Dc (computer program)

dc ("desk calculator") is a cross-platform reverse-polish calculator which supports arbitrary-precision arithmetic. Written by Robert Morris while at Bell Labs, it is one of the oldest Unix utilities, preceding even the invention of the C programming language. Like other utilities of that vintage, it has a powerful set of features but terse syntax.
Traditionally, the bc calculator program (with infix notation) was implemented on top of dc.
This article provides some examples in an attempt to give a general flavour of the language; for a complete list of commands and syntax, one should consult the man page for one's specific implementation.
History.
dc is the oldest surviving Unix language. When its home Bell Labs received a PDP-11, dcwritten in Bwas the first language to run on the new computer, even before an assembler. Ken Thompson has opined that dc was the very first program written on the machine.
Basic operations.
To multiply four and five in dc (note that most of the whitespace is optional):
$ cat « EOF > cal.txt
4 5 *
p
EOF
$ dc cal.txt
20
You can also get the result with the commands:
$ echo "4 5 * p" | dc
or
$ dc -
4 5*pq
20
$ dc
4 5 *
p
20
q
$ dc -e '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 codice_1 command is used to examine (print out to the screen) the top element on the stack. The codice_2 command quits the invoked instance of dc. Note that numbers must be spaced from each other even as some operators need not be.
The arithmetic precision is changed with the command codice_3, which sets the number of fractional digits (the number of digits following the point) to be used for arithmetic operations. Since the default precision is zero, this sequence of commands produces codice_4 as a result:
By adjusting the precision with codice_3, arbitrary number of decimal places can be produced. This command sequence outputs codice_6.
To evaluate formula_1: (codice_7 computes the square root of the top of the stack and codice_8 is used to input a negative number):
To swap the top two elements of the stack, use the codice_9 command. To duplicate the top element, use the codice_10 command.
Input/output.
To read a line from stdin, use the codice_11 command. This will evaluate the line as if it were a dc command, and so it is necessary that it be syntactically correct and potentially be a security problem since the codice_12 dc command will allow arbitrary command execution.
As mentioned above, codice_1 will print the top of the stack with a newline after it. codice_14 will pop the top of the stack and output it without a trailing newline. codice_15 will dump the entire stack with one entry per line.
dc also supports arbitrary input and output radices. The codice_16 command will pop the top of the stack and use it for the input base. Hex digits must be in upper case to avoid collisions with dc commands and are limited to A-F. The codice_17 command does the same for the output base, but keep in mind that the input base will affect the parsing of every numeric value afterwards so it is usually advisable to set the output base first. Therefore codice_18 sets the output radix to the current input radix, but generally not to 10 (ten). Nevertheless codice_19 resets the output base to 10 (ten), regardless of the input base. To read the values, the codice_20, codice_21 and codice_22 commands will push the current precision, input radix and output radix on to the top of the stack.
As an example, to convert from hex to binary:
$ echo 16i2o DEADBEEFp | dc
11011110101011011011111011101111
Language features.
Registers.
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: codice_23 pops the top of the stack and stores it in register c, and codice_24 pushes the value of register c onto the stack. For example:
Registers can also be treated as secondary stacks, so values can be pushed and popped between them and the main stack using the codice_25 and codice_26 commands.
Strings.
String values are enclosed in codice_27 and codice_28 characters and may be pushed on the stack and stored in registers. The codice_29 command will convert the low order byte of the numeric value into an ASCII character, or if the top of the stack is a string it will replace it with the first character of the string. There are no ways to build up strings or perform string manipulation other than executing it with the codice_30 command, or printing it with the codice_31 command.
The codice_32 character begins a comment to the end of the line.
Macros.
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 (i.e. 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:
and then (using the codice_30 command which executes the top of the stack) we can use it like this:
Conditionals.
Finally, we can use this macro mechanism to provide conditionals. The command codice_34 will pop two values from the stack, and execute the macro stored in register codice_9 only if they are equal. So this will print the string codice_36 only if the top of the stack is equal to 5:
Other conditionals are codice_37, codice_38, codice_39, codice_40, codice_41, which will execute the specified macro if the top two values on the stack are greater, less than or equal to ("not greater"), less than, greater than or equal to ("not less than"), and not equals, respectively.
Loops.
Looping is then possible by defining a macro which (conditionally) reinvokes itself. A simple factorial of the top of the stack might be implemented as:
The codice_42 command will exit from a macro, allowing an early return. codice_2 will quit from two levels of macros (and dc itself if there are less than two levels on the call stack). codice_44 will push the current stack depth before the codice_44 operation.
Examples.
Summing the entire stack.
This is implemented with a macro stored in register codice_29 which conditionally calls itself, performing an addition each time, until only one value remains on the stack. The codice_44 operator is used to push the number of entries in the stack onto the stack. The comparison operator codice_37 pops two values off the stack in making the comparison. 
dc -e "1 2 4 8 16 100 0d[+2z>a]salaxp"
And the result is 131. 
Summing all dc expressions as lines from file.
A bare number is a valid dc expression, so this can be used to sum a file where each line contains a single number. 
