STANDARD INPUT

See Input Files.

INPUT FILES

Input files shall be text files containing a sequence of comments, statements, and function definitions that shall be executed as they are read.

ENVIRONMENT VARIABLES

The following environment variables shall affect the execution of bc:

LANG

This variable shall determine the locale to use for the locale categories when both LC_ALL and the corresponding environment variable (beginning with LC_ ) do not specify a locale. See 2.6.

LC_ALL

This variable shall determine the locale to be used to override any values for locale categories specified by the settings of LANG or any environment variables beginning with LC_.

LC_CTYPE

This variable shall determine the locale for the interpretation of sequences of bytes of text data as characters (e.g., single- versus multibyte characters in arguments and input files).

LC_MESSAGES

This variable shall determine the language in which messages should be written.

ASYNCHRONOUS EVENTS

Default.

STANDARD OUTPUT

The output of the bc utility shall be controlled by the program read, and shall consist of zero or more lines containing the value of all executed expressions without assignments. The radix and precision of the output shall be controlled by the values of the obase and scale variables. See EXTENDED DESCRIPTION .

STANDARD ERROR

Used only for diagnostic messages.

OUTPUT FILES

None.

BC GRAMMAR

The grammar in this subclause and the lexical conventions in the following subclause shall together describe the syntax for bc programs. The general conventions for this style of grammar are described in 2.1.2. A valid program can be represented as the nonterminal symbol program in the grammar. Any discrepancies found between this grammar and other descriptions in this subclause ( EXTENDED DESCRIPTION ) shall be resolved in favor of this grammar.

%token EOF NEWLINE STRING LETTER NUMBER %token MUL_OP /∗ ’∗’, ’/’, ’%’ ∗/ %token ASSIGN_OP /∗ ’=’, ’+=’, ’-=’, ’∗=’, ’/=’, ’%=’, ’ˆ=’ ∗/ %token REL_OP /∗ ’==’, ’<=’, ’>=’, ’!=’, ’<’, ’>’ ∗/ %token INCR_DECR /∗ ’++’, ’--’ ∗/ %token Define Break Quit Length /∗ ’define’, ’break’, ’quit’, ’length’ ∗/ %token Return For If While Sqrt /∗ ’return’, ’for’, ’if’, ’while’, ’sqrt’ ∗/ %token Scale Ibase Obase Auto /∗ ’scale’, ’ibase’, ’obase’, ’auto’ ∗/ %start program

%% program : EOF

; input_item : semicolon_list NEWLINE

; semicolon_list : /∗ empty ∗/

; statement_list : /∗ empty ∗/

;

statement : expression

relational_expression ’;’ expression ’)’ statement

; function : Define LETTER ’(’ opt_parameter_list ’)’ ’{’ NEWLINE opt_auto_define_list statement_list ’}’ ; opt_parameter_list : /∗ empty ∗/

; parameter_list : LETTER

; opt_auto_define_list : /∗ empty ∗/

; define_list : LETTER

; opt_argument_list : /∗ empty ∗/

; argument_list : expression

; relational_expression : expression

; return_expression : /∗ empty ∗/

; expression : named_expression

; named_expression : LETTER

;

BC LEXICAL CONVENTIONS

The lexical conventions for bc programs, with respect to the preceding grammar, shall be as follows:

1. Except as noted, bc shall recognize the longest possible token or delimiter beginning at a given point.
2. A comment shall consist of any characters beginning with the two adjacent characters /∗ and terminated by the next occurrence of the two adjacent characters ∗/. Comments shall have no effect except to delimit lexical tokens.
3. The character <newline> shall be recognized as the token NEWLINE.
4. The token STRING shall represent a string constant; it shall consist of any characters beginning with the double-quote character (") and terminated by another occurrence of the double-quote character. The value of the string shall be the sequence of all characters between, but not including, the two double-quote characters. All characters shall be taken literally from the input, and there is no way to specify a string containing a double-quote character. The length of the value of each string shall be limited to BC_STRING_MAX bytes.
5. A <blank> shall have no effect except as an ordinary character if it appears within a STRING token, or to delimit a lexical token other than STRING.

