dc (desk calculator) is across-platformreverse-Polish calculator which supportsarbitrary-precision arithmetic.^[1] It was written byLorinda Cherry andRobert Morris atBell Labs.^[2] It is one of the oldestUnix utilities, preceding even the invention of theC programming language. Like other utilities of that vintage, it has a powerful set of features but terse syntax.^[3][4]Traditionally, thebc calculator program (withinfix notation) was implemented on top of dc, now the implementation of GNU dc bases on bc.^[5]

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 theman page for one's specific implementation.

dc is the oldest survivingUnix language program. When its homeBell Labs received aPDP-11, dc—written inB—was the first language to run on the new computer, even before an assembler.^[2]Ken Thompson has opined that dc was the very first program written on the machine.^[6]

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

$cat<<EOF>cal.txt4 5 *pEOF$dccal.txt20$

The results are also available from the commands:

$echo"4 5 * p"|dc

or

$dc-4 5*pq20$dc4 5 *p20q$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 onto the stack." Then thep command is used to examine (print out to the screen) the top element on the stack. Theq command quits the invoked instance of dc. Note that numbers must be spaced from each other even as some operators need not be.

Thearithmetic precision is changed with the commandk, which sets the number of fractional digits (the number of digits following thepoint) to be used for arithmetic operations. Since the default precision is zero, this sequence of commands produces0 as a result:

2 3 / p

By adjusting the precision withk, an arbitrary number of decimal places can be produced. This command sequence outputs.66666.

5 k2 3 / p

To evaluate${\displaystyle \sqrt{\frac{\left(12+{\left(-3\right)}^4\right)}{11}}-22}$: (v computes the square root of the top of the stack and_ is used to input a negative number):

12 _3 4 ^ + 11 / v 22 -p

To swap the top two elements of the stack, use ther command. To duplicate the top element, use thed command.

To read a line fromstdin, use the? command. This evaluates the line as if it were a dc command, and so it is necessary that it be syntactically correct and presents a potential security problem because the! dc command enables arbitrary command execution.

As mentioned above,p prints the top of the stack with a newline after it.n pops the top of the stack and prints it without a trailing newline.f prints the entire stack with one entry per line.

dc also supports arbitrary input and outputradices. Thei command pops the top of the stack and uses it for the input base. Hex digits must be in upper case to avoid collisions with dc commands and are limited to A-F. Theo command does the same for the output base, but keep in mind that the input base affects the parsing of every numeric value afterwards so it is usually advisable to set the output base first. Therefore10o sets the output radix to the current input radix, but generally not to 10 (ten). NeverthelessAo resets the output base to 10 (ten), regardless of the input base. To read the values, theK,I andO commands 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:

$echo16i2oDEADBEEFp|dc11011110101011011011111011101111

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

The mechanism underlying macros and conditionals is theregister, 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, andlc 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 using theS andL commands.

String values are enclosed in[ and] characters and may be pushed onto the stack and stored in registers. Thea command converts the low order byte of the numeric value into anASCII character, or if the top of the stack is a string it replaces 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 thex command, or printing it with theP command.

The# character begins a comment to the end of the line.

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:

[1 + 2 *] sm

and then (using thex 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 pops two values from the stack, and executes the macro stored in registerr only if they are equal. So this prints the stringequal only if the top two values on the stack are of equal value:

[[equal]p] sr 5 5 =r

Other conditionals are>,!>,<,!<,!=, which 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. Note that the order of the operands in inequality comparisons is the opposite of the order for arithmetic;5 3 - evaluates to5 - 3 = 2, but5 3 <t runs the contents of thet register because3 < 5.

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:

# F(x): return x!# if x-1 > 1#     return x * F(x-1)# otherwise#     return x[d1-d1<F*]dsFxp

The1Q command exits from a macro, allowing an early return.q quits from two levels of macros (and dc itself if there are less than two levels on the call stack).z pushes the current stack depth before thez operation.

This is implemented with a macro stored in registera which conditionally calls itself, performing an addition each time, until only one value remains on the stack. Thez operator is used to push the number of entries in the stack onto the stack. The comparison operator> pops two values off the stack in making the comparison.

dc-e"1 2 4 8 16 100 0d[+z1<a]dsaxp"

And the result is 131.

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 registera which conditionally calls itself, performing an addition each time, until only one value remains on the stack.

dc-e"0d[?+z1<a]dsaxp"<file

The? 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.

{echo"5";echo"7";}|dc-e"0d[?+z1<a]dsaxp"

And the result is 12.

The input lines can also be complex dc commands.

{echo"3 5 *";echo"4 3 *";echo"5dd++";}|dc-e"0d[?+z1<a]dsaxp"

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 inAWK.

