How To Think Like a Computer Scientist C++ Edition The Pretext Interactive Version

In mathematics, you have probably seen functions like $\sin$ and $\log \text{,}$ and you have learned to evaluate expressions like $\sin (\pi /2)$ and $\log (1/x)\text{.}$ First, you evaluate the expression in parentheses, which is called the argument of the function. For example, $\pi /2$ is approximately 1.571, and $1/x$ is 0.1 (if $x$ happens to be 10).

Then you can evaluate the function itself, either by looking it up in a table or by performing various computations. The $\sin$ of 1.571 is 1, and the $\log$ of 0.1 is -1 (assuming that $\log$ indicates the logarithm base 10).

This process can be applied repeatedly to evaluate more complicated expressions like $\log (1/\sin (\pi /2))\text{.}$ First we evaluate the argument of the innermost function, then evaluate the function, and so on.

C++ provides a set of built-in functions that includes most of the mathematical operations you can think of. The math functions are invoked using a syntax that is similar to mathematical notation:

The first example sets log to the logarithm of 17, base $e\text{.}$ There is also a function called log10 that takes logarithms base 10.

The second example finds the sine of the value of the variable angle. C++ assumes that the values you use with sin and the other trigonometric functions (cos, tan) are in radians.

If you don’t happen to know $\pi$ to 15 digits, you can calculate it using the acos function. The arccosine (or inverse cosine) of -1 is $\pi \text{,}$ because the cosine of $\pi$ is -1.

Before you can use any of the math functions, you have to include the math header file. Header files contain information the compiler needs about functions that are defined outside your program. For example, in the “Hello, world!” program we included a header file named iostream using an include statement:

#include <iostream>
using namespace std;

iostream

¹

en.cppreference.com/w/cpp/header/iostream

contains information about input and output (I/O) streams, including the object named cout. C++ has a powerful feature called namespaces, that allow you to write your own implementation of cout. But in most cases, we would need to use the standard implementation. To convey this to the compiler, we use the line

using namespace std;

Similarly, the cmath

²

en.cppreference.com/w/cpp/header/cmath

header file contains information about the math functions. You can include it at the beginning of your program along with iostream:

#include <cmath>