[inseparable changes from patch to perl 5.004_04]perl-5.004_04

[editor's note: this one imported like a charm!]

 TESTS  -

Subject: Improve pragma/locale test 102 - and don't fail, just warn
From: Jarkko Hietaniemi <jhi@anna.in-berlin.de>
Files: t/pragma/locale.t

Subject: Invalid test output in t/op/taint.t in trial 1
From: Dan Sugalski <sugalsd@lbcc.cc.or.us>
Files: t/op/taint.t

    t/op/taint.t prints out invalid ok messages for tests it skips.
    Rather than printing "ok 136" it prints "136 ok".
    
    p5p-msgid: 3.0.3.32.19970919160918.00857a50@stargate.lbcc.cc.or.us

 UTILITIES  -

Subject: Perldoc tiny patch to avoid $0
From: Ilya Zakharevich <ilya@math.ohio-state.edu>
Files: utils/perldoc.PL
Msg-ID: 199709122141.RAA16846@monk.mps.ohio-state.edu

    (applied based on p5p patch as commit 0b166b6635cf199f072db516b2a523ee659394d5)

Subject: h2ph broken in 5.004_02
From: David Mazieres <dm@reeducation-labor.lcs.mit.edu>
Files: utils/h2ph.PL
Msg-ID: 199708201700.KAA02621@www.chapin.edu

    (applied based on p5p patch as commit 4a8e146e38ec2045f1f817a7cb578e1b1f80f39f)

Subject: add key_t caddr_t to h2ph
From: Tony Sanders <sanders@bsdi.com>
Files: eg/sysvipc/ipcsem utils/h2ph.PL
Msg-ID: 199708272301.RAA12803@austin.bsdi.com

    (applied based on p5p patch as commit 0806a92ffc3a74ca70aa81051cdf2a306cd0a8af)

Subject: perldoc search ., lib and blib/* if -f 'Makefile.PL'
From: Tim Bunce <Tim.Bunce@ig.co.uk>
Files: utils/perldoc.PL

    Subject: perldoc finds wrong pod2man
    
    (from perldoc source)
    
        # We must look both in @INC for library modules and in PATH
        # for executables, like h2xs or perldoc itself.
    
    Unfortunately, searching PATH for installed perl executables like
    pod2man is INCORRECT.  perldoc should start by searching the
    directory it was executed from, which might not be in the PATH
    at all.
    
    Credited: Joseph "Moof-in'" Hall <joseph@cscaper.com>
    
    p5p-msgid: 199708251732.KAA19299@gadget.cscaper.com

Subject: 5.004m4t1: perlbug: NIS domainname gets into wrong places
From: Andreas J. Koenig <koenig@anna.mind.de>
Files: utils/perlbug.PL
Msg-ID: sfcg1qy38as.fsf@anna.in-berlin.de

    (applied based on p5p patch as commit 41f926b844140b7f7eaa9302113e45df3a9f9ff4)

Subject: add better local patch info to perlbug
From: Tim Bunce <Tim.Bunce@ig.co.uk>
Files: utils/perlbug.PL

Subject: perldoc - suggest modules if requested module not found
From: Anthony David <adavid@netinfo.com.au>
Files: utils/perldoc.PL

    private-msgid: 3439CD83.6969@netinfo.com.au

Subject: perldoc mail::foo tries to read binary /usr/ucb/mail
From: Tim Bunce <Tim.Bunce@ig.co.uk>
Files: utils/perldoc.PL

    Subject: perldoc weirdness
    
    perldoc mail::imap yields:
    
    {joseph}:79% perldoc mail::foo
    can't open /usr/ucb/mail: Permission denied at ./pod2man line 362.
    
