 @@ -1,1317 +1,1340 @@
-.\" $NetBSD: bc.1,v 1.6 2021/01/07 20:37:33 uwe Exp $
+.\" $NetBSD: bc.1,v 1.7 2021/01/07 21:21:35 uwe 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
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 .\"    Foundation may not be used to endorse or promote products derived from
 .\"    this software without specific prior written permission.
 .\"
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 .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 ([]).
+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
-.Dq Ic /*
+.Ql /*
 and end with the characters
-.Dq Ic */ .
+.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
-.Dq Ic #
+.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. A = 10.)
+(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
-.Dq ZZZ
+.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,
 .Dq expr
 refers to a complete expression and
 .Dq var
 refers to a simple or an array variable.
 A simple variable is just a
 .Ic name
 and an array variable is specified as
 .Ic name[expr] .
 Unless specifically mentioned the scale of the result is the maximum scale of the
 expressions involved.
 .Bl -tag -width 15n
 .It Ic "- expr"
 The result is the negation of the expression.
 .It Ic "++ var"
 The variable is incremented by one and the new value is the result of
 the expression.
 .It Ic "-- var"
 The variable is decremented by one and the new value is the result of the
 expression.
 .It Ic "var ++"
 The result of the expression is the value of
 the variable and then the variable is incremented by one.
 .It Ic "var --"
 The result of the expression is the value of the variable and then
 the variable is decremented by one.
 .It Ic "expr + expr"
 The result of the expression is the sum of the two expressions.
 .It Ic "expr - expr"
 The result of the expression is the difference of the two expressions.
 .It Ic "expr * expr"
 The result of the expression is the product of the two expressions.
 .It Ic "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 \fBscale\fR.
 .It Ic "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
 .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 Ic "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
 .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 "( expr )"
 This alters the standard precedence to force the evaluation of the
 expression.
 .It Ic "var = expr"
 The variable is assigned the value of the expression.
 .It Ic "var <op>= expr"
 This is equivalent to
 .Ic "var = var <op> expr"
 with the exception that the
 .Dq Ic var
 part is evaluated only once.
 This can make a difference if
 .Dq Ic 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 Ic "expr1 < expr2"
 The result is 1 if expr1 is strictly less than expr2.
 .It Ic "expr1 <= expr2"
 The result is 1 if expr1 is less than or equal to expr2.
 .It Ic "expr1 > expr2"
 The result is 1 if expr1 is strictly greater than expr2.
 .It Ic "expr1 >= expr2"
 The result is 1 if expr1 is greater than or equal to expr2.
 .It Ic "expr1 == expr2"
 The result is 1 if expr1 is equal to expr2.
 .It Ic "expr1 != expr2"
 The result is 1 if expr1 is not equal to expr2.
 .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 "!expr"
 The result is 1 if expr is 0.
 .It Ic "expr && expr"
 The result is 1 if both expressions are non-zero.
 .It Ic "expr || 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
-|| operator, left associative
+.Ql ||
 operator, left associative
 .It
-&& operator, left associative
+.Ql &&
 operator, left associative
 .It
-! operator, nonassociative
+.Ql \&!
 operator, nonassociative
 .It
 Relational operators, left associative
 .It
 Assignment operator, right associative
 .It
-+ and - operators, left associative
+.Ql +
 and
 .Ql -
 operators, left associative
 .It
-*, / and % operators, left associative
+.Ql * ,
 .Ql /
 and
 .Ql %
 operators, left associative
 .It
-^ operator, right associative
+.Ql ^
 operator, right associative
 .It
-unary - operator, nonassociative
+unary
 .Ql -
 operator, nonassociative
 .It
-++ and -- operators, nonassociative
+.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 Ic a = 3 < 5
+.Dl a = 3 < 5
 .Pp
 Most C programmers would assume this would assign the result of
-.Dq Ic 3 < 5
+.Dq Li 3 < 5
 (the value 1) to the variable
-.Dq Ic a .
+.Va a .
 What this does in
 .Nm
 is assign the value 3 to the variable
-.Dq Ic a
+.Va a
 and then compare 3 to 5.
 It is best to use parenthesis 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 ( Ar parameters ) Dc .
+.Do Ar name Ns Li \&( Ns Ar parameters Ns Li \&) 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<nl> ,
 where <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 ([]) are optional parts of the
+(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 Ic a=1
 is an assignment statement and
 .Do Ic ( a=1 ) Dc
 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
 .Dq \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 (.) which is not part of a number as a short
+use of a single period
-hand notation for
+.Pq Ql \&.
 which is not part of a number as a short hand notation for
 .Ic last . )
 .It Ar "string"
 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 (\e).
+Special characters start with the backslash character
 .Pq Ql \e .
 The special characters recognized by
 .Nm
 are
-.Sq a
+.Ql a
 (alert or bell),
-.Sq b
+.Ql b
 (backspace),
-.Sq f
+.Ql f
 (form feed),
-.Sq n
+.Ql n
 (newline),
-.Sq r
+.Ql r
 (carriage return),
-.Sq q
+.Ql q
 (double quote),
-.Sq t
+.Ql t
 (tab), and
-.Sq \e
+.Ql \e
 (backslash).
 Any other character following the backslash will be ignored.
 .It { Ar statement_list }
 This is the compound statement.
 It allows multiple statements to be grouped together for execution.
 .It Ic if ( Ar expression ) Ar statement1 [ Ic else Ar statement2 ]
 The
 .Ic if
 statement evaluates the
 .Ar expression
 and executes
 .Ar statement1
 or
 .Ar statement2
 depending on the value of the
 .Ar expression .
 If the
 .Ar expression
 is non-zero,
 .Ar statement1
 is executed.
 If
 .Ar statement2
 is present and the value of the
 .Ar expression
 is 0, then
 .Ar statement2
 is executed.
 (The
 .Ic else
 clause is an extension.)
 .It Ic while ( Ar expression ) 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 ( [ Ar expression1 ] ; [ Ar expression2 ] ; [ Ar expression3 ] ) Ar statement
 The
 .Ic for
 statement controls repeated execution of the
 .Ar statement .
 .Ar Expression1
 is evaluated before the loop.
 .Ar Expression2
 is evaluated
 before each execution of the
 .Ar statement .
 If it is non-zero, the
 .Ar statement
 is evaluated.
 If it is zero, the loop is terminated.
 After each execution of the statement,
 .Ar expression3
 is evaluated before the reevaluation of
 .Ar expression2 .
 If
 .Ar expression1
 or
 .Ar expression3
 are missing, nothing is evaluated at the point they would be evaluated.
 If
 .Ar expression2
 is missing, it is the same as substituting the value 1 for
 .Ar expression2 .
 (The optional expressions are an
 extension.
 POSIX
 .Nm
 requires all three expressions.)
 The following is equivalent code for the
 .Ic for
 statement:
-.Bd -literal
+.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 ( Ar expression )
 Return the value of the expression from a function.
 (See the section on  functions.)
 As an extension, the parenthesis 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 ( Ar parameters ) 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 Ar name [ ] 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 , ... ; 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 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,
 .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 ( Ar expression ) Dc ,
 computes the value of the expression
 and returns that value to the calling expression.
 There is an implied
 .Do Ic return ( 0 ) Dc
 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, "<---", "\n"; }
 define void px (x) { print "--->", x, "<---", "\n"; }
 py(1)
 --->1<---
 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 Li [] 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 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 Ic read No function
 POSIX
 .Nm
 does not have a
 .Ic 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.