Perform basic operations on complex numbers in a language without native support for complex numbers

Question

Your code has to provide the following functions:

read(x)

Reads a complex number from the standard input. It has to accept and evaluate something in the form of for example 1.42 + 3i.

print(x)

Prints the complex number in the form of, for example 1.23 - 4.32i

add(x,y)
sub(x,y)
mult(x,y)
div(x,y)

Adds, subtracts, multiplies and respectively divides the two complex numbers.

It is enough if your functions are accurate to two digits after the decimal point, of course, it can be more if you so wish. The input will never have more than two digits after the decimal point.

Any language without native support for complex numbers may be used. Similarly, libraries or other language features which deal with complex numbers are not permitted. The point is, you have to do all the handling of complex numbers by yourself.

Scoring

This is a code golf. The score is the sum of the lengths of the function bodies. For example, int add(int a, int b) {return a+b;} will have a length of 11 because of return a+b. Your solution must have a main program which demonstrates the use of the functions (for easier evaluation of your solution), but it will not be part of the scoring.

You can store the complex numbers in any way you wish, but the functions must have exactly the same amount of parameters as in the above description.

EDIT: For languages that support it, you can use operator overloading instead of the add, sub, etc. functions.

EDIT 2: To prohibit the cheap #define all_your_code_here A, I'll try to clarify the "only function bodies count" better: every character in the code counts, except for the overhead required to declare and define the functions and the libraries required to do basic I/O. By basic I/O I still mean no language features which directly deal with complex numbers. The main or equivalent where you call these functions don't count but you are not allowed to do anything besides using those functions for demonstrative purpose.

Answer 1

APL (33 + 16 + 1 + 1 + 14 + 17 = 82)

APL does have support for complex numbers if you use it (of the format 5J6, like Python's 5+6j), but it is of course not used.

I represent complex numbers as a 2-tuple of regular numbers, (A B) where A is the real part and B is the imaginary part. This means I can use APL's + and - operators directly, as they can be used on multidimensional types. (i.e. 1+2 3 4 gives 3 4 5 and 1 2+20 10 gives 21 12).

An APL function is represented as {body}. Functions are first-class objects. I have counted the function body without the braces, except for + and - which I've counted as 1 each.

read  ← {⎕ML←3⋄(1,1-2×'-'∊⍵)×⍎¨⍵⊂⍨⍵∊'.',⎕D} ⍝ 33 chars
print ← {⍕(⊃⍵)'+'(⊃⌽⍵)'i'}                   ⍝ 16 chars
add   ← +                                      ⍝ 1 char
sub   ← -                                      ⍝ 1 char
mul   ← {(-/⍺×⍵),+/⍺×⌽⍵}                      ⍝ 14 chars
div   ← {⍺mul 1 ¯1×⍵÷+/⍵*2}                   ⍝ 17 chars

Usage: (clarification: APL is evaluated right-to-left so this is actually calculating 8+9i ÷ 5+6i.)

      print (read⍞) div (read⍞)
5 + 6i
8 + 9i
1.540983607 + ¯0.04918032787 i

Answer 2

D (205 chars)

import stdio;

struct Complex{
  real a,b;

  this(real a,real b){
      this.a=a;
      this.b=b;
  }

  static Complex read(){
      Complex c;
      readf("%f%+fi",&c.a,&c.b);
      return c;
  }

  /** does both addition and substraction */
  Complex opOpBinary(op)(Complex o)if(op=="+"||op=="-"){
    mixin("return Complex(a"~op~"o.a,b"~op~"o.b);");
  }

  Complex opBinary(op)(Complex o)if(op=="*"){
    return Complex(a*o.a-b*o.b,a*o.b+b*o.a);
  }

  Complex opBinary(op)(Complex o)if(op=="/"){
    real z=c**2+d**2
    return this*Complex(o.a/z,-o.b/z);
  }

  void write(){
     writef("%f%+fi",a,b);
  }

}

using operator overloading

I didn't count the constructor

Answer 3

Python, 131 chars

add=lambda (a,b),(c,d):(a+c,b+d)
sub=lambda (a,b),(c,d):(a-c,b-d)
mul=lambda (a,b),(c,d):(a*c-b*d,a*d+b*c)
def div(x,(c,d)):z=c**2+d**2;return mul(x,(c/z,-d/z))
def _print(x):print"%f+%fi"%x
read=lambda:tuple(map(float,raw_input()[:-1].split('+')))

x=read()
y=read()
_print(add(x,y))
_print(sub(x,y))
_print(mul(x,y))
_print(div(x,y))

Makes lots of use of lambda unpacking, which I'm not including in my "body" count. (I'm counting everything after the first :). Kinda cheating, but I'm not really sure how to count it otherwise.

Answer 4

C# – 369 (I guess)

Func<float,float,float[]>C=(x,y)=>new[]{x,y};
Func<float[]>read=()=>{var m=new Regex(@"(\d*(\.\d*)?) *([+-]) *(\d*(\.\d*)?)i").Match(Console.ReadLine()).Groups;return C(float.Parse(m[1].Value),float.Parse(m[2].Value+m[4].Value));};
Action<float[]>print=x=>{Console.WriteLine("{0} {1} {2}i",x[0],x[1]>=0?"+":"-",Math.Abs(x[1]));};
Func<float[],float[],float[]>add=(x,y)=>C(x[0]+y[0],x[1]+y[1]);
Func<float[],float[],float[]>sub=(x,y)=>C(x[0]-y[0],x[1]-y[1]);
Func<float[],float[],float[]>mul=(x,y)=>C(x[0]*y[0]-x[1]*y[1],x[0]*y[1]+x[1]*y[0]);
Func<float[],float[],float[]>div=(x,y)=>mul(x,C(y[0],-y[1])).Select(_=>_/(y[0]*y[0]+y[1]*y[1])).ToArray();

var a = read();
var b = read();
var c = C(3, -7);
var d = C(2, 5);
var e = div(a,c);
var f = mul(b,d);
var g = add(e,f);
print(g);

Not sure about the character counting definition, really…

Answer 5

Haskell 698

Counted everything before main. This question struck me as being too straight forward, so I did everything in my power to make my answer more interesting. Also Haskell borks if you redefine Prelude functions (div, print, read), so I renamed those.

import Control.Arrow 
import Control.Monad
import Control.Applicative
import Data.List.Split
a=uncurry(***)
f!g=a(f,g)
j=join(!)
f%b=a$j f b
add=((+)%)
sub=((-)%)
o=join
g#h=(*)<$>g.fst<*>h.snd
c=o.curry
m=add<$>c((fst#fst)!(snd#fst))<*>c((negate.(snd#snd))!(fst#snd))
mul=curry m
b`d1v`c=b`mul`(j (/uncurry(+)(j(^2)c)).second negate$c)
s :: (Show a) => (a, a) -> String
s=uncurry(++).first(++" ").second((++"i").(let g('-':x)="- "++x;g x="+ "++x in g)).j show
pr1nt :: (Show a) => (a, a) -> IO ()
pr1nt=putStrLn.s
t=filter(`notElem`" i")
re4d :: (Read a, Num a) => String -> (a, a)
re4d s|elem '+'s=(\[x,y]->j(read.t)(x,y)).splitOn"+"$s
      |0<1=(\[x,y]->read!(negate.read.t)$(x,y)).splitOn"-"$s

main= do
  let p = pr1nt
  a <- fmap re4d getLine
  b <- fmap re4d getLine
  p $ a `add` b
  p $ a `sub` b
  p $ a `mul` b
  p $ a `d1v` b

This spits a "non-exhaustive pattern-match in input" if the input given does not match "a (+|-) bi".