.\" $NetBSD: bc.1,v 1.11 2022/05/26 08:06:58 mlelstv Exp $
.\"
.\" bc.1 - the bc manual
.\"
.\" Copyright (C) 1991-1994, 1997, 2000, 2003, 2012-2017 Free Software Foundation, Inc.
.\" Copyright (C) 2004, 2017 Philip A. Nelson
.\" Copyright (C) 2017 Thomas Klausner
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\"    notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\"    notice, this list of conditions and the following disclaimer in the
.\"    documentation and/or other materials provided with the distribution.
.\" 3. Neither the name of Philip A. Nelson nor the name of the Free Software
.\"    Foundation may not be used to endorse or promote products derived from
.\"    this software without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY PHILIP A. NELSON ``AS IS'' AND ANY EXPRESS OR
.\" IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
.\" OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
.\" IN NO EVENT SHALL PHILIP A. NELSON OR THE FREE SOFTWARE FOUNDATION BE
.\" LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
.\" THE POSSIBILITY OF SUCH DAMAGE.
.\"
.\"
.\"
.Dd April 16, 2017
.Dt BC 1
.Os
.Sh NAME
.Nm bc
.Nd arbitrary precision calculator language
.Sh SYNOPSIS
.Nm
.Op Fl hilqsvw
.Op long-options
.Op Ar
.Sh DESCRIPTION
.Nm
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.
.Nm
starts by processing code from all the files listed
on the command line in the order listed.
After all files have been processed,
.Nm
reads from the standard input.
All code is executed as it is read.
(If a file contains a command to halt the processor,
.Nm
will never read from the standard input.)
.Pp
This version of
.Nm
contains several extensions beyond traditional
.Nm
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.
.Ss OPTIONS
.Bl -tag -width "XXinteractiveXXXXXX"
.It Fl h , Fl Fl help
Print the usage and exit.
.It Fl i , Fl Fl interactive
Force interactive mode.
.It Fl l , Fl Fl mathlib
Define the standard math library.
.It Fl q , Fl Fl quiet
Quiet mode.
.It Fl s , Fl Fl standard
Process exactly the POSIX
.Nm
language.
.It Fl v , Fl Fl version
Print the version number and copyright and quit.
.It Fl w , Fl Fl warn
Give warnings for extensions to POSIX
.Nm .
.El
.Ss NUMBERS
The most basic element in
.Nm
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 of
.Nm
truncates results from divide and multiply operations.)
There are two attributes of numbers, the length and the scale.
The length is the
total number of significant decimal digits in a number and the scale
is the total number of decimal digits after the decimal point.
For example:
.Pp
.Bl -inset -offset indent -compact
.It Li .000001
has a length of 6 and scale of 6.
.It Li 1935.000
has a length of 7 and a scale of 3.
.El
.Ss 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
.Nm
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
.Pq Ql [] .
.Pp
There are four special variables,
.Ic scale ,
.Ic ibase ,
.Ic obase ,
and
.Ic last .
.Ic scale
defines how some operations use digits after the decimal point.
The default value of
.Ic scale
is 0.
.Ic ibase
and
.Ic obase
define the conversion base for input and output numbers.
The default for both input and output is base 10.
.Ic 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.
.Ss COMMENTS
Comments in
.Nm
start with the characters
.Ql /*
and end with the characters
.Ql */ .
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.
.Pp
To support the use of scripts for
.Nm ,
a single line comment has been added as an extension.
A single line comment starts at a
.Ql #
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.
.Ss 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
.Dq main
program.
Instead, code is executed as it is encountered.
(Functions, discussed in
detail later, are defined when encountered.)
.Pp
A simple expression is just a constant.
.Nm
converts constants
into internal decimal numbers using the current input base, specified
by the variable
.Ic ibase .
(There is an exception in functions.)
The legal values of
.Ic ibase
are 2 through 36.
(Base values greater than 16 are an extension.)
Assigning a value outside this range to
.Ic 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
.Ic ibase .
