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    Functions (Basics)Functions (Basics)Functions

    Basics Basics

    Example: Function that computes mean of 2 numbers
    double mean (double a, double b) {
      return (a + b) / 2;
    }
    
    int main() { cout << mean(2, 6); // prints 4 }
    • encapsulation of implementation details
    • easier reasoning about correctness and testing by breaking down problems into separate functions
    • avoids repeating code for common tasks

    // "call" at "call site"
    auto result = name(argument1, argument2);

    Return Types

    Full Return Type Deduction   (deduction = compiler determines type automatically)
    auto foo (int i, double d) {
      
      return i;
    }
    //  deduced return type: int
    auto foo (int i, double d) {
      return i;  //  int
      
      return d;  //  double
    } 
    //  COMPILER ERROR: Inconsistent return types!

    Parameters

    • none: f()
    • one or many: g(int a, double b, int c, …)
    • parameter names have to be unique within list

    const Parameters const

    int foo(int a, int const b) {
      a += 5;   // 
      b += 10;  //  COMPILER ERROR: can't modify const parameter
      return (a + b);
    }
    
    // calling foo: foo(2,9); // const has no effect here

    Any 2nd argument passed to foo will be copied testi into the local variable b ⇒ the fact that b is const has no effect outside of foo.

    If you don't need or must not change values of parameters then make them const!

    Defaulted Parameters Defaults

    double f (double a, double b = 1.5) {
        return (a * b);
    }
    int main() {
      cout <<  f(2);     // 1 argument  → 3.0
      cout <<  f(2, 3);  // 2 arguments → 6.0
    }
    void foo (int i = 0);  
    void foo (int n, double x = 2.5);  
    void foo (int a, int b = 1, float c = 3.5f);  
    
    void foo (int a, int b = 1, int c );
    Each parameter after first default must have default value, too!

    Overloading

    • functions with the same name but different parameter lists
    • cannot overload on return type alone

    Recursion

    = function calling itself
    • needs a break condition
    • looks more elegant than loops but in many cases slower
    • recursion depth is limited (by stack size)
    int factorial (int n) {
        // break condition:
        if(n < 2) return 1;  
        // recursive call: n! = n * (n-1)!
        return (n * factorial(n - 1));  
    }

    Declaration vs. Definition Declaration

    • can only call functions that are already known (from before/above)
    • only one definition allowed per source file (translation unit)
    • ok to have any number of declarations = announcing the existence of a function by specifying it's signature
    Example: Broken! (click!)
     COMPILER ERROR: - 'odd'/'even' not known before 'main'!
     COMPILER ERROR: - 'odd' not known before 'even'!
    
    int main() { int i = 0; cin >> i; if(odd(i)) cout << " is odd\n"; if(even(i)) cout << " is even\n"; }
    bool even(int n) { return !odd(n); }
    bool odd(int n) { return (n % 2); }
    Working (click!)
    bool even(int);  // declaration
    bool odd(int);   // declaration
    
    int main() { // definition int i = 0; cin >> i; if(odd(i)) cout << " is odd\n"; // OK, already declared if(even(i)) cout << " is even\n"; // OK, already declared }
    bool even(int n) { // definition return !odd(n); // OK, already declared }
    bool odd(int n) { // definition return (n % 2); }

    Design

    When implementing a function, think about:
    • Preconditions: What do you expect/demand from input values?
    • Postconditions: What guarantees should you give regarding output values?
    • Invariants: What do callers/users of your function expect to not change?
    • Purpose: Has your function a clearly defined purpose?
    • Name: Does the function's name reflect its purpose?
    • Parameters: Can a caller/user easily confuse their meaning?

    Users of a function should not be confused about its purpose, the meaning of its parameters, pre/postconditions and side effects.

    Interfaces should be easy to use correctly and hard to use incorrectly.  —  Scott Meyers

    Some Mathematical Functions Mathematical Functions Math

    #include <cmath>
    double sqrt (double x) √x square root
    double pow (double a, double b) ab power
    double abs (double x) |x| absolute value
    double sin (double x) sin(x) sine
    double cos (double x) cos(x) cosine
    double exp (double x) ex exponential
    double log (double x) log(x) logarithm
    double floor (double x) ⌊x⌋ next smaller integer
    double ceil (double x) ⌈x⌉ next larger integer
    double fmod (double x, double y) remainder of x/y
    More About Functions (more advanced material)(skips ahead to more advanced material):