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BC(1)			    General Commands Manual			 BC(1)

NAME
       bc - arbitrary-precision	decimal	arithmetic language and	calculator

SYNOPSIS
       bc [-cCghilPqRsvVw] [--digit-clamp] [--no-digit-clamp] [--global-
       stacks] [--help]	[--interactive]	[--mathlib] [--no-prompt] [--no-read-
       prompt] [--quiet] [--standard] [--warn] [--version] [-e expr]
       [--expression=expr...]  [-f file...]  [--file=file...]  [file...]  [-I
       ibase] [--ibase=ibase] [-O obase] [--obase=obase] [-S scale]
       [--scale=scale] [-E seed] [--seed=seed]

DESCRIPTION
       bc(1) is	an interactive processor for a language	first standardized in
       1991 by POSIX.  (See the	STANDARDS section.)  The language provides
       unlimited precision decimal arithmetic and is somewhat C-like, but
       there are differences.  Such differences	will be	noted in this
       document.

       After parsing and handling options, this	bc(1) reads any	files given on
       the command line	and executes them before reading from stdin.

       This bc(1) is a drop-in replacement for any bc(1), including (and
       especially) the GNU bc(1).  It also has many extensions and extra
       features	beyond other implementations.

       Note: If	running	this bc(1) on any script meant for another bc(1) gives
       a parse error, it is probably because a word this bc(1) reserves	as a
       keyword is used as the name of a	function, variable, or array.  To fix
       that, use the command-line option -r keyword, where keyword is the
       keyword that is used as a name in the script.  For more information,
       see the OPTIONS section.

       If parsing scripts meant	for other bc(1)	implementations	still does not
       work, that is a bug and should be reported.  See	the BUGS section.

OPTIONS
       The following are the options that bc(1)	accepts.

       -C, --no-digit-clamp
	      Disables clamping	of digits greater than or equal	to the current
	      ibase when parsing numbers.

	      This means that the value	added to a number from a digit is
	      always that digit's value	multiplied by the value	of ibase
	      raised to	the power of the digit's position, which starts	from 0
	      at the least significant digit.

	      If this and/or the -c or --digit-clamp options are given
	      multiple times, the last one given is used.

	      This option overrides the	BC_DIGIT_CLAMP environment variable
	      (see the ENVIRONMENT VARIABLES section) and the default, which
	      can be queried with the -h or --help options.

	      This is a	non-portable extension.

       -c, --digit-clamp
	      Enables clamping of digits greater than or equal to the current
	      ibase when parsing numbers.

	      This means that digits that the value added to a number from a
	      digit that is greater than or equal to the ibase is the value of
	      ibase minus 1 all	multiplied by the value	of ibase raised	to the
	      power of the digit's position, which starts from 0 at the	least
	      significant digit.

	      If this and/or the -C or --no-digit-clamp	options	are given
	      multiple times, the last one given is used.

	      This option overrides the	BC_DIGIT_CLAMP environment variable
	      (see the ENVIRONMENT VARIABLES section) and the default, which
	      can be queried with the -h or --help options.

	      This is a	non-portable extension.

       -E seed,	--seed=seed
	      Sets the builtin variable	seed to	the value seed assuming	that
	      seed is in base 10.  It is a fatal error if seed is not a	valid
	      number.

	      If multiple instances of this option are given, the last is
	      used.

	      This is a	non-portable extension.

       -e expr,	--expression=expr
	      Evaluates	expr.  If multiple expressions are given, they are
	      evaluated	in order.  If files are	given as well (see the -f and
	      --file options), 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.

	      If this option is	given on the command-line (i.e., not in
	      BC_ENV_ARGS, see the ENVIRONMENT VARIABLES section), then	after
	      processing all expressions and files, bc(1) will exit, unless -
	      (stdin) was given	as an argument at least	once to	-f or --file,
	      whether on the command-line or in	BC_ENV_ARGS.  However, if any
	      other -e,	--expression, -f, or --file arguments are given	after
	      -f- or equivalent	is given, bc(1)	will give a fatal error	and
	      exit.

	      This is a	non-portable extension.

       -f file,	--file=file
	      Reads in file and	evaluates it, line by line, as though it were
	      read through stdin.  If expressions are also given (see the -e
	      and --expression options), the expressions are evaluated in the
	      order given.

	      If this option is	given on the command-line (i.e., not in
	      BC_ENV_ARGS, see the ENVIRONMENT VARIABLES section), then	after
	      processing all expressions and files, bc(1) will exit, unless -
	      (stdin) was given	as an argument at least	once to	-f or --file.
	      However, if any other -e,	--expression, -f, or --file arguments
	      are given	after -f- or equivalent	is given, bc(1)	will give a
	      fatal error and exit.

	      This is a	non-portable extension.

       -g, --global-stacks
	      Turns the	globals	ibase, obase, scale, and seed into stacks.

	      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 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.

	      (Note: the function output(x,b) exists in	the extended math
	      library.	See the	LIBRARY	section.)

	      However, since using this	flag means that	functions cannot set
	      ibase, obase, scale, or seed 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,
	      scale, or	seed 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.

	      For functions that set seed, the value assigned to seed 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 seed has been set.

	      If a function desires to not affect the sequence of pseudo-
	      random numbers of	its parents, but wants to use the same seed,
	      it can use the following line:

		     seed = seed

	      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.

       -h, --help
	      Prints a usage message and exits.

       -I ibase, --ibase=ibase
	      Sets the builtin variable	ibase to the value ibase assuming that
	      ibase is in base 10.  It is a fatal error	if ibase is not	a
	      valid number.

	      If multiple instances of this option are given, the last is
	      used.

	      This is a	non-portable extension.

       -i, --interactive
	      Forces interactive mode.	(See the INTERACTIVE MODE section.)

	      This is a	non-portable extension.

       -L, --no-line-length
	      Disables line length checking and	prints numbers without
	      backslashes and newlines.	 In other words, this option sets
	      BC_LINE_LENGTH to	0 (see the ENVIRONMENT VARIABLES section).

	      This is a	non-portable extension.

       -l, --mathlib
	      Sets scale (see the SYNTAX section) to 20	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.

	      To learn what is in the libraries, see the LIBRARY section.

       -O obase, --obase=obase
	      Sets the builtin variable	obase to the value obase assuming that
	      obase is in base 10.  It is a fatal error	if obase is not	a
	      valid number.

	      If multiple instances of this option are given, the last is
	      used.

	      This is a	non-portable extension.

       -P, --no-prompt
	      Disables the prompt in TTY mode.	(The prompt is only enabled in
	      TTY mode.	 See the TTY MODE 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
	      BC_ENV_ARGS (see the ENVIRONMENT VARIABLES section).

	      These options override the BC_PROMPT and BC_TTY_MODE environment
	      variables	(see the ENVIRONMENT VARIABLES section).

	      This is a	non-portable extension.

       -q, --quiet
	      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	-v, -V,	or
	      --version	options	are given unless the BC_BANNER environment
	      variable is set and contains a non-zero integer or if this bc(1)
	      was built	with the header	displayed by default.  If any of that
	      is the case, then	this option does prevent bc(1) from printing
	      the header.

	      This is a	non-portable extension.

       -R, --no-read-prompt
	      Disables the read	prompt in TTY mode.  (The read prompt is only
	      enabled in TTY mode.  See	the TTY	MODE section.)	This is	mostly
	      for those	users that do not want a read prompt or	are not	used
	      to having	them in	bc(1).	Most of	those users would want to put
	      this option in BC_ENV_ARGS (see the ENVIRONMENT VARIABLES
	      section).	 This option is	also useful in hash bang lines of
	      bc(1) scripts that prompt	for user input.

	      This option does not disable the regular prompt because the read
	      prompt is	only used when the read() built-in function is called.

	      These options do override	the BC_PROMPT and BC_TTY_MODE
	      environment variables (see the ENVIRONMENT VARIABLES section),
	      but only for the read prompt.

	      This is a	non-portable extension.

       -r keyword, --redefine=keyword
	      Redefines	keyword	in order to allow it to	be used	as a function,
	      variable,	or array name.	This is	useful when this bc(1) gives
	      parse errors when	parsing	scripts	meant for other	bc(1)
	      implementations.

	      The keywords this	bc(1) allows to	be redefined are:

	      o	abs

	      o	asciify

	      o	continue

	      o	divmod

	      o	else

	      o	halt

	      o	irand

	      o	last

	      o	limits

	      o	maxibase

	      o	maxobase

	      o	maxrand

	      o	maxscale

	      o	modexp

	      o	print

	      o	rand

	      o	read

	      o	seed

	      o	stream

	      If any of	those keywords are used	as a function, variable, or
	      array name in a script, use this option with the keyword as the
	      argument.	 If multiple are used, use this	option for all of
	      them; it can be used multiple times.

