package Math::MPC;
use strict;
use warnings;
use constant MPC_RNDNN => 0;
use constant MPC_RNDZN => 1;
use constant MPC_RNDUN => 2;
use constant MPC_RNDDN => 3;
use constant MPC_RNDNZ => 16;
use constant MPC_RNDZZ => 17;
use constant MPC_RNDUZ => 18;
use constant MPC_RNDDZ => 19;
use constant MPC_RNDNU => 32;
use constant MPC_RNDZU => 33;
use constant MPC_RNDUU => 34;
use constant MPC_RNDDU => 35;
use constant MPC_RNDND => 48;
use constant MPC_RNDZD => 49;
use constant MPC_RNDUD => 50;
use constant MPC_RNDDD => 51;
use constant _UOK_T => 1;
use constant _IOK_T => 2;
use constant _NOK_T => 3;
use constant _POK_T => 4;
use constant _MATH_MPFR_T => 5;
use constant _MATH_GMPf_T => 6;
use constant _MATH_GMPq_T => 7;
use constant _MATH_GMPz_T => 8;
use constant _MATH_GMP_T => 9;
use constant _MATH_MPC_T => 10;
use subs qw(MPC_VERSION MPC_VERSION_MAJOR MPC_VERSION_MINOR
MPC_VERSION_PATCHLEVEL MPC_VERSION_STRING
MPC_VERSION MPC_VERSION_NUM);
use overload
'+' => \&overload_add,
'-' => \&overload_sub,
'*' => \&overload_mul,
'/' => \&overload_div,
'**' => \&overload_pow,
'+=' => \&overload_add_eq,
'-=' => \&overload_sub_eq,
'*=' => \&overload_mul_eq,
'/=' => \&overload_div_eq,
'**=' => \&overload_pow_eq,
'==' => \&overload_equiv,
'!=' => \&overload_not_equiv,
'!' => \&overload_not,
'=' => \&overload_copy,
'""' => \&overload_string,
'abs' => \&overload_abs,
'bool' => \&overload_true,
'exp' => \&overload_exp,
'log' => \&overload_log,
'sqrt' => \&overload_sqrt,
'sin' => \&overload_sin,
'cos' => \&overload_cos,
'atan2'=> \&overload_atan2;
require Exporter;
*import = \&Exporter::import;
require DynaLoader;
@Math::MPC::EXPORT_OK = qw(
MPC_RNDNN MPC_RNDND MPC_RNDNU MPC_RNDNZ MPC_RNDDN MPC_RNDUN MPC_RNDZN MPC_RNDDD
MPC_RNDDU MPC_RNDDZ MPC_RNDZD MPC_RNDUD MPC_RNDUU MPC_RNDUZ MPC_RNDZU MPC_RNDZZ
MPC_VERSION_MAJOR MPC_VERSION_MINOR MPC_VERSION_PATCHLEVEL MPC_VERSION_STRING
MPC_VERSION MPC_VERSION_NUM Rmpc_get_version
Rmpc_set_default_rounding_mode Rmpc_get_default_rounding_mode
Rmpc_set_prec Rmpc_set_default_prec Rmpc_get_default_prec
Rmpc_set_default_prec2 Rmpc_get_default_prec2
Rmpc_set_re_prec Rmpc_set_im_prec
Rmpc_get_prec Rmpc_get_prec2 Rmpc_get_re_prec Rmpc_get_im_prec
Rmpc_get_dc Rmpc_get_ldc
RMPC_RE RMPC_IM RMPC_INEX_RE RMPC_INEX_IM
Rmpc_clear Rmpc_clear_ptr Rmpc_clear_mpc
Rmpc_deref4 Rmpc_get_str
Rmpc_init2 Rmpc_init3
Rmpc_init2_nobless Rmpc_init3_nobless
Rmpc_strtoc Rmpc_set_str
Rmpc_set Rmpc_set_ui Rmpc_set_si Rmpc_set_d Rmpc_set_uj Rmpc_set_sj Rmpc_set_ld
Rmpc_set_z Rmpc_set_q Rmpc_set_f Rmpc_set_fr
Rmpc_set_z_z Rmpc_set_q_q Rmpc_set_f_f
Rmpc_set_ui_ui Rmpc_set_ui_si Rmpc_set_ui_d Rmpc_set_ui_uj Rmpc_set_ui_sj Rmpc_set_ui_ld Rmpc_set_ui_fr
Rmpc_set_si_ui Rmpc_set_si_si Rmpc_set_si_d Rmpc_set_si_uj Rmpc_set_si_sj Rmpc_set_si_ld Rmpc_set_si_fr
Rmpc_set_d_ui Rmpc_set_d_si Rmpc_set_d_d Rmpc_set_d_uj Rmpc_set_d_sj Rmpc_set_d_ld Rmpc_set_d_fr
Rmpc_set_uj_ui Rmpc_set_uj_si Rmpc_set_uj_d Rmpc_set_uj_uj Rmpc_set_uj_sj Rmpc_set_uj_ld Rmpc_set_uj_ld Rmpc_set_uj_fr
Rmpc_set_sj_ui Rmpc_set_sj_si Rmpc_set_sj_d Rmpc_set_sj_uj Rmpc_set_sj_sj Rmpc_set_sj_ld Rmpc_set_sj_fr
Rmpc_set_ld_ui Rmpc_set_ld_si Rmpc_set_ld_uj Rmpc_set_ld_d Rmpc_set_ld_sj Rmpc_set_ld_ld Rmpc_set_ld_fr
Rmpc_set_fr_ui Rmpc_set_fr_si Rmpc_set_fr_d Rmpc_set_fr_uj Rmpc_set_fr_sj Rmpc_set_fr_ld Rmpc_set_fr_fr
Rmpc_set_f_ui Rmpc_set_q_ui Rmpc_set_z_ui Rmpc_set_ui_f Rmpc_set_ui_q Rmpc_set_ui_z
Rmpc_set_f_si Rmpc_set_q_si Rmpc_set_z_si Rmpc_set_si_f Rmpc_set_si_q Rmpc_set_si_z
Rmpc_set_f_d Rmpc_set_q_d Rmpc_set_z_d Rmpc_set_d_f Rmpc_set_d_q Rmpc_set_d_z
Rmpc_set_f_uj Rmpc_set_q_uj Rmpc_set_z_uj Rmpc_set_uj_f Rmpc_set_uj_q Rmpc_set_uj_z
Rmpc_set_f_sj Rmpc_set_q_sj Rmpc_set_z_sj Rmpc_set_sj_f Rmpc_set_sj_q Rmpc_set_sj_z
Rmpc_set_f_ld Rmpc_set_q_ld Rmpc_set_z_ld Rmpc_set_ld_f Rmpc_set_ld_q Rmpc_set_ld_z
Rmpc_set_f_q Rmpc_set_q_f Rmpc_set_f_z Rmpc_set_z_f Rmpc_set_z_q Rmpc_set_q_z
Rmpc_set_f_fr Rmpc_set_q_fr Rmpc_set_z_fr Rmpc_set_fr_f Rmpc_set_fr_q Rmpc_set_fr_z
Rmpc_set_dc Rmpc_set_ldc
Rmpc_add Rmpc_add_ui Rmpc_add_fr
Rmpc_sub Rmpc_sub_ui Rmpc_ui_sub Rmpc_ui_ui_sub
Rmpc_mul Rmpc_mul_ui Rmpc_mul_si Rmpc_mul_fr Rmpc_mul_i Rmpc_sqr Rmpc_mul_2exp
