Provided by: bc_1.06.95-2_amd64 bug

NAME

       bc - An arbitrary precision calculator language

SYNTAX

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

DESCRIPTION

       bc  is  a language that supports arbitrary precision numbers with interactive execution of
       statements.  There are some similarities in the syntax to the C programming  language.   A
       standard math library is available by command line 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
       -h, --help
              Print the usage and exit.

       -i, --interactive
              Force interactive mode.

       -l, --mathlib
              Define the standard math library.

       -w, --warn
              Give warnings for extensions to POSIX bc.

       -s, --standard
              Process exactly the POSIX bc language.

       -q, --quiet
              Do not print the normal GNU bc welcome.

       -v, --version
              Print the version number and copyright and quit.

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

   VARIABLES
       Numbers are stored in two types of variables, simple variables and  arrays.   Both  simple
       variables and array variables are named.  Names begin with a letter followed by any number
       of letters, digits and underscores.  All letters must be lower case.  (Full  alpha-numeric
       names  are  an extension. In POSIX bc all names are a single lower case letter.)  The type
       of variable is clear by the context because all array variable names will be  followed  by
       brackets ([]).

       There  are  four special variables, scale, ibase, obase, and last.  scale defines how some
       operations use digits after the decimal point.  The default value of scale is 0. ibase and
       obase define the conversion base for input and output numbers.  The default for both input
       and output is base 10.  last (an extension) is a variable that has the value of  the  last
       printed  number.   These  will  be  discussed in further detail where appropriate.  All of
       these variables may have values assigned to them as well as used in expressions.

   COMMENTS
       Comments in bc start with the characters /* and end with the characters */.  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.

   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.  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
              name
       and an array variable is specified as
              name[expr]
       Unless  specifically  mentioned  the  scale  of  the  result  is  the maximum scale of the
       expressions involved.

       - expr The result is the negation of the expression.

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

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

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

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

       expr + expr
              The result of the expression is the sum of the two expressions.

       expr - expr
              The result of the expression is the difference of the two expressions.

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

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

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

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

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

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

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

       Relational  expressions are a special kind of expression that always evaluate to 0 or 1, 0
       if the relation is false and 1 if the relation is true.  These may  appear  in  any  legal
       expression.   (POSIX  bc  requires that relational 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 are:

       !expr  The result is 1 if expr is 0.

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

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

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

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

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

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

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

       read ( )
              The  read  function  (an  extension)  will  read  a number from the standard input,
              regardless of where the function occurs.   Beware, this can cause problems with the
              mixing  of  data and program in the standard input.  The best use for this function
              is in a previously written program that needs input from the user, but never allows
              program  code  to  be  input  from the user.  The value of the read function is the
              number read from the standard input using the 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 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 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 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
              statement.

       for ( [expression1] ; [expression2] ; [expression3] ) statement
              The  for  statement  controls  repeated execution of the statement.  Expression1 is
              evaluated before the loop.  Expression2 is evaluated before each execution  of  the
              statement.  If it is non-zero, the statement is 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.)  As an extension, the parenthesis are not required.

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

       limits Print the local limits enforced by the local version of bc.  This is an extension.

       quit   When  the  quit  statement  is  read, the bc processor is terminated, regardless of
              where the quit statement is found.  For example, "if (0 == 1) quit" will  cause  bc
              to terminate.

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

   FUNCTIONS
       Functions  provide  a  method  of  defining  a  computation  that  can  be executed later.
       Functions in bc always compute a value and return it to the caller.  Function  definitions
       are  "dynamic" in the sense that a function is undefined 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 funtion 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, "<---", "0; }
              define void px (x) { print "--->", x, "<---", "0; }
              py(1)
              --->1<---
              0
              px(1)
              --->1<---
       Since  py  is  not  a  void function, the call of py(1) prints the desired output and then
       prints a second line that is the value of the function.  Since the  value  of  a  function
       that  is  not given an explicit return statement is zero, the zero is printed.  For px(1),
       no zero is printed because the function is a void function.

       Also, call by variable for arrays was added.  To declare a call  by  variable  array,  the
       declaration  of  the array parameter in the function definition looks like "*name[]".  The
       call to the function remains the same as call by value arrays.

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

       s (x)  The sine of x, x is in radians.

       c (x)  The cosine of x, x is in radians.

       a (x)  The arctangent of x, arctangent returns radians.

       l (x)  The natural logarithm of x.

       e (x)  The exponential function of raising e to the value x.

       j (n,x)
              The Bessel function of integer order n of x.

