# NAME

Math::Complex_C - perl interface to C's double precision complex operations.

# DESCRIPTION

```
use warnings;
use strict;
use Math::Complex_C qw(:all);
# For brevity, use MCD which is an alias for Math::Complex_C::new
my $c = MCD(12.5, 1125); # assign as NV
my $root = MCD();
sqrt_c($root, $c);
print "Square root of $c is $root\n";
See also the Math::Complex_C test suite for some (simplistic) examples
of usage.
This module is written largely for the use of perl builds whose nvtype is
'double'. Run "perl -V:nvtype" to see what your perl's NV type is. If your
nvtype is 'long double' consider using Math::Complex_C::L instead, and if
your nvtype is '__float128' consider using Math::Complex_C::Q.
Irrespective of the nvtype, you can still use this module - it's just
that there are a number of functions returning 'double' - which, for 'long
double' and '__float128' builds do not utilise the full precision that the
'long double' or '__float128' NV provides.
OTOH, you *can* use Math::Complex_C::L and/or Math::Complex_C::Q (making
full use of the extra precision their operations provide) even if your
nvtype is double - so long as your compiler supports the building of those
modules. See the "Which Math::Complex_C" section of the README that ships
with this module's source for a more detailed explanation.
A number of the functions below accept string arguments. These arguments
will be tested by the perl API function looks_like_number() for the
presence of non-numeric characters. If any such non-numeric characters
are detected, then the global non-numeric flag (which is initially set to
0) will be incremented. You can query the value this global flag holds by
running Math::Complex_C::nnumflag() and you can manually alter the value of
the global using Math::Complex_C::set_nnum and Math::Complex_C::clear_nnum.
These functions are documented below.
```

# FUNCTIONS

```
$rop = Math::Complex_C->new($re, $im);
$rop = Math::Complex_C::new($re, $im);
$rop = MCD($re, $im); # MCD is an alias to Math::Complex_C::new()
$rop is a returned Math::Complex_C object; $re and $im are the real and
imaginary values (respectively) that $rop holds. They (ie $re, $im) can be
integer values (IV or UV), floating point values (NV) or numeric strings
IV, UV, and NV values will be cast to double before being assigned.
Strings (PV) will be assigned using C's strtod() function. Note that the
two arguments ($re and $im) are optional - ie they can be omitted.
If no arguments are supplied, then $rop will be assigned NaN for both the real
and imaginary parts.
If only one argument is supplied, and that argument is a Math::Complex_C
object then $rop will be a duplicate of that Math::Complex_C object.
Otherwise the single argument will be assigned to the real part of $rop, and
the imaginary part will be set to zero.
The functions croak if an invalid arg is supplied.
$rop = create_c();
$rop is a Math::Complex_C object, created with both real and imaginary
values set to NaN. (Same result as calling new() without any args.)
assign_c($rop, $re, $im);
The real part of $rop is set to the value of $re, the imaginary part is set to
the value of $im. $re and $im can be integers (IV or UV), floating point
values (NV) or strings (PV).
set_real_c($rop, $re);
The real part of $rop is set to the value of $re. $re can be an integer (IV or
UV), floating point value (NV) or a string (PV).
set_imag_c($rop, $im);
The imaginary part of $rop is set to the value of $re. $re can be an integer
(IV or UV), floating point value (NV) or a string (PV).
mul_c ($rop, $op1, $op2);
mul_c_iv($rop, $op1, $si);
mul_c_uv($rop, $op1, $ui);
mul_c_nv($rop, $op1, $nv);
mul_c_pv($rop, $op1, $pv);
Multiply $op1 by the 3rd arg, and store the result in $rop.
The "3rd arg" is (respectively, from top) a Math::Complex_C object,
a signed integer value (IV), an unsigned integer value (UV), a floating point
value (NV), a numeric string (PV). The UV, IV, NV and PV values are real only -
ie no imaginary component. The PV will be set to a long double value using C's
strtod() function. The UV, IV and NV values will be cast to long double
values.
add_c ($rop, $op1, $op2);
add_c_iv($rop, $op1, $si);
add_c_uv($rop, $op1, $ui);
add_c_nv($rop, $op1, $nv);
add_c_pv($rop, $op1, $pv);
As for mul_c(), etc., but performs addition.
div_c ($rop, $op1, $op2);
div_c_iv($rop, $op1, $si);
div_c_uv($rop, $op1, $ui);
div_c_nv($rop, $op1, $nv);
div_c_pv($rop, $op1, $pv);
As for mul_c(), etc., but performs division.
sub_c ($rop, $op1, $op2);
sub_c_iv($rop, $op1, $si);
sub_c_uv($rop, $op1, $ui);
sub_c_nv($rop, $op1, $nv);
sub_c_pv($rop, $op1, $pv);
As for mul_c(), etc., but performs subtraction.
$nv = real_c($op);
Returns the real part of $op as a (double precision) NV.
Wraps C's 'creal' function.
$nv = imag_c($op);
Returns the imaginary part of $op as a (double precision) NV.
$nv = arg_c($op);
Returns the argument of $op as a (double precision) NV.
Wraps C's 'carg' function.
$nv = abs_c($op);
Returns the absolute value of $op as a (double precision) NV.
Wraps C's 'cabs' function.
conj_c($rop, $op);
Sets $rop to the conjugate of $op.
Wraps C's 'conj' function.
acos_c($rop, $op);
Sets $rop to acos($op). Wraps C's 'cacos' function.
asin_c($rop, $op);
Sets $rop to asin($op). Wraps C's 'casin' function.
atan_c($rop, $op);
Sets $rop to atan($op). Wraps C's 'catan' function.
cos_c($rop, $op);
Sets $rop to cos($op). Wraps C's 'ccos' function.
sin_c($rop, $op);
Sets $rop to sin($op). Wraps C's 'csin' function.
tan_c($rop, $op);
Sets $rop to tan($op). Wraps C's 'ctan' function.
acosh_c($rop, $op);
Sets $rop to acosh($op). Wraps C's 'cacosh' function.
asinh_c($rop, $op);
Sets $rop to asinh($op). Wraps C's 'casinh' function.
atanh_c($rop, $op);
Sets $rop to atanh($op). Wraps C's 'catanh' function.
cosh_c($rop, $op);
Sets $rop to cosh($op). Wraps C's 'ccosh' function.
sinh_c($rop, $op);
Sets $rop to sinh($op). Wraps C's 'csinh' function.
tanh_c($rop, $op);
Sets $rop to tanh($op). Wraps C's 'ctanh' function.
exp_c($rop, $op);
Sets $rop to e ** $op. Wraps C's 'cexp' function.
log_c($rop, $op);
Sets $rop to log($op). Wraps C's 'clog' function.
pow_c($rop, $op1, $op2);
Sets $rop to $op1 ** $op2. Wraps C's 'cpow' function.
sqrt_c($rop, $op);
Sets $rop to sqrt($op). Wraps C's 'csqrt' function.
proj_c($rop, $op);
Sets $rop to a projection of $op onto the Riemann sphere.
Wraps C's 'cproj' function.
$nv = get_nan();
Sets $nv to NaN.
$nv = get_inf();
Sets $nv to Inf.
$bool = is_nan($nv);
Returns true if $nv is a NaN - else returns false
$bool = is_inf($nv);
Returns true if $nv is -Inf or +Inf - else returns false
```

