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\input texinfo  @c -*-texinfo-*-
@c %**start of header
@setfilename bc.info
@settitle bc Command Manual
@c %**end of header

@include texi-ver.incl

@c This file has the new style title page commands.
@c Run `makeinfo' rather than `texinfo-format-buffer'.

@smallbook

@c tex
@c \overfullrule=0pt
@c end tex

@ifinfo
@dircategory Math
@direntry
* bc: (bc).                    An arbitrary precision calculator language.
@end direntry
@end ifinfo

@titlepage
@title @command{bc}
@subtitle an arbitrary precision calculator language
@subtitle version @value{BC_VERSION}

@author Philip A. Nelson
@page

This manual documents @command{bc}, an arbitrary precision calculator language.

This manual is part of GNU @command{bc}.@*
@sp 4
Copyright (C) 1991, 1992, 1993, 1994, 1997, 2003, 2006 Free Software Foundation, Inc.
51 Franklin Street, Fifth Floor,  Boston, MA 02110-1301  USA.

Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
are preserved on all copies.

@ignore
Permission is granted to process this file through TeX and print the
results, provided the printed document carries copying permission
notice identical to this one except for the removal of this paragraph
(this paragraph not being relevant to the printed manual).
@end ignore

Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the entire
resulting derived work is distributed under the terms of a permission
notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation approved
by the Foundation.

You may contact the author by:
e-mail: @email{phil@@cs.wwu.edu}@*
us-mail: Philip A. Nelson@*
Computer Science Department, 9062@*
Western Washington University@*
Bellingham, WA 98226-9062

@end titlepage

@node Top, Introduction, (dir), (dir)

@menu
* Introduction::
* Basic Elements::
* Expressions::
* Statements::
* Functions::
* Examples::
* Readline and Libedit Options::
* Comparison with Other Implementations::
* Limits::
* Environment Variables::
@end menu

@node Introduction, Basic Elements, Top, Top
@chapter Introduction
@menu
* Description::
* Command Line Options::
@end menu

@node Description, Command Line Options, Introduction, Introduction
@section Description

@command{bc} [ -hlwsqv ] [long-options] [ @var{ file ...} ]

@command{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.
@command{bc} starts by processing code from all the files listed
on the command line in the order listed.  After all files have been
processed, @command{bc} reads from the standard input.  All code is
executed as it is read.  (If a file contains a command to halt the
processor, @command{bc} will never read from the standard input.)

This version of @command{bc} contains several extensions beyond
traditional @command{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.

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

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

@node Command Line Options, Numbers, Description, Introduction
@section Command Line Options

@command{bc} takes the following options from the command line:
@table @code

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

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

@item -w, --warn
Give warnings for extensions to POSIX @command{bc}.

@item -s, --standard
Process exactly the POSIX @command{bc} language.

@item -q, --quiet
Do not print the normal GNU @command{bc} welcome.

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

@end table


@node Basic Elements, Expressions, Introduction, Top
@chapter Basic Elements
@menu
* Numbers::
* Variables::
* Comments::
@end menu

@node Numbers, Variables, Command Line Options, Basic Elements
@section Numbers

The most basic element in @command{bc} is the number.  Numbers are
arbitrary precision numbers.  This precision is both in the integer
part and the fractional part.  All numbers are represented internally
in decimal and all computation is done in decimal.  (This version
truncates results from divide and multiply operations.)  There are two
attributes of numbers, the length and the scale.  The length is the
total number of digits used by @command{bc} to represent 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, while
1935.000 has a length of 7 and a scale of 3.

@node Variables, Comments, Numbers, Basic Elements
@section 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 alphanumeric
names are an extension. In POSIX @command{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, @var{scale}, @var{ibase}, @var{obase}, and
@var{last}.  @var{scale} defines how some operations use digits after the
decimal point.  The default value of @var{scale} is 0. @var{ibase}
and @var{obase} define the conversion base for input and output
numbers.  The default for both input and output is base 10.
@var{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.

@node Comments, , Variables, Basic Elements
@section Comments

Comments in @command{bc} start with the characters @code{/*} and end with
the characters @code{*/}.  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 @command{bc}, a single line comment has been
added as an extension.  A single line comment starts at a @code{#}
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.

