[p5sagit/p5-mst-13.2.git] / t / lib / complex.t

#!./perl

# $RCSfile$
#
# Regression tests for the Math::Complex pacakge
# -- Raphael Manfredi, September 1996
# -- Jarkko Hietaniemi, March-April 1997

BEGIN {
    chdir 't' if -d 't';
    @INC = '../lib';
}

use Math::Complex;

$test = 0;
$| = 1;
@script = ();
my $eps = 1e-11;

while (<DATA>) {
	s/^\s+//;
	next if $_ eq '' || /^\#/;
	chomp;
	$test_set = 0;		# Assume not a test over a set of values
	if (/^&(.+)/) {
		$op = $1;
		next;
	}
	elsif (/^\{(.+)\}/) {
		set($1, \@set, \@val);
		next;
	}
	elsif (s/^\|//) {
		$test_set = 1;	# Requests we loop over the set...
	}
	my @args = split(/:/);
	if ($test_set == 1) {
		my $i;
		for ($i = 0; $i < @set; $i++) {
			# complex number
			$target = $set[$i];
			# textual value as found in set definition
			$zvalue = $val[$i];
			test($zvalue, $target, @args);
		}
	} else {
		test($op, undef, @args);
	}
}

# test the divbyzeros

sub test_dbz {
    for my $op (@_) {
	$test++;

#	push(@script, qq(print "# '$op'\n";));
	push(@script, qq(eval '$op';));
	push(@script, qq(print 'not ' unless (\$@ =~ /Division by zero/);));
	push(@script, qq(print "ok $test\n";));
    }
}

test_dbz(
	 'i/0',
#	 'tan(pi/2)',	# may succeed thanks to floating point inaccuracies
#	 'sec(pi/2)',	# may succeed thanks to floating point inaccuracies
	 'csc(0)',
	 'cot(0)',
	 'atan(i)',
	 'asec(0)',
	 'acsc(0)',
	 'acot(i)',
#	 'tanh(pi/2)',	# may succeed thanks to floating point inaccuracies
#	 'sech(pi/2)',	# may succeed thanks to floating point inaccuracies
	 'csch(0)',
	 'coth(0)',
	 'atanh(1)',
	 'asech(0)',
	 'acsch(0)',
	 'acoth(1)'
	);

# test the 0**0

sub test_ztz {
	$test++;

#	push(@script, qq(print "# 0**0\n";));
	push(@script, qq(eval 'cplx(0)**cplx(0)';));
	push(@script, qq(print 'not ' unless (\$@ =~ /zero raised to the/);));
	push(@script, qq(print "ok $test\n";));
}

test_ztz;

# test the bad roots

sub test_broot {
    for my $op (@_) {
	$test++;

#	push(@script, qq(print "# root(2, $op)\n";));
	push(@script, qq(eval 'root(2, $op)';));
	push(@script, qq(print 'not ' unless (\$@ =~ /root must be/);));
	push(@script, qq(print "ok $test\n";));
    }
}

test_broot(qw(-3 -2.1 0 0.99));

print "1..$test\n";
eval join '', @script;
die $@ if $@;

sub abop {
	my ($op) = @_;

	push(@script, qq(print "# $op=\n";));
}

sub test {
	my ($op, $z, @args) = @_;
	my ($baop) = 0;
	$test++;
	my $i;
	$baop = 1 if ($op =~ s/;=$//);
	for ($i = 0; $i < @args; $i++) {
		$val = value($args[$i]);
		push @script, "\$z$i = $val;\n";
	}
	if (defined $z) {
		$args = "'$op'";		# Really the value
		$try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
		push @script, "\$res = $try; ";
		push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
	} else {
		my ($try, $args);
		if (@args == 2) {
			$try = "$op \$z0";
			$args = "'$args[0]'";
		} else {
			$try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
			$args = "'$args[0]', '$args[1]'";
		}
		push @script, "\$res = $try; ";
		push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
		if (@args > 2 and $baop) { # binary assignment ops
			$test++;
			# check the op= works
			push @script, <<EOB;
{
        my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));

	my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);

        my \$zb = cplx(\$z1r, \$z1i);

	\$za $op= \$zb;
	my (\$zbr, \$zbi) = \@{\$zb->cartesian};

	check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
EOB
			$test++;
			# check that the rhs has not changed
			push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
			push @script, qq(print "ok $test\n";);
			push @script, "}\n";
		}
	}
}

sub set {
	my ($set, $setref, $valref) = @_;
	@{$setref} = ();
	@{$valref} = ();
	my @set = split(/;\s*/, $set);
	my @res;
	my $i;
	for ($i = 0; $i < @set; $i++) {
		push(@{$valref}, $set[$i]);
		my $val = value($set[$i]);
		push @script, "\$s$i = $val;\n";
		push @{$setref}, "\$s$i";
	}
}

sub value {
	local ($_) = @_;
	if (/^\s*\((.*),(.*)\)/) {
		return "cplx($1,$2)";
	}
	elsif (/^\s*\[(.*),(.*)\]/) {
		return "cplxe($1,$2)";
	}
	elsif (/^\s*'(.*)'/) {
		my $ex = $1;
		$ex =~ s/\bz\b/$target/g;
		$ex =~ s/\br\b/abs($target)/g;
		$ex =~ s/\bt\b/arg($target)/g;
		$ex =~ s/\ba\b/Re($target)/g;
		$ex =~ s/\bb\b/Im($target)/g;
		return $ex;
	}
	elsif (/^\s*"(.*)"/) {
		return "\"$1\"";
	}
	return $_;
}

sub check {
	my ($test, $try, $got, $expected, @z) = @_;

