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 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 iden-tified identified
tified 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 deci-mal decimal
mal 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 con-version conversion
version 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 any-where anywhere
where 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 new-lines newlines
lines (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" pro-gram. program.
gram. 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 capi-tals. capitals.
tals. 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 per-formed performed
formed 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 variable and then the variable is incre-mented incremented
mented 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 gen-erated generated
erated 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 evalu-ated evaluated
ated 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 opera-tors operators
tors 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 assign-ment assignment
ment 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 func-
tions 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 pro-gram program
gram 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 expres-sion. expression.
sion.
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 impor-tant important
tant 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 sepa-rated separated
rated 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 print-ing printing
ing the numbers where each higher base digit is printed as a base 10 number. The multi-char-acter multi-character
acter 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 ignored.
{ statement_list }
This is the compound statement. It allows multiple statements to be grouped together for exe-cution. execution.
cution.
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 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 exe-cution execution
cution 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 evalu-ated. evaluated.
ated. 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 enclosing while statement or for state-ment. statement.
ment.
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 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.
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 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 run-time runtime
time 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 initial-ized initialized
ized 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 function
tion 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 new-lines. newlines.
lines. 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); }
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 implement a simple program for calcu-lating calculating
lating 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);
}
READLINE AND LIBEDIT OPTIONS
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 manu-
als 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
traditional way using dc(1). This version is a single process which parses and runs a byte code
translation of the program. There is an "undocumented" option (-c) that causes the program to output
the byte code to the standard output instead of running it. It was mainly used for debugging the
parser and preparing the math library.
A major source of differences is extensions, where a feature is extended to add more functionality
and additions, where new features are added. The following is the list of differences and exten-sions. extensions.
sions.
LANG 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 let-ters, letters,
ters, 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 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 func-tion function
tion 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 invali-date invalidate
date 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.
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 interruption. All auto variables and function parame-ters parameters
ters 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 dif-ferent. different.
ferent.
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 arguments
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
environment 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 ``Sub-ject:'' ``Subject:''
ject:'' 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 test-ing testing
ing the implementation. Many great suggestions were given. This is a much better product due to his
involvement.
. bc(1)
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