complex.pm

视频监控网络部分的协议ddns,的模块的实现代码,请大家大胆指正.

	my ($z1, $z2, $inverted) = @_;
	if ($inverted) {
	    return 1 if $z1 == 0 || $z2 == 1;
	    return 0 if $z2 == 0 && Re($z1) > 0;
	} else {
	    return 1 if $z2 == 0 || $z1 == 1;
	    return 0 if $z1 == 0 && Re($z2) > 0;
	}
	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 $z2->{c_dirty} == 0) ?
	       cplx(@{$w->_cartesian}) : $w;
}

#
# (_spaceship)
#
# Computes z1 <=> z2.
# Sorts on the real part first, then on the imaginary part. Thus 2-4i < 3+8i.
#
sub _spaceship {
	my ($z1, $z2, $inverted) = @_;
	my ($re1, $im1) = ref $z1 ? @{$z1->_cartesian} : ($z1, 0);
	my ($re2, $im2) = ref $z2 ? @{$z2->_cartesian} : ($z2, 0);
	my $sgn = $inverted ? -1 : 1;
	return $sgn * ($re1 <=> $re2) if $re1 != $re2;
	return $sgn * ($im1 <=> $im2);
}

#
# (_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 _negate {
	my ($z) = @_;
	if ($z->{c_dirty}) {
		my ($r, $t) = @{$z->_polar};
		$t = ($t <= 0) ? $t + pi : $t - pi;
		return (ref $z)->emake($r, $t);
	}
	my ($re, $im) = @{$z->_cartesian};
	return (ref $z)->make(-$re, -$im);
}

#
# (_conjugate)
#
# Compute complex's _conjugate.
#
sub _conjugate {
	my ($z) = @_;
	if ($z->{c_dirty}) {
		my ($r, $t) = @{$z->_polar};
		return (ref $z)->emake($r, -$t);
	}
	my ($re, $im) = @{$z->_cartesian};
	return (ref $z)->make($re, -$im);
}

#
# (abs)
#
# Compute or set complex's norm (rho).
#
sub abs {
	my ($z, $rho) = @_;
	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;
	    $z->{c_dirty} = 1;
	    return $rho;
	} else {
	    return ${$z->_polar}[0];
	}
}

sub _theta {
    my $theta = $_[0];

    if    ($$theta >   pi()) { $$theta -= pi2 }
    elsif ($$theta <= -pi()) { $$theta += pi2 }
}

#
# arg
#
# Compute or set complex's argument (theta).
#
sub arg {
	my ($z, $theta) = @_;
	return $z unless ref $z;
	if (defined $theta) {
	    _theta(\$theta);
	    $z->{'polar'} = [ ${$z->_polar}[0], $theta ];
	    $z->{p_dirty} = 0;
	    $z->{c_dirty} = 1;
	} else {
	    $theta = ${$z->_polar}[1];
	    _theta(\$theta);
	}
	return $theta;
}

#
# (sqrt)
#
# Compute sqrt(z).
#
# It is quite tempting to use wantarray here so that in list context
# sqrt() would return the two solutions.  This, however, would
# break things like
#
#	print "sqrt(z) = ", sqrt($z), "\n";
#
# The two values would be printed side by side without no intervening
# whitespace, quite confusing.
# Therefore if you want the two solutions use the root().
#
sub sqrt {
	my ($z) = @_;
	my ($re, $im) = ref $z ? @{$z->_cartesian} : ($z, 0);
	return $re < 0 ? cplx(0, CORE::sqrt(-$re)) : CORE::sqrt($re)
	    if $im == 0;
	my ($r, $t) = @{$z->_polar};
	return (ref $z)->emake(CORE::sqrt($r), $t/2);
}

#
# cbrt
#
# Compute cbrt(z) (cubic root).
#
# Why are we not returning three values?  The same answer as for sqrt().
#
sub cbrt {
	my ($z) = @_;
	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);
}

#
# _rootbad
#
# Die on bad root.
#
sub _rootbad {
    my $mess = "Root '$_[0]' illegal, root rank must be positive integer.\n";

    my @up = caller(1);

    $mess .= "Died at $up[1] line $up[2].\n";

    die $mess;
}

#
# root
#
# Computes all nth root for z, returning an array whose size is n.
# `n' must be a positive integer.
#
# The roots are given by (for k = 0..n-1):
#
# z^(1/n) = r^(1/n) (cos ((t+2 k pi)/n) + i sin ((t+2 k pi)/n))
#
sub root {
	my ($z, $n, $k) = @_;
	_rootbad($n) if ($n < 1 or int($n) != $n);
	my ($r, $t) = ref $z ?
	    @{$z->_polar} : (CORE::abs($z), $z >= 0 ? 0 : pi);
	my $theta_inc = pi2 / $n;
	my $rho = $r ** (1/$n);
	my $cartesian = ref $z && $z->{c_dirty} == 0;
	if (@_ == 2) {
	    my @root;
	    for (my $i = 0, my $theta = $t / $n;
		 $i < $n;
		 $i++, $theta += $theta_inc) {
		my $w = cplxe($rho, $theta);
		# Yes, $cartesian is loop invariant.
		push @root, $cartesian ? cplx(@{$w->_cartesian}) : $w;
	    }
	    return @root;
	} elsif (@_ == 3) {
	    my $w = cplxe($rho, $t / $n + $k * $theta_inc);
	    return $cartesian ? cplx(@{$w->_cartesian}) : $w;
	}
}

