[perl5.git] / t / lib / complex.t

#!./perl

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

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
	6	# -- Raphael Manfredi, September 1996
	7	# -- Jarkko Hietaniemi, March 1997
	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
	52	print "1..$test\n";
fe82cf6e	53	eval join '', @script;
89d0527d RM	54	die $@ if $@;
	55
	56	sub test {
	57	my ($op, $z, @args) = @_;
	58	$test++;
	59	my $i;
	60	for ($i = 0; $i < @args; $i++) {
	61	$val = value($args[$i]);
fe82cf6e	62	push @script, "\$z$i = $val;\n";
89d0527d RM	63	}
	64	if (defined $z) {
	65	$args = "'$op'"; # Really the value
0c721ce2	66	$try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
fe82cf6e CS	67	push @script, "\$res = $try; ";
fe82cf6e CS	68	push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
89d0527d RM	69	} else {
	70	my ($try, $args);
	71	if (@args == 2) {
	72	$try = "$op \$z0";
	73	$args = "'$args[0]'";
	74	} else {
	75	$try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
	76	$args = "'$args[0]', '$args[1]'";
	77	}
fe82cf6e CS	78	push @script, "\$res = $try; ";
fe82cf6e CS	79	push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
89d0527d RM	80	}
	81	}
	82
	83	sub set {
	84	my ($set, $setref, $valref) = @_;
	85	@{$setref} = ();
	86	@{$valref} = ();
	87	my @set = split(/;\s*/, $set);
	88	my @res;
	89	my $i;
	90	for ($i = 0; $i < @set; $i++) {
	91	push(@{$valref}, $set[$i]);
	92	my $val = value($set[$i]);
fe82cf6e CS	93	push @script, "\$s$i = $val;\n";
fe82cf6e CS	94	push @{$setref}, "\$s$i";
89d0527d RM	95	}
	96	}
	97
	98	sub value {
	99	local ($_) = @_;
	100	if (/^\s\((.),(.*)\)/) {
	101	return "cplx($1,$2)";
	102	}
	103	elsif (/^\s\[(.),(.*)\]/) {
	104	return "cplxe($1,$2)";
	105	}
	106	elsif (/^\s'(.)'/) {
	107	my $ex = $1;
	108	$ex =~ s/\bz\b/$target/g;
	109	$ex =~ s/\br\b/abs($target)/g;
	110	$ex =~ s/\bt\b/arg($target)/g;
	111	$ex =~ s/\ba\b/Re($target)/g;
	112	$ex =~ s/\bb\b/Im($target)/g;
	113	return $ex;
	114	}
	115	elsif (/^\s"(.)"/) {
	116	return "\"$1\"";
	117	}
	118	return $_;
	119	}
	120
	121	sub check {
	122	my ($test, $try, $got, $expected, @z) = @_;
0c721ce2 JH	123
	124	# print "# @_\n";
	125
	126	if ("$got" eq "$expected"
	127	\|\|
	128	($expected =~ /^-?\d/ && $got == $expected)
	129	\|\|
	130	(abs($got - $expected) < $eps)
	131	) {
89d0527d RM	132	print "ok $test\n";
	133	} else {
	134	print "not ok $test\n";
	135	my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
	136	print "# '$try' expected: '$expected' got: '$got' for $args\n";
	137	}
	138	}
	139	__END__
	140	&+
	141	(3,4):(3,4):(6,8)
	142	(-3,4):(3,-4):(0,0)
	143	(3,4):-3:(0,4)
	144	1:(4,2):(5,2)
	145	[2,0]:[2,pi]:(0,0)
	146
	147	&++
	148	(2,1):(3,1)
	149
	150	&-
	151	(2,3):(-2,-3)
	152	[2,pi/2]:[2,-(pi)/2]
	153	2:[2,0]:(0,0)
	154	[3,0]:2:(1,0)
	155	3:(4,5):(-1,-5)
	156	(4,5):3:(1,5)
	157
	158	&--
	159	(1,2):(0,2)
	160	[2,pi]:[3,pi]
	161
	162	&*
	163	(0,1):(0,1):(-1,0)
	164	(4,5):(1,0):(4,5)
	165	[2,2pi/3]:(1,0):[2,2pi/3]
