# Calculating with dc

![](keywords>bash shell scripting arithmetic calculate)

## Introduction

dc(1) is a non standard, but commonly found, reverse-polish Desk
Calculator. According to Ken Thompson, \"dc is the oldest language on
Unix; it was written on the PDP-7 and ported to the PDP-11 before Unix
\[itself\] was ported\".

Historically the standard bc(1) has been implemented as a *front-end to
dc*.

## Simple calculation

In brief, the *reverse polish notation* means the numbers are put on the
stack first, then an operation is applied to them. Instead of writing
`1+1`, you write `1 1+`.

By default `dc`, unlike `bc`, doesn't print anything, the result is
pushed on the stack. You have to use the \"p\" command to print the
element at the top of the stack. Thus a simple operation looks like:

    $ dc <<< '1 1+pq'
    2

I used a \"here string\" present in bash 3.x, ksh93 and zsh. if your
shell doesn't support this, you can use `echo '1 1+p' | dc` or if you
have GNU `dc`, you can use `dc -e '1 1 +p`\'.

Of course, you can also just run `dc` and enter the commands.

The classic operations are:

-   addition: `+`
-   subtraction: `-`
-   division: `/`
-   multiplication: `*`
-   remainder (modulo): `%`
-   exponentiation: `^`
-   square root: `v`

GNU `dc` adds a couple more.

To input a negative number you need to use the `_` (underscore)
character:

    $ dc <<< '1_1-p' 
    2

You can use the *digits* `0` to `9` and the *letters* `A` to `F` as
numbers, and a dot (`.`) as a decimal point. The `A` to `F` **must** be
capital letters in order not to be confused with the commands specified
with lower case characters. A number with a letter is considered
hexadecimal:

    dc <<< 'Ap'
    10 

The **output** is converted to **base 10** by default

## Scale And Base

`dc` is a calulator with abitrary precision, by default this precision
is 0. thus `dc <<< "5 4/p"` prints \"1\".

We can increase the precision using the `k` command. It pops the value
at the top of the stack and uses it as the precision argument:

    dc <<< '2k5 4/p' # prints 1.25
    dc <<< '4k5 4/p' # prints 1.2500
    dc <<< '100k 2vp' 
    1.4142135623730950488016887242096980785696718753769480731766797379907\
    324784621070388503875343276415727

dc supports *large* precision arguments.

You can change the base used to output (*print*) the numbers with `o`
and the base used to input (*type*) the numbers with `i`:

    dc << EOF
    20 p# prints 20, output is in base 10
    16o # the output is now in base 2 16
    20p # prints 14,  in hex
    16i # the output is now in hex
    p   # prints 14 this doesn't modify the number in the stack
    10p # prints 10 the output is done in base 16
    EOF

Note: when the input value is modified, the base is modified for all
commands, including `i`:

    dc << EOF
    16i 16o # base is 16 for input and output
    10p # prints 10
    10i # ! set the base to 10 i.e. to 16 decimal
    17p # prints 17 
    EOF

This code prints 17 while we might think that `10i` reverts the base
back to 10 and thus the number should be converted to hex and printed as
11. The problem is 10 was typed while the input base 16, thus the base
was set to 10 hexadecimal, i.e. 16 decimal.

    dc << EOF
    16o16o10p #prints 10
    Ai # set the base to A in hex i.e. 10
    17p # prints 11 in base 16
    EOF

## Stack

There are two basic commands to manipulate the stack:

-   `d` duplicates the top of the stack
-   `c` clears the stack

```{=html}
<!-- -->
```
    $ dc << EOF
    2   # put 2 on the stack
    d   # duplicate i.e. put another 2 on the stack
    *p  # multiply and print
    c p # clear and print
    EOF
    4
    dc: stack empty

`c p` results in an error, as we would expect, as c removes everything
on the stack. *Note: we can use `#` to put comments in the script.*

If you are lost, you can inspect (i.e. print) the stack using the
command `f`. The stack remains unchanged:

    dc <<< '1 2 d 4+f'
    6
    2
    1

Note how the first element that will be popped from the stack is printed
first, if you are used to an HP calculator, it's the reverse.

Don't hesitate to put `f` in the examples of this tutorial, it doesn't
change the result, and it's a good way to see what's going on.

