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<input type="hidden" name="sectok" value=""/><input type="hidden" name="id" value="howto:calculate-dc"/><input type="hidden" name="rev" value="0"/><input type="hidden" name="date" value="0"/><input type="hidden" name="prefix" value="."/><input type="hidden" name="suffix" value=""/><input type="hidden" name="changecheck" value="e7daf488331bf9af020089d89a6dee5e"/><input type="hidden" name="target" value="section"/><textarea name="wikitext" id="wiki__text" dir="auto" class="edit form-control" cols="80" rows="10" tabindex="1" readonly="readonly">
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====== 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".
|
||
|
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|
||
|
|
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:
|
||
|
|
|
||
|
|
<code>
|
||
|
|
$ dc <<< '1 1+pq'
|
||
|
|
2
|
||
|
|
</code>
|
||
|
|
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'''.
|
||
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|
||
|
|
Of course, you can also just run ''dc'' and enter the commands.
|
||
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|
||
|
|
The classic operations are:
|
||
|
|
* addition: ''+''
|
||
|
|
* subtraction: ''-''
|
||
|
|
* division: ''/''
|
||
|
|
* multiplication: ''*''
|
||
|
|
* remainder (modulo): ''%''
|
||
|
|
* exponentiation: ''^''
|
||
|
|
* square root: ''v''
|
||
|
|
GNU ''dc'' adds a couple more.
|
||
|
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|
||
|
|
To input a negative number you need to use the ''_'' (underscore) character:
|
||
|
|
<code>
|
||
|
|
$ dc <<< '1_1-p'
|
||
|
|
2
|
||
|
|
</code>
|
||
|
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|
||
|
|
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:
|
||
|
|
<code>
|
||
|
|
dc <<< 'Ap'
|
||
|
|
10
|
||
|
|
</code>
|
||
|
|
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 ''<nowiki>dc <<< "5 4/p"</nowiki>'' 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:
|
||
|
|
<code>
|
||
|
|
dc <<< '2k5 4/p' # prints 1.25
|
||
|
|
dc <<< '4k5 4/p' # prints 1.2500
|
||
|
|
dc <<< '100k 2vp'
|
||
|
|
1.4142135623730950488016887242096980785696718753769480731766797379907\
|
||
|
|
324784621070388503875343276415727
|
||
|
|
</code>
|
||
|
|
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'':
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
Note: when the input value is modified, the base is modified for all commands, including ''i'':
|
||
|
|
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
<code>
|
||
|
|
dc << EOF
|
||
|
|
16o16o10p #prints 10
|
||
|
|
Ai # set the base to A in hex i.e. 10
|
||
|
|
17p # prints 11 in base 16
|
||
|
|
EOF
|
||
|
|
</code>
|
||
|
|
|
||
|
|
===== Stack =====
|
||
|
|
|
||
|
|
There are two basic commands to manipulate the stack:
|
||
|
|
* ''d'' duplicates the top of the stack
|
||
|
|
* ''c'' clears the stack
|
||
|
|
|
||
|
|
<code>
|
||
|
|
$ 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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
''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:
|
||
|
|
|
||
|
|
<code>
|
||
|
|
dc <<< '1 2 d 4+f'
|
||
|
|
6
|
||
|
|
2
|
||
|
|
1
|
||
|
|
</code>
|
||
|
|
|
||
|
|
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:
|
||
|
|
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
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**.
|
||
|
|
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
===== Macros =====
|
||
|
|
|
||
|
|
''dc'' lets you push arbitrary strings on the stack when the strings are enclosed in ''[]''.
|
||
|
|
You can print it with ''p'': ''<nowiki>dc <<< '[Hello World!]p'</nowiki>'' and you can
|
||
|
|
evalute it with x: ''<nowiki>dc <<< '[1 2+]xp'</nowiki>''.
|
||
|
|
|
||
|
|
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!):
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
Now we have several cubes to calculate, we could use ''<nowiki>dd**</nowiki>'' several times, or
|
||
|
|
use a macro.
|
||
|
|
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
===== 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:
|
||
|
|
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
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 ''<nowiki>dc <<< "[f]sR 2 1 >R 1 2 >R f"</nowiki>''
|
||
|
|
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 ;)) :
|
||
|
|
|
||
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<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
We have recursivity, we have test, we have loops:
|
||
|
|
|
||
|
|
<code>
|
||
|
|
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
|
||
|
|
</code>
|
||
|
|
|
||
|
|
Of course code written this way is far too easy to read! Make sure to
|
||
|
|
remove all those extra spaces newlines and comments:
|
||
|
|
|
||
|
|
<code>
|
||
|
|
dc <<< '[lip1-si0li>L]sL10silLx'
|
||
|
|
dc <<< '[p1-d0<L]sL10lLx' # use the stack instead of a register
|
||
|
|
</code>
|
||
|
|
|
||
|
|
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)|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:
|
||
|
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* http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps (dead link)</textarea>
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<ul class="list-inline"><li><span class="iconify text-muted" data-icon="mdi:file-document-outline"></span> <span title="howto/calculate-dc.txt">howto/calculate-dc.txt</span></li><li><span class="iconify text-muted" data-icon="mdi:calendar"></span> Last modified: <span title="2018/06/21 23:36">2018/06/21 23:36</span></li><li class="text-muted">by <bdi>izxle</bdi></li></ul> </span>
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