### NAME

dc – an arbitrary precision calculator

### SYNOPSIS

dc [-V] [–version] [-h] [–help] [-e scriptexpression] [–expression=scriptexpression] [-f scriptfile] [–file=scriptfile] [file …]

### DESCRIPTION

dc is a reverse-polish desk calculator which supports unlimited preci‐

sion arithmetic. It also allows you to define and call macros. Nor‐

mally dc reads from the standard input; if any command arguments are

given to it, they are filenames, and dc reads and executes the contents

of the files before reading from standard input. All normal output is

to standard output; all error output is to standard error.

A reverse-polish calculator stores numbers on a stack. Entering a num‐

ber pushes it on the stack. Arithmetic operations pop arguments off

the stack and push the results.

To enter a number in dc, type the digits (using upper case letters A

through F as “digits” when working with input bases greater than ten),

with an optional decimal point. Exponential notation is not supported.

To enter a negative number, begin the number with “_”. “-” cannot

be used for this, as it is a binary operator for subtraction instead.

To enter two numbers in succession, separate them with spaces or new‐

lines. These have no meaning as commands.

### OPTIONS

dc may be invoked with the following command-line options:

-V

–version

Print out the version of dc that is being run and a copyright

notice, then exit.

-h

–help Print a usage message briefly summarizing these command-line

options and the bug-reporting address, then exit.

-e script

–expression=script

Add the commands in script to the set of commands to be run

while processing the input.

-f script-file

–file=script-file

Add the commands contained in the file script-file to the set of

commands to be run while processing the input.

If any command-line parameters remain after processing the above, these

parameters are interpreted as the names of input files to be processed.

A file name of – refers to the standard input stream. The standard

input will processed if no script files or expressions are specified.

Printing Commands

p Prints the value on the top of the stack, without altering the

stack. A newline is printed after the value.

n Prints the value on the top of the stack, popping it off, and

does not print a newline after.

P Pops off the value on top of the stack. If it it a string, it

is simply printed without a trailing newline. Otherwise it is a

number, and the integer portion of its absolute value is printed

out as a “base (UCHAR_MAX+1)” byte stream. Assuming that

(UCHAR_MAX+1) is 256 (as it is on most machines with 8-bit

bytes), the sequence KSK0k1/_1Ss [ls*]Sxd0>x

[256~Ssd0

also accomplish this function. (Much of the complexity of the

above native-dc code is due to the ~ computing the characters

backwards, and the desire to ensure that all registers wind up

back in their original states.)

f Prints the entire contents of the stack without altering any‐

thing. This is a good command to use if you are lost or want to

figure out what the effect of some command has been.

Arithmetic

+ Pops two values off the stack, adds them, and pushes the result.

The precision of the result is determined only by the values of

the arguments, and is enough to be exact.

– Pops two values, subtracts the first one popped from the second

one popped, and pushes the result.

* Pops two values, multiplies them, and pushes the result. The

number of fraction digits in the result depends on the current

precision value and the number of fraction digits in the two

arguments.

/ Pops two values, divides the second one popped from the first

one popped, and pushes the result. The number of fraction dig‐

its is specified by the precision value.

% Pops two values, computes the remainder of the division that the

/ command would do, and pushes that. The value computed is the

same as that computed by the sequence Sd dld/ Ld*- .

~ Pops two values, divides the second one popped from the first

one popped. The quotient is pushed first, and the remainder is

pushed next. The number of fraction digits used in the division

is specified by the precision value. (The sequence SdSn lnld/

LnLd% could also accomplish this function, with slightly differ‐

ent error checking.)

^ Pops two values and exponentiates, using the first value popped

as the exponent and the second popped as the base. The fraction

part of the exponent is ignored. The precision value specifies

the number of fraction digits in the result.

| Pops three values and computes a modular exponentiation. The

first value popped is used as the reduction modulus; this value

must be a non-zero number, and should be an integer. The second

popped is used as the exponent; this value must be a non-nega‐

tive number, and any fractional part of this exponent will be

ignored. The third value popped is the base which gets exponen‐

tiated, which should be an integer. For small integers this is

like the sequence Sm^Lm%, but, unlike ^, this command will work

with arbitrarily large exponents.

v Pops one value, computes its square root, and pushes that. The

precision value specifies the number of fraction digits in the

result.

