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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.1‐2017, 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.1‐2017, 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.1‐2017, bc shall output numeric
values by performing each of the following steps in order:
1. If the value is less than zero, a <hyphen-minus> ('-') 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( expression1, expression2 )
Bessel function of expression2 of the first kind of integer order expression1.
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.1‐2017 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.1‐2017 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.1‐2017.
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.1‐2017. 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.1‐2017, 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.1‐2017 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.1‐2017, 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
1003.1-2017, Standard for Information Technology -- Portable Operating System Interface
(POSIX), The Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by
the Institute of Electrical and Electronics Engineers, Inc and The Open Group. 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.opengroup.org/unix/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 .