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.TH "BC" "1" "July 2020" "Gavin D. Howard" "General Commands Manual"
.SH NAME
.PP
bc \- arbitrary\-precision arithmetic language and calculator
.SH SYNOPSIS
.PP
\f[B]bc\f[] [\f[B]\-ghilPqsvVw\f[]] [\f[B]\-\-global\-stacks\f[]]
[\f[B]\-\-help\f[]] [\f[B]\-\-interactive\f[]] [\f[B]\-\-mathlib\f[]]
[\f[B]\-\-no\-prompt\f[]] [\f[B]\-\-quiet\f[]] [\f[B]\-\-standard\f[]]
[\f[B]\-\-warn\f[]] [\f[B]\-\-version\f[]] [\f[B]\-e\f[] \f[I]expr\f[]]
[\f[B]\-\-expression\f[]=\f[I]expr\f[]...] [\f[B]\-f\f[]
\f[I]file\f[]...] [\f[B]\-file\f[]=\f[I]file\f[]...] [\f[I]file\f[]...]
.SH DESCRIPTION
.PP
bc(1) is an interactive processor for a language first standardized in
1991 by POSIX.
(The current standard is
here (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html).)
The language provides unlimited precision decimal arithmetic and is
somewhat C\-like, but there are differences.
Such differences will be noted in this document.
.PP
After parsing and handling options, this bc(1) reads any files given on
the command line and executes them before reading from \f[B]stdin\f[].
.PP
This bc(1) is a drop\-in replacement for \f[I]any\f[] bc(1), including
(and especially) the GNU bc(1).
.SH OPTIONS
.PP
The following are the options that bc(1) accepts.
.PP
\f[B]\-g\f[], \f[B]\-\-global\-stacks\f[]
.IP
.nf
\f[C]
Turns\ the\ globals\ **ibase**,\ **obase**,\ and\ **scale**\ into\ stacks.

This\ has\ the\ effect\ that\ a\ copy\ of\ the\ current\ value\ of\ all\ three\ are\ pushed
onto\ a\ stack\ for\ every\ function\ call,\ as\ well\ as\ popped\ when\ every\ function
returns.\ This\ means\ that\ functions\ can\ assign\ to\ any\ and\ all\ of\ those
globals\ without\ worrying\ that\ the\ change\ will\ affect\ other\ functions.
Thus,\ a\ hypothetical\ function\ named\ **output(x,b)**\ that\ simply\ printed
**x**\ in\ base\ **b**\ could\ be\ written\ like\ this:

\ \ \ \ define\ void\ output(x,\ b)\ {
\ \ \ \ \ \ \ \ obase=b
\ \ \ \ \ \ \ \ x
\ \ \ \ }

instead\ of\ like\ this:

\ \ \ \ define\ void\ output(x,\ b)\ {
\ \ \ \ \ \ \ \ auto\ c
\ \ \ \ \ \ \ \ c=obase
\ \ \ \ \ \ \ \ obase=b
\ \ \ \ \ \ \ \ x
\ \ \ \ \ \ \ \ obase=c
\ \ \ \ }

This\ makes\ writing\ functions\ much\ easier.

However,\ since\ using\ this\ flag\ means\ that\ functions\ cannot\ set\ **ibase**,
**obase**,\ or\ **scale**\ globally,\ functions\ that\ are\ made\ to\ do\ so\ cannot
work\ anymore.\ There\ are\ two\ possible\ use\ cases\ for\ that,\ and\ each\ has\ a
solution.

First,\ if\ a\ function\ is\ called\ on\ startup\ to\ turn\ bc(1)\ into\ a\ number
converter,\ it\ is\ possible\ to\ replace\ that\ capability\ with\ various\ shell
aliases.\ Examples:

\ \ \ \ alias\ d2o="bc\ \-e\ ibase=A\ \-e\ obase=8"
\ \ \ \ alias\ h2b="bc\ \-e\ ibase=G\ \-e\ obase=2"

Second,\ if\ the\ purpose\ of\ a\ function\ is\ to\ set\ **ibase**,\ **obase**,\ or
**scale**\ globally\ for\ any\ other\ purpose,\ it\ could\ be\ split\ into\ one\ to
three\ functions\ (based\ on\ how\ many\ globals\ it\ sets)\ and\ each\ of\ those
functions\ could\ return\ the\ desired\ value\ for\ a\ global.

If\ the\ behavior\ of\ this\ option\ is\ desired\ for\ every\ run\ of\ bc(1),\ then\ users
could\ make\ sure\ to\ define\ **BC_ENV_ARGS**\ and\ include\ this\ option\ (see\ the
**ENVIRONMENT\ VARIABLES**\ section\ for\ more\ details).

If\ **\-s**,\ **\-w**,\ or\ any\ equivalents\ are\ used,\ this\ option\ is\ ignored.

This\ is\ a\ **non\-portable\ extension**.
\f[]
.fi
.TP
.B \f[B]\-h\f[], \f[B]\-\-help\f[]
Prints a usage message and quits.
.RS
.RE
.TP
.B \f[B]\-i\f[], \f[B]\-\-interactive\f[]
Forces interactive mode.
(See the \f[B]INTERACTIVE MODE\f[] section.)
.RS
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]\-l\f[], \f[B]\-\-mathlib\f[]
Sets \f[B]scale\f[] (see the \f[B]SYNTAX\f[] section) to \f[B]20\f[] and
loads the included math library before running any code, including any
expressions or files specified on the command line.
.RS
.PP
To learn what is in the library, see the \f[B]LIBRARY\f[] section.
.RE
.TP
.B \f[B]\-P\f[], \f[B]\-\-no\-prompt\f[]
This option is a no\-op.
.RS
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]\-q\f[], \f[B]\-\-quiet\f[]
Do not print copyright header.
bc(1) will also suppress the header in non\-interactive mode.
.RS
.PP
This is mostly for compatibility with the GNU
bc(1) (https://www.gnu.org/software/bc/).
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]\-s\f[], \f[B]\-\-standard\f[]
Process exactly the language defined by the
standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
and error if any extensions are used.
