#!./perl
# $RCSfile: complex.t,v $
#
# Regression tests for the Math::Complex pacakge
# -- Raphael Manfredi since Sep 1996
# -- Jarkko Hietaniemi since Mar 1997
# -- Daniel S. Lewart since Sep 1997
BEGIN {
chdir 't' if -d 't';
@INC = '../lib';
}
use Math::Complex;
use vars qw($VERSION);
$VERSION = 1.92;
my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
$test = 0;
$| = 1;
my @script = (
'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' .
"\n\n"
);
my $eps = 1e-13;
if ($^O eq 'unicos') { # For some reason root() produces very inaccurate
$eps = 1e-10; # results in Cray UNICOS, and occasionally also
} # cos(), sin(), cosh(), sinh(). The division
# of doubles is the current suspect.
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);
}
}
#
sub test_mutators {
my $op;
$test++;
push(@script, <<'EOT');
{
my $z = cplx( 1, 1);
$z->Re(2);
$z->Im(3);
print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
print 'not ' unless Re($z) == 2 and Im($z) == 3;
EOT
push(@script, qq(print "ok $test\\n"}\n));
$test++;
push(@script, <<'EOT');
{
my $z = cplx( 1, 1);
$z->abs(3 * sqrt(2));
print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and
(arg($z) - pi / 4 ) < $eps and
(Re($z) - 3 ) < $eps and
(Im($z) - 3 ) < $eps;
EOT
push(@script, qq(print "ok $test\\n"}\n));
$test++;
push(@script, <<'EOT');
{
my $z = cplx( 1, 1);
$z->arg(-3 / 4 * pi);
print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and
(abs($z) - sqrt(2) ) < $eps and
(Re($z) + 1 ) < $eps and
(Im($z) + 1 ) < $eps;
EOT
push(@script, qq(print "ok $test\\n"}\n));
}
test_mutators();
my $constants = '
my $i = cplx(0, 1);
my $pi = cplx(pi, 0);
my $pii = cplx(0, pi);
my $pip2 = cplx(pi/2, 0);
my $zero = cplx(0, 0);
';
push(@script, $constants);
# test the divbyzeros
sub test_dbz {
for my $op (@_) {
$test++;
push(@script, <<EOT);
eval '$op';
(\$bad) = (\$@ =~ /(.+)/);
print "# $test op = $op divbyzero? \$bad...\n";
print 'not ' unless (\$@ =~ /Division by zero/);
EOT
push(@script, qq(print "ok $test\\n";\n));
}
}
# test the logofzeros
sub test_loz {
for my $op (@_) {
$test++;
push(@script, <<EOT);
eval '$op';
(\$bad) = (\$@ =~ /(.+)/);
print "# $test op = $op logofzero? \$bad...\n";
print 'not ' unless (\$@ =~ /Logarithm of zero/);
EOT
push(@script, qq(print "ok $test\\n";\n));
