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@settitle DC, An Arbitrary Precision Calculator
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@ifinfo
This file documents DC, an arbitrary precision calculator.

Published by the Free Software Foundation,
675 Massachusetts Avenue,
Cambridge, MA 02139 USA

Copyright (C) 1984 Free Software Foundation, Inc.

Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
are preserved on all copies.

@ignore
Permission is granted to process this file through TeX and print the
results, provided the printed document carries copying permission
notice identical to this one except for the removal of this paragraph
(this paragraph not being relevant to the printed manual).

@end ignore
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the entire
resulting derived work is distributed under the terms of a permission
notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation approved
by the Foundation.
@end ifinfo

@setchapternewpage odd

@titlepage
@title DC, An Arbitrary Precision Calculator

@author by Richard Stallman
@page
@vskip 0pt plus 1filll
Copyright @copyright{} 1984 Free Software Foundation, Inc.

@sp 2
Published by the Free Software Foundation, @*
675 Massachusetts Avenue, @*
Cambridge, MA 02139 USA

Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
are preserved on all copies.

Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the entire
resulting derived work is distributed under the terms of a permission
notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation approved
by the Foundation.

@end titlepage
@page

@node Top, Introduction, (dir), (dir)

@menu
* Introduction::                Introduction
* Printing Commands::           Printing Commands
* Arithmetic::                  Arithmetic
* Stack Control::               Stack Control
* Registers::                   Registers
* Parameters::                  Parameters
* Strings::                     Strings
* Status Inquiry::              Status Inquiry
* Notes::                       Notes
@end menu

@node Introduction, Printing Commands, Top, Top
@comment  node-name,  next,  previous,  up
@chapter Introduction

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 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 output
is to standard output.

To exit, use @samp{q}.  @kbd{C-c} does not exit; it is used to abort
macros that are looping, etc.  (Currently this is not true; @kbd{C-c}
does exit.)

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 @samp{_}.  @samp{-} 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
newlines.  These have no meaning as commands.

@node Printing Commands, Arithmetic, Introduction, Top
@chapter Printing Commands

@table @samp
@item p
Prints the value on the top of the stack,
without altering the stack.  A newline is printed
after the value.

@item P
Prints the value on the top of the stack,
popping it off, and does not print a newline after.

@item f
Prints the entire contents of the stack
and the contents of all of the registers,
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.
@end table

@node Arithmetic, Stack Control, Printing Commands, Top
@chapter Arithmetic

@table @samp
@item +
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.

@item -
Pops two values, subtracts the first one popped
from the second one popped, and pushes the result.

@item *
Pops two values, multiplies them, and pushes the result.
The number of fraction digits in the result is controlled
by the current precision flag (see below) and does not
depend on the values being multiplied.

@item /
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 precision flag.

@item %
Pops two values, computes the remainder of the division
that the @samp{/} command would do, and pushes that.
The division is done with as many fraction digits
as the precision flag specifies, and the remainder
is also computed with that many fraction digits.

@item ^
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 flag specifies the number of fraction
digits in the result.

@item v
Pops one value, computes its square root, and pushes that.
The precision flag specifies the number of fraction digits
in the result.
@end table

Most arithmetic operations are affected by the "precision flag",
which you can set with the @samp{k} command.  The default precision
value is zero, which means that all arithmetic except for
addition and subtraction produces integer results.

The remainder operation (@samp{%}) requires some explanation: applied to
arguments @samp{a} and @samp{b} it produces @samp{a - (b * (a / b))},
where @samp{a / b} is computed in the current precision.

@node Stack Control, Registers, Arithmetic, Top
@chapter Stack Control

@table @samp
@item c
Clears the stack, rendering it empty.

@item d
Duplicates the value on the top of the stack,
pushing another copy of it.  Thus,
`4d*p' computes 4 squared and prints it.
@end table

@node Registers, Parameters, Stack Control, Top
@chapter Registers

DC provides 128 memory registers, each named by a single
ASCII character.  You can store a number in a register
and retrieve it later.

@table @samp
@item s@var{r}
Pop the value off the top of the stack and store
it into register @var{r}.

@item l@var{r}
Copy the value in register @var{r}, and push it onto
the stack.  This does not alter the contents of @var{r}.

Each register also contains its own stack.  The current
register value is the top of the register's stack.

@item S@var{r}
Pop the value off the top of the (main) stack and
push it onto the stack of register @var{r}.
The previous value of the register becomes inaccessible.

@item L@var{r}
Pop the value off the top of register @var{r}'s stack
and push it onto the main stack.  The previous value
in register @var{r}'s stack, if any, is now accessible
via the `l@var{r}' command.
@end table

The @samp{f} command prints a list of all registers that have contents
stored in them, together with their contents.  Only the
current contents of each register (the top of its stack)
is printed.

@node Parameters, Strings, Registers, Top
@chapter 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;
@emph{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.  Each radix must be between 2
and 36 inclusive.  The precision must be zero or greater.  The precision
is always measured in decimal digits, regardless of the current input or
output radix.

@table @samp
@item i
Pops the value off the top of the stack
and uses it to set the input radix.

@item o
@itemx k
Similarly set the output radix and the precision.

@item I
Pushes the current input radix on the stack.

@item O
@itemx K
Similarly push the current output radix and the current precision.
@end table

@node Strings, Status Inquiry, Parameters, Top
@chapter 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).
Both 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 @samp{p} command can accept either and prints the object
according to its type.

@table @samp
@item [@var{characters}]
Makes a string containing @var{characters} and pushes it
on the stack.  For example, @samp{[foo]P} prints the
characters @samp{foo} (with no newline).

@item 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, @samp{[1p]x} executes the macro @samp{1p}, which
pushes 1 on the stack and prints @samp{1} on a separate line.

Macros are most often stored in registers;
@samp{[1p]sa} stores a macro to print @samp{1} into register @samp{a},
and @samp{lax} invokes the macro.

@item >@var{r}
Pops two values off the stack and compares them
assuming they are numbers, executing the contents
of register @var{r} as a macro if the original top-of-stack
is greater.  Thus, @samp{1 2>a} will invoke register @samp{a}'s contents
and @samp{2 1>a} will not.

@item <@var{r}
Similar but invokes the macro if the original top-of-stack
is less.

@item =@var{r}
Similar but invokes the macro if the two numbers popped
are equal.  This can also be validly used to compare two
strings for equality.

@item ?
Reads a line from the terminal and executes it.
This command allows a macro to request input from the user.

@item q
During the execution of a macro, this comand
does not exit DC.  Instead, it exits from that
macro and also from the macro which invoked it (if any).

@item Q
Pops a value off the stack and uses it as a count
of levels of macro execution to be exited.  Thus,
@samp{3Q} exits three levels.
@end table

@node Status Inquiry, Notes, Strings, Top
@chapter Status Inquiry

@table @samp
@item 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.

@item 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 -1.

@item z
Pushes the current stack depth; the number of
objects on the stack before the execution of the @samp{z} command.

@item I
Pushes the current value of the input radix.

@item O
Pushes the current value of the output radix.

@item K
Pushes the current value of the precision.
@end table

@node Notes,  , Status Inquiry, Top
@chapter Notes

The @samp{:} and @samp{;} commands of the Unix DC program are
not supported, as the documentation does not say what they do.
The @samp{!} command is not supported, but will be supported
as soon as a library for executing a line as a command exists.

@contents
@bye