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.\"
.\" SPDX-License-Identifier: BSD-2-Clause
.\"
.\" Copyright (c) 2018-2021 Gavin D. Howard and contributors.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions are met:
.\"
.\" * Redistributions of source code must retain the above copyright notice,
.\"   this list of conditions and the following disclaimer.
.\"
.\" * Redistributions in binary form must reproduce the above copyright notice,
.\"   this list of conditions and the following disclaimer in the documentation
.\"   and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
.\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
.\" LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
.\" POSSIBILITY OF SUCH DAMAGE.
.\"
.TH "BC" "1" "February 2021" "Gavin D. Howard" "General Commands Manual"
.SH NAME
.PP
bc - arbitrary-precision decimal arithmetic language and calculator
.SH SYNOPSIS
.PP
\f[B]bc\f[R] [\f[B]-ghilPqsvVw\f[R]] [\f[B]\[en]global-stacks\f[R]]
[\f[B]\[en]help\f[R]] [\f[B]\[en]interactive\f[R]]
[\f[B]\[en]mathlib\f[R]] [\f[B]\[en]no-prompt\f[R]]
[\f[B]\[en]quiet\f[R]] [\f[B]\[en]standard\f[R]] [\f[B]\[en]warn\f[R]]
[\f[B]\[en]version\f[R]] [\f[B]-e\f[R] \f[I]expr\f[R]]
[\f[B]\[en]expression\f[R]=\f[I]expr\f[R]\&...] [\f[B]-f\f[R]
\f[I]file\f[R]\&...] [\f[B]-file\f[R]=\f[I]file\f[R]\&...]
[\f[I]file\f[R]\&...]
.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[R].
.SH OPTIONS
.PP
The following are the options that bc(1) accepts.
.TP
\f[B]-g\f[R], \f[B]\[en]global-stacks\f[R]
Turns the globals \f[B]ibase\f[R], \f[B]obase\f[R], \f[B]scale\f[R], and
\f[B]seed\f[R] into stacks.
.RS
.PP
This has the effect that a copy of the current value of all four 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 \f[B]output(x,b)\f[R] that simply
printed \f[B]x\f[R] in base \f[B]b\f[R] could be written like this:
.IP
.nf
\f[C]
define void output(x, b) {
    obase=b
    x
}
\f[R]
.fi
.PP
instead of like this:
.IP
.nf
\f[C]
define void output(x, b) {
    auto c
    c=obase
    obase=b
    x
    obase=c
}
\f[R]
.fi
.PP
This makes writing functions much easier.
.PP
(\f[B]Note\f[R]: the function \f[B]output(x,b)\f[R] exists in the
extended math library.
See the \f[B]LIBRARY\f[R] section.)
.PP
However, since using this flag means that functions cannot set
\f[B]ibase\f[R], \f[B]obase\f[R], \f[B]scale\f[R], or \f[B]seed\f[R]
globally, functions that are made to do so cannot work anymore.
There are two possible use cases for that, and each has a solution.
.PP
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:
.IP
.nf
\f[C]
alias d2o=\[dq]bc -e ibase=A -e obase=8\[dq]
alias h2b=\[dq]bc -e ibase=G -e obase=2\[dq]
\f[R]
.fi
.PP
Second, if the purpose of a function is to set \f[B]ibase\f[R],
\f[B]obase\f[R], \f[B]scale\f[R], or \f[B]seed\f[R] globally for any
other purpose, it could be split into one to four functions (based on
how many globals it sets) and each of those functions could return the
desired value for a global.
.PP
For functions that set \f[B]seed\f[R], the value assigned to
\f[B]seed\f[R] is not propagated to parent functions.
This means that the sequence of pseudo-random numbers that they see will
not be the same sequence of pseudo-random numbers that any parent sees.
This is only the case once \f[B]seed\f[R] has been set.
.PP
If a function desires to not affect the sequence of pseudo-random
numbers of its parents, but wants to use the same \f[B]seed\f[R], it can
use the following line:
.IP
.nf
\f[C]
seed = seed
\f[R]
.fi
.PP
If the behavior of this option is desired for every run of bc(1), then
users could make sure to define \f[B]BC_ENV_ARGS\f[R] and include this
option (see the \f[B]ENVIRONMENT VARIABLES\f[R] section for more
details).
.PP
If \f[B]-s\f[R], \f[B]-w\f[R], or any equivalents are used, this option
is ignored.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]-h\f[R], \f[B]\[en]help\f[R]
Prints a usage message and quits.
.TP
\f[B]-i\f[R], \f[B]\[en]interactive\f[R]
Forces interactive mode.
(See the \f[B]INTERACTIVE MODE\f[R] section.)
.RS
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]-l\f[R], \f[B]\[en]mathlib\f[R]
Sets \f[B]scale\f[R] (see the \f[B]SYNTAX\f[R] section) to \f[B]20\f[R]
and loads the included math library and the extended math library before
running any code, including any expressions or files specified on the
command line.
.RS
.PP
To learn what is in the libraries, see the \f[B]LIBRARY\f[R] section.
.RE
.TP
\f[B]-P\f[R], \f[B]\[en]no-prompt\f[R]
Disables the prompt in TTY mode.
(The prompt is only enabled in TTY mode.
See the \f[B]TTY MODE\f[R] section) This is mostly for those users that
do not want a prompt or are not used to having them in bc(1).
Most of those users would want to put this option in
\f[B]BC_ENV_ARGS\f[R] (see the \f[B]ENVIRONMENT VARIABLES\f[R] section).
.RS
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]-q\f[R], \f[B]\[en]quiet\f[R]
This option is for compatibility with the GNU
bc(1) (https://www.gnu.org/software/bc/); it is a no-op.
Without this option, GNU bc(1) prints a copyright header.
This bc(1) only prints the copyright header if one or more of the
\f[B]-v\f[R], \f[B]-V\f[R], or \f[B]\[en]version\f[R] options are given.
.RS
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]-s\f[R], \f[B]\[en]standard\f[R]
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[R].
.RE
.TP
\f[B]-v\f[R], \f[B]-V\f[R], \f[B]\[en]version\f[R]
Print the version information (copyright header) and exit.
.RS
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]-w\f[R], \f[B]\[en]warn\f[R]
Like \f[B]-s\f[R] and \f[B]\[en]standard\f[R], 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[R].
.RE
.TP
\f[B]-e\f[R] \f[I]expr\f[R], \f[B]\[en]expression\f[R]=\f[I]expr\f[R]
Evaluates \f[I]expr\f[R].
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
If this option is given on the command-line (i.e., not in
\f[B]BC_ENV_ARGS\f[R], see the \f[B]ENVIRONMENT VARIABLES\f[R] section),
then after processing all expressions and files, bc(1) will exit, unless
\f[B]-\f[R] (\f[B]stdin\f[R]) was given as an argument at least once to
\f[B]-f\f[R] or \f[B]\[en]file\f[R], whether on the command-line or in
\f[B]BC_ENV_ARGS\f[R].
However, if any other \f[B]-e\f[R], \f[B]\[en]expression\f[R],
\f[B]-f\f[R], or \f[B]\[en]file\f[R] arguments are given after
\f[B]-f-\f[R] or equivalent is given, bc(1) will give a fatal error and
exit.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]-f\f[R] \f[I]file\f[R], \f[B]\[en]file\f[R]=\f[I]file\f[R]
Reads in \f[I]file\f[R] and evaluates it, line by line, as though it
were read through \f[B]stdin\f[R].
If expressions are also given (see above), the expressions are evaluated
in the order given.