#	print "# @_\n";

	if ("$got" eq "$expected"
	    ||
	    ($expected =~ /^-?\d/ && $got == $expected)
	    ||
	    (abs($got - $expected) < $eps)
	    ) {
		print "ok $test\n";
	} else {
		print "not ok $test\n";
		my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
		print "# '$try' expected: '$expected' got: '$got' for $args\n";
	}
}
__END__
&+;=
(3,4):(3,4):(6,8)
(-3,4):(3,-4):(0,0)
(3,4):-3:(0,4)
1:(4,2):(5,2)
[2,0]:[2,pi]:(0,0)

&++
(2,1):(3,1)

&-;=
(2,3):(-2,-3)
[2,pi/2]:[2,-(pi)/2]
2:[2,0]:(0,0)
[3,0]:2:(1,0)
3:(4,5):(-1,-5)
(4,5):3:(1,5)
(2,1):(3,5):(-1,-4)

&--
(1,2):(0,2)
[2,pi]:[3,pi]

&*;=
(0,1):(0,1):(-1,0)
(4,5):(1,0):(4,5)
[2,2*pi/3]:(1,0):[2,2*pi/3]
2:(0,1):(0,2)
(0,1):3:(0,3)
(0,1):(4,1):(-1,4)
(2,1):(4,-1):(9,2)

&/;=
(3,4):(3,4):(1,0)
(4,-5):1:(4,-5)
1:(0,1):(0,-1)
(0,6):(0,2):(3,0)
(9,2):(4,-1):(2,1)
[4,pi]:[2,pi/2]:[2,pi/2]
[2,pi/2]:[4,pi]:[0.5,-(pi)/2]

&**;=
(2,0):(3,0):(8,0)
(3,0):(2,0):(9,0)
(2,3):(4,0):(-119,-120)
(0,0):(1,0):(0,0)
(0,0):(2,3):(0,0)
(1,0):(0,0):(1,0)
(1,0):(1,0):(1,0)
(1,0):(2,3):(1,0)
(2,3):(0,0):(1,0)
(2,3):(1,0):(2,3)

&Re
(3,4):3
(-3,4):-3
[1,pi/2]:0

&Im
(3,4):4
(3,-4):-4
[1,pi/2]:1

&abs
(3,4):5
(-3,4):5

&arg
[2,0]:0
[-2,0]:pi

&~
(4,5):(4,-5)
(-3,4):(-3,-4)
[2,pi/2]:[2,-(pi)/2]

&<
(3,4):(1,2):0
(3,4):(3,2):0
(3,4):(3,8):1
(4,4):(5,129):1

&==
(3,4):(4,5):0
(3,4):(3,5):0
(3,4):(2,4):0
(3,4):(3,4):1

&sqrt
-9:(0,3)
(-100,0):(0,10)
(16,-30):(5,-3)

&stringify_cartesian
(-100,0):"-100"
(0,1):"i"
(4,-3):"4-3i"
(4,0):"4"
(-4,0):"-4"
(-2,4):"-2+4i"
(-2,-1):"-2-i"

&stringify_polar
[-1, 0]:"[1,pi]"
[1, pi/3]:"[1,pi/3]"
[6, -2*pi/3]:"[6,-2pi/3]"
[0.5, -9*pi/11]:"[0.5,-9pi/11]"

{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }

|'z + ~z':'2*Re(z)'
|'z - ~z':'2*i*Im(z)'
|'z * ~z':'abs(z) * abs(z)'

{ (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }

|'(root(z, 4))[1] ** 4':'z'
|'(root(z, 5))[3] ** 5':'z'
|'(root(z, 8))[7] ** 8':'z'
|'abs(z)':'r'
|'acot(z)':'acotan(z)'
|'acsc(z)':'acosec(z)'
|'acsc(z)':'asin(1 / z)'
|'asec(z)':'acos(1 / z)'
|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
|'cos(acos(z))':'z'
|'cos(z) ** 2 + sin(z) ** 2':1
|'cos(z)':'cosh(i*z)'
|'cosh(z) ** 2 - sinh(z) ** 2':1
|'cot(acot(z))':'z'
|'cot(z)':'1 / tan(z)'
|'cot(z)':'cotan(z)'
|'csc(acsc(z))':'z'
|'csc(z)':'1 / sin(z)'
|'csc(z)':'cosec(z)'
|'exp(log(z))':'z'
|'exp(z)':'exp(a) * exp(i * b)'
|'ln(z)':'log(z)'
|'log(exp(z))':'z'
|'log(z)':'log(r) + i*t'
|'log10(z)':'log(z) / log(10)'
|'logn(z, 2)':'log(z) / log(2)'
|'logn(z, 3)':'log(z) / log(3)'
|'sec(asec(z))':'z'
|'sec(z)':'1 / cos(z)'
|'sin(asin(z))':'z'
|'sin(i * z)':'i * sinh(z)'
|'sqrt(z) * sqrt(z)':'z'
|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
|'tan(atan(z))':'z'
|'z**z':'exp(z * log(z))'