	      Keywords are not redefined when parsing the builtin math library
	      (see the LIBRARY section).

	      It is a fatal error to redefine keywords mandated	by the POSIX
	      standard (see the	STANDARDS section).  It	is a fatal error to
	      attempt to redefine words	that this bc(1)	does not reserve as
	      keywords.

       -S scale, --scale=scale
	      Sets the builtin variable	scale to the value scale assuming that
	      scale is in base 10.  It is a fatal error	if scale is not	a
	      valid number.

	      If multiple instances of this option are given, the last is
	      used.

	      This is a	non-portable extension.

       -s, --standard
	      Process exactly the language defined by the standard (see	the
	      STANDARDS	section) and error if any extensions are used.

	      This is a	non-portable extension.

       -v, -V, --version
	      Print the	version	information (copyright header) and exits.

	      This is a	non-portable extension.

       -w, --warn
	      Like -s and --standard, except that warnings (and	not errors)
	      are printed for non-standard extensions and execution continues
	      normally.

	      This is a	non-portable extension.

       -z, --leading-zeroes
	      Makes bc(1) print	all numbers greater than -1 and	less than 1,
	      and not equal to 0, with a leading zero.

	      This can be set for individual numbers with the plz(x),
	      plznl(x)**, pnlz(x), and pnlznl(x) functions in the extended
	      math library (see	the LIBRARY section).

	      This is a	non-portable extension.

       All long	options	are non-portable extensions.

STDIN
       If no files or expressions are given by the -f, --file, -e, or
       --expression options, then bc(1)	reads from stdin.

       However,	there are a few	caveats	to this.

       First, stdin is evaluated a line	at a time.  The	only exception to this
       is if the parse cannot complete.	 That means that starting a string
       without ending it or starting a function, if statement, or loop without
       ending it will also cause bc(1) to not execute.

       Second, after an	if statement, bc(1) doesn't know if an else statement
       will follow, so it will not execute until it knows there	will not be an
       else statement.

STDOUT
       Any non-error output is written to stdout.  In addition,	if history
       (see the	HISTORY	section) and the prompt	(see the TTY MODE section) are
       enabled,	both are output	to stdout.

       Note: Unlike other bc(1)	implementations, this bc(1) will issue a fatal
       error (see the EXIT STATUS section) if it cannot	write to stdout, so if
       stdout is closed, as in bc >&-, it will quit with an error.  This is
       done so that bc(1) can report problems when stdout is redirected	to a
       file.

       If there	are scripts that depend	on the behavior	of other bc(1)
       implementations,	it is recommended that those scripts be	changed	to
       redirect	stdout to /dev/null.

STDERR
       Any error output	is written to stderr.

       Note: Unlike other bc(1)	implementations, this bc(1) will issue a fatal
       error (see the EXIT STATUS section) if it cannot	write to stderr, so if
       stderr is closed, as in bc 2>&-,	it will	quit with an error.  This is
       done so that bc(1) can exit with	an error code when stderr is
       redirected to a file.

       If there	are scripts that depend	on the behavior	of other bc(1)
       implementations,	it is recommended that those scripts be	changed	to
       redirect	stderr to /dev/null.

SYNTAX
       The syntax for bc(1) programs is	mostly C-like, with some differences.
       This bc(1) follows the POSIX standard (see the STANDARDS	section),
       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.

       In the sections below, E	means expression, S means statement, and I
       means identifier.

       Identifiers (I) start with a lowercase letter and can be	followed by
       any number (up to BC_NAME_MAX-1)	of lowercase letters (a-z), digits
       (0-9), and underscores (_).  The	regex is [a-z][a-z0-9_]*.  Identifiers
       with more than one character (letter) are a non-portable	extension.

       ibase is	a global variable determining how to interpret constant
       numbers.	 It is the "input" base, or the	number base used for
       interpreting input numbers.  ibase is initially 10.  If the -s
       (--standard) and	-w (--warn) flags were not given on the	command	line,
       the max allowable value for ibase is 36.	 Otherwise, it is 16.  The min
       allowable value for ibase is 2.	The max	allowable value	for ibase can
       be queried in bc(1) programs with the maxibase()	built-in function.

       obase is	a global variable determining how to output results.  It is
       the "output" base, or the number	base used for outputting numbers.
       obase is	initially 10.  The max allowable value for obase is
       BC_BASE_MAX and can be queried in bc(1) programs	with the maxobase()
       built-in	function.  The min allowable value for obase is	0.  If obase
       is 0, values are	output in scientific notation, and if obase is 1,
       values are output in engineering	notation.  Otherwise, values are
       output in the specified base.

       Outputting in scientific	and engineering	notations are non-portable
       extensions.

       The scale of an expression is the number	of digits in the result	of the
       expression right	of the decimal point, and scale	is a global variable
       that sets the precision of any operations, with exceptions.  scale is
       initially 0.  scale cannot be negative.	The max	allowable value	for
       scale is	BC_SCALE_MAX and can be	queried	in bc(1) programs with the
       maxscale() built-in function.

       bc(1) has both global variables and local variables.  All local
       variables are local to the function; they are parameters	or are
       introduced in the auto list of a	function (see the FUNCTIONS section).
       If a variable is	accessed which is not a	parameter or in	the auto list,
       it is assumed to	be global.  If a parent	function has a local variable
       version of a variable that a child function considers global, the value
       of that global variable in the child function is	the value of the
       variable	in the parent function,	not the	value of the actual global
       variable.

       All of the above	applies	to arrays as well.

       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 and the expression is	notsurrounded
       by parentheses.

       The value that is printed is also assigned to the special variable
       last.  A	single dot (.) may also	be used	as a synonym for last.	These
       are non-portable	extensions.

       Either semicolons or newlines may separate statements.

   Comments
       There are two kinds of comments:

       1. Block	comments are enclosed in /* and	*/.

       2. Line comments	go from	# until, and not including, the	next newline.
	  This is a non-portable extension.

   Named Expressions
       The following are named expressions in bc(1):

       1. Variables: I

       2. Array	Elements: I[E]

       3. ibase

       4. obase

       5. scale

       6. seed

       7. last or a single dot (.)

       Numbers 6 and 7 are non-portable	extensions.

       The meaning of seed is dependent	on the current pseudo-random number
       generator but is	guaranteed to not change except	for new	major
       versions.

       The scale and sign of the value may be significant.

       If a previously used seed value is assigned to seed and used again, the
       pseudo-random number generator is guaranteed to produce the same
       sequence	of pseudo-random numbers as it did when	the seed value was
       previously used.

       The exact value assigned	to seed	is not guaranteed to be	returned if
       seed is queried again immediately.  However, if seed does return	a
       different value,	both values, when assigned to seed, are	guaranteed to
       produce the same	sequence of pseudo-random numbers.  This means that
       certain values assigned to seed will not	produce	unique sequences of
       pseudo-random numbers.  The value of seed will change after any use of
       the rand() and irand(E) operands	(see the Operands subsection below),
       except if the parameter passed to irand(E) is 0,	1, or negative.

       There is	no limit to the	length (number of significant decimal digits)
       or scale	of the value that can be assigned to seed.

       Variables and arrays do not interfere; users can	have arrays named the
       same as variables.  This	also applies to	functions (see the FUNCTIONS
       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.

       Named expressions are required as the operand of	increment/decrement
       operators and as	the left side of assignment operators (see the
       Operators subsection).

   Operands
       The following are valid operands	in bc(1):

	1. Numbers (see	the Numbers subsection below).

	2. Array indices (I[E]).

	3. (E):	The value of E (used to	change precedence).

	4. sqrt(E): The	square root of E.  E must be non-negative.

	5. length(E): The number of significant	decimal	digits in E.  Returns
	   1 for 0 with	no decimal places.  If given a string, the length of
	   the string is returned.  Passing a string to	length(E) is a non-
	   portable extension.

	6. length(I[]):	The number of elements in the array I.	This is	a non-
	   portable extension.

	7. scale(E): The scale of E.

	8. abs(E): The absolute	value of E.  This is a non-portable extension.

	9. is_number(E): 1 if the given	argument is a number, 0	if it is a
	   string.  This is a non-portable extension.

       10. is_string(E): 1 if the given	argument is a string, 0	if it is a
	   number.  This is a non-portable extension.

       11. modexp(E, E,	E): Modular exponentiation, where the first expression
	   is the base,	the second is the exponent, and	the third is the
	   modulus.  All three values must be integers.	 The second argument
	   must	be non-negative.  The third argument must be non-zero.	This
	   is a	non-portable extension.

       12. divmod(E, E,	I[]): Division and modulus in one operation.  This is
	   for optimization.  The first	expression is the dividend, and	the
	   second is the divisor, which	must be	non-zero.  The return value is
	   the quotient, and the modulus is stored in index 0 of the provided
	   array (the last argument).  This is a non-portable extension.