Downsides of this solution are: the loop stops 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? operator in dc does not provide a clean way to discern reading a blank line from reading end of file.

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]PAP]sh[q]sz[lhx?d0=zAk.0254/.5+0kC~1/rn[ feet ]Pn[ inches]PAPdx]dx'

converts 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.

As an example, here is an implementation of theEuclidean algorithm to find theGCD:

dc-e'??[dSarLa%d0<a]dsax+p'# shortestdc-e'[a=]P?[b=]P?[dSarLa%d0<a]dsax+[GCD:]Pp'# easier-to-read version

Computing thefactorial of an input value,${\displaystyle n!=\prod _{i=1}^{n}i}$

dc-e'?[q]sQ[d1=Qd1-lFx*]dsFxp'

There exist alsoquines 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'

dc-e'2p3p[dl!d2+s!%0=@l!l^!<#]s#[s/0ds^]s@[p]s&[ddvs^3s!l#x0<&2+l.x]ds.x'

This program was written by Michel Charpentier. It outputs the sequence of prime numbers.Note that shorter implementation is possible, which needs fourteen symbols fewer.

dc-e'2p3p[pq]s$[l!2+ds!l^<$dl!%0<#]s#[+dvs^1s!l#x2l.x]ds.x'

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.^[7]

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 number2²⁰⁰-1 (input2 200^1-)

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 sped up even more, 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"

An implementation of theChudnovsky algorithm in the programming language dc. The program will print better and better approximations as it runs. But as pi is a transcendental number, the program will continue until interrupted or resource exhaustion of the machine it is run on.

dc-e'_640320[0ksslk3^16lkd12+sk*-lm*lhd1+sh3^/smlxlj*sxll545140134+dsllm*lxlnk/ls+dls!=P]sP3^sj7sn[6sk1ddshsxsm13591409dsllPx10005v426880*ls/K3-k1/pcln14+snlMx]dsMx'

A fast divide and conquer implementation of the same formula that doubles in size each iteration. It evaluates a finite number if sums as an exact rational number and only performs one large division and square root per iteration. It is fast, but will still quickly slow down as the size of the fraction increases.

dc-e'1Sk1SR13591409dSBSP426880dSQ4/3^9*SC[0r-]s-[lkE*1-k10005vlQ*lP/nAan0k]dSox[Lkd1+Skdd1+Sk3^lC*SQ2*1-d3*d*4-*dSR545140134LB+dSB*lk2%0=-SP]dszx[LRLRdLP*LPLQdLQ*SQ*+SP*SR]sc[d1-d0<yd0<yd0=z0=zlcx]sy0[lcxlox1+lyxllx]dslx'

A more complex example of dc use embedded in aPerl script performs aDiffie–Hellman key exchange. This was popular as asignature block amongcypherpunks during theITAR debates, where the short script could be run with only Perl and dc, ubiquitous programs on Unix-like operating systems:^[8]

#!/usr/bin/perl -- -export-a-crypto-system-sig Diffie-Hellman-2-lines($g,$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 theq command to return from a macro. With the GNU version of dc, the| command can be used to do arbitrary precision modular exponentiation without needing to write the X function.

#!/usr/bin/perlmy($g,$e,$m)=map{"\U$_"}@ARGV;die"$0 gen exp mod\n"unless$m;print`echo $g $e $m | dc -e '# Hex input and output16dio# Read m, e and g from stdin on one line?SmSeSg# Function z: return g * top of stack[lg*]sz# Function Q: remove the top of the stack and return 1[sb1q]sQ# Function X(e): recursively compute g^e % m# It is the same as Sm^Lm%, but handles arbitrarily large exponents.# Stack at entry: e# Stack at exit: g^e % m# Since e may be very large, this uses the property that g^e % m ==#     if( e == 0 )#         return 1#     x = (g^(e/2)) ^ 2#     if( e % 2 == 1 )#         x *= g#     return x %[    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] SXle          # Load e from the registerlXx         # compute g^e % mp           # Print the result'`;

If theenvironment variable DC_LINE_LENGTH exists and contains an integer that is greater than 1 and less than${\displaystyle 2^{16}-1}$, the output of number digits (according to the output base) will be restricted to this value, inserting thereafter backslashes and newlines. The default line length is 70. The special value of 0 disables line breaks.

• bc (programming language)
• Calculator input methods
• HP calculators
• Stack machine
• Reverse Polish notation

• Packagedc inDebian GNU/Linux repositories
• newest PackageGNU bc-1.08.1 including dc.
• dc(1) – Linux General CommandsManual
• dc(1) – Plan 9 Programmer's Manual, Volume 1
• Native Windows port ofbc, which includes dc.

• Cross-platform software
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• Free mathematics software
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