@node Expressions, Statements, Basic Elements, Top
@chapter Expressions

@menu 
* About Expressions and Special Variables::
* Basic Expressions::
* Relational Expressions::
* Boolean Expressions::
* Precedence::
* Special Expressions::
@end menu

@node About Expressions and Special Variables, Basic Expressions, Expressions, Expressions
@section About Expressions and Special Variables

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. @command{bc} converts constants
into internal decimal numbers using the current input base, specified by
the variable @var{ibase}. (There is an exception in functions.)  The
legal values of @var{ibase} are 2 through 36.  (Bases greater than
16 are an extension.)  Assigning a value outside
this range to @var{ibase} will result in a value of 2 or 36.  Input
numbers may contain the characters 0-9 and A-Z. (Note: They must be
capitals.  Lower case letters are variable names.)  Single digit numbers
always have the value of the digit regardless of the value of
@var{ibase}. (i.e. A = 10.)  For multi-digit numbers, @command{bc}
changes all input digits greater or equal to @var{ibase} to the value of
@var{ibase}-1.  This makes the number @code{ZZZ} 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 @var{scale}. Legal values of the variable @var{scale} are
0 to the maximum number representable by a C integer.

@node Basic Expressions, Relational Expressions, About Expressions and Special Variables, Expressions
@section Basic Expressions

In the following descriptions of legal expressions, "expr" refers to a
complete expression and "@var{var}" refers to a simple or an array variable.
A simple variable is just a 

@var{name}

and an array variable is specified as 

@var{name}[@var{expr}] 

Unless specifically mentioned the scale of the result is the maximum
scale of the expressions involved.

@table @code
@item - expr
The result is the negation of the expression.

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

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

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

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

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

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

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

@item 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 @code{scale}

@item 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 @var{scale}
digits.  That result is used to compute a-(a/b)*b to the scale of the
maximum of @var{scale}+scale(b) and scale(a).  If @var{scale} is set
to zero and both expressions are integers this expression is the
integer remainder function.

@item 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 @var{scale} if the exponent is negative.  If the exponent
is positive the scale of the result is the minimum of the scale of the
first expression times the value of the exponent and the maximum of
@var{scale} and the scale of the first expression.  (e.g. scale(a^b)
= min(scale(a)*b, max(@var{scale}, scale(a))).)  It should be noted
that expr^0 will always return the value of 1.

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

@item @var{var} = expr
The variable is assigned the value of the expression.

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

@node Relational Expressions, Boolean Expressions, Basic Expressions, Expressions
@section Relational Expressions

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 @command{bc}
requires that relational expressions are used only in @code{if},
@code{while}, and @code{for} statements and that only one relational
test may be done in them.)  The relational operators are

@table @code
@item expr1 < expr2
The result is 1 if expr1 is strictly less than expr2.

@item expr1 <= expr2
The result is 1 if expr1 is less than or equal to expr2.

@item expr1 > expr2
The result is 1 if expr1 is strictly greater than expr2.

@item expr1 >= expr2
The result is 1 if expr1 is greater than or equal to expr2.

@item expr1 == expr2
The result is 1 if expr1 is equal to expr2.

@item expr1 != expr2
The result is 1 if expr1 is not equal to expr2.
@end table

@node Boolean Expressions, Precedence, Relational Expressions, Expressions
@section Boolean Expressions

Boolean operations are also legal.  (POSIX @command{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:

@table @code
@item !expr
The result is 1 if expr is 0.

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

@item expr || expr
The result is 1 if either expression is non-zero.
@end table

@node Precedence, Special Expressions, Boolean Expressions, Expressions
@section Precedence

The expression precedence is as follows: (lowest to highest)

@example
|| 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
@end example

This precedence was chosen so that POSIX compliant @command{bc} programs
will run correctly. This will cause the use of the relational and
logical operators to have some unusual behavior when used with
assignment expressions.  Consider the expression:

@example
a = 3 < 5
@end example

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

@node Special Expressions, , Precedence, Expressions
@section Special Expressions

There are a few more special expressions that are provided in
@command{bc}.  These have to do with user-defined functions and standard
functions.  They all appear as
"@var{name}@code{(}@var{parameters}@code{)}".  @xref{Functions}, for
user-defined functions.  The standard functions are:

@table @code
@item length ( @var{expression} )
The value of the length function is the number of significant digits in the
expression.

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

@item scale ( @var{expression} )
The value of the @code{scale} function is the number of digits after the
decimal point in the expression.