{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }

|'cosh(acosh(z))':'z'
|'coth(acoth(z))':'z'
|'coth(z)':'1 / tanh(z)'
|'coth(z)':'cotanh(z)'
|'csch(acsch(z))':'z'
|'csch(z)':'1 / sinh(z)'
|'csch(z)':'cosech(z)'
|'sech(asech(z))':'z'
|'sech(z)':'1 / cosh(z)'
|'sinh(asinh(z))':'z'
|'tanh(atanh(z))':'z'

{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }

|'acos(cos(z)) ** 2':'z * z'
|'acosh(cosh(z)) ** 2':'z * z'
|'acoth(z)':'acotanh(z)'
|'acoth(z)':'atanh(1 / z)'
|'acsch(z)':'acosech(z)'
|'acsch(z)':'asinh(1 / z)'
|'asech(z)':'acosh(1 / z)'
|'asin(sin(z))':'z'
|'asinh(sinh(z))':'z'
|'atan(tan(z))':'z'
|'atanh(tanh(z))':'z'

&sin
( 2, 3):(  9.15449914691143, -4.16890695996656)
(-2, 3):( -9.15449914691143, -4.16890695996656)
(-2,-3):( -9.15449914691143,  4.16890695996656)
( 2,-3):(  9.15449914691143,  4.16890695996656)

&cos
( 2, 3):( -4.18962569096881, -9.10922789375534)
(-2, 3):( -4.18962569096881,  9.10922789375534)
(-2,-3):( -4.18962569096881, -9.10922789375534)
( 2,-3):( -4.18962569096881,  9.10922789375534)

&tan
( 2, 3):( -0.00376402564150,  1.00323862735361)
(-2, 3):(  0.00376402564150,  1.00323862735361)
(-2,-3):(  0.00376402564150, -1.00323862735361)
( 2,-3):( -0.00376402564150, -1.00323862735361)

&sec
( 2, 3):( -0.04167496441114,  0.09061113719624)
(-2, 3):( -0.04167496441114, -0.09061113719624)
(-2,-3):( -0.04167496441114,  0.09061113719624)
( 2,-3):( -0.04167496441114, -0.09061113719624)

&csc
( 2, 3):(  0.09047320975321,  0.04120098628857)
(-2, 3):( -0.09047320975321,  0.04120098628857)
(-2,-3):( -0.09047320975321, -0.04120098628857)
( 2,-3):(  0.09047320975321, -0.04120098628857)

&cot
( 2, 3):( -0.00373971037634, -0.99675779656936)
(-2, 3):(  0.00373971037634, -0.99675779656936)
(-2,-3):(  0.00373971037634,  0.99675779656936)
( 2,-3):( -0.00373971037634,  0.99675779656936)

&asin
( 2, 3):(  0.57065278432110,  1.98338702991654)
(-2, 3):( -0.57065278432110,  1.98338702991654)
(-2,-3):( -0.57065278432110, -1.98338702991654)
( 2,-3):(  0.57065278432110, -1.98338702991654)

&acos
( 2, 3):(  1.00014354247380, -1.98338702991654)
(-2, 3):(  2.14144911111600, -1.98338702991654)
(-2,-3):(  2.14144911111600,  1.98338702991654)
( 2,-3):(  1.00014354247380,  1.98338702991654)

&atan
( 2, 3):(  1.40992104959658,  0.22907268296854)
(-2, 3):( -1.40992104959658,  0.22907268296854)
(-2,-3):( -1.40992104959658, -0.22907268296854)
( 2,-3):(  1.40992104959658, -0.22907268296854)

&asec
( 2, 3):(  1.42041072246703,  0.23133469857397)
(-2, 3):(  1.72118193112276,  0.23133469857397)
(-2,-3):(  1.72118193112276, -0.23133469857397)
( 2,-3):(  1.42041072246703, -0.23133469857397)

&acsc
( 2, 3):(  0.15038560432786, -0.23133469857397)
(-2, 3):( -0.15038560432786, -0.23133469857397)
(-2,-3):( -0.15038560432786,  0.23133469857397)
( 2,-3):(  0.15038560432786,  0.23133469857397)

&acot
( 2, 3):(  0.16087527719832, -0.22907268296854)
(-2, 3):( -0.16087527719832, -0.22907268296854)
(-2,-3):( -0.16087527719832,  0.22907268296854)
( 2,-3):(  0.16087527719832,  0.22907268296854)

&sinh
( 2, 3):( -3.59056458998578,  0.53092108624852)
(-2, 3):(  3.59056458998578,  0.53092108624852)
(-2,-3):(  3.59056458998578, -0.53092108624852)
( 2,-3):( -3.59056458998578, -0.53092108624852)

&cosh
( 2, 3):( -3.72454550491532,  0.51182256998738)
(-2, 3):( -3.72454550491532, -0.51182256998738)
(-2,-3):( -3.72454550491532,  0.51182256998738)
( 2,-3):( -3.72454550491532, -0.51182256998738)