       13. asciify(E): If E is a string, returns a string that is the first
	   letter of its argument.  If it is a number, calculates the number
	   mod 256 and returns that number as a	one-character string.  This is
	   a non-portable extension.

       14. asciify(I[]): A string that is made up of the characters that would
	   result from running asciify(E) on each element of the array
	   identified by the argument.	This allows creating multi-character
	   strings and storing them.  This is a	non-portable extension.

       15. I(),	I(E), I(E, E), and so on, where	I is an	identifier for a non-
	   void	function (see the Void Functions subsection of the FUNCTIONS
	   section).  The E argument(s)	may also be arrays of the form I[],
	   which will automatically be turned into array references (see the
	   Array References subsection of the FUNCTIONS	section) if the
	   corresponding parameter in the function definition is an array
	   reference.

       16. read(): Reads a line	from stdin and uses that as an expression.
	   The result of that expression is the	result of the read() operand.
	   This	is a non-portable extension.

       17. maxibase(): The max allowable ibase.	 This is a non-portable
	   extension.

       18. maxobase(): The max allowable obase.	 This is a non-portable
	   extension.

       19. maxscale(): The max allowable scale.	 This is a non-portable
	   extension.

       20. line_length(): The line length set with BC_LINE_LENGTH (see the
	   ENVIRONMENT VARIABLES section).  This is a non-portable extension.

       21. global_stacks(): 0 if global	stacks are not enabled with the	-g or
	   --global-stacks options, non-zero otherwise.	 See the OPTIONS
	   section.  This is a non-portable extension.

       22. leading_zero(): 0 if	leading	zeroes are not enabled with the	-z or
	   -leading-zeroes options, non-zero otherwise.	 See the OPTIONS
	   section.  This is a non-portable extension.

       23. rand(): A pseudo-random integer between 0 (inclusive) and
	   BC_RAND_MAX (inclusive).  Using this	operand	will change the	value
	   of seed.  This is a non-portable extension.

       24. irand(E): A pseudo-random integer between 0 (inclusive) and the
	   value of E (exclusive).  If E is negative or	is a non-integer (E's
	   scale is not	0), an error is	raised,	and bc(1) resets (see the
	   RESET section) while	seed remains unchanged.	 If E is larger	than
	   BC_RAND_MAX,	the higher bound is honored by generating several
	   pseudo-random integers, multiplying them by appropriate powers of
	   BC_RAND_MAX+1, 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 seed, unless the value of E	is 0
	   or 1.  In that case,	0 is returned, and seed	is not changed.	 This
	   is a	non-portable extension.

       25. maxrand(): The max integer returned by rand().  This	is a non-
	   portable extension.

       The integers generated by rand()	and irand(E) are guaranteed to be as
       unbiased	as possible, subject to	the limitations	of the pseudo-random
       number generator.

       Note: The values	returned by the	pseudo-random number generator with
       rand() and irand(E) are guaranteed to NOT be cryptographically secure.
       This is a consequence of	using a	seeded pseudo-random number generator.
       However,	they are guaranteed to be reproducible with identical seed
       values.	This means that	the pseudo-random values from bc(1) should
       only be used where a reproducible stream	of pseudo-random numbers is
       ESSENTIAL.  In any other	case, use a non-seeded pseudo-random number
       generator.

   Numbers
       Numbers are strings made	up of digits, uppercase	letters, and at	most 1
       period for a radix.  Numbers can	have up	to BC_NUM_MAX digits.
       Uppercase letters are equal to 9	plus their position in the alphabet,
       starting	from 1 (i.e., A	equals 10, or 9+1).

       If a digit or letter makes no sense with	the current value of ibase
       (i.e., they are greater than or equal to	the current value of ibase),
       then the	behavior depends on the	existence of the -c/--digit-clamp or
       -C/--no-digit-clamp options (see	the OPTIONS section), the existence
       and setting of the BC_DIGIT_CLAMP environment variable (see the
       ENVIRONMENT VARIABLES section), or the default, which can be queried
       with the	-h/--help option.

       If clamping is off, then	digits or letters that are greater than	or
       equal to	the current value of ibase are not changed.  Instead, their
       given value is multiplied by the	appropriate power of ibase and added
       into the	number.	 This means that, with an ibase	of 3, the number AB is
       equal to	3^1*A+3^0*B, which is 3	times 10 plus 11, or 41.

       If clamping is on, then digits or letters that are greater than or
       equal to	the current value of ibase are set to the value	of the highest
       valid digit in ibase before being multiplied by the appropriate power
       of ibase	and added into the number.  This means that, with an ibase of
       3, the number AB	is equal to 3^1*2+3^0*2, which is 3 times 2 plus 2, or
       8.

       There is	one exception to clamping: single-character numbers (i.e., A
       alone).	Such numbers are never clamped and always take the value they
       would have in the highest possible ibase.  This means that A alone
       always equals decimal 10	and Z alone always equals decimal 35.  This
       behavior	is mandated by the standard (see the STANDARDS section)	and is
       meant to	provide	an easy	way to set the current ibase (with the i
       command)	regardless of the current value	of ibase.

       If clamping is on, and the clamped value	of a character is needed, use
       a leading zero, i.e., for A, use	0A.

       In addition, bc(1) accepts numbers in scientific	notation.  These have
       the form	<number>e<integer>.  The exponent (the portion after the e)
       must be an integer.  An example is 1.89237e9, which is equal to
       1892370000.  Negative exponents are also	allowed, so 4.2890e-3 is equal
       to 0.0042890.

       Using scientific	notation is an error or	warning	if the -s or -w,
       respectively, command-line options (or equivalents) are given.

       WARNING:	Both the number	and the	exponent in scientific notation	are
       interpreted according to	the current ibase, but the number is still
       multiplied by 10^exponent regardless of the current ibase.  For
       example,	if ibase is 16 and bc(1) is given the number string FFeA, the
       resulting decimal number	will be	2550000000000, and if bc(1) is given
       the number string 10e-4,	the resulting decimal number will be 0.0016.

       Accepting input as scientific notation is a non-portable	extension.

   Operators
       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.

       ++ --  Type: Prefix and Postfix

	      Associativity: None

	      Description: increment, decrement

       - !    Type: Prefix

	      Associativity: None

	      Description: negation, boolean not

       $      Type: Postfix

	      Associativity: None

	      Description: truncation

       @      Type: Binary

	      Associativity: Right

	      Description: set precision

       ^      Type: Binary

	      Associativity: Right

	      Description: power

       * / %  Type: Binary

	      Associativity: Left

	      Description: multiply, divide, modulus

       + -    Type: Binary

	      Associativity: Left

	      Description: add,	subtract

       << >>  Type: Binary

	      Associativity: Left

	      Description: shift left, shift right

       = <<= >>= += -= *= /= %=	^= @=
	      Type: Binary

	      Associativity: Right

	      Description: assignment

       == <= >=	!= < >
	      Type: Binary

	      Associativity: Left

	      Description: relational

       &&     Type: Binary

	      Associativity: Left

	      Description: boolean and

       ||     Type: Binary

	      Associativity: Left

	      Description: boolean or

       The operators will be described in more detail below.

       ++ --  The prefix and postfix increment and decrement operators behave
	      exactly like they	would in C.  They require a named expression
	      (see the Named Expressions subsection) as	an operand.

	      The prefix versions of these operators are more efficient; use
	      them where possible.

       -      The negation operator returns 0 if a user	attempts to negate any
	      expression with the value	0.  Otherwise, a copy of the
	      expression with its sign flipped is returned.

       !      The boolean not operator returns 1 if the	expression is 0, or 0
	      otherwise.

	      This is a	non-portable extension.

       $      The truncation operator returns a	copy of	the given expression
	      with all of its scale removed.

	      This is a	non-portable extension.

       @      The set precision	operator takes two expressions and returns a
	      copy of the first	with its scale equal to	the value of the
	      second expression.  That could either mean that the number is
	      returned without change (if the scale of the first expression
	      matches the value	of the second expression), extended (if	it is
	      less), or	truncated (if it is more).

	      The second expression must be an integer (no scale) and non-
	      negative.

	      This is a	non-portable extension.

       ^      The power	operator (not the exclusive or operator, as it would
	      be in C) takes two expressions and raises	the first to the power
	      of the value of the second.  The scale of	the result is equal to
	      scale.

	      The second expression must be an integer (no scale), and if it
	      is negative, the first value must	be non-zero.

       *      The multiply operator takes two expressions, multiplies them,
	      and returns the product.	If a is	the scale of the first
	      expression and b is the scale of the second expression, the
	      scale of the result is equal to min(a+b,max(scale,a,b)) where
	      min() and	max() return the obvious values.