Rmpc_div Rmpc_div_ui Rmpc_ui_div Rmpc_div_fr Rmpc_sqrt Rmpc_div_2exp
Rmpc_neg Rmpc_abs Rmpc_conj Rmpc_norm Rmpc_exp Rmpc_log
Rmpc_cmp Rmpc_cmp_si Rmpc_cmp_si_si
Rmpc_out_str Rmpc_inp_str c_string r_string i_string
TRmpc_out_str TRmpc_inp_str
Rmpc_sin Rmpc_cos Rmpc_sin_cos Rmpc_tan Rmpc_sinh Rmpc_cosh Rmpc_tanh
Rmpc_asin Rmpc_acos Rmpc_atan Rmpc_asinh Rmpc_acosh Rmpc_atanh
Rmpc_real Rmpc_imag Rmpc_arg Rmpc_proj
Rmpc_pow Rmpc_pow_d Rmpc_pow_ld Rmpc_pow_si Rmpc_pow_ui Rmpc_pow_z Rmpc_pow_fr
Rmpc_set_nan Rmpc_swap
Rmpc_mul_sj Rmpc_mul_ld Rmpc_mul_d Rmpc_div_sj Rmpc_sj_div Rmpc_div_ld Rmpc_ld_div Rmpc_div_d Rmpc_d_div
);
$Math::MPC::VERSION = '0.93';
DynaLoader::bootstrap Math::MPC $Math::MPC::VERSION;
%Math::MPC::EXPORT_TAGS =(mpc => [qw(
MPC_RNDNN MPC_RNDND MPC_RNDNU MPC_RNDNZ MPC_RNDDN MPC_RNDUN MPC_RNDZN MPC_RNDDD
MPC_RNDDU MPC_RNDDZ MPC_RNDZD MPC_RNDUD MPC_RNDUU MPC_RNDUZ MPC_RNDZU MPC_RNDZZ
MPC_VERSION_MAJOR MPC_VERSION_MINOR MPC_VERSION_PATCHLEVEL MPC_VERSION_STRING
MPC_VERSION MPC_VERSION_NUM Rmpc_get_version
Rmpc_set_default_rounding_mode Rmpc_get_default_rounding_mode
Rmpc_set_prec Rmpc_set_default_prec Rmpc_get_default_prec
Rmpc_set_default_prec2 Rmpc_get_default_prec2
Rmpc_set_re_prec Rmpc_set_im_prec
Rmpc_get_prec Rmpc_get_prec2 Rmpc_get_re_prec Rmpc_get_im_prec
Rmpc_get_dc Rmpc_get_ldc
RMPC_RE RMPC_IM RMPC_INEX_RE RMPC_INEX_IM
Rmpc_clear Rmpc_clear_ptr Rmpc_clear_mpc
Rmpc_deref4 Rmpc_get_str
Rmpc_init2 Rmpc_init3
Rmpc_init2_nobless Rmpc_init3_nobless
Rmpc_strtoc Rmpc_set_str
Rmpc_set Rmpc_set_ui Rmpc_set_si Rmpc_set_d Rmpc_set_uj Rmpc_set_sj Rmpc_set_ld
Rmpc_set_z Rmpc_set_q Rmpc_set_f Rmpc_set_fr
Rmpc_set_z_z Rmpc_set_q_q Rmpc_set_f_f
Rmpc_set_ui_ui Rmpc_set_ui_si Rmpc_set_ui_d Rmpc_set_ui_uj Rmpc_set_ui_sj Rmpc_set_ui_ld Rmpc_set_ui_fr
Rmpc_set_si_ui Rmpc_set_si_si Rmpc_set_si_d Rmpc_set_si_uj Rmpc_set_si_sj Rmpc_set_si_ld Rmpc_set_si_fr
Rmpc_set_d_ui Rmpc_set_d_si Rmpc_set_d_d Rmpc_set_d_uj Rmpc_set_d_sj Rmpc_set_d_ld Rmpc_set_d_fr
Rmpc_set_uj_ui Rmpc_set_uj_si Rmpc_set_uj_d Rmpc_set_uj_uj Rmpc_set_uj_sj Rmpc_set_uj_ld Rmpc_set_uj_ld Rmpc_set_uj_fr
Rmpc_set_sj_ui Rmpc_set_sj_si Rmpc_set_sj_d Rmpc_set_sj_uj Rmpc_set_sj_sj Rmpc_set_sj_ld Rmpc_set_sj_fr
Rmpc_set_ld_ui Rmpc_set_ld_si Rmpc_set_ld_uj Rmpc_set_ld_d Rmpc_set_ld_sj Rmpc_set_ld_ld Rmpc_set_ld_fr
Rmpc_set_fr_ui Rmpc_set_fr_si Rmpc_set_fr_d Rmpc_set_fr_uj Rmpc_set_fr_sj Rmpc_set_fr_ld Rmpc_set_fr_fr
Rmpc_set_f_ui Rmpc_set_q_ui Rmpc_set_z_ui Rmpc_set_ui_f Rmpc_set_ui_q Rmpc_set_ui_z
Rmpc_set_f_si Rmpc_set_q_si Rmpc_set_z_si Rmpc_set_si_f Rmpc_set_si_q Rmpc_set_si_z
Rmpc_set_f_d Rmpc_set_q_d Rmpc_set_z_d Rmpc_set_d_f Rmpc_set_d_q Rmpc_set_d_z
Rmpc_set_f_uj Rmpc_set_q_uj Rmpc_set_z_uj Rmpc_set_uj_f Rmpc_set_uj_q Rmpc_set_uj_z
Rmpc_set_f_sj Rmpc_set_q_sj Rmpc_set_z_sj Rmpc_set_sj_f Rmpc_set_sj_q Rmpc_set_sj_z
Rmpc_set_f_ld Rmpc_set_q_ld Rmpc_set_z_ld Rmpc_set_ld_f Rmpc_set_ld_q Rmpc_set_ld_z
Rmpc_set_f_q Rmpc_set_q_f Rmpc_set_f_z Rmpc_set_z_f Rmpc_set_z_q Rmpc_set_q_z
Rmpc_set_f_fr Rmpc_set_q_fr Rmpc_set_z_fr Rmpc_set_fr_f Rmpc_set_fr_q Rmpc_set_fr_z
Rmpc_set_dc Rmpc_set_ldc
Rmpc_add Rmpc_add_ui Rmpc_add_fr
Rmpc_sub Rmpc_sub_ui Rmpc_ui_sub Rmpc_ui_ui_sub
Rmpc_mul Rmpc_mul_ui Rmpc_mul_si Rmpc_mul_fr Rmpc_mul_i Rmpc_sqr Rmpc_mul_2exp
Rmpc_div Rmpc_div_ui Rmpc_ui_div Rmpc_div_fr Rmpc_sqrt Rmpc_div_2exp
Rmpc_neg Rmpc_abs Rmpc_conj Rmpc_norm Rmpc_exp Rmpc_log
Rmpc_cmp Rmpc_cmp_si Rmpc_cmp_si_si
Rmpc_out_str Rmpc_inp_str c_string r_string i_string
TRmpc_out_str TRmpc_inp_str
Rmpc_sin Rmpc_cos Rmpc_sin_cos Rmpc_tan Rmpc_sinh Rmpc_cosh Rmpc_tanh
Rmpc_asin Rmpc_acos Rmpc_atan Rmpc_asinh Rmpc_acosh Rmpc_atanh
Rmpc_real Rmpc_imag Rmpc_arg Rmpc_proj
Rmpc_pow Rmpc_pow_d Rmpc_pow_ld Rmpc_pow_si Rmpc_pow_ui Rmpc_pow_z Rmpc_pow_fr
Rmpc_set_nan Rmpc_swap
Rmpc_mul_sj Rmpc_mul_ld Rmpc_mul_d Rmpc_div_sj Rmpc_sj_div Rmpc_div_ld Rmpc_ld_div Rmpc_div_d Rmpc_d_div
)]);
*TRmpc_out_str = \&Rmpc_out_str;
*TRmpc_inp_str = \&Rmpc_inp_str;
*Rmpc_set_uj_si = \&Rmpc_set_uj_sj;
*Rmpc_set_ui_sj = \&Rmpc_set_uj_sj;
*Rmpc_set_sj_ui = \&Rmpc_set_sj_uj;
*Rmpc_set_si_uj = \&Rmpc_set_sj_uj;