.RS
.PP
If this option is given on the command-line (i.e., not in
\f[B]BC_ENV_ARGS\f[R], see the \f[B]ENVIRONMENT VARIABLES\f[R] section),
then after processing all expressions and files, bc(1) will exit, unless
\f[B]-\f[R] (\f[B]stdin\f[R]) was given as an argument at least once to
\f[B]-f\f[R] or \f[B]\[en]file\f[R].
However, if any other \f[B]-e\f[R], \f[B]\[en]expression\f[R],
\f[B]-f\f[R], or \f[B]\[en]file\f[R] arguments are given after
\f[B]-f-\f[R] or equivalent is given, bc(1) will give a fatal error and
exit.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.PP
All long options are \f[B]non-portable extensions\f[R].
.SH STDOUT
.PP
Any non-error output is written to \f[B]stdout\f[R].
In addition, if history (see the \f[B]HISTORY\f[R] section) and the
prompt (see the \f[B]TTY MODE\f[R] section) are enabled, both are output
to \f[B]stdout\f[R].
.PP
\f[B]Note\f[R]: Unlike other bc(1) implementations, this bc(1) will
issue a fatal error (see the \f[B]EXIT STATUS\f[R] section) if it cannot
write to \f[B]stdout\f[R], so if \f[B]stdout\f[R] is closed, as in
\f[B]bc >&-\f[R], it will quit with an error.
This is done so that bc(1) can report problems when \f[B]stdout\f[R] 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[R] to \f[B]/dev/null\f[R].
.SH STDERR
.PP
Any error output is written to \f[B]stderr\f[R].
.PP
\f[B]Note\f[R]: Unlike other bc(1) implementations, this bc(1) will
issue a fatal error (see the \f[B]EXIT STATUS\f[R] section) if it cannot
write to \f[B]stderr\f[R], so if \f[B]stderr\f[R] is closed, as in
\f[B]bc 2>&-\f[R], it will quit with an error.
This is done so that bc(1) can exit with an error code when
\f[B]stderr\f[R] 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[R] to \f[B]/dev/null\f[R].
.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[R] means expression, \f[B]S\f[R] means
statement, and \f[B]I\f[R] means identifier.
.PP
Identifiers (\f[B]I\f[R]) start with a lowercase letter and can be
followed by any number (up to \f[B]BC_NAME_MAX-1\f[R]) of lowercase
letters (\f[B]a-z\f[R]), digits (\f[B]0-9\f[R]), and underscores
(\f[B]_\f[R]).
The regex is \f[B][a-z][a-z0-9_]*\f[R].
Identifiers with more than one character (letter) are a
\f[B]non-portable extension\f[R].
.PP
\f[B]ibase\f[R] is a global variable determining how to interpret
constant numbers.
It is the \[lq]input\[rq] base, or the number base used for interpreting
input numbers.
\f[B]ibase\f[R] is initially \f[B]10\f[R].
If the \f[B]-s\f[R] (\f[B]\[en]standard\f[R]) and \f[B]-w\f[R]
(\f[B]\[en]warn\f[R]) flags were not given on the command line, the max
allowable value for \f[B]ibase\f[R] is \f[B]36\f[R].
Otherwise, it is \f[B]16\f[R].
The min allowable value for \f[B]ibase\f[R] is \f[B]2\f[R].
The max allowable value for \f[B]ibase\f[R] can be queried in bc(1)
programs with the \f[B]maxibase()\f[R] built-in function.
.PP
\f[B]obase\f[R] is a global variable determining how to output results.
It is the \[lq]output\[rq] base, or the number base used for outputting
numbers.
\f[B]obase\f[R] is initially \f[B]10\f[R].
The max allowable value for \f[B]obase\f[R] is \f[B]BC_BASE_MAX\f[R] and
can be queried in bc(1) programs with the \f[B]maxobase()\f[R] built-in
function.
The min allowable value for \f[B]obase\f[R] is \f[B]0\f[R].
If \f[B]obase\f[R] is \f[B]0\f[R], values are output in scientific
notation, and if \f[B]obase\f[R] is \f[B]1\f[R], values are output in
engineering notation.
Otherwise, values are output in the specified base.
.PP
Outputting in scientific and engineering notations are \f[B]non-portable
extensions\f[R].
.PP
The \f[I]scale\f[R] of an expression is the number of digits in the
result of the expression right of the decimal point, and \f[B]scale\f[R]
is a global variable that sets the precision of any operations, with
exceptions.
\f[B]scale\f[R] is initially \f[B]0\f[R].
\f[B]scale\f[R] cannot be negative.
The max allowable value for \f[B]scale\f[R] is \f[B]BC_SCALE_MAX\f[R]
and can be queried in bc(1) programs with the \f[B]maxscale()\f[R]
built-in function.
.PP
bc(1) has both \f[I]global\f[R] variables and \f[I]local\f[R] variables.
All \f[I]local\f[R] variables are local to the function; they are
parameters or are introduced in the \f[B]auto\f[R] list of a function
(see the \f[B]FUNCTIONS\f[R] section).
If a variable is accessed which is not a parameter or in the
\f[B]auto\f[R] list, it is assumed to be \f[I]global\f[R].
If a parent function has a \f[I]local\f[R] variable version of a
variable that a child function considers \f[I]global\f[R], the value of
that \f[I]global\f[R] 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[R] 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[R] the expression is
notsurrounded by parentheses.
.PP
The value that is printed is also assigned to the special variable
\f[B]last\f[R].
A single dot (\f[B].\f[R]) may also be used as a synonym for
\f[B]last\f[R].
These are \f[B]non-portable extensions\f[R].
.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[R] and \f[B]*/\f[R].
.IP "2." 3
Line comments go from \f[B]#\f[R] until, and not including, the next
newline.
This is a \f[B]non-portable extension\f[R].
.SS Named Expressions
.PP
The following are named expressions in bc(1):
.IP "1." 3
Variables: \f[B]I\f[R]
.IP "2." 3
Array Elements: \f[B]I[E]\f[R]
.IP "3." 3
\f[B]ibase\f[R]
.IP "4." 3
\f[B]obase\f[R]
.IP "5." 3
\f[B]scale\f[R]
.IP "6." 3
\f[B]seed\f[R]
.IP "7." 3
\f[B]last\f[R] or a single dot (\f[B].\f[R])
.PP
Numbers 6 and 7 are \f[B]non-portable extensions\f[R].
.PP
The meaning of \f[B]seed\f[R] is dependent on the current pseudo-random
number generator but is guaranteed to not change except for new major
versions.
.PP
The \f[I]scale\f[R] and sign of the value may be significant.
.PP
If a previously used \f[B]seed\f[R] value is assigned to \f[B]seed\f[R]
and used again, the pseudo-random number generator is guaranteed to
produce the same sequence of pseudo-random numbers as it did when the
\f[B]seed\f[R] value was previously used.
.PP
The exact value assigned to \f[B]seed\f[R] is not guaranteed to be
returned if \f[B]seed\f[R] is queried again immediately.
However, if \f[B]seed\f[R] \f[I]does\f[R] return a different value, both
values, when assigned to \f[B]seed\f[R], are guaranteed to produce the
same sequence of pseudo-random numbers.
This means that certain values assigned to \f[B]seed\f[R] will
\f[I]not\f[R] produce unique sequences of pseudo-random numbers.
The value of \f[B]seed\f[R] will change after any use of the
\f[B]rand()\f[R] and \f[B]irand(E)\f[R] operands (see the
\f[I]Operands\f[R] subsection below), except if the parameter passed to
\f[B]irand(E)\f[R] is \f[B]0\f[R], \f[B]1\f[R], or negative.
.PP
There is no limit to the length (number of significant decimal digits)
or \f[I]scale\f[R] of the value that can be assigned to \f[B]seed\f[R].
