Provided by: manpages-posix_2013a-2_all 
PROLOG
This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface
may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface
may not be implemented on Linux.
NAME
bc — arbitrary-precision arithmetic language
SYNOPSIS
bc [−l] [file...]
DESCRIPTION
The bc utility shall implement an arbitrary precision calculator. It shall take input from any files
given, then read from the standard input. If the standard input and standard output to bc are attached to
a terminal, the invocation of bc shall be considered to be interactive, causing behavioral constraints
described in the following sections.
OPTIONS
The bc utility shall conform to the Base Definitions volume of POSIX.1‐2008, Section 12.2, Utility Syntax
Guidelines.
The following option shall be supported:
−l (The letter ell.) Define the math functions and initialize scale to 20, instead of the default
zero; see the EXTENDED DESCRIPTION section.
OPERANDS
The following operand shall be supported:
file A pathname of a text file containing bc program statements. After all files have been read, bc
shall read the standard input.
STDIN
See the INPUT FILES section.
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 Provide a default value for the internationalization variables that are unset or null. (See the
Base Definitions volume of POSIX.1‐2008, Section 8.2, Internationalization Variables for the
precedence of internationalization variables used to determine the values of locale
categories.)
LC_ALL If set to a non-empty string value, override the values of all the other internationalization
variables.
LC_CTYPE Determine the locale for the interpretation of sequences of bytes of text data as characters
(for example, single-byte as opposed to multi-byte characters in arguments and input files).
LC_MESSAGES
Determine the locale that should be used to affect the format and contents of diagnostic
messages written to standard error.
NLSPATH Determine the location of message catalogs for the processing of LC_MESSAGES.
ASYNCHRONOUS EVENTS
Default.
STDOUT
The output of the bc utility shall be controlled by the program read, and 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 the EXTENDED DESCRIPTION
section.
STDERR
The standard error shall be used only for diagnostic messages.
OUTPUT FILES
None.
EXTENDED DESCRIPTION
Grammar
The grammar in this section and the lexical conventions in the following section shall together describe
the syntax for bc programs. The general conventions for this style of grammar are described in Section
1.3, Grammar Conventions. A valid program can be represented as the non-terminal symbol program in the
grammar. This formal syntax shall take precedence over the text syntax description.
%token EOF NEWLINE STRING LETTER NUMBER
%token MUL_OP
/* '*', '/', '%' */
%token ASSIGN_OP
/* '=', '+=', '−=', '*=', '/=', '%=', '^=' */
%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 program
;
input_item : semicolon_list NEWLINE
| function
;
semicolon_list : /* empty */
| statement
| semicolon_list ';' statement
| semicolon_list ';'
;
statement_list : /* empty */
| statement
| statement_list NEWLINE
| statement_list NEWLINE statement
| statement_list ';'
| statement_list ';' statement
;
statement : expression
| STRING
| Break
| Quit
| Return
| Return '(' return_expression ')'
| For '(' expression ';'
relational_expression ';'
expression ')' statement
| If '(' relational_expression ')' statement
| While '(' relational_expression ')' statement
| '{' statement_list '}'
;
function : Define LETTER '(' opt_parameter_list ')'
'{' NEWLINE opt_auto_define_list
statement_list '}'
;
opt_parameter_list : /* empty */
| parameter_list
;
parameter_list : LETTER
| define_list ',' LETTER
;
opt_auto_define_list : /* empty */
| Auto define_list NEWLINE
| Auto define_list ';'
;
define_list : LETTER
| LETTER '[' ']'
| define_list ',' LETTER
| define_list ',' LETTER '[' ']'
;
opt_argument_list : /* empty */
| argument_list
;
argument_list : expression
| LETTER '[' ']' ',' argument_list
;
relational_expression : expression
| expression REL_OP expression
;
return_expression : /* empty */
| expression
;
expression : named_expression
| NUMBER
| '(' expression ')'
| LETTER '(' opt_argument_list ')'
| '−' expression
| expression '+' expression
| expression '−' expression
| expression MUL_OP expression
| expression '^' expression
| INCR_DECR named_expression
| named_expression INCR_DECR
| named_expression ASSIGN_OP expression
| Length '(' expression ')'
| Sqrt '(' expression ')'
| Scale '(' expression ')'
;
named_expression : LETTER
| LETTER '[' expression ']'
| Scale
| Ibase
| Obase
;
Lexical Conventions in bc
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 <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 is 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.