(i.e.\&
.Ql A
=\~10.)
For multi-digit numbers,
.Nm
changes all input digits greater or equal to ibase to the value of
.Ic ibase - 1 .
This makes the number
.Ql ZZZ
always be the largest 3 digit number of the input base.
.Pp
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
.Ic scale .
Legal values of the variable
.Ic scale
are 0 to the maximum number representable by a C integer.
.Pp
In the following descriptions of legal expressions,
.Ar expr
refers to a complete expression and
.Ar var
refers to a simple or an array variable.
A simple variable is just a
.Dq Ar name
and an array variable is specified as
.Do Ar name Ns Ic \&[ Ns Ar expr Ns Ic \&] Dc .
Unless specifically mentioned the scale of the result is the maximum scale of the
expressions involved.
.Bl -tag -width 15n
.It Ic \&- Ns Ar expr
The result is the negation of the expression.
.It Ic \&++ Ns Ar var
The variable is incremented by one and the new value is the result of
the expression.
.It Ic \&-- Ns Ar var
The variable is decremented by one and the new value is the result of the
expression.
.It Ar var Ns Ic \&++
The result of the expression is the value of
the variable and then the variable is incremented by one.
.It Ar var Ns Ic \&--
The result of the expression is the value of the variable and then
the variable is decremented by one.
.It Ar expr Ic \&+ Ar expr
The result of the expression is the sum of the two expressions.
.It Ar expr Ic \&- Ar expr
The result of the expression is the difference of the two expressions.
.It Ar expr Ic \&* Ar expr
The result of the expression is the product of the two expressions.
.It Ar expr Ic \&/ Ar expr
The result of the expression is the quotient of the two expressions.
The scale of the result is the value of the variable
.Ic scale .
.It Ar expr Ic \&% Ar 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
.Ic scale
digits.
That result is used to compute a-(a/b)*b to the scale of the
maximum of
.Ic scale +
scale(b) and scale(a).
If
.Ic scale
is set to zero and both expressions are integers this expression is the
integer remainder function.
.It Ar expr Ic \&^ Ar 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
.Ic 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
.Ic scale
and the scale of the first expression.
(e.g. scale(a^b) = min(scale(a)*b, max(
.Ic scale ,
scale(a))).)
It should be noted
that expr^0 will always return the value of 1.
.It Ic \&( Ns Ar expr Ns Ic \&)
This alters the standard precedence to force the evaluation of the
expression.
.It Ar var Ic \&= Ar expr
The variable is assigned the value of the expression.
.It Ar var Ao Ns Ar op Ns Ac Ns Ic \&= Ar expr
This is equivalent to
.Ar var Ic \&= Ar var Ao Ns Ar op Ns Ac Ar expr
with the exception that the
.Ar var
part is evaluated only once.
This can make a difference if
.Ar var
is an array.
.El
.Pp
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
.Nm
requires that relational expressions are used only in
.Ic if ,
.Ic while ,
and
.Ic for
statements and that only one relational test may be
done in them.)
The relational operators are:
.Bl -tag -width 15n
.It Ar expr\s-2\d\fR1\fP\u\s+2 Ic \&< Ar expr\s-2\d\fR2\fP\u\s+2
The result is 1 if
.Ar expr\s-2\d\fR1\fP\u\s+2
is strictly less than
.Ar expr\s-2\d\fR2\fP\u\s+2 .
.It Ar expr\s-2\d\fR1\fP\u\s+2 Ic \&<= Ar expr\s-2\d\fR2\fP\u\s+2
The result is 1 if
.Ar expr\s-2\d\fR1\fP\u\s+2
is less than or equal to
.Ar expr\s-2\d\&2\u\s+2 .
.It Ar expr\s-2\d\fR1\fP\u\s+2 Ic \&> Ar expr\s-2\d\fR2\fP\u\s+2
The result is 1 if
.Ar expr\s-2\d\fR1\fP\u\s+2
is strictly greater than
.Ar expr\s-2\d\&2\u\s+2 .
