cartesian};
-	my $cy = CORE::cos($y);
-	my $sy = CORE::sin($y);
-	$ex = CORE::exp($x);
-	my $ex_1 = $ex ? 1 / $ex : $Inf;
-	return (ref $z)->make(CORE::cos($y) * ($ex - $ex_1)/2,
-			      CORE::sin($y) * ($ex + $ex_1)/2);
-}
-
-#
-# tanh
-#
-# Computes the hyperbolic tangent tanh(z) = sinh(z) / cosh(z).
-#
-sub tanh {
-	my ($z) = @_;
-	my $cz = cosh($z);
-	_divbyzero "tanh($z)", "cosh($z)" if ($cz == 0);
-	return sinh($z) / $cz;
-}
-
-#
-# sech
-#
-# Computes the hyperbolic secant sech(z) = 1 / cosh(z).
-#
-sub sech {
-	my ($z) = @_;
-	my $cz = cosh($z);
-	_divbyzero "sech($z)", "cosh($z)" if ($cz == 0);
-	return 1 / $cz;
-}
-
-#
-# csch
-#
-# Computes the hyperbolic cosecant csch(z) = 1 / sinh(z).
-#
-sub csch {
-	my ($z) = @_;
-	my $sz = sinh($z);
-	_divbyzero "csch($z)", "sinh($z)" if ($sz == 0);
-	return 1 / $sz;
-}
-
-#
-# cosech
-#
-# Alias for csch().
-#
-sub cosech { Math::Complex::csch(@_) }
-
-#
-# coth
-#
-# Computes the hyperbolic cotangent coth(z) = cosh(z) / sinh(z).
-#
-sub coth {
-	my ($z) = @_;
-	my $sz = sinh($z);
-	_divbyzero "coth($z)", "sinh($z)" if $sz == 0;
-	return cosh($z) / $sz;
-}
-
-#
-# cotanh
-#
-# Alias for coth().
-#
-sub cotanh { Math::Complex::coth(@_) }
-
-#
-# acosh
-#
-# Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).
-#
-sub acosh {
-	my ($z) = @_;
-	unless (ref $z) {
-	    $z = cplx($z, 0);
-	}
-	my ($re, $im) = @{$z->cartesian};
-	if ($im == 0) {
-	    return CORE::log($re + CORE::sqrt($re*$re - 1))
-		if $re >= 1;
-	    return cplx(0, CORE::atan2(CORE::sqrt(1 - $re*$re), $re))
-		if CORE::abs($re) < 1;
-	}
-	my $t = &sqrt($z * $z - 1) + $z;
-	# Try Taylor if looking bad (this usually means that
-	# $z was large negative, therefore the sqrt is really
-	# close to abs(z), summing that with z...)
-	$t = 1/(2 * $z) - 1/(8 * $z**3) + 1/(16 * $z**5) - 5/(128 * $z**7)
-	    if $t == 0;
-	my $u = &log($t);
-	$u->Im(-$u->Im) if $re < 0 && $im == 0;
-	return $re < 0 ? -$u : $u;
-}
-
-#
-# asinh
-#
-# Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))
-#
-sub asinh {
-	my ($z) = @_;
-	unless (ref $z) {
-	    my $t = $z + CORE::sqrt($z*$z + 1);
-	    return CORE::log($t) if $t;
-	}
-	my $t = &sqrt($z * $z + 1) + $z;
-	# Try Taylor if looking bad (this usually means that
-	# $z was large negative, therefore the sqrt is really
-	# close to abs(z), summing that with z...)
-	$t = 1/(2 * $z) - 1/(8 * $z**3) + 1/(16 * $z**5) - 5/(128 * $z**7)
-	    if $t == 0;
-	return &log($t);
-}
-
-#
-# atanh
-#
-# Computes the arc hyperbolic tangent atanh(z) = 1/2 log((1+z) / (1-z)).
-#
-sub atanh {
-	my ($z) = @_;
-	unless (ref $z) {
-	    return CORE::log((1 + $z)/(1 - $z))/2 if CORE::abs($z) < 1;
-	    $z = cplx($z, 0);
-	}
-	_divbyzero 'atanh(1)',  "1 - $z" if (1 - $z == 0);
-	_logofzero 'atanh(-1)'           if (1 + $z == 0);
-	return 0.5 * &log((1 + $z) / (1 - $z));
-}
-
-#
-# asech
-#
-# Computes the hyperbolic arc secant asech(z) = acosh(1 / z).
-#
-sub asech {
-	my ($z) = @_;
-	_divbyzero 'asech(0)', "$z" if ($z == 0);
-	return acosh(1 / $z);
-}
-
-#
-# acsch
-#
-# Computes the hyperbolic arc cosecant acsch(z) = asinh(1 / z).
-#
-sub acsch {
-	my ($z) = @_;
-	_divbyzero 'acsch(0)', $z if ($z == 0);
-	return asinh(1 / $z);
-}
-
-#
-# acosech
-#
-# Alias for acosh().
-#
-sub acosech { Math::Complex::acsch(@_) }
-
-#
-# acoth
-#
-# Computes the arc hyperbolic cotangent acoth(z) = 1/2 log((1+z) / (z-1)).
