NAME
bc - An arbitrary precision calculator language
SYNTAX
bc [ -lws ] [ file ... ]
VERSION
This man page documents GNU bc version 1.02.
DESCRIPTION
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 tradi-
tional 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.
OPTIONS
-l Define the standard math library.
-w Give warnings for extensions to POSIX bc.
-s Process exactly the POSIX bc language.
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 vari-
ables 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
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.
EXPRESSIONS
The numbers are manipulated by expressions and statements.
Since the language was designed to be interactive, state-
ments 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 con-
stants into internal decimal numbers using the current input
base, specified by the variable ibase. (There is an excep-
tion in functions.) The legal values of ibase are 2 through
16 (F). 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 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 vari-
able and then the variable is incremented by one.
var --
The result of the expression is the value of the vari-
able 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 expres-
sions. 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 pro-
grams 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 sig-
nificant digits in the expression.
read ( )
The read function (an extension) will read a number
from the standard input, regardless of where the func-
tion 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 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 new-
line 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.)
expression
This statement does one of two things. If the expres-
sion starts with "<variable> <assignment> ...", it is
considered to be an assignment statement. If the
expression is not an assignment statement, the expres-
sion 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 speci-
fied 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 interac-
tive nature of bc printing a number cause the side
effect of assigning the printed value the 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.
string
The string is printed to the output. Strings start
with a double quote character and contain all charac-
ters until the next double quote character. All char-
acters 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 the
the variable last. Strings in the print statement are
printed to the output and may contain special charac-
ters. Special characters start with the backslash
character (\). The special characters recognized by bc
are "b" (bell), "f" (form feed), "n" (newline), "r"
(carriage return), "t" (tab), and "\" (backslash). Any
other character following the backslash will be
ignored. This still does not allow the double quote
character to be part of any string.
{ statement_list }
This is the compound statement. It allows multiple
statements to be grouped together for execution.
if ( expression ) then 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 expres-
sion before each execution of the statement. Termina-
tion 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 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 expres-
sions.) 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
enclosing while statement or for statement.
continue
The continue statement (an extension) causes the most
recent enclosing for statement to start the next itera-
tion.
halt The halt statement (an extension) is an executed state-
ment 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.)
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
terminated, 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 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 nota-
tion is used for passing arrays as for defining array param-
eters. The named array is passed by variable to the func-
tion. 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 vari-
ables 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 func-
tion 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 vari-
ables in the fact that 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, state-
ments 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 ( 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.
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 follow-
ing functions:
s (x)
The sine of x in radians.
c (x)
The cosine of x in radians.
a (x)
The arctangent of x.
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 implement a simple program for calculating checkbook bal-
ances. 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);
}
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 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 pro-
gram 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 differ-
ences and extensions.
LANG This version does not conform to the POSIX stan-
dard 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 Strings are not allowed to contain NUL charac-
ters. 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 state-
ment, the while statement, and the second expres-
sion of the for statement. Also, only one rela-
tional 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.
array parameters
POSIX bc does not have array parameters. Other
implementations of bc may have call by value
array parameters.
=+, =-, =*, =/, =%, =^
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 implementa-
tions 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 defini-
tion, error recovery tries to find the beginning
of a statement and continue to parse the func-
tion. Once a syntax error is found in the func-
tion, the function will not be callable and
becomes undefined. Syntax errors in the interac-
tive execution code will invalidate the current
execution block. The execution block is ter-
minated 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.
Interrupts 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 interrup-
tion. 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 instal-
lation. 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 dis-
tributed. 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.
multiply
The multiply routine may yield incorrect results if a
number has more than LONG_MAX / 90 total digits. For
32 bit longs, this number is 23,860,929 digits.
code size
Each function and the "main" program are limited to
10240 bytes of compiled byte code each. This limit
(BC_MAX_SEGS) can be easily changed to have more than
10 segments of 1024 bytes.
variable names
The current limit on the number of unique names is
32767 for each of simple variables, arrays and func-
tions.
FILES
In most installations, bc is completely self-contained.
Where executable size is of importance or the C compiler
does not deal with very long strings, bc will read the stan-
dard math library from the file /usr/local/lib/libmath.b.
(The actual location may vary. It may be /lib/libmath.b.)
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.
AUTHOR
Philip A. Nelson
phil@cs.wwu.edu
ACKNOWLEDGEMENTS
The author would like to thank Steve Sommars
(sesv@iwtsf.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.