6. The combination of a <backslash> character immediately followed by a <newline> shall have no effect
other than to delimit lexical tokens with the following exceptions:
* It shall be interpreted as the character sequence "\<newline>" in STRING tokens.
* It shall be ignored as part of a multi-line NUMBER token.
7. The token NUMBER shall represent a numeric constant. It shall be recognized by the following grammar:
NUMBER : integer
| '.' integer
| integer '.'
| integer '.' integer
;
integer : digit
| integer digit
;
digit : 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7
| 8 | 9 | A | B | C | D | E | F
;
8. 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
Operations in bc.
9. The following keywords shall be recognized as tokens:
auto ibase length return while
break if obase scale
define for quit sqrt
10. 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
11. The following single-character and two-character sequences shall be recognized as the token
ASSIGN_OP:
= += −= *= /= %= ^=
12. If an '=' character, as the beginning of a token, is followed by a '−' character with no intervening
delimiter, the behavior is undefined.
13. The following single-characters shall be recognized as the token MUL_OP:
* / %
14. The following single-character and two-character sequences shall be recognized as the token REL_OP:
== <= >= != < >
15. The following two-character sequences shall be recognized as the token INCR_DECR:
++ −−
16. The following single characters shall be recognized as tokens whose names are the character:
<newline> ( ) , + − ; [ ] ^ { }
17. The token EOF is returned when the end of input is reached.
Operations in bc
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 shall begin at zero so an array is
indexed from 0 to {BC_DIM_MAX}−1. Subscripts shall be truncated to integers. The application shall
ensure that function identifiers are followed by parentheses, possibly enclosing arguments. The three
types of identifiers do not conflict.
The following table 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: Operators in bc
┌──────────────────────────┬───────────────┐
│ Operator │ Associativity │
├──────────────────────────┼───────────────┤
│++, −− │ N/A │
│unary − │ N/A │
│^ │ Right to left │
│*, /, % │ Left to right │
│+, binary − │ Left to right │
│=, +=, −=, *=, /=, %=, ^= │ 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 are named expressions; they 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
are 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 is 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 Lexical Conventions in bc,
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 (for example,
scale=0; 3.2/1), the result shall be truncated.
For all values of obase specified by this volume of POSIX.1‐2008, bc shall output numeric values by
performing each of the following steps in order:
1. If the value is less than zero, a <hyphen> ('−') character shall be output.
2. One of the following is 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),
most significant digit first. The most significant non-zero 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.
3. If the scale of the value is greater than zero and the numeric value is not 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 to 15, inclusive, respectively.
For bases greater than 16, each digit shall be written as a separate multi-digit decimal number. Each
digit except the most significant fractional digit shall be preceded by a single <space>. For bases from
17 to 100, bc shall write two-digit decimal numbers; for bases from 101 to 1000, three-digit decimal
strings, and so on. For example, the decimal number 1024 in base 25 would be written as:
01 15 24
and 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 shall 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> ('^'), shall bind right to left.
expression^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))
When scale is zero, the '%' operator is the mathematical remainder operator.
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 ('=', "+=", "−=", "*=", "/=", "%=", "^=") shall bind right to left.
named-expression=expression
This expression shall result 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 assignment 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 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 shall be pushed onto a stack. Until the function returns, reference to these names
shall refer 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>.
When a statement is a string, execution of the statement shall write the value of the string.
Statements separated by <semicolon> or <newline> characters shall be executed sequentially. In an
interactive invocation of bc, each time a <newline> 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
}
The application shall ensure that all three expressions are present.
The break statement shall cause 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 application shall ensure that the
auto statement is 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
are 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 specification of the result of the function. The first form shall be equivalent
to return(0). The value and scale of the result returned by the function shall be the value and scale of
the expression returned.