*Rmpc_set_uj_ui = \&Rmpc_set_uj_uj;
*Rmpc_set_ui_uj = \&Rmpc_set_uj_uj;
*Rmpc_set_sj_si = \&Rmpc_set_sj_sj;
*Rmpc_set_si_sj = \&Rmpc_set_sj_sj;
*Rmpc_set_d_ld = \&Rmpc_set_ld_ld;
*Rmpc_set_ld_d = \&Rmpc_set_ld_ld;
*Rmpc_mul_sj = \&Math::MPC::_mpc_mul_sj;
*Rmpc_mul_ld = \&Math::MPC::_mpc_mul_ld;
*Rmpc_mul_d = \&Math::MPC::_mpc_mul_d;
*Rmpc_div_sj = \&Math::MPC::_mpc_div_sj;
*Rmpc_sj_div = \&Math::MPC::_mpc_sj_div;
*Rmpc_div_ld = \&Math::MPC::_mpc_div_ld;
*Rmpc_ld_div = \&Math::MPC::_mpc_ld_div;
*Rmpc_div_d = \&Math::MPC::_mpc_div_d;
*Rmpc_d_div = \&Math::MPC::_mpc_d_div;
sub dl_load_flags {0} # Prevent DynaLoader from complaining and croaking
sub overload_string {
return "(" . _get_str($_[0], 10, 0, Rmpc_get_default_rounding_mode()) . ")";
}
### Was originally called Rmpc_get_str ###
sub _get_str {
my ($r_s, $i_s) = c_string($_[0], $_[1], $_[2], $_[3]);
# Changed to stay in step with change to mpc_out_str() format
#my $sep = $i_s =~ /\-/ ? ' -I*' : ' +I*';
#$i_s =~ s/\-//;
#my $s = $r_s . $sep . $i_s;
#return $s;
return $r_s . " " . $i_s;
}
sub c_string {
my $r_s = r_string($_[0], $_[1], $_[2], $_[3]);
my $i_s = i_string($_[0], $_[1], $_[2], $_[3]);
return ($r_s, $i_s);
}
sub r_string {
my($mantissa, $exponent) = _get_r_string($_[0], $_[1], $_[2], $_[3]);
if($mantissa =~ /\@nan\@/i || $mantissa =~ /\@inf\@/i) {return $mantissa}
if($mantissa =~ /\-/ && $mantissa !~ /[^0,\-]/) {return '-0'}
if($mantissa !~ /[^0,\-]/ ) {return '0'}
my $sep = $_[1] <= 10 ? 'e' : '@';
my $len = substr($mantissa, 0, 1) eq '-' ? 2 : 1;
if(!$_[2]) {
while(length($mantissa) > $len && substr($mantissa, -1, 1) eq '0') {
substr($mantissa, -1, 1, '');
}
}
$exponent--;
if(length($mantissa) == $len) {
if($exponent) {return $mantissa . $sep . $exponent}
return $mantissa;
}
substr($mantissa, $len, 0, '.');
if($exponent) {return $mantissa . $sep . $exponent}
return $mantissa;
}
sub i_string {
my($mantissa, $exponent) = _get_i_string($_[0], $_[1], $_[2], $_[3]);
if($mantissa =~ /\@nan\@/i || $mantissa =~ /\@inf\@/i) {return $mantissa}
if($mantissa =~ /\-/ && $mantissa !~ /[^0,\-]/) {return '-0'}
if($mantissa !~ /[^0,\-]/ ) {return '0'}
my $sep = $_[1] <= 10 ? 'e' : '@';
my $len = substr($mantissa, 0, 1) eq '-' ? 2 : 1;
if(!$_[2]) {
while(length($mantissa) > $len && substr($mantissa, -1, 1) eq '0') {
substr($mantissa, -1, 1, '');
}
}
$exponent--;
if(length($mantissa) == $len) {
if($exponent) {return $mantissa . $sep . $exponent}
return $mantissa;
}
substr($mantissa, $len, 0, '.');
if($exponent) {return $mantissa . $sep . $exponent}
return $mantissa;
}
sub Rmpc_deref4 {
my ($r_m, $r_e) = _get_r_string($_[0], $_[1], $_[2], $_[3]);
my ($i_m, $i_e) = _get_i_string($_[0], $_[1], $_[2], $_[3]);
return ($r_m, $r_e, $i_m, $i_e);
}
sub new {
# This function caters for 2 possibilities:
# 1) that 'new' has been called OOP style - in which
# case there will be a maximum of 3 args
# 2) that 'new' has been called as a function - in
# which case there will be a maximum of 2 args.
# If there are no args, then we just want to return an
# initialized Math::MPC object
my @prec = Rmpc_get_default_prec2();
if(!@_) {return Rmpc_init3(@prec)}
if(@_ > 3) {die "Too many arguments supplied to new()"}
# If 'new' has been called OOP style, the first arg is the string "Math::MPC"
# which we don't need - so let's remove it. However, if the first
# arg is a Math::MPFR or Math::MPC object (which is a possibility),
# then we'll get a fatal error when we check it for equivalence to
# the string "Math::MPC". So we first need to check that it's not
# an object - which we'll do by using the ref() function:
if(!ref($_[0]) && $_[0] eq "Math::MPC") {
shift;
if(!@_) {return Rmpc_init3(@prec)}
}
if(_itsa($_[0]) == _MATH_MPC_T) {
if(@_ > 1) {die "Too many arguments supplied to new() - expected no more than one"}
my $mpc = Rmpc_init3(@prec);
Rmpc_set($mpc, $_[0], Rmpc_get_default_rounding_mode());
return $mpc;
}
# @_ can now contain a maximum of 2 args - the real and (optionally)
# the imaginary components.
if(@_ > 2) {die "Too many arguments supplied to new() - expected no more than two"}
my ($arg1, $arg2, $type1, $type2);