1. The combination of a backslash character immediately followed by a <newline> character shall delimit lexical tokens with the following exceptions:

• It shall be interpreted as a literal <newline> in STRING tokens.

• It shall be ignored as part of a multiline NUMBER token.

1. The token NUMBER shall represent a numeric constant. It shall be recognized by the following grammar:

NUMBER : integer

; integer : digit

; digit : 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7

;

1. The value of a NUMBER token shall be interpreted as a numeral in the base specified by the value of the internal register ibase (described below). Each of the digit characters shall have the value from 0 to 15 in the order listed here, and the period character shall represent the radix point. The behavior is undefined if digits greater than or equal to the value of ibase appear in the token. (However, note the exception for single-digit values being assigned to ibase and obase themselves, in BC OPERATIONS ).
2. The following keywords shall be recognized as tokens:

auto for length return sqrt break ibase obase scale while define if quit

1. Any of the following characters occurring anywhere except within a keyword shall be recognized as the token LETTER: a b c d e f g h i j k l m n o p q r s t u v w x y z
2. The following single-character and two-character sequences shall be recognized as the token ASSIGN_OP: = += -= ∗= /= %= ˆ=
3. If an = character, as the beginning of a token, is followed by a − character with no intervening delimiter, the behavior is undefined.
4. The following single-characters shall be recognized as the token MUL_OP: ∗ / %
5. The following single-character and two-character sequences shall be recognized as the token REL_OP: == <= >= != < >
6. The following two-character sequences shall be recognized as the token INCR_DECR: ++ --

1. The following single characters shall be recognized as tokens whose names are the character: <newline> ( ) , + - ; [ ] ˆ { }

1. The token EOF shall be returned when the end of input is reached.

BC OPERATIONS

There are three kinds of identifiers: ordinary identifiers, array identifiers, and function identifiers. All three types consist of single lowercase letters. Array identifiers shall be followed by square brackets ([ ]). An array subscript is required except in an argument or auto list. Arrays are singly dimensioned and can contain up to BC_DIM_MAX elements. Indexing begins at zero so an array is indexed from 0 to BC_DIM_MAX −1. Subscripts shall be truncated to integers. Function identifiers shall be followed by parentheses, possibly enclosing arguments. The three types of identifiers do not conflict. Table 4-3 summarizes the rules for precedence and associativity of all operators. Operators on the same line shall have the same precedence; rows are in order of decreasing precedence.

Table 4-3 − bc Operators

Operator Associativity

++, − − not applicable unary − not applicable ˆ right to left ∗, /, % left to right +, binary − left to right =, +=, −=, ∗=, /=, %=, ˆ= right to left ==, <=, >=, !=, <, > none

Each expression or named expression has a scale, which is the number of decimal digits that shall be maintained as the fractional portion of the expression. Named expressions are places where values are stored. Named expressions shall be valid on the left side of an assignment. The value of a named expression shall be the value stored in the place named. Simple identifiers and array elements shall be named expressions; they shall have an initial value of zero and an initial scale of zero. The internal registers scale, ibase, and obase are all named expressions. The scale of an expression consisting of the name of one of these registers shall be zero; values assigned to any of these registers shall be truncated to integers. The scale register shall contain a global value used in computing the scale of expressions (as described below). The value of the register scale shall be limited to 0 ≤ scale ≤ BC_SCALE_MAX and shall have a default value of zero. The ibase and obase registers are the input and output number radix, respectively. The value of ibase shall be limited to

