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bc(1)									 bc(1)

NAME
       bc - An arbitrary precision calculator language

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 inter‐
       active 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 doc‐
       ument 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 pre‐
       cision 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 num‐
       bers, the length and the scale.	The length is the total number of sig‐
       nificant	 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 exam‐
       ple, 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  let‐
       ters  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	repre‐
       sentable 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 expres‐
	      sions.

       expr / expr
	      The result of the expression is the quotient of the two  expres‐
	      sions.   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  com‐
	      puted  in	 the following way.  To compute a%b, first a/b is com‐
	      puted 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 expo‐
	      nent and the maximum of scale and the scale of the first expres‐
	      sion.    (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 state‐
       ments 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 opera‐
       tors to have some unusual behavior when used  with  assignment  expres‐
       sions.  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 pro‐
	      gram 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 con‐
	      version 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 expres‐
	      sion.  If the expression is negative, a run time error is gener‐
	      ated.

   STATEMENTS
       Statements (as in most algebraic languages) provide the	sequencing  of
       expression  evaluation.	In bc statements are executed "as soon as pos‐
       sible."	Execution happens when a newline in encountered and  there  is
       one or more complete statements.	 Due to this immediate execution, new‐
       lines 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 sepa‐
       rated by semicolons and newlines.  The following is a list of bc state‐
       ments  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 out‐
	      put.  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 preci‐
	      sion, 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 num‐
	      ber 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  dou‐
	      ble  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 sepa‐
	      rated by commas.	Each string or expression is  printed  in  the
	      order  of the list.  No terminating newline is printed.  Expres‐
	      sions 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  charac‐
	      ters  start with the backslash character (\).  The special char‐
	      acters  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	state‐
	      ment1  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 expres‐
	      sion  is non-zero.  It evaluates the expression before each exe‐
	      cution 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 evalu‐
	      ated before each execution of the statement.  If it is non-zero,
	      the statement is evaluated.  If it is zero, the loop  is	termi‐
	      nated.   After  each  execution of the statement, expression3 is
	      evaluated before the reevaluation of  expression2.   If  expres‐
	      sion1  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 func‐
	      tions.)

       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 exe‐
       cuted 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 defi‐
       nition, zero or more parameters are defined by listing their names sep‐
       arated  by  commas.  Numbers are only call by value parameters.	Arrays
       are only call by variable.  Arrays are specified in the parameter defi‐
       nition by the notation "name[]".	  In the function call, actual parame‐
       ters 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  defini‐
       tions are dynamic, parameter numbers and types are checked when a func‐
       tion 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	 vari‐
       able.   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 ter‐
       mination of a function and the return of a value.  There are  two  ver‐
       sions  of  the return statement.	 The first form, "return", returns the
       value 0 to the calling expression.  The second form, "return (  expres‐
       sion )", 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 with‐
       out 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 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	imple‐
       ment 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 num‐
       ber 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 fea‐
       ture.  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  "undocu‐
       mented"	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 pro‐
	      cessing 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-char‐
	      acter  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" assign‐
	      ments.  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 exam‐
	      ple, "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 interac‐
	      tive 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	execu‐
       tion of the current execution block.  A runtime warning will not termi‐
       nate the current execution block.

       Interrupts
	      During an interactive session, the SIGINT signal (usually gener‐
	      ated  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  parame‐
	      ters  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
       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	 argu‐
	      ments  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 envi‐
	      ronment 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 new‐
	      line 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.Sommars@att.com)
       for  his extensive help in testing the implementation.  Many great sug‐
       gestions were given.  This is a much better product due to his involve‐
       ment.

				       .				 bc(1)
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