.It Ar expr\s-2\d\fR1\fP\u\s+2 Ic \&>= Ar expr\s-2\d\fR2\fP\u\s+2
The result is 1 if
.Ar expr\s-2\d\fR1\fP\u\s+2
is greater than or equal to
.Ar expr\s-2\d\&2\u\s+2 .
.It Ar expr\s-2\d\fR1\fP\u\s+2 Ic \&== Ar expr\s-2\d\fR2\fP\u\s+2
The result is 1 if
.Ar expr\s-2\d\fR1\fP\u\s+2
is equal to
.Ar expr\s-2\d\&2\u\s+2 .
.It Ar expr\s-2\d\fR1\fP\u\s+2 Ic \&!= Ar expr\s-2\d\fR2\fP\u\s+2
The result is 1 if
.Ar expr\s-2\d\fR1\fP\u\s+2
is not equal to
.Ar expr\s-2\d\&2\u\s+2 .
.El
.Pp
Boolean operations are also legal.
(POSIX
.Nm
does
.Em 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:
.Bl -tag -width 15n
.It Ic \&! Ns Ar expr
The result is 1 if
.Ar expr
is 0.
.It Ar expr Ic \&&& Ar expr
The result is 1 if both expressions are non-zero.
.It Ar expr Ic \&|| Ar expr
The result is 1 if either expression is non-zero.
.El
.Pp
The expression precedence is as follows: (lowest to highest)
.Bl -enum -offset indent
.It
.Ql ||
operator, left associative
.It
.Ql &&
operator, left associative
.It
.Ql \&!
operator, nonassociative
.It
Relational operators, left associative
.It
Assignment operator, right associative
.It
.Ql +
and
.Ql -
operators, left associative
.It
.Ql * ,
.Ql /
and
.Ql %
operators, left associative
.It
.Ql ^
operator, right associative
.It
unary
.Ql -
operator, nonassociative
.It
.Ql ++
and
.Ql --
operators, nonassociative
.El
.Pp
This precedence was chosen so that POSIX compliant
.Nm
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:
.Dl a = 3 < 5
.Pp
Most C programmers would assume this would assign the result of
.Dq Li 3 < 5
(the value 1) to the variable
.Va a .
What this does in
.Nm
is assign the value 3 to the variable
.Va a
and then compare 3 to 5.
It is best to use parentheses when using relational and logical operators
with the assignment operators.
.Pp
There are a few more special expressions that are provided in
.Nm .
These have to do with user defined functions and standard functions.
They all appear as
.Do Ar name Ns Ic \&( Ns Ar parameters Ns Ic \&) Dc .
See the section on functions for user defined functions.
The standard functions are:
.Bl -tag -width 20n
.It Fn length expression
The value of the length function is the number of significant digits in the
expression.
.It Fn read
The read function (an extension) will read a number from the standard
input, regardless of where the function occurs.
Beware, this can cause problems with the mixing of data and program in
the standard input.
The best use for this function is in a previously written program that
needs input from the user, but never allows program code to be input
from the user.
The value of the read function is the number read from
the standard input using the current value of the variable
.Ic ibase
for the conversion base.
.It Fn scale expression
The value of the scale function is the number of digits after the decimal
point in the expression.
.It Fn sqrt expression
The value of the sqrt function is the square root of the expression.
If
the expression is negative, a run time error is generated.
.El
.Ss STATEMENTS
Statements (as in most algebraic languages) provide the sequencing of
expression evaluation.
In
.Nm
statements are executed
.Dq 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
.Nm .
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
.Dq Ic \e Ns Ao nl Ac ,
where
.Aq nl
is the newline appears to
.Nm
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
.Nm
statements and what they do:
(Things enclosed in brackets
.Pq Oo Oc
are optional parts of the
statement.)
.Bl -tag -width 15n
.It Ar expression
This statement does one of two things.
If the expression starts with
.Ao Ar variable Ac Ao Ar assignment Ac ... ,
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,
.Dq Li a=1
is an assignment statement and
.Dq Li (a=1)
is an expression that has an embedded assignment.
