Arithmetic/Complex
You are encouraged to solve this task according to the task description, using any language you may know.
A complex number is a number which can be written as "a + b*i" (sometimes shown as "b + a*i") where a and b are real numbers and i is the square root of -1. Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by i.
Show addition, multiplication, negation, and inversion of complex numbers in separate functions (subtraction and division operations can be made with pairs of these operations). Print the results for each operation tested.
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
Ada
<ada>with Ada.Numerics.Generic_Complex_Types;
procedure Complex_Operations is
-- Ada provides a pre-defined generic package for complex types -- That package contains definitions for composition, -- negation, addition, subtraction, multiplication, division, -- conjugation, exponentiation, and absolute value, as well as -- basic comparison operations. -- Ada provides a second pre-defined package for sin, cos, tan, cot, -- arcsin, arccos, arctan, arccot, and the hyperbolic versions of -- those trigonometric functions. -- The package Ada.Numerics.Generic_Complex_Types requires definition -- with the real type to be used in the complex type definition. package Complex_Type is new Ada.Numerics.Generic_Complex_Types(Long_Float); use Complex_Type; A : Complex := Compose_From_Cartesian(Re => 1.0, Im => 1.0); B : Complex := Compose_From_Cartesian(Re => 3.14159, Im => 1.25); C : Complex;
begin
-- Addition C := A + B; -- Multiplication C := A * B; -- Inversion C := 1.0 / A; -- Negation C := -A;
end Complex_Operations;</ada>
C
The more recent C99 standard has built-in complex number primitive types, which can be declared with float, double, or long double precision. To use these types and their associated library functions, you must include the <complex.h> header. (Note: this is a different header than the <complex> templates that are defined by C++.) [1] [2] <c>
- include <complex.h>
void cprint(double complex c) {
printf("%lf%+lfI", creal(c), cimag(c));
} void complex_operations() {
double complex a = 1.0 + 1.0I; double complex b = 3.14159 + 1.2I;
double complex c;
printf("\na="); cprint(a);
printf("\nb="); cprint(b);
// addition
c = a + b;
printf("\na+b="); cprint(c);
// multiplication
c = a * b;
printf("\na*b="); cprint(c);
// inversion
c = 1.0 / a;
printf("\n1/c="); cprint(c);
// negation
c = -a;
printf("\n-a="); cprint(c); printf("\n");
} </c>
User-defined type: <c>typedef struct{
double real;
double imag;
} Complex;
Complex add(Complex a, Complex b){
Complex ans;
ans.real = a.real + b.real;
ans.imag = a.imag + b.imag;
return ans;
}
Complex mult(Complex a, Complex b){
Complex ans;
ans.real = a.real * b.real - a.imag * b.imag;
ans.imag = a.real * b.imag + a.imag * b.real;
return ans;
}
Complex inv(Complex a){
Complex ans;
double denom = a.real * a.real + a.imag * a.imag;
ans.real = a.real / denom;
ans.imag = -a.imag / denom;
return ans;
}
Complex neg(Complex a){
Complex ans;
ans.real = -a.real;
ans.imag = -a.imag;
return ans;
}
void put(Complex c) {
printf("%lf%+lfI", c.real, c.imag);
}
void complex_ops(void) {
Complex a = { 1.0, 1.0 };
Complex b = { 3.14159, 1.2 };
printf("\na="); put(a);
printf("\nb="); put(b);
printf("\na+b="); put(add(a,b));
printf("\na*b="); put(mult(a,b));
printf("\n1/a="); put(inv(a));
printf("\n-a="); put(neg(a)); printf("\n");
} </c>
C++
<cpp>
- include <complex>
using std::complex;
void complex_operations() {
complex<double> a(1.0, 1.0); complex<double> b(3.14159, 1.25);
complex<double> c;
// addition c = a + b; // multiplication c = a * b; // inversion c = 1.0 / a; // negation c = -a;
} </cpp>
D
Complex number is a D built-in type. <d>auto x = 1F+1i ; // auto type to cfloat auto y = 3.14159+1.2i ; // cdouble creal z ;
// addition z = x + y ; writefln(z) ; // => 4.14159+2.2i // multiplication z = x * y ; writefln(z) ; // => 1.94159+4.34159i // inversion z = 1.0 / x ; writefln(z) ; // => 0.5+-0.5i // negation z = -x ; writefln(z) ; // => -1+-1i</d>
Forth
There is no standard syntax or mechanism for complex numbers. The FSL provides several implementations suitable for different uses. This example uses the existing floating point stack, but other libraries define a separate complex stack and/or a fixed-point implementation suitable for microcontrollers and DSPs.
include complex.seq : ZNEGATE ( r i -- -r -i ) fswap fnegate fswap fnegate ; zvariable x zvariable y 1e 1e x z! pi 1.2e y z! x z@ y z@ z+ z. x z@ y z@ z* z. 1+0i x z@ z/ z. x z@ znegate z.
IDL
complex (and dcomplex for double-precision) is a built-in data type in IDL:
x=complex(1,1) y=complex(!pi,1.2) print,x+y ( 4.14159, 2.20000) print,x*y ( 1.94159, 4.34159) print,-x ( -1.00000, -1.00000) print,1/x ( 0.500000, -0.500000)
J
Complex numbers are a native numeric data type in J. Although the examples shown here are performed on scalars, all numeric operations naturally apply to arrays of complex numbers.
x=: 1j1 y=: 3.14159j1.2 x+y 4.14159j2.2 x*y 1.94159j4.34159 %x 0.5j_0.5 -x _1j_1
Java
<java>public class Complex{
public final double real; public final double imag;
public Complex(){this(0,0)}//default values to 0...force of habit
public Complex(double r, double i){real = r; imag = i;}
public Complex add(Complex b){
return new Complex(this.real + b.real, this.imag + b.imag);
}
public Complex mult(Complex b){
//FOIL of (a+bi)(c+di) with i*i = -1
return new Complex(this.real * b.real - this.imag * b.imag, this.real * b.imag + this.imag * b.real);
}
public Complex invert(){
//1/(a+bi) * (a-bi)/(a-bi) = 1/(a+bi) but it's more workable
double denom = real * real + imag * imag;
return new Complex(real/denom,-imag/denom);
}
public Complex neg(){
return new Complex(-real, -imag);
}
}</java>