2 ≤ ibase ≤ 16 The value of obase shall be limited to 2 ≤ obase ≤ BC_BASE_MAX When either ibase or obase is assigned a single digit value from the list in BC LEXICAL CONVENTIONS , the value shall be assumed in hexadecimal. (For example, ibase=A sets to base ten, regardless of the current ibase value.) Otherwise, the behavior is undefined when digits greater than or equal to the value of ibase appear in the input. Both ibase and obase shall have initial values of 10. Internal computations shall be conducted as if in decimal, regardless of the input and output bases, to the specified number of decimal digits. When an exact result is not achieved, (e.g., scale=0; 3.2/1) the result shall be truncated. For all values of obase specified by this standard, numerical values shall be output as follows:

1. If the value is less than zero, a hyphen (-) character shall be output.
2. One of the following shall be output, depending on the numerical value:

• If the absolute value of the numerical value is greater than or equal to one, the integer portion of the value shall be output as a series of digits appropriate to obase (as described below). The most significant nonzero digit shall be output next, followed by each successively less significant digit.
• If the absolute value of the numerical value is less than one but greater than zero and the scale of the numerical value is greater than zero, it is unspecified whether the character 0 is output.
• If the numerical value is zero, the character 0 shall be output.

1. If the scale of the value is greater than zero, a period character shall be output, followed by a series of digits appropriate to obase (as described below) representing the most significant portion of the fractional part of the value. If s represents the scale of the value being output, the number of digits output shall be s if obase is 10, less than or equal to s if obase is greater than 10, or greater than or equal to s if obase is less than 10. For obase values other than 10, this should be the number of digits needed to represent a precision of 10s.

For obase values from 2 to 16, valid digits are the first obase of the single characters 0 1 2 3 4 5 6 7 8 9 A B C D E F which represent the values zero through fifteen, respectively. For bases greater than 16, each ‘‘digit’’ shall be written as a separate multidigit decimal number. Each digit except the most significant fractional digit shall be preceded a single <space> character. For bases from 17 to 100, bc shall write two-digit decimal numbers; for bases from 101 to 999, three-digit decimal strings, and so on. For example, the decimal number 1024 in base 25 would be written as:

∆01∆15∆24

in base 125, as: ∆008∆024

Very large numbers shall be split across lines with 70 characters per line in the POSIX Locale; other locales may split at different character boundaries. Lines that are continued shall end with a backslash (\). A function call shall consist of a function name followed by parentheses containing a comma-separated list of expressions, which are the function arguments. A whole array passed as an argument shall be specified by the array name followed by empty square brackets. All function arguments shall be passed by value. As a result, changes made to the formal parameters have no effect on the actual arguments. If the function terminates by executing a return statement, the value of the function shall be the value of the expression in the parentheses of the return statement or shall be zero if no expression is provided or if there is no return statement. The result of sqrt(expression) shall be the square root of the expression. The result shall be truncated in the least significant decimal place. The scale of the result shall be the scale of the expression or the value of scale, whichever is larger. The result of length(expression) shall be the total number of significant decimal digits in the expression. The scale of the result shall be zero. The result of scale(expression) shall be the scale of the expression. The scale of the result shall be zero. A numeric constant shall be an expression. The scale shall be the number of digits that follow the radix point in the input representing the constant, or zero if no radix point appears. The sequence ( expression ) shall be an expression with the same value and scale as expression. The parentheses can be used to alter the normal precedence. The semantics of the unary and binary operators are as follows. −expression The result shall be the negative of the expression. The scale of the result shall be the scale of expression. The unary increment and decrement operators shall not modify the scale of the named expression upon which they operate. The scale of the result shall be the scale of that named expression. ++named-expression The named expression shall be incremented by one. The result shall be the value of the named expression after incrementing. − −named-expression The named expression shall be decremented by one. The result shall be the value of the named expression after decrementing.

