Complex_C.pm - metacpan.org

## This file generated by InlineX::C2XS (version 0.17) using Inline::C (version 0.48)
package Math::Complex_C;

require Exporter;
*import = \&Exporter::import;
require DynaLoader;

use Math::Complex_C::Long; # 'long double _Complex' support.

use overload
    '**'    => \&_overload_pow,
    '*'     => \&_overload_mul,
    '+'     => \&_overload_add,
    '/'     => \&_overload_div,
    '-'     => \&_overload_sub,
    '**='   => \&_overload_pow_eq,
    '*='    => \&_overload_mul_eq,
    '+='    => \&_overload_add_eq,
    '/='    => \&_overload_div_eq,
    '-='    => \&_overload_sub_eq,
    'sqrt'  => \&_overload_sqrt,
    '=='    => \&_overload_equiv,
    '!='    => \&_overload_not_equiv,
    '!'     => \&_overload_not,
    'bool'  => \&_overload_true,
    '='     => \&_overload_copy,
    '""'    => \&_overload_string,
    'abs'   => \&_overload_abs,
    'exp'   => \&_overload_exp,
    'log'   => \&_overload_log,
    'sin'   => \&_overload_sin,
    'cos'   => \&_overload_cos,
    'atan2' => \&_overload_atan2;

our $VERSION = '0.08';
$VERSION = eval $VERSION;

DynaLoader::bootstrap Math::Complex_C $VERSION;

@Math::Complex_C::EXPORT = ();
@Math::Complex_C::EXPORT_OK = qw(
    create_c assign_c mul_c mul_c_nv mul_c_iv mul_c_uv div_c div_c_nv div_c_iv div_c_uv add_c 
    add_c_nv add_c_iv add_c_uv sub_c sub_c_nv sub_c_iv sub_c_uv real_c 
    imag_c arg_c abs_c conj_c acos_c asin_c atan_c cos_c sin_c tan_c acosh_c asinh_c atanh_c 
    cosh_c sinh_c tanh_c exp_c log_c sqrt_c proj_c pow_c get_nan get_inf is_nan is_inf is_neg_zero

    create_cl assign_cl mul_cl mul_c_nvl mul_c_ivl mul_c_uvl div_cl div_c_nvl div_c_ivl div_c_uvl add_cl 
    add_c_nvl add_c_ivl add_c_uvl sub_cl sub_c_nvl sub_c_ivl sub_c_uvl real_cl real_cl2LD imag_cl2LD LD2cl
    imag_cl arg_cl abs_cl conj_cl acos_cl asin_cl atan_cl cos_cl sin_cl tan_cl acosh_cl asinh_cl atanh_cl
    cosh_cl sinh_cl tanh_cl exp_cl log_cl sqrt_cl proj_cl pow_cl get_nanl get_infl is_nanl is_infl

    d_to_str d_to_strp ld_to_str ld_to_strp d_set_prec d_get_prec long_set_prec long_get_prec
    );

%Math::Complex_C::EXPORT_TAGS = (all => [qw(
    create_c assign_c mul_c mul_c_nv mul_c_iv mul_c_uv div_c div_c_nv div_c_iv div_c_uv add_c 
    add_c_nv add_c_iv add_c_uv sub_c sub_c_nv sub_c_iv sub_c_uv real_c 
    imag_c arg_c abs_c conj_c acos_c asin_c atan_c cos_c sin_c tan_c acosh_c asinh_c atanh_c 
    cosh_c sinh_c tanh_c exp_c log_c sqrt_c proj_c pow_c get_nan get_inf is_nan is_inf is_neg_zero

    create_cl assign_cl mul_cl mul_c_nvl mul_c_ivl mul_c_uvl div_cl div_c_nvl div_c_ivl div_c_uvl add_cl 
    add_c_nvl add_c_ivl add_c_uvl sub_cl sub_c_nvl sub_c_ivl sub_c_uvl real_cl real_cl2LD imag_cl2LD LD2cl
    imag_cl arg_cl abs_cl conj_cl acos_cl asin_cl atan_cl cos_cl sin_cl tan_cl acosh_cl asinh_cl atanh_cl
    cosh_cl sinh_cl tanh_cl exp_cl log_cl sqrt_cl proj_cl pow_cl get_nanl get_infl is_nanl is_infl

    d_to_str d_to_strp ld_to_str ld_to_strp d_set_prec d_get_prec long_set_prec long_get_prec
    )]);

