DC(1)DC(1)NAMEdc - an arbitrary precision calculator
SYNOPSISdcDESCRIPTION
Dc is a reverse-polish desk calculator which supports
unlimited precision arithmetic. It also allows you to
define and call macros. Normally dc reads from the stan-
dard 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 stan-
dard error.
A reverse-polish calculator stores numbers on a stack.
Entering a number 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 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 succes-
sion, separate them with spaces or newlines. These have
no meaning as commands.
Printing Commands
p Prints the value on the top of the stack, without
altering the stack. A newline is printed after the
value.
P Prints the value on the top of the stack, popping
it off, and does not print a newline after.
f Prints the entire contents of the stack without
altering anything. 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 is controlled by the current precision value
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(see below) and does not depend on the values being
multiplied.
/ Pops two values, divides the second one popped from
the first one popped, and pushes the result. The
number of fraction digits is specified by the pre-
cision value.
% Pops two values, computes the remainder of the
division that the / command would do, and pushes
that. The division is done with as many fraction
digits as the precision value specifies, and the
remainder is also computed with that many fraction
digits.
~ 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 num-
ber of fraction digits used in the division is
specified by the precision value. (The sequence
SdSn lnld/ LnLd% could also accomplish this func-
tion, with slightly different 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 exponenti-
ation. 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-negative number, and any fractional part of
this exponent will be ignored. The third value
popped is the base which gets exponentiated. The
precision value specifies the number of fraction
digits in the result. For small numbers this is
like the sequence Sm lble^ Lm%, but, unlike ^, this
command will work with arbritrarily large expo-
nents.
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 subtraction produces
integer results.
The remainder operation % requires some explanation:
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applied to arguments ``a'' and ``b'' it produces ``a - (b
* (a / b))'', where ``a / b'' is computed in the current
precision.
Stack Control
c Clears the stack, rendering it empty.
d Duplicates the value on the top of the stack, push-
ing 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.
Registers
Dc provides 256 memory registers, each named by a single
character. You can store a number or a string in a regis-
ter and retrieve it later.
sr Pop the value off the top of the stack and store it
into register 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 36 inclusive. The
output radix must be at least 2. The precision must be
zero or greater. The precision is always measured in dec-
imal digits, regardless of the current input or output
radix.
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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 can 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 number 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 char-
acters 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 char-
acter 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-
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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 less.
=r Similar but invokes the macro if the two numbers
popped are equal.
? Reads a line from the terminal and executes it.
This command allows a macro to request input from
the user.
q exits from a macro and also from the macro which
invoked it. If called from the top level, or from
a macro which was called directly from the top
level, the q command will cause dc to exit.
Q Pops a value off the stack and uses it as a count
of levels of macro execution to be exited. Thus,
3Q exits three levels. The Q command will never
cause dc to exit.
Status Inquiry
Z Pops a value off the stack, calculates the number
of digits it has (or number of characters, if it is
a string) and pushes that number.
X Pops a value off the stack, calculates the number
of fraction digits it has, and pushes that number.
For a string, the value pushed is 0.
z Pushes the current stack depth; the number of
objects on the stack before the execution of the z
command.
Miscellaneous
! Will run the rest of the line as a system command.
# 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.
NOTES
The array operations : and ; are usually only used by tra-
ditional implementations of bc. (The GNU bc is self con-
tained and does not need dc to run.)
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DC(1)DC(1)BUGS
Email bug reports to bug-gnu-utils@prep.ai.mit.edu. Be
sure to include the word ``dc'' somewhere in the ``Sub-
ject:'' field.
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