.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[R] 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[R]/\f[B]decrement\f[R] operators and as the left side
of \f[B]assignment\f[R] operators (see the \f[I]Operators\f[R]
subsection).
.SS Operands
.PP
The following are valid operands in bc(1):
.IP " 1." 4
Numbers (see the \f[I]Numbers\f[R] subsection below).
.IP " 2." 4
Array indices (\f[B]I[E]\f[R]).
.IP " 3." 4
\f[B](E)\f[R]: The value of \f[B]E\f[R] (used to change precedence).
.IP " 4." 4
\f[B]sqrt(E)\f[R]: The square root of \f[B]E\f[R].
\f[B]E\f[R] must be non-negative.
.IP " 5." 4
\f[B]length(E)\f[R]: The number of significant decimal digits in
\f[B]E\f[R].
.IP " 6." 4
\f[B]length(I[])\f[R]: The number of elements in the array \f[B]I\f[R].
This is a \f[B]non-portable extension\f[R].
.IP " 7." 4
\f[B]scale(E)\f[R]: The \f[I]scale\f[R] of \f[B]E\f[R].
.IP " 8." 4
\f[B]abs(E)\f[R]: The absolute value of \f[B]E\f[R].
This is a \f[B]non-portable extension\f[R].
.IP " 9." 4
\f[B]I()\f[R], \f[B]I(E)\f[R], \f[B]I(E, E)\f[R], and so on, where
\f[B]I\f[R] is an identifier for a non-\f[B]void\f[R] function (see the
\f[I]Void Functions\f[R] subsection of the \f[B]FUNCTIONS\f[R] section).
The \f[B]E\f[R] argument(s) may also be arrays of the form
\f[B]I[]\f[R], which will automatically be turned into array references
(see the \f[I]Array References\f[R] subsection of the
\f[B]FUNCTIONS\f[R] section) if the corresponding parameter in the
function definition is an array reference.
.IP "10." 4
\f[B]read()\f[R]: Reads a line from \f[B]stdin\f[R] and uses that as an
expression.
The result of that expression is the result of the \f[B]read()\f[R]
operand.
This is a \f[B]non-portable extension\f[R].
.IP "11." 4
\f[B]maxibase()\f[R]: The max allowable \f[B]ibase\f[R].
This is a \f[B]non-portable extension\f[R].
.IP "12." 4
\f[B]maxobase()\f[R]: The max allowable \f[B]obase\f[R].
This is a \f[B]non-portable extension\f[R].
.IP "13." 4
\f[B]maxscale()\f[R]: The max allowable \f[B]scale\f[R].
This is a \f[B]non-portable extension\f[R].
.IP "14." 4
\f[B]rand()\f[R]: A pseudo-random integer between \f[B]0\f[R]
(inclusive) and \f[B]BC_RAND_MAX\f[R] (inclusive).
Using this operand will change the value of \f[B]seed\f[R].
This is a \f[B]non-portable extension\f[R].
.IP "15." 4
\f[B]irand(E)\f[R]: A pseudo-random integer between \f[B]0\f[R]
(inclusive) and the value of \f[B]E\f[R] (exclusive).
If \f[B]E\f[R] is negative or is a non-integer (\f[B]E\f[R]\[cq]s
\f[I]scale\f[R] is not \f[B]0\f[R]), an error is raised, and bc(1)
resets (see the \f[B]RESET\f[R] section) while \f[B]seed\f[R] remains
unchanged.
If \f[B]E\f[R] is larger than \f[B]BC_RAND_MAX\f[R], the higher bound is
honored by generating several pseudo-random integers, multiplying them
by appropriate powers of \f[B]BC_RAND_MAX+1\f[R], and adding them
together.
Thus, the size of integer that can be generated with this operand is
unbounded.
Using this operand will change the value of \f[B]seed\f[R], unless the
value of \f[B]E\f[R] is \f[B]0\f[R] or \f[B]1\f[R].
In that case, \f[B]0\f[R] is returned, and \f[B]seed\f[R] is
\f[I]not\f[R] changed.
This is a \f[B]non-portable extension\f[R].
.IP "16." 4
\f[B]maxrand()\f[R]: The max integer returned by \f[B]rand()\f[R].
This is a \f[B]non-portable extension\f[R].
.PP
The integers generated by \f[B]rand()\f[R] and \f[B]irand(E)\f[R] are
guaranteed to be as unbiased as possible, subject to the limitations of
the pseudo-random number generator.
.PP
\f[B]Note\f[R]: The values returned by the pseudo-random number
generator with \f[B]rand()\f[R] and \f[B]irand(E)\f[R] are guaranteed to
\f[I]NOT\f[R] be cryptographically secure.
This is a consequence of using a seeded pseudo-random number generator.
However, they \f[I]are\f[R] guaranteed to be reproducible with identical
\f[B]seed\f[R] values.
This means that the pseudo-random values from bc(1) should only be used
where a reproducible stream of pseudo-random numbers is
\f[I]ESSENTIAL\f[R].
In any other case, use a non-seeded pseudo-random number generator.
.SS Numbers
.PP
Numbers are strings made up of digits, uppercase letters, and at most
\f[B]1\f[R] period for a radix.
Numbers can have up to \f[B]BC_NUM_MAX\f[R] digits.
Uppercase letters are equal to \f[B]9\f[R] + their position in the
alphabet (i.e., \f[B]A\f[R] equals \f[B]10\f[R], or \f[B]9+1\f[R]).
If a digit or letter makes no sense with the current value of
\f[B]ibase\f[R], they are set to the value of the highest valid digit in
\f[B]ibase\f[R].
.PP
Single-character numbers (i.e., \f[B]A\f[R] alone) take the value that
they would have if they were valid digits, regardless of the value of
\f[B]ibase\f[R].
This means that \f[B]A\f[R] alone always equals decimal \f[B]10\f[R] and
\f[B]Z\f[R] alone always equals decimal \f[B]35\f[R].
.PP
In addition, bc(1) accepts numbers in scientific notation.
These have the form \f[B]<number>e<integer>\f[R].
The exponent (the portion after the \f[B]e\f[R]) must be an integer.
An example is \f[B]1.89237e9\f[R], which is equal to
\f[B]1892370000\f[R].
Negative exponents are also allowed, so \f[B]4.2890e-3\f[R] is equal to
\f[B]0.0042890\f[R].
.PP
Using scientific notation is an error or warning if the \f[B]-s\f[R] or
\f[B]-w\f[R], respectively, command-line options (or equivalents) are
given.
.PP
\f[B]WARNING\f[R]: Both the number and the exponent in scientific
notation are interpreted according to the current \f[B]ibase\f[R], but
the number is still multiplied by \f[B]10\[ha]exponent\f[R] regardless
of the current \f[B]ibase\f[R].
For example, if \f[B]ibase\f[R] is \f[B]16\f[R] and bc(1) is given the
number string \f[B]FFeA\f[R], the resulting decimal number will be
\f[B]2550000000000\f[R], and if bc(1) is given the number string
\f[B]10e-4\f[R], the resulting decimal number will be \f[B]0.0016\f[R].
.PP
Accepting input as scientific notation is a \f[B]non-portable
extension\f[R].