.RS
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]\-v\f[], \f[B]\-V\f[], \f[B]\-\-version\f[]
Print the version information (copyright header) and exit.
.RS
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]\-w\f[], \f[B]\-\-warn\f[]
Like \f[B]\-s\f[] and \f[B]\-\-standard\f[], except that warnings (and
not errors) are printed for non\-standard extensions and execution
continues normally.
.RS
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]\-e\f[] \f[I]expr\f[], \f[B]\-\-expression\f[]=\f[I]expr\f[]
Evaluates \f[I]expr\f[].
If multiple expressions are given, they are evaluated in order.
If files are given as well (see below), the expressions and files are
evaluated in the order given.
This means that if a file is given before an expression, the file is
read in and evaluated first.
.RS
.PP
In other bc(1) implementations, this option causes the program to
execute the expressions and then exit.
This bc(1) does not, unless the \f[B]BC_EXPR_EXIT\f[] is defined (see
the \f[B]ENVIRONMENT VARIABLES\f[] section).
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]\-f\f[] \f[I]file\f[], \f[B]\-\-file\f[]=\f[I]file\f[]
Reads in \f[I]file\f[] and evaluates it, line by line, as though it were
read through \f[B]stdin\f[].
If expressions are also given (see above), the expressions are evaluated
in the order given.
.RS
.PP
In other bc(1) implementations, this option causes the program to
execute the files and then exit.
This bc(1) does not, unless the \f[B]BC_EXPR_EXIT\f[] is defined (see
the \f[B]ENVIRONMENT VARIABLES\f[] section).
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.PP
All long options are \f[B]non\-portable extensions\f[].
.SH STDOUT
.PP
Any non\-error output is written to \f[B]stdout\f[].
.PP
\f[B]Note\f[]: Unlike other bc(1) implementations, this bc(1) will issue
a fatal error (see the \f[B]EXIT STATUS\f[] section) if it cannot write
to \f[B]stdout\f[], so if \f[B]stdout\f[] is closed, as in \f[B]bc
>&\-\f[], it will quit with an error.
This is done so that bc(1) can report problems when \f[B]stdout\f[] is
redirected to a file.
.PP
If there are scripts that depend on the behavior of other bc(1)
implementations, it is recommended that those scripts be changed to
redirect \f[B]stdout\f[] to \f[B]/dev/null\f[].
.SH STDERR
.PP
Any error output is written to \f[B]stderr\f[].
.PP
\f[B]Note\f[]: Unlike other bc(1) implementations, this bc(1) will issue
a fatal error (see the \f[B]EXIT STATUS\f[] section) if it cannot write
to \f[B]stderr\f[], so if \f[B]stderr\f[] is closed, as in \f[B]bc
2>&\-\f[], it will quit with an error.
This is done so that bc(1) can exit with an error code when
\f[B]stderr\f[] is redirected to a file.
.PP
If there are scripts that depend on the behavior of other bc(1)
implementations, it is recommended that those scripts be changed to
redirect \f[B]stderr\f[] to \f[B]/dev/null\f[].
.SH SYNTAX
.PP
The syntax for bc(1) programs is mostly C\-like, with some differences.
This bc(1) follows the POSIX
standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html),
which is a much more thorough resource for the language this bc(1)
accepts.
This section is meant to be a summary and a listing of all the
extensions to the standard.
.PP
In the sections below, \f[B]E\f[] means expression, \f[B]S\f[] means
statement, and \f[B]I\f[] means identifier.
.PP
Identifiers (\f[B]I\f[]) start with a lowercase letter and can be
followed by any number (up to \f[B]BC_NAME_MAX\-1\f[]) of lowercase
letters (\f[B]a\-z\f[]), digits (\f[B]0\-9\f[]), and underscores
(\f[B]_\f[]).
The regex is \f[B][a\-z][a\-z0\-9_]*\f[].
Identifiers with more than one character (letter) are a
\f[B]non\-portable extension\f[].
.PP
\f[B]ibase\f[] is a global variable determining how to interpret
constant numbers.
It is the "input" base, or the number base used for interpreting input
numbers.
\f[B]ibase\f[] is initially \f[B]10\f[].
If the \f[B]\-s\f[] (\f[B]\-\-standard\f[]) and \f[B]\-w\f[]
(\f[B]\-\-warn\f[]) flags were not given on the command line, the max
allowable value for \f[B]ibase\f[] is \f[B]36\f[].
Otherwise, it is \f[B]16\f[].
The min allowable value for \f[B]ibase\f[] is \f[B]2\f[].
The max allowable value for \f[B]ibase\f[] can be queried in bc(1)
programs with the \f[B]maxibase()\f[] built\-in function.
.PP
\f[B]obase\f[] is a global variable determining how to output results.
It is the "output" base, or the number base used for outputting numbers.
\f[B]obase\f[] is initially \f[B]10\f[].
The max allowable value for \f[B]obase\f[] is \f[B]BC_BASE_MAX\f[] and
can be queried in bc(1) programs with the \f[B]maxobase()\f[] built\-in
function.
The min allowable value for \f[B]obase\f[] is \f[B]2\f[].
Values are output in the specified base.
.PP
The \f[I]scale\f[] of an expression is the number of digits in the
result of the expression right of the decimal point, and \f[B]scale\f[]
is a global variable that sets the precision of any operations, with
exceptions.
\f[B]scale\f[] is initially \f[B]0\f[].
\f[B]scale\f[] cannot be negative.
The max allowable value for \f[B]scale\f[] is \f[B]BC_SCALE_MAX\f[] and
can be queried in bc(1) programs with the \f[B]maxscale()\f[] built\-in
function.
.PP
bc(1) has both \f[I]global\f[] variables and \f[I]local\f[] variables.
All \f[I]local\f[] variables are local to the function; they are
parameters or are introduced in the \f[B]auto\f[] list of a function
(see the \f[B]FUNCTIONS\f[] section).
If a variable is accessed which is not a parameter or in the
\f[B]auto\f[] list, it is assumed to be \f[I]global\f[].
