# -- Daniel S. Lewart Since Sep 1997
#
-require Exporter;
package Math::Complex;
-use 5.005_64;
-use strict;
+our($VERSION, @ISA, @EXPORT, %EXPORT_TAGS, $Inf);
+
+$VERSION = 1.32;
+
+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.
+}
-our($VERSION, @ISA, @EXPORT, %EXPORT_TAGS);
+use strict;
-my ( $i, $ip2, %logn );
+my $i;
+my %LOGN;
-$VERSION = sprintf("%s", q$Id: Complex.pm,v 1.26 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.\d+)/);
+require Exporter;
@ISA = qw(Exporter);
'*' => \&multiply,
'/' => \÷,
'**' => \&power,
+ '==' => \&numeq,
'<=>' => \&spaceship,
'neg' => \&negate,
'~' => \&conjugate,
# Package "privates"
#
-my $package = 'Math::Complex'; # Package name
my %DISPLAY_FORMAT = ('style' => 'cartesian',
'polar_pretty_print' => 1);
my $eps = 1e-14; # Epsilon
}
#
+# ip2
+#
+# Half of i.
+#
+sub ip2 () { i / 2 }
+
+#
# Attribute access/set routines
#
my ($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)];
+ return $self->{'polar'} = [CORE::sqrt($x*$x + $y*$y),
+ CORE::atan2($y, $x)];
}
#
if (defined $_[1]) {
$mess .= "(Because in the definition of $_[0], the divisor ";
- $mess .= "$_[1] " unless ($_[1] eq '0');
+ $mess .= "$_[1] " unless ("$_[1]" eq '0');
$mess .= "is 0)\n";
}
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 = $inverted ? &exp($z1 * &log($z2))
+ : &exp($z2 * &log($z1));
# If both arguments cartesian, return cartesian, else polar.
return $z1->{c_dirty} == 0 &&
(not ref $z2 or $z2->{c_dirty} == 0) ?
}
#
+# (numeq)
+#
+# Computes z1 == z2.
+#
+# (Required in addition to spaceship() because of NaNs.)
+sub numeq {
+ my ($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 == $im2 ? 1 : 0;
+}
+
+#
# (negate)
#
# Computes -z.
#
sub abs {
my ($z, $rho) = @_;
- return $z unless ref $z;
+ unless (ref $z) {
+ if (@_ == 2) {
+ $_[0] = $_[1];
+ } else {
+ return CORE::abs($z);
+ }
+ }
if (defined $rho) {
$z->{'polar'} = [ $rho, ${$z->polar}[1] ];
$z->{p_dirty} = 0;
sub sqrt {
my ($z) = @_;
my ($re, $im) = ref $z ? @{$z->cartesian} : ($z, 0);
- return $re < 0 ? cplx(0, CORE::sqrt(-$re)) : CORE::sqrt($re) if $im == 0;
+ 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), $t/2);
}
#
sub cbrt {
my ($z) = @_;
- return $z < 0 ? -CORE::exp(CORE::log(-$z)/3) : ($z > 0 ? CORE::exp(CORE::log($z)/3): 0)
+ 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);
}
# Die on bad root.
#
sub _rootbad {
- my $mess = "Root $_[0] not defined, root must be positive integer.\n";
+ my $mess = "Root $_[0] illegal, root rank must be positive integer.\n";
my @up = caller(1);
sub root {
my ($z, $n) = @_;
_rootbad($n) if ($n < 1 or int($n) != $n);
- my ($r, $t) = ref $z ? @{$z->polar} : (CORE::abs($z), $z >= 0 ? 0 : pi);
+ my ($r, $t) = ref $z ?
