From: Jarkko Hietaniemi <jhi@iki.fi>
Date: Tue, 2 May 2000 22:21:26 +0000 (+0000)
Subject: Complex tweakery.
X-Git-Url: http://git.shadowcat.co.uk/gitweb/gitweb.cgi?a=commitdiff_plain;h=9bc5fa8de0e98ff1317c3fdc7e35f6e13be0ac35;p=p5sagit%2Fp5-mst-13.2.git

Complex tweakery.

p4raw-id: //depot/cfgperl@6051
---

diff --git a/lib/Math/Complex.pm b/lib/Math/Complex.pm
index b13191b..daf190e 100644
--- a/lib/Math/Complex.pm
+++ b/lib/Math/Complex.pm
@@ -1105,10 +1105,13 @@ sub acosh {
 	    return cplx(0, CORE::atan2(CORE::sqrt(1 - $re*$re), $re))
 		if CORE::abs($re) < 1;
 	}
-	my $s = &sqrt($z*$z - 1);
-	my $t = $z + $s;
-	$t = 1/(2*$s) if $t == 0 || $t && &abs(cosh(&log($t)) - $z) > $eps;
-	return &log($t);
+	my $t = &sqrt($z * $z - 1) + $z;
+	# Try MacLaurin if looking bad.
+	$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;
+	return $re < 0 ? -$u : $u;
 }
 
 #
@@ -1122,10 +1125,10 @@ sub asinh {
 	    my $t = $z + CORE::sqrt($z*$z + 1);
 	    return CORE::log($t) if $t;
 	}
-	my $s = &sqrt($z*$z + 1);
-	my $t = $z + $s;
-	# Try Taylor series if looking bad.
-	$t = 1/(2*$s) if $t == 0 || $t && &abs(sinh(&log($t)) - $z) > $eps;
+	my $t = &sqrt($z * $z + 1) + $z;
+	# Try MacLaurin if looking bad.
+	$t = 1/(2 * $z) - 1/(8 * $z**3) + 1/(16 * $z**5) - 5/(128 * $z**7)
+	    if $t == 0;
 	return &log($t);
 }
 
@@ -1390,7 +1393,7 @@ sub stringify_polar {
 
 	if ($format{polar_pretty_print}) {
 	    my ($a, $b);
-	    for $a (2, 3, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72) {
+	    for $a (2..9) {
 		$b = $t * $a / pi;
 		if (int($b) == $b) {
 		    $b = $b < 0 ? "-" : "" if CORE::abs($b) == 1;
@@ -1734,7 +1737,7 @@ For instance:
 	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]),
+(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
diff --git a/t/lib/complex.t b/t/lib/complex.t
index 7312c09..d4beb8b 100755
--- a/t/lib/complex.t
+++ b/t/lib/complex.t
@@ -892,7 +892,7 @@ __END__
 ( 2,-3):(  1.96863792579310, -0.96465850440760)
 
 &acosh
-(-2.0,0):(  -1.31695789692482,  3.14159265358979)
+(-2.0,0):(   1.31695789692482,  3.14159265358979)
 (-1.0,0):(   0,                 3.14159265358979)
 (-0.5,0):(   0,                 2.09439510239320)
 ( 0.0,0):(   0,                 1.57079632679490)
@@ -902,8 +902,8 @@ __END__
 
 &acosh
 ( 2, 3):(  1.98338702991654,  1.00014354247380)
-(-2, 3):( -1.98338702991653, -2.14144911111600)
-(-2,-3):( -1.98338702991653,  2.14144911111600)
+(-2, 3):(  1.98338702991653,  2.14144911111600)
+(-2,-3):(  1.98338702991653, -2.14144911111600)
 ( 2,-3):(  1.98338702991654, -1.00014354247380)
 
 &atanh
@@ -922,15 +922,15 @@ __END__
 &asech
 (-2.0,0):(   0               , 2.09439510239320)
 (-1.0,0):(   0               , 3.14159265358979)
-(-0.5,0):(  -1.31695789692482, 3.14159265358979)
+(-0.5,0):(   1.31695789692482, 3.14159265358979)
 ( 0.5,0):(   1.31695789692482, 0               )
 ( 1.0,0):(   0               , 0               )
 ( 2.0,0):(   0               , 1.04719755119660)
 
 &asech
 ( 2, 3):(  0.23133469857397, -1.42041072246703)
-(-2, 3):( -0.23133469857397,  1.72118193112276)
-(-2,-3):( -0.23133469857397, -1.72118193112276)
+(-2, 3):(  0.23133469857397, -1.72118193112276)
+(-2,-3):(  0.23133469857397,  1.72118193112276)
 ( 2,-3):(  0.23133469857397,  1.42041072246703)
 
 &acsch