# $_[0] is the real component, $_[1] (if supplied)
# is the imaginary component.
$arg1 = shift;
$type1 = _itsa($arg1);
$arg2 = 0;
if(@_) {$arg2 = shift}
$type2 = _itsa($arg2);
# Die if either of the args are unacceptable.
if($type1 == 0)
{die "First argument to new() is inappropriate"}
if($type2 == 0)
{die "Second argument to new() is inappropriate"}
# Create a Math::MPC object that has $arg1 as its
# real component, and zero as its imaginary component.
my $mpc1 = _new_real($arg1);
# Create a Math::MPC object that has $arg2 as its
# imaginary component, and zero as its real component.
my $mpc2 = _new_im($arg2);
# Add the 2 created Math::MPC objects together and return
# the result
Rmpc_add($mpc1, $mpc1, $mpc2, MPC_RNDNN);
return $mpc1;
}
sub Rmpc_out_str {
if(@_ == 5) {
die "Inappropriate 4th arg supplied to Rmpc_out_str" if _itsa($_[3]) != _MATH_MPC_T;
return _Rmpc_out_str($_[0], $_[1], $_[2], $_[3], $_[4]);
}
if(@_ == 6) {
if(_itsa($_[3]) == _MATH_MPC_T) {return _Rmpc_out_strS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5])}
die "Incorrect args supplied to Rmpc_out_str" if _itsa($_[4]) != _MATH_MPC_T;
return _Rmpc_out_strP($_[0], $_[1], $_[2], $_[3], $_[4], $_[5]);
}
if(@_ == 7) {
die "Inappropriate 5th arg supplied to Rmpc_out_str" if _itsa($_[4]) != _MATH_MPC_T;
return _Rmpc_out_strPS($_[0], $_[1], $_[2], $_[3], $_[4], $_[5], $_[6]);
}
die "Wrong number of arguments supplied to Rmpc_out_str()";
}
sub MPC_VERSION {return _MPC_VERSION()}
sub MPC_VERSION_MAJOR {return _MPC_VERSION_MAJOR()}
sub MPC_VERSION_MINOR {return _MPC_VERSION_MINOR()}
sub MPC_VERSION_PATCHLEVEL {return _MPC_VERSION_PATCHLEVEL()}
sub MPC_VERSION_STRING {return _MPC_VERSION_STRING()}
sub MPC_VERSION_NUM {return _MPC_VERSION_NUM(@_)}
1;
__END__
=head1 NAME
Math::MPC - perl interface to the MPC (multi precision complex) library.
=head1 DEPENDENCIES
This module needs the MPC, MPFR and GMP C libraries. (Install GMP
first, followed by MPFR, followed by MPC.)
The GMP library is availble from http://gmplib.org
The MPFR library is available from http://www.mpfr.org/
The MPC library is available from
http://www.multiprecision.org/mpc/
=head1 DESCRIPTION
A multiple precision complex number module utilising the MPC library.
Basically, this module simply wraps the 'mpc' complex number functions
provided by that library.
Operator overloading is also available.
The following documentation heavily plagiarises the mpc documentation.
use warnings;
use Math::MPC qw(:mpc);
Rmpc_set_default_prec(500); # Set default precision to 500 bits
my $mpc1 = Math::MPC->new(12.5, 1125); # 12.5 + 1125*i
$mpc2 = sqrt($mpc1);
print "Square root of $mpc1 is $mpc2\n";
See also the Math::MPC test suite for some (simplistic) examples of
usage.
=head1 ROUNDING MODE
A complex rounding mode is of the form MPC_RNDxy where "x" and "y"
are one of "N" (to nearest), "Z" (towards zero), "U" (towards plus
infinity), "D" (towards minus infinity). The first letter refers to
the rounding mode for the real part, and the second one for the
imaginary part.
For example MPC_RNDZU indicates to round the real part towards
zero, and the imaginary part towards plus infinity.
The default rounding mode is MPC_RNDNN, but this can be changed
using the Rmpc_set_default_rounding_mode() function.
=head1 MEMORY MANAGEMENT
Objects can be created with the Rmpc_init2 and Rmpc_init3 functions,
which return an object that has been blessed into the package
Math::MPC. Alternatively, blessed objects can also be created by
calling the new() function (either as a function or as a method).
These objects will be automatically cleaned up by the DESTROY()
function whenever they go out of scope.
Rmpc_init2_nobless and Rmpc_init3_nobless are the same as Rmpc_init2
and Rmpc_init3, except that they return an unblessed object.
If you create Math::MPC objects using the '_nobless' versions,
it will then be up to you to clean up the memory associated with
these objects by calling Rmpc_clear($op) for each object.
Alternatively such objects will be cleaned up when the script ends.
I don't know why you would want to create unblessed objects. The
point is that you can if you want to.
=head1 MIXING MPC OBJECTS WITH MPFR & GMP OBJECTS
Some of the Math::MPC functions below take Math::MPFR, Math::GMP,
Math::GMPz, Math::GMPq, or Math::GMPf objects as arguments.
Obviously, to make use of these functions, you'll need to have
loaded the appropriate module.
=head1 FUNCTIONS
Most of the following functions are simply wrappers around an mpc
function of the same name. eg. Rmpc_neg() is a wrapper around
mpc_neg().
"$rop", "$op1", "$op2", etc. are Math::MPC objects - the
return value of one of the Rmpc_init* functions. They are in fact
references to mpc structures. The "$op" variables are the operands
and "$rop" is the variable that stores the result of the operation.
Generally, $rop, $op1, $op2, etc. can be the same perl variable
referencing the same mpc structure, though often they will be
distinct perl variables referencing distinct mpc structures.
Eg something like Rmpc_add($r1, $r1, $r1, $rnd),
where $r1 *is* the same reference to the same mpc structure,
would add $r1 to itself and store the result in $r1. Alternatively,
you could (courtesy of operator overloading) simply code it
as $r1 += $r1. Otoh, Rmpc_add($r1, $r2, $r3, $rnd), where each of the
arguments is a different reference to a different mpc structure
would add $r2 to $r3 and store the result in $r1. Alternatively
it could be coded as $r1 = $r2 + $r3.
In the documentation that follows:
"$ui" means an integer that will fit into a C 'unsigned long int',
"$si" means an integer that will fit into a C 'signed long int'.
"$uj" means an integer that will fit into a C 'uintmax_t'. Don't
use the _uj functions unless your perl was compiled with 64
bit integer support.
"$sj" means an integer that will fit into a C 'intmax_t'. Don't
use the _sj functions unless your perl was compiled with 64
bit integer support.
"$double" is a C double.
"$ld" is a C long double. Don't use the _ld functions unless your
perl was compiled with long double support.
"$bool" means a value (usually a 'signed long int') in which
the only interest is whether it evaluates as false or true.
"$str" simply means a string of symbols that represent a number,
eg '1234567890987654321234567@7' which might be a base 10 number,
or 'zsa34760sdfgq123r5@11' which would have to represent at least
a base 36 number (because "z" is a valid digit only in bases 36
and above). Valid bases for MPC numbers are 2 to 36 (inclusive).
"$rnd" is simply one of the 16 rounding mode values (discussed above).
"$p" is the (unsigned long) value for precision.
