## NAME

`bc`

—
arbitrary-precision arithmetic language
and calculator

## SYNOPSIS

`bc` |
[`-cl` ] [`-e`
expression] [file ...] |

## DESCRIPTION

`bc`

is an interactive processor for a
language which resembles C but provides unlimited precision arithmetic. It
takes input from any expressions on the command line and any files given,
then reads the standard input.

Options available:

`-c`

`bc`

is actually a preprocessor for dc(1), which it invokes automatically, unless the`-c`

(compile only) option is present. In this case the generated dc(1) instructions are sent to the standard output, instead of being interpreted by a running dc(1) process.`-e`

`expression`- Evaluate
`expression`. If multiple`-e`

options are specified, they are processed in the order given, separated by newlines. `-l`

- Include an arbitrary precision math library. The definitions in the library are available to command line expressions and are documented below.

The syntax for `bc`

programs is as follows:
‘L’ means letter a-z; ‘E’ means expression;
‘S’ means statement. As a non-portable extension, it is
possible to use long names in addition to single letter names. A long name
is a sequence starting with a lowercase letter followed by any number of
lowercase letters and digits. The underscore character (‘_’)
counts as a letter.

Comments

are enclosed in /* and */ are enclosed in # and the next newline

The newline is not part of the line comment, which in itself is a non-portable extension.

Names

simple variables: L array elements: L [ E ] The words `ibase', `obase', and `scale' The word `last' or a single dot

Other operands

arbitrarily long numbers with optional sign and decimal point ( E ) sqrt ( E ) length ( E ) number of significant decimal digits scale ( E ) number of digits right of decimal point L ( E , ... , E )

The sequence ‘\<newline><whitespace>’ is ignored within numbers.

Operators

The following arithmetic and logical operators can be used. The semantics of the operators is the same as in the C language. They are listed in order of decreasing precedence. Operators in the same group have the same precedence.

Operator |
Associativity |
Description |

++ -- | none | increment, decrement |

- | none | unary minus |

^ | right | power |

* / % | left | multiply, divide, modulus |

+ - | left | plus, minus |

= += -= *= /= %= ^= | right | assignment |

== <= >= != < > | none | relational |

! | none | boolean not |

&& | left | boolean and |

|| | left | boolean or |

Note the following:

- The relational operators may appear in any expression. The IEEE Std 1003.1-2008 (“POSIX.1”) standard only allows them in the conditional expression of an ‘if’, ‘while’ or ‘for’ statement.
- The relational operators have a lower precedence than the
assignment operators. This has the consequence that the expression
**a = b < c**is interpreted as**(a = b) < c**, which is probably not what the programmer intended. - In contrast with the C language, the relational operators all have the
same precedence, and are non-associative. The expression
**a < b < c**will produce a syntax error. - The boolean operators (!, && and ||) are non-portable extensions.
- The boolean not (!) operator has much lower precedence than the
same operator in the C language. This has the consequence that the
expression
**!a < b**is interpreted as**!(a < b)**. Prudent programmers use parentheses when writing expressions involving boolean operators.

Statements

E { S ; ... ; S } if ( E ) S if ( E ) S else S while ( E ) S for ( E ; E ; E ) S null statement break continue quit a string of characters, enclosed in double quotes print E ,..., E

A string may contain any character, except double quote. The if statement with an else branch is a non-portable extension. All three E's in a for statement may be empty. This is a non-portable extension. The continue and print statements are also non-portable extensions.

The print statement takes a list of comma-separated expressions. Each expression in the list is evaluated and the computed value is printed and assigned to the variable `last'. No trailing newline is printed. The expression may also be a string enclosed in double quotes. Within these strings the following escape sequences may be used: ‘\a’ for bell (alert), ‘\b’ for backspace, ‘\f’ for formfeed, ‘\n’ for newline, ‘\r’ for carriage return, ‘\t’ for tab, ‘\q’ for double quote and ‘\\’ for backslash. Any other character following a backslash will be ignored. Strings will not be assigned to `last'.

Function definitions

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

As a non-portable extension, the opening brace of the define statement may appear on the next line. The return statement may also appear in the following forms:

return return () return E

The first two are equivalent to the statement “return 0”. The last form is a non-portable extension. Not specifying a return statement is equivalent to writing “return (0)”.

Functions available in the math library, which is loaded by
specifying the `-l`

flag on the command line:

- s(x)
- sine
- c(x)
- cosine
- e(x)
- exponential
- l(x)
- log
- a(x)
- arctangent
- j(n,x)
- Bessel function

All function arguments are passed by value.

The value of a statement that is an expression is printed unless
the main operator is an assignment. The value printed is assigned to the
special variable `last'. This is a non-portable extension. A single dot may
be used as a synonym for `last'. Either semicolons or newlines may separate
statements. Assignment to `scale` influences the number
of digits to be retained on arithmetic operations in the manner of
dc(1). Assignments
to `ibase` or `obase` set the input
and output number radix respectively.

The same letter may be used as an array, a function, and a simple variable simultaneously. All variables are global to the program. `Auto' variables are pushed down during function calls. When using arrays as function arguments or defining them as automatic variables, empty square brackets must follow the array name.

For example

scale = 20 define e(x){ auto a, b, c, i, s a = 1 b = 1 s = 1 for(i=1; 1==1; i++){ a = a*x b = b*i c = a/b if(c == 0) return(s) s = s+c } }

defines a function to compute an approximate value of the exponential function and

```
for(i=1; i<=10; i++)
e(i)
```

prints approximate values of the exponential function of the first ten integers.

$ bc -l -e 'scale = 500; 4 * a(1)' -e quit

prints an approximation of pi.

## COMMAND LINE EDITING

`bc`

supports interactive command line
editing, via the editline(3) library. It is enabled by default if input is
from a tty. Previous lines can be recalled and edited with the arrow keys,
and other GNU Emacs-style editing keys may be used as well.

The editline(3) library is configured with a .editrc file - refer to editrc(5) for more information.

## FILES

- /usr/share/misc/bc.library
- math library, read when the
`-l`

option is specified on the command line.

## SEE ALSO

L. L. Cherry and R. H. Morris, BC — An Arbitrary Precision Desk-Calculator Language.

## STANDARDS

The `bc`

utility is compliant with the
IEEE Std 1003.1-2008 (“POSIX.1”)
specification.

The flags [`-ce`

], as well as the parts
noted above, are extensions to that specification.

## HISTORY

The `bc`

command first appeared in
Version 6 AT&T UNIX. A complete rewrite
of the `bc`

command first appeared in
OpenBSD 3.5.

## AUTHORS

The original version of the `bc`

command was
written by Robert Morris and
Lorinda Cherry. The current version of the
`bc`

utility was written by Otto
Moerbeek.

## BUGS

The ‘`quit`

’ statement is
interpreted when read, not when executed.

Some non-portable extensions, as found in the GNU version of the
`bc`

utility are not implemented (yet).