All numbers that are printed are printed in the base
specified by the variable
.Ic obase .
The legal values for
.Ic obase
are 2 through
.Dv BC_BASE_MAX .
(See the section
.Sx LIMITS . )
For bases 2 through 16, the usual method of writing numbers is used.
For bases greater than 16,
.Nm
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
.Dq Ic 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
.Ql \e
as the last character on a line.
The maximum number of characters printed
per line is 70.
Due to the interactive nature of
.Nm bc ,
printing a number causes the side effect of assigning the printed value to the
special variable
.Ic last .
This allows the user to recover the last value printed without having
to retype the expression that printed the number.
Assigning to
.Ic 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
.Ic last .
(Some installations may allow the
use of a single period
.Pq Ql \&.
which is not part of a number as a short hand notation for
.Ic last . )
.It Ic \*q Ns Ar string\| Ns Ic \*q
The
.Ar string
is printed to the output.
Strings start with a double quote
character and contain all characters until the next double quote character.
All characters are take literally, including any newline.
No newline character is printed after the string.
.It Ic  print Ar list
The
.Ic print
statement (an extension) provides another method of output.
The
.Ar 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
.Ic last .
Strings in the
.Ic print
statement are printed to the output and may contain special characters.
Special characters start with the backslash character
.Pq Ql \e .
The special characters recognized by
.Nm
are
.Ql a
(alert or bell),
.Ql b
(backspace),
.Ql f
(form feed),
.Ql n
(newline),
.Ql r
(carriage return),
.Ql q
(double quote),
.Ql t
(tab), and
.Ql \e
(backslash).
Any other character following the backslash will be ignored.
.It Ic \&{ Ar statement_list Ic \&}
This is the compound statement.
It allows multiple statements to be grouped together for execution.
.It Ic if \&( Ns Ar expression Ns Ic \&) Ar statement\s-2\d\fR1\fP\u\s+2 \
 Oo Ic else Ar statement\s-2\d\fR2\fP\u\s+2 Oc
The
.Ic if
statement evaluates the
.Ar expression
and executes
.Ar statement\s-2\d\fR1\fP\u\s+2
or
.Ar statement\s-2\d\fR2\fP\u\s+2
depending on the value of the
.Ar expression .
If the
.Ar expression
is non-zero,
.Ar statement\s-2\d\fR1\fP\u\s+2
is executed.
If
.Ar statement\s-2\d\fR2\fP\u\s+2
is present and the value of the
.Ar expression
is 0, then
.Ar statement\s-2\d\fR2\fP\u\s+2
is executed.
(The
.Ic else
clause is an extension.)
.It Ic while \&( Ns Ar expression Ns Ic \&) Ar statement
The
.Ic while
statement will execute the
.Ar statement
while the
.Ar expression
is non-zero.
It evaluates the
.Ar expression
before each execution of the
.Ar statement .
Termination of the loop is caused by a zero
.Ar expression
value or the execution of a
.Ic break
statement.
.It Ic for \&( Ns \
 Oo Ar expression\s-2\d\fR1\fP\u\s+2 Oc Ns Ic \&; \
 Oo Ar expression\s-2\d\fR2\fP\u\s+2 Oc Ns Ic \&; \
 Oo Ar expression\s-2\d\fR3\fP\u\s+2 Oc Ns Ic \&) \
 Ar statement
The
.Ic for
statement controls repeated execution of the
.Ar statement .
.Ar expression\s-2\d\fR1\fP\u\s+2
is evaluated before the loop.
.Ar expression\s-2\d\fR2\fP\u\s+2
is evaluated
before each execution of the
.Ar statement .
If it is non-zero, the
.Ar statement
is executed.
If it is zero, the loop is terminated.
After each execution of the
.Ar statement ,
.Ar expression\s-2\d\fR3\fP\u\s+2
is evaluated before the reevaluation of
.Ar expression\s-2\d\fR2\fP\u\s+2 .