*create_cl   = \&Math::Complex_C::Long::create_cl;
*assign_cl   = \&Math::Complex_C::Long::assign_cl;
*mul_cl      = \&Math::Complex_C::Long::mul_cl;
*mul_c_nvl   = \&Math::Complex_C::Long::mul_c_nvl;
*mul_c_ivl   = \&Math::Complex_C::Long::mul_c_ivl;
*mul_c_uvl   = \&Math::Complex_C::Long::mul_c_uvl ;
*div_cl      = \&Math::Complex_C::Long::div_cl;
*div_c_nvl   = \&Math::Complex_C::Long::div_c_nvl;
*div_c_ivl   = \&Math::Complex_C::Long::div_c_ivl;
*div_c_uvl   = \&Math::Complex_C::Long::div_c_uvl;
*add_cl      = \&Math::Complex_C::Long::add_cl;
*add_c_nvl   = \&Math::Complex_C::Long::add_c_nvl;
*add_c_ivl   = \&Math::Complex_C::Long::add_c_ivl;
*add_c_uvl   = \&Math::Complex_C::Long::add_c_uvl ;
*sub_cl      = \&Math::Complex_C::Long::sub_cl;
*sub_c_nvl   = \&Math::Complex_C::Long::sub_c_nvl;
*sub_c_ivl   = \&Math::Complex_C::Long::sub_c_ivl;
*sub_c_uvl   = \&Math::Complex_C::Long::sub_c_uvl;
*real_cl     = \&Math::Complex_C::Long::real_cl;
*imag_cl     = \&Math::Complex_C::Long::imag_cl;
*real_cl2LD  = \&Math::Complex_C::Long::real_cl2LD;
*imag_cl2LD  = \&Math::Complex_C::Long::imag_cl2LD;
*LD2cl       = \&Math::Complex_C::Long::LD2cl;
*arg_cl      = \&Math::Complex_C::Long::arg_cl;
*abs_cl      = \&Math::Complex_C::Long::abs_cl;
*conj_cl     = \&Math::Complex_C::Long::conj_cl;
*acos_cl     = \&Math::Complex_C::Long::acos_cl;
*asin_cl     = \&Math::Complex_C::Long::asin_cl;
*atan_cl     = \&Math::Complex_C::Long::atan_cl;
*cos_cl      = \&Math::Complex_C::Long::cos_cl;
*sin_cl      = \&Math::Complex_C::Long::sin_cl;
*tan_cl      = \&Math::Complex_C::Long::tan_cl;
*acosh_cl    = \&Math::Complex_C::Long::acosh_cl;
*asinh_cl    = \&Math::Complex_C::Long::asinh_cl;
*atanh_cl    = \&Math::Complex_C::Long::atanh_cl;
*cosh_cl     = \&Math::Complex_C::Long::cosh_cl;
*sinh_cl     = \&Math::Complex_C::Long::sinh_cl;
*tanh_cl     = \&Math::Complex_C::Long::tanh_cl;
*exp_cl      = \&Math::Complex_C::Long::exp_cl;
*log_cl      = \&Math::Complex_C::Long::log_cl;
*sqrt_cl     = \&Math::Complex_C::Long::sqrt_cl;
*proj_cl     = \&Math::Complex_C::Long::proj_cl;
*pow_cl      = \&Math::Complex_C::Long::pow_cl;
*get_nanl    = \&Math::Complex_C::Long::get_nanl;
*get_infl    = \&Math::Complex_C::Long::get_infl;
*is_nanl     = \&Math::Complex_C::Long::is_nanl;
*is_infl     = \&Math::Complex_C::Long::is_infl;
*ld_to_str   = \&Math::Complex_C::Long::ld_to_str;
*ld_to_strp  = \&Math::Complex_C::Long::ld_to_strp;
*long_get_prec = \&Math::Complex_C::Long::long_get_prec;
*long_set_prec = \&Math::Complex_C::Long::long_set_prec;