.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
\f[B]++\f[R] \f[B]\[en]\f[R]
Type: Prefix and Postfix
.RS
.PP
Associativity: None
.PP
Description: \f[B]increment\f[R], \f[B]decrement\f[R]
.RE
.TP
\f[B]-\f[R] \f[B]!\f[R]
Type: Prefix
.RS
.PP
Associativity: None
.PP
Description: \f[B]negation\f[R], \f[B]boolean not\f[R]
.RE
.TP
\f[B]$\f[R]
Type: Postfix
.RS
.PP
Associativity: None
.PP
Description: \f[B]truncation\f[R]
.RE
.TP
\f[B]\[at]\f[R]
Type: Binary
.RS
.PP
Associativity: Right
.PP
Description: \f[B]set precision\f[R]
.RE
.TP
\f[B]\[ha]\f[R]
Type: Binary
.RS
.PP
Associativity: Right
.PP
Description: \f[B]power\f[R]
.RE
.TP
\f[B]*\f[R] \f[B]/\f[R] \f[B]%\f[R]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]multiply\f[R], \f[B]divide\f[R], \f[B]modulus\f[R]
.RE
.TP
\f[B]+\f[R] \f[B]-\f[R]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]add\f[R], \f[B]subtract\f[R]
.RE
.TP
\f[B]<<\f[R] \f[B]>>\f[R]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]shift left\f[R], \f[B]shift right\f[R]
.RE
.TP
\f[B]=\f[R] \f[B]<<=\f[R] \f[B]>>=\f[R] \f[B]+=\f[R] \f[B]-=\f[R] \f[B]*=\f[R] \f[B]/=\f[R] \f[B]%=\f[R] \f[B]\[ha]=\f[R] \f[B]\[at]=\f[R]
Type: Binary
.RS
.PP
Associativity: Right
.PP
Description: \f[B]assignment\f[R]
.RE
.TP
\f[B]==\f[R] \f[B]<=\f[R] \f[B]>=\f[R] \f[B]!=\f[R] \f[B]<\f[R] \f[B]>\f[R]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]relational\f[R]
.RE
.TP
\f[B]&&\f[R]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]boolean and\f[R]
.RE
.TP
\f[B]||\f[R]
Type: Binary
.RS
.PP
Associativity: Left
.PP
Description: \f[B]boolean or\f[R]
.RE
.PP
The operators will be described in more detail below.
.TP
\f[B]++\f[R] \f[B]\[en]\f[R]
The prefix and postfix \f[B]increment\f[R] and \f[B]decrement\f[R]
operators behave exactly like they would in C.
They require a named expression (see the \f[I]Named Expressions\f[R]
subsection) as an operand.
.RS
.PP
The prefix versions of these operators are more efficient; use them
where possible.
.RE
.TP
\f[B]-\f[R]
The \f[B]negation\f[R] operator returns \f[B]0\f[R] if a user attempts
to negate any expression with the value \f[B]0\f[R].
Otherwise, a copy of the expression with its sign flipped is returned.
.TP
\f[B]!\f[R]
The \f[B]boolean not\f[R] operator returns \f[B]1\f[R] if the expression
is \f[B]0\f[R], or \f[B]0\f[R] otherwise.
.RS
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]$\f[R]
The \f[B]truncation\f[R] operator returns a copy of the given expression
with all of its \f[I]scale\f[R] removed.
.RS
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]\[at]\f[R]
The \f[B]set precision\f[R] operator takes two expressions and returns a
copy of the first with its \f[I]scale\f[R] equal to the value of the
second expression.
That could either mean that the number is returned without change (if
the \f[I]scale\f[R] of the first expression matches the value of the
second expression), extended (if it is less), or truncated (if it is
more).
.RS
.PP
The second expression must be an integer (no \f[I]scale\f[R]) and
non-negative.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]\[ha]\f[R]
The \f[B]power\f[R] operator (not the \f[B]exclusive or\f[R] operator,
as it would be in C) takes two expressions and raises the first to the
power of the value of the second.
The \f[I]scale\f[R] of the result is equal to \f[B]scale\f[R].
.RS
.PP
The second expression must be an integer (no \f[I]scale\f[R]), and if it
is negative, the first value must be non-zero.
.RE
.TP
\f[B]*\f[R]
The \f[B]multiply\f[R] operator takes two expressions, multiplies them,
and returns the product.
If \f[B]a\f[R] is the \f[I]scale\f[R] of the first expression and
\f[B]b\f[R] is the \f[I]scale\f[R] of the second expression, the
\f[I]scale\f[R] of the result is equal to
\f[B]min(a+b,max(scale,a,b))\f[R] where \f[B]min()\f[R] and
\f[B]max()\f[R] return the obvious values.
.TP
\f[B]/\f[R]
The \f[B]divide\f[R] operator takes two expressions, divides them, and
returns the quotient.
The \f[I]scale\f[R] of the result shall be the value of \f[B]scale\f[R].
.RS
.PP
The second expression must be non-zero.
.RE
.TP
\f[B]%\f[R]
The \f[B]modulus\f[R] operator takes two expressions, \f[B]a\f[R] and
\f[B]b\f[R], and evaluates them by 1) Computing \f[B]a/b\f[R] to current
\f[B]scale\f[R] and 2) Using the result of step 1 to calculate
\f[B]a-(a/b)*b\f[R] to \f[I]scale\f[R]
\f[B]max(scale+scale(b),scale(a))\f[R].
.RS
.PP
The second expression must be non-zero.
.RE
.TP
\f[B]+\f[R]
The \f[B]add\f[R] operator takes two expressions, \f[B]a\f[R] and
\f[B]b\f[R], and returns the sum, with a \f[I]scale\f[R] equal to the
max of the \f[I]scale\f[R]s of \f[B]a\f[R] and \f[B]b\f[R].
.TP
\f[B]-\f[R]
The \f[B]subtract\f[R] operator takes two expressions, \f[B]a\f[R] and
\f[B]b\f[R], and returns the difference, with a \f[I]scale\f[R] equal to
the max of the \f[I]scale\f[R]s of \f[B]a\f[R] and \f[B]b\f[R].
.TP
\f[B]<<\f[R]
The \f[B]left shift\f[R] operator takes two expressions, \f[B]a\f[R] and
\f[B]b\f[R], and returns a copy of the value of \f[B]a\f[R] with its
decimal point moved \f[B]b\f[R] places to the right.
.RS
.PP
The second expression must be an integer (no \f[I]scale\f[R]) and
non-negative.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]>>\f[R]
The \f[B]right shift\f[R] operator takes two expressions, \f[B]a\f[R]
and \f[B]b\f[R], and returns a copy of the value of \f[B]a\f[R] with its
decimal point moved \f[B]b\f[R] places to the left.
.RS
.PP
The second expression must be an integer (no \f[I]scale\f[R]) and
non-negative.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]=\f[R] \f[B]<<=\f[R] \f[B]>>=\f[R] \f[B]+=\f[R] \f[B]-=\f[R] \f[B]*=\f[R] \f[B]/=\f[R] \f[B]%=\f[R] \f[B]\[ha]=\f[R] \f[B]\[at]=\f[R]
The \f[B]assignment\f[R] operators take two expressions, \f[B]a\f[R] and
\f[B]b\f[R] where \f[B]a\f[R] is a named expression (see the \f[I]Named
Expressions\f[R] subsection).
.RS
.PP
For \f[B]=\f[R], \f[B]b\f[R] is copied and the result is assigned to
\f[B]a\f[R].
For all others, \f[B]a\f[R] and \f[B]b\f[R] are applied as operands to
the corresponding arithmetic operator and the result is assigned to
\f[B]a\f[R].
.PP
The \f[B]assignment\f[R] operators that correspond to operators that are
extensions are themselves \f[B]non-portable extensions\f[R].
.RE
.TP
\f[B]==\f[R] \f[B]<=\f[R] \f[B]>=\f[R] \f[B]!=\f[R] \f[B]<\f[R] \f[B]>\f[R]
The \f[B]relational\f[R] operators compare two expressions, \f[B]a\f[R]
and \f[B]b\f[R], and if the relation holds, according to C language
semantics, the result is \f[B]1\f[R].
