| #!./perl |
| |
| # |
| # Regression tests for the Math::Complex pacakge |
| # -- Raphael Manfredi since Sep 1996 |
| # -- Jarkko Hietaniemi since Mar 1997 |
| # -- Daniel S. Lewart since Sep 1997 |
| |
| use Math::Complex 1.54; |
| |
| 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. |
| |
| $test++; |
| push @script, "{ my \$t=$test; ".q{ |
| my $a = Math::Complex->new(1); |
| my $b = $a; |
| $a += 2; |
| print "not " unless "$a" eq "3" && "$b" eq "1"; |
| print "ok $t\n"; |
| }."}"; |
| |
| 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' => 'polar', 'format' => "%.4g"); |
| EOS |
| |
| $test++; |
| push @script, <<EOS; |
| print "# j = \$j\n"; |
| print "not " unless "\$j" =~ /^\\[1,2\\.094\\]\$/; |
| 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]" |
| [1, 0.5]:"[1, 0.5]" |
| |
| { (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 |