sub dl_load_flags {0} # Prevent DynaLoader from complaining and croaking

sub _overload_string {
    my($real, $imag) = (real_c($_[0]), imag_c($_[0]));
    my($r, $i) = d_to_str($_[0]);

    if($real == 0) {
      $r = $real =~ /^\-/ ? '-0' : '0';
    }
    elsif($real != $real) {
      $r = 'NaN';
    }
    elsif(($real / $real) != ($real / $real)) {
      $r = $real < 0 ? '-Inf' : 'Inf';
    }
    else {
      my @re = split /e/i, $r;
      while(substr($re[0], -1, 1) eq '0' && substr($re[0], -2, 1) ne '.') {
        chop $re[0];
      }
      $r = $re[0] . 'e' . $re[1];
    }

    if($imag == 0) {
      $i = $imag =~ /^\-/ ? '-0' : '0';
    }
    elsif($imag != $imag) {
      $i = 'NaN';
    }
    elsif(($imag / $imag) != ($imag / $imag)) {
      $i = $imag < 0 ? '-Inf' : 'Inf';
    }
    else {
      my @im = split /e/i, $i;
      while(substr($im[0], -1, 1) eq '0' && substr($im[0], -2, 1) ne '.') {
        chop $im[0];
      }
      $i = $im[0] . 'e' . $im[1];
    }

    return "(" . $r . " " . $i . ")";
}

sub new {

    my $ret = create_c();

    # This function caters for 2 possibilities:
    # 1) that 'new' has been called OOP style - in which 
    #    case there will be a maximum of 3 args
    # 2) that 'new' has been called as a function - in
    #    which case there will be a maximum of 2 args.
    # If there are no args, then we just want to return a
    # Math::Complex_C object

    if(!@_) {return $ret}
   
    if(@_ > 3) {die "Too many arguments supplied to new()"}

    # If 'new' has been called OOP style, the first arg is the string
    # "Math::Complex_C" which we don't need - so let's remove it.

    if($_[0] eq "Math::Complex_C") {
      shift;
      if(!@_) {return $ret}
    }

    if(@_ > 2) {die "Bad argument list supplied to new()"} 

    if(@_ == 2) {assign_c($ret, $_[0], $_[1])}
    else {assign_c($ret, $_[0], 0)}

    return $ret;    
}

1;

__END__

=head1 NAME

Math::Complex_C - perl interface to C's complex.h functions.

=head1 DEPENDENCIES

   In order to compile this module, a C compiler that provides
   complex.h is needed.

=head1 DESCRIPTION
   This module wraps the 'double _Complex' type (as a Math::Complex_C
   object) and the 'long double _Complex' type (as a Math::Complex_C::Long
   object).


   use warnings;
   use strict;
   use Math::Complex_C qw(:all);
   my $c =    Math::Complex_C->new(12.5, 1125); # 'double _Complex' type
   my $root = Math::Complex_C->new();
   my $cl = Math::Complex_C::Long->new(5.9,1.1); # 'long double _Complex'
   my $rootl = Math::Complex_C::Long->new();
   sqrt_c($root, $c);
   sqrt_cl($rootl, $cl);
   print "Square root of $c is $root\n";
   print "Square root of $c1 is $rootl\n";

   On many perls, the values printed out by the above code will be
   identical - see the README for some elaboration.