+ @{$z->polar} : (CORE::abs($z), $z >= 0 ? 0 : pi);
my @root;
my $k;
my $theta_inc = pit2 / $n;
#
sub Im {
my ($z, $Im) = @_;
- return $z unless ref $z;
+ return 0 unless ref $z;
if (defined $Im) {
$z->{'cartesian'} = [ ${$z->cartesian}[0], $Im ];
$z->{c_dirty} = 0;
sub logn {
my ($z, $n) = @_;
$z = cplx($z, 0) unless ref $z;
- my $logn = $logn{$n};
- $logn = $logn{$n} = CORE::log($n) unless defined $logn; # Cache log(n)
- return CORE::log($z) / $logn;
+ my $logn = $LOGN{$n};
+ $logn = $LOGN{$n} = CORE::log($n) unless defined $logn; # Cache log(n)
+ return &log($z) / $logn;
}
#
#
sub cos {
my ($z) = @_;
+ return CORE::cos($z) unless ref $z;
my ($x, $y) = @{$z->cartesian};
my $ey = CORE::exp($y);
- my $ey_1 = 1 / $ey;
- return (ref $z)->make(CORE::cos($x) * ($ey + $ey_1)/2,
- CORE::sin($x) * ($ey_1 - $ey)/2);
+ 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 - $ey)/2);
}
#
#
sub sin {
my ($z) = @_;
+ return CORE::sin($z) unless ref $z;
my ($x, $y) = @{$z->cartesian};
my $ey = CORE::exp($y);
- my $ey_1 = 1 / $ey;
- return (ref $z)->make(CORE::sin($x) * ($ey + $ey_1)/2,
- CORE::cos($x) * ($ey - $ey_1)/2);
+ 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 - $ey_1)/2);
}
#
#
sub tan {
my ($z) = @_;
- my $cz = CORE::cos($z);
- _divbyzero "tan($z)", "cos($z)" if (CORE::abs($cz) < $eps);
- return CORE::sin($z) / $cz;
+ my $cz = &cos($z);
+ _divbyzero "tan($z)", "cos($z)" if $cz == 0;
+ return &sin($z) / $cz;
}
#
#
sub sec {
my ($z) = @_;
- my $cz = CORE::cos($z);
+ my $cz = &cos($z);
_divbyzero "sec($z)", "cos($z)" if ($cz == 0);
return 1 / $cz;
}
#
sub csc {
my ($z) = @_;
- my $sz = CORE::sin($z);
+ my $sz = &sin($z);
_divbyzero "csc($z)", "sin($z)" if ($sz == 0);
return 1 / $sz;
}
#
sub cot {
my ($z) = @_;
- my $sz = CORE::sin($z);
+ my $sz = &sin($z);
_divbyzero "cot($z)", "sin($z)" if ($sz == 0);
- return CORE::cos($z) / $sz;
+ return &cos($z) / $sz;
}
#
#
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} : ($z, 0);
+ return CORE::atan2(CORE::sqrt(1-$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 $u = CORE::atan2(CORE::sqrt(1-$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);
}
#
#
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} : ($z, 0);
+ return CORE::atan2($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 $u = CORE::atan2($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, $v);
}
#
sub atan {
my ($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 ( $z == i);
- _divbyzero "atan(-i)" if (-$z == i);
- my $log = CORE::log((i + $z) / (i - $z));
- $ip2 = 0.5 * i unless defined $ip2;
- return $ip2 * $log;
+ _logofzero "atan(-i)" if (-$z == i); # -i is a bad file test...
+ my $log = &log((i + $z) / (i - $z));
+ return ip2 * $log;
}
#
#
sub acot {
my ($z) = @_;
- _divbyzero "acot(0)" if (CORE::abs($z) < $eps);
- return ($z >= 0) ? CORE::atan2(1, $z) : CORE::atan2(-1, -$z) unless ref $z;
- _divbyzero "acot(i)" if (CORE::abs($z - i) < $eps);
- _logofzero "acot(-i)" if (CORE::abs($z + i) < $eps);
+ _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);
}
my $ex;
unless (ref $z) {
$ex = CORE::exp($z);
- return ($ex + 1/$ex)/2;
+ return $ex ? ($ex + 1/$ex)/2 : $Inf;
}
my ($x, $y) = @{$z->cartesian};
$ex = CORE::exp($x);
- my $ex_1 = 1 / $ex;