-#
-sub acoth {
-	my ($z) = @_;
-	_divbyzero 'acoth(0)'            if ($z == 0);
-	unless (ref $z) {
-	    return CORE::log(($z + 1)/($z - 1))/2 if CORE::abs($z) > 1;
-	    $z = cplx($z, 0);
-	}
-	_divbyzero 'acoth(1)',  "$z - 1" if ($z - 1 == 0);
-	_logofzero 'acoth(-1)', "1 + $z" if (1 + $z == 0);
-	return &log((1 + $z) / ($z - 1)) / 2;
-}
-
-#
-# acotanh
-#
-# Alias for acot().
-#
-sub acotanh { Math::Complex::acoth(@_) }
-
-#
-# (atan2)
-#
-# Compute atan(z1/z2).
-#
-sub atan2 {
-	my ($z1, $z2, $inverted) = @_;
-	my ($re1, $im1, $re2, $im2);
-	if ($inverted) {
-	    ($re1, $im1) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
-	    ($re2, $im2) = @{$z1->cartesian};
-	} else {
-	    ($re1, $im1) = @{$z1->cartesian};
-	    ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
-	}
-	if ($im2 == 0) {
-	    return CORE::atan2($re1, $re2) if $im1 == 0;
-	    return ($im1<=>0) * pip2 if $re2 == 0;
-	}
-	my $w = atan($z1/$z2);
-	my ($u, $v) = ref $w ? @{$w->cartesian} : ($w, 0);
-	$u += pi   if $re2 < 0;
-	$u -= pit2 if $u > pi;
-	return cplx($u, $v);
-}
-
-#
-# display_format
-# ->display_format
-#
-# 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 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 %display_format = %DISPLAY_FORMAT;
-
-	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;
-	}
-
-	if (ref $self) { # Called as an object method
-	    $self->{display_format} = { %display_format };
-	    return
-		wantarray ?
-		    %{$self->{display_format}} :
-		    $self->{display_format}->{style};
-	}
-
-        # Called as a class method
-	%DISPLAY_FORMAT = %display_format;
-	return
-	    wantarray ?
-		%DISPLAY_FORMAT :
-		    $DISPLAY_FORMAT{style};
-}
-
-#
-# (stringify)
-#
-# Show nicely formatted complex number under its cartesian or polar form,
-# depending on the current display format:
-#
-# . If a specific display format has been recorded for this object, use it.
-# . Otherwise, use the generic current default for all complex numbers,
-#   which is a package global variable.
-#
-sub stringify {
-	my ($z) = shift;
-
-	my $style = $z->display_format;
-
-	$style = $DISPLAY_FORMAT{style} unless defined $style;
-
-	return $z->stringify_polar if $style =~ /^p/i;
-	return $z->stringify_cartesian;
-}
-
-#
-# ->stringify_cartesian
-#
-# Stringify as a cartesian representation 'a+bi'.
-#
-sub stringify_cartesian {
-	my $z  = shift;
-	my ($x, $y) = @{$z->cartesian};
-	my ($re, $im);
-
-	my %format = $z->display_format;
-	my $format = $format{format};
-
-	if ($x) {
-	    if ($x =~ /^NaN[QS]?$/i) {
-		$re = $x;
-	    } else {
-		if ($x =~ /^-?$Inf$/oi) {
-		    $re = $x;
-		} else {
-		    $re = defined $format ? sprintf($format, $x) : $x;
-		}
-	    }
-	} else {
-	    undef $re;
-	}
-
-	if ($y) {
-	    if ($y =~ /^(NaN[QS]?)$/i) {
-		$im = $y;
-	    } else {
-		if ($y =~ /^-?$Inf$/oi) {
-		    $im = $y;
-		} else {
-		    $im =
-			defined $format ?
-			    sprintf($format, $y) :
-			    ($y == 1 ? "" : ($y == -1 ? "-" : $y));
-		}
-	    }
-	    $im .= "i";
-	} else {
-	    undef $im;
-	}
-
-	my $str = $re;
-
-	if (defined $im) {
-	    if ($y < 0) {
-		$str .= $im;
-	    } elsif ($y > 0 || $im =~ /^NaN[QS]?i$/i)  {
-		$str .= "+" if defined $re;
-		$str .= $im;
-	    }
-	} elsif (!defined $re) {
-	    $str = "0";
-	}
-
-	return $str;
-}
-
-
-#
-# ->stringify_polar
-#
-# Stringify as a polar representation '[r,t]'.
-#
-sub stringify_polar {
-	my $z  = shift;
-	my ($r, $t) = @{$z->polar};
-	my $theta;
-
-	my %format = $z->display_format;
-	my $format = $format{format};
-
-	if ($t =~ /^NaN[QS]?$/i || $t =~ /^-?$Inf$/oi) {
-	    $theta = $t; 
-	} elsif ($t == pi) {
-	    $theta = "pi";
-	} elsif ($r == 0 || $t == 0) {
-	    $theta = defined $format ? sprintf($format, $t) : $t;
-	}
-
-	return "[$r,$theta]" if defined $theta;
-
-	#
-	# Try to identify pi/n and friends.
