Calculating with dc
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.
In brief, the reverse polish notation means the numbers are put
on the stack first, then an operation is applied to them. Instead
1+1, you write
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' 2I 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' | dcor 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:
- remainder (modulo):
- square root:
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
9 and the letters
F as numbers, and a dot (
.) as a decimal point.
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' 10The output is converted to base 10 by default
Scale And Base
dc is a calulator with abitrary precision, by default this precision is 0.
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\ 324784621070388503875343276415727dc 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
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
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
There are two basic commands to manipulate the stack:
dduplicates the top of the stack
cclears the stack
$ 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.
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 use 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 that 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
dc lets you push aribtrary strings on the stack when the strings are enclosed in
You can print it with
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 the 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 cube 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
>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
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.
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:
And more example, as well as a dc implementation in python here:
The manual for the 1971 dc from Bell Labs:
- http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps (dead link)