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

#!./perl

# $RCSfile$
#
# Regression tests for the new Math::Complex pacakge
# -- Raphael Manfredi, Septemeber 1996
# -- Jarkko Hietaniemi Manfredi, March 1997
BEGIN {
    chdir 't' if -d 't';
    @INC = '../lib';
}
use Math::Complex;

$test = 0;
$| = 1;
$script = '';
my $eps = 1e-4; # for example root() is quite bad

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 $script;
die $@ if $@;

sub test {
	my ($op, $z, @args) = @_;
	$test++;
	my $i;
	for ($i = 0; $i < @args; $i++) {
		$val = value($args[$i]);
		$script .= "\$z$i = $val;\n";
	}
	if (defined $z) {
		$args = "'$op'";		# Really the value
		$try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
		$script .= "\$res = $try; ";
		$script .= "check($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]'";
		}
		$script .= "\$res = $try; ";
		$script .= "check($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]);
		$script .= "\$s$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	#
	5	# Regression tests for the new Math::Complex pacakge
0c721ce2 JH	6	# -- Raphael Manfredi, Septemeber 1996
0c721ce2 JH	7	# -- Jarkko Hietaniemi Manfredi, March 1997
89d0527d RM	8	BEGIN {
	9	chdir 't' if -d 't';
	10	@INC = '../lib';
	11	}
	12	use Math::Complex;
	13
	14	$test = 0;
	15	$\| = 1;
	16	$script = '';
0c721ce2	17	my $eps = 1e-4; # for example root() is quite bad
89d0527d RM	18
89d0527d RM	19	while (<DATA>) {
0c721ce2 JH	20	s/^\s+//;
	21	next if $_ eq '' \|\| /^\#/;
	22	chomp;
	23	$test_set = 0; # Assume not a test over a set of values
89d0527d RM	24	if (/^&(.*)/) {
	25	$op = $1;
	26	next;
	27	}
	28	elsif (/^\{(.*)\}/) {
	29	set($1, \@set, \@val);
	30	next;
	31	}
	32	elsif (s/^\\|//) {
0c721ce2	33	$test_set = 1; # Requests we loop over the set...
89d0527d RM	34	}
89d0527d RM	35	my @args = split(/:/);
0c721ce2	36	if ($test_set == 1) {
89d0527d RM	37	my $i;
89d0527d RM	38	for ($i = 0; $i < @set; $i++) {
0c721ce2 JH	39	# complex number
	40	$target = $set[$i];
	41	# textual value as found in set definition
	42	$zvalue = $val[$i];
89d0527d RM	43	test($zvalue, $target, @args);
	44	}
	45	} else {
	46	test($op, undef, @args);
	47	}
	48	}
	49
	50	print "1..$test\n";
	51	eval $script;
	52	die $@ if $@;
	53
	54	sub test {
	55	my ($op, $z, @args) = @_;
	56	$test++;
	57	my $i;
	58	for ($i = 0; $i < @args; $i++) {
	59	$val = value($args[$i]);
	60	$script .= "\$z$i = $val;\n";
	61	}
	62	if (defined $z) {
	63	$args = "'$op'"; # Really the value
0c721ce2	64	$try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
89d0527d RM	65	$script .= "\$res = $try; ";
	66	$script .= "check($test, $args[0], \$res, \$z$#args, $args);\n";
	67	} else {
	68	my ($try, $args);
	69	if (@args == 2) {
	70	$try = "$op \$z0";