       /      The divide operator takes	two expressions, divides them, and
	      returns the quotient.  The scale of the result shall be the
	      value of scale.

	      The second expression must be non-zero.

       %      The modulus operator takes two expressions, a and	b, and
	      evaluates	them by	1) Computing a/b to current scale and 2) Using
	      the result of step 1 to calculate	a-(a/b)*b to scale
	      max(scale+scale(b),scale(a)).

	      The second expression must be non-zero.

       +      The add operator takes two expressions, a	and b, and returns the
	      sum, with	a scale	equal to the max of the	scales of a and	b.

       -      The subtract operator takes two expressions, a and b, and
	      returns the difference, with a scale equal to the	max of the
	      scales of	a and b.

       <<     The left shift operator takes two	expressions, a and b, and
	      returns a	copy of	the value of a with its	decimal	point moved b
	      places to	the right.

	      The second expression must be an integer (no scale) and non-
	      negative.

	      This is a	non-portable extension.

       >>     The right	shift operator takes two expressions, a	and b, and
	      returns a	copy of	the value of a with its	decimal	point moved b
	      places to	the left.

	      The second expression must be an integer (no scale) and non-
	      negative.

	      This is a	non-portable extension.

       = <<= >>= += -= *= /= %=	^= @=
	      The assignment operators take two	expressions, a and b where a
	      is a named expression (see the Named Expressions subsection).

	      For =, b is copied and the result	is assigned to a.  For all
	      others, a	and b are applied as operands to the corresponding
	      arithmetic operator and the result is assigned to	a.

	      The assignment operators that correspond to operators that are
	      extensions are themselves	non-portable extensions.

       == <= >=	!= < >
	      The relational operators compare two expressions,	a and b, and
	      if the relation holds, according to C language semantics,	the
	      result is	1.  Otherwise, it is 0.

	      Note that	unlike in C, these operators have a lower precedence
	      than the assignment operators, which means that a=b>c is
	      interpreted as (a=b)>c.

	      Also, unlike the standard	(see the STANDARDS section) requires,
	      these operators can appear anywhere any other expressions	can be
	      used.  This allowance is a non-portable extension.

       &&     The boolean and operator takes two expressions and returns 1 if
	      both expressions are non-zero, 0 otherwise.

	      This is not a short-circuit operator.

	      This is a	non-portable extension.

       ||     The boolean or operator takes two	expressions and	returns	1 if
	      one of the expressions is	non-zero, 0 otherwise.

	      This is not a short-circuit operator.

	      This is a	non-portable extension.

   Statements
       The following items are statements:

	1. E

	2. { S ; ...  ;	S }

	3. if (	E ) S

	4. if (	E ) S else S

	5. while ( E ) S

	6. for ( E ; E ; E ) S

	7. An empty statement

	8. break

	9. continue

       10. quit

       11. halt

       12. limits

       13. A string of characters, enclosed in double quotes

       14. print E , ...  , E

       15. stream E , ...  , E

       16. I(),	I(E), I(E, E), and so on, where	I is an	identifier for a void
	   function (see the Void Functions subsection of the FUNCTIONS
	   section).  The E argument(s)	may also be arrays of the form I[],
	   which will automatically be turned into array references (see the
	   Array References subsection of the FUNCTIONS	section) if the
	   corresponding parameter in the function definition is an array
	   reference.

       Numbers 4, 9, 11, 12, 14, 15, and 16 are	non-portable extensions.

       Also, as	a non-portable extension, 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 1.

       The break statement causes a loop to stop iterating and resume
       execution immediately following a loop.	This is	only allowed in	loops.

       The continue 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.

       The if else statement does the same thing as in C.

       The quit	statement causes bc(1) to quit,	even if	it is on a branch that
       will not	be executed (it	is a compile-time command).

       Warning:	The behavior of	this bc(1) on quit is slightly different from
       other bc(1) implementations.  Other bc(1) implementations will exit as
       soon as they finish parsing the line that a quit	command	is on.	This
       bc(1) will execute any completed	and executable statements that occur
       before the quit statement before	exiting.

       In other	words, for the bc(1) code below:

	      for (i = 0; i < 3; ++i) i; quit

       Other bc(1) implementations will	print nothing, and this	bc(1) will
       print 0,	1, and 2 on successive lines before exiting.

       The halt	statement causes bc(1) to quit,	if it is executed.  (Unlike
       quit if it is on	a branch of an if statement that is not	executed,
       bc(1) does not quit.)

       The limits statement prints the limits that this	bc(1) is subject to.
       This is like the	quit statement in that it is a compile-time command.

       An expression by	itself is evaluated and	printed, followed by a
       newline.

       Both scientific notation	and engineering	notation are available for
       printing	the results of expressions.  Scientific	notation is activated
       by assigning 0 to obase,	and engineering	notation is activated by
       assigning 1 to obase.  To deactivate them, just assign a	different
       value to	obase.

       Scientific notation and engineering notation are	disabled if bc(1) is
       run with	either the -s or -w command-line options (or equivalents).

       Printing	numbers	in scientific notation and/or engineering notation is
       a non-portable extension.

   Strings
       If strings appear as a statement	by themselves, they are	printed
       without a trailing newline.

       In addition to appearing	as a lone statement by themselves, strings can
       be assigned to variables	and array elements.  They can also be passed
       to functions in variable	parameters.

       If any statement	that expects a string is given a variable that had a
       string assigned to it, the statement acts as though it had received a
       string.

       If any math operation is	attempted on a string or a variable or array
       element that has	been assigned a	string,	an error is raised, and	bc(1)
       resets (see the RESET section).

       Assigning strings to variables and array	elements and passing them to
       functions are non-portable extensions.

   Print Statement
       The "expressions" in a print 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:

       \a: \a

       \b: \b

       \\: \

       \e: \

       \f: \f

       \n: \n

       \q: "

       \r: \r

       \t: \t

       Any other character following a backslash causes	the backslash and
       character to be printed as-is.

       Any non-string expression in a print statement shall be assigned	to
       last, like any other expression that is printed.

   Stream Statement
       The "expressions	in a stream statement may also be strings.

       If a stream statement is	given a	string,	it prints the string as	though
       the string had appeared as its own statement.  In other words, the
       stream statement	prints strings normally, without a newline.

       If a stream statement is	given a	number,	a copy of it is	truncated and
       its absolute value is calculated.  The result is	then printed as	though
       obase is	256 and	each digit is interpreted as an	8-bit ASCII character,
       making it a byte	stream.

   Order of Evaluation
       All expressions in a statment are evaluated left	to right, except as
       necessary to maintain order of operations.  This	means, for example,
       assuming	that i is equal	to 0, in the expression

	      a[i++] = i++

       the first (or 0th) element of a is set to 1, and	i is equal to 2	at the
       end of the expression.

       This includes function arguments.  Thus,	assuming i is equal to 0, this
       means that in the expression

	      x(i++, i++)

       the first argument passed to x()	is 0, and the second argument is 1,
       while i is equal	to 2 before the	function starts	executing.

FUNCTIONS
       Function	definitions are	as follows:

	      define I(I,...,I){
		  auto I,...,I
		  S;...;S
		  return(E)
	      }

       Any I in	the parameter list or auto list	may be replaced	with I[] to
       make a parameter	or auto	var an array, and any I	in the parameter list
       may be replaced with *I[] 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 I[] like normal
       array parameters	and will be automatically converted into references.

       As a non-portable extension, the	opening	brace of a define statement
       may appear on the next line.

       As a non-portable extension, the	return statement may also be in	one of
       the following forms:

       1. return

       2. return ( )

       3. return E

       The first two, or not specifying	a return statement, is equivalent to
       return (0), unless the function is a void function (see the Void
       Functions subsection below).

   Void	Functions
       Functions can also be void functions, defined as	follows:

	      define void I(I,...,I){
		  auto I,...,I
		  S;...;S
		  return
	      }

       They can	only be	used as	standalone expressions,	where such an
       expression would	be printed alone, except in a print statement.

       Void functions can only use the first two return	statements listed
       above.  They can	also omit the return statement entirely.

       The word	"void" is not treated as a keyword; it is still	possible to
       have variables, arrays, and functions named void.  The word "void" is
       only treated specially right after the define keyword.

       This is a non-portable extension.

   Array References
       For any array in	the parameter list, if the array is declared in	the
       form

	      *I[]

       it is a reference.  Any changes to the array in the function are
       reflected, when the function returns, to	the array that was passed in.

       Other than this,	all function arguments are passed by value.

       This is a non-portable extension.

LIBRARY
       All of the functions below, including the functions in the extended
       math library (see the Extended Library subsection below), are available
       when the	-l or --mathlib	command-line flags are given, except that the
       extended	math library is	not available when the -s option, the -w
       option, or equivalents are given.