-	#
-
-	$t -= int(CORE::abs($t) / pit2) * pit2;
-
-	if ($format{polar_pretty_print} && $t) {
-	    my ($a, $b);
-	    for $a (2..9) {
-		$b = $t * $a / pi;
-		if ($b =~ /^-?\d+$/) {
-		    $b = $b < 0 ? "-" : "" if CORE::abs($b) == 1;
-		    $theta = "${b}pi/$a";
-		    last;
-		}
-	    }
-	}
-
-        if (defined $format) {
-	    $r     = sprintf($format, $r);
-	    $theta = sprintf($format, $theta) unless defined $theta;
-	} else {
-	    $theta = $t unless defined $theta;
-	}
-
-	return "[$r,$theta]";
-}
-
-1;
-__END__
-
-=pod
-
-=head1 NAME
-
-Math::Complex - complex numbers and associated mathematical functions
-
-=head1 SYNOPSIS
-
-	use Math::Complex;
-
-	$z = Math::Complex->make(5, 6);
-	$t = 4 - 3*i + $z;
-	$j = cplxe(1, 2*pi/3);
-
-=head1 DESCRIPTION
-
-This package lets you create and manipulate complex numbers. By default,
-I<Perl> limits itself to real numbers, but an extra C<use> statement brings
-full complex support, along with a full set of mathematical functions
-typically associated with and/or extended to complex numbers.
-
-If you wonder what complex numbers are, they were invented to be able to solve
-the following equation:
-
-	x*x = -1
-
-and by definition, the solution is noted I<i> (engineers use I<j> instead since
-I<i> usually denotes an intensity, but the name does not matter). The number
-I<i> is a pure I<imaginary> number.
-
-The arithmetics with pure imaginary numbers works just like you would expect
-it with real numbers... you just have to remember that
-
-	i*i = -1
-
-so you have:
-
-	5i + 7i = i * (5 + 7) = 12i
-	4i - 3i = i * (4 - 3) = i
-	4i * 2i = -8
-	6i / 2i = 3
-	1 / i = -i
-
-Complex numbers are numbers that have both a real part and an imaginary
-part, and are usually noted:
-
-	a + bi
-
-where C<a> is the I<real> part and C<b> is the I<imaginary> part. The
-arithmetic with complex numbers is straightforward. You have to
-keep track of the real and the imaginary parts, but otherwise the
-rules used for real numbers just apply:
-
-	(4 + 3i) + (5 - 2i) = (4 + 5) + i(3 - 2) = 9 + i
-	(2 + i) * (4 - i) = 2*4 + 4i -2i -i*i = 8 + 2i + 1 = 9 + 2i
-
-A graphical representation of complex numbers is possible in a plane
-(also called the I<complex plane>, but it's really a 2D plane).
-The number
-
-	z = a + bi
-
-is the point whose coordinates are (a, b). Actually, it would
-be the vector originating from (0, 0) to (a, b). It follows that the addition
-of two complex numbers is a vectorial addition.
-
-Since there is a bijection between a point in the 2D plane and a complex
-number (i.e. the mapping is unique and reciprocal), a complex number
-can also be uniquely identified with polar coordinates:
-
-	[rho, theta]
-
-where C<rho> is the distance to the origin, and C<theta> the angle between
-the vector and the I<x> axis. There is a notation for this using the
-exponential form, which is:
-
-	rho * exp(i * theta)
-
-where I<i> is the famous imaginary number introduced above. Conversion
-between this form and the cartesian form C<a + bi> is immediate:
-
-	a = rho * cos(theta)
-	b = rho * sin(theta)
-
-which is also expressed by this formula:
-
-	z = rho * exp(i * theta) = rho * (cos theta + i * sin theta)
-
-In other words, it's the projection of the vector onto the I<x> and I<y>
-axes. Mathematicians call I<rho> the I<norm> or I<modulus> and I<theta>
-the I<argument> of the complex number. The I<norm> of C<z> will be
-noted C<abs(z)>.
-
-The polar notation (also known as the trigonometric
-representation) is much more handy for performing multiplications and
-divisions of complex numbers, whilst the cartesian notation is better
-suited for additions and subtractions. Real numbers are on the I<x>
-axis, and therefore I<theta> is zero or I<pi>.
-
-All the common operations that can be performed on a real number have
-been defined to work on complex numbers as well, and are merely
-I<extensions> of the operations defined on real numbers. This means
-they keep their natural meaning when there is no imaginary part, provided
-the number is within their definition set.
-
-For instance, the C<sqrt> routine which computes the square root of
-its argument is only defined for non-negative real numbers and yields a
-non-negative real number (it is an application from B<R+> to B<R+>).
-If we allow it to return a complex number, then it can be extended to
-negative real numbers to become an application from B<R> to B<C> (the
-set of complex numbers):
-
-	sqrt(x) = x >= 0 ? sqrt(x) : sqrt(-x)*i
-
-It can also be extended to be an application from B<C> to B<C>,
-whilst its restriction to B<R> behaves as defined above by using
-the following definition:
-
-	sqrt(z = [r,t]) = sqrt(r) * exp(i * t/2)
-
-Indeed, a negative real number can be noted C<[x,pi]> (the modulus
-I<x> is always non-negative, so C<[x,pi]> is really C<-x>, a negative
-number) and the above definition states that
-
-	sqrt([x,pi]) = sqrt(x) * exp(i*pi/2) = [sqrt(x),pi/2] = sqrt(x)*i
-
-which is exactly what we had defined for negative real numbers above.
-The C<sqrt> returns only one of the solutions: if you want the both,
-use the C<root> function.
-
-All the common mathematical functions defined on real numbers that
-are extended to complex numbers share that same property of working
-I<as usual> when the imaginary part is zero (otherwise, it would not
-be called an extension, would it?).
-
-A I<new> operation possible on a complex number that is
-the identity for real numbers is called the I<conjugate>, and is noted
-with an horizontal bar above the number, or C<~z> here.