	166	2:(0,1):(0,2)
	167	(0,1):3:(0,3)
	168	(0,1):(4,1):(-1,4)
	169	(2,1):(4,-1):(9,2)
	170
	171	&/
	172	(3,4):(3,4):(1,0)
	173	(4,-5):1:(4,-5)
	174	1:(0,1):(0,-1)
	175	(0,6):(0,2):(3,0)
	176	(9,2):(4,-1):(2,1)
	177	[4,pi]:[2,pi/2]:[2,pi/2]
	178	[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
	179
0c721ce2 JH	180	&Re
	181	(3,4):3
	182	(-3,4):-3
	183	[1,pi/2]:0
	184
	185	&Im
	186	(3,4):4
	187	(3,-4):-4
	188	[1,pi/2]:1
	189
89d0527d RM	190	&abs
	191	(3,4):5
	192	(-3,4):5
	193
0c721ce2 JH	194	&arg
	195	[2,0]:0
	196	[-2,0]:pi
	197
89d0527d RM	198	&~
	199	(4,5):(4,-5)
	200	(-3,4):(-3,-4)
	201	[2,pi/2]:[2,-(pi)/2]
	202
	203	&<
	204	(3,4):(1,2):0
	205	(3,4):(3,2):0
	206	(3,4):(3,8):1
	207	(4,4):(5,129):1
	208
	209	&==
	210	(3,4):(4,5):0
	211	(3,4):(3,5):0
	212	(3,4):(2,4):0
	213	(3,4):(3,4):1
	214
	215	&sqrt
0c721ce2	216	-9:(0,3)
89d0527d RM	217	(-100,0):(0,10)
	218	(16,-30):(5,-3)
	219
	220	&stringify_cartesian
	221	(-100,0):"-100"
	222	(0,1):"i"
	223	(4,-3):"4-3i"
	224	(4,0):"4"
	225	(-4,0):"-4"
	226	(-2,4):"-2+4i"
	227	(-2,-1):"-2-i"
	228
	229	&stringify_polar
	230	[-1, 0]:"[1,pi]"
	231	[1, pi/3]:"[1,pi/3]"
	232	[6, -2*pi/3]:"[6,-2pi/3]"
	233	[0.5, -9*pi/11]:"[0.5,-9pi/11]"
	234
	235	{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
	236
	237	\|'z + ~z':'2*Re(z)'
	238	\|'z - ~z':'2iIm(z)'
	239	\|'z * ~z':'abs(z) * abs(z)'
	240
0c721ce2	241	{ (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; -3; (-3, 0); (-2, -1); [2,1] }
89d0527d	242
0c721ce2 JH	243	\|'(root(z, 4))[1] ** 4':'z'
	244	\|'(root(z, 5))[3] ** 5':'z'
	245	\|'(root(z, 8))[7] ** 8':'z'
89d0527d	246	\|'abs(z)':'r'
0c721ce2 JH	247	\|'acot(z)':'acotan(z)'
	248	\|'acsc(z)':'acosec(z)'
	249	\|'acsc(z)':'asin(1 / z)'
	250	\|'asec(z)':'acos(1 / z)'
89d0527d	251	\|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d	252	\|'cos(acos(z))':'z'
89d0527d	253	\|'cos(z) 2 + sin(z) 2':1
89d0527d	254	\|'cos(z)':'cosh(i*z)'
0c721ce2 JH	255	\|'cosh(z) 2 - sinh(z) 2':1
	256	\|'cot(acot(z))':'z'
	257	\|'cot(z)':'1 / tan(z)'
	258	\|'cot(z)':'cotan(z)'
	259	\|'csc(acsc(z))':'z'
	260	\|'csc(z)':'1 / sin(z)'
	261	\|'csc(z)':'cosec(z)'
89d0527d	262	\|'exp(log(z))':'z'
0c721ce2 JH	263	\|'exp(z)':'exp(a) * exp(i * b)'
	264	\|'ln(z)':'log(z)'
	265	\|'log(exp(z))':'z'
	266	\|'log(z)':'log(r) + i*t'
89d0527d	267	\|'log10(z)':'log(z) / log(10)'
89d0527d	268	\|'logn(z, 2)':'log(z) / log(2)'
0c721ce2 JH	269	\|'logn(z, 3)':'log(z) / log(3)'
	270	\|'sec(asec(z))':'z'
	271	\|'sec(z)':'1 / cos(z)'
	272	\|'sin(asin(z))':'z'
	273	\|'sin(i * z)':'i * sinh(z)'
	274	\|'sqrt(z) * sqrt(z)':'z'
	275	\|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
	276	\|'tan(atan(z))':'z'
	277	\|'z*z':'exp(z log(z))'
89d0527d	278
0c721ce2	279	{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d	280
89d0527d	281	\|'cosh(acosh(z))':'z'
0c721ce2 JH	282	\|'coth(acoth(z))':'z'
	283	\|'coth(z)':'1 / tanh(z)'
	284	\|'coth(z)':'cotanh(z)'
	285	\|'csch(acsch(z))':'z'
	286	\|'csch(z)':'1 / sinh(z)'
