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bc



SYNTAX

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


VERSION

       This man page documents GNU bc version 1.06.


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  proces­
       sor, bc will never read from the standard input.)

       This version of bc contains several extensions beyond tra­
       ditional 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
       any number of letters, digits and underscores.   All  let­
       ters 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  com­
       ment  has  been added as an extension.  A single line com­
       ment 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, state­
       ments and expressions are executed as  soon  as  possible.
       There  is no "main" program.  Instead, code is executed as
       it is encountered.  (Functions, discussed in detail later,
       are defined when encountered.)

       A  simple  expression is just a constant. bc converts con­
       stants 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 con­
       tain the characters 0-9 and A-F. (Note: They must be capi­
       tals.  Lower case letters  are  variable  names.)   Single
       digit  numbers  always have the value of the digit regard­
       less of the value of ibase. (i.e. A  =  10.)   For  multi-
       digit  numbers,  bc  changes  all  input digits greater or
       refers to a complete expression and "var" refers to a sim­
       ple or an array variable.  A simple variable is just a
              name
       and an array variable is specified as
              name[expr]
       Unless  specifically  mentioned the scale of the result is
       the maximum scale of the expressions involved.

       - expr The result is the negation of the expression.

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

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

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

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

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

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

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

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

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

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

       var = expr
              The  variable  is assigned the value of the expres­
              sion.

       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 opera­
       tions  are  0  and 1 (for false and true) as in relational
       expressions.  The boolean operators are:

       !expr  The result is 1 if expr is 0.

       expr && expr
              ^ operator, right associative
              unary - operator, nonassociative
              ++ and -- operators, nonassociative

       This precedence was chosen so that POSIX compliant bc pro­
       grams 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(parame­
       ters)".   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 pre­
              viously 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 conver­
              sion 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
       the statement.)

       expression
              This  statement  does  one  of  two things.  If the
              expression  starts  with  "<variable>  <assignment>
              ...",  it  is considered to be an assignment state­
              ment.  If  the  expression  is  not  an  assignment
              statement,  the expression is evaluated and printed
              to the output.  After the number is printed, a new­
              line  is printed.  For example, "a=1" is an assign­
              ment 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  num­
              ber  of  characters  required to represent the base
              ten value of "obase-1".  Since numbers are of arbi­
              trary  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 charac­
              ters  printed  per line is 70.  Due to the interac­
              tive 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 char­
              acters  until the next double quote character.  All
              characters are take literally, including  any  new­
              line.   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
              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 exe­
              cutes 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 expres­
              sion 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 execu­
              tion 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 expres­
              sion2.  (The optional expressions are an extension.
              POSIX bc requires all three expressions.)  The fol­
              lowing is equivalent code for the for statement:
              expression1;
              while (expression2) {
                 statement;
                 expression3;
              }

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

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

       is performed at "compile" time.

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

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

       warranty
              Print  a longer warranty notice.  This is an exten­
              sion.

   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 def­
       inition 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 defini­
       tion by the notation "name[]".    In  the  function  call,
       actual  parameters are full expressions for number parame­
       ters.  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 spec­
       ified 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  ini­
       tialized  to zero and used throughout the execution of the
       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 expres­
       sion  and  returns  that  value to the calling expression.
       There is an implied "return (0)" at the end of every func­
       tion.   This  allows  a function to terminate and return 0
       without an explicit return statement.

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

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

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

   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 fol­
       lowing 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.

                 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
              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 implemen­
       tations.  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  fea­
       ture  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,  num­
              bers and the underscore character.

       Strings
              Strings  are not allowed to contain NUL characters.

       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 parame­
              ters 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" assign­
              ment operators to be  defined.   This  version  may
              allow  these "old style" assignments.  Use the lim­
              its statement to see if the installed version  sup­
              ports  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  num­
              bers.   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.
              ments.  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 ses­
              sion, 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
       BC_ENV_ARGS
              This  is  another mechanism to get arguments to bc.
              The format is the same as the  command  line  argu­
              ments.  These arguments are processed first, so any
              files listed in the environent arguments  are  pro­
              cessed  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 func­
              tions the user wants defined every time bc is  run.

       BC_LINE_LENGTH
              This  should  be an integer specifing the number of
              characters in an  output  line  for  numbers.  This
              includes  the  backslash and newline characters for
              long numbers.


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.Som­
       mars@att.com) for his extensive help in testing the imple­
       mentation.  Many great suggestions were given.  This is  a
       much better product due to his involvement.

                                .                           bc(1)
  
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