&tanh
( 2, 3):(  0.96538587902213, -0.00988437503832)
(-2, 3):( -0.96538587902213, -0.00988437503832)
(-2,-3):( -0.96538587902213,  0.00988437503832)
( 2,-3):(  0.96538587902213,  0.00988437503832)

&sech
( 2, 3):( -0.26351297515839, -0.03621163655877)
(-2, 3):( -0.26351297515839,  0.03621163655877)
(-2,-3):( -0.26351297515839, -0.03621163655877)
( 2,-3):( -0.26351297515839,  0.03621163655877)

&csch
( 2, 3):( -0.27254866146294, -0.04030057885689)
(-2, 3):(  0.27254866146294, -0.04030057885689)
(-2,-3):(  0.27254866146294,  0.04030057885689)
( 2,-3):( -0.27254866146294,  0.04030057885689)

&coth
( 2, 3):(  1.03574663776500,  0.01060478347034)
(-2, 3):( -1.03574663776500,  0.01060478347034)
(-2,-3):( -1.03574663776500, -0.01060478347034)
( 2,-3):(  1.03574663776500, -0.01060478347034)

&asinh
( 2, 3):(  1.96863792579310,  0.96465850440760)
(-2, 3):( -1.96863792579310,  0.96465850440761)
(-2,-3):( -1.96863792579310, -0.96465850440761)
( 2,-3):(  1.96863792579310, -0.96465850440760)

&acosh
( 2, 3):(  1.98338702991654,  1.00014354247380)
(-2, 3):( -1.98338702991653, -2.14144911111600)
(-2,-3):( -1.98338702991653,  2.14144911111600)
( 2,-3):(  1.98338702991654, -1.00014354247380)

&atanh
( 2, 3):(  0.14694666622553,  1.33897252229449)
(-2, 3):( -0.14694666622553,  1.33897252229449)
(-2,-3):( -0.14694666622553, -1.33897252229449)
( 2,-3):(  0.14694666622553, -1.33897252229449)

&asech
( 2, 3):(  0.23133469857397, -1.42041072246703)
(-2, 3):( -0.23133469857397,  1.72118193112276)
(-2,-3):( -0.23133469857397, -1.72118193112276)
( 2,-3):(  0.23133469857397,  1.42041072246703)

&acsch
( 2, 3):(  0.15735549884499, -0.22996290237721)
(-2, 3):( -0.15735549884499, -0.22996290237721)
(-2,-3):( -0.15735549884499,  0.22996290237721)
( 2,-3):(  0.15735549884499,  0.22996290237721)

&acoth
( 2, 3):(  0.14694666622553, -0.23182380450040)
(-2, 3):( -0.14694666622553, -0.23182380450040)
(-2,-3):( -0.14694666622553,  0.23182380450040)
( 2,-3):(  0.14694666622553,  0.23182380450040)

