mirror of
https://github.com/freebsd/freebsd-src
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965 lines
25 KiB
Perl
Executable file
965 lines
25 KiB
Perl
Executable file
#!./perl
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# $RCSfile: complex.t,v $
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#
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# Regression tests for the Math::Complex pacakge
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# -- Raphael Manfredi since Sep 1996
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# -- Jarkko Hietaniemi since Mar 1997
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# -- Daniel S. Lewart since Sep 1997
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BEGIN {
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chdir 't' if -d 't';
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unshift @INC, '../lib';
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}
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use Math::Complex;
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my $VERSION = sprintf("%s", q$Id: complex.t,v 1.9 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.d+)/);
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my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
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$test = 0;
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$| = 1;
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my @script = (
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'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' .
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"\n\n"
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);
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my $eps = 1e-13;
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if ($^O eq 'unicos') { # For some reason root() produces very inaccurate
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$eps = 1e-11; # results in Cray UNICOS, and occasionally also
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} # cos(), sin(), cosh(), sinh(). The division
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# of doubles is the current suspect.
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while (<DATA>) {
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s/^\s+//;
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next if $_ eq '' || /^\#/;
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chomp;
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$test_set = 0; # Assume not a test over a set of values
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if (/^&(.+)/) {
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$op = $1;
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next;
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}
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elsif (/^\{(.+)\}/) {
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set($1, \@set, \@val);
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next;
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}
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elsif (s/^\|//) {
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$test_set = 1; # Requests we loop over the set...
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}
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my @args = split(/:/);
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if ($test_set == 1) {
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my $i;
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for ($i = 0; $i < @set; $i++) {
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# complex number
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$target = $set[$i];
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# textual value as found in set definition
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$zvalue = $val[$i];
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test($zvalue, $target, @args);
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}
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} else {
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test($op, undef, @args);
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}
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}
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#
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sub test_mutators {
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my $op;
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$test++;
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push(@script, <<'EOT');
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{
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my $z = cplx( 1, 1);
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$z->Re(2);
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$z->Im(3);
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print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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print 'not ' unless Re($z) == 2 and Im($z) == 3;
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EOT
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push(@script, qq(print "ok $test\\n"}\n));
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$test++;
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push(@script, <<'EOT');
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{
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my $z = cplx( 1, 1);
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$z->abs(3 * sqrt(2));
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print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and
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(arg($z) - pi / 4 ) < $eps and
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(Re($z) - 3 ) < $eps and
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(Im($z) - 3 ) < $eps;
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EOT
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push(@script, qq(print "ok $test\\n"}\n));
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$test++;
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push(@script, <<'EOT');
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{
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my $z = cplx( 1, 1);
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$z->arg(-3 / 4 * pi);
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print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and
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(abs($z) - sqrt(2) ) < $eps and
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(Re($z) + 1 ) < $eps and
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(Im($z) + 1 ) < $eps;
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EOT
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push(@script, qq(print "ok $test\\n"}\n));
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}
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test_mutators();
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my $constants = '
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my $i = cplx(0, 1);
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my $pi = cplx(pi, 0);
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my $pii = cplx(0, pi);
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my $pip2 = cplx(pi/2, 0);
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my $zero = cplx(0, 0);
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';
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push(@script, $constants);
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# test the divbyzeros
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sub test_dbz {
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for my $op (@_) {
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$test++;
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push(@script, <<EOT);
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eval '$op';
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(\$bad) = (\$@ =~ /(.+)/);
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print "# $test op = $op divbyzero? \$bad...\n";
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print 'not ' unless (\$@ =~ /Division by zero/);
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EOT
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push(@script, qq(print "ok $test\\n";\n));
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}
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}
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# test the logofzeros
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sub test_loz {
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for my $op (@_) {
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$test++;
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push(@script, <<EOT);
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eval '$op';
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(\$bad) = (\$@ =~ /(.+)/);
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print "# $test op = $op logofzero? \$bad...\n";
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print 'not ' unless (\$@ =~ /Logarithm of zero/);
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EOT
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push(@script, qq(print "ok $test\\n";\n));
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}
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}
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test_dbz(
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'i/0',
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'acot(0)',
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'acot(+$i)',
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# 'acoth(-1)', # Log of zero.
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'acoth(0)',
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'acoth(+1)',
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'acsc(0)',
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'acsch(0)',
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'asec(0)',
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'asech(0)',
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'atan(-$i)',
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'atan($i)',
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# 'atanh(-1)', # Log of zero.