   EXAMPLES
       In /bin/sh,  the following will assign the value of "pi" to the shell variable pi.
               pi=$(echo "scale=10; 4*a(1)" | bc -l)

       The following is the definition of the exponential function  used  in  the  math  library.
       This function is written in POSIX bc.
              scale = 20

              /* Uses the fact that e^x = (e^(x/2))^2
                 When x is small enough, we use the series:
                   e^x = 1 + x + x^2/2! + x^3/3! + ...
              */

              define e(x) {
                auto  a, d, e, f, i, m, v, z

                /* Check the sign of x. */
                if (x<0) {
                  m = 1
                  x = -x
                }

                /* Precondition x. */
                z = scale;
                scale = 4 + z + .44*x;
                while (x > 1) {
                  f += 1;
                  x /= 2;
                }

                /* Initialize the variables. */
                v = 1+x
                a = x
                d = 1

                for (i=2; 1; i++) {
                  e = (a *= x) / (d *= i)
                  if (e == 0) {
                    if (f>0) while (f--)  v = v*v;
                    scale = z
                    if (m) return (1/v);
                    return (v/1);
                  }
                  v += e
                }
              }

       The  following is code that uses the extended features of bc to implement a simple program
       for calculating checkbook balances.  This program is best kept in a file so that it can be
       used many times without having to retype it at every use.
              scale=2
              print "\nCheck book program!\n"
              print "  Remember, deposits are negative transactions.\n"
              print "  Exit by a 0 transaction.\n\n"

              print "Initial balance? "; bal = read()
              bal /= 1
              print "\n"
              while (1) {
                "current balance = "; bal
                "transaction? "; trans = read()
                if (trans == 0) break;
                bal -= trans
                bal /= 1
              }
              quit

       The following is the definition of the recursive factorial function.
              define f (x) {
                if (x <= 1) return (1);
                return (f(x-1) * x);
              }

   READLINE AND LIBEDIT OPTIONS
       GNU  bc  can  be  compiled  (via  a configure option) to use the GNU readline input 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.

   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 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
              Strings  are not allowed to contain NUL characters.  POSIX says all characters must
              be included in strings.

       last   POSIX bc does not have a last variable.  Some implementations of bc use the  period
              (.) in a similar way.

       comparisons
              POSIX  bc allows comparisons only in the if statement, the while statement, and the
              second expression of the for statement.  Also, only  one  relational  operation  is
              allowed in each of those statements.

       if statement, else clause
              POSIX bc does not have an else clause.

       for statement
              POSIX bc requires all expressions to be present in the for statement.

       &&, ||, !
              POSIX bc does not have the logical operators.

       read function
              POSIX bc does not have a read function.

       print statement
              POSIX bc does not have a print statement .

       continue statement
              POSIX bc does not have a continue statement.

       return statement
              POSIX bc requires parentheses around the return expression.

       array parameters
              POSIX  bc does not (currently) support array parameters in full.  The POSIX grammar
              allows for arrays in function definitions, but does not provide a method to specify
              an  array  as  an  actual  parameter.   (This  is  most  likely an oversight in the
              grammar.)  Traditional  implementations  of  bc  have  only  call  by  value  array
              parameters.

       function format
              POSIX bc requires the opening brace on the same line as the define key word and the
              auto statement on the next line.

       =+, =-, =*, =/, =%, =^
              POSIX bc does not require these "old style" assignment  operators  to  be  defined.
              This  version may allow these "old style" assignments.  Use the limits statement to
              see if the installed version supports them.  If it does  support  the  "old  style"
              assignment  operators,  the  statement  "a  =-  1" will decrement a by 1 instead of
              setting a to the value -1.

       spaces in numbers
              Other implementations of bc allow spaces in numbers.  For example,  "x=1  3"  would
              assign  the  value  13  to the variable x.  The same statement would cause a syntax
              error in this version of bc.

       errors and execution
              This implementation varies from other implementations in terms of what code will be
              executed  when syntax and other errors are found in the program.  If a syntax error
              is found in a function definition, error recovery tries to find the beginning of  a
              statement  and continue to parse the function.  Once a syntax error is found in the
              function, the function will not be callable and becomes undefined.   Syntax  errors
              in the interactive execution code will invalidate the current execution block.  The
              execution block is terminated by an end of  line  that  appears  after  a  complete
              sequence of statements.  For example,
              a = 1
              b = 2
       has two execution blocks and
              { a = 1
                b = 2 }
       has  one  execution  block.  Any runtime error will terminate the execution of the current
       execution block.  A runtime warning will not terminate the current 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.

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

ENVIRONMENT VARIABLES

       The following environment variables are processed by bc:

       POSIXLY_CORRECT
              This is the same as the -s option.

       BC_ENV_ARGS
              This is another mechanism to get arguments to bc.  The format is the  same  as  the
              command  line  arguments.  These arguments are processed first, so any files listed
              in the environment arguments are processed before any command line argument  files.
              This  allows  the  user  to  set up "standard" options and files to be processed at
              every invocation of bc.  The files in the  environment  variables  would  typically
              contain  function definitions for functions the user wants defined every time bc is
              run.

       BC_LINE_LENGTH
              This should be an integer specifying the number of characters in an output line for
              numbers.  This  includes the backslash and newline characters for long numbers.  As
              an extension, the value of zero disables the multi-line feature.  Any  other  value
              of this variable that is less than 3 sets the line length to 70.

DIAGNOSTICS

       If  any  file  on  the  command  line  can  not be opened, bc will report that the file is
       unavailable and terminate.  Also, there are compile and run time diagnostics  that  should
       be self-explanatory.

BUGS

       Error recovery is not very good yet.

       Email  bug reports to bug-bc@gnu.org.  Be sure to include the word ``bc'' somewhere in the
       ``Subject:'' field.

AUTHOR

       Philip A. Nelson
       philnelson@acm.org

ACKNOWLEDGEMENTS

       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 involvement.