bc
bc(1) bc(1)
NAME
bc - An arbitrary precision calculator language
SYNTAX
bc [ -hlwsqv ] [long-options] [ file ... ]
VERSION
This man page documents GNU bc version 1.06.
DESCRIPTION
bc is a language that supports arbitrary precision numbers with inter-
active 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. Exten-
sions will be identified as such.
OPTIONS
-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.
NUMBERS
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.
VARIABLES
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
Comments in bc start with the characters /* and end with the charac-
ters */. 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.
EXPRESSIONS
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 maxi-
mum 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
name
and an array variable is specified as
name[expr]
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 expression.
-- var The variable is decremented by one and the new value is the
result of the expression.
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 expres-
sions.
expr / expr
The result of the expression is the quotient of the two expres-
sions. 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 com-
puted in the following way. To compute a%b, first a/b is com-
puted 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 expression.
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
Statements (as in most algebraic languages) provide the sequencing of
expression evaluation. In bc statements are executed "as soon as pos-
sible." 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 new-
line will cause a syntax error. Because newlines are statement sepa-
rators, it is possible to hide a newline by using the backslash char-
acter. 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.)
expression
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 vari-
able 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 dou-
ble 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 sepa-
rated by commas. Each string or expression is printed in the
order of the list. No terminating newline is printed. Expres-
sions 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 ignored.
{ 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 state-
ment1 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 exten-
sion.)
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
statement.
for ( [expression1] ; [expression2] ; [expression3] ) statement
The for statement controls repeated execution of the statement.
Expression1 is evaluated before the loop. Expression2 is eval-
uated 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:
expression1;
while (expression2) {
statement;
expression3;
}
break This statement causes a forced exit of the most recent enclos-
ing while statement or for statement.
continue
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 func-
tions.)
return ( expression )
Return the value of the expression from a function. (See the
section on functions.) As an extension, the parenthesis are
not required.
PSEUDO STATEMENTS
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 termi-
nated, regardless of where the quit statement is found. For
example, "if (0 == 1) quit" will cause bc to terminate.
warranty
Print a longer warranty notice. This is an extension.
FUNCTIONS
Functions provide a method of defining a computation that can be exe-
cuted 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 def-
inition, 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 parame-
ter 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 parame-
ters. 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 vari-
able. 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 func-
tion B has called them auto variables. Due to the fact that auto
variables and parameters are pushed onto a stack, bc supports recur-
sive functions.
The function body is a list of bc statements. Again, statements are
separated by semicolons or newlines. Return statements cause the ter-
mination of a function and the return of a value. There are two ver-
sions of the return statement. The first form, "return", returns the
value 0 to the calling expression. The second form, "return ( expres-
sion )", 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 defini-
tions are legal.
define d (n) { return (2*n); }
define d (n)
{ return (2*n); }
MATH LIBRARY
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.
EXAMPLES
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 imple-
ment a simple program for calculating checkbook balances. This pro-
gram 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);
}
READLINE AND LIBEDIT OPTIONS
GNU bc can be compiled (via a configure option) to use the GNU read-
line 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 his-
tory 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.
DIFFERENCES
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 tradi-
tional way using dc(1). This version is a single process which parses
and runs a byte code translation of the program. There is an "undocu-
mented" 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.
LANG This version does not conform to the POSIX standard in the pro-
cessing of the LANG environment variable and all environment
variables starting with LC_.
names Traditional and POSIX bc have single letter names for func-
tions, 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
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.
comparisons
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
parameters.
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 opera-
tors 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 exam-
ple, "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 execu-
tion 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 execu-
tion of the current execution block. A runtime warning will not ter-
minate the current execution block.
Interrupts
During an interactive session, the SIGINT signal (usually gen-
erated 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.
LIMITS
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.
BC_BASE_MAX
The maximum output base is currently set at 999. The maximum
input base is 16.
BC_DIM_MAX
This is currently an arbitrary limit of 65535 as distributed.
Your installation may be different.
BC_SCALE_MAX
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.
BC_STRING_MAX
The limit on the number of characters in a string is INT_MAX
characters.
exponent
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.
ENVIRONMENT VARIABLES
The following environment variables are processed by bc:
POSIXLY_CORRECT
This is the same as the -s option.
BC_ENV_ARGS
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 environent argu-
ments 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 envi-
ronment variables would typically contain function definitions
for functions the user wants defined every time bc is run.
BC_LINE_LENGTH
This should be an integer specifing the number of characters in
an output line for numbers. This includes the backslash and
newline characters for long numbers.
DIAGNOSTICS
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.
BUGS
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.
AUTHOR
Philip A. Nelson
philnelson@acm.org
ACKNOWLEDGEMENTS
The author would like to thank Steve Sommars (Steve.Sommars@att.com)
for his extensive help in testing the implementation. Many great sug-
gestions were given. This is a much better product due to his
involvement.
. bc(1)