-
-	 z = a + bi
-	~z = a - bi
-
-Simple... Now look:
-
-	z * ~z = (a + bi) * (a - bi) = a*a + b*b
-
-We saw that the norm of C<z> was noted C<abs(z)> and was defined as the
-distance to the origin, also known as:
-
-	rho = abs(z) = sqrt(a*a + b*b)
-
-so
-
-	z * ~z = abs(z) ** 2
-
-If z is a pure real number (i.e. C<b == 0>), then the above yields:
-
-	a * a = abs(a) ** 2
-
-which is true (C<abs> has the regular meaning for real number, i.e. stands
-for the absolute value). This example explains why the norm of C<z> is
-noted C<abs(z)>: it extends the C<abs> function to complex numbers, yet
-is the regular C<abs> we know when the complex number actually has no
-imaginary part... This justifies I<a posteriori> our use of the C<abs>
-notation for the norm.
-
-=head1 OPERATIONS
-
-Given the following notations:
-
-	z1 = a + bi = r1 * exp(i * t1)
-	z2 = c + di = r2 * exp(i * t2)
-	z = <any complex or real number>
-
-the following (overloaded) operations are supported on complex numbers:
-
-	z1 + z2 = (a + c) + i(b + d)
-	z1 - z2 = (a - c) + i(b - d)
-	z1 * z2 = (r1 * r2) * exp(i * (t1 + t2))
-	z1 / z2 = (r1 / r2) * exp(i * (t1 - t2))
-	z1 ** z2 = exp(z2 * log z1)
-	~z = a - bi
-	abs(z) = r1 = sqrt(a*a + b*b)
-	sqrt(z) = sqrt(r1) * exp(i * t/2)
-	exp(z) = exp(a) * exp(i * b)
-	log(z) = log(r1) + i*t
-	sin(z) = 1/2i (exp(i * z1) - exp(-i * z))
-	cos(z) = 1/2 (exp(i * z1) + exp(-i * z))
-	atan2(z1, z2) = atan(z1/z2)
-
-The following extra operations are supported on both real and complex
-numbers:
-
-	Re(z) = a
-	Im(z) = b
-	arg(z) = t
-	abs(z) = r
-
-	cbrt(z) = z ** (1/3)
-	log10(z) = log(z) / log(10)
-	logn(z, n) = log(z) / log(n)
-
-	tan(z) = sin(z) / cos(z)
-
-	csc(z) = 1 / sin(z)
-	sec(z) = 1 / cos(z)
-	cot(z) = 1 / tan(z)
-
-	asin(z) = -i * log(i*z + sqrt(1-z*z))
-	acos(z) = -i * log(z + i*sqrt(1-z*z))
-	atan(z) = i/2 * log((i+z) / (i-z))
-
-	acsc(z) = asin(1 / z)
-	asec(z) = acos(1 / z)
-	acot(z) = atan(1 / z) = -i/2 * log((i+z) / (z-i))
-
-	sinh(z) = 1/2 (exp(z) - exp(-z))
-	cosh(z) = 1/2 (exp(z) + exp(-z))
-	tanh(z) = sinh(z) / cosh(z) = (exp(z) - exp(-z)) / (exp(z) + exp(-z))
-
-	csch(z) = 1 / sinh(z)
-	sech(z) = 1 / cosh(z)
-	coth(z) = 1 / tanh(z)
-
-	asinh(z) = log(z + sqrt(z*z+1))
-	acosh(z) = log(z + sqrt(z*z-1))
-	atanh(z) = 1/2 * log((1+z) / (1-z))
-
-	acsch(z) = asinh(1 / z)
-	asech(z) = acosh(1 / z)
-	acoth(z) = atanh(1 / z) = 1/2 * log((1+z) / (z-1))
-
-I<arg>, I<abs>, I<log>, I<csc>, I<cot>, I<acsc>, I<acot>, I<csch>,
-I<coth>, I<acosech>, I<acotanh>, have aliases I<rho>, I<theta>, I<ln>,
-I<cosec>, I<cotan>, I<acosec>, I<acotan>, I<cosech>, I<cotanh>,
-I<acosech>, I<acotanh>, respectively.  C<Re>, C<Im>, C<arg>, C<abs>,
-C<rho>, and C<theta> can be used also also mutators.  The C<cbrt>
-returns only one of the solutions: if you want all three, use the
-C<root> function.
-
-The I<root> function is available to compute all the I<n>
-roots of some complex, where I<n> is a strictly positive integer.
-There are exactly I<n> such roots, returned as a list. Getting the
-number mathematicians call C<j> such that:
-
-	1 + j + j*j = 0;
-
-is a simple matter of writing:
-
-	$j = ((root(1, 3))[1];
-
-The I<k>th root for C<z = [r,t]> is given by:
-
-	(root(z, n))[k] = r**(1/n) * exp(i * (t + 2*k*pi)/n)
-
-The I<spaceship> comparison operator, E<lt>=E<gt>, is also defined. In
-order to ensure its restriction to real numbers is conform to what you
-would expect, the comparison is run on the real part of the complex
-number first, and imaginary parts are compared only when the real
-parts match.