# eof
Commit	Line	Data
89d0527d	1	#!./perl
	2
	3	# $RCSfile$
	4	#
5aabfad6	5	# Regression tests for the Math::Complex pacakge
5aabfad6	6	# -- Raphael Manfredi, September 1996
5cd24f17	7	# -- Jarkko Hietaniemi, March-April 1997
5aabfad6	8
89d0527d	9	BEGIN {
	10	chdir 't' if -d 't';
	11	@INC = '../lib';
	12	}
5aabfad6	13
89d0527d	14	use Math::Complex;
	15
	16	$test = 0;
	17	$\| = 1;
fe82cf6e	18	@script = ();
5aabfad6	19	my $eps = 1e-11;
89d0527d	20
89d0527d	21	while (<DATA>) {
0c721ce2	22	s/^\s+//;
	23	next if $_ eq '' \|\| /^\#/;
	24	chomp;
	25	$test_set = 0; # Assume not a test over a set of values
0e505df1	26	if (/^&(.+)/) {
89d0527d	27	$op = $1;
	28	next;
	29	}
0e505df1	30	elsif (/^\{(.+)\}/) {
89d0527d	31	set($1, \@set, \@val);
	32	next;
	33	}
	34	elsif (s/^\\|//) {
0c721ce2	35	$test_set = 1; # Requests we loop over the set...
89d0527d	36	}
89d0527d	37	my @args = split(/:/);
0c721ce2	38	if ($test_set == 1) {
89d0527d	39	my $i;
89d0527d	40	for ($i = 0; $i < @set; $i++) {
0c721ce2	41	# complex number
	42	$target = $set[$i];
	43	# textual value as found in set definition
	44	$zvalue = $val[$i];
89d0527d	45	test($zvalue, $target, @args);
	46	}
	47	} else {
	48	test($op, undef, @args);
	49	}
	50	}
	51
5cd24f17	52	# test the divbyzeros
5cd24f17	53
0e505df1	54	sub test_dbz {
	55	for my $op (@_) {
	56	$test++;
	57
	58	# push(@script, qq(print "# '$op'\n";));
	59	push(@script, qq(eval '$op';));
	60	push(@script, qq(print 'not ' unless (\$@ =~ /Division by zero/);));
	61	push(@script, qq(print "ok $test\n";));
	62	}
	63	}
	64
5cd24f17	65	test_dbz(
	66	'i/0',
	67	# 'tan(pi/2)', # may succeed thanks to floating point inaccuracies
	68	# 'sec(pi/2)', # may succeed thanks to floating point inaccuracies
	69	'csc(0)',
	70	'cot(0)',
	71	'atan(i)',
	72	'asec(0)',
	73	'acsc(0)',
	74	'acot(i)',
	75	# 'tanh(pi/2)', # may succeed thanks to floating point inaccuracies
	76	# 'sech(pi/2)', # may succeed thanks to floating point inaccuracies
	77	'csch(0)',
	78	'coth(0)',
	79	'atanh(1)',
	80	'asech(0)',
	81	'acsch(0)',
	82	'acoth(1)'
	83	);
	84
0e505df1	85	# test the 0**0
	86
	87	sub test_ztz {
	88	$test++;
	89
	90	# push(@script, qq(print "# 0**0\n";));
	91	push(@script, qq(eval 'cplx(0)**cplx(0)';));
	92	push(@script, qq(print 'not ' unless (\$@ =~ /zero raised to the/);));
	93	push(@script, qq(print "ok $test\n";));
	94	}
	95
	96	test_ztz;
	97
	98	# test the bad roots
	99
	100	sub test_broot {
5cd24f17	101	for my $op (@_) {
	102	$test++;
	103
0e505df1	104	# push(@script, qq(print "# root(2, $op)\n";));
	105	push(@script, qq(eval 'root(2, $op)';));
	106	push(@script, qq(print 'not ' unless (\$@ =~ /root must be/);));
5cd24f17	107	push(@script, qq(print "ok $test\n";));
	108	}
	109	}
	110
0e505df1	111	test_broot(qw(-3 -2.1 0 0.99));
0e505df1	112
89d0527d	113	print "1..$test\n";
fe82cf6e	114	eval join '', @script;
89d0527d	115	die $@ if $@;
89d0527d	116
0e505df1	117	sub abop {
	118	my ($op) = @_;
	119
	120	push(@script, qq(print "# $op=\n";));
	121	}
	122
89d0527d	123	sub test {
89d0527d	124	my ($op, $z, @args) = @_;
0e505df1	125	my ($baop) = 0;
89d0527d	126	$test++;
89d0527d	127	my $i;
0e505df1	128	$baop = 1 if ($op =~ s/;=$//);
89d0527d	129	for ($i = 0; $i < @args; $i++) {
89d0527d	130	$val = value($args[$i]);
fe82cf6e	131	push @script, "\$z$i = $val;\n";
89d0527d	132	}
	133	if (defined $z) {
	134	$args = "'$op'"; # Really the value
0c721ce2	135	$try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
fe82cf6e	136	push @script, "\$res = $try; ";
fe82cf6e	137	push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
89d0527d	138	} else {
	139	my ($try, $args);
	140	if (@args == 2) {
	141	$try = "$op \$z0";
	142	$args = "'$args[0]'";
	143	} else {
	144	$try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
	145	$args = "'$args[0]', '$args[1]'";
	146	}
fe82cf6e	147	push @script, "\$res = $try; ";
fe82cf6e	148	push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