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'atanh(+1)',
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'cot(0)',
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'coth(0)',
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'csc(0)',
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'tan($pip2)',
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'csch(0)',
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'tan($pip2)',
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);
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test_loz(
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'log($zero)',
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'acot(-$i)',
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'atanh(-1)',
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'acoth(-1)',
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);
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# test the bad roots
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sub test_broot {
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for my $op (@_) {
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$test++;
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push(@script, <<EOT);
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eval 'root(2, $op)';
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(\$bad) = (\$@ =~ /(.+)/);
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print "# $test op = $op badroot? \$bad...\n";
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print 'not ' unless (\$@ =~ /root must be/);
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EOT
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push(@script, qq(print "ok $test\\n";\n));
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}
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}
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test_broot(qw(-3 -2.1 0 0.99));
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sub test_display_format {
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push @script, <<EOS;
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my \$j = (root(1,3))[1];
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\$j->display_format('polar');
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EOS
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$test++;
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push @script, <<EOS;
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print "# display_format polar?\n";
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print "not " unless \$j->display_format eq 'polar';
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print "ok $test\n";
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EOS
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$test++;
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push @script, <<EOS;
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print "# j = \$j\n";
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print "not " unless "\$j" eq "[1,2pi/3]";
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print "ok $test\n";
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my %display_format;
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%display_format = \$j->display_format;
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EOS
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$test++;
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push @script, <<EOS;
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print "# display_format{style} polar?\n";
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print "not " unless \$display_format{style} eq 'polar';
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print "ok $test\n";
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EOS
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$test++;
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push @script, <<EOS;
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print "# keys %display_format == 2?\n";
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print "not " unless keys %display_format == 2;
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print "ok $test\n";
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\$j->display_format('style' => 'cartesian', 'format' => '%.5f');
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EOS
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$test++;
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push @script, <<EOS;
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print "# j = \$j\n";
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print "not " unless "\$j" eq "-0.50000+0.86603i";
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print "ok $test\n";
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%display_format = \$j->display_format;
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EOS
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$test++;
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push @script, <<EOS;
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print "# display_format{format} %.5f?\n";
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print "not " unless \$display_format{format} eq '%.5f';
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print "ok $test\n";
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EOS
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$test++;
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push @script, <<EOS;
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print "# keys %display_format == 3?\n";
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print "not " unless keys %display_format == 3;
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print "ok $test\n";
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\$j->display_format('format' => undef);
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EOS
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$test++;
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push @script, <<EOS;
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print "# j = \$j\n";
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print "not " unless "\$j" =~ /^-0\\.5\\+0.86602540\\d+i\$/;
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print "ok $test\n";
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\$j->display_format('style' => 'polar', 'polar_pretty_print' => 0);
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EOS
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$test++;
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push @script, <<EOS;
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print "# j = \$j\n";
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print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/;
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print "ok $test\n";
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\$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
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EOS
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$test++;
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push @script, <<EOS;
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print "# j = \$j\n";
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print "not " unless "\$j" eq "(-0.5)+(0.86603)i";
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print "ok $test\n";
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EOS
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}
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test_display_format();
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print "1..$test\n";
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eval join '', @script;
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die $@ if $@;
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sub abop {
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my ($op) = @_;
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push(@script, qq(print "# $op=\n";));
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}
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sub test {
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my ($op, $z, @args) = @_;
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my ($baop) = 0;
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$test++;
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my $i;
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$baop = 1 if ($op =~ s/;=$//);
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for ($i = 0; $i < @args; $i++) {
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$val = value($args[$i]);
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push @script, "\$z$i = $val;\n";
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}
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if (defined $z) {
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$args = "'$op'"; # Really the value
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$try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
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push @script, "\$res = $try; ";
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push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
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} else {
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my ($try, $args);
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if (@args == 2) {
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$try = "$op \$z0";
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$args = "'$args[0]'";
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} else {
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$try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
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$args = "'$args[0]', '$args[1]'";
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}
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push @script, "\$res = $try; ";
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push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
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if (@args > 2 and $baop) { # binary assignment ops
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$test++;
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# check the op= works
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push @script, <<EOB;
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{
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my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
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my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
