bc(1)

Name

bc — arbitrary-precision arithmetic language and calculator

Synopsis

bc [-hilqsvVw] [--help] [--interactive] [--mathlib] [--quiet] [--standard] [--warn] [--version] [-e expr] [--expression=expr...] [-f file...] [-file=file...] [file...]

Description

bc is an interactive processor for a language first standardized in 1991 by POSIX. (The current standard is here.) 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 reads any files given on the command line and executes them before reading from stdin.

With all build options enabled (except for extra math), this bc is a drop-in replacement for any bc, including (and especially) the GNU bc.

Options

-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.

-f file --file=file

Reads in file and evaluates it. If expressions are also given (see above), the expressions are evaluated in the order given.

-h --help

Prints a usage message and quits.

-i --interactive

Forces interactive mode.

Per the standard, bc has an interactive mode and a non-interactive mode. The interactive mode is turned on automatically when both stdin and stdout are hooked to a terminal, but this flag can turn it on in other cases. In interactive mode, bc attempts to recover from errors and flushes stdout as soon as execution is done for the current input.

-l --mathlib

Sets scale (see the Scale section) to 20 and loads the included math library before running any code, including any expressions or files specified on the command line.

To learn what is in the library, see the Library section.

-q --quiet

Do not print copyright header. bc will also suppress the header in non-interactive mode.

This is mostly for compatibility with the GNU bc.

-s --standard

Process exactly the language defined by the standard and error if any extensions are used.

-v -V --version

Print the version information (copyright header) and exit.

-w --warn

Like -s and --standard, except that warnings (and not errors) are given for non-standard extensions.

Build

See the build manual.

Language

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.

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 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 setting the precision of any operations, with exceptions. scale is initially 0.

bc has both global variables and local variables. All local variables are local to the function; they are parameters or are introduced in a function's auto list (see Functions). 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 global variable that is accessed by a function that it calls, 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 not surrounded by parentheses. The value that is printed is also assigned to the special variable last. This is a non-portable extension. A single dot may also be used as a synonym for last.

Either semicolons or newlines may separate statements.

Syntax

The syntax for bc programs is mostly C-like, with some differences. This bc follows the POSIX standard, which is a much more thorough resource for the language this bc 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 an extension.

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

1. Variables: I
2. Array Elements: I[E]
3. ibase
4. obase
5. scale
6. last or a single dot (.)

Variables and arrays do not interfere; users can have arrays named the same as variables. This also applies to functions, so a user can have a variable, array, and function that all have the same name.

Named expressions are required as the operand of increment/decrement operators and as the left side of assignment operators.

Operands

1. Numbers (see Numbers below).
2. (E): The value of E (used to change precedence).
3. sqrt(E): The square root of E.
4. length(E): The number of significant decimal digits in E.
5. length(I[]): The number of elements in the array I. This is a non-portable extension.
6. scale(E): E's scale.

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 equal 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) take the value that they would have if they were valid digits, regardless of the value of ibase. This means that A always equals decimal 10 and Z always equals decimal 35.

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.

Operators	Type	Associativity	Description
++ --	Prefix and Postfix	None	increment, decrement
- !	Prefix	None	negation, boolean not
$	Postfix	None	truncation
@	Binary	Right	set precision
^	Binary	Right	power
* / %	Binary	Left	multiply, divide, modulus
+ -	Binary	Left	plus, subtract
<< >>	Binary	Left	shift left, shift right
= <<= >>= += -= *= /= %= ^= @=	Binary	Right	assignment
== <= >= != < >	Binary	Left	relational
&&	Binary	Left	boolean and
||	Binary	Left	boolean or

They will be descrbed in more detail below.

++ --

These are the prefix and postfix increment and decrement operators. They behave exactly like they would in C.

-

This is the negation operator. If a user attempts to negate any expression with the value 0, an exact copy of the expression is returned. Otherwise, a copy of the expression with its sign flipped is returned.

!

This is the boolean not operator. It returns 1 if the expression is 0, or 0 otherwise.

This is a non-portable extension.

$

This is the truncation operator. It returns a copy of the given expression with all of its scale removed.

This is a non-portable extension.

This is only available if bc has been compiled with the extra math option enabled.

@

This is the set precision operator. It 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 first expression's scale 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.

This is only available if bc has been compiled with the extra math option enabled.

^

This is the power operator, not the exclusive or operator. It takes two expressions and raises the first to the power of the value of the second.

The second expression must be an integer (no scale).

*

This is the multiply operator. It 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.

/

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

%

This is the modulus operator. It takes two expressions, a and b, and evaluates them according to the following steps:

1. Compute a/b to current scale
2. Use the result of step 1 to calculate a-(a/b)*b to scale max(scale + scale(b), scale(a)).