## Registers

The GNU `dc` manual says that dc has at least **256 registers**
depending on the range of unsigned char. I\'m not sure how you are
supposed to use the NUL byte. Using a register is easy:

    dc <<EOF
    12 # put 12 on the stack
    sa # remove it from the stack (s), and put it in register 'a'
    10 # put 10 on the stack
    la # read (l) the value of register 'a' and push it on the stack
    +p # add the 2 values and print
    EOF

The above snippet uses newlines to embed comments, but it doesn't
really matter, you can use `echo '12sa10la+p'| dc`, with the same
results.

The register can contain more than just a value, **each register is a
stack on its own**.

    dc <<EOF
    12sa #store 12 in 'a'
    6Sa # with a capital S the 6 is removed
        # from the  main stack and pushed on the 'a' stack
    lap # prints 6, the value at the top of the 'a' stack
    lap # still prints 6
    Lap # prints 6 also but with a capital L, it pushes the value in 'a'
        # to the main stack and pulls it from the 'a' stack
    lap # prints 12, which is now at the top of the stack
    EOF

## Macros

`dc` lets you push arbitrary strings on the stack when the strings are
enclosed in `[]`. You can print it with `p`: `dc <<< '[Hello World!]p'`
and you can evalute it with x: `dc <<< '[1 2+]xp'`.

This is not that interesting until combined with registers. First,
let's say we want to calculate the square of a number (don't forget to
include `f` if you get lost!):

    dc << EOF
    3 # push our number on the stack
    d # duplicate it i.e. push 3 on the stack again
    d**p # duplicate again and calculate the product and print
    EOF

Now we have several cubes to calculate, we could use `dd**` several
times, or use a macro.

    dc << EOF
    [dd**] # push a string
    sa # save it in register a
    3 # push 3 on the stack
    lax # push the string "dd**" on the stack and execute it
    p # print the result
    4laxp # same operation for 4, in one line
    EOF

## Conditionals and Loops

`dc` can execute a macro stored in a register using the `lR x` combo,
but it can also execute macros conditionally. `>a` will execute the
macro stored in the register `a`, if the top of the stack is *greater
than* the second element of the stack. Note: the top of the stack
contains the last entry. When written, it appears as the reverse of what
we are used to reading:

    dc << EOF
    [[Hello World]p] sR  # store in 'R' a macro that prints Hello World
    2 1 >R           # do nothing 1 is at the top 2 is the second element
    1 2 >R           # prints Hello World
    EOF

Some `dc` have `>R <R =R`, GNU `dc` had some more, check your manual.
Note that the test \"consumes\" its operands: the 2 first elements are
popped off the stack (you can verify that
`dc <<< "[f]sR 2 1 >R 1 2 >R f"` doesn't print anything)

Have you noticed how we can *include* a macro (string) in a macro? and
as `dc` relies on a stack we can, in fact, use the macro recursively
(have your favorite control-c key combo ready ;)) :

    dc << EOF
    [ [Hello World] p   # our macro starts by printing Hello World
      lRx            ]  # and then executes the macro in R
    sR          # we store it in the register R
    lRx                 # and finally executes it.
    EOF

We have recursivity, we have test, we have loops:

    dc << EOF
    [ li       # put our index i on the stack 
      p        # print it, to see what's going on
      1 -      # we decrement the index by one
      si       # store decremented index (i=i-1)
     0 li >L   # if i > 0 then execute L
    ] sL       # store our macro with the name L
     
    10 si      # let's give to our index the value 10
    lLx        # and start our loop
    EOF

Of course code written this way is far too easy to read! Make sure to
remove all those extra spaces newlines and comments:

    dc <<< '[lip1-si0li>L]sL10silLx' 
    dc <<< '[p1-d0<L]sL10lLx' # use the stack instead of a register

I\'ll let you figure out the second example, it's not hard, it uses the
stack instead of a register for the index.

## Next

Check your dc manual, i haven't decribed everything, like arrays (only
documented with \"; : are used by bc(1) for array operations\" on
solaris, probably because *echo \'1 0:a 0Sa 2 0:a La 0;ap\' \| dc*
results in //Segmentation Fault (core dump) //, the latest solaris uses
GNU dc)

You can find more info and dc programs here:

-   <http://en.wikipedia.org/wiki/Dc_(Unix)>

And more example, as well as a dc implementation in python here:

-   <http://en.literateprograms.org/Category:Programming_language:dc>
-   <http://en.literateprograms.org/Desk_calculator_%28Python%29>

The manual for the 1971 dc from Bell Labs:

-   <http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps> (dead link)