   Standard Library
       The standard (see the STANDARDS section)	defines	the following
       functions for the math library:

       s(x)   Returns the sine of x, which is assumed to be in radians.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       c(x)   Returns the cosine of x, which is	assumed	to be in radians.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       a(x)   Returns the arctangent of	x, in radians.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       l(x)   Returns the natural logarithm of x.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       e(x)   Returns the mathematical constant	e raised to the	power of x.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       j(x, n)
	      Returns the bessel integer order n (truncated) of	x.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

   Extended Library
       The extended library is not loaded when the -s/--standard or -w/--warn
       options are given since they are	not part of the	library	defined	by the
       standard	(see the STANDARDS section).

       The extended library is a non-portable extension.

       p(x, y)
	      Calculates x to the power	of y, even if y	is not an integer, and
	      returns the result to the	current	scale.

	      It is an error if	y is negative and x is 0.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       r(x, p)
	      Returns x	rounded	to p decimal places according to the rounding
	      mode round half away from	0
	      (https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero).

       ceil(x, p)
	      Returns x	rounded	to p decimal places according to the rounding
	      mode round away from 0
	      (https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero).

       f(x)   Returns the factorial of the truncated absolute value of x.

       perm(n, k)
	      Returns the permutation of the truncated absolute	value of n of
	      the truncated absolute value of k, if k <= n.  If	not, it
	      returns 0.

       comb(n, k)
	      Returns the combination of the truncated absolute	value of n of
	      the truncated absolute value of k, if k <= n.  If	not, it
	      returns 0.

       l2(x)  Returns the logarithm base 2 of x.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       l10(x) Returns the logarithm base 10 of x.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       log(x, b)
	      Returns the logarithm base b of x.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       cbrt(x)
	      Returns the cube root of x.

       root(x, n)
	      Calculates the truncated value of	n, r, and returns the rth root
	      of x to the current scale.

	      If r is 0	or negative, this raises an error and causes bc(1) to
	      reset (see the RESET section).  It also raises an	error and
	      causes bc(1) to reset if r is even and x is negative.

       gcd(a, b)
	      Returns the greatest common divisor (factor) of the truncated
	      absolute value of	a and the truncated absolute value of b.

       lcm(a, b)
	      Returns the least	common multiple	of the truncated absolute
	      value of a and the truncated absolute value of b.

       pi(p)  Returns pi to p decimal places.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       t(x)   Returns the tangent of x,	which is assumed to be in radians.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       a2(y, x)
	      Returns the arctangent of	y/x, in	radians.  If both y and	x are
	      equal to 0, it raises an error and causes	bc(1) to reset (see
	      the RESET	section).  Otherwise, if x is greater than 0, it
	      returns a(y/x).  If x is less than 0, and	y is greater than or
	      equal to 0, it returns a(y/x)+pi.	 If x is less than 0, and y is
	      less than	0, it returns a(y/x)-pi.  If x is equal	to 0, and y is
	      greater than 0, it returns pi/2.	If x is	equal to 0, and	y is
	      less than	0, it returns -pi/2.

	      This function is the same	as the atan2() function	in many
	      programming languages.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       sin(x) Returns the sine of x, which is assumed to be in radians.

	      This is an alias of s(x).

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       cos(x) Returns the cosine of x, which is	assumed	to be in radians.

	      This is an alias of c(x).

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       tan(x) Returns the tangent of x,	which is assumed to be in radians.

	      If x is equal to 1 or -1,	this raises an error and causes	bc(1)
	      to reset (see the	RESET section).

	      This is an alias of t(x).

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       atan(x)
	      Returns the arctangent of	x, in radians.

	      This is an alias of a(x).

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       atan2(y,	x)
	      Returns the arctangent of	y/x, in	radians.  If both y and	x are
	      equal to 0, it raises an error and causes	bc(1) to reset (see
	      the RESET	section).  Otherwise, if x is greater than 0, it
	      returns a(y/x).  If x is less than 0, and	y is greater than or
	      equal to 0, it returns a(y/x)+pi.	 If x is less than 0, and y is
	      less than	0, it returns a(y/x)-pi.  If x is equal	to 0, and y is
	      greater than 0, it returns pi/2.	If x is	equal to 0, and	y is
	      less than	0, it returns -pi/2.

	      This function is the same	as the atan2() function	in many
	      programming languages.

	      This is an alias of a2(y,	x).

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       r2d(x) Converts x from radians to degrees and returns the result.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       d2r(x) Converts x from degrees to radians and returns the result.

	      This is a	transcendental function	(see the Transcendental
	      Functions	subsection below).

       frand(p)
	      Generates	a pseudo-random	number between 0 (inclusive) and 1
	      (exclusive) with the number of decimal digits after the decimal
	      point equal to the truncated absolute value of p.	 If p is not
	      0, then calling this function will change	the value of seed.  If
	      p	is 0, then 0 is	returned, and seed is not changed.

       ifrand(i, p)
	      Generates	a pseudo-random	number that is between 0 (inclusive)
	      and the truncated	absolute value of i (exclusive)	with the
	      number of	decimal	digits after the decimal point equal to	the
	      truncated	absolute value of p.  If the absolute value of i is
	      greater than or equal to 2, and p	is not 0, then calling this
	      function will change the value of	seed; otherwise, 0 is returned
	      and seed is not changed.

       srand(x)
	      Returns x	with its sign flipped with probability 0.5.  In	other
	      words, it	randomizes the sign of x.

       brand()
	      Returns a	random boolean value (either 0 or 1).

       band(a, b)
	      Takes the	truncated absolute value of both a and b and
	      calculates and returns the result	of the bitwise and operation
	      between them.

	      If you want to use signed	two's complement arguments, use	s2u(x)
	      to convert.

       bor(a, b)
	      Takes the	truncated absolute value of both a and b and
	      calculates and returns the result	of the bitwise or operation
	      between them.

	      If you want to use signed	two's complement arguments, use	s2u(x)
	      to convert.

       bxor(a, b)
	      Takes the	truncated absolute value of both a and b and
	      calculates and returns the result	of the bitwise xor operation
	      between them.

	      If you want to use signed	two's complement arguments, use	s2u(x)
	      to convert.

       bshl(a, b)
	      Takes the	truncated absolute value of both a and b and
	      calculates and returns the result	of a bit-shifted left by b
	      places.

	      If you want to use signed	two's complement arguments, use	s2u(x)
	      to convert.

       bshr(a, b)
	      Takes the	truncated absolute value of both a and b and
	      calculates and returns the truncated result of a bit-shifted
	      right by b places.

	      If you want to use signed	two's complement arguments, use	s2u(x)
	      to convert.

       bnotn(x,	n)
	      Takes the	truncated absolute value of x and does a bitwise not
	      as though	it has the same	number of bytes	as the truncated
	      absolute value of	n.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bnot8(x)
	      Does a bitwise not of the	truncated absolute value of x as
	      though it	has 8 binary digits (1 unsigned	byte).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bnot16(x)
	      Does a bitwise not of the	truncated absolute value of x as
	      though it	has 16 binary digits (2	unsigned bytes).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bnot32(x)
	      Does a bitwise not of the	truncated absolute value of x as
	      though it	has 32 binary digits (4	unsigned bytes).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bnot64(x)
	      Does a bitwise not of the	truncated absolute value of x as
	      though it	has 64 binary digits (8	unsigned bytes).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bnot(x)
	      Does a bitwise not of the	truncated absolute value of x as
	      though it	has the	minimum	number of power	of two unsigned	bytes.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brevn(x,	n)
	      Runs a bit reversal on the truncated absolute value of x as
	      though it	has the	same number of 8-bit bytes as the truncated
	      absolute value of	n.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brev8(x)
	      Runs a bit reversal on the truncated absolute value of x as
	      though it	has 8 binary digits (1 unsigned	byte).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brev16(x)
	      Runs a bit reversal on the truncated absolute value of x as
	      though it	has 16 binary digits (2	unsigned bytes).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brev32(x)
	      Runs a bit reversal on the truncated absolute value of x as
	      though it	has 32 binary digits (4	unsigned bytes).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brev64(x)
	      Runs a bit reversal on the truncated absolute value of x as
	      though it	has 64 binary digits (8	unsigned bytes).