    Credited: Joseph "Moof-in'" Hall <joseph@cscaper.com>
    
    p5p-msgid: 199710082014.NAA00808@gadget.cscaper.com

Subject: perldoc -f setpwent (for example) returns no descriptive text
From: Tim Bunce <Tim.Bunce@ig.co.uk>
Files: utils/perldoc.PL

Subject: perldoc diffs: don't search auto - much faster
From: "Joseph N. Hall" <joseph@5sigma.com>
Files: utils/perldoc.PL
Msg-ID: MailDrop1.2d7dPPC.971012211957@screechy.cscaper.com

    (applied based on p5p patch as commit 62b753c6ae4ab9bf22fbb6ec7ceac820bcef8fe4)

1 files changed, 228 insertions, 196 deletions

diff --git a/lib/Math/Complex.pm b/lib/Math/Complex.pm
index 33c60231aa..64477fa7f3 100644
--- a/lib/Math/Complex.pm
+++ b/lib/Math/Complex.pm
@@ -1,26 +1,29 @@
-# $RCSFile$
 #
 # Complex numbers and associated mathematical functions
-# -- Raphael Manfredi, September 1996
-# -- Jarkko Hietaniemi, March-April 1997
+# -- Raphael Manfredi	September 1996
+# -- Jarkko Hietaniemi	March-October 1997
+# -- Daniel S. Lewart	September-October 1997
+#
 
 require Exporter;
 package Math::Complex;
 
+$VERSION = 1.05;
+
+# $Id: Complex.pm,v 1.2 1997/10/15 10:08:39 jhi Exp $
+
 use strict;
 
 use vars qw($VERSION @ISA
 	    @EXPORT %EXPORT_TAGS
 	    $package $display
-	    $i $logn %logn);
+	    $i $ip2 $logn %logn);
 
 @ISA = qw(Exporter);
 
-$VERSION = 1.01;
-
 my @trig = qw(
 	      pi
-	      sin cos tan
+	      tan
 	      csc cosec sec cot cotan
 	      asin acos atan
 	      acsc acosec asec acot acotan
@@ -32,7 +35,7 @@ my @trig = qw(
 
 @EXPORT = (qw(
 	     i Re Im arg
-	     sqrt exp log ln
+	     sqrt log ln
 	     log10 logn cbrt root
 	     cplx cplxe
 	     ),
@@ -99,8 +102,11 @@ sub make {
 sub emake {
 	my $self = bless {}, shift;
 	my ($rho, $theta) = @_;
-	$theta += pi() if $rho < 0;
-	$self->{'polar'} = [abs($rho), $theta];
+	if ($rho < 0) {
+	    $rho   = -$rho;
+	    $theta = ($theta <= 0) ? $theta + pi() : $theta - pi();
+	}
+	$self->{'polar'} = [$rho, $theta];
 	$self->{p_dirty} = 0;
 	$self->{c_dirty} = 1;
 	return $self;
@@ -133,18 +139,30 @@ sub cplxe {
 #
 # pi
 #
-# The number defined as 2 * pi = 360 degrees
+# The number defined as pi = 180 degrees
 #
-
 use constant pi => 4 * atan2(1, 1);
 
 #
-# log2inv
+# pit2
 #
-# Used in log10().
+# The full circle
+#
+use constant pit2 => 2 * pi;
+
 #
+# pip2
+#
+# The quarter circle
+#
+use constant pip2 => pi / 2;
 
-use constant log10inv => 1 / log(10);
+#
+# uplog10
+#
+# Used in log10().
+#
+use constant uplog10 => 1 / log(10);
 
 #
 # i
@@ -155,7 +173,7 @@ sub i () {
         return $i if ($i);
 	$i = bless {};
 	$i->{'cartesian'} = [0, 1];
-	$i->{'polar'}     = [1, pi/2];
+	$i->{'polar'}     = [1, pip2];
 	$i->{c_dirty} = 0;
 	$i->{p_dirty} = 0;
 	return $i;
@@ -242,15 +260,28 @@ sub minus {
 # Computes z1*z2.
 #
 sub multiply {
-	my ($z1, $z2, $regular) = @_;
-	my ($r1, $t1) = @{$z1->polar};
-	$z2 = cplxe(abs($z2), $z2 >= 0 ? 0 : pi) unless ref $z2;
-	my ($r2, $t2) = @{$z2->polar};
-	unless (defined $regular) {
-		$z1->set_polar([$r1 * $r2, $t1 + $t2]);
+        my ($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);
+	    }
 	}
-	return (ref $z1)->emake($r1 * $r2, $t1 + $t2);
 }
 