"$mpf" is a Math::GMPf object (floating point). You'll need Math::GMPf
installed in order to create $mpf.
"$mpq" is a Math::GMPq object (rational). You'll need Nath::GMPq
installed in order to create $mpq.
"$mpz" is a Math::GMP or Math::GMPz object (integer). You'll need
Math::GMPz or Math::GMP installed in order to create $mpz.
"$mpfr" is a Math::MPFR object (floating point). You'll need to
'use Math::MPFR;' in order to create $mpfr. (Math::MPFR
a pre-requisite module for Math::MPC.)
"$cc" is a Math::Complex_C (double _Complex) object. You'll need to
'use Math::Complex_C' (or create your own double _Complex
object) in order to create $cc, and to use the functions that
take such an argument. (Math::Complex_C is *not* a
pre-requisite module for Math::MPC.)
"$lcc" is a Math::Complex_C::Long (long double _Complex) object.
You'll need to 'use Math::Complex_C' (or create your own
long double _Complex object in order to create $lcc, and
to use the functions that take such an argument.
######################
FUNCTION RETURN VALUES
Most MPC functions have a return value ($si) which is used to
indicate the position of the rounded real or imaginary parts with
respect to the exact (infinite precision) values. The functions
RMPC_INEX_RE($si) and RMPC_INEX_IM($si) return 0 if the corresponding
rounded value is exact, a negative value if the rounded value is less
than the exact one, and a positive value if it is greater than the
exact one. However, some functions do not completely fulfill this -
in some cases the sign is not guaranteed, and in some cases a
non-zero value is returned although the result is exact. In these
cases the function documentation explains the exact meaning of the
return value. However, the return value never wrongly indicates an
exact computation.
###########################
MANIPULATING ROUNDING MODES
Rmpc_set_default_rounding_mode($rnd);
Sets the default rounding mode to $rnd.
The default rounding mode is to nearest initially (MPC_RNDNN).
The default rounding mode is the rounding mode that is used in
overloaded operations.
$ui = Rmpc_get_default_rounding_mode();
Returns the numeric value of the current default rounding mode.
This will initially be 0 (MPC_RNDNN).
##########
INITIALIZATION
Normally, a variable should be initialized once only or at least
be cleared, using `Rmpc_clear', between initializations - but
don't explicitly call Rmpc_clear() on blessed objects. 'DESTROY'
(which calls 'Rmpc_clear') is automatically called on blessed
objects whenever they go out of scope.
First read the section 'MEMORY MANAGEMENT' (above).
Rmpc_set_default_prec($p);
Rmpc_set_default_prec2($p_re, $p_im);
Rmpc_set_default_prec sets the default precision to exactly $p
bits for both the real and imaginary parts. Rmpc_set_default_prec
sets the default precision to be *exactly* $p_re bits for the real
part, and *exactly* $p_im bits for the imaginary part. The
precision of a variable means the number of bits used to store its
mantissa. All subsequent calls to `new' will use this precision,
but previously initialized variables are unaffected. This is also
the precision that will be used during some overloaded operations
(see OPERATOR OVERLOADING below).
The default precision is set to 53 bits initially (for both
real and imaginary components).
$ui = Rmpc_get_default_prec();
($ui_re, $ui_im) = Rmpc_get_default_prec2();
Rmpc_get_default_prec returns the current default real precision
iff the default real precision is the same as the current default
imaginary precision. Otherwise it returns zero.
Rmpc_get_default_prec2 returns both current default real precision
and current default imaginary precision (in bits).
$ui = Rmpc_get_prec($op);
If the real and imaginary part of $op have the same precision,
it is returned. Otherwise 0 is returned.
$ui = Rmpc_get_re_prec($op);
$ui = Rmpc_get_im_prec($op)
($re_prec, $im_prec) = Rmpc_get_prec2($op);
Get (respectively) the precision of the real part of $op, the
precision of the imaginary part of $op, or an array containing
precision of both real and imaginary parts of $op.
$rop = Math::MPC->new();
$rop = Math::MPC::new();
$rop = new Math::MPC();
Initialize $rop, and set its real and imaginary parts to NaN.
The precision of $rop is the default precision, which can be
changed by a call to `Rmpc_set_default_prec' or
`Rmpc_set_default_prec2' (documented above).
$rop = Rmpc_init2($p);
$rop = Rmpc_init2_nobless($p);
Initialize $rop, set the precision (of both real and imaginary
parts) to be *exactly* $p bits, and set its real and imaginary
parts to NaN.
$rop = Rmpc_init3($p_re, $p_im);
$rop = Rmpc_init3_nobless($p_r, $p_i);
Initialize $rop, set the precision of the real part to be
*exactly* $p_re bits, set the precision of the imaginary part to
be *exactly* $p_im bits, and set its real and imaginary parts to
NaN.
Rmpc_set_prec($op, $p);
Reset the precision of $op to be exactly $p bits, and set its
real/imaginary parts to NaN.
Rmpc_set_re_prec($op, $p);
Rmpc_set_im_prec($op, $p);
Set (respectively) the precision of the real part of $op to be
exactly $p bits and the precision of the imaginary part of $op
to be exactly $p bits. In both cases the value is set to NaN.
(There are currently no corresponding MPC library functions.)
##########
ASSIGNMENT
$si = Rmpc_set($rop, $op, $rnd);
$si = Rmpc_set_ui($rop, $ui, $rnd);
$si2 = Rmpc_set_si($rop, $si1, $rnd);
$si = Rmpc_set_d($rop, $double, $rnd);
$si = Rmpc_set_uj($rop, $uj, $rnd);
$si = Rmpc_set_sj($rop, $sj, $rnd);
$si = Rmpc_set_ld($rop, $ld, $rnd);
$si = Rmpc_set_f($rop, $mpf, $rnd);
$si = Rmpc_set_q($rop, $mpq, $rnd);
$si = Rmpc_set_z($rop, $mpz, $rnd);
$si = Rmpc_set_fr($rop, $mpfr, $rnd);
$si = Rmpc_set_dc($rop, $cc, $rnd);
$si = Rmpc_set_ldc($rop, $lcc, $rnd);
Set the value of $rop from 2nd arg, rounded to the precision of
$rop towards the given direction $rnd.
Don't use Rmpc_set_ld unless perl has been built with long
double support. Don't use Rmpc_set_uj or Rmpc_set_sj unless
perl has been built with long long int support.
For Rmpc_set_dc and Rmpc_set_ldc, an mpc library (version 0.9
or later) that has been built with support for these data types
is needed.
$si = Rmpc_set_str($rop, $string, $base, $rnd);
$si = Rmpc_strtoc($rop, $string, $base, $rnd);
Set $rop to the value represented in $string (in base $base), rounded
in accordance with $rnd. See the mpc documentation for details.
$si = Rmpc_set_ui_ui($rop, $ui1, $ui2, $rnd);
$si3 = Rmpc_set_si_si($rop, $si1, $si2, $rnd);
$si = Rmpc_set_d_d($rop, $double1, $double2, $rnd);
$si = Rmpc_set_f_f($rop, $mpf1, $mpf2, $rnd);
$si = Rmpc_set_q_q($rop, $mpq1, $mpq2, $rnd);
$si = Rmpc_set_z_z($rop, $mpz1, $mpz2, $rnd);
$si = Rmpc_set_fr_fr($rop, $mpfr1, $mpfr2, $rnd);
Sets the real part of $rop from 2nd arg, and the imaginary part
of $rop from 3rd arg, according to the rounding mode $rnd.
