0**0 = 1, from

Subject: Math::Complex 0**0 patches
Message-Id: <199811020121.TAA28310@staff2.cso.uiuc.edu>
To: jhi@iki.fi (Jarkko Hietaniemi),
        Raphael_Manfredi@grenoble.hp.com (Raphael Manfredi)

p4raw-id: //depot/cfgperl@2177

diff --git a/lib/Math/Complex.pm b/lib/Math/Complex.pm
index e711c14..5b69039 100644 (file)
--- a/lib/Math/Complex.pm
+++ b/lib/Math/Complex.pm
@@ -14,7 +14,7 @@ use vars qw($VERSION @ISA @EXPORT %EXPORT_TAGS);
 
 my ( $i, $ip2, %logn );
 
-$VERSION = sprintf("%s", q$Id: Complex.pm,v 1.25 1998/02/05 16:07:37 jhi Exp $ =~ /(\d+\.\d+)/);
+$VERSION = sprintf("%s", q$Id: Complex.pm,v 1.26 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.\d+)/);
 
 @ISA = qw(Exporter);
 
@@ -401,38 +401,21 @@ sub divide {
 }
 
 #
-# _zerotozero
-#
-# Die on zero raised to the zeroth.
-#
-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 $mess;
-}
-
-#
 # (power)
 #
 # Computes z1**z2 = exp(z2 * log z1)).
 #
 sub power {
        my ($z1, $z2, $inverted) = @_;
-       my $z1z = $z1 == 0;
-       my $z2z = $z2 == 0;
-       _zerotozero if ($z1z and $z2z);
        if ($inverted) {
-           return 0 if ($z2z);
-           return 1 if ($z1z or $z2 == 1);
+           return 1 if $z1 == 0 || $z2 == 1;
+           return 0 if $z2 == 0 && Re($z1) > 0;
        } else {
-           return 0 if ($z1z);
-           return 1 if ($z2z or $z1 == 1);
+           return 1 if $z2 == 0 || $z1 == 1;
+           return 0 if $z1 == 0 && Re($z2) > 0;
        }
-       my $w = $inverted ? CORE::exp($z1 * CORE::log($z2)) : CORE::exp($z2 * CORE::log($z1));
+       my $w = $inverted ? CORE::exp($z1 * CORE::log($z2))
+                         : CORE::exp($z2 * CORE::log($z1));
        # If both arguments cartesian, return cartesian, else polar.
        return $z1->{c_dirty} == 0 &&
               (not ref $z2 or $z2->{c_dirty} == 0) ?
@@ -443,7 +426,7 @@ sub power {
 # (spaceship)
 #
 # Computes z1 <=> z2.
-# Sorts on the real part first, then on the imaginary part. Thus 2-4i > 3+8i.
+# Sorts on the real part first, then on the imaginary part. Thus 2-4i < 3+8i.
 #
 sub spaceship {
        my ($z1, $z2, $inverted) = @_;
@@ -1273,7 +1256,7 @@ sub gcd {
     my ($a, $b) = @_;
 
     my $id = "$a $b";
-    
+
     unless (exists $gcd{$id}) {
        $gcd{$id} = _gcd($a, $b);
        $gcd{"$b $a"} = $gcd{$id};
@@ -1702,7 +1685,7 @@ Here are some examples:
 The division (/) and the following functions
 
        log     ln      log10   logn
-       tan     sec     csc     cot
+       tan     sec     csc     cot
        atan    asec    acsc    acot
        tanh    sech    csch    coth
        atanh   asech   acsch   acoth

diff --git a/t/lib/complex.t b/t/lib/complex.t
index 2bb14f0..c073f50 100755 (executable)
--- a/t/lib/complex.t
+++ b/t/lib/complex.t
@@ -14,7 +14,7 @@ BEGIN {
 
 use Math::Complex;
 
-$VERSION = sprintf("%s", q$Id: complex.t,v 1.8 1998/02/05 16:03:39 jhi Exp $ =~ /(\d+\.d+)/);
+my $VERSION = sprintf("%s", q$Id: complex.t,v 1.9 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.d+)/);
 
 my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
 
@@ -173,20 +173,6 @@ test_loz(
         'acoth(-1)',
        );
 
-# test the 0**0
-
-sub test_ztz {
-    $test++;
-
-    push(@script, <<'EOT');
-eval 'cplx(0)**cplx(0)';
-print 'not ' unless ($@ =~ /zero raised to the zeroth/);
-EOT
-    push(@script, qq(print "ok $test\\n";\n));
-}
-
-test_ztz;
-
 # test the bad roots
 
 sub test_broot {
@@ -387,6 +373,7 @@ __END__
 (1,0):(2,3):(1,0)
 (2,3):(0,0):(1,0)
 (2,3):(1,0):(2,3)
+(0,0):(0,0):(1,0)
 
 &Re
 (3,4):3
@@ -876,4 +863,3 @@ __END__
 ( 2,-3):(  0.14694666622553,  0.23182380450040)
 
 # eof
-