This version of bc contains several extensions beyond traditional bc implementations and the POSIX draft standard. Command line options can cause these extensions to print a warning or to be rejected. This document describes the language accepted by this processor. Extensions will be identified as such.
.000001 has a length of 6 and scale of 6. 1935.000 has a length of 7 and a scale of 3.
There are four special variables, scale, ibase, obase, and last. scale defines how some operations use digits after the decimal point. The default value of scale is 0. ibase and obase define the conversion base for input and output numbers. The default for both input and output is base 10. last (an extension) is a variable that has the value of the last printed number. These will be discussed in further detail where appropriate. All of these variables may have values assigned to them as well as used in expressions.
To support the use of scripts for bc, a single line comment has been added as an extension. A single line comment starts at a # character and continues to the next end of the line. The end of line character is not part of the comment and is processed normally.
A simple expression is just a constant. bc converts constants into internal decimal numbers using the current input base, specified by the variable ibase. (There is an exception in functions.) The legal values of ibase are 2 through 36. (Bases greater than 16 are an extension.) Assigning a value outside this range to ibase will result in a value of 2 or 36. Input numbers may contain the characters 0en9 and AenZ. (Note: They must be capitals. Lower case letters are variable names.) Single digit numbers always have the value of the digit regardless of the value of ibase. (i.e. A = 10.) For multi-digit numbers, bc changes all input digits greater or equal to ibase to the value of ibase-1. This makes the number ZZZ always be the largest 3 digit number of the input base.
Full expressions are similar to many other high level languages. Since there is only one kind of number, there are no rules for mixing types. Instead, there are rules on the scale of expressions. Every expression has a scale. This is derived from the scale of original numbers, the operation performed and in many cases, the value of the variable scale. Legal values of the variable scale are 0 to the maximum number representable by a C integer.
In the following descriptions of legal expressions, "expr" refers to a complete expression and "var" refers to a simple or an array variable. A simple variable is just a
nameand an array variable is specified as
name[expr]Unless specifically mentioned the scale of the result is the maximum scale of the expressions involved.
Relational expressions are a special kind of expression that always evaluate to 0 or 1, 0 if the relation is false and 1 if the relation is true. These may appear in any legal expression. (POSIX bc requires that relational expressions are used only in if, while, and for statements and that only one relational test may be done in them.) The relational operators are
Boolean operations are also legal. (POSIX bc does NOT have boolean operations). The result of all boolean operations are 0 and 1 (for false and true) as in relational expressions. The boolean operators are:
The expression precedence is as follows: (lowest to highest)
|| operator, left associative && operator, left associative ! operator, nonassociative Relational operators, left associative Assignment operator, right associative + and - operators, left associative *, / and % operators, left associative ^ operator, right associative unary - operator, nonassociative ++ and -- operators, nonassociative
This precedence was chosen so that POSIX compliant bc programs will run correctly. This will cause the use of the relational and logical operators to have some unusual behavior when used with assignment expressions. Consider the expression:
a = 3 < 5
Most C programmers would assume this would assign the result of "3 < 5" (the value 1) to the variable "a". What this does in bc is assign the value 3 to the variable "a" and then compare 3 to 5. It is best to use parenthesis when using relational and logical operators with the assignment operators.
There are a few more special expressions that are provided in bc. These have to do with user defined functions and standard functions. They all appear as ",name/(,parameters/)". See the section on functions for user defined functions. The standard functions are:
expression1;
while (expression2) {
statement;
expression3;
}
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. All parameters are call by value parameters. 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 value 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.
Several extensions
have been added to functions. First, 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.
CW
define d (n) { return (2*n); }
define d (n)
{ return (2*n); }
Functions may be defined as void. A void function returns no value and
thus may not be used in any place that needs a value. A void function does
not produce any output when called by itself on an input line. The key
word void is placed between the key word define and the function name.
For example, consider the following session.
CW
define py (y) { print "--->", y, "<---", "\n"; }
define void px (x) { print "--->", x, "<---", "\n"; }
py(1)
--->1<---
0
px(1)
--->1<---
Since py is not a void function, the call of py(1)
prints the desired output
and then prints a second line that is the value of the function. Since
the value of a function that is not given an explicit return statement
is zero, the zero is printed. For px(1)
, no zero is printed because the
function is a void function. Also, call by variable for arrays was added. To declare a call by variable array, the declaration of the array parameter in the function definition looks like ",*name/[]". The call to the function remains the same as call by value arrays.
CW pi=$(echo "scale=10; 4*a(1) " | bc -l)
The following is the definition of
the exponential function used in the math library. This function is written
in POSIX bc.
CW
scale = 20
/* Uses the fact that e^x = (e^(x/2))^2
When x is small enough, we use the series:
e^x = 1 + x + x^2/2! + x^3/3! + ...
*/
define e(x) {
auto a, d, e, f, i, m, v, z
/* Check the sign of x. */
if (x<0) {
m = 1
x = -x
}
/* Precondition x. */
z = scale;
scale = 4 + z + .44*x;
while (x > 1) {
f += 1;
x /= 2;
}
/* Initialize the variables. */
v = 1+x
a = x
d = 1
for (i=2; 1; i++) {
e = (a *= x) / (d *= i)
if (e == 0) {
if (f>0) while (f--) v = v*v;
scale = z
if (m) return (1/v);
return (v/1);
}
v += e
}
}
The following is code that uses the extended features of bc to implement
a simple program for calculating checkbook balances. This program is best
kept in a file so that it can be used many times without having to retype
it at every use.
CW
scale=2
print "\nCheck book program!\n"
print " Remember, deposits are negative transactions.\n"
print " Exit by a 0 transaction.\n\n"
print "Initial balance? "; bal = read()
bal /= 1
print "\n"
while (1) {
"current balance = "; bal
"transaction? "; trans = read()
if (trans == 0) break;
bal -= trans
bal /= 1
}
quit
The following is the definition of the recursive factorial function.
CW
define f (x) {
if (x <= 1) return (1);
return (f(x-1) * x);
}
A major source of differences is extensions, where a feature is extended to add more functionality and additions, where new features are added. The following is the list of differences and extensions.
a = 1 b = 2has two execution blocks and
{ a = 1
b = 2 }
has one execution block. Any runtime error will terminate the execution
of the current execution block. A runtime warning will not terminate the
current execution block.
Email bug reports to bug-bc@gnu.org. Be sure to include the word ‘‘bc’’ somewhere in the ‘‘Subject:’’ field.
Philip A. Nelson philnelson@acm.org