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bc(1)                       General Commands Manual                      bc(1)

       bc - An arbitrary precision calculator language

       bc [ -hlwsqv ] [long-options] [  file ... ]

       This man page documents GNU bc version 1.06.

       bc is a language that supports arbitrary precision numbers with
       interactive execution of statements.  There are some similarities in
       the syntax to the C programming language.  A standard math library is
       available by command line option.  If requested, the math library is
       defined before processing any files.  bc starts by processing code from
       all the files listed on the command line in the order listed.  After
       all files have been processed, bc reads from the standard input.  All
       code is executed as it is read.  (If a file contains a command to halt
       the processor, bc will never read from the standard input.)

       This version of bc contains several extensions beyond traditional bc
       implementations and the POSIX draft standard.  Command line options can
       cause these extensions to print a warning or to be rejected.  This
       document describes the language accepted by this processor.  Extensions
       will be identified as such.

       -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.

       The most basic element in bc is the number.  Numbers are arbitrary
       precision numbers.  This precision is both in the integer part and the
       fractional part.  All numbers are represented internally in decimal and
       all computation is done in decimal.  (This version truncates results
       from divide and multiply operations.)  There are two attributes of
       numbers, the length and the scale.  The length is the total number of
       significant decimal digits in a number and the scale is the total
       number of decimal digits after the decimal point.  For example:
               .000001 has a length of 6 and scale of 6.
               1935.000 has a length of 7 and a scale of 3.

       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 in bc start with the characters /* and end with the characters
       */.  Comments may start anywhere and appear as a single space in the
       input.  (This causes comments to delimit other input items.  For
       example, a comment can not be found in the middle of a variable name.)
       Comments include any newlines (end of line) between the start and the
       end of the comment.

       To support the use of scripts for bc, a single line comment has been
       added as an extension.  A single line comment starts at a # character
       and continues to the next end of the line.  The end of line character
       is not part of the comment and is processed normally.

       The numbers are manipulated by expressions and statements.  Since the
       language was designed to be interactive, statements and expressions are
       executed as soon as possible.  There is no "main" program.  Instead,
       code is executed as it is encountered.  (Functions, discussed in detail
       later, are defined when encountered.)

       A simple expression is just a constant. bc converts constants into
       internal decimal numbers using the current input base, specified by the
       variable ibase. (There is an exception in functions.)  The legal values
       of ibase are 2 through 16.  Assigning a value outside this range to
       ibase will result in a value of 2 or 16.  Input numbers may contain the
       characters 0-9 and A-F. (Note: They must be capitals.  Lower case
       letters are variable names.)  Single digit numbers always have the
       value of the digit regardless of the value of ibase. (i.e. A = 10.)
       For multi-digit numbers, bc changes all input digits greater or equal
       to ibase to the value of ibase-1.  This makes the number FFF always be
       the largest 3 digit number of the input base.

       Full expressions are similar to many other high level languages.  Since
       there is only one kind of number, there are no rules for mixing types.
       Instead, there are rules on the scale of expressions.  Every expression
       has a scale.  This is derived from the scale of original numbers, the
       operation performed and in many cases, the value of the variable scale.
       Legal values of the variable scale are 0 to the maximum number
       representable by a C integer.

       In the following descriptions of legal expressions, "expr" refers to a
       complete expression and "var" refers to a simple or an array variable.
       A simple variable is just a
       and an array variable is specified as
       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

       expr * expr
              The result of the expression is the product of the two

       expr / expr
              The result of the expression is the quotient of the two
              expressions.  The scale of the result is the value of the
              variable scale.

       expr % expr
              The result of the expression is the "remainder" and it is
              computed in the following way.  To compute a%b, first a/b is
              computed to scale digits.  That result is used to compute
              a-(a/b)*b to the scale of the maximum of scale+scale(b) and
              scale(a).  If scale is set to zero and both expressions are
              integers this expression is the integer remainder function.

       expr ^ expr
              The result of the expression is the value of the first raised to
              the second. The second expression must be an integer.  (If the
              second expression is not an integer, a warning is generated and
              the expression is truncated to get an integer value.)  The scale
              of the result is scale if the exponent is negative.  If the
              exponent is positive the scale of the result is the minimum of
              the scale of the first expression times the value of the
              exponent and the maximum of scale and the scale of the first
              expression.  (e.g. scale(a^b) = min(scale(a)*b, max( scale,
              scale(a))).)  It should be noted that expr^0 will always return
              the value of 1.

       ( expr )
              This alters the standard precedence to force the evaluation of
              the expression.

       var = expr
              The variable is assigned the value of the expression.

       var <op>= expr
              This is equivalent to "var = var <op> expr" with the exception
              that the "var" part is evaluated only once.  This can make a
              difference if "var" is an array.

        Relational expressions are a special kind of expression that always
       evaluate to 0 or 1, 0 if the relation is false and 1 if the relation is
       true.  These may appear in any legal expression.  (POSIX bc requires
       that relational expressions are used only in if, while, and for
       statements and that only one relational test may be done in them.)  The
       relational operators are

       expr1 < expr2
              The result is 1 if expr1 is strictly less than expr2.

       expr1 <= expr2
              The result is 1 if expr1 is less than or equal to expr2.

       expr1 > expr2
              The result is 1 if expr1 is strictly greater than expr2.

       expr1 >= expr2
              The result is 1 if expr1 is greater than or equal to expr2.

       expr1 == expr2
              The result is 1 if expr1 is equal to expr2.

       expr1 != expr2
              The result is 1 if expr1 is not equal to expr2.