	71	$args = "'$args[0]'";
	72	} else {
	73	$try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
	74	$args = "'$args[0]', '$args[1]'";
	75	}
	76	$script .= "\$res = $try; ";
	77	$script .= "check($test, '$try', \$res, \$z$#args, $args);\n";
	78	}
	79	}
	80
	81	sub set {
	82	my ($set, $setref, $valref) = @_;
	83	@{$setref} = ();
	84	@{$valref} = ();
	85	my @set = split(/;\s*/, $set);
	86	my @res;
	87	my $i;
	88	for ($i = 0; $i < @set; $i++) {
	89	push(@{$valref}, $set[$i]);
	90	my $val = value($set[$i]);
	91	$script .= "\$s$i = $val;\n";
	92	push(@{$setref}, "\$s$i");
	93	}
	94	}
	95
	96	sub value {
	97	local ($_) = @_;
	98	if (/^\s\((.),(.*)\)/) {
	99	return "cplx($1,$2)";
	100	}
	101	elsif (/^\s\[(.),(.*)\]/) {
	102	return "cplxe($1,$2)";
	103	}
	104	elsif (/^\s'(.)'/) {
	105	my $ex = $1;
	106	$ex =~ s/\bz\b/$target/g;
	107	$ex =~ s/\br\b/abs($target)/g;
	108	$ex =~ s/\bt\b/arg($target)/g;
	109	$ex =~ s/\ba\b/Re($target)/g;
	110	$ex =~ s/\bb\b/Im($target)/g;
	111	return $ex;
	112	}
	113	elsif (/^\s"(.)"/) {
	114	return "\"$1\"";
	115	}
	116	return $_;
	117	}
	118
	119	sub check {
	120	my ($test, $try, $got, $expected, @z) = @_;
0c721ce2 JH	121
	122	# print "# @_\n";
	123
	124	if ("$got" eq "$expected"
	125	\|\|
	126	($expected =~ /^-?\d/ && $got == $expected)
	127	\|\|
	128	(abs($got - $expected) < $eps)
	129	) {
89d0527d RM	130	print "ok $test\n";
	131	} else {
	132	print "not ok $test\n";
	133	my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
	134	print "# '$try' expected: '$expected' got: '$got' for $args\n";
	135	}
	136	}
	137	__END__
	138	&+
	139	(3,4):(3,4):(6,8)
	140	(-3,4):(3,-4):(0,0)
	141	(3,4):-3:(0,4)
	142	1:(4,2):(5,2)
	143	[2,0]:[2,pi]:(0,0)
	144
	145	&++
	146	(2,1):(3,1)
	147
	148	&-
	149	(2,3):(-2,-3)
	150	[2,pi/2]:[2,-(pi)/2]
	151	2:[2,0]:(0,0)
	152	[3,0]:2:(1,0)
	153	3:(4,5):(-1,-5)
	154	(4,5):3:(1,5)
	155
	156	&--
	157	(1,2):(0,2)
	158	[2,pi]:[3,pi]
	159
	160	&*
	161	(0,1):(0,1):(-1,0)
	162	(4,5):(1,0):(4,5)
	163	[2,2pi/3]:(1,0):[2,2pi/3]
	164	2:(0,1):(0,2)
	165	(0,1):3:(0,3)
	166	(0,1):(4,1):(-1,4)
	167	(2,1):(4,-1):(9,2)
	168
	169	&/
	170	(3,4):(3,4):(1,0)
	171	(4,-5):1:(4,-5)
	172	1:(0,1):(0,-1)
	173	(0,6):(0,2):(3,0)
	174	(9,2):(4,-1):(2,1)
	175	[4,pi]:[2,pi/2]:[2,pi/2]
	176	[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
	177
0c721ce2 JH	178	&Re
	179	(3,4):3
	180	(-3,4):-3
	181	[1,pi/2]:0
	182
	183	&Im
	184	(3,4):4
	185	(3,-4):-4
	186	[1,pi/2]:1
	187
89d0527d RM	188	&abs
	189	(3,4):5
	190	(-3,4):5
	191
0c721ce2 JH	192	&arg
	193	[2,0]:0
	194	[-2,0]:pi
	195
89d0527d RM	196	&~
	197	(4,5):(4,-5)
	198	(-3,4):(-3,-4)
	199	[2,pi/2]:[2,-(pi)/2]
	200
	201	&<
	202	(3,4):(1,2):0
	203	(3,4):(3,2):0
	204	(3,4):(3,8):1
	205	(4,4):(5,129):1
	206
	207	&==