$si = Rmpc_set_uj_uj($rop, $uj1, $uj2, $rnd);
$si = Rmpc_set_sj_sj($rop, $sj1, $sj2, $rnd);
$si = Rmpc_set_ld_ld($rop, $ld1, $ld2, $rnd);
Don't use the first 2 functions unless Math::MPC::_has_longlong()
returns a true value. Don't use the 3rd function unless
Math::MPC::_has_longdouble() returns true.
Sets the real part of $rop from 2nd arg, and the imaginary part
of $rop from 3rd arg, according to the rounding mode $rnd.
$si = Rmpc_set_x_y($rop, $op1, $op2, $rnd);
You need to replace the 'x' and the 'y' with any one of 'ui',
'si', 'd', 'uj', 'sj', 'ld', 'f', 'q', 'z' and 'fr' - eg:
Rmpc_set_ui_d($rop, $ui, $double, $rnd);
Don't use the 'uj' or 'sj' variants if Math::MPC::_has_longlong()
doesn't return a true value. And don't use the 'ld' variants if
Math::MPC_haslongdouble() doesn't return a true value.
Sets the real part of $rop from 2nd arg, and the imaginary part
of $rop from 3rd arg, according to the rounding mode $rnd.
################################################
COMBINED INITIALIZATION AND ASSIGNMENT
NOTE: Do NOT use these functions if $rop has already been initialised
or created by calling new(). Instead use the Rmpc_set* functions in
the section 'ASSIGNMENT' (above).
First read the section 'MEMORY MANAGEMENT' (above).
$rop = Math::MPC->new($arg1 [, $arg2]);
$rop = Math::MPC::new($arg1 [, $arg2]);
$rop = new Math::MPC($arg1, [, $arg2]);
Returns a Math::MPC object whose real component has a value of $arg1,
rounded in the default rounding direction, with default precision.
If $arg2 is supplied, the imaginary component of the returned
Math::MPC object is set to $arg2, rounded in the default rounding
direction, with default precision. Otherwise the imaginary component
of the returned Math::MPC object is set to zero. $arg1 & $arg2 can be
either a number (signed integer, unsigned integer, signed fraction or
unsigned fraction), a string that represents a numeric value, a
Math::MPFR object, a Math::GMP object, a Math::GMPz object, a
Math::GMPq object or a Math::GMPf object.
If a string argument begins with "0b" or "0B", then the string is
treated as a base 2 string. Elsif it begins with "0x" or "0X" it is
treated as a base 16 string. Else it is treated as a base 10 string.
##########
ARITHMETIC
$si = Rmpc_add($rop, $op1, $op2, $rnd);
$si = Rmpc_add_ui($rop, $op, $ui, $rnd);
$si = Rmpc_add_fr($rop, $op, $mpfr, $rnd);
Set $rop to 2nd arg + 3rd arg rounded in the direction $rnd.
$si = Rmpc_sub($rop, $op1, $op2, $rnd);
$si = Rmpc_sub_ui($rop, $op, $ui, $rnd);
$si = Rmpc_ui_sub($rop, $ui, $op, $rnd);
Set $rop to 2nd arg - 3rd arg rounded in the direction $rnd.
$si = Rmpc_ui_ui_sub($rop, $ui_r, $ui_i, $op, $rnd);
The real part of $rop is set to $ui_r minus the real part of $op
(rounded in the direction $rnd) - and the imaginary part of $rop
is set to $ui_r minus the imaginary part of $op (rounded in the
direction $rnd)
$si = Rmpc_mul($rop, $op1, $op2, $rnd);
$si = Rmpc_mul_ui($rop, $op, $ui, $rnd);
$si = Rmpc_mul_si($rop, $op, $si1, $rnd);
$si = Rmpc_mul_sj($rop, $op, $sj, $rnd); # Math::MPC XSub
$si = Rmpc_mul_d($rop, $op, $double, $rnd);# Math::MPC XSub
$si = Rmpc_mul_ld($rop, $op, $ld, $rnd); # Math::MPC XSub
$si = Rmpc_mul_fr($rop, $op, $mpfr, $rnd);
Set $rop to 2nd arg * 3rd arg rounded in the direction $rnd.
The 'sj'/'ld' versions are available only on perls built with
'64 bit int'/'long double' support.
$si = Rmpc_mul_i($rop, $op, $si1, $rnd);
If $si1 >= 0 (non-negative), set $rop to $op times the
imaginary unit i - else set $rop to $op times -i.
$si = Rmpc_div($rop, $op1, $op2, $rnd);
$si = Rmpc_div_ui($rop, $op, $ui, $rnd);
$si = Rmpc_ui_div($rop, $ui, $op, $rnd);
$si = Rmpc_div_d($rop, $op, $double, $rnd); # Math::MPC XSub
$si = Rmpc_d_div($rop, $double, $op, $rnd); # Math::MPC XSub
$si = Rmpc_div_sj($rop, $op, $sj, $rnd); # Math::MPC XSub
$si = Rmpc_sj_div($rop, $sj, $op, $rnd); # Math::MPC XSub
$si = Rmpc_div_ld($rop, $op, $ld, $rnd); # Math::MPC XSub
$si = Rmpc_ld_div($rop, $ld, $op, $rnd); # Math::MPC XSub
$si = Rmpc_div_fr($rop, $op, $mpfr, $rnd);
Set $rop to 2nd arg / 3rd arg rounded in the direction $rnd.
The 'sj'/'ld' versions are available only on perls built with
'64 bit int'/'long double' support.
$si = Rmpc_sqr($rop, $op, $rnd);
Set $rop to the square of $op, rounded in direction $rnd.
$si = Rmpc_sqrt($rop, $op, $rnd);
Set $rop to the square root of the 2nd arg rounded in the
direction $rnd. When the return value is 0, it means the result
is exact. Else it's unknown whether the result is exact or not.
$si = Rmpc_pow($rop, $op1, $op2, $rnd);
$si = Rmpc_pow_d($rop, $op1, $double, $rnd);
$si = Rmpc_pow_ld($rop, $op1, $ld, $rnd);
$si2 = Rmpc_pow_si($rop, $op1, $si, $rnd);
$si = Rmpc_pow_ui($rop, $op1, $ui, $rnd);
$si = Rmpc_pow_z($rop, $op1, $mpz, $rnd);
$si = Rmpc_pow_fr($rop, $op1, $mpfr, $rnd);
Set $op to ($op1 ** 3rd arg) rounded in the direction $rnd.
Rmpc_pow_ld is available only on perls that have "long double"
support.
$si = Rmpc_neg($rop, $op, $rnd);
Set $rop to -$op rounded in the direction $rnd. Just
changes the sign if $rop and $op are the same variable.
$si = Rmpc_conj($rop, $op, $rnd);
Set $rop to the conjugate of $op rounded in the direction $rnd.
Just changes the sign of the imaginary part if $rop and $op are
the same variable.
