#!./perl
-# $RCSfile$
+# $RCSfile: complex.t,v $
#
-# Regression tests for the new Math::Complex pacakge
-# -- Raphael Manfredi, Sept 1996
+# 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';
+ unshift @INC, '../lib';
}
+
use Math::Complex;
+my $VERSION = sprintf("%s", q$Id: complex.t,v 1.9 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.d+)/);
+
+my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
+
$test = 0;
$| = 1;
-$script = '';
-$epsilon = 1e-10;
+my @script = (
+ 'my ($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
+ $eps = 1e-10; # results in Cray UNICOS, and occasionally also
+} # cos(), sin(), cosh(), sinh(). The division
+ # of doubles is the current suspect.
while (<DATA>) {
- next if /^#/ || /^\s*$/;
- chop;
- $set_test = 0; # Assume not a test over a set of values
- if (/^&(.*)/) {
+ s/^\s+//;
+ next if $_ eq '' || /^\#/;
+ chomp;
+ $test_set = 0; # Assume not a test over a set of values
+ if (/^&(.+)/) {
$op = $1;
next;
}
- elsif (/^\{(.*)\}/) {
+ elsif (/^\{(.+)\}/) {
set($1, \@set, \@val);
next;
}
elsif (s/^\|//) {
- $set_test = 1; # Requests we loop over the set...
+ $test_set = 1; # Requests we loop over the set...
}
my @args = split(/:/);
- if ($set_test) {
+ if ($test_set == 1) {
my $i;
for ($i = 0; $i < @set; $i++) {
- $target = $set[$i]; # complex number
- $zvalue = $val[$i]; # textual value as found in set definition
+ # complex number
+ $target = $set[$i];
+ # textual value as found in set definition
+ $zvalue = $val[$i];
test($zvalue, $target, @args);
}
} else {
}
}
+#
+
+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 {
+ push @script, <<EOS;
+ my \$j = (root(1,3))[1];
+
+ \$j->display_format('polar');
+EOS
+
+ $test++;
+ push @script, <<EOS;
+ print "# 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 $test\n";
+EOS
+}
+
+test_display_format();
+
print "1..$test\n";
-eval $script;
+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]);
- $script .= "\$z$i = $val;\n";
+ push @script, "\$z$i = $val;\n";
}
if (defined $z) {
$args = "'$op'"; # Really the value
- $try = "abs(\$z0 - \$z1) <= 1e-10 ? \$z1 : \$z0";
- $script .= "\$res = $try; ";
- $script .= "check($test, $args[0], \$res, \$z$#args, $args);\n";
+ $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 =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
$args = "'$args[0]', '$args[1]'";
}
- $script .= "\$res = $try; ";
- $script .= "check($test, '$try', \$res, \$z$#args, $args);\n";
+ 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 $test\\n";\n);
+ push @script, "}\n";
+ }
}
}
for ($i = 0; $i < @set; $i++) {
push(@{$valref}, $set[$i]);
my $val = value($set[$i]);
- $script .= "\$s$i = $val;\n";
- push(@{$setref}, "\$s$i");
+ push @script, "\$s$i = $val;\n";
+ push @{$setref}, "\$s$i";
}
}
if (/^\s*\((.*),(.*)\)/) {
return "cplx($1,$2)";
}
+ elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
+ return "cplx($1,0)";
+ }
elsif (/^\s*\[(.*),(.*)\]/) {
return "cplxe($1,$2)";
}
sub check {
my ($test, $try, $got, $expected, @z) = @_;
- if ("$got" eq "$expected" || ($expected =~ /^-?\d/ && $got == $expected)) {
+
+ print "# @_\n";
+
+ if ("$got" eq "$expected"
+ ||
+ ($expected =~ /^-?\d/ && $got == $expected)
+ ||
+ (abs($got - $expected) < $eps)
+ ) {
print "ok $test\n";
} else {
print "not ok $test\n";
print "# '$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)
&++
(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]
(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)
[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)
(3,4):(3,4):1
&sqrt
+-9:(0,3)
(-100,0):(0,10)
(16,-30):(5,-3)
|'z - ~z':'2*i*Im(z)'
|'z * ~z':'abs(z) * abs(z)'
-{ (4,3); [3,2]; (-3,4); (0,2); 3; 1; (-5, 0); [2,1] }
+{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
-|'exp(z)':'exp(a) * exp(i * b)'
+|'(root(z, 4))[1] ** 4':'z'
+|'(root(z, 5))[3] ** 5':'z'
+|'(root(z, 8))[7] ** 8':'z'
|'abs(z)':'r'
-|'sqrt(z) * sqrt(z)':'z'
-|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
+|'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)'
-|'log(z)':'log(r) + i*t'
-|'sin(asin(z))':'z'
|'cos(acos(z))':'z'
-|'tan(atan(z))':'z'
-|'cotan(acotan(z))':'z'
-|'cos(z) ** 2 + sin(z) ** 2':1
-|'cosh(z) ** 2 - sinh(z) ** 2':1
+|'addsq(cos(z), sin(z))':1
|'cos(z)':'cosh(i*z)'
-|'cotan(z)':'1 / tan(z)'
-|'cotanh(z)':'1 / tanh(z)'
-|'i*sin(z)':'sinh(i*z)'
-|'z**z':'exp(z * log(z))'
-|'log(exp(z))':'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, 3)':'log(z) / log(3)'
|'logn(z, 2)':'log(z) / log(2)'
-|'(root(z, 4))[1] ** 4':'z'
-|'(root(z, 8))[7] ** 8':'z'
+|'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; (-1,0.5); (0,0.5); 0.5; (2, 0) }
+{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
-|'sinh(asinh(z))':'z'
|'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'
-|'cotanh(acotanh(z))':'z'
-{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); (0,-0.5); 0.5; (1.1, 0) }
+{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
-|'asin(sin(z))':'z'
|'acos(cos(z)) ** 2':'z * z'
-|'atan(tan(z))':'z'
-|'asinh(sinh(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
projects / p5sagit/p5-mst-13.2.git / blobdiff