History
dc is the oldest survivingBasic operations
To multiply four and five in dc (note that most of the whitespace is optional):p
command is used to examine (print out to the screen) the top element on the stack. The q
command quits the invoked instance of dc. Note that numbers must be spaced from each other even as some operators need not be.
The k
, 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 0
as a result:
2 3 / pBy adjusting the precision with
k
, an arbitrary number of decimal places can be produced. This command sequence outputs .66666
.
5 k 2 3 / pTo evaluate : (
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 - pTo swap the top two elements of the stack, use the
r
command. To duplicate the top element, use the d
command.
Input/output
To read a line from?
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 output radices. The i
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. The o
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. Therefore 10o
sets the output radix to the current input radix, but generally not to 10 (ten). Nevertheless Ao
resets the output base to 10 (ten), regardless of the input base. To read the values, the K
, I
and O
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:
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:sc
pops the top of the stack and stores it in register c, and lc
pushes the value of register c onto the stack. For example:
3 sc 4 lc * pRegisters can also be treated as secondary stacks, so values can be pushed and popped between them and the main stack using the
S
and L
commands.
Strings
String values are enclosed in and ">/code> and
/code> characters and may be pushed onto the stack and stored in registers. The a
command converts the low order byte of the numeric value into an ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
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 the x
command, or printing it with the P
command.
The #
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:
+ 2 *sm
and then (using the x
command which executes the top of the stack) we can use it like this:
3 lm x p
Conditionals
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 register r
only if they are equal. So this prints the string equal
only if the top of the stack is equal to 5:
equal] sm 5 =m
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; evaluates to , but runs the contents of the register because .
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:
# F(x): return x!
# if x-1 > 1
# return x * F(x-1)
# otherwise
# return x
1-d1sFxp
The 1Q
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 the z
operation.
Examples
Summing the entire stack
This is implemented with a macro stored in register a
which conditionally calls itself, performing an addition each time, until only one value remains on the stack. The z
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 a">2z>aalaxp"
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 a
which conditionally calls itself, performing an addition each time, until only one value remains on the stack.
cat file , dc -e "0d a">+2z>aalaxp"
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.
, dc -e "0d a">+2z>aalaxp"
And the result is 12.
The input lines can also be complex dc commands.
, dc -e "0d a">+2z>aalaxp"
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 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.
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 exitsj]sh z hx?d0=z10k39.370079*.5+0k12~1/rn[_feet_n[_inches.html" ;"title="feet_.html" ;"title="hx?d0=z10k39.370079*.5+0k12~1/rn[ feet ">hx?d0=z10k39.370079*.5+0k12~1/rn[ feet n[ inches">feet_.html" ;"title="hx?d0=z10k39.370079*.5+0k12~1/rn[ feet ">hx?d0=z10k39.370079*.5+0k12~1/rn[ feet n[ inches10Pdx]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.
Greatest common divisor
As an example, here is an implementation of the Euclidean algorithm
In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an e ...
to find the GCD:
dc -e '?? SarLa%d0sax+p' # shortest
dc -e ' =? =? SarLa%d0sax+ CD:p' # easier-to-read version
Factorial
Computing the factorial
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial:
\begin
n! &= n \times (n-1) \times (n-2) \ ...
of an input value,
dc -e '? Q 1=Qd1-lFx*sFxp'
Quines in dc
There exist also quines in the programming language dc; programs that produce its source code as output.
dc -e ' 1Pn[dx3Pn.html"_;"title="x.html"_;"title="1Pn[dx">1Pn[dx3Pn">x.html"_;"title="1Pn[dx">1Pn[dx3Pnx'
dc_-e_'[91PP93P[dx.html" ;"title="x">1Pn[dx3Pn.html" ;"title="x.html" ;"title="1Pn[dx">1Pn[dx3Pn">x.html" ;"title="1Pn[dx">1Pn[dx3Pnx'
dc -e '[91PP93P[dx">x">1Pn[dx3Pn.html" ;"title="x.html" ;"title="1Pn[dx">1Pn[dx3Pn">x.html" ;"title="1Pn[dx">1Pn[dx3Pnx'
dc -e '[91PP93P[dx]dx'
Printing all prime numbers
echo '2p3p l!d2+s!%0=@l!l^!<##[s/0ds^]s@ & dvs^3s!l#x0<&2+l.xs.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 l!d2+s!%0=@l!l^!<## *ds^@ & dvs^3s!l#x0<&2+l.xs.x' , dc
Integer factorization
dc -e ' =? 2 ip/dli%0=1dvsr12sid2%0=13sidvsr .">li%0=1lrli2+dsi!>.s.xd1<2'
This program was also written by Michel Charpentier.
