NAME
aribas - Multiprecision Arithmetic Interpreter
SYNOPSIS
aribas [options] [<ari-file> [<arg1> <arg2> ...]]
This man page was written for Debian since the orginal software did not
contain a man page.
DESCRIPTION
Aribas is an interactive interpreter suitable for big integer
arithmetic and multiprecision floating point arithmetic. It has a
syntax similar to Pascal or Modula-2, but contains also features from
other programming languages like C, Lisp, Oberon.
USAGE
The simplest way to use aribas is as a calculator for (big integer)
arithmetic. After aribas is started, it displays a prompt ==> and is
ready to accept input. Simply enter the expression you want to
calculate, followed by a full stop, and then press RETURN, for example
==> 123 + 456*789.
Aribas answers
-: 359907
The symbol -: introduces the result.
IMPORTANT. To mark the end of your input, you must always type a full
stop ’.’ and then press RETURN.
You can assign the result of a calculation to a variable, as in
==> F6 := 2**64 + 1.
-: 18446_74407_37095_51617
This calculates the 6th Fermat number (** denotes exponentiation) and
assigns it to the variable F6 (note that aribas is case sensitive, so
this is not the same as f6). Later you can use this variable for
example in the expression
==> 123**(F6 - 1) mod F6.
-: 688_66214_58712_63971
which shows (by Fermat’s theorem) that F6 is not a prime number.
The three most recent results are stored in the pseudo variables _, __,
and ___. For example you can store the last result in the variable x by
the command
==> x := _.
-: 688_66214_58712_63971
As you can see in the above examples, aribas uses the underscore _ to
structure the output of big integers (>= 2**32). Also for input of
integers you may use the underscore, the only condition is that
immediately before and after the underscore there are digits, example:
==> z := 123_4567_890.
-: 1234567890
Here the output contains no underscore, which shows that z is less than
2**32.
Aribas has several built-in functions for factorization, for example
rho_factorize, which uses Pollard’s rho algorithm.
==> rho_factorize(F6).
working ..
factor found after 512 iterations
-: 274177
To find the remaining cofactor, give the command
==> x := F6 div _.
-: 6728_04213_10721
To test whether this factor is prime, Rabin’s probabilistic test
rab_primetest can be applied:
==> rab_primetest(x).
-: true
The function rho_factorize is good for finding small factors (say up to
10 decimal digits); for more complicated factorization tasks a more
powerful algorithm like the quadratic sieve qs_factorize should be used
==> qs_factorize(2**128+1).
(Depending on the power of your computer, it will take a few seconds up
to a few minutes to get a prime factor of the 7th Fermat number.)
Control structures
The for loop and the while loop in aribas have a syntax as in Modula-2.
For example, the following command sequence calculates the factorial of
100.
==> x := 1;
for i := 2 to 100 do
x := x*i;
end;
x.
As you can see in this example, the input may extend over several
lines.
The above for loop is equivalent to the following while loop
==> x := 1; i := 2;
while i <= 100 do
x := x*i;
inc(i);
end;
x.
The branching construct
if ... then ... elsif ... else ... end
has also the same syntax as in Modula-2.
Multiprecision floating point arithmetic
Aribas supports different types of floating point numbers which are
internally represented with mantissas of different bit-length:
single_float 32 bits
double_float 64 bits
long_float 128 bits
and several higher precisions up to an implementation dependent limit,
typically 1024 or 5120 bits, which can be determined by the function
max_floatprec(). By default, when calculating with numbers of data type
real, single_floats are used. This corresponds to a precision of 9 to
10 decimal places. A precision of 5120 bits corresponds to over 1500
decimal places.
The precision can be changed using the function set_floatprec. The
function takes one integer argument, which is the desired precision in
bits. It is automatically rounded to the next higher available value.
For example, after
==> set_floatprec(100).
-: 128
the floating point precision is 128 bits and you can calculate
==> arctan(sqrt(3)).
-: 1.04719_75511_96597_74615_42144_61093_16762_8
==> _/pi.
-: 0.33333_33333_33333_33333_33333_33333_33333_33
User defined functions
The user can define his or her own functions. A typical example looks
like
==> function fac(n: integer): integer;
var
x,i: integer;
begin
x := 1;
for i := 2 to n do
x := x*i;
end;
return x;
end.
If you have entered this correctly, aribas echoes the function name
-: fac
and from now on you can use fac in the same way as a built-in function,
e.g.
==> fac(32).