}
}
test_dbz(
'i/0',
'acot(0)',
'acot(+$i)',
# 'acoth(-1)', # Log of zero.
'acoth(0)',
'acoth(+1)',
'acsc(0)',
'acsch(0)',
'asec(0)',
'asech(0)',
'atan($i)',
# 'atanh(-1)', # Log of zero.
'atanh(+1)',
'cot(0)',
'coth(0)',
'csc(0)',
'csch(0)',
);
test_loz(
'log($zero)',
'atan(-$i)',
'acot(-$i)',
'atanh(-1)',
'acoth(-1)',
);
# test the bad roots
sub test_broot {
for my $op (@_) {
$test++;
push(@script, <<EOT);
eval 'root(2, $op)';
(\$bad) = (\$@ =~ /(.+)/);
print "# $test op = $op badroot? \$bad...\n";
print 'not ' unless (\$@ =~ /root rank must be/);
EOT
push(@script, qq(print "ok $test\\n";\n));
}
}
test_broot(qw(-3 -2.1 0 0.99));
sub test_display_format {
$test++;
push @script, <<EOS;
print "# package display_format cartesian?\n";
print "not " unless Math::Complex->display_format eq 'cartesian';
print "ok $test\n";
EOS
push @script, <<EOS;
my \$j = (root(1,3))[1];
\$j->display_format('polar');
EOS
$test++;
push @script, <<EOS;
print "# j display_format polar?\n";
print "not " unless \$j->display_format eq 'polar';
print "ok $test\n";
EOS
$test++;
push @script, <<EOS;
print "# j = \$j\n";
print "not " unless "\$j" eq "[1,2pi/3]";
print "ok $test\n";
my %display_format;
%display_format = \$j->display_format;
EOS
$test++;
push @script, <<EOS;
print "# display_format{style} polar?\n";
print "not " unless \$display_format{style} eq 'polar';
print "ok $test\n";
EOS
$test++;
push @script, <<EOS;
print "# keys %display_format == 2?\n";
print "not " unless keys %display_format == 2;
print "ok $test\n";
\$j->display_format('style' => 'cartesian', 'format' => '%.5f');
EOS
$test++;
push @script, <<EOS;
print "# j = \$j\n";
print "not " unless "\$j" eq "-0.50000+0.86603i";
print "ok $test\n";
%display_format = \$j->display_format;
EOS
$test++;
push @script, <<EOS;
print "# display_format{format} %.5f?\n";
print "not " unless \$display_format{format} eq '%.5f';
print "ok $test\n";
EOS
$test++;
push @script, <<EOS;
print "# keys %display_format == 3?\n";
print "not " unless keys %display_format == 3;
print "ok $test\n";
\$j->display_format('format' => undef);
EOS
$test++;
push @script, <<EOS;
print "# j = \$j\n";
print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/;
print "ok $test\n";
\$j->display_format('style' => 'polar', 'polar_pretty_print' => 0);
EOS
$test++;
push @script, <<EOS;
print "# j = \$j\n";
print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/;
print "ok $test\n";
\$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
EOS
$test++;
push @script, <<EOS;
print "# j = \$j\n";
print "not " unless "\$j" eq "(-0.5)+(0.86603)i";
print "ok $test\n";
EOS
$test++;
push @script, <<EOS;
print "# j display_format cartesian?\n";
print "not " unless \$j->display_format eq 'cartesian';
print "ok $test\n";
EOS
}
test_display_format();
sub test_remake {
$test++;
push @script, <<EOS;
print "# remake 2+3i\n";
my \$z = cplx('2+3i');
print "not " unless \$z == Math::Complex->make(2,3);
print "ok $test\n";
EOS
$test++;
push @script, <<EOS;
print "# remake 3i\n";
my \$z = Math::Complex->make('3i');
print "not " unless \$z == cplx(0,3);
print "ok $test\n";
EOS
$test++;
push @script, <<EOS;
print "# remake [2,3]\n";
my \$z = cplxe('[2,3]');
print "not " unless \$z == Math::Complex->emake(2,3);
print "ok $test\n";
EOS
$test++;
push @script, <<EOS;
print "# remake [2]\n";
my \$z = Math::Complex->emake('[2]');
print "not " unless \$z == cplxe(2);
print "ok $test\n";
EOS
}
test_remake();
print "1..$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 $test\\n";\n);
push @script, "}\n";
}
}
}
sub set {
my ($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*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
return "cplx($1,0)";
}
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 $args\n";