If
.Ar expression\s-2\d\fR1\fP\u\s+2
or
.Ar expression\s-2\d\fR3\fP\u\s+2
are missing, nothing is evaluated at the point they would be evaluated.
If
.Ar expression\s-2\d\fR2\fP\u\s+2
is missing, it is the same as substituting the value 1 for
.Ar expression\s-2\d\fR2\fP\u\s+2 .
(The optional expressions are an
extension.
POSIX
.Nm
requires all three expressions.)
The following is equivalent code for the
.Ic for
statement:
.Bd -literal -offset indent
expression1;
while (expression2) {
   statement;
   expression3;
}
.Ed
.It Ic break
This statement causes a forced exit of the most recent enclosing
.Ic while
statement or
.Ic for
statement.
.It Ic continue
The
.Ic continue
statement (an extension) causes the most recent enclosing
.Ic for
statement to start the next iteration.
.It Ic halt
The
.Ic halt
statement (an extension) is an executed statement that causes the
.Nm
processor to quit only when it is executed.
For example,
.Dl if (0 == 1) halt
will not cause
.Nm
to terminate because the halt is not executed.
.It Ic return
Return the value 0 from a function.
(See the section on functions.)
.It Ic return Ic \&( Ns Ar expression Ns Ic \&)
Return the value of the expression from a function.
(See the section on  functions.)
As an extension, the parentheses are not required.
.El
.Ss PSEUDO STATEMENTS
These statements are not statements in the traditional sense.
They are not executed statements.
Their function is performed at
.Dq compile
time.
.Bl -tag -width 15n
.It Ic limits
Print the local limits enforced by the local version of
.Nm
This is an extension.
.It Ic quit
When the
.Ic quit
statement is read, the
.Nm
processor
is terminated, regardless of where the quit statement is found.
For example,
.Dl if (0 == 1) quit
will cause
.Nm
to terminate.
.It Ic warranty
Print a longer warranty notice.
This is an extension.
.El
.Ss FUNCTIONS
Functions provide a method of defining a computation that can be executed
later.
Functions in
.Nm
always compute a value and return it to the caller.
Function definitions are
.Dq 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:
.Bd -literal -offset indent
define name ( parameters ) { newline
    auto_list   statement_list }
.Ed
.Pp
A function call is just an expression of the form
.Do Ar name Ns Ic \&( Ns Ar parameters Ns Ic \&) Dc .
.Pp
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
.Do Fa name Ns Ic \&[] Dc .
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.
.Pp
The
.Ar auto_list
is an optional list of variables that are for
.Dq local
use.
The syntax of the auto list (if present) is
.Do Ic auto Ar name Ns Ic \&, Ar \&... Ns Ic \&; Dc .
(The semicolon is optional.)
Each
.Ar 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
.Ar A
calls function
.Ar B ,
.Ar B
may access function
.Ar A Ns 's
auto variables by just using the same name, unless function
.Ar B
has
called them auto variables.
Due to the fact that auto variables and parameters are pushed onto a
stack,
.Nm
supports recursive functions.
.Pp
The function body is a list of
.Nm
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,
.Dq Ic return ,
returns the value 0 to the calling expression.
The second form,
.Do Ic return Ic \&( Ns Ar expression Ns Ic \&) Dc ,
computes the value of the expression
and returns that value to the calling expression.
There is an implied
.Dq Li return (0)
at the end of every function.
This allows a function
to terminate and return 0 without an explicit return statement.
.Pp
Functions also change the usage of the variable
.Ic ibase .
All constants in the function body will be converted using the value of
.Ic ibase
at the time of the function call.
Changes of
.Ic ibase
will be ignored during the execution of the function except for the
standard function
.Fn read ,
which will always use the current value
of
.Ic ibase
for conversion of numbers.
.Pp
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
.Ic define
keyword and all other parts must be on following lines.
This version of
.Nm
will allow any number of newlines before and after the opening brace of the
function.
For example, the following definitions are legal.