named-expression++ The named expression shall be incremented by one. The result shall be the value of the named expression before incrementing. named-expression− − The named expression shall be decremented by one. The result shall be the value of the named expression before decrementing. The exponentiation operator, circumflex (ˆ), shall bind right to left. expression ˆ expression The result shall be the first expression raised to the power of the second expression. If the second expression is not an integer, the behavior is undefined. If a is the scale of the left expression and b is the absolute value of the right expression, the scale of the result shall be: if b >= 0 min(a ∗ b, max(scale, a)) if b < 0 scale

The multiplicative operators (∗, /, %) shall bind left to right. expression ∗ expression The result shall be the product of the two expressions. If a and b are the scales of the two expressions, then the scale of the result shall be: min(a+b,max(scale,a,b)) expression / expression The result shall be the quotient of the two expressions. The scale of the result shall be the value of scale. expression % expression For expressions a and b, a % b shall be evaluated equivalent to the steps:

1. Compute a/b to current scale.
2. Use the result to compute a - (a / b) ∗ b to scale max(scale + scale(b), scale(a)) The scale of the result shall be max(scale + scale(b), scale(a))

The additive operators (+, −) shall bind left to right. expression + expression The result shall be the sum of the two expressions. The scale of the result shall be the maximum of the scales of the expressions. expression − expression The result shall be the difference of the two expressions. The scale of

the result shall be the maximum of the scales of the expressions. The assignment operators (=, +=, −=, ∗=, /=, %=, ˆ=) shall bind right to left. named-expression = expression This expression results in assigning the value of the expression on the right to the named expression on the left. The scale of both the named expression and the result shall be the scale of expression. The compound assignments forms named-expression <operator>= expression shall be equivalent to: named-expression = named-expression <operator> expression except that the named-expression shall be evaluated only once. Unlike all other operators, the relational operators (<, >, <=, >=, ==, !=) shall be only valid as the object of an if, while, or inside a for statement. expression1 < expression2 The relation shall be true if the value of expression1 is strictly less than the value of expression2. expression1 > expression2 The relation shall be true if the value of expression1 is strictly greater than the value of expression2. expression1 <= expression2 The relation shall be true if the value of expression1 is less than or equal to the value of expression2. expression1 >= expression2 The relation shall be true if the value of expression1 is greater than or equal to the value of expression2. expression1 == expression2 The relation shall be true if the values of expression1 and expression2 are equal. expression1 != expression2 The relation shall be true if the values of expression1 and expression2 are unequal. There are only two storage classes in bc, global and automatic (local). Only identifiers that are to be local to a function need be declared with the auto command. The arguments to a function shall be local to the function. All other identifiers are assumed to be global and available to all functions. All identifiers, global and local, have initial values of zero. Identifiers declared as auto shall be allocated on entry to the function and released on returning from the function. They therefore do not retain values between function calls. Auto arrays shall be specified by the array name followed by empty square brackets. On entry to a function, the old values of the names that appear as parameters and as automatic variables are pushed onto a stack. Until return is made from the function,

reference to these names refers only to the new values. References to any of these names from other functions that are called from this function also refer to the new value until one of those functions uses the same name for a local variable. When a statement is an expression, unless the main operator is an assignment, execution of the statement shall write the value of the expression followed by a <newline> character. When a statement is a string, execution of the statement shall write the value of the string. Statements separated by semicolon or <newline> shall be executed sequentially. In an interactive invocation of bc, each time a <newline> character is read that satisfies the grammatical production input_item : semicolon_list NEWLINE the sequential list of statements making up the semicolon_list shall be executed immediately and any output produced by that execution shall be written without any delay due to buffering. In an if statement [if (relation) statement] the statement shall be executed if the relation is true. The while statement [while (relation) statement] implements a loop in which the relation is tested; each time the relation is true, the statement shall be executed and the relation retested. When the relation is false, execution shall resume after statement. A for statement [for (expression; relation; expression) statement] shall be the same as: first-expression while (relation) { statement last-expression } All three expressions shall be present. The break statement causes termination of a for or while statement. The auto statement [auto identifier[,identifier] . . . ] shall cause the values of the identifiers to be pushed down. The identifiers can be ordinary identifiers or array identifiers. Array identifiers shall be specified by following the array name by empty square brackets. The auto statement shall be the first statement in a function definition.