       Boolean operations are also legal.  (POSIX bc does NOT have boolean
       operations). The result of all boolean operations are 0 and 1 (for
       false and true) as in relational expressions.  The boolean operators

       !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 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

       Statements (as in most algebraic languages) provide the sequencing of
       expression evaluation.  In bc statements are executed "as soon as
       possible."  Execution happens when a newline in encountered and there
       is one or more complete statements.  Due to this immediate execution,
       newlines are very important in bc. In fact, both a semicolon and a
       newline are used as statement separators.  An improperly placed newline
       will cause a syntax error.  Because newlines are statement separators,
       it is possible to hide a newline by using the backslash character.  The
       sequence "\<nl>", where <nl> is the newline appears to bc as whitespace
       instead of a newline.  A statement list is a series of statements
       separated by semicolons and newlines.  The following is a list of bc
       statements and what they do: (Things enclosed in brackets ([]) are
       optional parts of the statement.)

              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 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

       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 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

       for ( [expression1] ; [expression2] ; [expression3] ) statement
              The for statement controls repeated execution of the statement.
              Expression1 is evaluated before the loop.  Expression2 is
              evaluated before each execution of the statement.  If it is non-
              zero, the statement is evaluated.  If it is zero, the loop is
              terminated.  After each execution of the statement, expression3
              is evaluated before the reevaluation of expression2.  If
              expression1 or expression3 are missing, nothing is evaluated at
              the point they would be evaluated.  If expression2 is missing,
              it is the same as substituting the value 1 for expression2.
              (The optional expressions are an extension. POSIX bc requires
              all three expressions.)  The following is equivalent code for
              the for statement:
              while (expression2) {

       break  This statement causes a forced exit of the most recent enclosing
              while statement or for statement.

              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

       return ( expression )
              Return the value of the expression from a function.  (See the
              section on functions.)  As an extension, the parenthesis are not

       These statements are not statements in the traditional sense.  They are
       not executed statements.  Their function is performed at "compile"

       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.

              Print a longer warranty notice.  This is an extension.

       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 runtime error.  A runtime error will also occur for the call to
       an undefined function.

       The auto_list is an optional list of variables that are for "local"
       use.  The syntax of the auto list (if present) is "auto name, ... ;".
       (The semicolon is optional.)  Each name is the name of an auto
       variable.  Arrays may be specified by using the same notation as used
       in parameters.  These variables have their values pushed onto a stack
       at the start of the function.  The variables are then initialized to
       zero and used throughout the execution of the function.  At function
       exit, these variables are popped so that the original value (at the
       time of the function call) of these variables are restored.  The
       parameters are really auto variables that are initialized to a value
       provided in the function call.  Auto variables are different than
       traditional local variables because if function A calls function B, B
       may access function A's auto variables by just using the same name,
       unless function B has called them auto variables.  Due to the fact that
       auto variables and parameters are pushed onto a stack, bc supports
       recursive functions.

       The function body is a list of bc statements.  Again, statements are
       separated by semicolons or newlines.  Return statements cause the
       termination of a function and the return of a value.  There are two
       versions of the return statement.  The first form, "return", returns
       the value 0 to the calling expression.  The second form, "return (
       expression )", computes the value of the expression and returns that
       value to the calling expression.  There is an implied "return (0)" at
       the end of every function.  This allows a function to terminate and
       return 0 without an explicit return statement.

       Functions also change the usage of the variable ibase.  All constants
       in the function body will be converted using the value of ibase at the
       time of the function call.  Changes of ibase will be ignored during the
       execution of the function except for the standard function read, which
       will always use the current value of ibase for conversion of numbers.

       As an extension, the format of the definition has been slightly
       relaxed.  The standard requires the opening brace be on the same line
       as the define keyword and all other parts must be on following lines.
       This version of bc will allow any number of newlines before and after
       the opening brace of the function.  For example, the following
       definitions are legal.

              define d (n) { return (2*n); }
              define d (n)
                { return (2*n); }

       If bc is invoked with the -l option, a math library is preloaded and
       the default scale is set to 20.   The math functions will calculate
       their results to the scale set at the time of their call.  The math
       library defines the following functions:

       s (x)  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.

       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.

              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

       The following is the definition of the recursive factorial function.

              define f (x) {
                if (x <= 1) return (1);
                return (f(x-1) * x);

       GNU bc can be compiled (via a configure option) to use the GNU readline
       input editor library or the BSD libedit library.  This allows the user
       to do 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
       manuals for the GNU readline, history and BSD libedit libraries.  One
       can not enable both readline and libedit at the same time.

       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 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 extended to be multi-
              character names that start with a letter and may contain
              letters, numbers and the underscore character.

              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.

              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

       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

       &&, ||, !
              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

       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

       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.

              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 parameters are removed during the clean up process.
              During a non-interactive session, the SIGINT signal will
              terminate the entire run of bc.

       The following are the limits currently in place for this bc processor.
       Some of them may have been changed by an installation.  Use the limits
       statement to see the actual values.

              The maximum output base is currently set at 999.  The maximum
              input base is 16.

              This is currently an arbitrary limit of 65535 as distributed.
              Your installation may be different.

              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.

              The limit on the number of characters in a string is INT_MAX

              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.

       The following environment variables are processed by bc:

              This is the same as the -s option.

              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.

              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.

       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.

       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 ``Subject:'' field.

       Philip A. Nelson

       The author would like to thank Steve Sommars (Steve.Sommars@att.com)
       for his extensive help in testing the implementation.  Many great
       suggestions were given.  This is a much better product due to his

                                       .                                 bc(1)