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

either one value: `int`, `double`, …

double square (double x) {
  return (x * x);
}
int max (int x, int y) {
  if(x > y) return x; else return y;
}

or nothing: `void`

void print_squares (int n) {
  for(int i = 1; i <= n; ++i)
    cout << square(i) << '\n';
}

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 2^nd argument passed to foo will be copied test_i 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

same name, different parameter lists

int abs (int i) {
  return ((i < 0) ? –i : i);
}

double abs (double d) {
  return ((d < 0.0) ? –d : d);
}
int a = -5;
double b = -2.23;
auto x = abs(a); // int abs(int)
auto y = abs(b); // double abs(double)

same name, same parameter lists

int foo (int i) { 
  return (2 * i);
}

double foo (int i) { 
  return (2.5 * i);
}

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 Math

`#include <cmath>`
`double sqrt (double x)`	√x	square root
`double pow (double a, double b)`	a^b	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)`	e^x	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

Type Basics

Beginner's Guide / First Steps

Memory