bc
bc and Other Implementations
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 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.
Email bug reports to bug-bc@gnu.org. Be sure to include the word "bc" somewhere in the "Subject:" field.
bc takes the following options from the command line:
-h, --help
-l, --mathlib
-w, --warn
bc.
-s, --standard
bc language.
-q, --quiet
bc welcome.
-v, --version
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, while 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 alphanumeric
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 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
++ var
-- var
var ++
var --
expr + expr
expr - expr
expr * expr
expr / expr
scale
expr % expr
expr ^ expr
( expr )
var = expr
var <op>= expr
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
expr1 <= expr2
expr1 > expr2
expr1 >= expr2
expr1 == expr2
expr1 != 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
expr && expr
expr || expr
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 parentheses 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 section Functions, for
user-defined functions. The standard functions are:
length ( expression )
read ( )
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 )
scale function is the number of digits after the
decimal point in the expression.
sqrt ( expression )
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.)
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.)
print list
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 (\e).
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 "\e" (backslash). Any other
character following the backslash will be ignored.
if ( expression ) statement1 [else statement2]
else clause is an extension.)
while ( expression ) statement
break statement.
for ( [expression1] ; [expression2] ; [expression3] ) statement
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:
expression1;
while (expression2) {
statement;
expression3;
}
break
while
statement or for statement.
continue
continue statement (an extension) causes the most recent enclosing
for statement to start the next iteration.
halt
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 ( expression )
These statements are not statements in the traditional sense. They are not executed statements. Their function is performed at "compile" time.
limits
bc. This
is an extension.
quit
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
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:
definename(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 notation is used
for passing arrays as for defining array parameters. 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 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.
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
definitions are legal.
define d (n) { return (2*n); }
define d (n)
{ return (2*n); }
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)
c (x)
a (x)
l (x)
e (x)
j (n,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.
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
more 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. A
value of -1 means that an unlimited number of history lines are
retained. This is the default value. 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. 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.
bc and Other Implementations
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. 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.
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.
bc does not have a \fBlast variable. Some implementations
of bc use the period (.) in a similar way.
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.
bc does not have an else clause.
bc requires all expressions to be present in the
for statement.
bc does not have the logical operators.
bc does not have a read function.
bc does not have a print statement.
bc does not have a continue statement.
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.
bc requires the opening brace on the same line as the
define key word and the auto statement on the next line.
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.
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.
a = 1 b = 2has two execution blocks and
{ a = 1
b = 2 }
has one execution block. Any runtime error will terminate the execution
of the current execution block. A runtime warning will not terminate the
current execution block.
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.
BC_BASE_MAX
BC_DIM_MAX
BC_SCALE_MAX
BC_STRING_MAX
exponent
multiply
variable names
The following environment variables are processed by bc:
POSIXLY_CORRECT
BC_ENV_ARGS
bc. The format
is the same as the command line arguments. These arguments are
processed first, so any files listed in the environent 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 run.
BC_LINE_LENGTH
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