Go to the first, previous, next, last section, table of contents.


Functions provide a method of defining a computation that can be executed later. Functions in bc always compute a value and return it to the caller. Function definitions are "dynamic" in the sense that a function is undefined until a definition is encountered in the input. That definition is then used until another definition function for the same name is encountered. The new definition then replaces the older definition. A function is defined as follows:

define name ( parameters ) { newline
    auto_list   statement_list }

A function call is just an expression of the form "name (parameters)".

Parameters are numbers or arrays (an extension). In the function definition, zero or more parameters are defined by listing their names separated by commas. Numbers are only call by value parameters. Arrays are only call by variable. Arrays are specified in the parameter definition by the notation "name[ ]". In the function call, actual parameters are full expressions for number parameters. The same notation is used for passing arrays as for defining array parameters. The named array is passed by variable to the function. Since function definitions are dynamic, parameter numbers and types are checked when a function is called. Any mismatch in number or types of parameters will cause a runtime error. A runtime error will also occur for the call to an undefined function.

The auto_list is an optional list of variables that are for "local" use. The syntax of the auto list (if present) is "auto name, ... ;". (The semicolon is optional.) Each name is the name of an auto variable. Arrays may be specified by using the same notation as used in parameters. These variables have their values pushed onto a stack at the start of the function. The variables are then initialized to zero and used throughout the execution of the function. At function exit, these variables are popped so that the original value (at the time of the function call) of these variables are restored. The parameters are really auto variables that are initialized to a value provided in the function call. Auto variables are different than traditional local variables because if function A calls function B, B may access function A's auto variables by just using the same name, unless function B has called them auto variables. Due to the fact that auto variables and parameters are pushed onto a stack, bc supports recursive functions.

The function body is a list of bc statements. Again, statements are separated by semicolons or newlines. Return statements cause the termination of a function and the return of a value. There are two versions of the return statement. The first form, "return", returns the value 0 to the calling expression. The second form, "return ( expression )", computes the value of the expression and returns that value to the calling expression. There is an implied "return (0)" at the end of every function. This allows a function to terminate and return 0 without an explicit return statement.

Functions also change the usage of the variable ibase. All constants in the function body will be converted using the value of ibase at the time of the function call. Changes of ibase will be ignored during the execution of the function except for the standard function read, which will always use the current value of ibase for conversion of numbers.

As an extension, the format of the definition has been slightly relaxed. The standard requires the opening brace be on the same line as the define keyword and all other parts must be on following lines. This version of bc will allow any number of newlines before and after the opening brace of the function. For example, the following definitions are legal.

   define d (n) { return (2*n); }
   define d (n)
       { return (2*n); }

Math Library Functions

If bc is invoked with the -l option, a math library is preloaded and the default scale is set to 20. The math functions will calculate their results to the scale set at the time of their call. The math library defines the following functions:

s (x)
The sine of x, x is in radians.
c (x)
The cosine of x, x is in radians.
a (x)
The arctangent of x, arctangent returns radians.
l (x)
The natural logarithm of x.
e (x)
The exponential function of raising e to the value x.
j (n,x)
The bessel function of integer order n of x.

Go to the first, previous, next, last section, table of contents.