@item sqrt ( @var{expression} )
The value of the @code{sqrt} function is the square root of the
expression.  If the expression is negative, a run time error is
generated.
@end table

@node Statements, Functions, Expressions, Top
@chapter Statements

@menu
* Pseudo Statements::
@end menu

Statements (as in most algebraic languages) provide the sequencing of
expression evaluation.  In @command{bc} statements are executed "as soon
as possible."  Execution happens when a newline in encountered and there
is one or more complete statements.  Due to this immediate execution,
newlines are very important in @command{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
@command{bc} as whitespace instead of a newline.  A statement list is a
series of statements separated by semicolons and newlines.  The
following is a list of @command{bc} statements and what they do: (Things
enclosed in brackets ( [ ] ) are optional parts of the statement.)

@table @code
@item @var{expression}
This statement does one of two things.  If the expression starts with
"<variable> <assignment> ...", it is considered to be an assignment
statement.  If the expression is not an assignment statement, the
expression is evaluated and printed to the output.  After the number is
printed, a newline is printed.  For example, "a=1" is an assignment
statement and "(a=1)" is an expression that has an embedded assignment.
All numbers that are printed are printed in the base specified by the
variable @var{obase}. The legal values for @var{obase} are 2 through
BC_BASE_MAX (@pxref{Environment Variables}).  For bases 2 through 16,
the usual method of writing numbers is used.  For bases greater than 16,
@command{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
"@var{obase} -1".  Since numbers are of arbitrary precision, some
numbers may not be printable on a single output line.  These long
numbers will be split across lines using the "\" as the last character
on a line.  The maximum number of characters printed per line is 70.
Due to the interactive nature of @command{bc}, printing a number causes
the side effect of assigning the printed value to the special variable
@var{last}. This allows the user to recover the last value printed
without having to retype the expression that printed the number.
Assigning to @var{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
@var{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
@var{last}.)

@item @var{string}
The string is printed to the output.  Strings start with a double quote
character and contain all characters until the next double quote character.
All characters are taken literally, including any newline.  No newline
character is printed after the string.

@item print @var{list}
The @code{print} statement (an extension) provides another method of
output.  The @var{list} is a list of strings and expressions separated by
commas.  Each string or expression is printed in the order of the list.
No terminating newline is printed.  Expressions are evaluated and their
value is printed and assigned to the variable @code{last}. Strings in
the print statement are printed to the output and may contain special
characters.  Special characters start with the backslash character (\e).
The special characters recognized by @command{bc} are "a" (alert or
bell), "b" (backspace), "f" (form feed), "n" (newline), "r" (carriage
return), "q" (double quote), "t" (tab), and "\e" (backslash).  Any other
character following the backslash will be ignored.

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

@item if ( @var{expression} ) @var{statement1} [else @var{statement2}]
The if statement evaluates the expression and executes statement1 or
statement2 depending on the value of the expression.  If the expression
is non-zero, statement1 is executed.  If statement2 is present and
the value of the expression is 0, then statement2 is executed.  (The
@code{else} clause is an extension.)

@item while ( @var{expression} ) @var{statement}
The while statement will execute the statement while the expression
is non-zero.  It evaluates the expression before each execution of
the statement.   Termination of the loop is caused by a zero
expression value or the execution of a @code{break} statement.

@item for ( [@var{expression1}] ; [@var{expression2}] ; [@var{expression3}] ) @var{statement}
The @code{for} statement controls repeated execution of the statement.
@var{Expression1} is evaluated before the loop.  @var{Expression2} is
evaluated before each execution of the statement.  If it is non-zero,
the statement is evaluated.  If it is zero, the loop is terminated.
After each execution of the statement, @var{expression3} is evaluated
before the reevaluation of expression2.  If @var{expression1} or
@var{expression3} are missing, nothing is evaluated at the point they
would be evaluated.  If @var{expression2} is missing, it is the same as
substituting the value 1 for @var{expression2}.  (The optional
expressions are an extension. POSIX @command{bc} requires all three
expressions.)  The following is equivalent code for the @code{for}
statement:

@example
expression1;
while (expression2) @{
   statement;
   expression3;
@}
@end example

@item break
This statement causes a forced exit of the most recent enclosing @code{while}
statement or @code{for} statement.

@item continue
The @code{continue} statement (an extension)  causes the most recent enclosing
@code{for} statement to start the next iteration.

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

@item return
Return the value 0 from a function.  (@xref{Functions}.)

@item return ( @var{expression} )
Return the value of the expression from a function.  (@xref{Functions}.)
As an extension, the parenthesis are not required.
@end table

@node Pseudo Statements, , Statements, Statements
@section Pseudo Statements

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

@table @code
@item limits
Print the local limits enforced by the local version of @command{bc}.  This
is an extension.

