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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.

-h, --help
Print the usage and exit.

-i, --interactive
Force interactive mode.

-l, --mathlib
Define the standard math library.

-w, --warn
Give warnings for extensions to POSIX bc.

-s, --standard
Process exactly the POSIX bc language.

-q, --quiet
Do not print the normal GNU bc welcome.

-v, --version
Print the version number and copyright and quit.

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 significant decimal
digits in 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 16. Assigning a value
outside this range to ibase will result in a value of 2 or 16. Input numbers may contain
the characters 0–9 and A–F. (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 FFF 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

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
and an array variable is specified as
Unless specifically mentioned the scale of the result is the maximum scale of the
expressions involved.

- expr The result is the negation of the expression.

++ var The variable is incremented by one and the new value is the result of the

-- var The variable is decremented by one and the new value is the result of the

var ++
The result of the expression is the value of the variable and then the variable is
incremented by one.

var -- The result of the expression is the value of the variable and then the variable is
decremented by one.

expr + expr
The result of the expression is the sum of the two expressions.

expr - expr
The result of the expression is the difference of the two expressions.

expr * expr
The result of the expression is the product of the two expressions.

expr / expr
The result of the expression is the quotient of the two expressions. The scale of
the result is the value of the variable scale.

expr % expr
The result of the expression is the "remainder" and it is computed in the following
way. To compute a%b, first a/b is computed to scale digits. That result is used
to compute a-(a/b)*b to the scale of the maximum of scale+scale(b) and scale(a).
If scale is set to zero and both expressions are integers this expression is the
integer remainder function.

expr ^ expr
The result of the expression is the value of the first raised to the second. The
second expression must be an integer. (If the second expression is not an integer,
a warning is generated and the expression is truncated to get an integer value.)
The scale of the result is scale if the exponent is negative. If the exponent is
positive the scale of the result is the minimum of the scale of the first
expression times the value of the exponent and the maximum of scale and the scale
of the first expression. (e.g. scale(a^b) = min(scale(a)*b, max( scale,
scale(a))).) It should be noted that expr^0 will always return the value of 1.

( expr )
This alters the standard precedence to force the evaluation of the expression.

var = expr
The variable is assigned the value of the expression.

var <op>= expr
This is equivalent to "var = var <op> expr" with the exception that the "var" part
is evaluated only once. This can make a difference if "var" is an array.

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

expr1 < expr2
The result is 1 if expr1 is strictly less than expr2.

expr1 <= expr2
The result is 1 if expr1 is less than or equal to expr2.

expr1 > expr2
The result is 1 if expr1 is strictly greater than expr2.

expr1 >= expr2
The result is 1 if expr1 is greater than or equal to expr2.

expr1 == expr2
The result is 1 if expr1 is equal to expr2.

expr1 != expr2
The result is 1 if expr1 is not equal to expr2.

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:

!expr The result is 1 if expr is 0.

expr && expr
The result is 1 if both expressions are non-zero.

expr || expr
The result is 1 if either expression is non-zero.

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:

length ( expression )
The value of the length function is the number of significant digits in the

read ( )
The read function (an extension) will read a number from the standard input,
regardless of where the function occurs. Beware, this can cause problems with the
mixing of data and program in the standard input. The best use for this function
is in a previously written program that needs input from the user, but never allows
program code to be input from the user. The value of the read function is the
number read from the standard input using the current value of the variable ibase
for the conversion base.

scale ( expression )
The value of the scale function is the number of digits after the decimal point in
the expression.

sqrt ( expression )
The value of the sqrt function is the square root of the expression. If the
expression is negative, a run time error is generated.

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.)