If a parent function has a \f[I]local\f[] variable version of a variable
that a child function considers \f[I]global\f[], the value of that
\f[I]global\f[] variable in the child function is the value of the
variable in the parent function, not the value of the actual
\f[I]global\f[] variable.
.PP
All of the above applies to arrays as well.
.PP
The value of a statement that is an expression (i.e., any of the named
expressions or operands) is printed unless the lowest precedence
operator is an assignment operator \f[I]and\f[] the expression is
notsurrounded by parentheses.
.PP
The value that is printed is also assigned to the special variable
\f[B]last\f[].
A single dot (\f[B].\f[]) may also be used as a synonym for
\f[B]last\f[].
These are \f[B]non\-portable extensions\f[].
.PP
Either semicolons or newlines may separate statements.
.SS Comments
.PP
There are two kinds of comments:
.IP "1." 3
Block comments are enclosed in \f[B]/*\f[] and \f[B]*/\f[].
.IP "2." 3
Line comments go from \f[B]#\f[] until, and not including, the next
newline.
This is a \f[B]non\-portable extension\f[].
.SS Named Expressions
.PP
The following are named expressions in bc(1):
.IP "1." 3
Variables: \f[B]I\f[]
.IP "2." 3
Array Elements: \f[B]I[E]\f[]
.IP "3." 3
\f[B]ibase\f[]
.IP "4." 3
\f[B]obase\f[]
.IP "5." 3
\f[B]scale\f[]
.IP "6." 3
\f[B]last\f[] or a single dot (\f[B].\f[])
.PP
Number 6 is a \f[B]non\-portable extension\f[].
.PP
Variables and arrays do not interfere; users can have arrays named the
same as variables.
This also applies to functions (see the \f[B]FUNCTIONS\f[] section), so
a user can have a variable, array, and function that all have the same
name, and they will not shadow each other, whether inside of functions
or not.
.PP
Named expressions are required as the operand of
\f[B]increment\f[]/\f[B]decrement\f[] operators and as the left side of
\f[B]assignment\f[] operators (see the \f[I]Operators\f[] subsection).
.SS Operands
.PP
The following are valid operands in bc(1):
.IP " 1." 4
Numbers (see the \f[I]Numbers\f[] subsection below).
.IP " 2." 4
Array indices (\f[B]I[E]\f[]).
.IP " 3." 4
\f[B](E)\f[]: The value of \f[B]E\f[] (used to change precedence).
.IP " 4." 4
\f[B]sqrt(E)\f[]: The square root of \f[B]E\f[].
\f[B]E\f[] must be non\-negative.
.IP " 5." 4
\f[B]length(E)\f[]: The number of significant decimal digits in
\f[B]E\f[].
.IP " 6." 4
\f[B]length(I[])\f[]: The number of elements in the array \f[B]I\f[].
This is a \f[B]non\-portable extension\f[].
.IP " 7." 4
\f[B]scale(E)\f[]: The \f[I]scale\f[] of \f[B]E\f[].
.IP " 8." 4
\f[B]abs(E)\f[]: The absolute value of \f[B]E\f[].
This is a \f[B]non\-portable extension\f[].
.IP " 9." 4
\f[B]I()\f[], \f[B]I(E)\f[], \f[B]I(E, E)\f[], and so on, where
\f[B]I\f[] is an identifier for a non\-\f[B]void\f[] function (see the
\f[I]Void Functions\f[] subsection of the \f[B]FUNCTIONS\f[] section).
The \f[B]E\f[] argument(s) may also be arrays of the form \f[B]I[]\f[],
which will automatically be turned into array references (see the
\f[I]Array References\f[] subsection of the \f[B]FUNCTIONS\f[] section)
if the corresponding parameter in the function definition is an array
reference.
.IP "10." 4
\f[B]read()\f[]: Reads a line from \f[B]stdin\f[] and uses that as an
expression.
The result of that expression is the result of the \f[B]read()\f[]
operand.
This is a \f[B]non\-portable extension\f[].
.IP "11." 4
\f[B]maxibase()\f[]: The max allowable \f[B]ibase\f[].
This is a \f[B]non\-portable extension\f[].
.IP "12." 4
\f[B]maxobase()\f[]: The max allowable \f[B]obase\f[].
This is a \f[B]non\-portable extension\f[].
.IP "13." 4
\f[B]maxscale()\f[]: The max allowable \f[B]scale\f[].
This is a \f[B]non\-portable extension\f[].
.SS Numbers
.PP
Numbers are strings made up of digits, uppercase letters, and at most
\f[B]1\f[] period for a radix.
Numbers can have up to \f[B]BC_NUM_MAX\f[] digits.
Uppercase letters are equal to \f[B]9\f[] + their position in the
alphabet (i.e., \f[B]A\f[] equals \f[B]10\f[], or \f[B]9+1\f[]).
If a digit or letter makes no sense with the current value of
\f[B]ibase\f[], they are set to the value of the highest valid digit in
\f[B]ibase\f[].
.PP
Single\-character numbers (i.e., \f[B]A\f[] alone) take the value that
they would have if they were valid digits, regardless of the value of
\f[B]ibase\f[].
This means that \f[B]A\f[] alone always equals decimal \f[B]10\f[] and
\f[B]Z\f[] alone always equals decimal \f[B]35\f[].
.SS Operators
.PP
The following arithmetic and logical operators can be used.
They are listed in order of decreasing precedence.
Operators in the same group have the same precedence.