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 the result returned by these functions shall be the value of the scale register at the time
the function is invoked. The value of the scale register after these functions have completed their
execution shall be the same value it had upon invocation. The behavior is undefined if any of these
functions is invoked with an argument outside the domain of the mathematical function.
EXIT STATUS
The following exit values shall be returned:
0 All input files were processed successfully.
unspecified
An error occurred.
CONSEQUENCES OF ERRORS
If any file operand is specified and the named file cannot be accessed, bc shall write a diagnostic
message to standard error and terminate without any further action.
In an interactive invocation of bc, the utility should print an error message and recover following any
error in the input. In a non-interactive invocation of bc, invalid input causes undefined behavior.
The following sections are informative.
APPLICATION USAGE
Automatic variables in bc do not work in exactly the same way as in either C or PL/1.
For historical reasons, the exit status from bc cannot be relied upon to indicate that an error has
occurred. Returning zero after an error is possible. Therefore, bc should be used primarily by
interactive users (who can react to error messages) or by application programs that can somehow validate
the answers returned as not including error messages.
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 the <period>
is also used in output.
EXAMPLES
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 = 1
b = 1
s = 1
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)
}
RATIONALE
The bc utility is implemented historically as a front-end processor for dc; dc was not selected to be
part of this volume of POSIX.1‐2008 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 has been left unspecified for several reasons:
* The bc utility is used in both interactive and non-interactive situations. Different exit codes may
be appropriate for the two uses.
* It is unclear when a non-zero exit should be given; divide-by-zero, undefined functions, and syntax
errors are all possibilities.
* It is not clear what utility the exit status has.
* In the 4.3 BSD, System V, and Ninth Edition implementations, bc works in conjunction with dc. The dc
utility 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 section 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 reviewers
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 historical practice, and
it was not within the scope of this volume of POSIX.1‐2008 to define such a language and utility. If and
when they are defined, it may be appropriate to include them in a future version of this standard. This
left the following alternatives:
1. Exclude any calculator language from this volume of POSIX.1‐2008.
The consensus of the standard developers was that a simple programmatic calculator language is very
useful for both applications and interactive users. 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 developers.
2. Standardize the historical dc, possibly with minor modifications.
The consensus of the standard developers 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 historical 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 historical applications and require significant modification to
historical implementations, almost no modifications were made. The one significant modification that
was made was the replacement of the historical bc assignment operators "=+", and so on, with the more
modern "+=", and so on. 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 backwards-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 historical implementations of bc, and has been maintained for the sake
of historical applications despite its non-intuitive nature.
Historical 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 that are greater than 16. This is because numeric
constants are recognized syntactically, rather than lexically, as described in this volume of
POSIX.1‐2008. They are built from lexical tokens of single hexadecimal digits and <period> characters.
Since <blank> characters between tokens are not visible at the syntactic level, it is not possible to
recognize the multi-digit ``digits'' used in the higher bases properly. 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 this volume
of POSIX.1‐2008, as it does not impact the behavior of conforming applications (and correct bc programs).
Historical 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> 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 conforming 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. Historical implementations use a faster approximation, and this is
permitted. Note that the requirements apply only to values of obase that this volume of POSIX.1‐2008
requires implementations to support (in particular, not to 1, 0, or negative bases, if an implementation
supports them as an extension).
Historical implementations of bc did not allow array parameters to be passed as the last parameter to a
function. New implementations are encouraged to remove this restriction even though it is not required by
the grammar.
FUTURE DIRECTIONS
None.
SEE ALSO
Section 1.3, Grammar Conventions, awk
The Base Definitions volume of POSIX.1‐2008, Chapter 8, Environment Variables, Section 12.2, Utility
Syntax Guidelines
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2013 Edition,
Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, Copyright (C) 2013 by the Institute of Electrical and Electronics Engineers, Inc
and The Open Group. (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the event
of any discrepancy between this version and the original IEEE and The Open Group Standard, the original
IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at
http://www.unix.org/online.html .
Any typographical or formatting errors that appear in this page are most likely to have been introduced
during the conversion of the source files to man page format. To report such errors, see
https://www.kernel.org/doc/man-pages/reporting_bugs.html .