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bc(1)									 bc(1)

       bc - An arbitrary precision calculator language

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

       This man	page documents GNU bc version 1.06.

       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.

       -h, --help
	      Print the	usage and exit.

       -i, --interactive
	      Force interactive	mode.

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

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

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

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

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

       The most	basic element in bc is the number.  Numbers are	arbitrary 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.

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

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

       Comments	in bc start with the characters	/* and end with	the characters
       */.  Comments may start anywhere	and appear as a	single	space  in  the
       input.	(This causes comments to delimit other input items.  For 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.

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

       - expr The result is the	negation of the	expression.

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

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

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

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

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

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

       expr * expr
	      The result of the	expression is the product of the  two  expres-

       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

       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

       !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-

       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.)

	      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:
	      while (expression2) {

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

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

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

       return Return the value 0 from a	function.  (See	the section  on	 func-

       return (	expression )
	      Return  the  value  of the expression from a function.  (See the
	      section on functions.)  As an extension, the parenthesis are not

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

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

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

	      Print a longer warranty notice.  This is an extension.

       Functions provide a method of defining a	computation that can  be  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);	}

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

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

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

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

       l (x)  The natural logarithm of x.

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

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

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

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

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

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

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

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

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

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

       The  following  is code that uses the extended features of bc to	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.
	      print "\nCheck book program!\n"
	      print "  Remember, deposits are negative transactions.\n"
	      print "  Exit by a 0 transaction.\n\n"

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

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

       GNU bc can be compiled (via a configure option) to use the GNU readline
       input  editor library or	the BSD	libedit	library.  This allows the user
       to do editing of	lines before sending them to bc.  It also allows for a
       history	of previous lines typed.  When this option is selected,	bc has
       one more	special	variable.  This	special	variable, history is the  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.

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

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

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

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

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

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

       read function
	      POSIX bc does not	have a read function.

       print statement
	      POSIX bc does not	have a print statement .

       continue	statement
	      POSIX bc does not	have a continue	statement.

       return statement
	      POSIX bc requires	parentheses around the return expression.

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

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

       =+, =-, =*, =/, =%, =^
	      POSIX bc does not	require	these "old style" assignment operators
	      to be defined.  This version may allow these "old	style" 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.

	      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.

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

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

	      This is currently	an arbitrary limit of  65535  as  distributed.
	      Your installation	may be different.

	      The  number  of  digits  after  the  decimal point is limited to
	      INT_MAX digits.  Also, the number	of digits before  the  decimal
	      point is limited to INT_MAX digits.

	      The  limit  on  the  number of characters	in a string is INT_MAX

	      The value	of the exponent	in the raise operation (^) is  limited
	      to LONG_MAX.

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

       The following environment variables are processed by bc:

	      This is the same as the -s option.

	      This is another mechanism	to get arguments to bc.	 The format is
	      the  same	 as  the  command line arguments.  These arguments are
	      processed	first, so any files listed in  the  environment	 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.

	      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.

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

       Error recovery is not very good yet.

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

       Philip A. Nelson

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

				       .				 bc(1)


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