-
-=head1 CREATION
-
-To create a complex number, use either:
-
-	$z = Math::Complex->make(3, 4);
-	$z = cplx(3, 4);
-
-if you know the cartesian form of the number, or
-
-	$z = 3 + 4*i;
-
-if you like. To create a number using the polar form, use either:
-
-	$z = Math::Complex->emake(5, pi/3);
-	$x = cplxe(5, pi/3);
-
-instead. The first argument is the modulus, the second is the angle
-(in radians, the full circle is 2*pi).  (Mnemonic: C<e> is used as a
-notation for complex numbers in the polar form).
-
-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).
-
-It is also possible to have a complex number as either argument of
-either the C<make> or C<emake>: the appropriate component of
-the argument will be used.
-
-	$z1 = cplx(-2,  1);
-	$z2 = cplx($z1, 4);
-
-=head1 STRINGIFICATION
-
-When printed, a complex number is usually shown under its cartesian
-style I<a+bi>, but there are legitimate cases where the polar style
-I<[r,t]> is more appropriate.
-
-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 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->display_format('cartesian');
-	print "j = $j\n";		# Prints "j = -0.5+0.866025403784439i"
-
-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.
-
-	$j->display_format(style => "polar");
-
-The one parameter calling convention also still works.
-
-	$j->display_format("polar");
-
-There are two new display parameters.
-
-The first one is C<"format">, which is a sprintf()-style format string
-to be used for both numeric parts of the complex number(s).  The is
-somewhat system-dependent but most often it corresponds to C<"%.15g">.
-You can revert to the default by setting the C<format> 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' => undef);
-	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.
-This is a potential incompatibility with earlier versions if you
-have been calling the C<display_format> method in list context.
-
-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
-
-Thanks to overloading, the handling of arithmetics with complex numbers
-is simple and almost transparent.
-
-Here are some examples:
-
-	use Math::Complex;
-
-	$j = cplxe(1, 2*pi/3);	# $j ** 3 == 1
-	print "j = $j, j**3 = ", $j ** 3, "\n";
-	print "1 + j + j**2 = ", 1 + $j + $j**2, "\n";
-
-	$z = -16 + 0*i;			# Force it to be a complex
-	print "sqrt($z) = ", sqrt($z), "\n";
-
-	$k = exp(i * 2*pi/3);
-	print "$j - $k = ", $j - $k, "\n";
-
-	$z->Re(3);			# Re, Im, arg, abs,
-	$j->arg(2);			# (the last two aka rho, theta)
-					# can be used also as mutators.
-
-=head1 ERRORS DUE TO DIVISION BY ZERO OR LOGARITHM OF ZERO
-
-The division (/) and the following functions
-
-	log	ln	log10	logn
-	tan	sec	csc	cot
-	atan	asec	acsc	acot
-	tanh	sech	csch	coth
-	atanh	asech	acsch	acoth
-
-cannot be computed for all arguments because that would mean dividing
-by zero or taking logarithm of zero. These situations cause fatal
-runtime errors looking like this
-
-	cot(0): Division by zero.
-	(Because in the definition of cot(0), the divisor sin(0) is 0)
-	Died at ...
-
-or
-
-	atanh(-1): Logarithm of zero.
-	Died at...
-
-For the C<csc>, C<cot>, C<asec>, C<acsc>, C<acot>, C<csch>, C<coth>,
-C<asech>, C<acsch>, the argument cannot be C<0> (zero).  For the the
-logarithmic functions and the C<atanh>, C<acoth>, the argument cannot
-be C<1> (one).  For the C<atanh>, C<acoth>, the argument cannot be
-C<-1> (minus one).  For the C<atan>, C<acot>, the argument cannot be
-C<i> (the imaginary unit).  For the C<atan>, C<acoth>, the argument
-cannot be C<-i> (the negative imaginary unit).  For the C<tan>,
-C<sec>, C<tanh>, the argument cannot be I<pi/2 + k * pi>, where I<k>
-is any integer.
-
-Note that because we are operating on approximations of real numbers,
-these errors can happen when merely `too close' to the singularities
-listed above.
-
-=head1 ERRORS DUE TO INDIGESTIBLE ARGUMENTS
-
-The C<make> and C<emake> accept both real and complex arguments.
-When they cannot recognize the arguments they will die with error
-messages like the following
-
-    Math::Complex::make: Cannot take real part of ...
-    Math::Complex::make: Cannot take real part of ...
-    Math::Complex::emake: Cannot take rho of ...
-    Math::Complex::emake: Cannot take theta of ...
-
-=head1 BUGS
-
-Saying C<use Math::Complex;> exports many mathematical routines in the
-caller environment and even overrides some (C<sqrt>, C<log>).
-This is construed as a feature by the Authors, actually... ;-)
-
-All routines expect to be given real or complex numbers. Don't attempt to
-use BigFloat, since Perl has currently no rule to disambiguate a '+'
-operation (for instance) between two overloaded entities.
-
-In Cray UNICOS there is some strange numerical instability that results
-in root(), cos(), sin(), cosh(), sinh(), losing accuracy fast.  Beware.
-The bug may be in UNICOS math libs, in UNICOS C compiler, in Math::Complex.
-Whatever it is, it does not manifest itself anywhere else where Perl runs.
-
-=head1 AUTHORS
-
-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>>.
-
-=cut
-
-1;
-
-# eof
diff --git a/contrib/perl5/lib/Math/Trig.pm b/contrib/perl5/lib/Math/Trig.pm
deleted file mode 100644
index b28f150..0000000
--- a/contrib/perl5/lib/Math/Trig.pm
+++ /dev/null
@@ -1,456 +0,0 @@
-#
-# Trigonometric functions, mostly inherited from Math::Complex.