   Note that Math::Complex_C and Math::Complex_C::Long objects use
   different functions (sqrt_c vs sqrt_cl, in the above example).

   See also the Math::Complex_C test suite for some (simplistic) examples
   of usage.

=head1 FUNCTIONS

   $rop = Math::Complex_C->new([$re, [$im]]);
   $rop = Math::Complex_C::new([$re, [$im]]);
   $rop = new Math::Complex_C([$re, [$im]]);
   $ropl = Math::Complex_C::Long->new([$re, [$im]]);
   $ropl = Math::Complex_C::Long::new([$re, [$im]]);
   $ropl = new Math::Complex_C::Long([$re, [$im]]);
    $rop/$ropl is a Math::Complex_C/Math::Complex_C::Long object;
    $re and $im are the real and imaginary values (respectively) that $rop
    holds. They can be an integer (signed or unsigned) or a floating point
    value.Integer values (IV/UV) will be converted to floating point (NV)
    before being assigned.
    Note that the two arguments ($re $im) are optional - ie can be omitted.
    If no arguments are supplied to new, then $rop will be assigned NaN for
    both the real and imaginary parts.
    If only one argument is supplied, then $rop will be assigned that value
    for the real part, and 0 for the imaginary part.
    
   $rop = create_c();
   $ropl = create_cl();
    $rop/$ropl is a Math::Complex_C/Math::Complex_C::Long object (created
    with both real and imaginary values set to NaN).

   assign_c($rop, $re, $im);
   assign_cl($ropl, $re, $im); 
    The real part of $rop/$ropl is set to the value of $re, the imaginary
    part is set to the value of $im.
    $re and $im can be an integer (signed or unsigned) or a floating point
    value. Integer values (IV/UV) will be converted to floating point (NV)
    before being assigned.

   LD2cl($ropl, $r_ld, $i_ld); #$r_ld & $i_ld are Math::LongDouble objects
    Assign the real and imaginary part of $ropl from the Math::LongDouble
    objects $r_ld and $i_ld (respectively).

   mul_c($rop, $op1, $op2);
   mul_c_iv($rop, $op1, $si);
   mul_c_uv($rop, $op1, $ui);
   mul_c_nv($rop, $op1, $nv);
   mul_cl($ropl, $op1, $op2);
   mul_c_ivl($ropl, $op1, $si);
   mul_c_uvl($ropl, $op1, $ui);
   mul_c_nvl($ropl, $op1, $nv);
    Multiply $op1 by the 3rd arg, and store the result in $rop/$ropl.
    The "3rd arg" is (respectively, from the top) a Math::Complex_C object,
    a signed integer value (IV), an unsigned integer value (UV), and a
    floating point value (NV).

   add_c($rop, $op1, $op2);
   add_c_iv($rop, $op1, $si);
   add_c_uv($rop, $op1, $ui);
   add_c_nv($rop, $op1, $nv);
   add_cl($ropl, $op1, $op2);
   add_c_ivl($ropl, $op1, $si);
   add_c_uvl($ropl, $op1, $ui);
   add_c_nvl($ropl, $op1, $nv);
    As for mul_c(), etc., but performs addition.

   div_c($rop, $op1, $op2);
   div_c_iv($rop, $op1, $si);
   div_c_uv($rop, $op1, $ui);
   div_c_nv($rop, $op1, $nv);
   div_cl($ropl, $op1, $op2);
   div_c_ivl($ropl, $op1, $si);
   div_c_uvl($ropl, $op1, $ui);
   div_c_nvl($ropl, $op1, $nv);
    As for mul_c(), etc., but performs division.

   sub_c($rop, $op1, $op2);
   sub_c_iv($rop, $op1, $si);
   sub_c_uv($rop, $op1, $ui);
   sub_c_nv($rop, $op1, $nv);
   sub_cl($ropl, $op1, $op2);
   sub_c_ivl($ropl, $op1, $si);
   sub_c_uvl($ropl, $op1, $ui);
   sub_c_nvl($ropl, $op1, $nv);
    As for mul_c(), etc., but performs subtraction.

