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bc(1) General Commands Manual bc(1)
NAME
bc - An arbitrary precision calculator language
SYNTAX
bc [ -hlwsqv ] [long-options] [ file ... ]
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 op-
tion. 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.
OPTIONS
-h, --help
Print the usage and exit.
-i, --interactive
Force interactive mode.
-l, --mathlib
Define the standard math library.
-w, --warn
Give warnings for extensions to POSIX bc.
-s, --standard
Process exactly the POSIX bc language.
-q, --quiet
Do not print the normal GNU bc welcome.
-v, --version
Print the version number and copyright and quit.
NUMBERS
The most basic element in bc is the number. Numbers are arbitrary precision numbers. This precision is both in the
integer part and the fractional part. All numbers are represented internally in decimal and all computation is done
in decimal. (This version truncates results from divide and multiply operations.) There are two attributes of num-
bers, the length and the scale. The length is the total number of decimal digits used by bc to represent 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 */. 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 com-
ment and is processed normally.
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 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
36. (Bases greater than 16 are an extension.) Assigning a value outside this range to ibase will result in a value of
2 or 36. Input numbers may contain the characters 0-9 and A-Z. (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 ZZZ 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 vari-
able 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 sim-
ple or an array variable. A simple variable is just a
name
and an array variable is specified as
name[expr]
Unless specifically mentioned the scale of the result is the maximum scale of the expressions involved.
- expr The result is the negation of the expression.
++ var The variable is incremented by one and the new value is the result of the expression.
-- var The variable is decremented by one and the new value is the result of the expression.
var ++
The result of the expression is the value of the variable and then the variable is incremented by one.
var -- The result of the expression is the value of the variable and then the variable is decremented by one.
expr + expr
The result of the expression is the sum of the two expressions.
expr - expr
The result of the expression is the difference of the two expressions.
expr * expr
The result of the expression is the product of the two 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 expres-
sions are used only in if, while, and for statements and that only one relational test may be done in them.) The re-
lational 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 opera-
tions are 0 and 1 (for false and true) as in relational expressions. The boolean operators are:
!expr The result is 1 if expr is 0.
expr && expr
The result is 1 if both expressions are non-zero.
expr || expr
The result is 1 if either expression is non-zero.
The expression precedence is as follows: (lowest to highest)
|| operator, left associative
&& operator, left associative
! operator, nonassociative
Relational operators, left associative
Assignment operator, right associative
+ and - operators, left associative
*, / and % operators, left associative
^ operator, right associative
unary - operator, nonassociative
++ and -- operators, nonassociative
This precedence was chosen so that POSIX compliant bc programs will run correctly. This will cause the use of the
relational and logical operators to have some unusual behavior when used with assignment expressions. Consider the
expression:
a = 3 < 5
Most C programmers would assume this would assign the result of "3 < 5" (the value 1) to the variable "a". What this
does in bc is assign the value 3 to the variable "a" and then compare 3 to 5. It is best to use parenthesis when us-
ing 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 pro-
gram code to be input from the user. The value of the read function is the number read from the standard in-
put 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
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 state-
ments separated by semicolons and newlines. The following is a list of bc statements and what they do: (Things en-
closed in brackets ([]) are optional parts of the statement.)
expression
This statement does one of two things. If the expression starts with "<variable> <assignment> ...", it is
considered to be an assignment statement. If the expression is not an assignment statement, the expression is
evaluated and printed to the output. After the number is printed, a newline is printed. For example, "a=1"
is an assignment statement and "(a=1)" is an expression that has an embedded assignment. All numbers that are
printed are printed in the base specified by the variable obase. The legal values for obase are 2 through
BC_BASE_MAX. (See the section LIMITS.) For bases 2 through 16, the usual method of writing numbers is used.
For bases greater than 16, bc uses a multi-character digit method of printing the numbers where each higher
base digit is printed as a base 10 number. The multi-character digits are separated by spaces. Each digit
contains the number of characters required to represent the base ten value of "obase-1". Since numbers are of
arbitrary precision, some numbers may not be printable on a single output line. These long numbers will be
split across lines using the "\" as the last character on a line. The maximum number of characters printed
per line is 70. Due to the interactive nature of bc, printing a number causes the side effect of assigning
the printed value to the special 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
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 ex-
pressions 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 recognized by bc are "a" (alert or bell),
"b" (backspace), "f" (form feed), "n" (newline), "r" (carriage return), "q" (double quote), "t" (tab), and "\"
(backslash). Any other character following the backslash will be ignored.