$si = Rmpc_abs($mpfr, $op, $rnd);
Set the floating-point number $mpfr to the absolute value of $op,
rounded in the direction $rnd. Return 0 iff the result is exact.
$si = Rmpc_norm($mpfr, $op, $rnd);
Set the floating-point number $mpfr to the norm of $op (ie the
square of its absolute value), rounded in the direction $rnd.
Return 0 iff the result is exact.
$si = Rmpc_mul_2exp($rop, $op, $ui, $rnd);
Set $rop to $op times 2 raised to $ui rounded according to $rnd.
Just increases the exponents of the real and imaginary parts by
$ui when $rop and $op are identical.
$si = Rmpc_div_2exp($rop, $op, $ui, $rnd);
Set $rop to $op divided by 2 raised to $ui rounded according to
$rnd. Just decreases the exponents of the real and imaginary
parts by $ui when $rop and $op are identical.
Rmpc_swap($op1, $op2);
Swap the values (and precisions) of op1 and op2 efficiently.
##########
COMPARISON
$si = Rmpc_cmp($op1, $op2);
$si = Rmpc_cmp_si($op, $si1);
Compare 1st and 2nd args. The return value $si can be decomposed
into $x = RMPC_INEX_RE($si) and $y = RMPC_INEX_IM($si), such that $x
is positive if the real part of the 1st arg is greater than that of
the 2nd arg, zero if both real parts are equal, and negative if the
real part of the 1st arg is less than that of the 2nd arg.
Likewise for $y.
Both 1st and 2nd args are considered to their full own precision,
which may differ.
It is not allowed that one of the operands has a NaN (Not-a-Number)
part.
The storage of the return value is such that equality can be simply
checked with Rmpc_cmp($first_arg, $second_arg) == 0.
$si = Rmpc_cmp_si_si($op, $si1, $si2);
As for the above comparison functions - except that $op is being
compared with $si1 + ($si2 * i).
#######
SPECIAL
$si = Rmpc_exp($rop, $op, $rnd);
Set $rop to the exponential of $op, rounded according to $rnd
with the precision of $rop.
$si = Rmpc_log($rop, $op, $rnd);
Set $rop to the log of $op, rounded according to $rnd with the
precision of $rop.
$si = Rmpc_arg ($mpfr, $op, $rnd);
Set $mpfr to the argument of $op, with a branch cut along the
negative real axis. ($mpfr is a Math::MPFR object.)
$si = Rmpc_proj ($rop, $op, $rnd);
Compute a projection of $op onto the Riemann sphere. Set $rop
to $op, rounded in the direction $rnd, except when at least one
part of $op is infinite (even if the other part is a NaN) in
which case the real part of $rop is set to plus infinity and its
imaginary part to a signed zero with the same sign as the
imaginary part of $op.
Rmpc_set_nan($op);
Set $op to 'NaN +I*NaN'.
##########
TRIGONOMETRIC
$si = Rmpc_sin($rop, $op, $rnd);
Set $rop to the sine of $op, rounded according to $rnd with the
precision of $rop.
$si = Rmpc_cos($rop, $op, $rnd);
Set $rop to the cosine of $op, rounded according to $rnd with
the precision of $rop.
$si = Rmpc_sin_cos($r_sin, $r_cos, $op, $rnd_sin, $rnd_cos);
Needs version 0.9 or later of the mpc C library.
Set $r_sin/$r_cos to the sin/cos of $op, rounded according to
$rnd_sin/$rnd_cos.
(If the mpc C library is pre version 0.9, calling this
function will cause the program to die with an appropriate
error message.)
$si = Rmpc_tan($rop, $op, $rnd);
Set $rop to the tangent of $op, rounded according to $rnd with
the precision of $rop.
$si = Rmpc_sinh($rop, $op, $rnd);
Set $rop to the hyperbolic sine of $op, rounded according to
$rnd with the precision of $rop.
$si = Rmpc_cosh($rop, $op, $rnd);
Set $rop to the hyperbolic cosine of $op, rounded according to
$rnd with the precision of $rop.
$si = Rmpc_tanh($rop, $op, $rnd);
Set $rop to the hyperbolic tangent of $op, rounded according to
$rnd with the precision of $rop.
$si = Rmpc_asin ($rop, $op, $rnd);
Set $rop to the inverse sine of $op, rounded according to
$rnd with the precision of $rop.
$si = Rmpc_acos ($rop, $op, $rnd);
Set $rop to the inverse cosine of $op, rounded according to
$rnd with the precision of $rop.
$si = Rmpc_atan ($rop, $op, $rnd);
Set $rop to the inverse tangent of $op, rounded according to
$rnd with the precision of $rop.
$si = Rmpc_asinh ($rop, $op, $rnd);
Set $rop to the inverse hyperbolic sine of $op, rounded
according to $rnd with the precision of $rop.
$si = Rmpc_acosh ($rop, $op, $rnd);
Set $rop to the inverse hyperbolic cosine of $op, rounded
according to$rnd with the precision of $rop.
$si = Rmpc_atanh ($rop, $op, $rnd);
Set $rop to the inverse hyperbolic tangent of $op, rounded
according to$rnd with the precision of $rop.
##########
CONVERSION
($real, $im) = c_string($op, $base, $digits, $rnd);
$real = r_string($op, $base, $digits, $rnd);
$im = i_string($op, $base, $digits, $rnd);
$real is a string containing the value of the real part of $op.
$im is a string containing the value of the imaginary part of $op.
$real and $im will be of the form XeY (X@Y for bases greater than 10)
- where X is the mantissa (in base $base) and Y is the exponent (in
base 10).
For example, -31.4132' would be returned as -3.14132e1. $digits is the
number of digits that will be written in the mantissa. If $digits is
zero, the mantissa will contain the maximum number of digits
accurately representable. The mantissa will be rounded in the
direction specified by $rnd.
@vals = Rmpc_deref4($op, $base, $digits, $rnd);
@vals contains (in order) the real mantissa, the real exponent, the
imaginary mantissa, and the imaginary exponent of $op.The mantissas,
expressed in base $base and rounded according to $rnd), contain an
implicit radix point to the left of the first (ie leftmost) digit.
The exponents are always expressed in base 10. $digits is the number
of digits that will be written in the mantissa. If $digits is zero
the mantissa will contain the maximum number of digits accurately
representable.
RMPC_RE($mpfr, $op);
RMPC_IM($mpfr, $op);
Set $mpfr to the value of the real (respectively imaginary) component
of $op. $mpfr will be an exact copy of the real/imaginary component
of op - ie the precision of $mpfr will be set to the precision of the
real/imaginary component of $op before the copy is made. Hence no need
for a rounding arg to be supplied.
$si = Rmpc_real($mpfr, $op, $rnd);
$si = Rmpc_imag($mpfr, $op, $rnd);
Set $mpfr to the value of the real (respectively imaginary) part of
$op, rounded in the direction $rnd. ($mpfr is a Math::MPFR object.)
#############
I-O FUNCTIONS
$ul = Rmpc_inp_str($rop, $stream, $base, $rnd);
Input a string in base $base from $stream, rounded according to $rnd,
and put the read complex in $rop. Each of the real and imaginary
parts should be of the form X@Ym or, if the base is 10 or less,
alternatively XeY or XEY. (X is the mantissa, Y is the exponent.