-: 2_63130_83693_36935_30167_21801_21600_00000
Note that inside function definitions all used variables must be
explicitly declared, whereas on top level of the aribas interpreter
variables can be simply created by assignments. Here is another
example, which shows some other data types supported by aribas:
==> function sqrt_list(n: integer): array of real;
var
vec: array[n] of real;
i: integer;
begin
for i := 1 to n do
vec[i-1] := sqrt(i);
end;
return vec;
end.
This function returns an array of the square roots of the integers from
1 to n, for example
==> sqrt_list(10).
-: (1.00000000, 1.41421356, 1.73205081, 2.00000000,
2.23606798, 2.44948974, 2.64575131, 2.82842712, 3.00000000,
3.16227766)
In a bigger programming project where you need several functions you
would not enter them directly at the aribas prompt but prepare the
function definitions with an external text editor and save them in a
file with the extension .ari , for example abcd.ari . This file can
then be loaded by aribas using the command
==> load("abcd").
If there is a syntax error in the file, you get an error message of the
form
error in line <= 23 of loaded file
if: end expected
which tells you (in this example) that there is an error in the if
construct in line 23 or earlier in the file. (Note that the error
messages are sometimes not very precise.) You can then correct the
error and load the file again.
Online help
The command
==> symbols(aribas).
returns a list of all keywords and names of builtin functions of
aribas. This list has about 200 entries, and begins and ends as
follows:
(ARGV, _, __, ___, abs, alloc, and, arccos, arcsin, arctan, arctan2,
aribas, array, atof, atoi, begin, binary, bit_and, bit_clear,
bit_length, ...... , tolower, toupper, transcript, true, trunc, type,
user, var, version, while, write, write_block, write_byte, writeln)
For most of the symbols in this list, you can get a short online help
using the function help(). For example, the command
==> help(ARGV).
gives an information on the builtin variable ARGV, whereas
==> help(while).
describes the syntax of the while loop. If you need more information
than that contained in the online help, consult the documentation which
can be found in /usr/share/doc/aribas.
How to exit
To end an aribas session, type exit at the aribas prompt
==> exit
and then press the RETURN (ENTER) key.
If you don’t want to leave aribas, but want to break out of an infinite
loop or a calculation that lasts too long, type CONTROL-C (if you are
running aribas from within Emacs, you must press CONTROL-C twice). This
will (in most cases) stop the current calculation and return to the
aribas prompt.
When you are not using the Emacs interface but the command line version
of aribas, you sometimes get into the following situation: Some
previous line contains a typing error, but you cannot return to that
line to correct it. In this case you should simply type a full stop
’.’ , followed by RETURN. You will get an error message which you can
safely ignore, and a new prompt ==> appears, allowing you to try again.
COMMAND LINE ARGUMENTS
aribas [options] [<ari-file> [<arg1> <arg2> ...]]
options
The following options are available:
-q (quiet mode) Suppresses all messages to the screen (version no,
copyright notice, etc.) when aribas is started
-v (verbose mode, default) Does not suppress messages to the screen
when aribas is started.
-c <cols>
aribas does its own line breaking when writing to the screen.
Normally it supposes that the screen (or the window in which
aribas runs) has 80 columns. With the -c option you can set
another number, which must be between 40 and 160 (in decimal
representation). For example, if you run aribas in an Xterm
window with 72 columns, use the option -c72 (or -c 72, the space
between -c and the number is optional).
-m <mem>
Here <mem> is a number (in decimal representation) between 500
and 32000. This number indicates how many Kilobytes of RAM
aribas should use for the aribas heap. The default value depends
on the options used when aribas was compiled. Typically, under
UNIX or LINUX it is 6 Megabytes, corresponding to -m6000
-h <path of help file>
The online help of aribas depends on a file aribas.hlp which
should be situated in the range of the environment variable
PATH. If this is not the case you can specify the exact path of
the help file with the -h option. If for example the file
aribas.hlp is in the directory /usr/local/lib, use the option -h
/usr/local/lib (the space after -h is not necessary). The -h
option can also be used if the help file has a different name.
If the help file is named help-aribas and lies in the directory
/home/joe/ari, use -h/home/joe/ari/help-aribas.
With a properly installed Debian package of aribas it should not
be necessary to use this option.