	287	\|'csch(z)':'cosech(z)'
	288	\|'sech(asech(z))':'z'
	289	\|'sech(z)':'1 / cosh(z)'
	290	\|'sinh(asinh(z))':'z'
89d0527d	291	\|'tanh(atanh(z))':'z'
89d0527d	292
0c721ce2	293	{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d	294
89d0527d	295	\|'acos(cos(z)) ** 2':'z * z'
89d0527d	296	\|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2 JH	297	\|'acoth(z)':'acotanh(z)'
	298	\|'acoth(z)':'atanh(1 / z)'
	299	\|'acsch(z)':'acosech(z)'
	300	\|'acsch(z)':'asinh(1 / z)'
	301	\|'asech(z)':'acosh(1 / z)'
	302	\|'asin(sin(z))':'z'
	303	\|'asinh(sinh(z))':'z'
	304	\|'atan(tan(z))':'z'
89d0527d RM	305	\|'atanh(tanh(z))':'z'
89d0527d RM	306
0c721ce2 JH	307	&sin
	308	( 2, 3):( 9.15449914691143, -4.16890695996656)
	309	(-2, 3):( -9.15449914691143, -4.16890695996656)
	310	(-2,-3):( -9.15449914691143, 4.16890695996656)
	311	( 2,-3):( 9.15449914691143, 4.16890695996656)
	312
	313	&cos
	314	( 2, 3):( -4.18962569096881, -9.10922789375534)
	315	(-2, 3):( -4.18962569096881, 9.10922789375534)
	316	(-2,-3):( -4.18962569096881, -9.10922789375534)
	317	( 2,-3):( -4.18962569096881, 9.10922789375534)
	318
	319	&tan
	320	( 2, 3):( -0.00376402564150, 1.00323862735361)
	321	(-2, 3):( 0.00376402564150, 1.00323862735361)
	322	(-2,-3):( 0.00376402564150, -1.00323862735361)
	323	( 2,-3):( -0.00376402564150, -1.00323862735361)
	324
	325	&sec
	326	( 2, 3):( -0.04167496441114, 0.09061113719624)
	327	(-2, 3):( -0.04167496441114, -0.09061113719624)
	328	(-2,-3):( -0.04167496441114, 0.09061113719624)
	329	( 2,-3):( -0.04167496441114, -0.09061113719624)
	330
	331	&csc
	332	( 2, 3):( 0.09047320975321, 0.04120098628857)
	333	(-2, 3):( -0.09047320975321, 0.04120098628857)
	334	(-2,-3):( -0.09047320975321, -0.04120098628857)
	335	( 2,-3):( 0.09047320975321, -0.04120098628857)
	336
	337	&cot
	338	( 2, 3):( -0.00373971037634, -0.99675779656936)
	339	(-2, 3):( 0.00373971037634, -0.99675779656936)
	340	(-2,-3):( 0.00373971037634, 0.99675779656936)
	341	( 2,-3):( -0.00373971037634, 0.99675779656936)
	342
	343	&asin
	344	( 2, 3):( 0.57065278432110, 1.98338702991654)
	345	(-2, 3):( -0.57065278432110, 1.98338702991654)
	346	(-2,-3):( -0.57065278432110, -1.98338702991654)
	347	( 2,-3):( 0.57065278432110, -1.98338702991654)
	348
	349	&acos
	350	( 2, 3):( 1.00014354247380, -1.98338702991654)
	351	(-2, 3):( 2.14144911111600, -1.98338702991654)
	352	(-2,-3):( 2.14144911111600, 1.98338702991654)
	353	( 2,-3):( 1.00014354247380, 1.98338702991654)
	354
	355	&atan
	356	( 2, 3):( 1.40992104959658, 0.22907268296854)
	357	(-2, 3):( -1.40992104959658, 0.22907268296854)
	358	(-2,-3):( -1.40992104959658, -0.22907268296854)
	359	( 2,-3):( 1.40992104959658, -0.22907268296854)
	360
	361	&asec
	362	( 2, 3):( 1.42041072246703, 0.23133469857397)
	363	(-2, 3):( 1.72118193112276, 0.23133469857397)
	364	(-2,-3):( 1.72118193112276, -0.23133469857397)
	365	( 2,-3):( 1.42041072246703, -0.23133469857397)
	366
	367	&acsc
	368	( 2, 3):( 0.15038560432786, -0.23133469857397)
	369	(-2, 3):( -0.15038560432786, -0.23133469857397)
