

bc(1)                     Minix Programmer's Manual                      bc(1)


NAME
     bc - An arbitrary precision calculator language

SYNTAX
     bc [ -lws ] [  file ... ]

VERSION
     This man page documents GNU bc version 1.02.

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

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

  OPTIONS

     -l   Define the standard math library.

     -w   Give warnings for extensions to POSIX bc.

     -s   Process exactly the POSIX bc language.

  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  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.







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  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.

  EXPRESSIONS
     The numbers are manipulated by expressions  and  statements.   Since  the
     language  was  designed to be interactive, statements and expressions are
     executed as soon as possible.  There is no "main" 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 (F).  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.


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     Legal  values  of  the  variable  scale  are  0  to  the  maximum  number
     representable by a C integer.

     In the following descriptions of legal expressions, "expr"  refers  to  a
     complete expression and "var" refers to a simple or an array variable.  A
     simple variable is just a
          name
     and an array variable is specified as
          name[expr]
     Unless specifically mentioned the scale of  the  result  is  the  maximum
     scale of the expressions involved.

     - expr
          The result is the negation of the expression.

     ++ var
          The variable is incremented by one and the new value is  the  result
          of the expression.

     -- var
          The variable is decremented by one and the new value is  the  result
          of the expression.

     var ++
           The result of the expression is the value of the variable and  then
          the variable is 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


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          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.




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     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 are:

     !expr
          The result is 1 if expr is 0.

     expr && expr
          The result is 1 if both expressions are non-zero.

     expr || expr
          The result is 1 if either expression is non-zero.

     The expression precedence is as follows: (lowest to highest)
          || operator, left associative
          && operator, left associative
          ! operator, nonassociative
          Relational operators, left associative
          Assignment operator, right associative
          + and - operators, left associative
          *, / and % operators, left associative
          ^ operator, right associative
          unary - operator, nonassociative
          ++ and -- operators, nonassociative

     This precedence was chosen so that POSIX compliant bc programs  will  run
     correctly.  This  will  cause  the  use  of  the  relational  and logical
     operators to  have  some  unusual  behavior  when  used  with  assignment
     expressions.  Consider the expression:
          a = 3 < 5

     Most C programmers would assume this would assign the result of "3  <  5"
     (the  value  1)  to the variable "a".  What this does in bc is assign the
     value 3 to the variable "a" and then compare 3 to 5.  It is best  to  use
     parenthesis   when  using  relational  and  logical  operators  with  the
     assignment operators.

     There are a few more special expressions that are provided in bc.   These
     have  to do with user defined functions and standard functions.  They all
     appear as "name(parameters)".  See the  section  on  functions  for  user
     defined functions.  The standard functions are:

     length ( expression )
          The value of the length function is the number of significant digits
          in the expression.




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     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 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 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.)

     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


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          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 cause the side effect of
          assigning the printed value the  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.

     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  the  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 "b" (bell),  "f"  (form  feed),  "n"  (newline),  "r"  (carriage
          return),  "t"  (tab),  and  "\"  (backslash).   Any  other character
          following the backslash will be ignored.  This still does not  allow
          the double quote character to be part of any string.

     { statement_list }
          This is the compound statement.  It allows multiple statements to be
          grouped together for execution.

     if ( expression ) then 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.





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     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:
               expression1;
               while (expression2) {
                  statement;
                  expression3;
               }

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

     continue
          The continue  statement  (an  extension)   causes  the  most  recent
          enclosing for statement to start the next iteration.

     halt The halt statement (an extension)  is  an  executed  statement  that
          causes  the  bc  processor  to  quit  only when it is executed.  For
          example, "if (0 == 1) halt" will not cause bc to  terminate  because
          the halt is not executed.

     return
          Return the value 0 from a function.  (See the section on functions.)

     return ( expression )
          Return the value of  the  expression  from  a  function.   (See  the
          section on functions.)

  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.



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     warranty
          Print a longer warranty notice.  This is an extension.

  FUNCTIONS
     Functions provide a method of defining a computation that can be executed
     later.   Functions  in  bc  always  compute  a value and return it to the
     caller.  Function definitions are "dynamic" in the sense that a  function
     is  undefined  until  a  definition  is  encountered  in the input.  That
     definition is then used until another definition function  for  the  same
     name  is  encountered.   The  new  definition  then  replaces  the  older
     definition.  A function is defined as follows:
          define name ( parameters ) { newline
              auto_list   statement_list }
     A function call is just an expression of the form "name(parameters)".

