7  200 ˆ¿Â 0ÁÀ"ˆl–ßi~” Še¶¥8 Eq¦®Õ1hßà ƒh¹ÂÁ0 0 ˆl–Ãa¾”êh¥8 ]¸î•1hßÄ „iö™_‹uÐb &=LV[(ÄÃ?÷ # # Complex numbers and associated mathematical functions # -- Raphael Manfredi Since Sep 1996 # -- Jarkko Hietaniemi Since Mar 1997 # -- Daniel S. Lewart Since Sep 1997 # package Math::Complex; { use 5.006; } use strict; our $VERSION = 1.59; use Config; our($Inf, $ExpInf); BEGIN { my %DBL_MAX = ( 4 => '1.70141183460469229e+38', 8 => '1.7976931348623157e+308', # AFAICT the 10, 12, and 16-byte long doubles # all have the same maximum. 10 => '1.1897314953572317650857593266280070162E+4932', 12 => '1.1897314953572317650857593266280070162E+4932', 16 => '1.1897314953572317650857593266280070162E+4932', ); my $nvsize = $Config{nvsize} || ($Config{uselongdouble} && $Config{longdblsize}) || $Config{doublesize}; die "Math::Complex: Could not figure out nvsize\n" unless defined $nvsize; die "Math::Complex: Cannot not figure out max nv (nvsize = $nvsize)\n" unless defined $DBL_MAX{$nvsize}; my $DBL_MAX = eval $DBL_MAX{$nvsize}; die "Math::Complex: Could not figure out max nv (nvsize = $nvsize)\n" unless defined $DBL_MAX; my $BIGGER_THAN_THIS = 1e30; # Must find something bigger than this. if ($^O eq 'unicosmk') { $Inf = $DBL_MAX; } else { local $SIG{FPE} = { }; local $!; # We do want an arithmetic overflow, Inf INF inf Infinity. for my $t ( 'exp(99999)', # Enough even with 128-bit long doubles. 'inf', 'Inf', 'INF', 'infinity', 'Infinity', 'INFINITY', '1e99999', ) { local $^W = 0; my $i = eval "$t+1.0"; if (defined $i && $i > $BIGGER_THAN_THIS) { $Inf = $i; last; } } $Inf = $DBL_MAX unless defined $Inf; # Oh well, close enough. die "Math::Complex: Could not get Infinity" unless $Inf > $BIGGER_THAN_THIS; $ExpInf = exp(99999); } # print "# On this machine, Inf = '$Inf'\n"; } use Scalar::Util qw(set_prototype); use warnings; no warnings 'syntax'; # To avoid the (_) warnings. BEGIN { # For certain functions that we override, in 5.10 or better # we can set a smarter prototype that will handle the lexical $_ # (also a 5.10+ feature). if ($] >= 5.010000) { set_prototype \&abs, '_'; set_prototype \&cos, '_'; set_prototype \&exp, '_'; set_prototype \&log, '_'; set_prototype \&sin, '_'; set_prototype \&sqrt, '_'; } } my $i; my %LOGN; # Regular expression for floating point numbers. # These days we could use Scalar::Util::lln(), I guess. my $gre = qr'\s*([\+\-]?(?:(?:(?:\d+(?:_\d+)*(?:\.\d*(?:_\d+)*)?|\.\d+(?:_\d+)*)(?:[eE][\+\-]?\d+(?:_\d+)*)?))|inf)'i; require Exporter; our @ISA = qw(Exporter); my @trig = qw( pi tan csc cosec sec cot cotan asin acos atan acsc acosec asec acot acotan sinh cosh tanh csch cosech sech coth cotanh asinh acosh atanh acsch acosech asech acoth acotanh ); our @EXPORT = (qw( i Re Im rho theta arg sqrt log ln log10 logn cbrt root cplx cplxe atan2 ), @trig); my @pi = qw(pi pi2 pi4 pip2 pip4 Inf); our @EXPORT_OK = @pi; our %EXPORT_TAGS = ( 'trig' => [@trig], 'pi' => [@pi], ); use overload '=' => \&_copy, '+=' => \&_plus, '+' => \&_plus, '-=' => \&_minus, '-' => \&_minus, '*=' => \&_multiply, '*' => \&_multiply, '/=' => \&_divide, '/' => \&_divide, '**=' => \&_power, '**' => \&_power, '==' => \&_numeq, '<=>' => \&_spaceship, 'neg' => \&_negate, '~' => \&_conjugate, 'abs' => \&abs, 'sqrt' => \&sqrt, 'exp' => \&exp, 'log' => \&log, 'sin' => \&sin, 'cos' => \&cos, 'atan2' => \&atan2, '""' => \&_stringify; # # Package "privates" # my %DISPLAY_FORMAT = ('style' => 'cartesian', 'polar_pretty_print' => 1); my $eps = 1e-14; # Epsilon # # Object attributes (internal): # cartesian [real, imaginary] -- cartesian form # polar [rho, theta] -- polar