{ statement_list }
This is the compound statement. It allows multiple statements to be grouped together for execution.
if ( expression ) statement1 [else statement2]
The if statement evaluates the expression and executes 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 evalu-
ated. 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 fol-
lowing 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 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 un-
til 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. All parameters are call by value parameters. 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 value 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 er-
ror 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 speci-
fied 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 vari-
ables. 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 ( ex-
pression )", computes the value of the expression and returns that value to the calling expression. There is an im-
plied "return (0)" at the end of every function. This allows a function to terminate and return 0 without an ex-
plicit 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.
Several extensions have been added to functions. First, 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 follow-
ing 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); }
Functions may be defined as void. A void function returns no value and thus may not be used in any place that needs
a value. A void function does not produce any output when called by itself on an input line. The key word void is
placed between the key word define and the function name. For example, consider the following session.
define py (y) { print "--->", y, "<---", "\n"; }
define void px (x) { print "--->", x, "<---", "\n"; }
py(1)
--->1<---
0
px(1)
--->1<---
Since py is not a void function, the call of py(1) prints the desired output and then prints a second line that is
the value of the function. Since the value of a function that is not given an explicit return statement is zero, the
zero is printed. For px(1), no zero is printed because the function is a void function.
Also, call by variable for arrays was added. To declare a call by variable array, the declaration of the array pa-
rameter in the function definition looks like "*name[]". The call to the function remains the same as call by value
arrays.
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 func-
tions 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, 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 editor library or the BSD libedit li-
brary. This allows the user to do editing of lines before sending them to bc. It also allows for a history of pre-
vious 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 manuals for the GNU readline, history and BSD libedit libraries. One can not enable both readline and
libedit at the same time.
DIFFERENCES
This version of bc was implemented from the POSIX P1003.2/D11 draft and contains several differences and extensions
relative to the draft and traditional implementations. It is not implemented in the 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 "undocu-
mented" option (-c) that causes the program to output the byte code to the standard output instead of running it. It
was mainly used for debugging the parser and preparing the math library.
A major source of differences is extensions, where a feature is extended to add more functionality and additions,
where new features are added. The following is the list of differences and extensions.
LANG environment
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 ex-
tended to be multi-character names that start with a letter and may contain letters, numbers and the under-
score 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 func-
tion 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 parame-
ters.
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 execution block.
Interrupts
During an interactive session, the SIGINT signal (usually generated by the control-C character from the termi-
nal) 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 de-
fined and the value of all non-auto variables are the value at the point of interruption. All auto variables
and function parameters are removed during the clean up process. During a non-interactive session, the SIGINT
signal will terminate the entire run of bc.
LIMITS
The following are the limits currently in place for this bc processor. Some of them may have been changed by an in-
stallation. Use the limits statement to see the actual values.
BC_BASE_MAX
The maximum output base is currently set at 999. The maximum input base is 16.
BC_DIM_MAX
This is currently an arbitrary limit of 65535 as distributed. Your installation may be different.
BC_SCALE_MAX
The number of digits after the decimal point is limited to INT_MAX digits. Also, the number of digits before
the decimal point is limited to INT_MAX digits.
BC_STRING_MAX
The limit on the number of characters in a string is INT_MAX characters.
exponent
The value of the exponent in the raise operation (^) is limited to LONG_MAX.
variable names
The current limit on the number of unique names is 32767 for each of simple variables, arrays and functions.
ENVIRONMENT VARIABLES
The following environment variables are processed by bc:
POSIXLY_CORRECT
This is the same as the -s option.
BC_ENV_ARGS
This is another mechanism to get arguments to bc. The format is the same as the command line arguments.
These arguments are processed first, so any files listed in the environment 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
This should be an integer specifying the number of characters in an output line for numbers. This includes
the backslash and newline characters for long numbers. As an extension, the value of zero disables the multi-
line feature. Any other value of this variable that is less than 3 sets the line length to 70.
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 extensive help in testing the implemen-
tation. Many great suggestions were given. This is a much better product due to his involvement.
GNU Project 2006-06-11 bc(1)
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