.\" Licensed under the Gnu Public License, Version 2 .\" .\" $Id: ssystem.1.2 1996/06/30 13:33:54 bousch Exp $ .\" .TH ARIBAS 1 "February 2010" "ARIBAS" .SH NAME aribas \- Multiprecision Arithmetic Interpreter .SH SYNOPSIS .B aribas [\fIoptions\fR] [<\fIari-file\fR> [<\fIarg1\fR> <\fIarg2\fR> ...]] This man page was written for Debian since the original software did not contain a man page. .SH DESCRIPTION \fBAribas\fR 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. .\"--------------------------------------------------------- .SH USAGE The simplest way to use \fBaribas\fR is as a calculator for (big integer) arithmetic. After \fBaribas\fR is started, it displays a prompt .BR ==> 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 .nf ==> 123 + 456*789. .fi \fBAribas\fR answers .nf \-: 359907 .fi The symbol \fB\-:\fR introduces the result. .br .BR IMPORTANT. To mark the end of your input, you must always type a full stop '.' and then press RETURN. .br .PP You can assign the result of a calculation to a variable, as in .nf ==> F6 := 2**64 + 1. \-: 18446_74407_37095_51617 .fi This calculates the 6th Fermat number (\fB**\fR denotes exponentiation) and assigns it to the variable \fBF6\fR (note that \fBaribas\fR is case sensitive, so this is not the same as \fBf6\fR). Later you can use this variable for example in the expression .nf ==> 123**(F6 \- 1) mod F6. \-: 688_66214_58712_63971 .fi which shows (by Fermat's theorem) that F6 is not a prime number. .br The three most recent results are stored in the pseudo variables \fB_\fR, \fB__\fR, and \fB___\fR. For example you can store the last result in the variable x by the command .nf ==> x := _. \-: 688_66214_58712_63971 .fi As you can see in the above examples, \fBaribas\fR uses the underscore \fB_\fR 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: .nf ==> z := 123_4567_890. \-: 1234567890 .fi Here the output contains no underscore, which shows that z is less than 2**32. .P \fBAribas\fR has several built-in functions for factorization, for example \fIrho_factorize\fR, which uses Pollard's rho algorithm. .nf ==> rho_factorize(F6). working .. factor found after 512 iterations \-: 274177 .fi To find the remaining cofactor, give the command .nf ==> x := F6 div _. \-: 6728_04213_10721 .fi To test whether this factor is prime, Rabin's probabilistic test \fIrab_primetest\fR can be applied: .nf ==> rab_primetest(x). \-: true .fi The function \fIrho_factorize\fR 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 \fIqs_factorize\fR should be used .nf ==> qs_factorize(2**128+1). .fi (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.) .\"--------------------------------------------------------- .SS Control structures The \fIfor\fR loop and the \fIwhile\fR loop in \fBaribas\fR have a syntax as in Modula-2. For example, the following command sequence calculates the factorial of 100. .nf ==> x := 1; for i := 2 to 100 do x := x*i; end; x. .fi As you can see in this example, the input may extend over several lines. .P The above \fIfor\fR loop is equivalent to the following \fIwhile\fR loop .nf ==> x := 1; i := 2; while i <= 100 do x := x*i; inc(i); end; x. .fi .P The branching construct .br .B if .I ... .B then .I ... .B elsif .I ... .B else .I ... .B end .br has also the same syntax as in Modula-2. .\"--------------------------------------------------------- .SS Multiprecision floating point arithmetic \fBAribas\fR supports different types of floating point numbers which are internally represented with mantissas of different bit-length: .nf single_float 32 bits double_float 64 bits long_float 128 bits .fi and several higher precisions up to an implementation dependent limit, typically 1024 or 5120 bits, which can be determined by the function \fImax_floatprec()\fR. By default, when calculating with numbers of data type \fIreal\fR, 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 \fIset_floatprec\fR. 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 .nf ==> set_floatprec(100). \-: 128 .fi the floating point precision is 128 bits and you can calculate .nf ==> arctan(sqrt(3)). -: 1.04719_75511_96597_74615_42144_61093_16762_8 ==> _/pi. -: 0.33333_33333_33333_33333_33333_33333_33333_33 .fi .