There is a shorter
dc -e " =? fp/dlf%0=FdvsrF sfJdvsr2sf lf%0=Flfdd2%+1+sflrsMx"
and a faster solution (try with the 200-bit number (input 2 200^1-
)
dc -e " =? fp/dlf% 0=FdvsrFdvsr2sfd2%0=F3sfd3%0=F5sf M">lf%0=Flfd4+sflr>MN N">lf%0=Flfd2+sflr>NsMx Md1
Note that the latter can be sped up even more, if the access to a constant is replaced by a register access.
dc -e " =? fp/dlf%l0=FdvsrF2s2dvsr2sf4s4d2%0=F3sfd3%0=F5sf M">lf%l0=Flfdl4+sflr>MN N">lf%l0=Flfdl2+sflr>NsMx Md1
Calculating Pi
An implementation of the Chudnovsky algorithm
The Chudnovsky algorithm is a fast method for calculating the digits of , based on Ramanujan’s formulae. It was published by the Chudnovsky brothers in 1988.
It was used in the world record calculations of 2.7 trillion digits of in Decembe ...
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 ksslk3^16lkd12+sk*-lm*lhd1+sh3^/smlxlj*sxll545140134+dsllm*lxlnk/ls+dls!=PP3^sj7sn sk1ddshsxsm13591409dsllPx10005v426880*ls/K3-k1/pcln14+snlMxsMx'
Diffie–Hellman key exchange
A more complex example of dc use embedded in a Perl
Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it also referred to its redesigned "sister language", Perl 6, before the latter's name was offic ...
script performs a Diffie–Hellman key exchange
Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include:
* Diffie–Hellman–Merkle key exchange
* Diffie–Hellman key agreement
* Diffie–Hellman key establishment
* Diffie–Hellman key negotiation
* Exponential key exc ...
. This was popular as a signature block
A signature block (often abbreviated as signature, sig block, sig file, .sig, dot sig, siggy, or just sig) is a personalized block of text automatically appended at the bottom of an email message, Usenet article, or forum post.
Email and Usenet ...
among cypherpunk
A cypherpunk is any individual advocating widespread use of strong cryptography and privacy-enhancing technologies as a route to social and political change. Originally communicating through the Cypherpunks electronic mailing list, informal g ...
s during the ITAR
International Traffic in Arms Regulations (ITAR) is a United States regulatory regime to restrict and control the export of defense and military related technologies to safeguard U.S. national security and further U.S. foreign policy objective ...
debates, where the short script could be run with only Perl and dc, ubiquitous programs on Unix-like operating systems:
#!/usr/bin/perl -- -export-a-crypto-system-sig Diffie-Hellman-2-lines
($g, $e, $m) = @ARGV, $m , , die "$0 gen exp mod\n";
print `echo "16dio1 2%Sa2/d0X$e" g*EszlXx+p , dc`
A commented version is slightly easier to understand and shows how to use loops, conditionals, and the q
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/perl
my ($g, $e, $m) = map @ARGV;
die "$0 gen exp mod\n" unless $m;
print `echo $g $e $m , dc -e '
# Hex input and output
16dio
# Read m, e and g from stdin on one line
?SmSeSg
# Function z: return g * top of stack
g*z
# Function Q: remove the top of the stack and return 1
b1qQ
# 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 e0 (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%21
lm % # compute (g^e) % m
] SX
le # Load e from the register
lXx # compute g^e % m
p # Print the result
'`;
Environment Variables
If the environment variable DC_LINE_LENGTH exists and contains an integer that
is greater than 1 and less than , 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.
See also
* bc (programming language)
bc, for ''basic calculator'' (often referred to as ''bench calculator''), is "''an arbitrary-precision calculator language''" with syntax similar to the C programming language. bc is typically used as either a mathematical scripting language or ...
* Calculator input methods
There are various ways in which calculators interpret keystrokes. These can be categorized into two main types:
* On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate resul ...
* HP calculators
HP calculators are various calculators manufactured by the Hewlett-Packard company over the years.
Their desktop models included the HP 9800 series, while their handheld models started with the HP-35. Their focus has been on high-end scientif ...
* Stack machine
In computer science, computer engineering and programming language implementations, a stack machine is a computer processor or a virtual machine in which the primary interaction is moving short-lived temporary values to and from a push down ...
References
External links
* Packag
dc
in Debian GNU/Linux
Debian (), also known as Debian GNU/Linux, is a Linux distribution composed of free and open-source software, developed by the community-supported Debian Project, which was established by Ian Murdock on August 16, 1993. The first version of Deb ...
repositories
*
Native Windows port
of '' bc'', which includes dc.
dc embedded in a webpage
{{Unix commands
Cross-platform software
Unix software
Software calculators
Free mathematics software
Numerical programming languages
Stack-oriented programming languages
Plan 9 commands