Math Functions

You don't have to write every function yourself. C comes with a library of ready-made functions, and you have already used some of them: printf, strlen, toupper. The header file math.h holds functions for math:

• sqrt(x) returns the square root of x: sqrt(16) is 4.0.
• pow(x, y) returns x to the power of y: pow(2, 10) is 1024.0.
• round(x) rounds x to the nearest whole number: round(3.7) is 4.0. A half is rounded away from zero, so round(2.5) is 3.0.
• fabs(x) returns the absolute value of x, the number without its minus sign: fabs(-3.5) is 3.5.

They are functions like the ones you write: they take arguments and return a value. All four return a double, so print them with %f or %.2f. To use them, add #include <math.h> at the top of the program, next to #include <stdio.h>:

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("%.2f\n", sqrt(16));
    printf("%.2f\n", pow(2, 10));
    printf("%.2f\n", round(3.7));
    printf("%.2f\n", fabs(-3.5));
    return 0;
}

This program prints:

4.00
1024.00
4.00
3.50

Printing them with %d is a compile error here: format specifies type 'int' but the argument has type 'double'. And if you forget the #include, the program doesn't compile either:

#include <stdio.h>

int main(void) {
    printf("%.2f\n", sqrt(16));
    return 0;
}

main.c:4:22: error: call to undeclared library function 'sqrt' with type 'double (double)'; ISO C99 and later do not support implicit function declarations [-Wimplicit-function-declaration]
    4 |     printf("%.2f\n", sqrt(16));
      |                      ^
main.c:4:22: note: include the header <math.h> or explicitly provide a declaration for 'sqrt'
1 error generated.

The first line is one you know: a call to a function that the compiler doesn't know yet, this time a library function. The note says what to do: include the header <math.h>, or declare sqrt yourself. Now you can see what the #include is for: math.h holds the prototypes of these functions.

The absolute value of a whole number has its own function, abs, in another header file, stdlib.h (the standard library). It takes and returns an int, so you print it with %d:

#include <stdio.h>
#include <stdlib.h>

int main(void) {
    int morning = -5;
    int noon = 3;
    printf("Change: %d degrees\n", abs(noon - morning));
    printf("%d\n", abs(-7));
    return 0;
}

This program prints:

Change: 8 degrees
7

Use abs for whole numbers and fabs for decimal ones: abs(-2.5) quietly returns 2. And you can call library functions inside your own functions, which is what you will do now.