.TP
.B \f[B]++\f[] \f[B]\-\-\f[]
Type: Prefix and Postfix
.RS
.PP
Associativity: None
.PP
Description: \f[B]increment\f[], \f[B]decrement\f[]
.RE
.TP
.B \f[B]\-\f[] \f[B]!\f[]
Type: Prefix
.RS
.PP
Associativity: None
.PP
Description: \f[B]negation\f[], \f[B]boolean not\f[]
.RE
.TP
.B \f[B]^\f[]
Type: Binary
.RS
.PP
Associativity: Right
.PP
Description: \f[B]power\f[]
.RE
.TP
.B \f[B]*\f[] \f[B]/\f[] \f[B]%\f[]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]multiply\f[], \f[B]divide\f[], \f[B]modulus\f[]
.RE
.TP
.B \f[B]+\f[] \f[B]\-\f[]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]add\f[], \f[B]subtract\f[]
.RE
.TP
.B \f[B]=\f[] \f[B]+=\f[] \f[B]\-=\f[] \f[B]*=\f[] \f[B]/=\f[] \f[B]%=\f[] \f[B]^=\f[]
Type: Binary
.RS
.PP
Associativity: Right
.PP
Description: \f[B]assignment\f[]
.RE
.TP
.B \f[B]==\f[] \f[B]<=\f[] \f[B]>=\f[] \f[B]!=\f[] \f[B]<\f[] \f[B]>\f[]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]relational\f[]
.RE
.TP
.B \f[B]&&\f[]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]boolean and\f[]
.RE
.TP
.B \f[B]||\f[]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]boolean or\f[]
.RE
.PP
The operators will be described in more detail below.
.TP
.B \f[B]++\f[] \f[B]\-\-\f[]
The prefix and postfix \f[B]increment\f[] and \f[B]decrement\f[]
operators behave exactly like they would in C.
They require a named expression (see the \f[I]Named Expressions\f[]
subsection) as an operand.
.RS
.PP
The prefix versions of these operators are more efficient; use them
where possible.
.RE
.TP
.B \f[B]\-\f[]
The \f[B]negation\f[] operator returns \f[B]0\f[] if a user attempts to
negate any expression with the value \f[B]0\f[].
Otherwise, a copy of the expression with its sign flipped is returned.
.RS
.RE
.TP
.B \f[B]!\f[]
The \f[B]boolean not\f[] operator returns \f[B]1\f[] if the expression
is \f[B]0\f[], or \f[B]0\f[] otherwise.
.RS
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]^\f[]
The \f[B]power\f[] operator (not the \f[B]exclusive or\f[] operator, as
it would be in C) takes two expressions and raises the first to the
power of the value of the second.
.RS
.PP
The second expression must be an integer (no \f[I]scale\f[]), and if it
is negative, the first value must be non\-zero.
.RE
.TP
.B \f[B]*\f[]
The \f[B]multiply\f[] operator takes two expressions, multiplies them,
and returns the product.
If \f[B]a\f[] is the \f[I]scale\f[] of the first expression and
\f[B]b\f[] is the \f[I]scale\f[] of the second expression, the
\f[I]scale\f[] of the result is equal to
\f[B]min(a+b,max(scale,a,b))\f[] where \f[B]min()\f[] and \f[B]max()\f[]
return the obvious values.
.RS
.RE
.TP
.B \f[B]/\f[]
The \f[B]divide\f[] operator takes two expressions, divides them, and
returns the quotient.
The \f[I]scale\f[] of the result shall be the value of \f[B]scale\f[].
.RS
.PP
The second expression must be non\-zero.
.RE
.TP
.B \f[B]%\f[]
The \f[B]modulus\f[] operator takes two expressions, \f[B]a\f[] and
\f[B]b\f[], and evaluates them by 1) Computing \f[B]a/b\f[] to current
\f[B]scale\f[] and 2) Using the result of step 1 to calculate
\f[B]a\-(a/b)*b\f[] to \f[I]scale\f[]
\f[B]max(scale+scale(b),scale(a))\f[].
.RS
.PP
The second expression must be non\-zero.
.RE
.TP
.B \f[B]+\f[]
The \f[B]add\f[] operator takes two expressions, \f[B]a\f[] and
\f[B]b\f[], and returns the sum, with a \f[I]scale\f[] equal to the max
of the \f[I]scale\f[]s of \f[B]a\f[] and \f[B]b\f[].
.RS
.RE
.TP
.B \f[B]\-\f[]
The \f[B]subtract\f[] operator takes two expressions, \f[B]a\f[] and
\f[B]b\f[], and returns the difference, with a \f[I]scale\f[] equal to
the max of the \f[I]scale\f[]s of \f[B]a\f[] and \f[B]b\f[].
.RS
.RE
.TP
.B \f[B]=\f[] \f[B]+=\f[] \f[B]\-=\f[] \f[B]*=\f[] \f[B]/=\f[] \f[B]%=\f[] \f[B]^=\f[]
The \f[B]assignment\f[] operators take two expressions, \f[B]a\f[] and
\f[B]b\f[] where \f[B]a\f[] is a named expression (see the \f[I]Named
Expressions\f[] subsection).
.RS
.PP
For \f[B]=\f[], \f[B]b\f[] is copied and the result is assigned to
\f[B]a\f[].
For all others, \f[B]a\f[] and \f[B]b\f[] are applied as operands to the
corresponding arithmetic operator and the result is assigned to
\f[B]a\f[].
.RE
.TP
.B \f[B]==\f[] \f[B]<=\f[] \f[B]>=\f[] \f[B]!=\f[] \f[B]<\f[] \f[B]>\f[]
The \f[B]relational\f[] operators compare two expressions, \f[B]a\f[]
and \f[B]b\f[], and if the relation holds, according to C language
semantics, the result is \f[B]1\f[].
Otherwise, it is \f[B]0\f[].
.RS
.PP
Note that unlike in C, these operators have a lower precedence than the
\f[B]assignment\f[] operators, which means that \f[B]a=b>c\f[] is
interpreted as \f[B](a=b)>c\f[].
.PP
Also, unlike the
standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
requires, these operators can appear anywhere any other expressions can
be used.
This allowance is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]&&\f[]
The \f[B]boolean and\f[] operator takes two expressions and returns
\f[B]1\f[] if both expressions are non\-zero, \f[B]0\f[] otherwise.
.RS
.PP
This is \f[I]not\f[] a short\-circuit operator.
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.TP
.B \f[B]||\f[]
The \f[B]boolean or\f[] operator takes two expressions and returns
\f[B]1\f[] if one of the expressions is non\-zero, \f[B]0\f[] otherwise.
.RS
.PP
This is \f[I]not\f[] a short\-circuit operator.
.PP
This is a \f[B]non\-portable extension\f[].