 #
@@ -268,7 +299,7 @@ sub _divbyzero {
     }
 
     my @up = caller(1);
-    
+
     $mess .= "Died at $up[1] line $up[2].\n";
 
     die $mess;
@@ -281,20 +312,45 @@ sub _divbyzero {
 #
 sub divide {
 	my ($z1, $z2, $inverted) = @_;
-	my ($r1, $t1) = @{$z1->polar};
-	$z2 = cplxe(abs($z2), $z2 >= 0 ? 0 : pi) unless ref $z2;
-	my ($r2, $t2) = @{$z2->polar};
-	unless (defined $inverted) {
-		_divbyzero "$z1/0" if ($r2 == 0);
-		$z1->set_polar([$r1 / $r2, $t1 - $t2]);
-		return $z1;
-	}
-	if ($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);
-		return (ref $z1)->emake($r2 / $r1, $t2 - $t1);
-	} else {
+		$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);
-		return (ref $z1)->emake($r1 / $r2, $t1 - $t2);
+		$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);
+		}
+	    }
 	}
 }
 
@@ -307,7 +363,7 @@ sub _zerotozero {
     my $mess = "The zero raised to the zeroth power is not defined.\n";
 
     my @up = caller(1);
-    
+
     $mess .= "Died at $up[1] line $up[2].\n";
 
     die $mess;
@@ -330,14 +386,7 @@ sub power {
 	    return 0 if ($z1z);
 	    return 1 if ($z2z or $z1 == 1);
 	}
-	$z2 = cplx($z2) unless ref $z2;
-	unless (defined $inverted) {
-		my $z3 = exp($z2 * log $z1);
-		$z1->set_cartesian([@{$z3->cartesian}]);
-		return $z1;
-	}
-	return exp($z2 * log $z1) unless $inverted;
-	return exp($z1 * log $z2);
+	return $inverted ? exp($z1 * log $z2) : exp($z2 * log $z1);
 }
 
 #
@@ -364,7 +413,8 @@ sub negate {
 	my ($z) = @_;
 	if ($z->{c_dirty}) {
 		my ($r, $t) = @{$z->polar};
-		return (ref $z)->emake($r, pi + $t);
+		$t = ($t <= 0) ? $t + pi : $t - pi;
+		return (ref $z)->emake($r, $t);
 	}
 	my ($re, $im) = @{$z->cartesian};
 	return (ref $z)->make(-$re, -$im);
@@ -392,9 +442,8 @@ sub conjugate {
 #
 sub abs {
 	my ($z) = @_;
-	return abs($z) unless ref $z;
 	my ($r, $t) = @{$z->polar};
-	return abs($r);
+	return $r;
 }
 
 #
@@ -406,6 +455,8 @@ sub arg {
 	my ($z) = @_;
 	return ($z < 0 ? pi : 0) unless ref $z;
 	my ($r, $t) = @{$z->polar};
+	if    ($t >   pi()) { $t -= pit2 }
+	elsif ($t <= -pi()) { $t += pit2 }
 	return $t;
 }
 
@@ -416,7 +467,9 @@ sub arg {
 #
 sub sqrt {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
+	return $z >= 0 ? sqrt($z) : cplx(0, sqrt(-$z)) unless ref $z;
+	my ($re, $im) = @{$z->cartesian};
+	return cplx($re < 0 ? (0, sqrt(-$re)) : (sqrt($re), 0)) if $im == 0;
 	my ($r, $t) = @{$z->polar};
 	return (ref $z)->emake(sqrt($r), $t/2);
 }
@@ -428,9 +481,10 @@ sub sqrt {
 #
 sub cbrt {
 	my ($z) = @_;
-	return cplx($z, 0) ** (1/3) unless ref $z;
+	return $z < 0 ? -exp(log(-$z)/3) : ($z > 0 ? exp(log($z)/3): 0)
+	    unless ref $z;
 	my ($r, $t) = @{$z->polar};
-	return (ref $z)->emake($r**(1/3), $t/3);
+	return (ref $z)->emake(exp(log($r)/3), $t/3);
 }
 
