# 4.6. Exercises

If you skipped the section on Linkage, then Exercise 4.2, Exercise 4.3, and Exercise 4.4 will cause you problems; it's up to you whether or not you want to read it and then try them.

Write a function and the appropriate declaration for the following tasks:

Exercise 4.1. A function called `abs_val` that returns `int` and takes an `int` argument. It returns the absolute value of its argument, by negating it if it is negative.

Exercise 4.2. A function called `output` that takes a single character argument and sends it to the program output with `putchar`. It will remember the current line number and column number reached on the output device—the only values passed to the function are guaranteed to be alphanumeric, punctuation, space and newline characters.

Exercise 4.3. Construct a program to test `output`, where that function is in a separate file from the functions that are used to test it. In the same file as `output` will be two functions called `current_line` and `current_column` which return the values of the line and column counters. Ensure that those counters are made accessible only from the file that contains them.

Exercise 4.4. Write and test a recursive function that performs the admittedly dull task of printing a list of numbers from 100 down to 1. On entry to the function it increments a static variable. If the variable has a value below 100, it calls itself again. Then it prints the value of the variable, decrements it and returns. Check that it works.

Exercise 4.5. Write functions to calculate the sine and cosine of their input. Choose appropriate types for both argument and return value. The series (given below) can be used to approximate the answer. The function should return when the value of the final term is less than 0.000001 of the current value of the function.

```sin x = x - pow(x,3)/fact(3) + pow(x,5)/fact(5)...
cos x = 1 - pow(x,2)/fact(2) + pow(x,4)/fact(4)...```

Note the fact that the sign in front of each term alternates (`--+--+--+...`). `pow(x,n)` returns `x` to the nth power, `fact(n)` factorial of `n` (1 × 2 × 3 × ⋯ × n). You will have to write such functions. Check the results against published tables.

## Footnotes

1. Stroustrup B. (1991). The C++ Programming Language 2nd edn. Reading, MA: Addison-Wesley