.RE
.SS Statements
.PP
The following items are statements:
.IP " 1." 4
\f[B]E\f[]
.IP " 2." 4
\f[B]{\f[] \f[B]S\f[] \f[B];\f[] ...
\f[B];\f[] \f[B]S\f[] \f[B]}\f[]
.IP " 3." 4
\f[B]if\f[] \f[B](\f[] \f[B]E\f[] \f[B])\f[] \f[B]S\f[]
.IP " 4." 4
\f[B]if\f[] \f[B](\f[] \f[B]E\f[] \f[B])\f[] \f[B]S\f[] \f[B]else\f[]
\f[B]S\f[]
.IP " 5." 4
\f[B]while\f[] \f[B](\f[] \f[B]E\f[] \f[B])\f[] \f[B]S\f[]
.IP " 6." 4
\f[B]for\f[] \f[B](\f[] \f[B]E\f[] \f[B];\f[] \f[B]E\f[] \f[B];\f[]
\f[B]E\f[] \f[B])\f[] \f[B]S\f[]
.IP " 7." 4
An empty statement
.IP " 8." 4
\f[B]break\f[]
.IP " 9." 4
\f[B]continue\f[]
.IP "10." 4
\f[B]quit\f[]
.IP "11." 4
\f[B]halt\f[]
.IP "12." 4
\f[B]limits\f[]
.IP "13." 4
A string of characters, enclosed in double quotes
.IP "14." 4
\f[B]print\f[] \f[B]E\f[] \f[B],\f[] ...
\f[B],\f[] \f[B]E\f[]
.IP "15." 4
\f[B]I()\f[], \f[B]I(E)\f[], \f[B]I(E, E)\f[], and so on, where
\f[B]I\f[] is an identifier for a \f[B]void\f[] function (see the
\f[I]Void Functions\f[] subsection of the \f[B]FUNCTIONS\f[] section).
The \f[B]E\f[] argument(s) may also be arrays of the form \f[B]I[]\f[],
which will automatically be turned into array references (see the
\f[I]Array References\f[] subsection of the \f[B]FUNCTIONS\f[] section)
if the corresponding parameter in the function definition is an array
reference.
.PP
Numbers 4, 9, 11, 12, 14, and 15 are \f[B]non\-portable extensions\f[].
.PP
Also, as a \f[B]non\-portable extension\f[], any or all of the
expressions in the header of a for loop may be omitted.
If the condition (second expression) is omitted, it is assumed to be a
constant \f[B]1\f[].
.PP
The \f[B]break\f[] statement causes a loop to stop iterating and resume
execution immediately following a loop.
This is only allowed in loops.
.PP
The \f[B]continue\f[] statement causes a loop iteration to stop early
and returns to the start of the loop, including testing the loop
condition.
This is only allowed in loops.
.PP
The \f[B]if\f[] \f[B]else\f[] statement does the same thing as in C.
.PP
The \f[B]quit\f[] statement causes bc(1) to quit, even if it is on a
branch that will not be executed (it is a compile\-time command).
.PP
The \f[B]halt\f[] statement causes bc(1) to quit, if it is executed.
(Unlike \f[B]quit\f[] if it is on a branch of an \f[B]if\f[] statement
that is not executed, bc(1) does not quit.)
.PP
The \f[B]limits\f[] statement prints the limits that this bc(1) is
subject to.
This is like the \f[B]quit\f[] statement in that it is a compile\-time
command.
.PP
An expression by itself is evaluated and printed, followed by a newline.
.SS Print Statement
.PP
The "expressions" in a \f[B]print\f[] statement may also be strings.
If they are, there are backslash escape sequences that are interpreted
specially.
What those sequences are, and what they cause to be printed, are shown
below:
.PP
.TS
tab(@);
l l.
T{
\f[B]\\a\f[]
T}@T{
\f[B]\\a\f[]
T}
T{
\f[B]\\b\f[]
T}@T{
\f[B]\\b\f[]
T}
T{
\f[B]\\\\\f[]
T}@T{
\f[B]\\\f[]
T}
T{
\f[B]\\e\f[]
T}@T{
\f[B]\\\f[]
T}
T{
\f[B]\\f\f[]
T}@T{
\f[B]\\f\f[]
T}
T{
\f[B]\\n\f[]
T}@T{
\f[B]\\n\f[]
T}
T{
\f[B]\\q\f[]
T}@T{
\f[B]"\f[]
T}
T{
\f[B]\\r\f[]
T}@T{
\f[B]\\r\f[]
T}
T{
\f[B]\\t\f[]
T}@T{
\f[B]\\t\f[]
T}
.TE
.PP
Any other character following a backslash causes the backslash and
character to be printed as\-is.
.PP
Any non\-string expression in a print statement shall be assigned to
\f[B]last\f[], like any other expression that is printed.
.SS Order of Evaluation
.PP
All expressions in a statment are evaluated left to right, except as
necessary to maintain order of operations.
This means, for example, assuming that \f[B]i\f[] is equal to
\f[B]0\f[], in the expression
.IP
.nf
\f[C]
a[i++]\ =\ i++
\f[]
.fi
.PP
the first (or 0th) element of \f[B]a\f[] is set to \f[B]1\f[], and
\f[B]i\f[] is equal to \f[B]2\f[] at the end of the expression.
.PP
This includes function arguments.
Thus, assuming \f[B]i\f[] is equal to \f[B]0\f[], this means that in the
expression
.IP
.nf
\f[C]
x(i++,\ i++)
\f[]
.fi
.PP
the first argument passed to \f[B]x()\f[] is \f[B]0\f[], and the second
argument is \f[B]1\f[], while \f[B]i\f[] is equal to \f[B]2\f[] before
the function starts executing.
.SH FUNCTIONS
.PP
Function definitions are as follows:
.IP
.nf
\f[C]
define\ I(I,...,I){
\ \ \ \ auto\ I,...,I
\ \ \ \ S;...;S
\ \ \ \ return(E)
}
\f[]
.fi
.PP
Any \f[B]I\f[] in the parameter list or \f[B]auto\f[] list may be
replaced with \f[B]I[]\f[] to make a parameter or \f[B]auto\f[] var an
array, and any \f[B]I\f[] in the parameter list may be replaced with
\f[B]*I[]\f[] to make a parameter an array reference.