#
# Re
#
# Return or set Re(z).
#
sub Re {
	my ($z, $Re) = @_;
	return $z unless ref $z;
	if (defined $Re) {
	    $z->{'cartesian'} = [ $Re, ${$z->_cartesian}[1] ];
	    $z->{c_dirty} = 0;
	    $z->{p_dirty} = 1;
	} else {
	    return ${$z->_cartesian}[0];
	}
}

#
# Im
#
# Return or set Im(z).
#
sub Im {
	my ($z, $Im) = @_;
	return 0 unless ref $z;
	if (defined $Im) {
	    $z->{'cartesian'} = [ ${$z->_cartesian}[0], $Im ];
	    $z->{c_dirty} = 0;
	    $z->{p_dirty} = 1;
	} else {
	    return ${$z->_cartesian}[1];
	}
}

#
# rho
#
# Return or set rho(w).
#
sub rho {
    Math::Complex::abs(@_);
}

#
# theta
#
# Return or set theta(w).
#
sub theta {
    Math::Complex::arg(@_);
}

#
# (exp)
#
# Computes exp(z).
#
sub exp {
	my ($z) = @_;
	my ($x, $y) = @{$z->_cartesian};
	return (ref $z)->emake(CORE::exp($x), $y);
}

#
# _logofzero
#
# Die on logarithm of zero.
#
sub _logofzero {
    my $mess = "$_[0]: Logarithm of zero.\n";

    if (defined $_[1]) {
	$mess .= "(Because in the definition of $_[0], the argument ";
	$mess .= "$_[1] " unless ($_[1] eq '0');
	$mess .= "is 0)\n";
    }

    my @up = caller(1);

    $mess .= "Died at $up[1] line $up[2].\n";

    die $mess;
}

#
# (log)
#
# Compute log(z).
#
sub log {
	my ($z) = @_;
	unless (ref $z) {
	    _logofzero("log") if $z == 0;
	    return $z > 0 ? CORE::log($z) : cplx(CORE::log(-$z), pi);
	}
	my ($r, $t) = @{$z->_polar};
	_logofzero("log") if $r == 0;
	if    ($t >   pi()) { $t -= pi2 }
	elsif ($t <= -pi()) { $t += pi2 }
	return (ref $z)->make(CORE::log($r), $t);
}

#
# ln
#
# Alias for log().
#
sub ln { Math::Complex::log(@_) }

#
# log10
#
# Compute log10(z).
#

sub log10 {
	return Math::Complex::log($_[0]) * _uplog10;
}

#
# logn
#
# Compute logn(z,n) = log(z) / log(n)
#
sub logn {
	my ($z, $n) = @_;
	$z = cplx($z, 0) unless ref $z;
	my $logn = $LOGN{$n};
	$logn = $LOGN{$n} = CORE::log($n) unless defined $logn;	# Cache log(n)
	return &log($z) / $logn;
}

#
# (cos)
#
# Compute cos(z) = (exp(iz) + exp(-iz))/2.
#
sub cos {
	my ($z) = @_;
	return CORE::cos($z) unless ref $z;
	my ($x, $y) = @{$z->_cartesian};
	my $ey = CORE::exp($y);
	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);
}

#
# (sin)
#
# Compute sin(z) = (exp(iz) - exp(-iz))/2.
#
sub sin {
	my ($z) = @_;
	return CORE::sin($z) unless ref $z;
	my ($x, $y) = @{$z->_cartesian};
	my $ey = CORE::exp($y);
	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);
}

#
# tan
#
# Compute tan(z) = sin(z) / cos(z).
#
sub tan {
	my ($z) = @_;
	my $cz = &cos($z);
	_divbyzero "tan($z)", "cos($z)" if $cz == 0;
	return &sin($z) / $cz;
}

#
# sec
#
# Computes the secant sec(z) = 1 / cos(z).
#
sub sec {
	my ($z) = @_;
	my $cz = &cos($z);
	_divbyzero "sec($z)", "cos($z)" if ($cz == 0);
	return 1 / $cz;
}

#
# csc
#
# Computes the cosecant csc(z) = 1 / sin(z).
#
sub csc {
	my ($z) = @_;
	my $sz = &sin($z);
	_divbyzero "csc($z)", "sin($z)" if ($sz == 0);
	return 1 / $sz;
}

#
# cosec
#
# Alias for csc().
#
sub cosec { Math::Complex::csc(@_) }

#
# cot
#
# Computes cot(z) = cos(z) / sin(z).
#
sub cot {
	my ($z) = @_;
	my $sz = &sin($z);
	_divbyzero "cot($z)", "sin($z)" if ($sz == 0);
	return &cos($z) / $sz;
}

#
# cotan
#
# Alias for cot().
#
sub cotan { Math::Complex::cot(@_) }

#
# acos
#
# Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)).
#
sub acos {
	my $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 $beta  = ($t1 - $t2)/2;
	$alpha = 1 if $alpha < 1;
	if    ($beta >  1) { $beta =  1 }
	elsif ($beta < -1) { $beta = -1 }
	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 (ref $z)->make($u, $v);
}

#
# asin
#
# Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)).
#
sub asin {
	my $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 $beta  = ($t1 - $t2)/2;
	$alpha = 1 if $alpha < 1;
	if    ($beta >  1) { $beta =  1 }
	elsif ($beta < -1) { $beta = -1 }
	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 (ref $z)->make($u, $v);
}

#
# atan
#
# Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)).