Dc (Unix)

dc is a reverse-polish desk calculator which supports unlimited precision arithmetics. It is one of the oldest Unix utilities, predating even the invention of the C programming language; like other utilities of that vintage, it has a powerful set of features but an extremely terse syntax. Traditionally, the more user-friendly (with its infix notation) bc calculator program was implemented on top of dc, although more modern implementations are no longer related.

This article provides some examples in an attempt to give a flavour of the language; for a complete list of commands and syntax you should consult a manual page for your implementation.

To multiply four and five in dc (note that most of the whitespace is optional):

4 5 * p

This translates into "push four and five onto the stack, then, with the multiplication operator, pop two elements from the stack, multiply them and push the result back on the stack." Then the 'p' command is used to examine (print out to the screen) the top element on the stack.

To change the precision, the command is k. Since the default precision is zero, this sequence of commands produces '0' as a result: 2 3 / p

By adjusting the precision with k, arbitrary number of decimal places can be produced. This command sequence outputs '.66666'.

5 k 2 3 / p

To evaluate (12 + 3^4)/11-22:

12 3 4 ^ + 11 / 22 - p

In addition to these basic arithmetic and stack operations, dc includes support for macros, conditionals and storing of results for later retrieval.

The mechanism underlying macros and conditionals is the register, which in dc is a storage location with a single character name which can be stored to and retrieved from: 'sc' pops the top of the stack and stores it in register c, and 'lc' pushes the value of register c onto the stack. For example:

3 sc 4 lc * p

Registers can also be treated as secondary stacks, so values can be pushed and popped between them and the main stack.

Macros are then implemented by allowing registers and stack entries to be strings as well as numbers. A string can be printed, but it can also be executed (ie processed as a sequence of dc commands). So for instance we can store a macro to add one and then multiply by 2 into register m:

[1 + 2 *] sm

and then (using the 'x' command which executes the top of the stack) we can use it like this:

3 lm x p

Finally, we can use this macro mechanism to provide conditionals. The command '=r' will pop two values from the stack, and execute the macro stored in register r only if they are equal. So this will print the string 'equal' only if the top of the stack is equal to 5:

[equal] p] sm 5 =m

Looping is then possible by defining a macro which (conditionally) reinvokes itself.

As an example of a relatively simple program in dc, this command (in 1 line):

dc -e ' [Enter a number (metres), or 0 to exit] psj] sh [q] sz [lhx?d0=z10k39.370079*.5+0k12~1/rn [ feet ] Pn [ inches] P10Pdx] dx'

will convert distances from metres to feet and inches; the bulk of it is concerned with prompting for input, printing output in a suitable format and looping round to convert another number.

As an example, here is an implementation of the Euclidean algorithm to find the GCD:

dc -e '?? [dSarLa%d0

References

*
* [http://plan9.bell-labs.com/7thEdMan/vol2/dc The sources for the manual page for 7th Edition Unix dc]
* Ritchie, Dennis M. (Sep. 1979) [http://cm.bell-labs.com/cm/cs/who/dmr/hist.html The Evolution of the Unix Timesharing System]