-# -- Jarkko Hietaniemi, since April 1997
-# -- Raphael Manfredi, September 1996 (indirectly: because of Math::Complex)
-#
-
-require Exporter;
-package Math::Trig;
-
-use 5.005_64;
-use strict;
-
-use Math::Complex qw(:trig);
-
-our($VERSION, $PACKAGE, @ISA, @EXPORT, @EXPORT_OK, %EXPORT_TAGS);
-
-@ISA = qw(Exporter);
-
-$VERSION = 1.00;
-
-my @angcnv = qw(rad2deg rad2grad
-	     deg2rad deg2grad
-	     grad2rad grad2deg);
-
-@EXPORT = (@{$Math::Complex::EXPORT_TAGS{'trig'}},
-	   @angcnv);
-
-my @rdlcnv = qw(cartesian_to_cylindrical
-		cartesian_to_spherical
-		cylindrical_to_cartesian
-		cylindrical_to_spherical
-		spherical_to_cartesian
-		spherical_to_cylindrical);
-
-@EXPORT_OK = (@rdlcnv, 'great_circle_distance');
-
-%EXPORT_TAGS = ('radial' => [ @rdlcnv ]);
-
-sub pi2  () { 2 * pi }
-sub pip2 () { pi / 2 }
-
-sub DR  () { pi2/360 }
-sub RD  () { 360/pi2 }
-sub DG  () { 400/360 }
-sub GD  () { 360/400 }
-sub RG  () { 400/pi2 }
-sub GR  () { pi2/400 }
-
-#
-# Truncating remainder.
-#
-
-sub remt ($$) {
-    # Oh yes, POSIX::fmod() would be faster. Possibly. If it is available.
-    $_[0] - $_[1] * int($_[0] / $_[1]);
-}
-
-#
-# Angle conversions.
-#
-
-sub rad2rad($)     { remt($_[0], pi2) }
-
-sub deg2deg($)     { remt($_[0], 360) }
-
-sub grad2grad($)   { remt($_[0], 400) }
-
-sub rad2deg ($;$)  { my $d = RD * $_[0]; $_[1] ? $d : deg2deg($d) }
-
-sub deg2rad ($;$)  { my $d = DR * $_[0]; $_[1] ? $d : rad2rad($d) }
-
-sub grad2deg ($;$) { my $d = GD * $_[0]; $_[1] ? $d : deg2deg($d) }
-
-sub deg2grad ($;$) { my $d = DG * $_[0]; $_[1] ? $d : grad2grad($d) }
-
-sub rad2grad ($;$) { my $d = RG * $_[0]; $_[1] ? $d : grad2grad($d) }
-
-sub grad2rad ($;$) { my $d = GR * $_[0]; $_[1] ? $d : rad2rad($d) }
-
-sub cartesian_to_spherical {
-    my ( $x, $y, $z ) = @_;
-
-    my $rho = sqrt( $x * $x + $y * $y + $z * $z );
-
-    return ( $rho,
-             atan2( $y, $x ),
-             $rho ? acos( $z / $rho ) : 0 );
-}
-
-sub spherical_to_cartesian {
-    my ( $rho, $theta, $phi ) = @_;
-
-    return ( $rho * cos( $theta ) * sin( $phi ),
-             $rho * sin( $theta ) * sin( $phi ),
-             $rho * cos( $phi   ) );
-}
-
-sub spherical_to_cylindrical {
-    my ( $x, $y, $z ) = spherical_to_cartesian( @_ );
-
-    return ( sqrt( $x * $x + $y * $y ), $_[1], $z );
-}
-
-sub cartesian_to_cylindrical {
-    my ( $x, $y, $z ) = @_;
-
-    return ( sqrt( $x * $x + $y * $y ), atan2( $y, $x ), $z );
-}
-
-sub cylindrical_to_cartesian {
-    my ( $rho, $theta, $z ) = @_;
-
-    return ( $rho * cos( $theta ), $rho * sin( $theta ), $z );
-}
-
-sub cylindrical_to_spherical {
-    return ( cartesian_to_spherical( cylindrical_to_cartesian( @_ ) ) );
-}
-
-sub great_circle_distance {
-    my ( $theta0, $phi0, $theta1, $phi1, $rho ) = @_;
-
-    $rho = 1 unless defined $rho; # Default to the unit sphere.
-
-    my $lat0 = pip2 - $phi0;
-    my $lat1 = pip2 - $phi1;
-
-    return $rho *
-        acos(cos( $lat0 ) * cos( $lat1 ) * cos( $theta0 - $theta1 ) +
-             sin( $lat0 ) * sin( $lat1 ) );
-}
-
-=pod
-
-=head1 NAME
-
-Math::Trig - trigonometric functions
-
-=head1 SYNOPSIS
-
-	use Math::Trig;
-
-	$x = tan(0.9);
-	$y = acos(3.7);
-	$z = asin(2.4);
-
-	$halfpi = pi/2;
-
-	$rad = deg2rad(120);
-
-=head1 DESCRIPTION
-
-C<Math::Trig> defines many trigonometric functions not defined by the
-core Perl which defines only the C<sin()> and C<cos()>.  The constant
-B<pi> is also defined as are a few convenience functions for angle
-conversions.