Callers of functions that take array references should not put an
asterisk in the call; they must be called with just \f[B]I[]\f[] like
normal array parameters and will be automatically converted into
references.
.PP
As a \f[B]non\-portable extension\f[], the opening brace of a
\f[B]define\f[] statement may appear on the next line.
.PP
As a \f[B]non\-portable extension\f[], the return statement may also be
in one of the following forms:
.IP "1." 3
\f[B]return\f[]
.IP "2." 3
\f[B]return\f[] \f[B](\f[] \f[B])\f[]
.IP "3." 3
\f[B]return\f[] \f[B]E\f[]
.PP
The first two, or not specifying a \f[B]return\f[] statement, is
equivalent to \f[B]return (0)\f[], unless the function is a
\f[B]void\f[] function (see the \f[I]Void Functions\f[] subsection
below).
.SS Void Functions
.PP
Functions can also be \f[B]void\f[] functions, defined as follows:
.IP
.nf
\f[C]
define\ void\ I(I,...,I){
\ \ \ \ auto\ I,...,I
\ \ \ \ S;...;S
\ \ \ \ return
}
\f[]
.fi
.PP
They can only be used as standalone expressions, where such an
expression would be printed alone, except in a print statement.
.PP
Void functions can only use the first two \f[B]return\f[] statements
listed above.
They can also omit the return statement entirely.
.PP
The word "void" is not treated as a keyword; it is still possible to
have variables, arrays, and functions named \f[B]void\f[].
The word "void" is only treated specially right after the
\f[B]define\f[] keyword.
.PP
This is a \f[B]non\-portable extension\f[].
.SS Array References
.PP
For any array in the parameter list, if the array is declared in the
form
.IP
.nf
\f[C]
*I[]
\f[]
.fi
.PP
it is a \f[B]reference\f[].
Any changes to the array in the function are reflected, when the
function returns, to the array that was passed in.
.PP
Other than this, all function arguments are passed by value.
.PP
This is a \f[B]non\-portable extension\f[].
.SH LIBRARY
.PP
All of the functions below are available when the \f[B]\-l\f[] or
\f[B]\-\-mathlib\f[] command\-line flags are given.
.SS Standard Library
.PP
The
standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
defines the following functions for the math library:
.TP
.B \f[B]s(x)\f[]
Returns the sine of \f[B]x\f[], which is assumed to be in radians.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[] subsection below).
.RE
.TP
.B \f[B]c(x)\f[]
Returns the cosine of \f[B]x\f[], which is assumed to be in radians.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[] subsection below).
.RE
.TP
.B \f[B]a(x)\f[]
Returns the arctangent of \f[B]x\f[], in radians.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[] subsection below).
.RE
.TP
.B \f[B]l(x)\f[]
Returns the natural logarithm of \f[B]x\f[].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[] subsection below).
.RE
.TP
.B \f[B]e(x)\f[]
Returns the mathematical constant \f[B]e\f[] raised to the power of
\f[B]x\f[].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[] subsection below).
.RE
.TP
.B \f[B]j(x, n)\f[]
Returns the bessel integer order \f[B]n\f[] (truncated) of \f[B]x\f[].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[] subsection below).
.RE
.SS Transcendental Functions
.PP
All transcendental functions can return slightly inaccurate results (up
to 1 ULP (https://en.wikipedia.org/wiki/Unit_in_the_last_place)).
This is unavoidable, and this
article (https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT) explains
why it is impossible and unnecessary to calculate exact results for the
transcendental functions.
.PP
Because of the possible inaccuracy, I recommend that users call those
functions with the precision (\f[B]scale\f[]) set to at least 1 higher
than is necessary.
If exact results are \f[I]absolutely\f[] required, users can double the
precision (\f[B]scale\f[]) and then truncate.
.PP
The transcendental functions in the standard math library are:
.IP \[bu] 2
\f[B]s(x)\f[]
.IP \[bu] 2
\f[B]c(x)\f[]
.IP \[bu] 2
\f[B]a(x)\f[]
.IP \[bu] 2
\f[B]l(x)\f[]
.IP \[bu] 2
\f[B]e(x)\f[]
.IP \[bu] 2
\f[B]j(x, n)\f[]
.SH RESET
.PP
When bc(1) encounters an error or a signal that it has a non\-default
handler for, it resets.
This means that several things happen.
.PP
First, any functions that are executing are stopped and popped off the
stack.
The behavior is not unlike that of exceptions in programming languages.
Then the execution point is set so that any code waiting to execute
(after all functions returned) is skipped.
.PP
Thus, when bc(1) resets, it skips any remaining code waiting to be
executed.
Then, if it is interactive mode, and the error was not a fatal error
(see the \f[B]EXIT STATUS\f[] section), it asks for more input;
otherwise, it exits with the appropriate return code.
.PP
Note that this reset behavior is different from the GNU bc(1), which
attempts to start executing the statement right after the one that
caused an error.
.SH PERFORMANCE
.PP
Most bc(1) implementations use \f[B]char\f[] types to calculate the
value of \f[B]1\f[] decimal digit at a time, but that can be slow.
This bc(1) does something different.
.PP
It uses large integers to calculate more than \f[B]1\f[] decimal digit
at a time.
If built in a environment where \f[B]BC_LONG_BIT\f[] (see the
\f[B]LIMITS\f[] section) is \f[B]64\f[], then each integer has
\f[B]9\f[] decimal digits.
If built in an environment where \f[B]BC_LONG_BIT\f[] is \f[B]32\f[]
then each integer has \f[B]4\f[] decimal digits.
This value (the number of decimal digits per large integer) is called
\f[B]BC_BASE_DIGS\f[].
.PP
The actual values of \f[B]BC_LONG_BIT\f[] and \f[B]BC_BASE_DIGS\f[] can
be queried with the \f[B]limits\f[] statement.
.PP
In addition, this bc(1) uses an even larger integer for overflow
checking.
