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CHAP. 5]
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We can even nest function calls, like this:
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Most of the mathematical functions that you find on a pocket calculator are declared in the <cmath> header file, including all those shown in the table below.
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Some Functions Defined in the <cmath> Header
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acos(x) asin(x) atan(x) ceil(x) cos(x) exp(x) fabs(x) floor(x) log(x) log10(x) pow(x,p) sin(x) sqrt(x) tan(x)
Description
inverse cosine of x (in radians) inverse sine of x (in radians) inverse tangent of x (in radians) ceiling of x (rounds up) cosine of x (in radians) exponential of x (base e) absolute value of x floor of x (rounds down) natural logarithm of x (base e) common logarithm of x (base 10) x to the power p sine of x (in radians) square root of x tangent of x (in radians)
Example
acos(0.2) returns 1.36944 asin(0.2) returns 0.201358 atan(0.2) returns 0.197396 ceil(3.141593) returns 4.0 cos(2) returns -0.416147 exp(2) returns 7.38906 fabs(-2) returns 2.0 floor(3.141593) returns 3.0 log(2) returns 0.693147 log10(2) returns 0.30103 pow(2,3) returns 8.0 sin(2) returns 0.909297 sqrt(2) returns 1.41421 tan(2) returns -2.18504
Notice that every mathematical function returns a double type. If an integer is passed to the function, it is promoted to a double before the function processes it. The table below lists some of the more useful header files in the Standard C++ Library.
Some of the Header Files in the Standard C++ Library
Header File
<cassert> <ctype> <cfloat> <climits> <cmath> <cstdio> <cstdlib> <cstring> <ctime>
Description
Defines the assert() function Defines functions to test characters Defines constants relevant to floats Defines the integer limits on your local system Defines mathematical functions Defines functions for standard input and output Defines utility functions Defines functions for processing strings Defines time and date functions
These are derived from the Standard C Library. They are used the same way that Standard C++ header files such as <iostream> are used. For example, if you want to use the random number function rand() from the <cstdlib> header file, include the following preprocessor directive at the beginning of your main program file:
#include <cstdlib>
The Standard C Library is described in greater detail in 8 and in Appendix F.
FUNCTIONS
[CHAP. 5
5.3 USER-DEFINED FUNCTIONS The great variety of functions provided by the Standard C++ Library is still not sufficient for most programming tasks. Programmers also need to be able to define their own functions. EXAMPLE 5.3 A cube() Function
Here is a simple example of a user-defined function: int cube(int x) { // returns cube of x: return x*x*x; } The function returns the cube of the integer passed to it. Thus the call cube(2) would return 8.
A user-defined function has two parts: its head and its body. The syntax for the head of a function is
return-type name(parameter-list)
This specifies for the compiler the function s return type, its name, and its parameter list. In Example 5.3, the function s return type is int, its name is cube, and its parameter list is int x. So its head is
int cube(int x)
The body of a function is the block of code that follows its head. It contains the code that performs the function s action, including the return statement that specifies the value that the function sends back to the place where it was called. The body of the cube function is
{ // returns cube of x: return x*x*x; }
This is about as simple a body as a function could have. Usually the body is much larger. But the function s head typically fits on a single line. Note that main() itself is a function. Its head is
int main()
and its body is the program itself. Its return type is int, its name is main, and its parameter list is empty. A function s return statement serves two purposes: it terminates the execution of the function, and it returns a value to the calling program. Its syntax is
return expression; where expression is any expression whose value could be assigned to a variable whose type is
the same as the function s return type. 5.4 TEST DRIVERS Whenever you create your own function, you should immediately test it with a simple program. Such a program is called a test driver for the function. Its only purpose is to test the function. It is a temporary, ad hoc program that should be quick and dirty. That means that you need not include all the usual niceties such as user prompts, output labels, and documentation. Once you have used it to test your function thoroughly you can discard it.
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