Otherwise, it is \f[B]0\f[R].
.RS
.PP
Note that unlike in C, these operators have a lower precedence than the
\f[B]assignment\f[R] operators, which means that \f[B]a=b>c\f[R] is
interpreted as \f[B](a=b)>c\f[R].
.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[R].
.RE
.TP
\f[B]&&\f[R]
The \f[B]boolean and\f[R] operator takes two expressions and returns
\f[B]1\f[R] if both expressions are non-zero, \f[B]0\f[R] otherwise.
.RS
.PP
This is \f[I]not\f[R] a short-circuit operator.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.TP
\f[B]||\f[R]
The \f[B]boolean or\f[R] operator takes two expressions and returns
\f[B]1\f[R] if one of the expressions is non-zero, \f[B]0\f[R]
otherwise.
.RS
.PP
This is \f[I]not\f[R] a short-circuit operator.
.PP
This is a \f[B]non-portable extension\f[R].
.RE
.SS Statements
.PP
The following items are statements:
.IP " 1." 4
\f[B]E\f[R]
.IP " 2." 4
\f[B]{\f[R] \f[B]S\f[R] \f[B];\f[R] \&... \f[B];\f[R] \f[B]S\f[R]
\f[B]}\f[R]
.IP " 3." 4
\f[B]if\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R]
.IP " 4." 4
\f[B]if\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R]
\f[B]else\f[R] \f[B]S\f[R]
.IP " 5." 4
\f[B]while\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R]
.IP " 6." 4
\f[B]for\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B];\f[R] \f[B]E\f[R]
\f[B];\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R]
.IP " 7." 4
An empty statement
.IP " 8." 4
\f[B]break\f[R]
.IP " 9." 4
\f[B]continue\f[R]
.IP "10." 4
\f[B]quit\f[R]
.IP "11." 4
\f[B]halt\f[R]
.IP "12." 4
\f[B]limits\f[R]
.IP "13." 4
A string of characters, enclosed in double quotes
.IP "14." 4
\f[B]print\f[R] \f[B]E\f[R] \f[B],\f[R] \&... \f[B],\f[R] \f[B]E\f[R]
.IP "15." 4
\f[B]I()\f[R], \f[B]I(E)\f[R], \f[B]I(E, E)\f[R], and so on, where
\f[B]I\f[R] is an identifier for a \f[B]void\f[R] function (see the
\f[I]Void Functions\f[R] subsection of the \f[B]FUNCTIONS\f[R] section).
The \f[B]E\f[R] argument(s) may also be arrays of the form
\f[B]I[]\f[R], which will automatically be turned into array references
(see the \f[I]Array References\f[R] subsection of the
\f[B]FUNCTIONS\f[R] 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[R].
.PP
Also, as a \f[B]non-portable extension\f[R], 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[R].
.PP
The \f[B]break\f[R] 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[R] 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[R] \f[B]else\f[R] statement does the same thing as in C.
.PP
The \f[B]quit\f[R] 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[R] statement causes bc(1) to quit, if it is executed.
(Unlike \f[B]quit\f[R] if it is on a branch of an \f[B]if\f[R] statement
that is not executed, bc(1) does not quit.)
.PP
The \f[B]limits\f[R] statement prints the limits that this bc(1) is
subject to.
This is like the \f[B]quit\f[R] statement in that it is a compile-time
command.
.PP
An expression by itself is evaluated and printed, followed by a newline.
.PP
Both scientific notation and engineering notation are available for
printing the results of expressions.
Scientific notation is activated by assigning \f[B]0\f[R] to
\f[B]obase\f[R], and engineering notation is activated by assigning
\f[B]1\f[R] to \f[B]obase\f[R].
To deactivate them, just assign a different value to \f[B]obase\f[R].
.PP
Scientific notation and engineering notation are disabled if bc(1) is
run with either the \f[B]-s\f[R] or \f[B]-w\f[R] command-line options
(or equivalents).
.PP
Printing numbers in scientific notation and/or engineering notation is a
\f[B]non-portable extension\f[R].
.SS Print Statement
.PP
The \[lq]expressions\[rq] in a \f[B]print\f[R] 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]\[rs]a\f[R]
T}@T{
\f[B]\[rs]a\f[R]
T}
T{
\f[B]\[rs]b\f[R]
T}@T{
\f[B]\[rs]b\f[R]
T}
T{
\f[B]\[rs]\[rs]\f[R]
T}@T{
\f[B]\[rs]\f[R]
T}
T{
\f[B]\[rs]e\f[R]
T}@T{
\f[B]\[rs]\f[R]
T}
T{
\f[B]\[rs]f\f[R]
T}@T{
\f[B]\[rs]f\f[R]
T}
T{
\f[B]\[rs]n\f[R]
T}@T{
\f[B]\[rs]n\f[R]
T}
T{
\f[B]\[rs]q\f[R]
T}@T{
\f[B]\[dq]\f[R]
T}
T{
\f[B]\[rs]r\f[R]
T}@T{
\f[B]\[rs]r\f[R]
T}
T{
\f[B]\[rs]t\f[R]
T}@T{
\f[B]\[rs]t\f[R]
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[R], 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[R] is equal to
\f[B]0\f[R], in the expression
.IP
.nf
\f[C]
a[i++] = i++
\f[R]
.fi
.PP
the first (or 0th) element of \f[B]a\f[R] is set to \f[B]1\f[R], and
\f[B]i\f[R] is equal to \f[B]2\f[R] at the end of the expression.
.PP
This includes function arguments.
Thus, assuming \f[B]i\f[R] is equal to \f[B]0\f[R], this means that in
the expression
.IP
.nf
\f[C]
x(i++, i++)
\f[R]
.fi
.PP
the first argument passed to \f[B]x()\f[R] is \f[B]0\f[R], and the
second argument is \f[B]1\f[R], while \f[B]i\f[R] is equal to
\f[B]2\f[R] 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[R]
.fi
.PP
Any \f[B]I\f[R] in the parameter list or \f[B]auto\f[R] list may be
replaced with \f[B]I[]\f[R] to make a parameter or \f[B]auto\f[R] var an
array, and any \f[B]I\f[R] in the parameter list may be replaced with
\f[B]*I[]\f[R] 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[R] like
normal array parameters and will be automatically converted into
references.
.PP
As a \f[B]non-portable extension\f[R], the opening brace of a
\f[B]define\f[R] statement may appear on the next line.
.PP
As a \f[B]non-portable extension\f[R], the return statement may also be
in one of the following forms:
.IP "1." 3
\f[B]return\f[R]
.IP "2." 3
\f[B]return\f[R] \f[B](\f[R] \f[B])\f[R]
.IP "3." 3
\f[B]return\f[R] \f[B]E\f[R]
.PP
The first two, or not specifying a \f[B]return\f[R] statement, is
equivalent to \f[B]return (0)\f[R], unless the function is a
\f[B]void\f[R] function (see the \f[I]Void Functions\f[R] subsection
below).
.SS Void Functions
.PP
Functions can also be \f[B]void\f[R] functions, defined as follows:
.IP
.nf
\f[C]
define void I(I,...,I){
    auto I,...,I
    S;...;S
    return
}
\f[R]
.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[R] statements
listed above.
They can also omit the return statement entirely.
.PP
The word \[lq]void\[rq] is not treated as a keyword; it is still
possible to have variables, arrays, and functions named \f[B]void\f[R].
The word \[lq]void\[rq] is only treated specially right after the
\f[B]define\f[R] keyword.
