BC(1P) POSIX Programmer's Manual BC(1P)
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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
IEEE Std 1003.1-2001, 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
IEEE Std 1003.1-2001, Section 8.2, Internationalization Vari-
ables 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 follow-
ing section shall together describe the syntax for bc programs. The
general conventions for this style of grammar are described in 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 con-
sist of any characters beginning with the double-quote character (
' )' and terminated by another occurrence of the double-quote char-
acter. 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 charac-
ter 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 unde-
fined.
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 iden-
tifiers, and function identifiers. All three types consist of single
lowercase letters. Array identifiers shall be followed by square brack-
ets ( "[]" ). 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 associativ-
ity 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 identi-
fiers 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 expres-
sions. The scale of an expression consisting of the name of one of
these registers shall be zero; values assigned to any of these regis-
ters 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 hexa-
decimal. (For example, ibase=A sets to base ten, regardless of the cur-
rent 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 dig-
its. 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
IEEE Std 1003.1-2001, 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) repre-
senting 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
10**s.
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 deci-
mal 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 charac-
ter boundaries. Lines that are continued shall end with a backslash (
'\' ).
A function call shall consist of a function name followed by parenthe-
ses containing a comma-separated list of expressions, which are the
function arguments. A whole array passed as an argument shall be speci-
fied 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 expres-
sion. 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 signifi-
cant 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 num-
ber 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 nor-
mal 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 inte-
ger, 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 expres-
sions.
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 func-
tion. 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 there-
fore 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 func-
tions 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 semicolons or <newline>s 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 rela-
tion is false, execution shall resume after statement.
A for statement( for( expression; relation; expression) statement)
shall be the same as:
first-expressionwhile (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 state-
ment.
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 previ-
ously defined, the define statement shall replace the previous defini-
tion. 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 specifi-
cation of the result of the function. The first form shall be equiva-
lent 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 speci-
fied:
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 unde-
fined 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-interac-
tive 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 mes-
sages.
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 unam-
biguous, while the locale-specific character is used in input and out-
put. Because there is no distinction between source and input in bc,
this arrangement would not be possible. Using the locale-specific char-
acter in bc's input would introduce ambiguities into the language; con-
sider 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 confus-
ing 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 'pi' to the variable x:
x=$(printf "%s\n" 'scale = 10; 104348/33215' | bc)
The following bc program prints the same approximation of 'pi', 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
IEEE Std 1003.1-2001 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 sev-
eral reasons:
* The bc utility is used in both interactive and non-interactive situ-
ations. 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 use-
ful. 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 inter-
preter 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 IEEE Std 1003.1-2001 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 IEEE Std 1003.1. This left the following alterna-
tives:
1. Exclude any calculator language from this volume of
IEEE Std 1003.1-2001.
The consensus of the standard developers was that a simple programmatic
calculator language is very useful for both applications and interac-
tive 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 writers.
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 incom-
patibilities with C were resolved. Since most of the changes considered
most desirable would break historical applications and require signifi-
cant modification to historical implementations, almost no modifica-
tions 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 IEEE Std 1003.1-2001.
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 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
IEEE Std 1003.1-2001, 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 con-
forming 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 per-
mitted. Note that the requirements apply only to values of obase that
this volume of IEEE Std 1003.1-2001 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
Grammar Conventions, awk
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 6, Copyright (C) 2001-2003 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 .
IEEE/The Open Group 2003 BC(1P)
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