}
}
sub addsq {
my ($z1, $z2) = @_;
return ($z1 + i*$z2) * ($z1 - i*$z2);
}
sub subsq {
my ($z1, $z2) = @_;
return ($z1 + $z2) * ($z1 - $z2);
}
__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)
(0,0):(0,0):(1,0)
&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)'
{ (0.5, 0); (-0.5, 0); (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'
|'addsq(cos(z), sin(z))':1
|'cos(z)':'cosh(i*z)'
|'subsq(cosh(z), sinh(z))':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'
&log
(-2.0,0):( 0.69314718055995, 3.14159265358979)
(-1.0,0):( 0 , 3.14159265358979)
(-0.5,0):( -0.69314718055995, 3.14159265358979)
( 0.5,0):( -0.69314718055995, 0 )
( 1.0,0):( 0 , 0 )
( 2.0,0):( 0.69314718055995, 0 )
&log
( 2, 3):( 1.28247467873077, 0.98279372324733)
(-2, 3):( 1.28247467873077, 2.15879893034246)
(-2,-3):( 1.28247467873077, -2.15879893034246)
( 2,-3):( 1.28247467873077, -0.98279372324733)
&sin
(-2.0,0):( -0.90929742682568, 0 )
(-1.0,0):( -0.84147098480790, 0 )
(-0.5,0):( -0.47942553860420, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.47942553860420, 0 )
( 1.0,0):( 0.84147098480790, 0 )
( 2.0,0):( 0.90929742682568, 0 )
&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
(-2.0,0):( -0.41614683654714, 0 )
(-1.0,0):( 0.54030230586814, 0 )
(-0.5,0):( 0.87758256189037, 0 )
( 0.0,0):( 1 , 0 )
( 0.5,0):( 0.87758256189037, 0 )
( 1.0,0):( 0.54030230586814, 0 )
( 2.0,0):( -0.41614683654714, 0 )
&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
(-2.0,0):( 2.18503986326152, 0 )
(-1.0,0):( -1.55740772465490, 0 )
(-0.5,0):( -0.54630248984379, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.54630248984379, 0 )
( 1.0,0):( 1.55740772465490, 0 )
( 2.0,0):( -2.18503986326152, 0 )
&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
(-2.0,0):( -2.40299796172238, 0 )
(-1.0,0):( 1.85081571768093, 0 )
(-0.5,0):( 1.13949392732455, 0 )
( 0.0,0):( 1 , 0 )
( 0.5,0):( 1.13949392732455, 0 )
( 1.0,0):( 1.85081571768093, 0 )
( 2.0,0):( -2.40299796172238, 0 )
&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
(-2.0,0):( -1.09975017029462, 0 )
(-1.0,0):( -1.18839510577812, 0 )
(-0.5,0):( -2.08582964293349, 0 )
( 0.5,0):( 2.08582964293349, 0 )
( 1.0,0):( 1.18839510577812, 0 )
( 2.0,0):( 1.09975017029462, 0 )
&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
(-2.0,0):( 0.45765755436029, 0 )
(-1.0,0):( -0.64209261593433, 0 )
(-0.5,0):( -1.83048772171245, 0 )
( 0.5,0):( 1.83048772171245, 0 )
( 1.0,0):( 0.64209261593433, 0 )
( 2.0,0):( -0.45765755436029, 0 )
&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
(-2.0,0):( -1.57079632679490, 1.31695789692482)
(-1.0,0):( -1.57079632679490, 0 )
(-0.5,0):( -0.52359877559830, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.52359877559830, 0 )
( 1.0,0):( 1.57079632679490, 0 )
( 2.0,0):( 1.57079632679490, -1.31695789692482)
&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
(-2.0,0):( 3.14159265358979, -1.31695789692482)
(-1.0,0):( 3.14159265358979, 0 )
(-0.5,0):( 2.09439510239320, 0 )
( 0.0,0):( 1.57079632679490, 0 )
( 0.5,0):( 1.04719755119660, 0 )
( 1.0,0):( 0 , 0 )
( 2.0,0):( 0 , 1.31695789692482)
&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
(-2.0,0):( -1.10714871779409, 0 )
(-1.0,0):( -0.78539816339745, 0 )
(-0.5,0):( -0.46364760900081, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.46364760900081, 0 )
( 1.0,0):( 0.78539816339745, 0 )
( 2.0,0):( 1.10714871779409, 0 )
&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
(-2.0,0):( 2.09439510239320, 0 )
(-1.0,0):( 3.14159265358979, 0 )
(-0.5,0):( 3.14159265358979, -1.31695789692482)
( 0.5,0):( 0 , 1.31695789692482)
( 1.0,0):( 0 , 0 )
( 2.0,0):( 1.04719755119660, 0 )
&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
(-2.0,0):( -0.52359877559830, 0 )