.Bd -literal -offset indent
define d (n) { return (2*n); }
define d (n)
  { return (2*n); }
.Ed
.Pp
Functions may be defined as
.Ic void .
A
.Ic void
funtion returns no value and thus may not be used in any place that needs
a value.
A
.Ic void
function does not produce any output when called by itself
on an input line.
The key word
.Ic void
is placed between the key word
.Ic define
and the function name.
For example, consider the following session.
.Bd -literal -offset indent
define py (y) { print "--->", y, "<---", "\en"; }
define void px (x) { print "--->", x, "<---", "\en"; }
py(1)
--->1<---
0
px(1)
--->1<---
.Ed
.Pp
Since
.Fn py
is not a void function, the call of
.Ql 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
.Ql px(1) ,
no zero is printed because the function is a void function.
.Pp
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
.Do Fa name Ns Ic \&[] Dc .
The call to the
function remains the same as call by value arrays.
.Ss MATH LIBRARY
If
.Nm
is invoked with the
.Fl 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:
.Bl -tag -width 15n
.It Fn s x
The sine of
.Fa x ,
.Fa x
is in radians.
.It Fn c x
The cosine of
.Fa x ,
.Fa x
is in radians.
.It Fn a x
The arctangent of
.Fa x ,
arctangent returns radians.
.It Fn l x
The natural logarithm of
.Fa x .
.It Fn e x
The exponential function of raising
.Va e
to the value
.Fa x .
.It Fn j n x
The Bessel function of integer order
.Fa n
of
.Fa x .
.El
.Sh ENVIRONMENT
The following environment variables are processed by
.Nm :
.Bl -tag -width 15n
.It Ev POSIXLY_CORRECT
This is the same as the
.Fl s
option.
.It Dv BC_ENV_ARGS
This is another mechanism to get arguments to
.Nm .
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
.Dq standard
options and files to be
processed at every invocation of
.Nm .
The files in the environment variables would typically contain
function definitions for functions the user wants defined every time
.Nm
is run.
.It Dv 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.
.El
.Sh EXAMPLES
In
.Pa /bin/sh ,
the following will assign the value of
.Ar pi
to the shell variable
.Ar pi .
.Bd -literal -offset indent
pi=$(echo "scale=10; 4*a(1)" | bc -l)
.Ed
.Pp
The following is the definition of the exponential function used in the
math library.
This function is written in POSIX
.Nm .
.Bd -literal -offset indent
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
  }
}
.Ed
.Pp
The following is code that uses the extended features of
.Nm
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.
.Bd -literal -offset indent
scale=2
print "\enCheck book program!\en"
print "  Remember, deposits are negative transactions.\en"
print "  Exit by a 0 transaction.\en\en"

print "Initial balance? "; bal = read()
bal /= 1
print "\en"
while (1) {
  "current balance = "; bal
  "transaction? "; trans = read()
  if (trans == 0) break;
  bal -= trans
  bal /= 1
}
quit
.Ed
.Pp
The following is the definition of the recursive factorial function.
.Bd -literal -offset indent
define f (x) {
  if (x <= 1) return (1);
  return (f(x-1) * x);
}
.Ed
.Ss EDITLINE OPTIONS
.Nm
is compiled using the
.Xr editline 3
library.
This allows the user to do editing of lines before sending them
to
.Nm .
It also allows for a history of previous lines typed.
This adds to
.Nm
one more special variable.
This special variable,
.Ic history
is the number of lines of history retained.
The default value of \-1 means that an unlimited
number of history lines are retained.
Setting the value of
.Ic 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 manual for the
.Xr editline 3
library.
.Ss DIFFERENCES
This version of
.Nm
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
.Xr dc 1 .
This version is a single process which parses and runs a byte code
translation of the program.
There is an
.Dq undocumented
option
.Fl ( 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.
.Pp
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.
.Bl -tag -width 15n
.It Ev LANG No environment
This version does not conform to the POSIX standard in the processing
of the
.Ev LANG
environment variable and all environment variables starting
with
.Ev LC_ .