\"--------------------------------------------------------- .SS User defined functions The user can define his or her own functions. A typical example looks like .nf ==> 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. .fi If you have entered this correctly, \fBaribas\fR echoes the function name .nf \-: fac .fi and from now on you can use \fIfac\fR in the same way as a built-in function, e.g. .nf ==> fac(32). \-: 2_63130_83693_36935_30167_21801_21600_00000 .fi Note that inside function definitions all used variables must be explicitly declared, whereas on top level of the \fBaribas\fR interpreter variables can be simply created by assignments. Here is another example, which shows some other data types supported by \fBaribas\fR: .nf ==> 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. .fi This function returns an array of the square roots of the integers from 1 to n, for example .nf ==> sqrt_list(10). \-: (1.00000000, 1.41421356, 1.73205081, 2.00000000, 2.23606798, 2.44948974, 2.64575131, 2.82842712, 3.00000000, 3.16227766) .fi In a bigger programming project where you need several functions you would not enter them directly at the \fBaribas\fR prompt but prepare the function definitions with an external text editor and save them in a file with the extension \fB.ari\fR , for example \fBabcd.ari\fR . This file can then be loaded by \fBaribas\fR using the command .nf ==> load("abcd"). .fi If there is a syntax error in the file, you get an error message of the form .nf error in line <= 23 of loaded file if: end expected .fi which tells you (in this example) that there is an error in the \fBif\fR 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. .\"-------------------------------------------------------- .SS Online help The command .nf ==> symbols(aribas). .fi returns a list of all keywords and names of builtin functions of \fBaribas\fR. This list has about 200 entries, and begins and ends as follows: .P (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) .P For most of the symbols in this list, you can get a short online help using the function \fIhelp()\fR. For example, the command .nf ==> help(ARGV). .fi gives an information on the builtin variable \fIARGV\fR, whereas .nf ==> help(while). .fi describes the syntax of the \fIwhile\fR loop. If you need more information than that contained in the online help, consult the documentation which can be found in \fI/usr/share/doc/aribas\fR. .\"-------------------------------------------------------- .SS How to exit To end an \fBaribas\fR session, type \fIexit\fR at the \fBaribas\fR prompt .nf ==> exit .fi and then press the RETURN (ENTER) key. .P If you don't want to leave \fBaribas\fR, but want to break out of an infinite loop or a calculation that lasts too long, type CONTROL-C (if you are running \fBaribas\fR from within Emacs, you must press CONTROL-C twice). This will (in most cases) stop the current calculation and return to the \fBaribas\fR prompt. .P When you are not using the Emacs interface but the command line version of \fBaribas\fR, 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 '\fB.\fR' , followed by RETURN. You will get an error message which you can safely ignore, and a new prompt \fB==>\fR appears, allowing you to try again. .\"-------------------------------------------------------- .SH COMMAND LINE ARGUMENTS .PP .B aribas [\fIoptions\fR] [<\fIari-file\fR> [<\fIarg1\fR> <\fIarg2\fR> ...]] .SS options The following options are available: .TP .B \-q (quiet mode) Suppresses all messages to the screen (version no, copyright notice, etc.) when \fBaribas\fR is started .TP .B \-v (verbose mode, default) Does not suppress messages to the screen when \fBaribas\fR is started. .TP .B \-c \fBaribas\fR does its own line breaking when writing to the screen. Normally it supposes that the screen (or the window in which \fBaribas\fR 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 \fBaribas\fR in an Xterm window with 72 columns, use the option \-c72 (or \-c 72, the space between \-c and the number is optional). .TP .B \-m Here is a number (in decimal representation) between 500 and 32000. This number indicates how many Kilobytes of RAM \fBaribas\fR should