	208	(3,4):(4,5):0
	209	(3,4):(3,5):0
	210	(3,4):(2,4):0
	211	(3,4):(3,4):1
	212
	213	&sqrt
0c721ce2	214	-9:(0,3)
89d0527d RM	215	(-100,0):(0,10)
	216	(16,-30):(5,-3)
	217
	218	&stringify_cartesian
	219	(-100,0):"-100"
	220	(0,1):"i"
	221	(4,-3):"4-3i"
	222	(4,0):"4"
	223	(-4,0):"-4"
	224	(-2,4):"-2+4i"
	225	(-2,-1):"-2-i"
	226
	227	&stringify_polar
	228	[-1, 0]:"[1,pi]"
	229	[1, pi/3]:"[1,pi/3]"
	230	[6, -2*pi/3]:"[6,-2pi/3]"
	231	[0.5, -9*pi/11]:"[0.5,-9pi/11]"
	232
	233	{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
	234
	235	\|'z + ~z':'2*Re(z)'
	236	\|'z - ~z':'2iIm(z)'
	237	\|'z * ~z':'abs(z) * abs(z)'
	238
0c721ce2	239	{ (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; -3; (-3, 0); (-2, -1); [2,1] }
89d0527d	240
0c721ce2 JH	241	\|'(root(z, 4))[1] ** 4':'z'
	242	\|'(root(z, 5))[3] ** 5':'z'
	243	\|'(root(z, 8))[7] ** 8':'z'
89d0527d	244	\|'abs(z)':'r'
0c721ce2 JH	245	\|'acot(z)':'acotan(z)'
	246	\|'acsc(z)':'acosec(z)'
	247	\|'acsc(z)':'asin(1 / z)'
	248	\|'asec(z)':'acos(1 / z)'
89d0527d	249	\|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d	250	\|'cos(acos(z))':'z'
89d0527d	251	\|'cos(z) 2 + sin(z) 2':1
89d0527d	252	\|'cos(z)':'cosh(i*z)'
0c721ce2 JH	253	\|'cosh(z) 2 - sinh(z) 2':1
	254	\|'cot(acot(z))':'z'
	255	\|'cot(z)':'1 / tan(z)'
	256	\|'cot(z)':'cotan(z)'
	257	\|'csc(acsc(z))':'z'
	258	\|'csc(z)':'1 / sin(z)'
	259	\|'csc(z)':'cosec(z)'
89d0527d	260	\|'exp(log(z))':'z'
0c721ce2 JH	261	\|'exp(z)':'exp(a) * exp(i * b)'
	262	\|'ln(z)':'log(z)'
	263	\|'log(exp(z))':'z'
	264	\|'log(z)':'log(r) + i*t'
89d0527d	265	\|'log10(z)':'log(z) / log(10)'
89d0527d	266	\|'logn(z, 2)':'log(z) / log(2)'
0c721ce2 JH	267	\|'logn(z, 3)':'log(z) / log(3)'
	268	\|'sec(asec(z))':'z'
	269	\|'sec(z)':'1 / cos(z)'
	270	\|'sin(asin(z))':'z'
	271	\|'sin(i * z)':'i * sinh(z)'
	272	\|'sqrt(z) * sqrt(z)':'z'
	273	\|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
	274	\|'tan(atan(z))':'z'
	275	\|'z*z':'exp(z log(z))'
89d0527d	276
0c721ce2	277	{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d	278
89d0527d	279	\|'cosh(acosh(z))':'z'
0c721ce2 JH	280	\|'coth(acoth(z))':'z'
	281	\|'coth(z)':'1 / tanh(z)'
	282	\|'coth(z)':'cotanh(z)'
	283	\|'csch(acsch(z))':'z'
	284	\|'csch(z)':'1 / sinh(z)'
	285	\|'csch(z)':'cosech(z)'
	286	\|'sech(asech(z))':'z'
	287	\|'sech(z)':'1 / cosh(z)'
	288	\|'sinh(asinh(z))':'z'
89d0527d	289	\|'tanh(atanh(z))':'z'
89d0527d	290
0c721ce2	291	{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d	292
89d0527d	293	\|'acos(cos(z)) ** 2':'z * z'
89d0527d	294	\|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2 JH	295	\|'acoth(z)':'acotanh(z)'
	296	\|'acoth(z)':'atanh(1 / z)'
	297	\|'acsch(z)':'acosech(z)'
	298	\|'acsch(z)':'asinh(1 / z)'
