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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 execu-
tion 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 implementa-
tions and the POSIX draft standard. Command line options can cause these exten-
sions to print a warning or to be rejected. This document describes the language
accepted by this processor. Extensions 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 num-
bers. 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 deci-
mal. (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 characters */. Com-
ments 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 pro-
cessed 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 pos-
sible. There is no "main" program. Instead, code is executed as it is encoun-
tered. (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 vari-
able 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 nega-
tive. 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 expres-
sion.
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 rela-
tional 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 cur-
rent 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 hap-
pens 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 new-
line. A statement list is a series of statements separated by semicolons and new-
lines. 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 state-
ment. If the expression is not an assignment statement, the expression is
evaluated and printed to the output. After the number is printed, a newline
is printed. For example, "a=1" is an assignment statement and "(a=1)" is an
expression that has an embedded assignment. All numbers that are printed
are printed in the base specified by the variable obase. The legal values
for obase are 2 through BC_BASE_MAX. (See the section LIMITS.) For bases 2
through 16, the usual method of writing numbers is used. For bases greater
than 16, bc uses a multi-character digit method of printing the numbers
where each higher base digit is printed as a base 10 number. The multi-
character digits are separated by spaces. Each digit contains the number of
characters required to represent the base ten value of "obase-1". Since
numbers are of arbitrary precision, some numbers may not be printable on a
single output line. These long numbers will be split across lines using the
"\" as the last character on a line. The maximum number of characters
printed per line is 70. Due to the interactive nature of bc, printing a
number causes the side effect of assigning the printed value to the special
variable last. This allows the user to recover the last value printed with-
out 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 char-
acter 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 charac-
ters start with the backslash character (\). The special characters recog-
nized 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 statement1 or state-
ment2 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 execu-
tion 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 execu-
tion 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 expres-
sion1 or expression3 are missing, nothing is evaluated at the point they
would be evaluated. If expression2 is missing, it is the same as substitut-
ing the value 1 for expression2. (The optional expressions are an exten-
sion. 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 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 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 exe-
cuted 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 defi-
nitions 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 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 syn-
tax 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 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 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 func-
tion 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 stan-
dard 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 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);
}
READLINE AND LIBEDIT OPTIONS
GNU bc can be compiled (via a configure option) to use the GNU readline input edi-
tor 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 spe-
cial variable, history is the number of lines of history retained. For readline, a
value of -1 means that an unlimited number of history lines are retained. Setting
the value of history to a positive number restricts the number of history lines to
the number given. The value of 0 disables the history feature. The default value
is 100. For more information, read the user manuals for the GNU readline, history
and BSD libedit libraries. One can not enable both readline and libedit at the
same time.
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 implemen-
tations. 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 debug-
ging 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 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 characters. POSIX says all charac-
ters 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 function definition, error recovery tries to
find the beginning of a statement and continue to parse the function. Once
a syntax error is found in the function, the function will not be callable
and becomes undefined. Syntax errors in the interactive execution code will
invalidate the current execution block. The execution block is terminated
by an end of line that appears after a complete sequence of statements. For
example,
a = 1
b = 2
has two execution blocks and
{ a = 1
b = 2 }
has one execution block. Any runtime error will terminate the execution of the
current execution block. A runtime warning will not terminate the current execu-
tion 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 indi-
cating 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 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 instal-
lation 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 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 environ-
ment 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 AT gnu.org. Be sure to include the word ''bc'' somewhere
in the ''Subject:'' field.
AUTHOR
Philip A. Nelson
philnelson AT acm.org
ACKNOWLEDGEMENTS
The author would like to thank Steve Sommars (Steve.Sommars AT att.com) for his exten-
sive help in testing the implementation. Many great suggestions were given. This
is a much better product due to his involvement.
. bc(1)
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