     Parameters are  numbers  or  arrays  (an  extension).   In  the  function
     definition,  zero  or  more parameters are defined by listing their names
     separated by commas.  Numbers are only call by value parameters.   Arrays
     are  only  call  by  variable.   Arrays  are  specified  in the parameter
     definition by the notation  "name[]".    In  the  function  call,  actual
     parameters are full expressions for number parameters.  The same notation
     is used for passing arrays as for defining array parameters.   The  named
     array  is passed by variable to the function.  Since function definitions
     are dynamic, parameter numbers and types are checked when a  function  is
     called.   Any  mismatch  in  number  or  types of parameters will cause a
     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 in the fact that
     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


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     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.

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

     s (x)
          The sine of x in radians.

     c (x)
          The cosine of x in radians.

     a (x)
          The arctangent of x.

     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) {


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            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()


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            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);
          }


  DIFFERENCES
     This version of bc was implemented from the POSIX P1003.2/D11  draft  and
     contains  several  differences  and  extensions relative to the draft and
     traditional implementations.  It is not implemented  in  the  traditional
     way using dc(1). This version is a single process which parses and runs a
     byte code translation of the program.  There is an "undocumented"  option
     (-c)  that  causes  the  program  to output the byte code to the standard
     output instead of running it.  It  was  mainly  used  for  debugging  the
     parser and preparing the math library.

     A major source of differences is extensions, where a feature is  extended
     to  add  more  functionality and additions, where new features are added.
     The following is the list of differences and extensions.

     LANG       This version does not conform to the  POSIX  standard  in  the
                processing   of   the   LANG   environment  variable  and  all
                environment variables starting with LC_.

     names      Traditional  and  POSIX  bc  have  single  letter  names   for
                functions,  variables  and arrays.  They have been extended to
                be multi-character names that start  with  a  letter  and  may
                contain letters, numbers and the underscore character.

     Strings    Strings are not allowed to contain NUL characters.  POSIX says
                all 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.



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     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.

     array parameters
                POSIX   bc   does   not   have   array   parameters.     Other
                implementations of bc may have call by value array parameters.

     =+, =-, =*, =/, =%, =^
                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


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                has two execution blocks and
                     { a = 1
                       b = 2 }
                has one execution block.  Any runtime error will terminate the
                execution  of  the current execution block.  A runtime warning
                will not terminate the current execution block.

     Interrupts During an interactive  session,  the  SIGINT  signal  (usually
                generated  by  the control-C character from the terminal) will
                cause  execution  of  the  current  execution  block   to   be
                interrupted.   It  will  display  a "runtime" error indicating
                which function was interrupted.  After all runtime  structures
                have  been cleaned up, a message will be printed to notify the
                user that bc is ready for more input.  All previously  defined
                functions  remain  defined  and  the  value  of  all  non-auto
                variables are the value at the  point  of  interruption.   All
                auto  variables and function parameters are removed during the
                clean up  process.   During  a  non-interactive  session,  the
                SIGINT signal will terminate the entire run of bc.

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

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

     BC_DIM_MAX This is currently an arbitrary limit of 65535 as  distributed.
                Your 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.

     multiply   The multiply routine may yield incorrect results if  a  number
                has  more  than LONG_MAX / 90 total digits.  For 32 bit longs,
                this number is 23,860,929 digits.





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     code size  Each function and the "main"  program  are  limited  to  10240
                bytes  of  compiled  byte code each.  This limit (BC_MAX_SEGS)
                can be easily changed to have more than 10  segments  of  1024
                bytes.

     variable names
                The current limit on the number of unique names is  32767  for
                each of simple variables, arrays and functions.

FILES
     In most installations, bc is completely self-contained.  Where executable
     size  is  of  importance  or  the C compiler does not deal with very long
     strings,  bc  will  read  the  standard  math  library  from   the   file
     /usr/local/lib/libmath.b.   (The  actual  location  may  vary.  It may be
     /lib/libmath.b.)

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.

AUTHOR
     Philip A. Nelson
     phil@cs.wwu.edu

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




















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