This statement does one of two things. If the expression starts with "<variable>
<assignment> ...", it is considered to be an assignment statement. If the
expression is not an assignment statement, the expression is evaluated and printed
to the output. After the number is printed, a newline is printed. For example,
"a=1" is an assignment statement and "(a=1)" is an expression that has an embedded
assignment. All numbers that are printed are printed in the base specified by the
variable obase. The legal values for obase are 2 through BC_BASE_MAX. (See the
section LIMITS.) For bases 2 through 16, the usual method of writing numbers is
used. For bases greater than 16, bc uses a multi-character digit method of
printing the numbers where each higher base digit is printed as a base 10 number.
The multi-character digits are separated by spaces. Each digit contains the number
of characters required to represent the base ten value of "obase-1". Since numbers
are of arbitrary precision, some numbers may not be printable on a single output
line. These long numbers will be split across lines using the "\" as the last
character on a line. The maximum number of characters printed per line is 70. Due
to the interactive nature of bc, printing a number causes the side effect of
assigning the printed value to the special variable last. This allows the user to
recover the last value printed without having to retype the expression that printed
the number. Assigning to last is legal and will overwrite the last printed value
with the assigned value. The newly assigned value will remain until the next
number is printed or another value is assigned to last. (Some installations may
allow the use of a single period (.) which is not part of a number as a short hand
notation for for last.)

string The string is printed to the output. Strings start with a double quote character
and contain all characters until the next double quote character. All characters
are take literally, including any newline. No newline character is printed after
the string.

print list
The print statement (an extension) provides another method of output. The "list"
is a list of strings and expressions separated by commas. Each string or
expression is printed in the order of the list. No terminating newline is printed.
Expressions are evaluated and their value is printed and assigned to the variable
last. Strings in the print statement are printed to the output and may contain
special characters. Special characters start with the backslash character (\).
The special characters recognized by bc are "a" (alert or bell), "b" (backspace),
"f" (form feed), "n" (newline), "r" (carriage return), "q" (double quote), "t"
(tab), and "\" (backslash). Any other character following the backslash will be

{ statement_list }
This is the compound statement. It allows multiple statements to be grouped
together for execution.

if ( expression ) statement1 [else statement2]
The if statement evaluates the expression and executes statement1 or statement2
depending on the value of the expression. If the expression is non-zero,
statement1 is executed. If statement2 is present and the value of the expression
is 0, then statement2 is executed. (The else clause is an extension.)

while ( expression ) statement
The while statement will execute the statement while the expression is non-zero.
It evaluates the expression before each execution of the statement. Termination
of the loop is caused by a zero expression value or the execution of a break

for ( [expression1] ; [expression2] ; [expression3] ) statement
The for statement controls repeated execution of the statement. Expression1 is
evaluated before the loop. Expression2 is evaluated before each execution of the
statement. If it is non-zero, the statement is evaluated. If it is zero, the loop
is terminated. After each execution of the statement, expression3 is evaluated
before the reevaluation of expression2. If expression1 or expression3 are missing,
nothing is evaluated at the point they would be evaluated. If expression2 is
missing, it is the same as substituting the value 1 for expression2. (The optional
expressions are an extension. POSIX bc requires all three expressions.) The
following is equivalent code for the for statement:
while (expression2) {

break This statement causes a forced exit of the most recent enclosing while statement or
for statement.

The continue statement (an extension) causes the most recent enclosing for
statement to start the next iteration.

halt The halt statement (an extension) is an executed statement that causes the bc
processor to quit only when it is executed. For example, "if (0 == 1) halt" will
not cause bc to terminate because the halt is not executed.

return Return the value 0 from a function. (See the section on functions.)

return ( expression )
Return the value of the expression from a function. (See the section on
functions.) As an extension, the parenthesis are not required.

These statements are not statements in the traditional sense. They are not executed
statements. Their function is performed at "compile" time.

limits Print the local limits enforced by the local version of bc. This is an extension.

quit When the quit statement is read, the bc processor is terminated, regardless of
where the quit statement is found. For example, "if (0 == 1) quit" will cause bc
to terminate.

Print a longer warranty notice. This is an extension.

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"; }
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.

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.

In /bin/sh, the following will assign the value of "pi" to the shell variable pi.
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.
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.
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

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

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.