This is again implemented with a macro stored in register codice_29 which conditionally calls itself, performing an addition each time, until only one value remains on the stack. 
cat file | dc -e "0d[?+2z>a]salaxp"
The codice_11 operator reads another command from the input stream. If the input line contains a decimal number, that value is added to the stack. When the input file reaches end of file, the command is null, and no value is added to the stack.
And the result is 12. 
The input lines can also be complex dc commands. 
And the result is 42. 
Note that since dc supports arbitrary precision, there is no concern about numeric overflow or loss of precision, no matter how many lines the input stream contains, unlike a similarly concise solution in [[AWK]].
Downsides of this solution are: the loop will cease on encountering a blank line in the input stream (technically, any input line which does not add at least one numeric value to the stack); and, for handling negative numbers, leading instances of '-' to denote a negative sign must be change to '_' in the input stream, because of dc's nonstandard negative sign. The codice_11 operator in dc does not provide a clean way to discern reading a blank line from reading end of file.
Unit conversion.
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 around to convert another number.
Greatest common divisor.
As an example, here is an implementation of the [[Euclidean algorithm]] to find the [[Greatest common divisor|GCD]]:
dc -e '??[dSarLa%d0<a]dsax+p' # shortest
dc -e '[a=]P?[b=]P?[dSarLa%d0<a]dsax+[GCD:]Pp' # easier-to-read version
Factorial.
Computing the [[factorial]] of an input value, formula_2
dc -e '?[q]sQ[d1=Qd1-lFx*]dsFxp'
Quines in dc.
There exist also [[Quine (computing)|quines]] in the programming language dc; programs that produce its source code as output.
dc -e '[91Pn[dx]93Pn]dx'
dc -e '[91PP93P[dx]P]dx'
Printing all prime numbers.
echo '2p3p[dl!d2+s!%0=@l!l^!<#]s#[s/0ds^]s@[p]s&[ddvs^3s!l#x0<&2+l.x]ds.x' | dc
This program was written by Michel Charpentier. 
It outputs the sequence of prime numbers.
Note that it can be shortened by one symbol, which seems to be the minimal solution.
echo '2p3p[dl!d2+s!%0=@l!l^!<#]s#[0*ds^]s@[p]s&[ddvs^3s!l#x0<&2+l.x]ds.x' | dc
Integer factorization.
dc -e '[n=]P?[p]s2[lip/dli%0=1dvsr]s12sid2%0=13sidvsr[dli%0=1lrli2+dsi!>.]ds.xd1<2'
This program was also written by Michel Charpentier. 
There is a shorter
dc -e "[n=]P?[lfp/dlf%0=Fdvsr]sF[dsf]sJdvsr2sf[dlf%0=Flfdd2%+1+sflr<Jd1<M]dsMx"
and a faster solution (try with the 200-bit number (input codice_52)
dc -e "[n=]P?[lfp/dlf% 0=Fdvsr]sFdvsr2sfd2%0=F3sfd3%0=F5sf[dlf%0=Flfd4+sflr>M]sN[dlf%0=Flfd2+sflr>N]dsMx[p]sMd1<M" 
Note that the latter can be even speeded up, if the access to a constant is replaced by a register access.
dc -e "[n=]P?[lfp/dlf%l0=Fdvsr]sF2s2dvsr2sf4s4d2%0=F3sfd3%0=F5sf[dlf%l0=Flfdl4+sflr>M]sN[dlf%l0=Flfdl2+sflr>N]dsMx[p]sMd1<M"
Diffie–Hellman key exchange.
A more complex example of dc use embedded in a [[Perl]] script performs a [[Diffie–Hellman key exchange]]. This was popular as a [[signature block]] among [[cypherpunk]]s during the [[ITAR]] debates, where the short script could be run with only Perl and dc, ubiquitous programs on Unix-like operating systems:
($g, $e, $m) = @ARGV, $m || die "$0 gen exp mod\n";
print `echo "16dio1[d2%Sa2/d0<X+d*La1=z\U$m%0]SX$e"[$g*]\EszlXx+p | dc`
A commented version is slightly easier to understand and shows how to use loops, conditionals, and the codice_2 command to return from a macro. With the GNU version of dc, the codice_54 command can be used to do arbitrary precision modular exponentiation without needing to write the X function.
my ($g, $e, $m) = map { "\U$_" } @ARGV;
die "$0 gen exp mod\n" unless $m;
print `echo $g $e $m | dc -e '
16dio
?SmSeSg
[lg*]sz
[sb1q]sQ
 d 0=Q # return 1 if e==0 (otherwise, stack: e)
 d 2% Sa # Store e%2 in a (stack: e)
 2/ # compute e/2
 lXx # call X(e/2)
 d* # compute X(e/2)^2
 La1=z # multiply by g if e%2==1
 lm % # compute (g^e) % m
] SX
le # Load e from the register
lXx # compute g^e % m
p # Print the result
External links.
[[Category:Cross-platform software]]
[[Category:Unix software]]
[[Category:Software calculators]]
[[Category:Free mathematics software]]
[[Category:Numerical programming languages]]
[[Category:Stack-oriented programming languages]]
[[Category:Plan 9 commands]]