The mantissa is always in the specified base. The exponent is always
read in decimal. This function first reads the real part, followed by
the imaginary part. The argument $base may be in the range 0,2..36.
Return the number of bytes read, or if an error occurred, return 0.
$ul =
Rmpc_out_str([$pre,] $stream, $base, $digits, $op, $rnd [, $suf]);
This function changed from 1st release (version 0.45) of Math::MPC.
Output $op to $stream, in base $base, rounded according to $rnd. First
the real part is printed, followed by the imaginary part. The base may
be 0,2..36. Print at most $digits significant digits for each
part, or if $digits is 0, the maximum number of digits accurately
representable by $op. In addition to the significant digits, a decimal
point at the right of the first digit and a trailing exponent, in the
form eYYY , are printed. (If $base is greater than 10, "@" will be
used as exponent delimiter.) $pre and $suf are optional arguments
containing a string that will be prepended/appended to the output.
Return the number of bytes written. (The contents of $pre and $suf
are not included in the count.)
$string = Rmpc_get_str($base, $how_many, $op, $rnd);
Convert $op to a string containing the real and imaginary parts of
$op. The number of significant digits for both real and imaginary
parts is specified by $how_many. It is also possible to let
$how_many be zero, in which case the number of digits is chosen large
enough so that re-reading the printed value with the same precision,
assuming both output and input use rounding to nearest, will recover
the original value of $op. See the mpc documentation for details.
Rmpc_get_dc($cc, $op, $rnd);
Rmpc_get_ldc($lcc, $op, $rnd);
Set the 'double _Complex'/'long double _Complex' object to the value
of $op, rounded according to $rnd. Needs an mpc library (version 0.9
or later) that has been built with support for these data types.
####################
OPERATOR OVERLOADING
Overloading works with numbers, strings (bases 2, 10, and 16
only - see step '4.' below) and Math::MPC objects.
Overloaded operations are performed using the current
"default rounding mode" (which you can determine using the
'Rmpc_get_default_rounding_mode' function, and change using
the 'Rmpc_set_default_rounding_mode' function).
Be aware that when you use overloading with a string operand,
the overload subroutine converts that string operand to a
Math::MPC object with *current default precision*, and using
the *current default rounding mode*.
Be aware also, that the sign of zero is not always handled
correctly by the overload subroutines. If it's important to you
that the sign of zero be handled correctly, don't use the
overloaded operators. (For multiplication, division, addition
and subtraction the sign of zero will be handled correctly by the
overloaded operators if both operands are Math::MPC objects.)
For the purposes of the overloaded 'not', '!' and 'bool'
operators, a "false" Math::MPC object is one with real and
imaginary parts that are both "false" - where "false" currently
means either 0 or NaN.
(A "true" Math::MPC object is, of course, simply one that is not
"false".)
The following operators are overloaded:
+ - * / ** sqrt (Return object has default precision)
+= -= *= /= **= (Precision remains unchanged)
== !=
! bool
abs (Returns an MPFR object, blessed into package Math::MPFR)
exp log (Return object has default precision)
sin cos (Return object has default precision)
= (The copy has the same precision as the copied object.)
""
Attempting to use the overloaded operators with objects that
have been blessed into some package other than 'Math::MPC'
will not work. The workaround is to convert this "foreign"
object to a Math::MPC object - thus allowing it to work with
the overloaded operator.
In those situations where the overload subroutine operates on 2
perl variables, then obviously one of those perl variables is
a Math::MPC object. To determine the value of the other variable
the subroutine works through the following steps (in order),
using the first value it finds, or croaking if it gets
to step 6:
1. If the variable is an unsigned long then that value is used.
The variable is considered to be an unsigned long if
(perl 5.8 on) the UOK flag is set or if (perl 5.6) SvIsUV()
returns true.(In the case of perls built with -Duse64bitint,
the variable is treated as an unsigned long long int if the
UOK flag is set.)
2. If the variable is a signed long int, then that value is used.
The variable is considered to be a signed long int if the
IOK flag is set. (In the case of perls built with
-Duse64bitint, the variable is treated as a signed long long
int if the IOK flag is set.)
3. If the variable is a double, then that value is used. The
variable is considered to be a double if the NOK flag is set.
(In the case of perls built with -Duselongdouble, the variable
is treated as a long double if the NOK flag is set.)
4. If the variable is a string (ie the POK flag is set) then the
value of that string is used. If the POK flag is set, but the
string is not a valid number, the subroutine croaks with an
appropriate error message. If the string starts with '0b' or
'0B' it is regarded as a base 2 number. If it starts with '0x'
or '0X' it is regarded as a base 16 number. Otherwise it is
regarded as a base 10 number.
5. If the variable is a Math::MPC object then the value of that
object is used.
6. If none of the above is true, then the second variable is
deemed to be of an invalid type. The subroutine croaks with
an appropriate error message.
#####################
MISCELLANEOUS
$ui = MPC_VERSION_MAJOR;
Returns the 'x' in the 'x.y.z' of the MPC library version.
Value is as specified by the header file (mpc.h) that was
used to build Math::MPC.
$ui =MPC_VERSION_MINOR;
Returns the 'y' in the 'x.y.z' of the MPC library version.
Value is as specified by the header file (mpc.h) that was
used to build Math::MPC.
$ui = MPC_VERSION_PATCHLEVEL;
Returns the 'z' in the 'x.y.z' of the MPC library version.
Value is as specified by the header file (mpc.h) that was
used to build Math::MPC.
$ui = MPC_VERSION();
An integer value derived from the library's major, minor and
patchlevel values. Value is as specified by the header file
(mpc.h) that was used to build Math::MPC.
$ui = MPC_VERSION_NUM($major, $minor, $patchlevel);
Returns an integer in the same format as used by MPC_VERSION,
using the given $major, $minor and $patchlevel. Value is as
specified by the header file (mpc.h) that was used to build
Math::MPC.
$string = MPC_VERSION_STRING;
$string contains the MPC library version ('x.y.z'), as defined
by the header file (mpc.h) that was used to build Math::MPC
$string = Rmpc_get_version();
$string contains the MPC library version ('x.y.z'), as defined
by the mpc library being used by Math::MPC.
$MPFR_version = Math::MPC::mpfr_v();
$MPFR_version is set to the version of the mpfr library
being used by the mpc library that Math::MPC uses.
(The function is not exportable.)
$GMP_version = Math::MPC::gmp_v();
$GMP_version is set to the version of the gmp library being
used by the mpc library that Math::MPC uses.
(The function is not exportable.)
####################
=head1 TODO
For completeness, we probably should wrap mpc_realref and
mpc_imagref - though I don't think there's much to be
achieved by doing this in a *perl* context.
=head1 BUGS
You can get segfaults if you pass the wrong type of
argument to the functions - so if you get a segfault, the
first thing to do is to check that the argument types
you have supplied are appropriate.
Also, as mentioned above in the "OPERATOR OVERLOADING" section,
the overloaded operators are not guaranteed to handle the sign
of zero correctly.
=head1 LICENSE
This program is free software; you may redistribute it and/or
modify it under the same terms as Perl itself.
Copyright 2006-2009, 2010, 2011 Sisyphus
=head1 AUTHOR
Sisyphus
=cut