.PP
This is a \f[B]non-portable extension\f[R].
.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[R]
.fi
.PP
it is a \f[B]reference\f[R].
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[R].
.SH LIBRARY
.PP
All of the functions below, including the functions in the extended math
library (see the \f[I]Extended Library\f[R] subsection below), are
available when the \f[B]-l\f[R] or \f[B]\[en]mathlib\f[R] command-line
flags are given, except that the extended math library is not available
when the \f[B]-s\f[R] option, the \f[B]-w\f[R] option, or equivalents
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
\f[B]s(x)\f[R]
Returns the sine of \f[B]x\f[R], which is assumed to be in radians.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]c(x)\f[R]
Returns the cosine of \f[B]x\f[R], which is assumed to be in radians.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]a(x)\f[R]
Returns the arctangent of \f[B]x\f[R], in radians.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]l(x)\f[R]
Returns the natural logarithm of \f[B]x\f[R].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]e(x)\f[R]
Returns the mathematical constant \f[B]e\f[R] raised to the power of
\f[B]x\f[R].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]j(x, n)\f[R]
Returns the bessel integer order \f[B]n\f[R] (truncated) of \f[B]x\f[R].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.SS Extended Library
.PP
The extended library is \f[I]not\f[R] loaded when the
\f[B]-s\f[R]/\f[B]\[en]standard\f[R] or \f[B]-w\f[R]/\f[B]\[en]warn\f[R]
options are given since they are not part of the library defined by the
standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html).
.PP
The extended library is a \f[B]non-portable extension\f[R].
.TP
\f[B]p(x, y)\f[R]
Calculates \f[B]x\f[R] to the power of \f[B]y\f[R], even if \f[B]y\f[R]
is not an integer, and returns the result to the current
\f[B]scale\f[R].
.RS
.PP
It is an error if \f[B]y\f[R] is negative and \f[B]x\f[R] is
\f[B]0\f[R].
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]r(x, p)\f[R]
Returns \f[B]x\f[R] rounded to \f[B]p\f[R] decimal places according to
the rounding mode round half away from
\f[B]0\f[R] (https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero).
.TP
\f[B]ceil(x, p)\f[R]
Returns \f[B]x\f[R] rounded to \f[B]p\f[R] decimal places according to
the rounding mode round away from
\f[B]0\f[R] (https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero).
.TP
\f[B]f(x)\f[R]
Returns the factorial of the truncated absolute value of \f[B]x\f[R].
.TP
\f[B]perm(n, k)\f[R]
Returns the permutation of the truncated absolute value of \f[B]n\f[R]
of the truncated absolute value of \f[B]k\f[R], if \f[B]k <= n\f[R].
If not, it returns \f[B]0\f[R].
.TP
\f[B]comb(n, k)\f[R]
Returns the combination of the truncated absolute value of \f[B]n\f[R]
of the truncated absolute value of \f[B]k\f[R], if \f[B]k <= n\f[R].
If not, it returns \f[B]0\f[R].
.TP
\f[B]l2(x)\f[R]
Returns the logarithm base \f[B]2\f[R] of \f[B]x\f[R].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]l10(x)\f[R]
Returns the logarithm base \f[B]10\f[R] of \f[B]x\f[R].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]log(x, b)\f[R]
Returns the logarithm base \f[B]b\f[R] of \f[B]x\f[R].
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]cbrt(x)\f[R]
Returns the cube root of \f[B]x\f[R].
.TP
\f[B]root(x, n)\f[R]
Calculates the truncated value of \f[B]n\f[R], \f[B]r\f[R], and returns
the \f[B]r\f[R]th root of \f[B]x\f[R] to the current \f[B]scale\f[R].
.RS
.PP
If \f[B]r\f[R] is \f[B]0\f[R] or negative, this raises an error and
causes bc(1) to reset (see the \f[B]RESET\f[R] section).
It also raises an error and causes bc(1) to reset if \f[B]r\f[R] is even
and \f[B]x\f[R] is negative.
.RE
.TP
\f[B]pi(p)\f[R]
Returns \f[B]pi\f[R] to \f[B]p\f[R] decimal places.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]t(x)\f[R]
Returns the tangent of \f[B]x\f[R], which is assumed to be in radians.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]a2(y, x)\f[R]
Returns the arctangent of \f[B]y/x\f[R], in radians.
If both \f[B]y\f[R] and \f[B]x\f[R] are equal to \f[B]0\f[R], it raises
an error and causes bc(1) to reset (see the \f[B]RESET\f[R] section).
Otherwise, if \f[B]x\f[R] is greater than \f[B]0\f[R], it returns
\f[B]a(y/x)\f[R].
If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is greater than
or equal to \f[B]0\f[R], it returns \f[B]a(y/x)+pi\f[R].
If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is less than
\f[B]0\f[R], it returns \f[B]a(y/x)-pi\f[R].
If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is greater than
\f[B]0\f[R], it returns \f[B]pi/2\f[R].
If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is less than
\f[B]0\f[R], it returns \f[B]-pi/2\f[R].
.RS
.PP
This function is the same as the \f[B]atan2()\f[R] function in many
programming languages.
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]sin(x)\f[R]
Returns the sine of \f[B]x\f[R], which is assumed to be in radians.
.RS
.PP
This is an alias of \f[B]s(x)\f[R].
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]cos(x)\f[R]
Returns the cosine of \f[B]x\f[R], which is assumed to be in radians.
.RS
.PP
This is an alias of \f[B]c(x)\f[R].
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]tan(x)\f[R]
Returns the tangent of \f[B]x\f[R], which is assumed to be in radians.
.RS
.PP
If \f[B]x\f[R] is equal to \f[B]1\f[R] or \f[B]-1\f[R], this raises an
error and causes bc(1) to reset (see the \f[B]RESET\f[R] section).
.PP
This is an alias of \f[B]t(x)\f[R].
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]atan(x)\f[R]
Returns the arctangent of \f[B]x\f[R], in radians.
.RS
.PP
This is an alias of \f[B]a(x)\f[R].
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]atan2(y, x)\f[R]
Returns the arctangent of \f[B]y/x\f[R], in radians.
If both \f[B]y\f[R] and \f[B]x\f[R] are equal to \f[B]0\f[R], it raises
an error and causes bc(1) to reset (see the \f[B]RESET\f[R] section).
Otherwise, if \f[B]x\f[R] is greater than \f[B]0\f[R], it returns
\f[B]a(y/x)\f[R].
If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is greater than
or equal to \f[B]0\f[R], it returns \f[B]a(y/x)+pi\f[R].
If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is less than
\f[B]0\f[R], it returns \f[B]a(y/x)-pi\f[R].
If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is greater than
\f[B]0\f[R], it returns \f[B]pi/2\f[R].
If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is less than
\f[B]0\f[R], it returns \f[B]-pi/2\f[R].
.RS
.PP
This function is the same as the \f[B]atan2()\f[R] function in many
programming languages.
.PP
This is an alias of \f[B]a2(y, x)\f[R].
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]r2d(x)\f[R]
Converts \f[B]x\f[R] from radians to degrees and returns the result.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]d2r(x)\f[R]
Converts \f[B]x\f[R] from degrees to radians and returns the result.
.RS
.PP
This is a transcendental function (see the \f[I]Transcendental
Functions\f[R] subsection below).
.RE
.TP
\f[B]frand(p)\f[R]
Generates a pseudo-random number between \f[B]0\f[R] (inclusive) and
\f[B]1\f[R] (exclusive) with the number of decimal digits after the
decimal point equal to the truncated absolute value of \f[B]p\f[R].