	299	\|'asech(z)':'acosh(1 / z)'
	300	\|'asin(sin(z))':'z'
	301	\|'asinh(sinh(z))':'z'
	302	\|'atan(tan(z))':'z'
89d0527d RM	303	\|'atanh(tanh(z))':'z'
89d0527d RM	304
0c721ce2 JH	305	&sin
	306	( 2, 3):( 9.15449914691143, -4.16890695996656)
	307	(-2, 3):( -9.15449914691143, -4.16890695996656)
	308	(-2,-3):( -9.15449914691143, 4.16890695996656)
	309	( 2,-3):( 9.15449914691143, 4.16890695996656)
	310
	311	&cos
	312	( 2, 3):( -4.18962569096881, -9.10922789375534)
	313	(-2, 3):( -4.18962569096881, 9.10922789375534)
	314	(-2,-3):( -4.18962569096881, -9.10922789375534)
	315	( 2,-3):( -4.18962569096881, 9.10922789375534)
	316
	317	&tan
	318	( 2, 3):( -0.00376402564150, 1.00323862735361)
	319	(-2, 3):( 0.00376402564150, 1.00323862735361)
	320	(-2,-3):( 0.00376402564150, -1.00323862735361)
	321	( 2,-3):( -0.00376402564150, -1.00323862735361)
	322
	323	&sec
	324	( 2, 3):( -0.04167496441114, 0.09061113719624)
	325	(-2, 3):( -0.04167496441114, -0.09061113719624)
	326	(-2,-3):( -0.04167496441114, 0.09061113719624)
	327	( 2,-3):( -0.04167496441114, -0.09061113719624)
	328
	329	&csc
	330	( 2, 3):( 0.09047320975321, 0.04120098628857)
	331	(-2, 3):( -0.09047320975321, 0.04120098628857)
	332	(-2,-3):( -0.09047320975321, -0.04120098628857)
	333	( 2,-3):( 0.09047320975321, -0.04120098628857)
	334
	335	&cot
	336	( 2, 3):( -0.00373971037634, -0.99675779656936)
	337	(-2, 3):( 0.00373971037634, -0.99675779656936)
	338	(-2,-3):( 0.00373971037634, 0.99675779656936)
	339	( 2,-3):( -0.00373971037634, 0.99675779656936)
	340
	341	&asin
	342	( 2, 3):( 0.57065278432110, 1.98338702991654)
	343	(-2, 3):( -0.57065278432110, 1.98338702991654)
	344	(-2,-3):( -0.57065278432110, -1.98338702991654)
	345	( 2,-3):( 0.57065278432110, -1.98338702991654)
	346
	347	&acos
	348	( 2, 3):( 1.00014354247380, -1.98338702991654)
	349	(-2, 3):( 2.14144911111600, -1.98338702991654)
	350	(-2,-3):( 2.14144911111600, 1.98338702991654)
	351	( 2,-3):( 1.00014354247380, 1.98338702991654)
	352
	353	&atan
	354	( 2, 3):( 1.40992104959658, 0.22907268296854)
	355	(-2, 3):( -1.40992104959658, 0.22907268296854)
	356	(-2,-3):( -1.40992104959658, -0.22907268296854)
	357	( 2,-3):( 1.40992104959658, -0.22907268296854)
	358
	359	&asec
	360	( 2, 3):( 1.42041072246703, 0.23133469857397)
	361	(-2, 3):( 1.72118193112276, 0.23133469857397)
	362	(-2,-3):( 1.72118193112276, -0.23133469857397)
	363	( 2,-3):( 1.42041072246703, -0.23133469857397)
	364
	365	&acsc
	366	( 2, 3):( 0.15038560432786, -0.23133469857397)
	367	(-2, 3):( -0.15038560432786, -0.23133469857397)
	368	(-2,-3):( -0.15038560432786, 0.23133469857397)
369	( 2,-3):( 0.15038560432786, 0.23133469857397)
370
371	&acot
372	( 2, 3):( 0.16087527719832, -0.22907268296854)
373	(-2, 3):( -0.16087527719832, -0.22907268296854)