This integer type depends on the value of \f[B]BC_LONG_BIT\f[], but is
always at least twice as large as the integer type used to store digits.
.SH LIMITS
.PP
The following are the limits on bc(1):
.TP
.B \f[B]BC_LONG_BIT\f[]
The number of bits in the \f[B]long\f[] type in the environment where
bc(1) was built.
This determines how many decimal digits can be stored in a single large
integer (see the \f[B]PERFORMANCE\f[] section).
.RS
.RE
.TP
.B \f[B]BC_BASE_DIGS\f[]
The number of decimal digits per large integer (see the
\f[B]PERFORMANCE\f[] section).
Depends on \f[B]BC_LONG_BIT\f[].
.RS
.RE
.TP
.B \f[B]BC_BASE_POW\f[]
The max decimal number that each large integer can store (see
\f[B]BC_BASE_DIGS\f[]) plus \f[B]1\f[].
Depends on \f[B]BC_BASE_DIGS\f[].
.RS
.RE
.TP
.B \f[B]BC_OVERFLOW_MAX\f[]
The max number that the overflow type (see the \f[B]PERFORMANCE\f[]
section) can hold.
Depends on \f[B]BC_LONG_BIT\f[].
.RS
.RE
.TP
.B \f[B]BC_BASE_MAX\f[]
The maximum output base.
Set at \f[B]BC_BASE_POW\f[].
.RS
.RE
.TP
.B \f[B]BC_DIM_MAX\f[]
The maximum size of arrays.
Set at \f[B]SIZE_MAX\-1\f[].
.RS
.RE
.TP
.B \f[B]BC_SCALE_MAX\f[]
The maximum \f[B]scale\f[].
Set at \f[B]BC_OVERFLOW_MAX\-1\f[].
.RS
.RE
.TP
.B \f[B]BC_STRING_MAX\f[]
The maximum length of strings.
Set at \f[B]BC_OVERFLOW_MAX\-1\f[].
.RS
.RE
.TP
.B \f[B]BC_NAME_MAX\f[]
The maximum length of identifiers.
Set at \f[B]BC_OVERFLOW_MAX\-1\f[].
.RS
.RE
.TP
.B \f[B]BC_NUM_MAX\f[]
The maximum length of a number (in decimal digits), which includes
digits after the decimal point.
Set at \f[B]BC_OVERFLOW_MAX\-1\f[].
.RS
.RE
.TP
.B Exponent
The maximum allowable exponent (positive or negative).
Set at \f[B]BC_OVERFLOW_MAX\f[].
.RS
.RE
.TP
.B Number of vars
The maximum number of vars/arrays.
Set at \f[B]SIZE_MAX\-1\f[].
.RS
.RE
.PP
The actual values can be queried with the \f[B]limits\f[] statement.
.PP
These limits are meant to be effectively non\-existent; the limits are
so large (at least on 64\-bit machines) that there should not be any
point at which they become a problem.
In fact, memory should be exhausted before these limits should be hit.
.SH ENVIRONMENT VARIABLES
.PP
bc(1) recognizes the following environment variables:
.TP
.B \f[B]POSIXLY_CORRECT\f[]
If this variable exists (no matter the contents), bc(1) behaves as if
the \f[B]\-s\f[] option was given.
.RS
.RE
.TP
.B \f[B]BC_ENV_ARGS\f[]
This is another way to give command\-line arguments to bc(1).
They should be in the same format as all other command\-line arguments.
These are always processed first, so any files given in
\f[B]BC_ENV_ARGS\f[] will be processed before arguments and files given
on the command\-line.
This gives the user the ability to set up "standard" options and files
to be used at every invocation.
The most useful thing for such files to contain would be useful
functions that the user might want every time bc(1) runs.
.RS
.PP
The code that parses \f[B]BC_ENV_ARGS\f[] will correctly handle quoted
arguments, but it does not understand escape sequences.
For example, the string \f[B]"/home/gavin/some bc file.bc"\f[] will be
correctly parsed, but the string \f[B]"/home/gavin/some "bc"
file.bc"\f[] will include the backslashes.
.PP
The quote parsing will handle either kind of quotes, \f[B]\[aq]\f[] or
\f[B]"\f[].
Thus, if you have a file with any number of single quotes in the name,
you can use double quotes as the outside quotes, as in \f[B]"some
\[aq]bc\[aq] file.bc"\f[], and vice versa if you have a file with double
quotes.
However, handling a file with both kinds of quotes in
\f[B]BC_ENV_ARGS\f[] is not supported due to the complexity of the
parsing, though such files are still supported on the command\-line
where the parsing is done by the shell.
.RE
.TP
.B \f[B]BC_LINE_LENGTH\f[]
If this environment variable exists and contains an integer that is
greater than \f[B]1\f[] and is less than \f[B]UINT16_MAX\f[]
(\f[B]2^16\-1\f[]), bc(1) will output lines to that length, including
the backslash (\f[B]\\\f[]).
The default line length is \f[B]70\f[].
.RS
.RE
.TP
.B \f[B]BC_EXPR_EXIT\f[]
If this variable exists (no matter the contents), bc(1) will exit
immediately after executing expressions and files given by the
\f[B]\-e\f[] and/or \f[B]\-f\f[] command\-line options (and any
equivalents).
.RS
.RE
.SH EXIT STATUS
.PP
bc(1) returns the following exit statuses:
.TP
.B \f[B]0\f[]
No error.
.RS
.RE
.TP
.B \f[B]1\f[]
A math error occurred.
This follows standard practice of using \f[B]1\f[] for expected errors,
since math errors will happen in the process of normal execution.
.RS
.PP
Math errors include divide by \f[B]0\f[], taking the square root of a
negative number, attempting to convert a negative number to a hardware
integer, overflow when converting a number to a hardware integer, and
attempting to use a non\-integer where an integer is required.
.PP
Converting to a hardware integer happens for the second operand of the
power (\f[B]^\f[]) operator and the corresponding assignment operator.
.RE
.TP
.B \f[B]2\f[]
A parse error occurred.
