Complex tweaks.

p4raw-id: //depot/cfgperl@6073

diff --git a/lib/Math/Complex.pm b/lib/Math/Complex.pm
index 82872b7..e5434f4 100644 (file)
--- a/lib/Math/Complex.pm
+++ b/lib/Math/Complex.pm
@@ -874,7 +874,8 @@ sub acos {
        my $z = $_[0];
        return CORE::atan2(CORE::sqrt(1-$z*$z), $z)
            if (! ref $z) && CORE::abs($z) <= 1;
-       my ($x, $y) = ref $z ? @{$z->cartesian} : ($z, 0);
+       $z = cplx($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);
@@ -886,7 +887,7 @@ sub acos {
        my $u = CORE::atan2(CORE::sqrt(1-$beta*$beta), $beta);
        my $v = CORE::log($alpha + CORE::sqrt($alpha*$alpha-1));
        $v = -$v if $y > 0 || ($y == 0 && $x < -1);
-       return __PACKAGE__->make($u, $v);
+       return (ref $z)->make($u, $v);
 }
 
 #
@@ -898,7 +899,8 @@ sub asin {
        my $z = $_[0];
        return CORE::atan2($z, CORE::sqrt(1-$z*$z))
            if (! ref $z) && CORE::abs($z) <= 1;
-       my ($x, $y) = ref $z ? @{$z->cartesian} : ($z, 0);
+       $z = cplx($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);
@@ -910,7 +912,7 @@ sub asin {
        my $u =  CORE::atan2($beta, CORE::sqrt(1-$beta*$beta));
        my $v = -CORE::log($alpha + CORE::sqrt($alpha*$alpha-1));
        $v = -$v if $y > 0 || ($y == 0 && $x < -1);
-       return __PACKAGE__->make($u, $v);
+       return (ref $z)->make($u, $v);
 }
 
 #
@@ -1101,11 +1103,13 @@ sub acosh {
                if CORE::abs($re) < 1;
        }
        my $t = &sqrt($z * $z - 1) + $z;
-       # Try MacLaurin if looking bad.
+       # 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 $im == 0;
+       $u->Im(-$u->Im) if $re < 0 && $im == 0;
        return $re < 0 ? -$u : $u;
 }
 
@@ -1121,7 +1125,9 @@ sub asinh {
            return CORE::log($t) if $t;
        }
        my $t = &sqrt($z * $z + 1) + $z;
-       # Try MacLaurin if looking bad.
+       # 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);
@@ -1324,15 +1330,16 @@ sub stringify_cartesian {
        }
 
        if ($y) {
-           if ($y == 1)     { $im = ""  }
-           elsif ($y == -1) { $im = "-" }
-           elsif ($y =~ /^(NaN[QS]?)$/i) {
+           if ($y =~ /^(NaN[QS]?)$/i) {
                $im = $y;
            } else {
                if ($y =~ /^-?$Inf$/oi) {
                    $im = $y;
                } else {
-                   $im = defined $format ? sprintf($format, $y) : $y;
+                   $im =
+                       defined $format ?
+                           sprintf($format, $y) :
+                           ($y == 1 ? "" : ($y == -1 ? "-" : $y));
                }
            }
            $im .= "i";
@@ -1742,29 +1749,33 @@ C<display_format> object method can now be called using
 a parameter hash instead of just a one parameter.
 
 The old display format style, which can have values C<"cartesian"> or
-C<"polar">, can be changed using the C<"style"> parameter.  (The one
-parameter calling convention also still works.)
+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 parts of the complex number(s).  The
-default is C<undef>, which corresponds usually (this is somewhat
-system-dependent) to C<"%.15g">.  You can revert to the default by
-setting the format string to C<undef>.
+The 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' => '%.6f');
+       $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.  If
-you want to know the whole truth for a complex number, you must call
-both the class method and the object method:
+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
@@ -1828,8 +1839,7 @@ 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.  For example C<tan(2*atan2(1,1)+1e-15)> will die of
-division by zero.
+listed above.
 
 =head1 ERRORS DUE TO INDIGESTIBLE ARGUMENTS