 #
@@ -442,7 +496,7 @@ sub _rootbad {
     my $mess = "Root $_[0] not defined, root must be positive integer.\n";
 
     my @up = caller(1);
-    
+
     $mess .= "Died at $up[1] line $up[2].\n";
 
     die $mess;
@@ -464,7 +518,7 @@ sub root {
 	my ($r, $t) = ref $z ? @{$z->polar} : (abs($z), $z >= 0 ? 0 : pi);
 	my @root;
 	my $k;
-	my $theta_inc = 2 * pi / $n;
+	my $theta_inc = pit2 / $n;
 	my $rho = $r ** (1/$n);
 	my $theta;
 	my $complex = ref($z) || $package;
@@ -505,7 +559,6 @@ sub Im {
 #
 sub exp {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
 	my ($x, $y) = @{$z->cartesian};
 	return (ref $z)->emake(exp($x), $y);
 }
@@ -513,7 +566,7 @@ sub exp {
 #
 # _logofzero
 #
-# Die on division by zero.
+# Die on logarithm of zero.
 #
 sub _logofzero {
     my $mess = "$_[0]: Logarithm of zero.\n";
@@ -525,7 +578,7 @@ sub _logofzero {
     }
 
     my @up = caller(1);
-    
+
     $mess .= "Died at $up[1] line $up[2].\n";
 
     die $mess;
@@ -538,11 +591,14 @@ sub _logofzero {
 #
 sub log {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
-	my ($x, $y) = @{$z->cartesian};
+	unless (ref $z) {
+	    _logofzero("log") if $z == 0;
+	    return $z > 0 ? log($z) : cplx(log(-$z), pi);
+	}
 	my ($r, $t) = @{$z->polar};
-	$t -= 2 * pi if ($t >  pi() and $x < 0);
-	$t += 2 * pi if ($t < -pi() and $x < 0);
+	_logofzero("log") if $r == 0;
+	if    ($t >   pi()) { $t -= pit2 }
+	elsif ($t <= -pi()) { $t += pit2 }
 	return (ref $z)->make(log($r), $t);
 }
 
@@ -560,11 +616,7 @@ sub ln { Math::Complex::log(@_) }
 #
 
 sub log10 {
-	my ($z) = @_;
-
-	return log(cplx($z, 0)) * log10inv unless ref $z;
-	my ($r, $t) = @{$z->polar};
-	return (ref $z)->make(log($r) * log10inv, $t * log10inv);
+	return Math::Complex::log($_[0]) * uplog10;
 }
 
 #
@@ -587,7 +639,6 @@ sub logn {
 #
 sub cos {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
 	my ($x, $y) = @{$z->cartesian};
 	my $ey = exp($y);
 	my $ey_1 = 1 / $ey;
@@ -602,7 +653,6 @@ sub cos {
 #
 sub sin {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
 	my ($x, $y) = @{$z->cartesian};
 	my $ey = exp($y);
 	my $ey_1 = 1 / $ey;
@@ -656,7 +706,7 @@ sub cosec { Math::Complex::csc(@_) }
 #
 # cot
 #
-# Computes cot(z) = 1 / tan(z).
+# Computes cot(z) = cos(z) / sin(z).
 #
 sub cot {
 	my ($z) = @_;
@@ -678,21 +728,20 @@ sub cotan { Math::Complex::cot(@_) }
 # Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)).
 #
 sub acos {
-	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
-	my ($re, $im) = @{$z->cartesian};
-	return atan2(sqrt(1 - $re * $re), $re)
-	    if ($im == 0 and abs($re) <= 1.0);
-	my $acos = ~i * log($z + sqrt($z*$z - 1));
-	if ($im == 0 ||
-	    (abs($re) < 1 && abs($im) < 1) ||
-	    (abs($re) > 1 && abs($im) > 1
-	     && !($re >  1 && $im >  1)
-	     && !($re < -1 && $im < -1))) {
-	    # this rule really, REALLY, must be simpler
-	    return -$acos;
-	}
-	return $acos;
+	my $z = $_[0];
+	return atan2(sqrt(1-$z*$z), $z) if (! ref $z) && abs($z) <= 1;
+	my ($x, $y) = ref $z ? @{$z->cartesian} : ($z, 0);
+	my $t1 = sqrt(($x+1)*($x+1) + $y*$y);
+	my $t2 = sqrt(($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 $u = atan2(sqrt(1-$beta*$beta), $beta);
+	my $v = log($alpha + sqrt($alpha*$alpha-1));
+	$v = -$v if $y > 0 || ($y == 0 && $x < -1);
+	return $package->make($u, $v);
 }
 