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brev(x)
	      Runs a bit reversal on the truncated absolute value of x as
	      though it	has the	minimum	number of power	of two unsigned	bytes.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       broln(x,	p, n)
	      Does a left bitwise rotatation of	the truncated absolute value
	      of x, as though it has the same number of	unsigned 8-bit bytes
	      as the truncated absolute	value of n, by the number of places
	      equal to the truncated absolute value of p modded	by the 2 to
	      the power	of the number of binary	digits in n 8-bit bytes.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brol8(x,	p)
	      Does a left bitwise rotatation of	the truncated absolute value
	      of x, as though it has 8 binary digits (1	unsigned byte),	by the
	      number of	places equal to	the truncated absolute value of	p
	      modded by	2 to the power of 8.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brol16(x, p)
	      Does a left bitwise rotatation of	the truncated absolute value
	      of x, as though it has 16	binary digits (2 unsigned bytes), by
	      the number of places equal to the	truncated absolute value of p
	      modded by	2 to the power of 16.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brol32(x, p)
	      Does a left bitwise rotatation of	the truncated absolute value
	      of x, as though it has 32	binary digits (2 unsigned bytes), by
	      the number of places equal to the	truncated absolute value of p
	      modded by	2 to the power of 32.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brol64(x, p)
	      Does a left bitwise rotatation of	the truncated absolute value
	      of x, as though it has 64	binary digits (2 unsigned bytes), by
	      the number of places equal to the	truncated absolute value of p
	      modded by	2 to the power of 64.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brol(x, p)
	      Does a left bitwise rotatation of	the truncated absolute value
	      of x, as though it has the minimum number	of power of two
	      unsigned 8-bit bytes, by the number of places equal to the
	      truncated	absolute value of p modded by 2	to the power of	the
	      number of	binary digits in the minimum number of 8-bit bytes.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       brorn(x,	p, n)
	      Does a right bitwise rotatation of the truncated absolute	value
	      of x, as though it has the same number of	unsigned 8-bit bytes
	      as the truncated absolute	value of n, by the number of places
	      equal to the truncated absolute value of p modded	by the 2 to
	      the power	of the number of binary	digits in n 8-bit bytes.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bror8(x,	p)
	      Does a right bitwise rotatation of the truncated absolute	value
	      of x, as though it has 8 binary digits (1	unsigned byte),	by the
	      number of	places equal to	the truncated absolute value of	p
	      modded by	2 to the power of 8.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bror16(x, p)
	      Does a right bitwise rotatation of the truncated absolute	value
	      of x, as though it has 16	binary digits (2 unsigned bytes), by
	      the number of places equal to the	truncated absolute value of p
	      modded by	2 to the power of 16.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bror32(x, p)
	      Does a right bitwise rotatation of the truncated absolute	value
	      of x, as though it has 32	binary digits (2 unsigned bytes), by
	      the number of places equal to the	truncated absolute value of p
	      modded by	2 to the power of 32.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bror64(x, p)
	      Does a right bitwise rotatation of the truncated absolute	value
	      of x, as though it has 64	binary digits (2 unsigned bytes), by
	      the number of places equal to the	truncated absolute value of p
	      modded by	2 to the power of 64.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bror(x, p)
	      Does a right bitwise rotatation of the truncated absolute	value
	      of x, as though it has the minimum number	of power of two
	      unsigned 8-bit bytes, by the number of places equal to the
	      truncated	absolute value of p modded by 2	to the power of	the
	      number of	binary digits in the minimum number of 8-bit bytes.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bmodn(x,	n)
	      Returns the modulus of the truncated absolute value of x by 2 to
	      the power	of the multiplication of the truncated absolute	value
	      of n and 8.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bmod8(x,	n)
	      Returns the modulus of the truncated absolute value of x by 2 to
	      the power	of 8.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bmod16(x, n)
	      Returns the modulus of the truncated absolute value of x by 2 to
	      the power	of 16.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bmod32(x, n)
	      Returns the modulus of the truncated absolute value of x by 2 to
	      the power	of 32.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bmod64(x, n)
	      Returns the modulus of the truncated absolute value of x by 2 to
	      the power	of 64.

	      If you want to a use signed two's	complement argument, use
	      s2u(x) to	convert.

       bunrev(t)
	      Assumes t	is a bitwise-reversed number with an extra set bit one
	      place more significant than the real most	significant bit	(which
	      was the least significant	bit in the original number).  This
	      number is	reversed and returned without the extra	set bit.

	      This function is used to implement other bitwise functions; it
	      is not meant to be used by users,	but it can be.

       plz(x) If x is not equal	to 0 and greater that -1 and less than 1, it
	      is printed with a	leading	zero, regardless of the	use of the -z
	      option (see the OPTIONS section) and without a trailing newline.

	      Otherwise, x is printed normally,	without	a trailing newline.

       plznl(x)
	      If x is not equal	to 0 and greater that -1 and less than 1, it
	      is printed with a	leading	zero, regardless of the	use of the -z
	      option (see the OPTIONS section) and with	a trailing newline.

	      Otherwise, x is printed normally,	with a trailing	newline.

       pnlz(x)
	      If x is not equal	to 0 and greater that -1 and less than 1, it
	      is printed without a leading zero, regardless of the use of the
	      -z option	(see the OPTIONS section) and without a	trailing
	      newline.

	      Otherwise, x is printed normally,	without	a trailing newline.

       pnlznl(x)
	      If x is not equal	to 0 and greater that -1 and less than 1, it
	      is printed without a leading zero, regardless of the use of the
	      -z option	(see the OPTIONS section) and with a trailing newline.

	      Otherwise, x is printed normally,	with a trailing	newline.

       ubytes(x)
	      Returns the numbers of unsigned integer bytes required to	hold
	      the truncated absolute value of x.

       sbytes(x)
	      Returns the numbers of signed, two's-complement integer bytes
	      required to hold the truncated value of x.

       s2u(x) Returns x	if it is non-negative.	If it is negative, then	it
	      calculates what x	would be as a 2's-complement signed integer
	      and returns the non-negative integer that	would have the same
	      representation in	binary.

       s2un(x,n)
	      Returns x	if it is non-negative.	If it is negative, then	it
	      calculates what x	would be as a 2's-complement signed integer
	      with n bytes and returns the non-negative	integer	that would
	      have the same representation in binary.  If x cannot fit into n
	      2's-complement signed bytes, it is truncated to fit.

       hex(x) Outputs the hexadecimal (base 16)	representation of x.

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       binary(x)
	      Outputs the binary (base 2) representation of x.

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       output(x, b)
	      Outputs the base b representation	of x.

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       uint(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as
	      an unsigned integer in as	few power of two bytes as possible.
	      Both outputs are split into bytes	separated by spaces.

	      If x is not an integer or	is negative, an	error message is
	      printed instead, but bc(1) is not	reset (see the RESET section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       int(x) Outputs the representation, in binary and	hexadecimal, of	x as a
	      signed, two's-complement integer in as few power of two bytes as
	      possible.	 Both outputs are split	into bytes separated by
	      spaces.

	      If x is not an integer, an error message is printed instead, but
	      bc(1) is not reset (see the RESET	section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       uintn(x,	n)
	      Outputs the representation, in binary and	hexadecimal, of	x as
	      an unsigned integer in n bytes.  Both outputs are	split into
	      bytes separated by spaces.

	      If x is not an integer, is negative, or cannot fit into n	bytes,
	      an error message is printed instead, but bc(1) is	not reset (see
	      the RESET	section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       intn(x, n)
	      Outputs the representation, in binary and	hexadecimal, of	x as a
	      signed, two's-complement integer in n bytes.  Both outputs are
	      split into bytes separated by spaces.

	      If x is not an integer or	cannot fit into	n bytes, an error
	      message is printed instead, but bc(1) is not reset (see the
	      RESET section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       uint8(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as
	      an unsigned integer in 1 byte.  Both outputs are split into
	      bytes separated by spaces.

	      If x is not an integer, is negative, or cannot fit into 1	byte,
	      an error message is printed instead, but bc(1) is	not reset (see
	      the RESET	section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       int8(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as a
	      signed, two's-complement integer in 1 byte.  Both	outputs	are
	      split into bytes separated by spaces.

	      If x is not an integer or	cannot fit into	1 byte,	an error
	      message is printed instead, but bc(1) is not reset (see the
	      RESET section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       uint16(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as
	      an unsigned integer in 2 bytes.  Both outputs are	split into
	      bytes separated by spaces.

	      If x is not an integer, is negative, or cannot fit into 2	bytes,
	      an error message is printed instead, but bc(1) is	not reset (see
	      the RESET	section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       int16(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as a
	      signed, two's-complement integer in 2 bytes.  Both outputs are
	      split into bytes separated by spaces.

	      If x is not an integer or	cannot fit into	2 bytes, an error
	      message is printed instead, but bc(1) is not reset (see the
	      RESET section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       uint32(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as
	      an unsigned integer in 4 bytes.  Both outputs are	split into
	      bytes separated by spaces.