LANG environment
This version does not conform to the POSIX standard in the processing of the LANG
environment variable and all environment variables starting with LC_.

names Traditional and POSIX bc have single letter names for functions, variables and
arrays. They have been extended to be multi-character names that start with a
letter and may contain letters, numbers and the underscore character.

Strings are not allowed to contain NUL characters. POSIX says all characters must
be included in strings.

last POSIX bc does not have a last variable. Some implementations of bc use the period
(.) in a similar way.

POSIX bc allows comparisons only in the if statement, the while statement, and the
second expression of the for statement. Also, only one relational operation is
allowed in each of those statements.

if statement, else clause
POSIX bc does not have an else clause.

for statement
POSIX bc requires all expressions to be present in the for statement.

&&, ||, !
POSIX bc does not have the logical operators.

read function
POSIX bc does not have a read function.

print statement
POSIX bc does not have a print statement.

continue statement
POSIX bc does not have a continue statement.

return statement
POSIX bc requires parentheses around the return expression.

array parameters
POSIX bc does not (currently) support array parameters in full. The POSIX grammar
allows for arrays in function definitions, but does not provide a method to specify
an array as an actual parameter. (This is most likely an oversight in the
grammar.) Traditional implementations of bc have only call by value array

function format
POSIX bc requires the opening brace on the same line as the define key word and the
auto statement on the next line.

=+, =-, =*, =/, =%, =^
POSIX bc does not require these "old style" assignment operators to be defined.
This version may allow these "old style" assignments. Use the limits statement to
see if the installed version supports them. If it does support the "old style"
assignment operators, the statement "a =- 1" will decrement a by 1 instead of
setting a to the value -1.

spaces in numbers
Other implementations of bc allow spaces in numbers. For example, "x=1 3" would
assign the value 13 to the variable x. The same statement would cause a syntax
error in this version of bc.

errors and execution
This implementation varies from other implementations in terms of what code will be
executed when syntax and other errors are found in the program. If a syntax error
is found in a function definition, error recovery tries to find the beginning of a
statement and continue to parse the function. Once a syntax error is found in the
function, the function will not be callable and becomes undefined. Syntax errors
in the interactive execution code will invalidate the current execution block. The
execution block is terminated by an end of line that appears after a complete
sequence of statements. For example,
a = 1
b = 2
has 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.

During an interactive session, the SIGINT signal (usually generated by the control-
C character from the terminal) will cause execution of the current execution block
to be interrupted. It will display a "runtime" error indicating which function was
interrupted. After all runtime structures have been cleaned up, a message will be
printed to notify the user that bc is ready for more input. All previously defined
functions remain defined and the value of all non-auto variables are the value at
the point of interruption. All auto variables and function parameters are removed
during the clean up process. During a non-interactive session, the SIGINT signal
will terminate the entire run of bc.

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 maximum output base is currently set at 999. The maximum input base is 16.

This is currently an arbitrary limit of 65535 as distributed. Your installation
may be different.

The number of digits after the decimal point is limited to INT_MAX digits. Also,
the number of digits before the decimal point is limited to INT_MAX digits.

The limit on the number of characters in a string is INT_MAX characters.

The value of the exponent in the raise operation (^) is limited to LONG_MAX.

variable names
The current limit on the number of unique names is 32767 for each of simple
variables, arrays and functions.


The following environment variables are processed by bc:

This is the same as the -s option.

This is another mechanism to get arguments to bc. The format is the same as the
command line arguments. These arguments are processed first, so any files listed
in the environment arguments are processed before any command line argument files.
This allows the user to set up "standard" options and files to be processed at
every invocation of bc. The files in the environment variables would typically
contain function definitions for functions the user wants defined every time bc is

This should be an integer specifying the number of characters in an output line for
numbers. This includes the backslash and newline characters for long numbers. As
an extension, the value of zero disables the multi-line feature. Any other value
of this variable that is less than 3 sets the line length to 70.


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.

Use bc online using onworks.net services

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