	370	(-2,-3):( -0.15038560432786, 0.23133469857397)
371	( 2,-3):( 0.15038560432786, 0.23133469857397)
372
373	&acot
374	( 2, 3):( 0.16087527719832, -0.22907268296854)
375	(-2, 3):( -0.16087527719832, -0.22907268296854)
376	(-2,-3):( -0.16087527719832, 0.22907268296854)
377	( 2,-3):( 0.16087527719832, 0.22907268296854)
378
379	&sinh
380	( 2, 3):( -3.59056458998578, 0.53092108624852)
381	(-2, 3):( 3.59056458998578, 0.53092108624852)
382	(-2,-3):( 3.59056458998578, -0.53092108624852)
383	( 2,-3):( -3.59056458998578, -0.53092108624852)
384
385	&cosh
386	( 2, 3):( -3.72454550491532, 0.51182256998738)
387	(-2, 3):( -3.72454550491532, -0.51182256998738)
388	(-2,-3):( -3.72454550491532, 0.51182256998738)
389	( 2,-3):( -3.72454550491532, -0.51182256998738)
390
391	&tanh
392	( 2, 3):( 0.96538587902213, -0.00988437503832)
393	(-2, 3):( -0.96538587902213, -0.00988437503832)
394	(-2,-3):( -0.96538587902213, 0.00988437503832)
395	( 2,-3):( 0.96538587902213, 0.00988437503832)
396
397	&sech
398	( 2, 3):( -0.26351297515839, -0.03621163655877)
399	(-2, 3):( -0.26351297515839, 0.03621163655877)
400	(-2,-3):( -0.26351297515839, -0.03621163655877)
401	( 2,-3):( -0.26351297515839, 0.03621163655877)
402
403	&csch
404	( 2, 3):( -0.27254866146294, -0.04030057885689)
405	(-2, 3):( 0.27254866146294, -0.04030057885689)
406	(-2,-3):( 0.27254866146294, 0.04030057885689)
407	( 2,-3):( -0.27254866146294, 0.04030057885689)
408
409	&coth
410	( 2, 3):( 1.03574663776500, 0.01060478347034)
411	(-2, 3):( -1.03574663776500, 0.01060478347034)
412	(-2,-3):( -1.03574663776500, -0.01060478347034)
413	( 2,-3):( 1.03574663776500, -0.01060478347034)
414
415	&asinh
416	( 2, 3):( 1.96863792579310, 0.96465850440760)
417	(-2, 3):( -1.96863792579310, 0.96465850440761)
418	(-2,-3):( -1.96863792579310, -0.96465850440761)
419	( 2,-3):( 1.96863792579310, -0.96465850440760)
420
421	&acosh
422	( 2, 3):( 1.98338702991654, 1.00014354247380)
423	(-2, 3):( -1.98338702991653, -2.14144911111600)
424	(-2,-3):( -1.98338702991653, 2.14144911111600)
425	( 2,-3):( 1.98338702991654, -1.00014354247380)
426
427	&atanh
428	( 2, 3):( 0.14694666622553, 1.33897252229449)
429	(-2, 3):( -0.14694666622553, 1.33897252229449)
430	(-2,-3):( -0.14694666622553, -1.33897252229449)
431	( 2,-3):( 0.14694666622553, -1.33897252229449)
432
433	&asech
434	( 2, 3):( 0.23133469857397, -1.42041072246703)
435	(-2, 3):( -0.23133469857397, 1.72118193112276)
436	(-2,-3):( -0.23133469857397, -1.72118193112276)
437	( 2,-3):( 0.23133469857397, 1.42041072246703)
438
439	&acsch
440	( 2, 3):( 0.15735549884499, -0.22996290237721)
441	(-2, 3):( -0.15735549884499, -0.22996290237721)
442	(-2,-3):( -0.15735549884499, 0.22996290237721)
443	( 2,-3):( 0.15735549884499, 0.22996290237721)
444
445	&acoth
446	( 2, 3):( 0.14694666622553, -0.23182380450040)
447	(-2, 3):( -0.14694666622553, -0.23182380450040)
448	(-2,-3):( -0.14694666622553, 0.23182380450040)
449	( 2,-3):( 0.14694666622553, 0.23182380450040)
450
451	# eof