+

This is the add operator. It takes two expressions, a and b, and returns the sum, with a scale equal to:

max(scale(a), scale(b))

where max returns the obvious value.

-

This is the subtract operator. It takes two expressions, a and b, and returns the difference, with a scale equal to:

max(scale(a), scale(b))

where max returns the obvious value.

<<

This is the left shift operator. It takes two expressions, a and b, and returns 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.

This is only available if bc has been compiled with the extra math option enabled.

>>

This is the right shift operator. It takes two expressions, a and b, and returns 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.

This is only available if bc has been compiled with the extra math option enabled.

= <<= >>= += -= *= /= %= ^= @=

These are the assignment operators. They take two expressions, a and b where a is a named expression.

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 operators and the result is assigned to a.

The assignment operators that correspond to operators that are extensions are themselves extensions.

Also, those assignment operators that are extensions are only available if bc has been compiled with the extra math option enabled.

== <= >= != < >

These are the relational operators. They 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 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 requires, these operators can appear anywhere any other expressions can be used. This allowance is an extension.

&&

This is the boolean and operator. It takes two expressions and returns 1 if both expressions are non-zero, 1 otherwise.

This is not a short-circuit operator.

This is a non-portable extension.

||

This is the boolean or operator. It takes two expressions and returns 1 if one of the expressions is non-zero, 1 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

Numbers 4, 9, 11, 12, and 14 are extensions.

Also, as an 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 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 to quit, if it is executed. (Unlike quit if it is on a branch of an if statement that is not executed, bc does not quit.)

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

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:

Sequence	Prints
\a	alert
\b	backspace
\\	\
\e	\
\f	formfeed
\n	newline
\q	"
\r	carriage return
\t	tab

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.

Functions

Function definitions follow what is required by the bc spec:

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.

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

The return statement may also be in the following forms:

1. return
2. return ( )
3. return E

The first two, or not specifying a return statement, is equivalent to return (0).

Void Functions

Functions can also be void functions, defined as follows:

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

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.

The word void is not treated as a keyword; it is still possible to have variables, arrays, and functions named void.

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.

This is only available if bc has been compiled with the array references option enabled.

Library

All of the functions below, including the functions in the extended library if bc has been compiled with the extra math option enabled, are available when the -l or --mathlib command-line flags are given.

Standard Library

The standard defines the following functions for the math library:

s(x)

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

c(x)

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

a(x)

Returns the arctangent of x, in radians.

l(x)

Returns the natural logarithm of x.

e(x)

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

j(x, n)

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

Extended Library

In addition to the standard library, if bc has been built with the extra math option, the following functions are available when either the -l or --mathlib options are given.

However, 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.

abs(x)

Returns the absolute value of x.

r(x, p)

Rounds x to p decimal places according to the rounding mode round half away from 0.

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.

l10(x)

Returns the logarithm base 10 of x.

log(x, b)

Returns the logarithm base b of x.

pi(p)

Returns pi to p decimal places.

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.

hex(x)

Outputs the hexadecimal (base 16) representation of x.

This is a void function.

binary(x)

Outputs the binary (base 2) representation of x.

This is a void function.

output(x, b)

Outputs the base b representation of x.

This is a void function.

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.

This is a void function.

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.

This is a void function.

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.

intn(x, n)

Outputs the representation, in binary and hexadecimal, of x as an 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.

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.

int8(x)

Outputs the representation, in binary and hexadecimal, of x as an 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.

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.

int16(x)

Outputs the representation, in binary and hexadecimal, of x as an 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.

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.

int32(x)

Outputs the representation, in binary and hexadecimal, of x as an 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.

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.

int64(x)

Outputs the representation, in binary and hexadecimal, of x as an 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.

hex_uint(x, n)

Outputs the representation of the truncated absolute value of x as a 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.

binary_uint(x, n)

Outputs the representation of the truncated absolute value of x as a 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.

output_uint(x, n)

Outputs the representation of the truncated absolute value of x as a unsigned integer in the current obase using n bytes. Not all of the value will be output if n is too small.

This is a void function.

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.

Signal Handling

If bc has been compiled with the signal handling, sending a SIGINT to it will cause it to stop its current execution and reset, asking for more input.

Otherwise, any signals cause bc to exit.

Command Line History

bc supports interactive command-line editing, if compiled with the history option enabled. If stdin is hooked to a terminal, it is enabled. Previous lines can be recalled and edited with the arrow keys.

See Also

dc(1)

Standards

The bc utility is compliant with the IEEE Std 1003.1-2017 (“POSIX.1-2017”) specification. The flags -efhiqsvVw, all long options, and the extensions noted above are extensions to that specification.

Authors

This bc was made from scratch by Gavin D. Howard.

Bugs

None are known. Report bugs at GitHub.