-
-=head1 TRIGONOMETRIC FUNCTIONS
-
-The tangent
-
-=over 4
-
-=item B<tan>
-
-=back
-
-The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot
-are aliases)
-
-B<csc>, B<cosec>, B<sec>, B<sec>, B<cot>, B<cotan>
-
-The arcus (also known as the inverse) functions of the sine, cosine,
-and tangent
-
-B<asin>, B<acos>, B<atan>
-
-The principal value of the arc tangent of y/x
-
-B<atan2>(y, x)
-
-The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc
-and acotan/acot are aliases)
-
-B<acsc>, B<acosec>, B<asec>, B<acot>, B<acotan>
-
-The hyperbolic sine, cosine, and tangent
-
-B<sinh>, B<cosh>, B<tanh>
-
-The cofunctions of the hyperbolic sine, cosine, and tangent (cosech/csch
-and cotanh/coth are aliases)
-
-B<csch>, B<cosech>, B<sech>, B<coth>, B<cotanh>
-
-The arcus (also known as the inverse) functions of the hyperbolic
-sine, cosine, and tangent
-
-B<asinh>, B<acosh>, B<atanh>
-
-The arcus cofunctions of the hyperbolic sine, cosine, and tangent
-(acsch/acosech and acoth/acotanh are aliases)
-
-B<acsch>, B<acosech>, B<asech>, B<acoth>, B<acotanh>
-
-The trigonometric constant B<pi> is also defined.
-
-$pi2 = 2 * B<pi>;
-
-=head2 ERRORS DUE TO DIVISION BY ZERO
-
-The following functions
-
-	acoth
-	acsc
-	acsch
-	asec
-	asech
-	atanh
-	cot
-	coth
-	csc
-	csch
-	sec
-	sech
-	tan
-	tanh
-
-cannot be computed for all arguments because that would mean dividing
-by zero or taking logarithm of zero. These situations cause fatal
-runtime errors looking like this
-
-	cot(0): Division by zero.
-	(Because in the definition of cot(0), the divisor sin(0) is 0)
-	Died at ...
-
-or
-
-	atanh(-1): Logarithm of zero.
-	Died at...
-
-For the C<csc>, C<cot>, C<asec>, C<acsc>, C<acot>, C<csch>, C<coth>,
-C<asech>, C<acsch>, the argument cannot be C<0> (zero).  For the
-C<atanh>, C<acoth>, the argument cannot be C<1> (one).  For the
-C<atanh>, C<acoth>, the argument cannot be C<-1> (minus one).  For the
-C<tan>, C<sec>, C<tanh>, C<sech>, the argument cannot be I<pi/2 + k *
-pi>, where I<k> is any integer.
-
-=head2 SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS
-
-Please note that some of the trigonometric functions can break out
-from the B<real axis> into the B<complex plane>. For example
-C<asin(2)> has no definition for plain real numbers but it has
-definition for complex numbers.
-
-In Perl terms this means that supplying the usual Perl numbers (also
-known as scalars, please see L<perldata>) as input for the
-trigonometric functions might produce as output results that no more
-are simple real numbers: instead they are complex numbers.
-
-The C<Math::Trig> handles this by using the C<Math::Complex> package
-which knows how to handle complex numbers, please see L<Math::Complex>
-for more information. In practice you need not to worry about getting
-complex numbers as results because the C<Math::Complex> takes care of
-details like for example how to display complex numbers. For example:
-
-	print asin(2), "\n";
-
-should produce something like this (take or leave few last decimals):
-
-	1.5707963267949-1.31695789692482i
-
-That is, a complex number with the real part of approximately C<1.571>
-and the imaginary part of approximately C<-1.317>.
-
-=head1 PLANE ANGLE CONVERSIONS
-
-(Plane, 2-dimensional) angles may be converted with the following functions.
-
-	$radians  = deg2rad($degrees);
-	$radians  = grad2rad($gradians);
-
-	$degrees  = rad2deg($radians);
-	$degrees  = grad2deg($gradians);
-
-	$gradians = deg2grad($degrees);
-	$gradians = rad2grad($radians);
-
-The full circle is 2 I<pi> radians or I<360> degrees or I<400> gradians.
-The result is by default wrapped to be inside the [0, {2pi,360,400}[ circle.
-If you don't want this, supply a true second argument:
-
-	$zillions_of_radians  = deg2rad($zillions_of_degrees, 1);
-	$negative_degrees     = rad2deg($negative_radians, 1);
-
-You can also do the wrapping explicitly by rad2rad(), deg2deg(), and
-grad2grad().
-
-=head1 RADIAL COORDINATE CONVERSIONS
-
-B<Radial coordinate systems> are the B<spherical> and the B<cylindrical>
-systems, explained shortly in more detail.
-
-You can import radial coordinate conversion functions by using the
-C<:radial> tag:
-
-    use Math::Trig ':radial';
-
-    ($rho, $theta, $z)     = cartesian_to_cylindrical($x, $y, $z);
-    ($rho, $theta, $phi)   = cartesian_to_spherical($x, $y, $z);
-    ($x, $y, $z)           = cylindrical_to_cartesian($rho, $theta, $z);
-    ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z);
-    ($x, $y, $z)           = spherical_to_cartesian($rho, $theta, $phi);
-    ($rho_c, $theta, $z)   = spherical_to_cylindrical($rho_s, $theta, $phi);
-
-B<All angles are in radians>.