 #
@@ -701,12 +750,20 @@ sub acos {
 # Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)).
 #
 sub asin {
-	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
-	my ($re, $im) = @{$z->cartesian};
-	return atan2($re, sqrt(1 - $re * $re))
-	    if ($im == 0 and abs($re) <= 1.0);
-	return ~i * log(i * $z + sqrt(1 - $z*$z));
+	my $z = $_[0];
+	return atan2($z, sqrt(1-$z*$z)) if (! ref $z) && abs($z) <= 1;
+	my ($x, $y) = ref $z ? @{$z->cartesian} : ($z, 0);
+	my $t1 = sqrt(($x+1)*($x+1) + $y*$y);
+	my $t2 = sqrt(($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 $u =  atan2($beta, sqrt(1-$beta*$beta));
+	my $v = -log($alpha + sqrt($alpha*$alpha-1));
+	$v = -$v if $y > 0 || ($y == 0 && $x < -1);
+	return $package->make($u, $v);
 }
 
 #
@@ -716,10 +773,12 @@ sub asin {
 #
 sub atan {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
+	return atan2($z, 1) unless ref $z;
 	_divbyzero "atan(i)"  if ( $z == i);
 	_divbyzero "atan(-i)" if (-$z == i);
-	return i/2*log((i + $z) / (i - $z));
+	my $log = log((i + $z) / (i - $z));
+	$ip2 = 0.5 * i unless defined $ip2;
+	return $ip2 * $log;
 }
 
 #
@@ -730,16 +789,7 @@ sub atan {
 sub asec {
 	my ($z) = @_;
 	_divbyzero "asec($z)", $z if ($z == 0);
-	$z = cplx($z, 0) unless ref $z;
-	my ($re, $im) = @{$z->cartesian};
-	if ($im == 0 && abs($re) >= 1.0) {
-	    my $ire = 1 / $re;
-	    return atan2(sqrt(1 - $ire * $ire), $ire);
-	}
-	my $asec = acos(1 / $z);
-	return ~$asec if $re < 0 && $re > -1 && $im == 0;
-	return -$asec if $im && !($re > 0 && $im > 0) && !($re < 0 && $im < 0);
-	return $asec;
+	return acos(1 / $z);
 }
 
 #
@@ -750,15 +800,7 @@ sub asec {
 sub acsc {
 	my ($z) = @_;
 	_divbyzero "acsc($z)", $z if ($z == 0);
-	$z = cplx($z, 0) unless ref $z;
-	my ($re, $im) = @{$z->cartesian};
-	if ($im == 0 && abs($re) >= 1.0) {
-	    my $ire = 1 / $re;
-	    return atan2($ire, sqrt(1 - $ire * $ire));
-	}
-	my $acsc = asin(1 / $z);
-	return ~$acsc if $re < 0 && $re > -1 && $im == 0;
-	return $acsc;
+	return asin(1 / $z);
 }
 