   $nv = real_c($op);
   $nv = real_cl($op);
    Returns the (floating point) value of the real component of $op.
    Wraps C's 'creal/creall' function.

   $nv = imag_c($op);
   $nv = imag_cl($op);
    Returns the (floating point) value of the imaginary component of $op.
    Wraps C's 'cimag/cimagl' function.

   real_cl2LD($ld, $opl); # $ld is a Math::LongDouble object
   imag_cl2LD($ld, $opl); # $ld is a Math::LongDouble object
    Set the Math::LongDouble object $ld to the value of $opl's real/imag
    value (using creall and cimagl to obtain $opl's real and imag values.

   $nv = arg_c($op);
   $nv = arg_cl($op);
    Returns the (floating point) value of the argument of $op.
    Wraps C's 'carg/cargl' function.

   $nv = abs_c($op);
   $nv = abs_cl($op);
    Returns the (floating point) absolute value of $op.
    Wraps C's 'cabs/cabsl' function.

   conj_c($rop, $op);
   conj_cl($ropl, $op);
    Sets $rop/$ropl to the conjugate of $op.
    Wraps C's 'conj/conjl' function.

   acos_c($rop, $op);
   acos_cl($ropl, $op);
    Sets $rop/$ropl to acos($op).
    Wraps C's 'cacos/cacosl' function.

   asin_c($rop, $op);
   asin_cl($ropl, $op);
    Sets $rop/$ropl to asin($op).
    Wraps C's 'casin/casinl' function.

   atan_c($rop, $op);
   atan_cl($ropl, $op);
    Sets $rop/$ropl to atan($op).
    Wraps C's 'catan/catanl' function.

   cos_c($rop, $op);
   cos_cl($ropl, $op);
    Sets $rop/$ropl to cos($op).
    Wraps C's 'ccos/ccosl' function.

   sin_c($rop, $op);
   sin_cl($ropl, $op);
    Sets $rop/$ropl to sin($op).
    Wraps C's 'csin/csinl' function.

   tan_c($rop, $op);
   tan_cl($ropl, $op);
    Sets $rop/$ropl to tan($op).
    Wraps C's 'ctan/ctanl' function.

   acosh_c($rop, $op);
   acosh_cl($ropl, $op);
    Sets $rop/$ropl to acosh($op).
    Wraps C's 'cacosh/cacoshl' function.

   asinh_c($rop, $op);
   asinh_cl($ropl, $op);
    Sets $rop/$ropl to asinh($op).
    Wraps C's 'casinh/casinhl' function.

   atanh_c($rop, $op);
   atanh_cl($ropl, $op);
    Sets $rop/$ropl to atanh($op).
    Wraps C's 'catanh/catanhl' function.

   cosh_c($rop, $op);
   cosh_cl($ropl, $op);
    Sets $rop/$ropl to cosh($op).
    Wraps C's 'ccosh/ccoshl' function.

   sinh_c($rop, $op);
   sinh_cl($rop, $op);
    Sets $rop/$ropl to sinh($op).
    Wraps C's 'csinh/csinhl' function.

   tanh_c($rop, $op);
   tanh_cl($ropl, $op);
    Sets $rop/$ropl to tanh($op).
    Wraps C's 'ctanh/ctanhl' function.

   exp_c($rop, $op);
   exp_cl($rop1, $op);
    Sets $rop/$ropl to e ** $op.
    Wraps C's 'cexp/cexpl' function.

   log_c($rop, $op);
   log_cl($ropl, $op);
    Sets $rop/$ropl to log($op).
    Wraps C's 'clog/clogl' function.

   pow_c($rop, $op1, $op2);
   pow_cl($ropl, $op1, $op2);
    Sets $rop/$ropl to $op1 ** $op2.
    Wraps C's 'cpow/cpowl' function.

   sqrt_c($rop, $op);
   sqrt_cl($ropl, $op);
    Sets $rop/$ropl to sqrt($op).
    Wraps C's 'csqrt/csqrtl' function.

   proj_c($rop, $op);
   proj_cl($ropl, $op);
    Sets $rop/$ropl to a projection of $op onto the Riemann sphere.
    Wraps C's 'cproj/cprojl' function.