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

@item warranty
Print a longer warranty notice.  This is an extension.
@end table

@node Functions, Examples, Statements, Top
@chapter Functions

@menu
* Math Library Functions::
@end menu

Functions provide a method of defining a computation that can be
executed later.  Functions in @command{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:

@example
@code{define} @var{name} @code{(} @var{parameters} @code{)} @code{@{} @var{newline}
    @var{auto_list   statement_list} @code{@}}
@end example

A function call is just an expression of the form
"@code{name} @code{(}@var{parameters}@code{)}".

Parameters are numbers or arrays (an extension).  In the function definition,
zero or more parameters are defined by listing their names separated by
commas.  All parameters  are call by value parameters.
Arrays are specified in the parameter definition by
the notation "@var{name}@code{[ ]}".   In the function call, actual parameters
are full expressions for number parameters.  The same notation is used
for passing arrays as for defining array parameters.  The named array is
passed by value to the function.  Since function definitions are dynamic,
parameter numbers and types are checked when a function is called.  Any
mismatch in number or types of parameters will cause a runtime error.
A runtime error will also occur for the call to an undefined function.

The @var{auto_list} is an optional list of variables that are for
"local" use.  The syntax of the auto list (if present) is "@code{auto}
@var{name}, ... ;".  (The semicolon is optional.)  Each @var{name} is
the name of an auto variable.  Arrays may be specified by using the
same notation as used in parameters.  These variables have their
values pushed onto a stack at the start of the function.  The
variables are then initialized to zero and used throughout the
execution of the function.  At function exit, these variables are
popped so that the original value (at the time of the function call)
of these variables are restored.  The parameters are really auto
variables that are initialized to a value provided in the function
call.  
Auto variables are different than traditional local variables
because if function A calls function B, B may access function
A's auto variables by just using the same name, unless function B has
called them auto variables.  Due to the fact that auto variables and
parameters are pushed onto a stack, @command{bc} supports recursive functions.

The function body is a list of @command{bc} statements.  Again, statements
are separated by semicolons or newlines.  Return statements cause the
termination of a function and the return of a value.  There are two
versions of the return statement.  The first form, "@code{return}", returns
the value 0 to the calling expression.  The second form, 
"@code{return} ( @var{expression} )", computes the value of the expression
and returns that value to the calling expression.  There is an implied
"@code{return} (0)" at the end of every function.  This allows a function
to terminate and return 0 without an explicit @code{return} statement.

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

Several extensions have been added to functions.  First, the format of
the definition has been slightly relaxed.  The standard requires the
opening brace be on the same line as the @code{define} keyword and all
other parts must be on following lines.  This version of @command{bc}
will allow any number of newlines before and after the opening brace of
the function.  For example, the following definitions are legal.

@example
   define d (n) @{ return (2*n); @}
   define d (n)
       @{ return (2*n); @}
@end example

Functions may be defined as @code{void}.  A void
funtion returns no value and thus may not be used in any place that needs
a value.  A void function does not produce any output when called by itself
on an input line.  The key word @code{void} is placed between the key word
@code{define} and the function name.  For example, consider the following
session.

@example
define py (y) @{ print "--->", y, "<---", "\n"; @}
define void px (x) @{ print "--->", x, "<---", "\n"; @}
py(1)
--->1<---
0
px(1)
--->1<---
@end example

Since @code{py} is not a void function, the call of @code{py(1)} prints
the desired output and then prints a second line that is the value of
the function.  Since the value of a function that is not given an
explicit return statement is zero, the zero is printed.  For @code{px(1)},
no zero is printed because the function is a void function.

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

@node Math Library Functions, , Functions, Functions
@section Math Library Functions

If @command{bc} is invoked with the @code{-l} option, a math library is
preloaded and the default @var{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:

@table @code
@item s (@var{x})
The sine of @var{x}, @var{x} is in radians.

@item c (@var{x})
The cosine of @var{x}, @var{x} is in radians.

@item a (@var{x})
The arctangent of @var{x}, arctangent returns radians.

@item l (@var{x})
The natural logarithm of @var{x}.

@item e (@var{x})
The exponential function of raising @var{e} to the value @var{x}.