 #
@@ -775,8 +817,7 @@ sub acosec { Math::Complex::acsc(@_) }
 #
 sub acot {
 	my ($z) = @_;
-	_divbyzero "acot($z)"           if ($z == 0);
-	$z = cplx($z, 0) unless ref $z;
+	return ($z >= 0) ? atan2(1, $z) : atan2(-1, -$z) unless ref $z;
 	_divbyzero "acot(i)", if ( $z == i);
 	_divbyzero "acot(-i)" if (-$z == i);
 	return atan(1 / $z);
@@ -796,15 +837,14 @@ sub acotan { Math::Complex::acot(@_) }
 #
 sub cosh {
 	my ($z) = @_;
-	my $real;
+	my $ex;
 	unless (ref $z) {
-	    $z = cplx($z, 0);
-	    $real = 1;
+	    $ex = exp($z);
+	    return ($ex + 1/$ex)/2;
 	}
 	my ($x, $y) = @{$z->cartesian};
-	my $ex = exp($x);
+	$ex = exp($x);
 	my $ex_1 = 1 / $ex;
-	return cplx(0.5 * ($ex + $ex_1), 0) if $real;
 	return (ref $z)->make(cos($y) * ($ex + $ex_1)/2,
 			      sin($y) * ($ex - $ex_1)/2);
 }
@@ -816,15 +856,14 @@ sub cosh {
 #
 sub sinh {
 	my ($z) = @_;
-	my $real;
+	my $ex;
 	unless (ref $z) {
-	    $z = cplx($z, 0);
-	    $real = 1;
+	    $ex = exp($z);
+	    return ($ex - 1/$ex)/2;
 	}
 	my ($x, $y) = @{$z->cartesian};
-	my $ex = exp($x);
+	$ex = exp($x);
 	my $ex_1 = 1 / $ex;
-	return cplx(0.5 * ($ex - $ex_1), 0) if $real;
 	return (ref $z)->make(cos($y) * ($ex - $ex_1)/2,
 			      sin($y) * ($ex + $ex_1)/2);
 }
@@ -894,14 +933,19 @@ sub cotanh { Math::Complex::coth(@_) }
 #
 # acosh
 #
-# Computes the arc hyperbolic cosine acosh(z) = log(z +- sqrt(z*z-1)).
+# Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).
 #
 sub acosh {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
+	unless (ref $z) {
+	    return log($z + sqrt($z*$z-1)) if $z >= 1;
+	    $z = cplx($z, 0);
+	}
 	my ($re, $im) = @{$z->cartesian};
-	return log($re + sqrt(cplx($re*$re - 1, 0)))
-	    if ($im == 0 && $re < 0);
+	if ($im == 0) {
+	    return cplx(log($re + sqrt($re*$re - 1)), 0) if $re >= 1;
+	    return cplx(0, atan2(sqrt(1-$re*$re), $re)) if abs($re) <= 1;
+	}
 	return log($z + sqrt($z*$z - 1));
 }
 
@@ -912,7 +956,6 @@ sub acosh {
 #
 sub asinh {
 	my ($z) = @_;
-	$z = cplx($z, 0) unless ref $z;
 	return log($z + sqrt($z*$z + 1));
 }
 
@@ -923,14 +966,13 @@ sub asinh {
 #
 sub atanh {
 	my ($z) = @_;
+	unless (ref $z) {
+	    return log((1 + $z)/(1 - $z))/2 if abs($z) < 1;
+	    $z = cplx($z, 0);
+	}
 	_divbyzero 'atanh(1)',  "1 - $z" if ($z ==  1);
 	_logofzero 'atanh(-1)'           if ($z == -1);
-	$z = cplx($z, 0) unless ref $z;
-	my ($re, $im) = @{$z->cartesian};
-	if ($im == 0 && $re > 1) {
-	    return cplx(atanh(1 / $re), pi/2);
-	}
-	return log((1 + $z) / (1 - $z)) / 2;
+	return 0.5 * log((1 + $z) / (1 - $z));
 }
 
 #
@@ -941,12 +983,6 @@ sub atanh {
 sub asech {
 	my ($z) = @_;
 	_divbyzero 'asech(0)', $z if ($z == 0);
-	$z = cplx($z, 0) unless ref $z;
-	my ($re, $im) = @{$z->cartesian};
-	if ($im == 0 && $re < 0) {
-	    my $ire = 1 / $re;
-	    return log($ire + sqrt(cplx($ire*$ire - 1, 0)));
-	}
 	return acosh(1 / $z);
 }
 