.It names
Traditional and POSIX
.Nm
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.
.It strings
Strings are not allowed to contain
.Tn NUL
characters.
POSIX says all characters must be included in strings.
.It Ic last
POSIX
.Nm
does not have a
.Ic last
variable.
Some implementations
of
.Nm
use the period
.Pq Ql \&.
in a similar way.
.It comparisons
POSIX
.Nm
allows comparisons only in the
.Ic if
statement, the
.Ic while
statement, and the second expression of the
.Ic for
statement.
Also, only one relational operation is allowed in each of those statements.
.It Ic if No statement , Ic else No clause
POSIX
.Nm
does not have an
.Ic else
clause.
.It Ic for No statement
POSIX
.Nm
requires all expressions to be present in the
.Ic for
statement.
.It Li && , || , \&!
POSIX
.Nm
does not have the logical operators.
.It Fn read No function
POSIX
.Nm
does not have a
.Fn read
function.
.It Ic print No statement
POSIX
.Nm
does not have a
.Ic print
statement .
.It Ic continue No statement
POSIX
.Nm
does not have a
.Ic continue
statement.
.It Ic return No statement
POSIX
.Nm
requires parentheses around the return expression.
.It array parameters
POSIX
.Nm
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
.Nm
have only call-by-value array parameters.
.It function format
POSIX
.Nm
requires the opening brace on the same line as the
.Ic define
key word and the
.Ic auto
statement on the next line.
.It Li =+ , =- , =* , =/ , =% , =^
POSIX
.Nm
does not require these
.Dq old style
assignment operators to be defined.
This version may allow these
.Dq old style
assignments.
Use the
.Ic limits
statement to see if the installed version supports them.
If it does support the
.Dq old style
assignment operators, the statement
.Dq Li a =- 1
will decrement
.Va a
by 1 instead of setting
.Va a
to the value \-1.
.It spaces in numbers
Other implementations of
.Nm
allow spaces in numbers.
For example,
.Dq Li x=1 3
would assign the value 13 to the variable
.Va x .
The same statement
would cause a syntax error in this version of
.Nm .
.It 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,
.Bd -literal
a = 1
b = 2
.Ed
has two execution blocks and
.Bd -literal
{ a = 1
  b = 2 }
.Ed
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.
.It interrupts
During an interactive session, the
.Dv 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
.Dq 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
.Nm
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
.Dv SIGINT
signal will terminate the entire run of
.Nm .
.El
.Ss LIMITS
The following are the limits currently in place for this
.Nm
processor.
Some of them may have been changed by an installation.
Use the
.Ic limits
statement to see the actual values.
.Bl -tag -width 15n
.It Dv BC_BASE_MAX
The maximum output base is currently set at 999.
The maximum input base is 16.
.It Dv BC_DIM_MAX
This is currently an arbitrary limit of 65535 as distributed.
Your installation may be different.
.It Dv  BC_SCALE_MAX
The number of digits after the decimal point is limited to
.Dv INT_MAX
digits.
Also, the number of digits before the decimal point is limited to
.Dv INT_MAX
digits.
.It Dv BC_STRING_MAX
The limit on the number of characters in a string is
.Dv INT_MAX
characters.
.It exponent
The value of the exponent in the raise operation
.Pq Ql ^
is limited to
.Dv LONG_MAX .
.It variable names
The current limit on the number of unique names is 32767 for each of
simple variables, arrays and functions.
.El
.Sh DIAGNOSTICS
If any file on the command line can not be opened,
.Nm
will report
that the file is unavailable and terminate.
Also, there are compile
and run time diagnostics that should be self-explanatory.
.Sh HISTORY
This man page documents bc version nb1.0.
.Sh AUTHORS
.An Philip A. Nelson Aq Mt phil@NetBSD.org
.Ss ACKNOWLEDGEMENTS
The author would like to thank Steve Sommars for his extensive help in
testing the implementation.
Many great suggestions were given.
This is a much better product due to his involvement.
.Sh BUGS
Error recovery is not very good yet.