If \f[B]p\f[R] is not \f[B]0\f[R], then calling this function will
change the value of \f[B]seed\f[R].
If \f[B]p\f[R] is \f[B]0\f[R], then \f[B]0\f[R] is returned, and
\f[B]seed\f[R] is \f[I]not\f[R] changed.
.TP
\f[B]ifrand(i, p)\f[R]
Generates a pseudo-random number that is between \f[B]0\f[R] (inclusive)
and the truncated absolute value of \f[B]i\f[R] (exclusive) with the
number of decimal digits after the decimal point equal to the truncated
absolute value of \f[B]p\f[R].
If the absolute value of \f[B]i\f[R] is greater than or equal to
\f[B]2\f[R], and \f[B]p\f[R] is not \f[B]0\f[R], then calling this
function will change the value of \f[B]seed\f[R]; otherwise, \f[B]0\f[R]
is returned and \f[B]seed\f[R] is not changed.
.TP
\f[B]srand(x)\f[R]
Returns \f[B]x\f[R] with its sign flipped with probability
\f[B]0.5\f[R].
In other words, it randomizes the sign of \f[B]x\f[R].
.TP
\f[B]brand()\f[R]
Returns a random boolean value (either \f[B]0\f[R] or \f[B]1\f[R]).
.TP
\f[B]ubytes(x)\f[R]
Returns the numbers of unsigned integer bytes required to hold the
truncated absolute value of \f[B]x\f[R].
.TP
\f[B]sbytes(x)\f[R]
Returns the numbers of signed, two\[cq]s-complement integer bytes
required to hold the truncated value of \f[B]x\f[R].
.TP
\f[B]hex(x)\f[R]
Outputs the hexadecimal (base \f[B]16\f[R]) representation of
\f[B]x\f[R].
.RS
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]binary(x)\f[R]
Outputs the binary (base \f[B]2\f[R]) representation of \f[B]x\f[R].
.RS
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]output(x, b)\f[R]
Outputs the base \f[B]b\f[R] representation of \f[B]x\f[R].
.RS
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]uint(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
an unsigned integer in as few power of two bytes as possible.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer or is negative, an error message is
printed instead, but bc(1) is not reset (see the \f[B]RESET\f[R]
section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]int(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
a signed, two\[cq]s-complement integer in as few power of two bytes as
possible.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer, an error message is printed instead,
but bc(1) is not reset (see the \f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]uintn(x, n)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
an unsigned integer in \f[B]n\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer, is negative, or cannot fit into
\f[B]n\f[R] bytes, an error message is printed instead, but bc(1) is not
reset (see the \f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]intn(x, n)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
a signed, two\[cq]s-complement integer in \f[B]n\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer or cannot fit into \f[B]n\f[R] bytes,
an error message is printed instead, but bc(1) is not reset (see the
\f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]uint8(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
an unsigned integer in \f[B]1\f[R] byte.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer, is negative, or cannot fit into
\f[B]1\f[R] byte, an error message is printed instead, but bc(1) is not
reset (see the \f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]int8(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
a signed, two\[cq]s-complement integer in \f[B]1\f[R] byte.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer or cannot fit into \f[B]1\f[R] byte, an
error message is printed instead, but bc(1) is not reset (see the
\f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]uint16(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
an unsigned integer in \f[B]2\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer, is negative, or cannot fit into
\f[B]2\f[R] bytes, an error message is printed instead, but bc(1) is not
reset (see the \f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]int16(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
a signed, two\[cq]s-complement integer in \f[B]2\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer or cannot fit into \f[B]2\f[R] bytes,
an error message is printed instead, but bc(1) is not reset (see the
\f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]uint32(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
an unsigned integer in \f[B]4\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer, is negative, or cannot fit into
\f[B]4\f[R] bytes, an error message is printed instead, but bc(1) is not
reset (see the \f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]int32(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
a signed, two\[cq]s-complement integer in \f[B]4\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer or cannot fit into \f[B]4\f[R] bytes,
an error message is printed instead, but bc(1) is not reset (see the
\f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]uint64(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
an unsigned integer in \f[B]8\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer, is negative, or cannot fit into
\f[B]8\f[R] bytes, an error message is printed instead, but bc(1) is not
reset (see the \f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]int64(x)\f[R]
Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as
a signed, two\[cq]s-complement integer in \f[B]8\f[R] bytes.
Both outputs are split into bytes separated by spaces.
.RS
.PP
If \f[B]x\f[R] is not an integer or cannot fit into \f[B]8\f[R] bytes,
an error message is printed instead, but bc(1) is not reset (see the
\f[B]RESET\f[R] section).
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]hex_uint(x, n)\f[R]
Outputs the representation of the truncated absolute value of
\f[B]x\f[R] as an unsigned integer in hexadecimal using \f[B]n\f[R]
bytes.
Not all of the value will be output if \f[B]n\f[R] is too small.
.RS
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]binary_uint(x, n)\f[R]
Outputs the representation of the truncated absolute value of
\f[B]x\f[R] as an unsigned integer in binary using \f[B]n\f[R] bytes.
Not all of the value will be output if \f[B]n\f[R] is too small.
.RS
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]output_uint(x, n)\f[R]
Outputs the representation of the truncated absolute value of
\f[B]x\f[R] as an unsigned integer in the current \f[B]obase\f[R] (see
the \f[B]SYNTAX\f[R] section) using \f[B]n\f[R] bytes.
Not all of the value will be output if \f[B]n\f[R] is too small.
.RS
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.RE
.TP
\f[B]output_byte(x, i)\f[R]
Outputs byte \f[B]i\f[R] of the truncated absolute value of \f[B]x\f[R],
where \f[B]0\f[R] is the least significant byte and \f[B]number_of_bytes
- 1\f[R] is the most significant byte.
.RS
.PP
This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R]
subsection of the \f[B]FUNCTIONS\f[R] section).
.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[R]) set to at least 1 higher
than is necessary.
If exact results are \f[I]absolutely\f[R] required, users can double the
precision (\f[B]scale\f[R]) and then truncate.
.PP
The transcendental functions in the standard math library are:
.IP \[bu] 2
\f[B]s(x)\f[R]
.IP \[bu] 2
\f[B]c(x)\f[R]
.IP \[bu] 2
\f[B]a(x)\f[R]
.IP \[bu] 2
\f[B]l(x)\f[R]
.IP \[bu] 2
\f[B]e(x)\f[R]
.IP \[bu] 2
\f[B]j(x, n)\f[R]
.PP
The transcendental functions in the extended math library are:
.IP \[bu] 2
\f[B]l2(x)\f[R]
.IP \[bu] 2
\f[B]l10(x)\f[R]
.IP \[bu] 2
\f[B]log(x, b)\f[R]
.IP \[bu] 2
\f[B]pi(p)\f[R]
.IP \[bu] 2
\f[B]t(x)\f[R]
.IP \[bu] 2
\f[B]a2(y, x)\f[R]
.IP \[bu] 2
\f[B]sin(x)\f[R]
.IP \[bu] 2
\f[B]cos(x)\f[R]
.IP \[bu] 2
\f[B]tan(x)\f[R]
.IP \[bu] 2
\f[B]atan(x)\f[R]
.IP \[bu] 2
\f[B]atan2(y, x)\f[R]
.IP \[bu] 2
\f[B]r2d(x)\f[R]
.IP \[bu] 2
\f[B]d2r(x)\f[R]
.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[R] 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[R] types to calculate the
value of \f[B]1\f[R] 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[R] decimal digit
at a time.
If built in a environment where \f[B]BC_LONG_BIT\f[R] (see the
\f[B]LIMITS\f[R] section) is \f[B]64\f[R], then each integer has
\f[B]9\f[R] decimal digits.
