Complex

Complex numbers in SPVM are described.

Complex Types

Complex types are Complex_2f and Complex_2d.

The Complex_2f type is a multi-numeric type for a float complex number.

use Complex_2f;

my $z : Complex_2f;
$z->{re} = 1.5f;
$z->{im} = 1.7f;

The Complex_2d type is a multi-numeric type for a double complex number.

use Complex_2d;

my $z : Complex_2d;
$z->{re} = 1.5;
$z->{im} = 1.7;

Math Module

The Math module has methods to manipulate complex numbers.

cpanm SPVM::Math

Creating Complex Numbers

Complex numbers can be created by the complexf method and the complex method.

use Math;

# Complex_2f
my $z = Math->complexf(1.5f, 1.7f);

# Complex_2d
my $z = Math->complex(1.5, 1.7);

Complex Operations

These are addition, subtraction, multiplication, scalar product, and division of complex numbers.

float Complex numbers:

use Math;

my $z1 = Math->complexf(1.5f, 1.7f);
my $z2 = Math->complexf(2.5f, 2.7f);

# Addition
my $z_add = Math->caddf($z1, $z2);

# Subtraction
my $z_method = Math->csubf($z1, $z2);

# Multiplication
my $z_mul = Math->cmulf($z1, $z2);

# Scalar Product
my $z_scamul = Math->cscamulf(3, $z2);

# Division
my $z_div = Math->cdivf($z1, $z2);

double Complex numbers:

use Math;

my $z1 = Math->complex(1.5, 1.7);
my $z2 = Math->complex(2.5, 2.7);

# Addition
my $z_add = Math->cadd($z1, $z2);

# Subtraction
my $z_method = Math->csub($z1, $z2);

# Multiplication
my $z_mul = Math->cmul($z1, $z2);

# Scalar Product
my $z_scamul = Math->cscamul(3, $z2);

# Division
my $z_div = Math->cdiv($z1, $z2);

Trigonometric Functions

These are trigonometric functions.

float complex numbers:

use Math;

my $z = Math->complexf(1.5f, 1.7f);

# Addition
my $z_sin = Math->csinf($z);

# Subtract
my $z_cos = Math->ccosf($z);

# Multiply
my $z_tan = Math->ctanf($z);

double complex numers:

use Math;

my $z = Math->complex(1.5, 1.7);

# Addition
my $z_sin = Math->csin($z);

# Subtract
my $z_cos = Math->ccos($z);

# Multiply
my $z_tan = Math->ctan($z);

Complex Array

An array of complex numbers with contiguous memory areas can be created.

float complex array:

use Complex_2f;

my $zs = new Complex_2f[100];

for (my $i = 0; $i < @$zs; $i++) {
  my $z = $zs->[$i];
  $z->{re} = 1.5f;
  $z->{im} = 1.7f;
}

double complex array:

use Complex_2d;

my $zs = new Complex_2d[100];

for (my $i = 0; $i < @$zs; $i++) {
  my $z = $zs->[$i];
  $z->{re} = 1.5;
  $z->{im} = 1.7;
}

Passing Complex Numbers from Perl

Hash references are used to pass complex numbers to SPVM from Perl,

use SPVM 'MyComplex';

my $z1 = {re => 1.7, im => 2.7};
my $z2 = {re => 7.5, im => 2.5};

# method calc_complex : Complex_2d ($z1 : Complex_2d, $z2 : Complex_2d);
my $z_ret = SPVM::MyComplex->calc_complex($z1, $z2);