0e505df1	149	if (@args > 2 and $baop) { # binary assignment ops
	150	$test++;
	151	# check the op= works
	152	push @script, <<EOB;
	153	{
	154	my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
	155
	156	my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
	157
	158	my \$zb = cplx(\$z1r, \$z1i);
	159
	160	\$za $op= \$zb;
	161	my (\$zbr, \$zbi) = \@{\$zb->cartesian};
	162
	163	check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
	164	EOB
	165	$test++;
	166	# check that the rhs has not changed
	167	push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
	168	push @script, qq(print "ok $test\n";);
	169	push @script, "}\n";
	170	}
89d0527d	171	}
	172	}
	173
	174	sub set {
	175	my ($set, $setref, $valref) = @_;
	176	@{$setref} = ();
	177	@{$valref} = ();
	178	my @set = split(/;\s*/, $set);
	179	my @res;
	180	my $i;
	181	for ($i = 0; $i < @set; $i++) {
	182	push(@{$valref}, $set[$i]);
	183	my $val = value($set[$i]);
fe82cf6e	184	push @script, "\$s$i = $val;\n";
fe82cf6e	185	push @{$setref}, "\$s$i";
89d0527d	186	}
	187	}
	188
	189	sub value {
	190	local ($_) = @_;
	191	if (/^\s\((.),(.*)\)/) {
	192	return "cplx($1,$2)";
	193	}
	194	elsif (/^\s\[(.),(.*)\]/) {
	195	return "cplxe($1,$2)";
	196	}
	197	elsif (/^\s'(.)'/) {
	198	my $ex = $1;
	199	$ex =~ s/\bz\b/$target/g;
	200	$ex =~ s/\br\b/abs($target)/g;
	201	$ex =~ s/\bt\b/arg($target)/g;
	202	$ex =~ s/\ba\b/Re($target)/g;
	203	$ex =~ s/\bb\b/Im($target)/g;
	204	return $ex;
	205	}
	206	elsif (/^\s"(.)"/) {
	207	return "\"$1\"";
	208	}
	209	return $_;
	210	}
	211
	212	sub check {
	213	my ($test, $try, $got, $expected, @z) = @_;
0c721ce2	214
	215	# print "# @_\n";
	216
	217	if ("$got" eq "$expected"
	218	\|\|
	219	($expected =~ /^-?\d/ && $got == $expected)
	220	\|\|
	221	(abs($got - $expected) < $eps)
	222	) {
89d0527d	223	print "ok $test\n";
	224	} else {
	225	print "not ok $test\n";
	226	my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
	227	print "# '$try' expected: '$expected' got: '$got' for $args\n";
	228	}
	229	}
	230	__END__
0e505df1	231	&+;=
89d0527d	232	(3,4):(3,4):(6,8)
	233	(-3,4):(3,-4):(0,0)
	234	(3,4):-3:(0,4)
	235	1:(4,2):(5,2)
	236	[2,0]:[2,pi]:(0,0)
	237
	238	&++
	239	(2,1):(3,1)
	240
0e505df1	241	&-;=
89d0527d	242	(2,3):(-2,-3)
	243	[2,pi/2]:[2,-(pi)/2]
	244	2:[2,0]:(0,0)
	245	[3,0]:2:(1,0)
	246	3:(4,5):(-1,-5)
	247	(4,5):3:(1,5)
0e505df1	248	(2,1):(3,5):(-1,-4)
89d0527d	249
	250	&--
	251	(1,2):(0,2)
	252	[2,pi]:[3,pi]
	253
0e505df1	254	&*;=
89d0527d	255	(0,1):(0,1):(-1,0)
	256	(4,5):(1,0):(4,5)
	257	[2,2pi/3]:(1,0):[2,2pi/3]
	258	2:(0,1):(0,2)
	259	(0,1):3:(0,3)
	260	(0,1):(4,1):(-1,4)
	261	(2,1):(4,-1):(9,2)
	262
0e505df1	263	&/;=
89d0527d	264	(3,4):(3,4):(1,0)
	265	(4,-5):1:(4,-5)
	266	1:(0,1):(0,-1)
	267	(0,6):(0,2):(3,0)
	268	(9,2):(4,-1):(2,1)
	269	[4,pi]:[2,pi/2]:[2,pi/2]
	270	[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
	271
0e505df1	272	&**;=
	273	(2,0):(3,0):(8,0)
	274	(3,0):(2,0):(9,0)
	275	(2,3):(4,0):(-119,-120)
ace5de91	276	(0,0):(1,0):(0,0)
	277	(0,0):(2,3):(0,0)
	278	(1,0):(0,0):(1,0)
	279	(1,0):(1,0):(1,0)
	280	(1,0):(2,3):(1,0)
	281	(2,3):(0,0):(1,0)
	282	(2,3):(1,0):(2,3)
0e505df1	283
0c721ce2	284	&Re
	285	(3,4):3
	286	(-3,4):-3
	287	[1,pi/2]:0
	288
	289	&Im
	290	(3,4):4
	291	(3,-4):-4
	292	[1,pi/2]:1
	293
89d0527d	294	&abs
	295	(3,4):5
	296	(-3,4):5
	297
0c721ce2	298	&arg
	299	[2,0]:0
	300	[-2,0]:pi
	301
89d0527d	302	&~
	303	(4,5):(4,-5)
	304	(-3,4):(-3,-4)
	305	[2,pi/2]:[2,-(pi)/2]
	306
	307	&<
	308	(3,4):(1,2):0
	309	(3,4):(3,2):0
	310	(3,4):(3,8):1
	311	(4,4):(5,129):1
	312
	313	&==
	314	(3,4):(4,5):0
	315	(3,4):(3,5):0
	316	(3,4):(2,4):0
	317	(3,4):(3,4):1
	318
	319	&sqrt
0c721ce2	320	-9:(0,3)
89d0527d	321	(-100,0):(0,10)
	322	(16,-30):(5,-3)
	323
	324	&stringify_cartesian
	325	(-100,0):"-100"
	326	(0,1):"i"
	327	(4,-3):"4-3i"
	328	(4,0):"4"
	329	(-4,0):"-4"
	330	(-2,4):"-2+4i"
	331	(-2,-1):"-2-i"
	332