If built in an environment where \f[B]BC_LONG_BIT\f[R] is \f[B]32\f[R]
then each integer has \f[B]4\f[R] decimal digits.
This value (the number of decimal digits per large integer) is called
\f[B]BC_BASE_DIGS\f[R].
.PP
The actual values of \f[B]BC_LONG_BIT\f[R] and \f[B]BC_BASE_DIGS\f[R]
can be queried with the \f[B]limits\f[R] 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[R], 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
\f[B]BC_LONG_BIT\f[R]
The number of bits in the \f[B]long\f[R] 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[R] section).
.TP
\f[B]BC_BASE_DIGS\f[R]
The number of decimal digits per large integer (see the
\f[B]PERFORMANCE\f[R] section).
Depends on \f[B]BC_LONG_BIT\f[R].
.TP
\f[B]BC_BASE_POW\f[R]
The max decimal number that each large integer can store (see
\f[B]BC_BASE_DIGS\f[R]) plus \f[B]1\f[R].
Depends on \f[B]BC_BASE_DIGS\f[R].
.TP
\f[B]BC_OVERFLOW_MAX\f[R]
The max number that the overflow type (see the \f[B]PERFORMANCE\f[R]
section) can hold.
Depends on \f[B]BC_LONG_BIT\f[R].
.TP
\f[B]BC_BASE_MAX\f[R]
The maximum output base.
Set at \f[B]BC_BASE_POW\f[R].
.TP
\f[B]BC_DIM_MAX\f[R]
The maximum size of arrays.
Set at \f[B]SIZE_MAX-1\f[R].
.TP
\f[B]BC_SCALE_MAX\f[R]
The maximum \f[B]scale\f[R].
Set at \f[B]BC_OVERFLOW_MAX-1\f[R].
.TP
\f[B]BC_STRING_MAX\f[R]
The maximum length of strings.
Set at \f[B]BC_OVERFLOW_MAX-1\f[R].
.TP
\f[B]BC_NAME_MAX\f[R]
The maximum length of identifiers.
Set at \f[B]BC_OVERFLOW_MAX-1\f[R].
.TP
\f[B]BC_NUM_MAX\f[R]
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[R].
.TP
\f[B]BC_RAND_MAX\f[R]
The maximum integer (inclusive) returned by the \f[B]rand()\f[R]
operand.
Set at \f[B]2\[ha]BC_LONG_BIT-1\f[R].
.TP
Exponent
The maximum allowable exponent (positive or negative).
Set at \f[B]BC_OVERFLOW_MAX\f[R].
.TP
Number of vars
The maximum number of vars/arrays.
Set at \f[B]SIZE_MAX-1\f[R].
.PP
The actual values can be queried with the \f[B]limits\f[R] 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
\f[B]POSIXLY_CORRECT\f[R]
If this variable exists (no matter the contents), bc(1) behaves as if
the \f[B]-s\f[R] option was given.
.TP
\f[B]BC_ENV_ARGS\f[R]
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[R] will be processed before arguments and files given
on the command-line.
This gives the user the ability to set up \[lq]standard\[rq] 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[R] will correctly handle quoted
arguments, but it does not understand escape sequences.
For example, the string \f[B]\[lq]/home/gavin/some bc file.bc\[rq]\f[R]
will be correctly parsed, but the string \f[B]\[lq]/home/gavin/some
\[dq]bc\[dq] file.bc\[rq]\f[R] will include the backslashes.
.PP
The quote parsing will handle either kind of quotes, \f[B]\[cq]\f[R] or
\f[B]\[lq]\f[R]. 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]\[rq]some `bc' file.bc\[dq]\f[R], 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[R] 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
\f[B]BC_LINE_LENGTH\f[R]
If this environment variable exists and contains an integer that is
greater than \f[B]1\f[R] and is less than \f[B]UINT16_MAX\f[R]
(\f[B]2\[ha]16-1\f[R]), bc(1) will output lines to that length,
including the backslash (\f[B]\[rs]\f[R]).
The default line length is \f[B]70\f[R].
.SH EXIT STATUS
.PP
bc(1) returns the following exit statuses:
.TP
\f[B]0\f[R]
No error.
.TP
\f[B]1\f[R]
A math error occurred.
This follows standard practice of using \f[B]1\f[R] 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[R], taking the square root of a
negative number, using a negative number as a bound for the
pseudo-random number generator, 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]\[ha]\f[R]), places (\f[B]\[at]\f[R]), left shift
(\f[B]<<\f[R]), and right shift (\f[B]>>\f[R]) operators and their
corresponding assignment operators.
.RE
.TP
\f[B]2\f[R]
A parse error occurred.
.RS
.PP
Parse errors include unexpected \f[B]EOF\f[R], 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[R] subsection of the \f[B]SYNTAX\f[R] section),
giving an invalid \f[B]auto\f[R] list, having a duplicate
\f[B]auto\f[R]/function parameter, failing to find the end of a code
block, attempting to return a value from a \f[B]void\f[R] function,
attempting to use a variable as a reference, and using any extensions
when the option \f[B]-s\f[R] or any equivalents were given.
.RE
.TP
\f[B]3\f[R]
A runtime error occurred.
.RS
.PP
Runtime errors include assigning an invalid number to \f[B]ibase\f[R],
\f[B]obase\f[R], or \f[B]scale\f[R]; give a bad expression to a
\f[B]read()\f[R] call, calling \f[B]read()\f[R] inside of a
\f[B]read()\f[R] 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[R] function call as a value in an
expression.
.RE
.TP
\f[B]4\f[R]
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[R] is special; when a fatal error occurs, bc(1)
always exits and returns \f[B]4\f[R], 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[R] section), since
bc(1) resets its state (see the \f[B]RESET\f[R] 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[R] flag or \f[B]\[en]interactive\f[R] 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[R] flag or \f[B]\[en]interactive\f[R] 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[R]
and \f[B]stdout\f[R] are hooked to a terminal, but the \f[B]-i\f[R] flag
and \f[B]\[en]interactive\f[R] 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[R] section), and in normal execution, flushes
\f[B]stdout\f[R] as soon as execution is done for the current input.
.SH TTY MODE
.PP
If \f[B]stdin\f[R], \f[B]stdout\f[R], and \f[B]stderr\f[R] are all
connected to a TTY, bc(1) turns on \[lq]TTY mode.\[rq]
.PP
The prompt is enabled in TTY mode.
.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[R] and \f[B]stdout\f[R]
to be connected to a terminal.
.SH SIGNAL HANDLING
.PP
Sending a \f[B]SIGINT\f[R] 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[R] section), it will
reset (see the \f[B]RESET\f[R] section).
Otherwise, it will clean up and exit.
.PP
Note that \[lq]current input\[rq] can mean one of two things.
If bc(1) is processing input from \f[B]stdin\f[R] 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[R] if no other file exists.
.PP
This means that if a \f[B]SIGINT\f[R] 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[R] and \f[B]SIGQUIT\f[R] cause bc(1) to clean up and
exit, and it uses the default handler for all other signals.
.SH SEE ALSO
.PP
dc(1)
.SH STANDARDS
.PP
bc(1) is compliant with the IEEE Std 1003.1-2017
(\[lq]POSIX.1-2017\[rq]) (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
specification.
The flags \f[B]-efghiqsvVw\f[R], 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[R]) as a radix point, regardless of
the value of \f[B]LC_NUMERIC\f[R].
.SH BUGS
.PP
None are known.
Report bugs at https://git.yzena.com/gavin/bc.
.SH AUTHORS
.PP
Gavin D.
Howard <gavin@yzena.com> and contributors.