@@ -975,13 +1011,12 @@ sub acosech { Math::Complex::acsch(@_) }
 #
 sub acoth {
 	my ($z) = @_;
+	unless (ref $z) {
+	    return log(($z + 1)/($z - 1))/2 if abs($z) > 1;
+	    $z = cplx($z, 0);
+	}
 	_divbyzero 'acoth(1)', "$z - 1" if ($z ==  1);
 	_logofzero 'acoth(-1)'          if ($z == -1);
-	$z = cplx($z, 0) unless ref $z;
-	my ($re, $im) = @{$z->cartesian};
-	if ($im == 0 and abs($re) < 1) {
-	    return cplx(acoth(1/$re) , pi/2);
-	}
 	return log((1 + $z) / ($z - 1)) / 2;
 }
 
@@ -999,17 +1034,23 @@ sub acotanh { Math::Complex::acoth(@_) }
 #
 sub atan2 {
 	my ($z1, $z2, $inverted) = @_;
-	my ($re1, $im1) = ref $z1 ? @{$z1->cartesian} : ($z1, 0);
-	my ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
-	my $tan;
-	if (defined $inverted && $inverted) {	# atan(z2/z1)
-		return pi * ($re2 > 0 ? 1 : -1) if $re1 == 0 && $im1 == 0;
-		$tan = $z2 / $z1;
+	my ($re1, $im1, $re2, $im2);
+	if ($inverted) {
+	    ($re1, $im1) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
+	    ($re2, $im2) = @{$z1->cartesian};
 	} else {
-		return pi * ($re1 > 0 ? 1 : -1) if $re2 == 0 && $im2 == 0;
-		$tan = $z1 / $z2;
+	    ($re1, $im1) = @{$z1->cartesian};
+	    ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
+	}
+	if ($im2 == 0) {
+	    return cplx(atan2($re1, $re2), 0) if $im1 == 0;
+	    return cplx(($im1<=>0) * pip2, 0) if $re2 == 0;
 	}
-	return atan($tan);
+	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);
 }
 
 #
@@ -1017,7 +1058,7 @@ sub atan2 {
 # ->display_format
 #
 # Set (fetch if no argument) display format for all complex numbers that
-# don't happen to have overrriden it via ->display_format
+# don't happen to have overridden it via ->display_format
 #
 # When called as a method, this actually sets the display format for
 # the current object.
@@ -1076,16 +1117,17 @@ sub stringify_cartesian {
 	my $z  = shift;
 	my ($x, $y) = @{$z->cartesian};
 	my ($re, $im);
+	my $eps = 1e-14;
 
-	$x = int($x + ($x < 0 ? -1 : 1) * 1e-14)
-		if int(abs($x)) != int(abs($x) + 1e-14);
-	$y = int($y + ($y < 0 ? -1 : 1) * 1e-14)
-		if int(abs($y)) != int(abs($y) + 1e-14);
+	$x = int($x + ($x < 0 ? -1 : 1) * $eps)
+		if int(abs($x)) != int(abs($x) + $eps);
+	$y = int($y + ($y < 0 ? -1 : 1) * $eps)
+		if int(abs($y)) != int(abs($y) + $eps);
 
-	$re = "$x" if abs($x) >= 1e-14;
-	if ($y == 1)				{ $im = 'i' }
-	elsif ($y == -1)			{ $im = '-i' }
-	elsif (abs($y) >= 1e-14)	{ $im = $y . "i" }
+	$re = "$x" if abs($x) >= $eps;
+        if ($y == 1)                           { $im = 'i' }
+        elsif ($y == -1)                       { $im = '-i' }
+        elsif (abs($y) >= $eps)                { $im = $y . "i" }
 
 	my $str = '';
 	$str = $re if defined $re;
@@ -1110,10 +1152,9 @@ sub stringify_polar {
 
 	return '[0,0]' if $r <= $eps;
 