	      If x is not an integer, is negative, or cannot fit into 4	bytes,
	      an error message is printed instead, but bc(1) is	not reset (see
	      the RESET	section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       int32(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as a
	      signed, two's-complement integer in 4 bytes.  Both outputs are
	      split into bytes separated by spaces.

	      If x is not an integer or	cannot fit into	4 bytes, an error
	      message is printed instead, but bc(1) is not reset (see the
	      RESET section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       uint64(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as
	      an unsigned integer in 8 bytes.  Both outputs are	split into
	      bytes separated by spaces.

	      If x is not an integer, is negative, or cannot fit into 8	bytes,
	      an error message is printed instead, but bc(1) is	not reset (see
	      the RESET	section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       int64(x)
	      Outputs the representation, in binary and	hexadecimal, of	x as a
	      signed, two's-complement integer in 8 bytes.  Both outputs are
	      split into bytes separated by spaces.

	      If x is not an integer or	cannot fit into	8 bytes, an error
	      message is printed instead, but bc(1) is not reset (see the
	      RESET section).

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       hex_uint(x, n)
	      Outputs the representation of the	truncated absolute value of x
	      as an unsigned integer in	hexadecimal using n bytes.  Not	all of
	      the value	will be	output if n is too small.

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       binary_uint(x, n)
	      Outputs the representation of the	truncated absolute value of x
	      as an unsigned integer in	binary using n bytes.  Not all of the
	      value will be output if n	is too small.

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       output_uint(x, n)
	      Outputs the representation of the	truncated absolute value of x
	      as an unsigned integer in	the current obase (see the SYNTAX
	      section) using n bytes.  Not all of the value will be output if
	      n	is too small.

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

       output_byte(x, i)
	      Outputs byte i of	the truncated absolute value of	x, where 0 is
	      the least	significant byte and number_of_bytes - 1 is the	most
	      significant byte.

	      This is a	void function (see the Void Functions subsection of
	      the FUNCTIONS section).

   Transcendental Functions
       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 the article at
       https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT explains why it
       is impossible and unnecessary to	calculate exact	results	for the
       transcendental functions.

       Because of the possible inaccuracy, I recommend that users call those
       functions with the precision (scale) set	to at least 1 higher than is
       necessary.  If exact results are	absolutely required, users can double
       the precision (scale) and then truncate.

       The transcendental functions in the standard math library are:

       o s(x)

       o c(x)

       o a(x)

       o l(x)

       o e(x)

       o j(x, n)

       The transcendental functions in the extended math library are:

       o l2(x)

       o l10(x)

       o log(x,	b)

       o pi(p)

       o t(x)

       o a2(y, x)

       o sin(x)

       o cos(x)

       o tan(x)

       o atan(x)

       o atan2(y, x)

       o r2d(x)

       o d2r(x)

RESET
       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.

       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.

       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 EXIT STATUS	section), it asks for more input;
       otherwise, it exits with	the appropriate	return code.

       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.

PERFORMANCE
       Most bc(1) implementations use char types to calculate the value	of 1
       decimal digit at	a time,	but that can be	slow.  This bc(1) does
       something different.

       It uses large integers to calculate more	than 1 decimal digit at	a
       time.  If built in a environment	where BC_LONG_BIT (see the LIMITS
       section)	is 64, then each integer has 9 decimal digits.	If built in an
       environment where BC_LONG_BIT is	32 then	each integer has 4 decimal
       digits.	This value (the	number of decimal digits per large integer) is
       called BC_BASE_DIGS.

       The actual values of BC_LONG_BIT	and BC_BASE_DIGS can be	queried	with
       the limits statement.

       In addition, this bc(1) uses an even larger integer for overflow
       checking.  This integer type depends on the value of BC_LONG_BIT, but
       is always at least twice	as large as the	integer	type used to store
       digits.

LIMITS
       The following are the limits on bc(1):

       BC_LONG_BIT
	      The number of bits in the	long 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	PERFORMANCE section).

       BC_BASE_DIGS
	      The number of decimal digits per large integer (see the
	      PERFORMANCE section).  Depends on	BC_LONG_BIT.

       BC_BASE_POW
	      The max decimal number that each large integer can store (see
	      BC_BASE_DIGS) plus 1.  Depends on	BC_BASE_DIGS.

       BC_OVERFLOW_MAX
	      The max number that the overflow type (see the PERFORMANCE
	      section) can hold.  Depends on BC_LONG_BIT.

       BC_BASE_MAX
	      The maximum output base.	Set at BC_BASE_POW.

       BC_DIM_MAX
	      The maximum size of arrays.  Set at SIZE_MAX-1.

       BC_SCALE_MAX
	      The maximum scale.  Set at BC_OVERFLOW_MAX-1.

       BC_STRING_MAX
	      The maximum length of strings.  Set at BC_OVERFLOW_MAX-1.

       BC_NAME_MAX
	      The maximum length of identifiers.  Set at BC_OVERFLOW_MAX-1.

       BC_NUM_MAX
	      The maximum length of a number (in decimal digits), which
	      includes digits after the	decimal	point.	Set at
	      BC_OVERFLOW_MAX-1.

       BC_RAND_MAX
	      The maximum integer (inclusive) returned by the rand() operand.
	      Set at 2^BC_LONG_BIT-1.

       Exponent
	      The maximum allowable exponent (positive or negative).  Set at
	      BC_OVERFLOW_MAX.

       Number of vars
	      The maximum number of vars/arrays.  Set at SIZE_MAX-1.

       The actual values can be	queried	with the limits	statement.

       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.

ENVIRONMENT VARIABLES
       As non-portable extensions, bc(1) recognizes the	following environment
       variables:

       POSIXLY_CORRECT
	      If this variable exists (no matter the contents),	bc(1) behaves
	      as if the	-s option was given.

       BC_ENV_ARGS
	      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 BC_ENV_ARGS 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.

	      The code that parses BC_ENV_ARGS will correctly handle quoted
	      arguments, but it	does not understand escape sequences.  For
	      example, the string "/home/gavin/some bc file.bc"	will be
	      correctly	parsed,	but the	string "/home/gavin/some "bc" file.bc"
	      will include the backslashes.

	      The quote	parsing	will handle either kind	of quotes, ' or	".
	      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
	      "some `bc' file.bc", and vice versa if you have a	file with
	      double quotes.  However, handling	a file with both kinds of
	      quotes in	BC_ENV_ARGS 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.

       BC_LINE_LENGTH
	      If this environment variable exists and contains an integer that
	      is greater than 1	and is less than UINT16_MAX (2^16-1), bc(1)
	      will output lines	to that	length,	including the backslash	(\).
	      The default line length is 70.

	      The special value	of 0 will disable line length checking and
	      print numbers without regard to line length and without
	      backslashes and newlines.

       BC_BANNER
	      If this environment variable exists and contains an integer,
	      then a non-zero value activates the copyright banner when	bc(1)
	      is in interactive	mode, while zero deactivates it.

	      If bc(1) is not in interactive mode (see the INTERACTIVE MODE
	      section),	then this environment variable has no effect because
	      bc(1) does not print the banner when not in interactive mode.

	      This environment variable	overrides the default, which can be
	      queried with the -h or --help options.

       BC_SIGINT_RESET
	      If bc(1) is not in interactive mode (see the INTERACTIVE MODE
	      section),	then this environment variable has no effect because
	      bc(1) exits on SIGINT when not in	interactive mode.

	      However, when bc(1) is in	interactive mode, then if this
	      environment variable exists and contains an integer, a non-zero
	      value makes bc(1)	reset on SIGINT, rather	than exit, and zero
	      makes bc(1) exit.	 If this environment variable exists and is
	      not an integer, then bc(1) will exit on SIGINT.

	      This environment variable	overrides the default, which can be
	      queried with the -h or --help options.

       BC_TTY_MODE
	      If TTY mode is not available (see	the TTY	MODE section), then
	      this environment variable	has no effect.

	      However, when TTY	mode is	available, then	if this	environment
	      variable exists and contains an integer, then a non-zero value
	      makes bc(1) use TTY mode,	and zero makes bc(1) not use TTY mode.

	      This environment variable	overrides the default, which can be
	      queried with the -h or --help options.

       BC_PROMPT
	      If TTY mode is not available (see	the TTY	MODE section), then
	      this environment variable	has no effect.

	      However, when TTY	mode is	available, then	if this	environment
	      variable exists and contains an integer, a non-zero value	makes
	      bc(1) use	a prompt, and zero or a	non-integer makes bc(1)	not
	      use a prompt.  If	this environment variable does not exist and
	      BC_TTY_MODE does,	then the value of the BC_TTY_MODE environment
	      variable is used.

	      This environment variable	and the	BC_TTY_MODE environment
	      variable override	the default, which can be queried with the -h
	      or --help	options.