	333	&stringify_polar
	334	[-1, 0]:"[1,pi]"
	335	[1, pi/3]:"[1,pi/3]"
	336	[6, -2*pi/3]:"[6,-2pi/3]"
	337	[0.5, -9*pi/11]:"[0.5,-9pi/11]"
	338
	339	{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
	340
	341	\|'z + ~z':'2*Re(z)'
	342	\|'z - ~z':'2iIm(z)'
	343	\|'z * ~z':'abs(z) * abs(z)'
	344
f4837644	345	{ (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
89d0527d	346
0c721ce2	347	\|'(root(z, 4))[1] ** 4':'z'
	348	\|'(root(z, 5))[3] ** 5':'z'
	349	\|'(root(z, 8))[7] ** 8':'z'
89d0527d	350	\|'abs(z)':'r'
0c721ce2	351	\|'acot(z)':'acotan(z)'
	352	\|'acsc(z)':'acosec(z)'
	353	\|'acsc(z)':'asin(1 / z)'
	354	\|'asec(z)':'acos(1 / z)'
89d0527d	355	\|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d	356	\|'cos(acos(z))':'z'
89d0527d	357	\|'cos(z) 2 + sin(z) 2':1
89d0527d	358	\|'cos(z)':'cosh(i*z)'
0c721ce2	359	\|'cosh(z) 2 - sinh(z) 2':1
	360	\|'cot(acot(z))':'z'
	361	\|'cot(z)':'1 / tan(z)'
	362	\|'cot(z)':'cotan(z)'
	363	\|'csc(acsc(z))':'z'
	364	\|'csc(z)':'1 / sin(z)'
	365	\|'csc(z)':'cosec(z)'
89d0527d	366	\|'exp(log(z))':'z'
0c721ce2	367	\|'exp(z)':'exp(a) * exp(i * b)'
	368	\|'ln(z)':'log(z)'
	369	\|'log(exp(z))':'z'
	370	\|'log(z)':'log(r) + i*t'
89d0527d	371	\|'log10(z)':'log(z) / log(10)'
89d0527d	372	\|'logn(z, 2)':'log(z) / log(2)'
0c721ce2	373	\|'logn(z, 3)':'log(z) / log(3)'
	374	\|'sec(asec(z))':'z'
	375	\|'sec(z)':'1 / cos(z)'
	376	\|'sin(asin(z))':'z'
	377	\|'sin(i * z)':'i * sinh(z)'
	378	\|'sqrt(z) * sqrt(z)':'z'
	379	\|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
	380	\|'tan(atan(z))':'z'
	381	\|'z*z':'exp(z log(z))'
89d0527d	382
0c721ce2	383	{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d	384
89d0527d	385	\|'cosh(acosh(z))':'z'
0c721ce2	386	\|'coth(acoth(z))':'z'
	387	\|'coth(z)':'1 / tanh(z)'
	388	\|'coth(z)':'cotanh(z)'
	389	\|'csch(acsch(z))':'z'
	390	\|'csch(z)':'1 / sinh(z)'
	391	\|'csch(z)':'cosech(z)'
	392	\|'sech(asech(z))':'z'
	393	\|'sech(z)':'1 / cosh(z)'
	394	\|'sinh(asinh(z))':'z'
89d0527d	395	\|'tanh(atanh(z))':'z'
89d0527d	396
0c721ce2	397	{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d	398
89d0527d	399	\|'acos(cos(z)) ** 2':'z * z'
89d0527d	400	\|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2	401	\|'acoth(z)':'acotanh(z)'
	402	\|'acoth(z)':'atanh(1 / z)'
	403	\|'acsch(z)':'acosech(z)'
	404	\|'acsch(z)':'asinh(1 / z)'
	405	\|'asech(z)':'acosh(1 / z)'
	406	\|'asin(sin(z))':'z'
	407	\|'asinh(sinh(z))':'z'
	408	\|'atan(tan(z))':'z'
89d0527d	409	\|'atanh(tanh(z))':'z'
89d0527d	410
0c721ce2	411	&sin
	412	( 2, 3):( 9.15449914691143, -4.16890695996656)
	413	(-2, 3):( -9.15449914691143, -4.16890695996656)
	414	(-2,-3):( -9.15449914691143, 4.16890695996656)
	415	( 2,-3):( 9.15449914691143, 4.16890695996656)
	416
	417	&cos
	418	( 2, 3):( -4.18962569096881, -9.10922789375534)
	419	(-2, 3):( -4.18962569096881, 9.10922789375534)
	420	(-2,-3):( -4.18962569096881, -9.10922789375534)
	421	( 2,-3):( -4.18962569096881, 9.10922789375534)
	422
	423	&tan
	424	( 2, 3):( -0.00376402564150, 1.00323862735361)
	425	(-2, 3):( 0.00376402564150, 1.00323862735361)
	426	(-2,-3):( 0.00376402564150, -1.00323862735361)
	427	( 2,-3):( -0.00376402564150, -1.00323862735361)
	428
	429	&sec
	430	( 2, 3):( -0.04167496441114, 0.09061113719624)
	431	(-2, 3):( -0.04167496441114, -0.09061113719624)
	432	(-2,-3):( -0.04167496441114, 0.09061113719624)
	433	( 2,-3):( -0.04167496441114, -0.09061113719624)
	434
	435	&csc
	436	( 2, 3):( 0.09047320975321, 0.04120098628857)
	437	(-2, 3):( -0.09047320975321, 0.04120098628857)
	438	(-2,-3):( -0.09047320975321, -0.04120098628857)
	439	( 2,-3):( 0.09047320975321, -0.04120098628857)
	440
	441	&cot
	442	( 2, 3):( -0.00373971037634, -0.99675779656936)
	443	(-2, 3):( 0.00373971037634, -0.99675779656936)
	444	(-2,-3):( 0.00373971037634, 0.99675779656936)
	445	( 2,-3):( -0.00373971037634, 0.99675779656936)
	446
	447	&asin
	448	( 2, 3):( 0.57065278432110, 1.98338702991654)