-p <ari-search-path>
With this option you can specify a search path for loading files
with aribas source code. <ari-search-path> may be either the
(absolute) pathname of one directory or several pathnames
separated by colons. Suppose that you have called aribas with
the option
-p/usr/local/lib/aribas:~/ari/examples
and that your home directory is /home/alice/. Then the command
==> load("factor").
will search the file factor.ari first in the current directory,
then in the directory /usr/local/lib/aribas and finally in
/home/alice/ari/examples.
-b Batch mode when loading an aribas source code file from the
command line, see below.
One letter options which require no arguments may be merged, for
example
aribas -q -b
is equivalent to
aribas -qb
Further command line arguments
<ari-file>
The next command line argument after the options is interpreted
as the name of a file with aribas source code. If the file name
has the extension .ari, this extension may be omitted. The file
is loaded as if the command load("<ari-file>") had been given
after the start of aribas at the aribas prompt. If the file is
not found in the current directory it is searched in the
directories specified by the -p option. If the option -b was
given, the file is loaded and executed. Afterwards aribas exits
without showing it’s prompt. If the file cannot be loaded
completely because of an error, aribas exits immediately after
the error message.
<arg1> <arg2> ...
When further command line arguments follow <ari-file>, they are
collected (as strings) together with <ari-file> in the vector
ARGV which can be accessed from within aribas. Example: If you
call aribas with the command line
aribas startup 4536 eisenstein
and the current directory contains the file startup.ari, then
aribas loads it and the vector ARGV has the form
==> ARGV.
-: ("startup", "4536", "eisenstein")
If you need some arguments as numbers and not as strings, you
can transform them by atoi (or atof); in our example
==> x := atoi(ARGV[1]).
-: 4536
will do it. The length of the vector ARGV can be determined by
length(ARGV).
RUNNING ARIBAS WITHIN EMACS
You can run aribas from within Emacs by giving the command (in Emacs’
minibuffer)
M-x run-aribas
(If you don’t have a META key, use ESC x instead of M-x) Then aribas
will be loaded into an Emacs window with name *aribas* and you can edit
your input to aribas with the usual Emacs commands.
If your input ends with a full stop ’.’ and you press RETURN, it is
sent to aribas. If however your complete input does not end with a
full stop, (for example in response to a readln), the input is sent to
aribas by C-j (Control-j) or C-c RETURN.
If you want to repeat a previous input, M-p (or ESC p) cycles backward
through input history, and M-n (or ESC n) cycles forward.
A Control-C is sent to aribas by C-c C-c (press C-c twice).
It is also possible to start aribas from Emacs with command line
arguments. For this purpose the command
C-u M-x run-aribas
has to be given. Then a prompt
run-aribas: aribas
appears in the Minibuffer of Emacs and you can complete the command
line, for example
run-aribas: aribas startup 4536 eisenstein
(see above).
CONFIGURATION FILE
Options for running aribas can be specified also using a configuration
file with name .arirc. Aribas searches for a configuration file in the
following order:
1) the current directory
2) the home directory of the user
There is a third possibility: You can define an environment variable
ARIRC containing the name of the configuration file (which may be
different from .arirc), including the full path.
In the configuration file you can specify all command line options
described above which begin with a - sign, however a separate line must
be used for every single option. Lines beginning with the character #
or empty lines are ignored. In addition to the options described
above, the configuration file may contain aribas source code. For this
purpose there must be a line reading
-init
Then everything after this line is treated as aribas source code and
executed when aribas is started.
The existence of a configuration file for aribas does not exclude the
possibility to give command line arguments. If an option (e.g. the -m
option) is specified both in the configuration file and the command
line but with different values, then the specification at the command
line is valid. Analogously, a -v option on the command line overrides a
-q option in the configuration file. If there is -init code in the
configuration file and an <ari-file> argument at the command line, then
the -init code is executed first and afterwards the <ari-file> is
loaded and its code executed.
FILES
$ARIRC, .arirc, $HOME/.arirc
Optional configuration file.
ENVIRONMENT VARIABLES
$ARIRC Location of the optional configuration file.
SEE ALSO
emacs(1)
More information on how to use aribas can be found in
/usr/share/doc/aribas.
The aribas home page is
http://www.mathematik.uni-muenchen.de/~forster/sw/aribas.html
BUGS
Bug reports should be sent by email to
forster@mathematik.uni-muenchen.de
AUTHOR
Otto Forster <forster@mathematik.uni-muenchen.de> is the author of the
aribas program. This man page was compiled by Ralf Treinen
<treinen@debian.org> from the aribas documentation for the Debian
package of aribas, and supplemented by the author.