   $rop = get_nan();
   $ropl = get_nanl();
    Sets $rop/$ropl to NaN.

   $rop = get_inf();
   $ropl = get_infl();
    Sets $rop/$ropl to Inf.

   $bool = is_nan($op);
   $bool = is_nanl($op);
    Returns true if $op is a NaN - else returns false

   $bool = is_inf($op);
   $bool = is_infl($op);
    Returns true if $op is -Inf or +Inf - else returns false

   $bool = is_neg_zero($nv);
    Returns true if $nv is -0. Else returns false - hence the function
    returns false (and warns) if $nv is not an NV (since only an NV 
    can be -0).
    Perl can't be relied upon to print the '-' sign if the NV is -0.
    For example, 5.12.0 *will* print it, but 5.14.0 won't.
    Therefore, if we care about the sign, we need to check using this
    XSub.

=head1 OUTPUT FUNCTIONS

   Default precision for output of Math::Complex_C objects is 15
   decimal digits.
   Default precision for output of Math::Complex_C::Long objects
   is 18 decimal digits.
   These defaults can be altered using d_set_prec/long_set_prec
   (see below).

   d_set_prec($si);       # for Math::Complex_C objects.
   long_set_prec($si);    # for Math::Complex_C::Long objects.
   $si = d_get_prec();    # for Math::Complex_C objects.
   $si = long_get_prec(); # for Math::Complex_C::Long objects.
    Set/get the precision of output values

   $str = d_to_str($op);  # for Math::Complex_C objects.
   $str = ld_to_str($op); # for Math::Complex_C::Long objects.
    Express the value of $op in a string of the form "(real imag)".
    Both "real" and "imag" will be expressed in scientific 
    notation, to the precision returned by by the relevant
    *_get_prec() function (above). Use the relevant *_set_prec
    function to alter this precision.
    The representation of Infs and NaNs will be platform-dependent.

   $str = d_to_strp($op, $si);  # for Math::Complex_C objects.
   $str = ld_to_strp($op, $si); # for Math::Complex_C::Long objects.
    As for d_to_str/ld_to_str, except that the precision setting for
    the output value is set by the 2nd arg (which must be greater
    than 1).
    

=head1 OPERATOR OVERLOADING

   Both Math::Complex_C and Math::Complex_C::Long overload the
   following operators:
    *, +, /, -, **,
    *=, +=, /=, -=, **=,
    !, bool,
    ==, !=,
    =, "",
    abs, exp, log, cos, sin, atan2, sqrt

    Cross-class overloading is not implemented - that is, you
    cannot use both a Math::Complex_C::Long object and a 
    Math::Complex_C object in the same overloaded operation.
    You can operate on these objects using only an IV, UV, NV or
    another object of the same type. (PV values are not allowed.)

    Note: For the purposes of the overloaded 'not', '!' and 'bool'
    operators, a "false" Math::Complex_C object is one with real 
    and imaginary parts that are both "false" - where "false"
    currently means either 0 (including -0) or NaN.
    (A "true" Math::Complex_C object is, of course, simply one
    that is not "false".)

    If the value passed to the overloaded '**', '**=' or
    'equivalence' operators is an IV/UV (integer), it will be
    converted to an NV (floating point value) before the calculation
    is performed.

=head1 LICENSE

   This module is free software; you may redistribute it and/or 
   modify it under the same terms as Perl itself.
   Copyright 2011, 2013 Sisyphus.

=head1 AUTHOR

   Sisyphus <sisyphus at(@) cpan dot (.) org>

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