BC(1) General Commands Manual BC(1)
NAME
bc - arbitrary-precision decimal arithmetic language and calculator
SYNOPSIS
bc [-ghilPqRsvVw] [--global-stacks] [--help] [--interactive]
[--mathlib] [--no-prompt] [--no-read-prompt] [--quiet] [--standard]
[--warn] [--version] [-e expr] [--expression=expr...] [-f file...]
[--file=file...] [file...]
DESCRIPTION
bc(1) is an interactive processor for a language first standardized in
1991 by POSIX. (The current standard is here
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html).)
The language provides unlimited precision decimal arithmetic and is
somewhat C-like, but there are differences. Such differences will be
noted in this document.
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.
-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 quits.
-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.
-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.
-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:
•abs
•asciify
•continue
•divmod
•else
•halt
•irand
•last
•limits
•maxibase
•maxobase
•maxrand
•maxscale
•modexp
•print
•rand
•read
•seed
•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. It is a fatal error to attempt to redefine words that
this bc(1) does not reserve as keywords.
-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.
This is a non-portable extension.
-s, --standard
Process exactly the language defined by the standard
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
and error if any extensions are used.
This is a non-portable extension.
-v, -V, --version
Print the version information (copyright header) and exit.
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.
-e expr, --expression=expr
Evaluates expr. If multiple expressions are given, they are
evaluated in order. If files are given as well (see below), the
expressions and files are evaluated in the order given. This
means that if a file is given before an expression, the file is
read in and evaluated first.
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 above),
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.
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) read 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
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html),
which is a much more thorough resource for the language this bc(1)
accepts. This section is meant to be a summary and a listing of all
the extensions to the standard.
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. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. maxibase(): The max allowable ibase. This is a non-portable
extension.
15. maxobase(): The max allowable obase. This is a non-portable
extension.
16. maxscale(): The max allowable scale. This is a non-portable
extension.
17. line_length(): The line length set with BC_LINE_LENGTH (see the
ENVIRONMENT VARIABLES section). This is a non-portable extension.
18. 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.
19. 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.
20. 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.
21. 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.
22. 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 + their position in the alphabet
(i.e., A equals 10, or 9+1). If a digit or letter makes no sense with
the current value of ibase, they are set to the value of the highest
valid digit in ibase.
Single-character numbers (i.e., A alone) take the value that they would
have if they were valid digits, regardless of the value of ibase. This
means that A alone always equals decimal 10 and Z alone always equals
decimal 35.
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
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
requires, these operators can appear anywhere any other
expressions can be used. This allowance is a 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).
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
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
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
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html).
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 this article
(https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT) explains why it
is impossible and unnecessary to calculate exact results for the
transcendental functions.
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:
•s(x)
•c(x)
•a(x)
•l(x)
•e(x)
•j(x, n)
The transcendental functions in the extended math library are:
•l2(x)
•l10(x)
•log(x, b)
•pi(p)
•t(x)
•a2(y, x)
•sin(x)
•cos(x)
•tan(x)
•atan(x)
•atan2(y, x)
•r2d(x)
•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
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 non-zero value makes bc(1) not exit.
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
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html),
bc(1) has an interactive mode and a non-interactive mode. Interactive
mode is turned on automatically when both 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) specification
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html),
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")
(https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html)
specification. The flags -efghiqsvVw, all long options, and the
extensions noted above are extensions to that specification.
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
None are known. Report bugs at https://git.yzena.com/gavin/bc.
AUTHORS
Gavin D. Howard <gavin@yzena.com> and contributors.
Gavin D. Howard June 2021 BC(1)
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