374	(-2,-3):( -0.16087527719832, 0.22907268296854)
375	( 2,-3):( 0.16087527719832, 0.22907268296854)
376
377	&sinh
378	( 2, 3):( -3.59056458998578, 0.53092108624852)
379	(-2, 3):( 3.59056458998578, 0.53092108624852)
380	(-2,-3):( 3.59056458998578, -0.53092108624852)
381	( 2,-3):( -3.59056458998578, -0.53092108624852)
382
383	&cosh
384	( 2, 3):( -3.72454550491532, 0.51182256998738)
385	(-2, 3):( -3.72454550491532, -0.51182256998738)
386	(-2,-3):( -3.72454550491532, 0.51182256998738)
387	( 2,-3):( -3.72454550491532, -0.51182256998738)
388
389	&tanh
390	( 2, 3):( 0.96538587902213, -0.00988437503832)
391	(-2, 3):( -0.96538587902213, -0.00988437503832)
392	(-2,-3):( -0.96538587902213, 0.00988437503832)
393	( 2,-3):( 0.96538587902213, 0.00988437503832)
394
395	&sech
396	( 2, 3):( -0.26351297515839, -0.03621163655877)
397	(-2, 3):( -0.26351297515839, 0.03621163655877)
398	(-2,-3):( -0.26351297515839, -0.03621163655877)
399	( 2,-3):( -0.26351297515839, 0.03621163655877)
400
401	&csch
402	( 2, 3):( -0.27254866146294, -0.04030057885689)
403	(-2, 3):( 0.27254866146294, -0.04030057885689)
404	(-2,-3):( 0.27254866146294, 0.04030057885689)
405	( 2,-3):( -0.27254866146294, 0.04030057885689)
406
407	&coth
408	( 2, 3):( 1.03574663776500, 0.01060478347034)
409	(-2, 3):( -1.03574663776500, 0.01060478347034)
410	(-2,-3):( -1.03574663776500, -0.01060478347034)
411	( 2,-3):( 1.03574663776500, -0.01060478347034)
412
413	&asinh
414	( 2, 3):( 1.96863792579310, 0.96465850440760)
415	(-2, 3):( -1.96863792579310, 0.96465850440761)
416	(-2,-3):( -1.96863792579310, -0.96465850440761)
417	( 2,-3):( 1.96863792579310, -0.96465850440760)
418
419	&acosh
420	( 2, 3):( 1.98338702991654, 1.00014354247380)
421	(-2, 3):( -1.98338702991653, -2.14144911111600)
422	(-2,-3):( -1.98338702991653, 2.14144911111600)
423	( 2,-3):( 1.98338702991654, -1.00014354247380)
424
425	&atanh
426	( 2, 3):( 0.14694666622553, 1.33897252229449)
427	(-2, 3):( -0.14694666622553, 1.33897252229449)
428	(-2,-3):( -0.14694666622553, -1.33897252229449)
429	( 2,-3):( 0.14694666622553, -1.33897252229449)
430
431	&asech
432	( 2, 3):( 0.23133469857397, -1.42041072246703)
433	(-2, 3):( -0.23133469857397, 1.72118193112276)
434	(-2,-3):( -0.23133469857397, -1.72118193112276)
435	( 2,-3):( 0.23133469857397, 1.42041072246703)
436
437	&acsch
438	( 2, 3):( 0.15735549884499, -0.22996290237721)
439	(-2, 3):( -0.15735549884499, -0.22996290237721)
440	(-2,-3):( -0.15735549884499, 0.22996290237721)
441	( 2,-3):( 0.15735549884499, 0.22996290237721)
442
443	&acoth
444	( 2, 3):( 0.14694666622553, -0.23182380450040)
445	(-2, 3):( -0.14694666622553, -0.23182380450040)
446	(-2,-3):( -0.14694666622553, 0.23182380450040)
447	( 2,-3):( 0.14694666622553, 0.23182380450040)
448
449	# eof