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Diffstat (limited to 'cpan/Math-Complex/t/Complex.t')
| -rw-r--r-- | cpan/Math-Complex/t/Complex.t | 1136 |
1 files changed, 1136 insertions, 0 deletions
diff --git a/cpan/Math-Complex/t/Complex.t b/cpan/Math-Complex/t/Complex.t new file mode 100644 index 0000000000..687d6220df --- /dev/null +++ b/cpan/Math-Complex/t/Complex.t @@ -0,0 +1,1136 @@ +#!./perl + +# +# Regression tests for the Math::Complex pacakge +# -- Raphael Manfredi since Sep 1996 +# -- Jarkko Hietaniemi since Mar 1997 +# -- Daniel S. Lewart since Sep 1997 + +BEGIN { + if ($ENV{PERL_CORE}) { + chdir 't' if -d 't'; + #@INC = '../lib'; + } +} + +use Math::Complex 1.54; + +use vars qw($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 $pip4 = cplx(pi/4, 0); +my $zero = cplx(0, 0); +my $inf = 9**9**9; +'; + +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($i)', +# 'atanh(-1)', # Log of zero. + 'atanh(+1)', + 'cot(0)', + 'coth(0)', + 'csc(0)', + 'csch(0)', + 'atan(cplx(0, 1), cplx(1, 0))', + ); + +test_loz( + 'log($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"; + \$z = cplx('2+3i'); + print "not " unless \$z == Math::Complex->make(2,3); + print "ok $test\n"; +EOS + + $test++; + push @script, <<EOS; + print "# make 3i\n"; + \$z = Math::Complex->make('3i'); + print "not " unless \$z == cplx(0,3); + print "ok $test\n"; +EOS + + $test++; + push @script, <<EOS; + print "# emake [2,3]\n"; + \$z = Math::Complex->emake('[2,3]'); + print "not " unless \$z == cplxe(2,3); + print "ok $test\n"; +EOS + + $test++; + push @script, <<EOS; + print "# make (2,3)\n"; + \$z = Math::Complex->make('(2,3)'); + print "not " unless \$z == cplx(2,3); + print "ok $test\n"; +EOS + + $test++; + push @script, <<EOS; + print "# emake [2,3pi/8]\n"; + \$z = Math::Complex->emake('[2,3pi/8]'); + print "not " unless \$z == cplxe(2,3*\$pi/8); + print "ok $test\n"; +EOS + + $test++; + push @script, <<EOS; + print "# emake [2]\n"; + \$z = Math::Complex->emake('[2]'); + print "not " unless \$z == cplxe(2); + print "ok $test\n"; +EOS +} + +sub test_no_args { + push @script, <<'EOS'; +{ + print "# cplx, cplxe, make, emake without arguments\n"; +EOS + + $test++; + push @script, <<EOS; + my \$z0 = cplx(); + print ((\$z0->Re() == 0) ? "ok $test\n" : "not ok $test\n"); +EOS + + $test++; + push @script, <<EOS; + print ((\$z0->Im() == 0) ? "ok $test\n" : "not ok $test\n"); +EOS + + $test++; + push @script, <<EOS; + my \$z1 = cplxe(); + print ((\$z1->rho() == 0) ? "ok $test\n" : "not ok $test\n"); +EOS + + $test++; + push @script, <<EOS; + print ((\$z1->theta() == 0) ? "ok $test\n" : "not ok $test\n"); +EOS + + $test++; + push @script, <<EOS; + my \$z2 = Math::Complex->make(); + print ((\$z2->Re() == 0) ? "ok $test\n" : "not ok $test\n"); +EOS + + $test++; + push @script, <<EOS; + print ((\$z2->Im() == 0) ? "ok $test\n" : "not ok $test\n"); +EOS + + $test++; + push @script, <<EOS; + my \$z3 = Math::Complex->emake(); + print ((\$z3->rho() == 0) ? "ok $test\n" : "not ok $test\n"); +EOS + + $test++; + push @script, <<EOS; + print ((\$z3->theta() == 0) ? "ok $test\n" : "not ok $test\n"); +} +EOS +} + +sub test_atan2 { + push @script, <<'EOS'; +print "# atan2() with some real arguments\n"; +EOS + my @real = (-1, 0, 1); + for my $x (@real) { + for my $y (@real) { + next if $x == 0 && $y == 0; + $test++; + push @script, <<EOS; +print ((Math::Complex::atan2($y, $x) == CORE::atan2($y, $x)) ? "ok $test\n" : "not ok $test\n"); +EOS + } + } + push @script, <<'EOS'; + print "# atan2() with some complex arguments\n"; +EOS + $test++; + push @script, <<EOS; + print (abs(atan2(0, cplx(0, 1))) < $eps ? "ok $test\n" : "not ok $test\n"); +EOS + $test++; + push @script, <<EOS; + print (abs(atan2(cplx(0, 1), 0) - \$pip2) < $eps ? "ok $test\n" : "not ok $test\n"); +EOS + $test++; + push @script, <<EOS; + print (abs(atan2(cplx(0, 1), cplx(0, 1)) - \$pip4) < $eps ? "ok $test\n" : "not ok $test\n"); +EOS + $test++; + push @script, <<EOS; + print (abs(atan2(cplx(0, 1), cplx(1, 1)) - cplx(0.553574358897045, 0.402359478108525)) < $eps ? "ok $test\n" : "not ok $test\n"); +EOS +} + +sub test_decplx { +} + +test_remake(); + +test_no_args(); + +test_atan2(); + +test_decplx(); + +print "1..$test\n"; +#print @script, "\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 == $expected) + || + (abs(Math::Complex->make($got) - Math::Complex->make($expected)) < $eps) + || + (abs($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' +|'(root(z, 8, 0)) ** 8':'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 |