A define statement: define LETTER ( opt_parameter_list ) { opt_auto_define_list statement_list } defines a function named LETTER. If a function named LETTER was previously defined, the define statement shall replace the previous definition. The expression LETTER ( opt_argument_list ) shall invoke the function named LETTER. The behavior is undefined if the number of arguments in the invocation does not match the number of parameters in the definition. Functions shall be defined before they are invoked. A function shall be considered to be defined within its own body, so recursive calls shall be valid. The values of numeric constants within a function shall be interpreted in the base specified by the value of the ibase register when the function is invoked. The return statements [return and return(expression)] shall cause termination of a function, popping of its auto variables, and specifies the result of the function. The first form shall be equivalent to return(0). The value and scale of an invocation of the function shall be the value and scale of the expression in parentheses. The quit statement (quit) shall stop execution of a bc program at the point where the statement occurs in the input, even if it occurs in a function definition, or in an if, for, or while statement. The following functions shall be defined when the −l option is specified: s ( Expression ) Sine of argument in radians c ( Expression ) Cosine of argument in radians a ( Expression ) Arctangent of argument l ( Expression ) Natural logarithm of argument e ( Expression ) Exponential function of argument j ( Expression , Expression ) Bessel function of integer order The scale of an invocation of each of these functions shall be the value of the scale register when the function is invoked. The behavior is undefined if any of these functions is invoked with an argument outside the domain of the mathematical function.

EXAMPLES

This description is based on BC—An Arbitrary Precision Desk-Calculator Language by Lorinda Cherry and Robert Morris, in the BSD User Manual B28. Automatic variables in bc do not work in exactly the same way as in either C or PL/1. In the shell, the following assigns an approximation of the first ten digits of π to the variable x: x=$(printf "%s\n" ’scale = 10; 104348/33215’ | bc ) The following bc program prints the same approximation of π, with a label, to standard output: scale = 10 "pi equals " 104348 / 33215 The following defines a function to compute an approximate value of the exponential function (note that such a function is predefined if the −l option is specified):

scale = 20 define e(x){ auto a, b, c, i, s a = b = s = for (i = 1; 1 == 1; i++){ a = a∗x b = b∗i c = a/b if (c == 0) { return(s) } s = s+c } } The following prints approximate values of the exponential function of the first ten integers: for (i = 1; i <= 10; ++i) { e(i) }

HISTORY OF DECISIONS MADE

The bc utility is traditionally implemented as a front-end processor for dc; dc was not selected to be part of the standard because bc was thought to have a more intuitive programmatic interface. Current implementations that implement bc using dc are expected to be compliant. The Exit Status for error conditions been left unspecified for several reasons:

1. The bc utility is used in both interactive and noninteractive situations. Different exit codes may be appropriate for the two uses.
2. It is unclear when a nonzero exit should be given; divide-by-zero, undefined functions, and syntax errors are all possibilities.
3. It is not clear what utility the exit status has.
4. In the bc(1) BSD, System V, and Ninth Edition implementations, bc works in conjunction with dc. dc is the parent, bc is the child. This was done to cleanly terminate bc if dc aborted.

The decision to have bc exit upon encountering an inaccessible input file is based on the belief that bc file1 file2 is used most often when at least file1 contains data/function declarations/initializations. Having bc continue with prerequisite files missing is probably not useful. There is no implication in the Consequences of Errors subclause that bc must check all its files for accessibility before opening any of them. There was considerable debate on the appropriateness of the language accepted by bc. Several members of the balloting group preferred to see either a pure

subset of the C language or some changes to make the language more compatible with C. While the bc language has some obvious similarities to C, it has never claimed to be compatible with any version of C. An interpreter for a subset of C might be a very worthwhile utility, and it could potentially make bc obsolete. However, no such utility is known in existing practice, and it was not within the scope of POSIX. 2 to define such a language and utility. If and when they are defined, it may be appropriate to include them in a future revision of this standard. This left the following alternatives:

1. Exclude any calculator language from the standard. The consensus of the working group was that a simple programmatic calculator language is very useful. Also, an interactive version of such a calculator would be very important for the POSIX. 2a revision. The only arguments for excluding any calculator were that it would become obsolete if and when a C-compatible one emerged, or that the absence would encourage the development of such a C-compatible one. These arguments did not sufficiently address the needs of current application writers.
2. Standardize the existing dc, possibly with minor modifications. The consensus of the working group was that dc is a fundamentally less usable language and that that would be far too severe a penalty for avoiding the issue of being similar to but incompatible with C.
3. Standardize the existing bc, possibly with minor modifications. This was the approach taken. Most of the proponents of changing the language would not have been satisfied until most or all of the incompatibilities with C were resolved. Since most of the changes considered most desirable would break existing applications and require significant modification to existing implementations, almost no modifications were made. The one significant modification that was made was the replacement of the traditional bc ’s assignment operators =+ et al. with the more modern += et al. The older versions are considered to be fundamentally flawed because of the lexical ambiguity in uses like a=-1 In order to permit implementations to deal with backward compatibility as they see fit, the behavior of this one ambiguous construct was made undefined. (At least three implementations have been known to support this change already, so the degree of change involved should not be great.)

The % operator is the mathematical remainder operator when scale is zero. The behavior of this operator for other values of scale is from traditional implementations of bc, and has been maintained for the sake of existing applications despite its nonintuitive nature. The bc utility always uses the period (.) character to represent a radix point, regardless of any decimal-point character specified as part of the current locale.

In languages like C or awk, the period character is used in program source, so it can be portable and unambiguous, while the locale-specific character is used in input and output. Because there is no distinction between source and input in bc, this arrangement would not be possible. Using the locale-specific character in bc ’s input would introduce ambiguities into the language; consider the following example in a locale with a comma as the decimal-point character: define f(a,b) { ... } ... f(1,2,3) Because of such ambiguities, the period character is used in input. Having input follow different conventions from output would be confusing in either pipeline usage or interactive usage, so period is also used in output. Traditional implementations permit setting ibase and obase to a broader range of values. This includes values less than 2, which were not seen as sufficiently useful to standardize. These implementations do not interpret input properly for values of ibase outside greater than 16. This is because numeric constants are recognized syntactically, rather than lexically, as described in the standard. They are built from lexical tokens of single hexadecimal digits and periods. Since <blank>s between tokens are not visible at the syntactic level, it is not possible to properly recognize the multidigit ‘‘digits’’ used in the higher bases. The ability to recognize input in these bases was not considered useful enough to require modifying these implementations. Note that the recognition of numeric constants at the syntactic level is not a problem with conformance to the standard, as it does not impact the behavior of portable applications (and correct bc programs). Traditional implementations also accept input with all of the digits 0-9 and A-F regardless of the value of ibase; since digits with value greater than or equal to ibase are not really appropriate, the behavior when they appear is undefined, except for the common case of ibase=8; /∗ Process in octal base ∗/ ... ibase=A /∗ Restore decimal base ∗/ In some historical implementations, if the expression to be written is an uninitialized array element, a leading <space> character and/or up to four leading 0 characters may be output before the character zero. This behavior is considered a bug; it is unlikely that any currently portable application relies on echo ’b[3]’ | bc returning 00000 rather than 0. Exact calculation of the number of fractional digits to output for a given value in a base other than 10 can be computationally expensive. Traditional implementations use a faster approximation, and this is permitted. Note that the requirements apply only to values of obase that the standard requires implementations

to support (in particular, not to 1, 0, or negative bases, if an implementation supports them as an extension).