       BC_EXPR_EXIT
	      If any expressions or expression files are given on the command-
	      line with	-e, --expression, -f, or --file, then if this
	      environment variable exists and contains an integer, a non-zero
	      value makes bc(1)	exit after executing the expressions and
	      expression files,	and a zero value makes bc(1) not exit.

	      This environment variable	overrides the default, which can be
	      queried with the -h or --help options.

       BC_DIGIT_CLAMP
	      When parsing numbers and if this environment variable exists and
	      contains an integer, a non-zero value makes bc(1)	clamp digits
	      that are greater than or equal to	the current ibase so that all
	      such digits are considered equal to the ibase minus 1, and a
	      zero value disables such clamping	so that	those digits are
	      always equal to their value, which is multiplied by the power of
	      the ibase.

	      This never applies to single-digit numbers, as per the standard
	      (see the STANDARDS section).

	      This environment variable	overrides the default, which can be
	      queried with the -h or --help options.

EXIT STATUS
       bc(1) returns the following exit	statuses:

       0      No error.

       1      A	math error occurred.  This follows standard practice of	using
	      1	for expected errors, since math	errors will happen in the
	      process of normal	execution.

	      Math errors include divide by 0, 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, overflow when calculating the size	of a
	      number, and attempting to	use a non-integer where	an integer is
	      required.

	      Converting to a hardware integer happens for the second operand
	      of the power (^),	places (@), left shift (<<), and right shift
	      (>>) operators and their corresponding assignment	operators.

       2      A	parse error occurred.

	      Parse errors include unexpected EOF, 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 Named	Expressions subsection of the SYNTAX
	      section),	giving an invalid auto list, having a duplicate
	      auto/function parameter, failing to find the end of a code
	      block, attempting	to return a value from a void function,
	      attempting to use	a variable as a	reference, and using any
	      extensions when the option -s or any equivalents were given.

       3      A	runtime	error occurred.

	      Runtime errors include assigning an invalid number to any	global
	      (ibase, obase, or	scale),	giving a bad expression	to a read()
	      call, calling read() inside of a read() call, type errors,
	      passing the wrong	number of arguments to functions, attempting
	      to call an undefined function, and attempting to use a void
	      function call as a value in an expression.

       4      A	fatal error occurred.

	      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.

       The exit	status 4 is special; when a fatal error	occurs,	bc(1) always
       exits and returns 4, no matter what mode	bc(1) is in.

       The other statuses will only be returned	when bc(1) is not in
       interactive mode	(see the INTERACTIVE MODE section), since bc(1)	resets
       its state (see the RESET	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 -i flag or --interactive option.

       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 -i
       flag or --interactive option.

INTERACTIVE MODE
       Per the standard	(see the STANDARDS section), bc(1) has an interactive
       mode and	a non-interactive mode.	 Interactive mode is turned on
       automatically when both stdin and stdout	are hooked to a	terminal, but
       the -i flag and --interactive option can	turn it	on in other
       situations.

       In interactive mode, bc(1) attempts to recover from errors (see the
       RESET section), and in normal execution,	flushes	stdout as soon as
       execution is done for the current input.	 bc(1) may also	reset on
       SIGINT instead of exit, depending on the	contents of, or	default	for,
       the BC_SIGINT_RESET environment variable	(see the ENVIRONMENT VARIABLES
       section).

TTY MODE
       If stdin, stdout, and stderr are	all connected to a TTY,	then "TTY
       mode" is	considered to be available, and	thus, bc(1) can	turn on	TTY
       mode, subject to	some settings.

       If there	is the environment variable BC_TTY_MODE	in the environment
       (see the	ENVIRONMENT VARIABLES section),	then if	that environment
       variable	contains a non-zero integer, bc(1) will	turn on	TTY mode when
       stdin, stdout, and stderr are all connected to a	TTY.  If the
       BC_TTY_MODE environment variable	exists but is not a non-zero integer,
       then bc(1) will not turn	TTY mode on.

       If the environment variable BC_TTY_MODE does not	exist, the default
       setting is used.	 The default setting can be queried with the -h	or
       --help options.

       TTY mode	is different from interactive mode because interactive mode is
       required	in the bc(1) standard (see the STANDARDS section), and
       interactive mode	requires only stdin and	stdout to be connected to a
       terminal.

   Command-Line	History
       Command-line history is only enabled if TTY mode	is, i.e., that stdin,
       stdout, and stderr are connected	to a TTY and the BC_TTY_MODE
       environment variable (see the ENVIRONMENT VARIABLES section) and	its
       default do not disable TTY mode.	 See the COMMAND LINE HISTORY section
       for more	information.

   Prompt
       If TTY mode is available, then a	prompt can be enabled.	Like TTY mode
       itself, it can be turned	on or off with an environment variable:
       BC_PROMPT (see the ENVIRONMENT VARIABLES	section).

       If the environment variable BC_PROMPT exists and	is a non-zero integer,
       then the	prompt is turned on when stdin,	stdout,	and stderr are
       connected to a TTY and the -P and --no-prompt options were not used.
       The read	prompt will be turned on under the same	conditions, except
       that the	-R and --no-read-prompt	options	must also not be used.

       However,	if BC_PROMPT does not exist, the prompt	can be enabled or
       disabled	with the BC_TTY_MODE environment variable, the -P and --no-
       prompt options, and the -R and --no-read-prompt options.	 See the
       ENVIRONMENT VARIABLES and OPTIONS sections for more details.

SIGNAL HANDLING
       Sending a SIGINT	will cause bc(1) to do one of two things.

       If bc(1)	is not in interactive mode (see	the INTERACTIVE	MODE section),
       or the BC_SIGINT_RESET environment variable (see	the ENVIRONMENT
       VARIABLES section), or its default, is either not an integer or it is
       zero, bc(1) will	exit.

       However,	if bc(1) is in interactive mode, and the BC_SIGINT_RESET or
       its default is an integer and non-zero, then bc(1) will stop executing
       the current input and reset (see	the RESET section) upon	receiving a
       SIGINT.

       Note that "current input" can mean one of two things.  If bc(1) is
       processing input	from stdin in interactive mode,	it will	ask for	more
       input.  If bc(1)	is processing input from a file	in interactive mode,
       it will stop processing the file	and start processing the next file, if
       one exists, or ask for input from stdin if no other file	exists.

       This means that if a SIGINT 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.

       SIGTERM and SIGQUIT cause bc(1) to clean	up and exit, and it uses the
       default handler for all other signals.  The one exception is SIGHUP; in
       that case, and only when	bc(1) is in TTY	mode (see the TTY MODE
       section), a SIGHUP will cause bc(1) to clean up and exit.

COMMAND	LINE HISTORY
       bc(1) supports interactive command-line editing.

       If bc(1)	can be in TTY mode (see	the TTY	MODE section), history can be
       enabled.	 This means that command-line history can only be enabled when
       stdin, stdout, and stderr are all connected to a	TTY.

       Like TTY	mode itself, it	can be turned on or off	with the environment
       variable	BC_TTY_MODE (see the ENVIRONMENT VARIABLES section).

       If history is enabled, previous lines can be recalled and edited	with
       the arrow keys.

       Note: tabs are converted	to 8 spaces.

LOCALES
       This bc(1) ships	with support for adding	error messages for different
       locales and thus, supports LC_MESSAGES.

SEE ALSO
       dc(1)

STANDARDS
       bc(1) is	compliant with the IEEE	Std 1003.1-2017	("POSIX.1-2017")
       specification at
       https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html .
       The flags -efghiqsvVw, all long options,	and the	extensions noted above
       are extensions to that specification.

       In addition, the	behavior of the	quit implements	an interpretation of
       that specification that is different from all known implementations.
       For more	information see	the Statements subsection of the SYNTAX
       section.

       Note that the specification explicitly says that	bc(1) only accepts
       numbers that use	a period (.) as	a radix	point, regardless of the value
       of LC_NUMERIC.

       This bc(1) supports error messages for different	locales, and thus, it
       supports	LC_MESSAGES.

BUGS
       Before version 6.1.0, this bc(1)	had incorrect behavior for the quit
       statement.

       No other	bugs are known.	 Report	bugs at
       https://git.gavinhoward.com/gavin/bc .

AUTHORS
       Gavin D.	 Howard	<gavin@gavinhoward.com>	and contributors.

Gavin D. Howard			 October 2022				 BC(1)

NAME | SYNOPSIS | DESCRIPTION | OPTIONS | STDIN | STDOUT | STDERR | SYNTAX | FUNCTIONS | LIBRARY | RESET | PERFORMANCE | LIMITS | ENVIRONMENT VARIABLES | EXIT STATUS | INTERACTIVE MODE | TTY MODE | SIGNAL HANDLING | COMMAND LINE HISTORY | LOCALES | SEE ALSO | STANDARDS | BUGS | AUTHORS

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