	449	(-2, 3):( -0.57065278432110, 1.98338702991654)
	450	(-2,-3):( -0.57065278432110, -1.98338702991654)
	451	( 2,-3):( 0.57065278432110, -1.98338702991654)
	452
	453	&acos
	454	( 2, 3):( 1.00014354247380, -1.98338702991654)
	455	(-2, 3):( 2.14144911111600, -1.98338702991654)
	456	(-2,-3):( 2.14144911111600, 1.98338702991654)
	457	( 2,-3):( 1.00014354247380, 1.98338702991654)
	458
	459	&atan
	460	( 2, 3):( 1.40992104959658, 0.22907268296854)
	461	(-2, 3):( -1.40992104959658, 0.22907268296854)
	462	(-2,-3):( -1.40992104959658, -0.22907268296854)
	463	( 2,-3):( 1.40992104959658, -0.22907268296854)
	464
	465	&asec
	466	( 2, 3):( 1.42041072246703, 0.23133469857397)
	467	(-2, 3):( 1.72118193112276, 0.23133469857397)
	468	(-2,-3):( 1.72118193112276, -0.23133469857397)
	469	( 2,-3):( 1.42041072246703, -0.23133469857397)
	470
	471	&acsc
	472	( 2, 3):( 0.15038560432786, -0.23133469857397)
	473	(-2, 3):( -0.15038560432786, -0.23133469857397)
	474	(-2,-3):( -0.15038560432786, 0.23133469857397)
475	( 2,-3):( 0.15038560432786, 0.23133469857397)
476
477	&acot
478	( 2, 3):( 0.16087527719832, -0.22907268296854)
479	(-2, 3):( -0.16087527719832, -0.22907268296854)
480	(-2,-3):( -0.16087527719832, 0.22907268296854)
481	( 2,-3):( 0.16087527719832, 0.22907268296854)
482
483	&sinh
484	( 2, 3):( -3.59056458998578, 0.53092108624852)
485	(-2, 3):( 3.59056458998578, 0.53092108624852)
486	(-2,-3):( 3.59056458998578, -0.53092108624852)
487	( 2,-3):( -3.59056458998578, -0.53092108624852)
488
489	&cosh
490	( 2, 3):( -3.72454550491532, 0.51182256998738)
491	(-2, 3):( -3.72454550491532, -0.51182256998738)
492	(-2,-3):( -3.72454550491532, 0.51182256998738)
493	( 2,-3):( -3.72454550491532, -0.51182256998738)
494
495	&tanh
496	( 2, 3):( 0.96538587902213, -0.00988437503832)
497	(-2, 3):( -0.96538587902213, -0.00988437503832)
498	(-2,-3):( -0.96538587902213, 0.00988437503832)
499	( 2,-3):( 0.96538587902213, 0.00988437503832)
500
501	&sech
502	( 2, 3):( -0.26351297515839, -0.03621163655877)
503	(-2, 3):( -0.26351297515839, 0.03621163655877)
504	(-2,-3):( -0.26351297515839, -0.03621163655877)
505	( 2,-3):( -0.26351297515839, 0.03621163655877)
506
507	&csch
508	( 2, 3):( -0.27254866146294, -0.04030057885689)
509	(-2, 3):( 0.27254866146294, -0.04030057885689)
510	(-2,-3):( 0.27254866146294, 0.04030057885689)
511	( 2,-3):( -0.27254866146294, 0.04030057885689)
512
513	&coth
514	( 2, 3):( 1.03574663776500, 0.01060478347034)
515	(-2, 3):( -1.03574663776500, 0.01060478347034)
516	(-2,-3):( -1.03574663776500, -0.01060478347034)
517	( 2,-3):( 1.03574663776500, -0.01060478347034)
518
519	&asinh
520	( 2, 3):( 1.96863792579310, 0.96465850440760)
521	(-2, 3):( -1.96863792579310, 0.96465850440761)
522	(-2,-3):( -1.96863792579310, -0.96465850440761)
523	( 2,-3):( 1.96863792579310, -0.96465850440760)
524
525	&acosh
526	( 2, 3):( 1.98338702991654, 1.00014354247380)
527	(-2, 3):( -1.98338702991653, -2.14144911111600)
528	(-2,-3):( -1.98338702991653, 2.14144911111600)
529	( 2,-3):( 1.98338702991654, -1.00014354247380)
530
531	&atanh
532	( 2, 3):( 0.14694666622553, 1.33897252229449)
533	(-2, 3):( -0.14694666622553, 1.33897252229449)
534	(-2,-3):( -0.14694666622553, -1.33897252229449)
535	( 2,-3):( 0.14694666622553, -1.33897252229449)
536
537	&asech
538	( 2, 3):( 0.23133469857397, -1.42041072246703)
539	(-2, 3):( -0.23133469857397, 1.72118193112276)
540	(-2,-3):( -0.23133469857397, -1.72118193112276)
541	( 2,-3):( 0.23133469857397, 1.42041072246703)
542
543	&acsch
544	( 2, 3):( 0.15735549884499, -0.22996290237721)
545	(-2, 3):( -0.15735549884499, -0.22996290237721)
546	(-2,-3):( -0.15735549884499, 0.22996290237721)
547	( 2,-3):( 0.15735549884499, 0.22996290237721)
548
549	&acoth
550	( 2, 3):( 0.14694666622553, -0.23182380450040)
551	(-2, 3):( -0.14694666622553, -0.23182380450040)
552	(-2,-3):( -0.14694666622553, 0.23182380450040)
553	( 2,-3):( 0.14694666622553, 0.23182380450040)
554
555	# eof