Most arithmetic operations are affected by the “precision value”,

which you can set with the k command. The default precision value is

zero, which means that all arithmetic except for addition and subtrac‐

tion produces integer results.

Stack Control

c Clears the stack, rendering it empty.

d Duplicates the value on the top of the stack, pushing another

copy of it. Thus, “4d*p” computes 4 squared and prints it.

r Reverses the order of (swaps) the top two values on the stack.

(This can also be accomplished with the sequence SaSbLaLb.)

Registers

dc provides at least 256 memory registers, each named by a single char‐

acter. You can store a number or a string in a register and retrieve

it later.

sr Pop the value off the top of the stack and store it into regis‐

ter r.

lr Copy the value in register r and push it onto the stack. This

does not alter the contents of r.

Each register also contains its own stack. The current register value

is the top of the register’s stack.

Sr Pop the value off the top of the (main) stack and push it onto

the stack of register r. The previous value of the register

becomes inaccessible.

Lr Pop the value off the top of register r’s stack and push it onto

the main stack. The previous value in register r’s stack, if

any, is now accessible via the lr command.

Parameters

dc has three parameters that control its operation: the precision, the

input radix, and the output radix. The precision specifies the number

of fraction digits to keep in the result of most arithmetic operations.

The input radix controls the interpretation of numbers typed in; all

numbers typed in use this radix. The output radix is used for printing

numbers.

The input and output radices are separate parameters; you can make them

unequal, which can be useful or confusing. The input radix must be

between 2 and 16 inclusive. The output radix must be at least 2. The

precision must be zero or greater. The precision is always measured in

decimal digits, regardless of the current input or output radix.

i Pops the value off the top of the stack and uses it to set the

input radix.

o Pops the value off the top of the stack and uses it to set the

output radix.

k Pops the value off the top of the stack and uses it to set the

precision.

I Pushes the current input radix on the stack.

O Pushes the current output radix on the stack.

K Pushes the current precision on the stack.

Strings

dc has a limited ability to operate on strings as well as on numbers;

the only things you can do with strings are print them and execute them

as macros (which means that the contents of the string are processed as

dc commands). All registers and the stack can hold strings, and dc

always knows whether any given object is a string or a number. Some

commands such as arithmetic operations demand numbers as arguments and

print errors if given strings. Other commands can accept either a num‐

ber or a string; for example, the p command can accept either and

prints the object according to its type.

[characters]
Makes a string containing characters (contained between balanced

[ and ] characters), and pushes it on the stack. For example,

[foo]P prints the characters foo (with no newline).

a The top-of-stack is popped. If it was a number, then the low-

order byte of this number is converted into a string and pushed

onto the stack. Otherwise the top-of-stack was a string, and

the first character of that string is pushed back.

x Pops a value off the stack and executes it as a macro. Normally

it should be a string; if it is a number, it is simply pushed

back onto the stack. For example, [1p]x executes the macro 1p

which pushes 1 on the stack and prints 1 on a separate line.

Macros are most often stored in registers; [1p]sa stores a macro to

print 1 into register a, and lax invokes this macro.

>r Pops two values off the stack and compares them assuming they

are numbers, executing the contents of register r as a macro if

the original top-of-stack is greater. Thus, 1 2>a will invoke

register a’s contents and 2 1>a will not.

!>r Similar but invokes the macro if the original top-of-stack is

not greater than (less than or equal to) what was the second-to-

top.

you want to run a command starting with <, =, or > you will need

to add a space after the !.

# Will interpret the rest of the line as a comment.

:r Will pop the top two values off of the stack. The old second-

to-top value will be stored in the array r, indexed by the old

top-of-stack value.

;r Pops the top-of-stack and uses it as an index into the array r.

The selected value is then pushed onto the stack.

Note that each stacked instance of a register has its own array associ‐

ated with it. Thus 1 0:a 0Sa 2 0:a La 0;ap will print 1, because the 2

was stored in an instance of 0:a that was later popped.

FILES

~/.dcrc The commands in this file will be executed when dc is

first run.

### BUGS

Email bug reports to bug-dc@gnu.org.

GNU Project 2006-06-11 dc