.RS
.PP
Parse errors include unexpected \f[B]EOF\f[], using an invalid
character, failing to find the end of a string or comment, using a token
where it is invalid, giving an invalid expression, giving an invalid
print statement, giving an invalid function definition, attempting to
assign to an expression that is not a named expression (see the
\f[I]Named Expressions\f[] subsection of the \f[B]SYNTAX\f[] section),
giving an invalid \f[B]auto\f[] list, having a duplicate
\f[B]auto\f[]/function parameter, failing to find the end of a code
block, attempting to return a value from a \f[B]void\f[] function,
attempting to use a variable as a reference, and using any extensions
when the option \f[B]\-s\f[] or any equivalents were given.
.RE
.TP
.B \f[B]3\f[]
A runtime error occurred.
.RS
.PP
Runtime errors include assigning an invalid number to \f[B]ibase\f[],
\f[B]obase\f[], or \f[B]scale\f[]; give a bad expression to a
\f[B]read()\f[] call, calling \f[B]read()\f[] inside of a
\f[B]read()\f[] call, type errors, passing the wrong number of arguments
to functions, attempting to call an undefined function, and attempting
to use a \f[B]void\f[] function call as a value in an expression.
.RE
.TP
.B \f[B]4\f[]
A fatal error occurred.
.RS
.PP
Fatal errors include memory allocation errors, I/O errors, failing to
open files, attempting to use files that do not have only ASCII
characters (bc(1) only accepts ASCII characters), attempting to open a
directory as a file, and giving invalid command\-line options.
.RE
.PP
The exit status \f[B]4\f[] is special; when a fatal error occurs, bc(1)
always exits and returns \f[B]4\f[], no matter what mode bc(1) is in.
.PP
The other statuses will only be returned when bc(1) is not in
interactive mode (see the \f[B]INTERACTIVE MODE\f[] section), since
bc(1) resets its state (see the \f[B]RESET\f[] section) and accepts more
input when one of those errors occurs in interactive mode.
This is also the case when interactive mode is forced by the
\f[B]\-i\f[] flag or \f[B]\-\-interactive\f[] option.
.PP
These exit statuses allow bc(1) to be used in shell scripting with error
checking, and its normal behavior can be forced by using the
\f[B]\-i\f[] flag or \f[B]\-\-interactive\f[] option.
.SH INTERACTIVE MODE
.PP
Per the
standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html),
bc(1) has an interactive mode and a non\-interactive mode.
Interactive mode is turned on automatically when both \f[B]stdin\f[] and
\f[B]stdout\f[] are hooked to a terminal, but the \f[B]\-i\f[] flag and
\f[B]\-\-interactive\f[] option can turn it on in other cases.
.PP
In interactive mode, bc(1) attempts to recover from errors (see the
\f[B]RESET\f[] section), and in normal execution, flushes
\f[B]stdout\f[] as soon as execution is done for the current input.
.SH TTY MODE
.PP
If \f[B]stdin\f[], \f[B]stdout\f[], and \f[B]stderr\f[] are all
connected to a TTY, bc(1) turns on "TTY mode."
.PP
TTY mode is required for history to be enabled (see the \f[B]COMMAND
LINE HISTORY\f[] section).
It is also required to enable special handling for \f[B]SIGINT\f[]
signals.
.PP
TTY mode is different from interactive mode because interactive mode is
required in the bc(1)
specification (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html),
and interactive mode requires only \f[B]stdin\f[] and \f[B]stdout\f[] to
be connected to a terminal.
.SH SIGNAL HANDLING
.PP
Sending a \f[B]SIGINT\f[] will cause bc(1) to stop execution of the
current input.
If bc(1) is in TTY mode (see the \f[B]TTY MODE\f[] section), it will
reset (see the \f[B]RESET\f[] section).
Otherwise, it will clean up and exit.
.PP
Note that "current input" can mean one of two things.
If bc(1) is processing input from \f[B]stdin\f[] in TTY mode, it will
ask for more input.
If bc(1) is processing input from a file in TTY mode, it will stop
processing the file and start processing the next file, if one exists,
or ask for input from \f[B]stdin\f[] if no other file exists.
.PP
This means that if a \f[B]SIGINT\f[] is sent to bc(1) as it is executing
a file, it can seem as though bc(1) did not respond to the signal since
it will immediately start executing the next file.
This is by design; most files that users execute when interacting with
bc(1) have function definitions, which are quick to parse.
If a file takes a long time to execute, there may be a bug in that file.
The rest of the files could still be executed without problem, allowing
the user to continue.
.PP
\f[B]SIGTERM\f[] and \f[B]SIGQUIT\f[] cause bc(1) to clean up and exit,
and it uses the default handler for all other signals.
The one exception is \f[B]SIGHUP\f[]; in that case, when bc(1) is in TTY
mode, a \f[B]SIGHUP\f[] will cause bc(1) to clean up and exit.
.SH COMMAND LINE HISTORY
.PP
bc(1) supports interactive command\-line editing.
If bc(1) is in TTY mode (see the \f[B]TTY MODE\f[] section), history is
enabled.
Previous lines can be recalled and edited with the arrow keys.
.PP
\f[B]Note\f[]: tabs are converted to 8 spaces.
.SH LOCALES
.PP
This bc(1) ships with support for adding error messages for different
locales and thus, supports \f[B]LC_MESSAGES\f[].
.SH SEE ALSO
.PP
dc(1)
.SH STANDARDS
.PP
bc(1) is compliant with the IEEE Std 1003.1\-2017
(“POSIX.1\-2017”) (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
specification.
The flags \f[B]\-efghiqsvVw\f[], all long options, and the extensions
noted above are extensions to that specification.
.PP
Note that the specification explicitly says that bc(1) only accepts
numbers that use a period (\f[B].\f[]) as a radix point, regardless of
the value of \f[B]LC_NUMERIC\f[].
.PP
This bc(1) supports error messages for different locales, and thus, it
supports \f[B]LC_MESSAGES\f[].
.SH BUGS
.PP
None are known.
Report bugs at https://git.yzena.com/gavin/bc.
.SH AUTHORS
.PP
Gavin D.
Howard <yzena.tech@gmail.com> and contributors.