bc(1)

NAME

bc — arbitrary-precision arithmetic language

SYNOPSIS

bc [-c] [-l] [file...]

DESCRIPTION

bc is an interactive processor for a language that resembles C but provides unlimited-precision arithmetic. It takes input from any files given, then reads the standard input.

Options

bc recognizes the following command-line options:

-c: Compile only. bc is actually a preprocessor for dc which bc invokes automatically (see dc(1)). Specifying -c prevents invoking dc, and sends the dc input to standard output.
-l: causes an arbitrary-precision math library to be predefined. As a side effect, the scale factor is set.

Program Syntax

L: a single letter in the range a through z;
E: expression;
S: statement;
R: relational expression.

Comments

Comments are enclosed in /* and */.

Names

Names include:

simple variables: L
array elements: L [ E ]
The words ibase,obase, and scale
stacks: L

Other Operands

Other operands include:

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 )

Strings of ASCII characters enclosed in quotes ("").

Arithmetic Operators:

Arithmetic operators yield an E as a result and include:

+ - * / % ^: (% is remainder (not mod, see below); ^ is power).
++ --: (prefix and append; apply to names)
= += -= *= /= %= ^=

Relational Operators

Relational operators yield an R when used as E op E:

==  <=  >=  !=  <  > 

Statements

E
{ S ; ... ; S }
if ( R ) S
while ( R ) S
for ( E ; R ; E ) S
null statement
break
quit

Function Definitions

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

Functions in -l Math Library

Functions in the -l math library include:

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. Trigonometric angles are in radians where 2 pi radians = 360 degrees.

The value of a statement that is an expression is printed unless the main operator is an assignment. No operators are defined for strings, but the string is printed if it appears in a context where an expression result would be printed. Either semicolons or new-lines can 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, again as defined by dc(1).

The same letter can be used simultaneously as an array, a function, and a simple variable. 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.

The % operator yields the remainder at the current scale, not the integer modulus. Thus, at scale 1, 7 % 3 is .1 (one tenth), not 1. This is because (at scale 1) 7 / 3 is 2.3 with .1 as the remainder.

EXAMPLES

Define a function to compute an approximate value of the exponential function:

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 
        } 
} 

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

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

WARNINGS

There are currently no && (AND) or || (OR) comparisons.

The for statement must have all three expressions.

quit is interpreted when read, not when executed.

bc's parser is not robust in the face of input errors. Some simple expression such as 2+2 helps get it back into phase.

The assignment operators: =+ =- =* =/ =% and =^ are obsolete. Any occurences of these operators cause a syntax error with the exception of =- which is interpreted as = followed by a unary minus.

Neither entire arrays nor functions can be passed as function parameters.

FILES

/usr/bin/dc: desk calculator executable program
/usr/lib/lib.b: mathematical library

STANDARDS CONFORMANCE

bc: XPG4, POSIX.2