@item j (@var{n}, @var{x})
The Bessel function of integer order @var{n} of @var{x}.
@end table

@node Examples, Readline and Libedit Options, Functions, Top
@chapter Examples

In /bin/sh,  the following will assign the value of "pi" to the shell
variable @var{pi}.
@example

pi=$(echo "scale=10; 4*a(1)" | bc -l)

@end example

The following is the definition of the exponential function used in the
math library.  This function is written in POSIX @command{bc}.

@example

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
  @}
@}

@end example

The following is code that uses the extended features of @command{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.

@example

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

@end example


The following is the definition of the recursive factorial function.

@example

define f (x) @{
  if (x <= 1) return (1);
  return (f(x-1) * x);
@}

@end example

@node Readline and Libedit Options, Comparison with Other Implementations, Examples, Top
@chapter Readline and Libedit Options

GNU @command{bc} can be compiled (via a configure option) to use the GNU
@command{readline} input editor library or the BSD @command{libedit}
library.  This allows the user to do
more editing of lines before sending them to @command{bc}.  It also
allows for a history of previous lines typed.  When this option is
selected, @command{bc} has one more special variable.  This special
variable, @var{history} is the number of lines of history retained.  A
value of -1 means that an unlimited number of history lines are
retained.  This is the default value.  Setting the value of
@var{history} to a positive number restricts the number of history lines
to the number given.  The value of 0 disables the history feature.  For
more information, read the user manuals for the GNU @command{readline},
@command{history} and BSD @command{libedit} libraries.  One can not
enable both @command{readline} and @command{libedit} at the same time.

@node Comparison with Other Implementations, Limits, Readline and Libedit Options, Top
@chapter Comparison with Other Implementations

This version of @command{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 @command{dc}.  This version is a single process
which parses and runs a byte code translation of the program.  There is
an "undocumented" option (-c) that causes the program to output the byte
code to the standard output instead of running it.  It was mainly used
for debugging the parser and preparing the math library.

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

@table @asis

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

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

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

@item last
POSIX @command{bc} does not have a \fBlast variable.  Some implementations
of @command{bc} use the period (.) in a similar way.  

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

@item @code{if} statement, @code{else} clause
POSIX @command{bc} does not have an @code{else} clause.

@item @code{for} statement
POSIX @command{bc} requires all expressions to be present in the
@code{for} statement.

@item @code{&&,} @code{||}, @code{!}
POSIX @command{bc} does not have the logical operators.

@item @code{read} function
POSIX @command{bc} does not have a @code{read} function.

@item @code{print} statement
POSIX @command{bc} does not have a @code{print} statement.

@item @code{continue} statement
POSIX @command{bc} does not have a continue statement.

@item array parameters
POSIX @command{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 @command{bc} have only call by value array parameters.

@item function format
POSIX @command{bc} requires the opening brace on the same line as the 
@code{define} key word and the @code{auto} statement on the next line.

@item @code{=+}, @code{=-}, @code{=*}, @code{=/}, @code{=%}, @code{=^}
POSIX @command{bc} does not require these "old style" assignment
operators to be defined.  This version may allow these "old style"
assignments.  Use the @code{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 @code{a} by 1 instead
of setting @code{a} to the value -1.

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

@item errors and execution
This implementation varies from other implementations in terms of what
code will be executed when syntax and other errors are found in the
program.  If a syntax error is found in a function definition, error
recovery tries to find the beginning of a statement and continue to
parse the function.  Once a syntax error is found in the function, the
function will not be callable and becomes undefined.
Syntax errors in the interactive execution code will invalidate the
current execution block.  The execution block is terminated by an
end of line that appears after a complete sequence of statements.
For example, 

@example
a = 1
b = 2
@end example

has two execution blocks and

@example
@{ a = 1
  b = 2 @}
@end example

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.

@item 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 @command{bc} is ready for more input.  All previously defined
functions remain defined and the value of all non-auto variables are the
value at the point of interruption.  All auto variables and function
parameters are removed during the clean up process.  During a
non-interactive session, the SIGINT signal will terminate the entire run
of @command{bc}.
@end table

@node Limits, Environment Variables, Comparison with Other Implementations, Top
@chapter Limits

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

@table @code

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

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

@item 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.

@item BC_STRING_MAX
The limit on the number of characters in a string is INT_MAX characters.

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

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

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

@node Environment Variables, , Limits, Top
@chapter Environment Variables

The following environment variables are processed by @command{bc}:

@table @code


@item POSIXLY_CORRECT
This is the same as the -s option (@pxref{Command Line Options}).

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

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

@contents
@bye