[perl5.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

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)'
	);

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

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

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

sub test {
	my ($op, $z, @args) = @_;
	$test++;
	my $i;
	for ($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";
	}
}

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)

&--
(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]

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