| bc(1) | General Commands Manual | bc(1) |
bc - An arbitrary precision calculator language
bc [ -hlwsqv ] [long-options] [ file ... ]
bc is a language that supports arbitrary precision numbers with interactive execution of statements. There are some similarities in the syntax to the C programming language. A standard math library is available by command line option. If requested, the math library is defined before processing any files. bc starts by processing code from all the files listed on the command line in the order listed. After all files have been processed, bc reads from the standard input. All code is executed as it is read. (If a file contains a command to halt the processor, bc will never read from the standard input.)
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.
The most basic element in bc is the number. Numbers are arbitrary precision numbers. This precision is both in the integer part and the fractional part. All numbers are represented internally in decimal and all computation is done in decimal. (This version truncates results from divide and multiply operations.) There are two attributes of numbers, the length and the scale. The length is the total number of decimal digits used by bc to represent a number and the scale is the total number of decimal digits after the decimal point. For example:
.000001 has a length of 6 and scale of 6.
1935.000 has a length of 7 and a scale of 3.
Numbers are stored in two types of variables, simple variables and arrays. Both simple variables and array variables are named. Names begin with a letter followed by any number of letters, digits and underscores. All letters must be lower case. (Full alpha-numeric names are an extension. In POSIX bc all names are a single lower case letter.) The type of variable is clear by the context because all array variable names will be followed by brackets ([]).
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.
Comments in bc start with the characters /* and end with the characters */. Comments may start anywhere and appear as a single space in the input. (This causes comments to delimit other input items. For example, a comment can not be found in the middle of a variable name.) Comments include any newlines (end of line) between the start and the end of the comment.
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.
The numbers are manipulated by expressions and statements. Since the language was designed to be interactive, statements and expressions are executed as soon as possible. There is no "main" program. Instead, code is executed as it is encountered. (Functions, discussed in detail later, are defined when encountered.)
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 0–9 and A–Z. (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
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:
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:
Statements (as in most algebraic languages) provide the sequencing of expression evaluation. In bc statements are executed "as soon as possible." Execution happens when a newline in encountered and there is one or more complete statements. Due to this immediate execution, newlines are very important in bc. In fact, both a semicolon and a newline are used as statement separators. An improperly placed newline will cause a syntax error. Because newlines are statement separators, it is possible to hide a newline by using the backslash character. The sequence "\<nl>", where <nl> is the newline appears to bc as whitespace instead of a newline. A statement list is a series of statements separated by semicolons and newlines. The following is a list of bc statements and what they do: (Things enclosed in brackets ([]) are optional parts of the statement.)
expression1;
while (expression2) {
statement;
expression3;
}
These statements are not statements in the traditional sense. They are not executed statements. Their function is performed at "compile" time.
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. 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.
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.
define py (y) { print "--->", y, "<---", "\n"; } define void px (x) { print "--->", x, "<---", "\n"; } py(1) --->1<--- 0 px(1) --->1<---
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.
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:
In /bin/sh, the following will assign the value of "pi" to the shell variable pi.
The following is the definition of the exponential function used in the math library. This function is written in POSIX bc.
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.
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.
define f (x) {
if (x <= 1) return (1);
return (f(x-1) * x); }
GNU bc can be compiled (via a configure option) to use the GNU readline input editor library or the BSD libedit library. This allows the user to do editing of lines before sending them to bc. It also allows for a history of previous lines typed. When this option is selected, bc has one more special variable. This special variable, history is the number of lines of history retained. For readline, a value of -1 means that an unlimited number of history lines are retained. Setting the value of history to a positive number restricts the number of history lines to the number given. The value of 0 disables the history feature. The default value is 100. For more information, read the user manuals for the GNU readline, history and BSD libedit libraries. One can not enable both readline and libedit at the same time.
This version of bc was implemented from the POSIX P1003.2/D11 draft and contains several differences and extensions relative to the draft and traditional implementations. It is not implemented in the traditional way using dc(1). This version is a single process which parses and runs a byte code translation of the program. There is an "undocumented" option (-c) that causes the program to output the byte code to the standard output instead of running it. It was mainly used for debugging the parser and preparing the math library.
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 = 2
{ 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.
The following are the limits currently in place for this bc processor. Some of them may have been changed by an installation. Use the limits statement to see the actual values.
The following environment variables are processed by bc:
If any file on the command line can not be opened, bc will report that the file is unavailable and terminate. Also, there are compile and run time diagnostics that should be self-explanatory.
Error recovery is not very good yet.
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
The author would like to thank Steve Sommars (Steve.Sommars@att.com) for his extensive help in testing the implementation. Many great suggestions were given. This is a much better product due to his involvement.
| 2006-06-11 | GNU Project |