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my \$zb = cplx(\$z1r, \$z1i);
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\$za $op= \$zb;
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my (\$zbr, \$zbi) = \@{\$zb->cartesian};
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check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
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EOB
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$test++;
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# check that the rhs has not changed
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push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
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push @script, qq(print "ok $test\\n";\n);
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push @script, "}\n";
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}
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}
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}
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sub set {
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my ($set, $setref, $valref) = @_;
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@{$setref} = ();
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@{$valref} = ();
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my @set = split(/;\s*/, $set);
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my @res;
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my $i;
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for ($i = 0; $i < @set; $i++) {
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push(@{$valref}, $set[$i]);
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my $val = value($set[$i]);
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push @script, "\$s$i = $val;\n";
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push @{$setref}, "\$s$i";
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}
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}
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sub value {
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local ($_) = @_;
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if (/^\s*\((.*),(.*)\)/) {
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return "cplx($1,$2)";
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}
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elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
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return "cplx($1,0)";
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}
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elsif (/^\s*\[(.*),(.*)\]/) {
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return "cplxe($1,$2)";
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}
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elsif (/^\s*'(.*)'/) {
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my $ex = $1;
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$ex =~ s/\bz\b/$target/g;
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$ex =~ s/\br\b/abs($target)/g;
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$ex =~ s/\bt\b/arg($target)/g;
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$ex =~ s/\ba\b/Re($target)/g;
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$ex =~ s/\bb\b/Im($target)/g;
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return $ex;
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}
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elsif (/^\s*"(.*)"/) {
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return "\"$1\"";
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}
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return $_;
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}
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sub check {
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my ($test, $try, $got, $expected, @z) = @_;
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print "# @_\n";
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if ("$got" eq "$expected"
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||
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($expected =~ /^-?\d/ && $got == $expected)
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||
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(abs($got - $expected) < $eps)
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) {
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print "ok $test\n";
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} else {
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print "not ok $test\n";
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my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
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print "# '$try' expected: '$expected' got: '$got' for $args\n";
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}
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}
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sub addsq {
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my ($z1, $z2) = @_;
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return ($z1 + i*$z2) * ($z1 - i*$z2);
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}
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sub subsq {
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my ($z1, $z2) = @_;
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return ($z1 + $z2) * ($z1 - $z2);
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}
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__END__
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&+;=
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(3,4):(3,4):(6,8)
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(-3,4):(3,-4):(0,0)
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(3,4):-3:(0,4)
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1:(4,2):(5,2)
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[2,0]:[2,pi]:(0,0)
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&++
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(2,1):(3,1)
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&-;=
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(2,3):(-2,-3)
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[2,pi/2]:[2,-(pi)/2]
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2:[2,0]:(0,0)
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[3,0]:2:(1,0)
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3:(4,5):(-1,-5)
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(4,5):3:(1,5)
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(2,1):(3,5):(-1,-4)
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&--
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(1,2):(0,2)
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[2,pi]:[3,pi]
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&*;=
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(0,1):(0,1):(-1,0)
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(4,5):(1,0):(4,5)
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[2,2*pi/3]:(1,0):[2,2*pi/3]
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2:(0,1):(0,2)
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(0,1):3:(0,3)
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(0,1):(4,1):(-1,4)
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(2,1):(4,-1):(9,2)
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&/;=
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(3,4):(3,4):(1,0)
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(4,-5):1:(4,-5)
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1:(0,1):(0,-1)
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(0,6):(0,2):(3,0)
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(9,2):(4,-1):(2,1)
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[4,pi]:[2,pi/2]:[2,pi/2]
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[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
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&**;=
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(2,0):(3,0):(8,0)
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(3,0):(2,0):(9,0)
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(2,3):(4,0):(-119,-120)
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(0,0):(1,0):(0,0)
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(0,0):(2,3):(0,0)
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(1,0):(0,0):(1,0)
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(1,0):(1,0):(1,0)
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(1,0):(2,3):(1,0)
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(2,3):(0,0):(1,0)
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(2,3):(1,0):(2,3)
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(0,0):(0,0):(1,0)
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&Re
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(3,4):3
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(-3,4):-3
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[1,pi/2]:0
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&Im
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(3,4):4
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(3,-4):-4
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[1,pi/2]:1
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&abs
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(3,4):5
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(-3,4):5
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&arg
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[2,0]:0
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[-2,0]:pi
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&~
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(4,5):(4,-5)
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(-3,4):(-3,-4)
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[2,pi/2]:[2,-(pi)/2]
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&<
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(3,4):(1,2):0
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(3,4):(3,2):0
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(3,4):(3,8):1
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(4,4):(5,129):1
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&==
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(3,4):(4,5):0
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(3,4):(3,5):0
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(3,4):(2,4):0
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(3,4):(3,4):1
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|
&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
|