-	my $tpi = 2 * pi;
-	my $nt = $t / $tpi;
-	$nt = ($nt - int($nt)) * $tpi;
-	$nt += $tpi if $nt < 0;			# Range [0, 2pi]
+	my $nt = $t / pit2;
+	$nt = ($nt - int($nt)) * pit2;
+	$nt += pit2 if $nt < 0;			# Range [0, 2pi]
 
 	if (abs($nt) <= $eps)		{ $theta = 0 }
 	elsif (abs(pi-$nt) <= $eps)	{ $theta = 'pi' }
@@ -1131,9 +1172,9 @@ sub stringify_polar {
 	# Okay, number is not a real. Try to identify pi/n and friends...
 	#
 
-	$nt -= $tpi if $nt > pi;
+	$nt -= pit2 if $nt > pi;
 	my ($n, $k, $kpi);
-	
+
 	for ($k = 1, $kpi = pi; $k < 10; $k++, $kpi += pi) {
 		$n = int($kpi / $nt + ($nt > 0 ? 1 : -1) * 0.5);
 		if (abs($kpi/$n - $nt) <= $eps) {
@@ -1164,7 +1205,7 @@ 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);
@@ -1241,7 +1282,7 @@ between this form and the cartesian form C<a + bi> is immediate:
 
 which is also expressed by this formula:
 
-	z = rho * exp(i * theta) = rho * (cos theta + i * sin theta) 
+	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>
@@ -1251,8 +1292,8 @@ 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 substractions. Real numbers are on the I<x>
-axis, and therefore I<theta> is zero.
+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
@@ -1261,8 +1302,8 @@ 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 positive real numbers and yields a
-positive real number (it is an application from B<R+> to B<R+>).
+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):
@@ -1275,10 +1316,9 @@ 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 positive, so C<[x,pi]> is really C<-x>, a
-negative number)
-and the above definition states that
+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
 
@@ -1342,7 +1382,6 @@ the following (overloaded) operations are supported on complex numbers:
 	log(z1) = log(r1) + i*t1
 	sin(z1) = 1/2i (exp(i * z1) - exp(-i * z1))
 	cos(z1) = 1/2 (exp(i * z1) + exp(-i * z1))
-	abs(z1) = r1
 	atan2(z1, z2) = atan(z1/z2)
 
 The following extra operations are supported on both real and complex
@@ -1363,7 +1402,7 @@ numbers:
 	cot(z) = 1 / tan(z)
 
 	asin(z) = -i * log(i*z + sqrt(1-z*z))
-	acos(z) = -i * log(z + sqrt(z*z-1))
+	acos(z) = -i * log(z + i*sqrt(1-z*z))
 	atan(z) = i/2 * log((i+z) / (i-z))
 
 	acsc(z) = asin(1 / z)
@@ -1377,7 +1416,7 @@ numbers:
 	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))
@@ -1423,21 +1462,21 @@ if you know the cartesian form of the number, or
 
 	$z = 3 + 4*i;
 
-if you like. To create a number using the trigonometric form, use either:
+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).  (Mnmemonic: C<e> is used as a
-notation for complex numbers in the trigonometric form).
+(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 positive (it represents the distance to the origin in the complex
+must be non-negative (it represents the distance to the origin in the complex
 plane).
 
 =head1 STRINGIFICATION
@@ -1534,17 +1573,8 @@ argument cannot be I<pi/2 + k * pi>, where I<k> is any integer.
 =head1 BUGS
 
 Saying C<use Math::Complex;> exports many mathematical routines in the
-caller environment and even overrides some (C<sin>, C<cos>, C<sqrt>,
-C<log>, C<exp>).  This is construed as a feature by the Authors,
-actually... ;-)
-
-The code is not optimized for speed, although we try to use the cartesian
-form for addition-like operators and the trigonometric form for all
-multiplication-like operators.
-
-The arg() routine does not ensure the angle is within the range [-pi,+pi]
-(a side effect caused by multiplication and division using the trigonometric
-representation).
+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 '+'
@@ -1555,6 +1585,8 @@ operation (for instance) between two overloaded entities.
 Raphael Manfredi <F<Raphael_Manfredi@grenoble.hp.com>> and
 Jarkko Hietaniemi <F<jhi@iki.fi>>.
 
+Extensive patches by Daniel S. Lewart <F<d-lewart@uiuc.edu>>.
+
 =cut
 
 # eof