# OUTPUT FUNCTIONS

```
Default precision for output of Math::Complex_C objects is whatever is
17 decimal digits.
This default can be altered using d_set_prec (see below).
d_set_prec($si);
$si = d_get_prec();
Set/get the precision (decimal digits) of output values
$str = d_to_str($op);
Return a string of the form "real imag".
Both "real" and "imag" will be expressed in scientific
notation, to the precision returned by the d_get_prec() function (above).
Use d_set_prec() to alter this precision.
Infinities are stringified to 'inf' (or '-inf' for -ve infinity).
NaN values (including positive and negative NaN vlaues) are stringified to
'nan'.
$str = d_to_strp($op, $si);
As for d_to_str, except that the precision setting for the output value
is set by the 2nd arg (which must be greater than 1).
$rop = str_to_d($str);
Takes a string as per that returned by d_to_str() or d_to_strp().
Returns a Math::Complex_C object set to the value represented by that
string.
```

# OPERATOR OVERLOADING

```
Math::Complex_C overloads the following operators:
*, +, /, -, **,
*=, +=, /=, -=, **=,
!, bool,
==, !=,
"",
abs, exp, log, cos, sin, atan2, sqrt,
=
NOTE: Making use of the '=' overloading is not recommended unless
you understand its caveats. See 'perldoc overload' and
read it thoroughly, including the documentation regarding
'copy constructors'.
Note: abs() returns a (double precision) NV, not a Math::Complex_C object.
Overloaded arithmetic operations are provided the following types:
IV, UV, NV, PV, Math::Complex_C object.
The IV, UV, NV and PV values are real only (ie no imaginary
component). The PV values will be converted to double values
using C's strtod() function. The IV, UV and NV values will be
cast to double precision values.
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".)
```

# OTHER FUNCTIONS

```
$iv = Math::Complex_C::nnumflag(); # not exported
Returns the value of the non-numeric flag. This flag is
initialized to zero, but incemented by 1 whenever a function
is handed a string containing non-numeric characters. The
value of the flag therefore tells us how many times functions
have been handed such a string. The flag can be reset to 0 by
running clear_nnum().
Math::Complex_C::set_nnum($iv); # not exported
Resets the global non-numeric flag to the value specified by
$iv.
Math::Complex_C::clear_nnum(); # not exported
Resets the global non-numeric flag to 0.(Essentially the same
as running set_nnum(0).)
```

# LICENSE

```
This module is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
Copyright 2014, 2016 Sisyphus.
```

# AUTHOR

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