+ my $ex_1 = $ex ? 1 / $ex : $Inf;
return (ref $z)->make(CORE::cos($y) * ($ex + $ex_1)/2,
CORE::sin($y) * ($ex - $ex_1)/2);
}
my ($z) = @_;
my $ex;
unless (ref $z) {
+ return 0 if $z == 0;
$ex = CORE::exp($z);
- return ($ex - 1/$ex)/2;
+ 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 = 1 / $ex;
+ my $ex_1 = $ex ? 1 / $ex : $Inf;
return (ref $z)->make(CORE::cos($y) * ($ex - $ex_1)/2,
CORE::sin($y) * ($ex + $ex_1)/2);
}
sub coth {
my ($z) = @_;
my $sz = sinh($z);
- _divbyzero "coth($z)", "sinh($z)" if ($sz == 0);
+ _divbyzero "coth($z)", "sinh($z)" if $sz == 0;
return cosh($z) / $sz;
}
sub acosh {
my ($z) = @_;
unless (ref $z) {
- return CORE::log($z + CORE::sqrt($z*$z-1)) if $z >= 1;
$z = cplx($z, 0);
}
my ($re, $im) = @{$z->cartesian};
if ($im == 0) {
- return cplx(CORE::log($re + CORE::sqrt($re*$re - 1)), 0) if $re >= 1;
- return cplx(0, CORE::atan2(CORE::sqrt(1-$re*$re), $re)) if CORE::abs($re) <= 1;
+ 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;
}
- return CORE::log($z + CORE::sqrt($z*$z - 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 : $u;
}
#
# asinh
#
-# Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z-1))
+# Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))
#
sub asinh {
my ($z) = @_;
- return CORE::log($z + CORE::sqrt($z*$z + 1));
+ 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);
}
#
return CORE::log((1 + $z)/(1 - $z))/2 if CORE::abs($z) < 1;
$z = cplx($z, 0);
}
- _divbyzero 'atanh(1)', "1 - $z" if ($z == 1);
- _logofzero 'atanh(-1)' if ($z == -1);
- return 0.5 * CORE::log((1 + $z) / (1 - $z));
+ _divbyzero 'atanh(1)', "1 - $z" if (1 - $z == 0);
+ _logofzero 'atanh(-1)' if (1 + $z == 0);
+ return 0.5 * &log((1 + $z) / (1 - $z));
}
#
#
sub asech {
my ($z) = @_;
- _divbyzero 'asech(0)', $z if ($z == 0);
+ _divbyzero 'asech(0)', "$z" if ($z == 0);
return acosh(1 / $z);
}
#
sub acoth {
my ($z) = @_;
- _divbyzero 'acoth(0)' if (CORE::abs($z) < $eps);
+ _divbyzero 'acoth(0)' if ($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)', "$z - 1" if (CORE::abs($z - 1) < $eps);
- _logofzero 'acoth(-1)', "1 / $z" if (CORE::abs($z + 1) < $eps);
- return CORE::log((1 + $z) / ($z - 1)) / 2;
+ _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;
}
#
($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
}
if ($im2 == 0) {
- return cplx(CORE::atan2($re1, $re2), 0) if $im1 == 0;
- return cplx(($im1<=>0) * pip2, 0) if $re2 == 0;
+ return CORE::atan2($re1, $re2) if $im1 == 0;
+ return ($im1<=>0) * pip2 if $re2 == 0;
}
my $w = atan($z1/$z2);
my ($u, $v) = ref $w ? @{$w->cartesian} : ($w, 0);
my %obj = %{$self->{display_format}};
@display_format{keys %obj} = values %obj;
}
- if (@_ == 1) {
- $display_format{style} = shift;
- } else {
- my %new = @_;
- @display_format{keys %new} = values %new;
- }
- } else { # Called as a class method
- if (@_ = 1) {
- $display_format{style} = $self;
- } else {
- my %new = @_;
- @display_format{keys %new} = values %new;
- }
- undef $self;
+ }
+ if (@_ == 1) {
+ $display_format{style} = shift;
+ } else {
+ my %new = @_;
+ @display_format{keys %new} = values %new;
}
- if (defined $self) {
+ if (ref $self) { # Called as an object method
$self->{display_format} = { %display_format };
return
wantarray ?