-
-=head2 COORDINATE SYSTEMS
-
-B<Cartesian> coordinates are the usual rectangular I<(x, y,
-z)>-coordinates.
-
-Spherical coordinates, I<(rho, theta, pi)>, are three-dimensional
-coordinates which define a point in three-dimensional space.  They are
-based on a sphere surface.  The radius of the sphere is B<rho>, also
-known as the I<radial> coordinate.  The angle in the I<xy>-plane
-(around the I<z>-axis) is B<theta>, also known as the I<azimuthal>
-coordinate.  The angle from the I<z>-axis is B<phi>, also known as the
-I<polar> coordinate.  The `North Pole' is therefore I<0, 0, rho>, and
-the `Bay of Guinea' (think of the missing big chunk of Africa) I<0,
-pi/2, rho>.  In geographical terms I<phi> is latitude (northward
-positive, southward negative) and I<theta> is longitude (eastward
-positive, westward negative).
-
-B<BEWARE>: some texts define I<theta> and I<phi> the other way round,
-some texts define the I<phi> to start from the horizontal plane, some
-texts use I<r> in place of I<rho>.
-
-Cylindrical coordinates, I<(rho, theta, z)>, are three-dimensional
-coordinates which define a point in three-dimensional space.  They are
-based on a cylinder surface.  The radius of the cylinder is B<rho>,
-also known as the I<radial> coordinate.  The angle in the I<xy>-plane
-(around the I<z>-axis) is B<theta>, also known as the I<azimuthal>
-coordinate.  The third coordinate is the I<z>, pointing up from the
-B<theta>-plane.
-
-=head2 3-D ANGLE CONVERSIONS
-
-Conversions to and from spherical and cylindrical coordinates are
-available.  Please notice that the conversions are not necessarily
-reversible because of the equalities like I<pi> angles being equal to
-I<-pi> angles.
-
-=over 4
-
-=item cartesian_to_cylindrical
-
-        ($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z);
-
-=item cartesian_to_spherical
-
-        ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z);
-
-=item cylindrical_to_cartesian
-
-        ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z);
-
-=item cylindrical_to_spherical
-
-        ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z);
-
-Notice that when C<$z> is not 0 C<$rho_s> is not equal to C<$rho_c>.
-
-=item spherical_to_cartesian
-
-        ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi);
-
-=item spherical_to_cylindrical
-
-        ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi);
-
-Notice that when C<$z> is not 0 C<$rho_c> is not equal to C<$rho_s>.
-
-=back
-
-=head1 GREAT CIRCLE DISTANCES
-
-You can compute spherical distances, called B<great circle distances>,
-by importing the C<great_circle_distance> function:
-
-	use Math::Trig 'great_circle_distance'
-
-  $distance = great_circle_distance($theta0, $phi0, $theta1, $phi1, [, $rho]);
-
-The I<great circle distance> is the shortest distance between two
-points on a sphere.  The distance is in C<$rho> units.  The C<$rho> is
-optional, it defaults to 1 (the unit sphere), therefore the distance
-defaults to radians.
-
-If you think geographically the I<theta> are longitudes: zero at the
-Greenwhich meridian, eastward positive, westward negative--and the
-I<phi> are latitudes: zero at the North Pole, northward positive,
-southward negative.  B<NOTE>: this formula thinks in mathematics, not
-geographically: the I<phi> zero is at the North Pole, not at the
-Equator on the west coast of Africa (Bay of Guinea).  You need to
-subtract your geographical coordinates from I<pi/2> (also known as 90
-degrees).
-
-  $distance = great_circle_distance($lon0, pi/2 - $lat0,
-                                    $lon1, pi/2 - $lat1, $rho);
-
-=head1 EXAMPLES
-
-To calculate the distance between London (51.3N 0.5W) and Tokyo (35.7N
-139.8E) in kilometers:
-
-        use Math::Trig qw(great_circle_distance deg2rad);
-
-        # Notice the 90 - latitude: phi zero is at the North Pole.
-	@L = (deg2rad(-0.5), deg2rad(90 - 51.3));
-        @T = (deg2rad(139.8),deg2rad(90 - 35.7));
-
-        $km = great_circle_distance(@L, @T, 6378);
-
-The answer may be off by few percentages because of the irregular
-(slightly aspherical) form of the Earth.  The used formula
-
-	lat0 = 90 degrees - phi0
-	lat1 = 90 degrees - phi1
-	d = R * arccos(cos(lat0) * cos(lat1) * cos(lon1 - lon01) +
-                       sin(lat0) * sin(lat1))
-
-is also somewhat unreliable for small distances (for locations
-separated less than about five degrees) because it uses arc cosine
-which is rather ill-conditioned for values close to zero.
-
-=head1 BUGS
-
-Saying C<use Math::Trig;> exports many mathematical routines in the
-caller environment and even overrides some (C<sin>, C<cos>).  This is
-construed as a feature by the Authors, actually... ;-)
-
-The code is not optimized for speed, especially because we use
-C<Math::Complex> and thus go quite near complex numbers while doing
-the computations even when the arguments are not. This, however,
-cannot be completely avoided if we want things like C<asin(2)> to give
-an answer instead of giving a fatal runtime error.
-
-=head1 AUTHORS
-
-Jarkko Hietaniemi <F<jhi@iki.fi>> and 
-Raphael Manfredi <F<Raphael_Manfredi@pobox.com>>.
-
-=cut
-
-# eof