Provided by: bc_1.06.95-9build1_i386 bug


       bc - An arbitrary precision calculator language


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


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

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

       -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.  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 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.

       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 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); }

       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"; }
       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 parameter in the  function
       definition  looks like "*name[]".  The call to the function remains the
       same as call by value arrays.

       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.  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.


       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   Be  sure  to  include  the  word
       ``bc'' somewhere in the ``Subject:'' field.


       Philip A. Nelson


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