$self->{display_format}->{style};
}
+ # Called as a class method
%DISPLAY_FORMAT = %display_format;
return
wantarray ?
my ($x, $y) = @{$z->cartesian};
my ($re, $im);
- $x = int($x + ($x < 0 ? -1 : 1) * $eps)
- if int(CORE::abs($x)) != int(CORE::abs($x) + $eps);
- $y = int($y + ($y < 0 ? -1 : 1) * $eps)
- if int(CORE::abs($y)) != int(CORE::abs($y) + $eps);
-
- $re = "$x" if CORE::abs($x) >= $eps;
-
my %format = $z->display_format;
my $format = $format{format};
- if ($y == 1) { $im = 'i' }
- elsif ($y == -1) { $im = '-i' }
- elsif (CORE::abs($y) >= $eps) {
- $im = (defined $format ? sprintf($format, $y) : $y) . "i";
+ if ($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;
}
- my $str = '';
- $str = defined $format ? sprintf($format, $re) : $re
- if defined $re;
+ if ($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) {
+ } elsif ($y > 0 || $im =~ /^NaN[QS]?i$/i) {
$str .= "+" if defined $re;
$str .= $im;
}
+ } elsif (!defined $re) {
+ $str = "0";
}
return $str;
}
-# Helper for stringify_polar, a Greatest Common Divisor with a memory.
-
-sub _gcd {
- my ($a, $b) = @_;
-
- use integer;
-
- # Loops forever if given negative inputs.
-
- if ($b and $a > $b) { return gcd($a % $b, $b) }
- elsif ($a and $b > $a) { return gcd($b % $a, $a) }
- else { return $a ? $a : $b }
-}
-
-my %gcd;
-
-sub gcd {
- my ($a, $b) = @_;
-
- my $id = "$a $b";
-
- unless (exists $gcd{$id}) {
- $gcd{$id} = _gcd($a, $b);
- $gcd{"$b $a"} = $gcd{$id};
- }
-
- return $gcd{$id};
-}
-
#
# ->stringify_polar
#
my ($r, $t) = @{$z->polar};
my $theta;
- return '[0,0]' if $r <= $eps;
-
my %format = $z->display_format;
+ my $format = $format{format};
- my $nt = $t / pit2;
- $nt = ($nt - int($nt)) * pit2;
- $nt += pit2 if $nt < 0; # Range [0, 2pi]
-
- if (CORE::abs($nt) <= $eps) { $theta = 0 }
- elsif (CORE::abs(pi-$nt) <= $eps) { $theta = 'pi' }
-
- if (defined $theta) {
- $r = int($r + ($r < 0 ? -1 : 1) * $eps)
- if int(CORE::abs($r)) != int(CORE::abs($r) + $eps);
- $theta = int($theta + ($theta < 0 ? -1 : 1) * $eps)
- if ($theta ne 'pi' and
- int(CORE::abs($theta)) != int(CORE::abs($theta) + $eps));
- return "\[$r,$theta\]";
+ 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;
+
#
- # Okay, number is not a real. Try to identify pi/n and friends...
+ # Try to identify pi/n and friends.
#
- $nt -= pit2 if $nt > pi;
-
- if ($format{polar_pretty_print} && CORE::abs($nt) >= deg1) {
- my ($n, $k, $kpi);
-
- for ($k = 1, $kpi = pi; $k < 10; $k++, $kpi += pi) {
- $n = int($kpi / $nt + ($nt > 0 ? 1 : -1) * 0.5);
- if (CORE::abs($kpi/$n - $nt) <= $eps) {
- $n = CORE::abs($n);
- my $gcd = gcd($k, $n);
- if ($gcd > 1) {
- $k /= $gcd;
- $n /= $gcd;
- }
- next if $n > 360;
- $theta = ($nt < 0 ? '-':'').
- ($k == 1 ? 'pi':"${k}pi");
- $theta .= '/'.$n if $n > 1;
+ $t -= int(CORE::abs($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;
}
}
}
- $theta = $nt unless defined $theta;
-
- $r = int($r + ($r < 0 ? -1 : 1) * $eps)
- if int(CORE::abs($r)) != int(CORE::abs($r) + $eps);
- $theta = int($theta + ($theta < 0 ? -1 : 1) * $eps)
- if ($theta !~ m(^-?\d*pi/\d+$) and
- int(CORE::abs($theta)) != int(CORE::abs($theta) + $eps));
-
- my $format = $format{format};
if (defined $format) {
$r = sprintf($format, $r);
- $theta = sprintf($format, $theta);
+ $theta = sprintf($format, $theta) unless defined $theta;
+ } else {
+ $theta = $t unless defined $theta;
}
- return "\[$r,$theta\]";
+ return "[$r,$theta]";
}
1;
__END__
=pod
+
=head1 NAME
Math::Complex - complex numbers and associated mathematical functions
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
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
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
projects / p5sagit/p5-mst-13.2.git / blobdiff