(-1.0,0):( -1.57079632679490, 0 )
(-0.5,0):( -1.57079632679490, 1.31695789692482)
( 0.5,0):( 1.57079632679490, -1.31695789692482)
( 1.0,0):( 1.57079632679490, 0 )
( 2.0,0):( 0.52359877559830, 0 )
&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
(-2.0,0):( -0.46364760900081, 0 )
(-1.0,0):( -0.78539816339745, 0 )
(-0.5,0):( -1.10714871779409, 0 )
( 0.5,0):( 1.10714871779409, 0 )
( 1.0,0):( 0.78539816339745, 0 )
( 2.0,0):( 0.46364760900081, 0 )
&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
(-2.0,0):( -3.62686040784702, 0 )
(-1.0,0):( -1.17520119364380, 0 )
(-0.5,0):( -0.52109530549375, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.52109530549375, 0 )
( 1.0,0):( 1.17520119364380, 0 )
( 2.0,0):( 3.62686040784702, 0 )
&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
(-2.0,0):( 3.76219569108363, 0 )
(-1.0,0):( 1.54308063481524, 0 )
(-0.5,0):( 1.12762596520638, 0 )
( 0.0,0):( 1 , 0 )
( 0.5,0):( 1.12762596520638, 0 )
( 1.0,0):( 1.54308063481524, 0 )
( 2.0,0):( 3.76219569108363, 0 )
&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
(-2.0,0):( -0.96402758007582, 0 )
(-1.0,0):( -0.76159415595576, 0 )
(-0.5,0):( -0.46211715726001, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.46211715726001, 0 )
( 1.0,0):( 0.76159415595576, 0 )
( 2.0,0):( 0.96402758007582, 0 )
&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
(-2.0,0):( 0.26580222883408, 0 )
(-1.0,0):( 0.64805427366389, 0 )
(-0.5,0):( 0.88681888397007, 0 )
( 0.0,0):( 1 , 0 )
( 0.5,0):( 0.88681888397007, 0 )
( 1.0,0):( 0.64805427366389, 0 )
( 2.0,0):( 0.26580222883408, 0 )
&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
(-2.0,0):( -0.27572056477178, 0 )
(-1.0,0):( -0.85091812823932, 0 )
(-0.5,0):( -1.91903475133494, 0 )
( 0.5,0):( 1.91903475133494, 0 )
( 1.0,0):( 0.85091812823932, 0 )
( 2.0,0):( 0.27572056477178, 0 )
&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
(-2.0,0):( -1.03731472072755, 0 )
(-1.0,0):( -1.31303528549933, 0 )
(-0.5,0):( -2.16395341373865, 0 )
( 0.5,0):( 2.16395341373865, 0 )
( 1.0,0):( 1.31303528549933, 0 )
( 2.0,0):( 1.03731472072755, 0 )
&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
(-2.0,0):( -1.44363547517881, 0 )
(-1.0,0):( -0.88137358701954, 0 )
(-0.5,0):( -0.48121182505960, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.48121182505960, 0 )
( 1.0,0):( 0.88137358701954, 0 )
( 2.0,0):( 1.44363547517881, 0 )
&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
(-2.0,0):( 1.31695789692482, 3.14159265358979)
(-1.0,0):( 0, 3.14159265358979)
(-0.5,0):( 0, 2.09439510239320)
( 0.0,0):( 0, 1.57079632679490)
( 0.5,0):( 0, 1.04719755119660)
( 1.0,0):( 0 , 0 )
( 2.0,0):( 1.31695789692482, 0 )
&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
(-2.0,0):( -0.54930614433405, 1.57079632679490)
(-0.5,0):( -0.54930614433405, 0 )
( 0.0,0):( 0 , 0 )
( 0.5,0):( 0.54930614433405, 0 )
( 2.0,0):( 0.54930614433405, 1.57079632679490)
&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
(-2.0,0):( 0 , 2.09439510239320)
(-1.0,0):( 0 , 3.14159265358979)
(-0.5,0):( 1.31695789692482, 3.14159265358979)
( 0.5,0):( 1.31695789692482, 0 )
( 1.0,0):( 0 , 0 )
( 2.0,0):( 0 , 1.04719755119660)
&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
(-2.0,0):( -0.48121182505960, 0 )
(-1.0,0):( -0.88137358701954, 0 )
(-0.5,0):( -1.44363547517881, 0 )
( 0.5,0):( 1.44363547517881, 0 )
( 1.0,0):( 0.88137358701954, 0 )
( 2.0,0):( 0.48121182505960, 0 )
&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
(-2.0,0):( -0.54930614433405, 0 )
(-0.5,0):( -0.54930614433405, 1.57079632679490)
( 0.5,0):( 0.54930614433405, 1.57079632679490)
( 2.0,0):( 0.54930614433405, 0 )
&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
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