use for the \fBaribas\fR heap. The default value depends on the options used when \fBaribas\fR was compiled. Typically, under UNIX or LINUX it is 6 Megabytes, corresponding to \-m6000 .TP .B \-h The online help of \fBaribas\fR 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 \fBaribas\fR it should not be necessary to use this option. .TP .B \-p With this option you can specify a search path for loading files with \fBaribas\fR source code. may be either the (absolute) pathname of one directory or several pathnames separated by colons. Suppose that you have called \fBaribas\fR 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. .TP .B \-b Batch mode when loading an \fBaribas\fR source code file from the command line, see below. .P One letter options which require no arguments may be merged, for example aribas \-q \-b is equivalent to aribas \-qb .\"--------------------------------------------------------- .SS Further command line arguments .TP .B The next command line argument after the options is interpreted as the name of a file with \fBaribas\fR source code. If the file name has the extension .ari, this extension may be omitted. The file is loaded as if the command \fIload("")\fR had been given after the start of \fBaribas\fR at the \fBaribas\fR 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 \fBaribas\fR exits without showing it's prompt. If the file cannot be loaded completely because of an error, \fBaribas\fR exits immediately after the error message. .TP .B ... When further command line arguments follow \fI\fR, they are collected (as strings) together with \fI\fR in the vector \fIARGV\fR which can be accessed from within \fBaribas\fR. Example: If you call \fBaribas\fR with the command line aribas startup 4536 eisenstein and the current directory contains the file startup.ari, then \fBaribas\fR loads it and the vector \fIARGV\fR has the form .nf ==> ARGV. \-: ("startup", "4536", "eisenstein") .fi If you need some arguments as numbers and not as strings, you can transform them by \fIatoi\fR (or \fIatof\fR); in our example .nf ==> x := atoi(ARGV[1]). \-: 4536 .fi will do it. The length of the vector \fIARGV\fR can be determined by \fIlength(ARGV)\fR. .\"------------------------------------------------------------- .SH RUNNING ARIBAS WITHIN EMACS You can run \fBaribas\fR from within Emacs by giving the command (in Emacs' minibuffer) .nf M-x run-aribas .fi (If you don't have a META key, use ESC x instead of M-x) Then \fBaribas\fR will be loaded into an Emacs window with name *aribas* and you can edit your input to \fBaribas\fR with the usual Emacs commands. .P If your input ends with a full stop '.' and you press RETURN, it is sent to \fBaribas\fR. If however your complete input does not end with a full stop, (for example in response to a \fIreadln\fR), the input is sent to \fBaribas\fR by C-j (Control-j) or C-c RETURN. .P 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. .P A Control-C is sent to \fBaribas\fR by C-c C-c (press C-c twice). .P It is also possible to start \fBaribas\fR from Emacs with command line arguments. For this purpose the command .nf C-u M-x run-aribas .fi has to be given. Then a prompt .nf run-aribas: aribas .fi appears in the Minibuffer of Emacs and you can complete the command line, for example .nf run-aribas: aribas startup 4536 eisenstein .fi (see above). .\"------------------------------------------------------------- .SH CONFIGURATION FILE Options for running \fBaribas\fR can be specified also using a configuration file with name \fB.arirc\fR. \fBAribas\fR 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 \fBARIRC\fR 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 \fBaribas\fR source code. For this purpose there must be a line reading .B \-init Then everything after this line is treated as \fBaribas\fR source code and executed when \fBaribas\fR is started. The existence of a configuration file for \fBaribas\fR 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 argument at the command line, then the \-init code is executed first and afterwards the is loaded and its code executed. .SH FILES .TP .B $ARIRC, .arirc, $HOME/.arirc Optional configuration file. .SH ENVIRONMENT VARIABLES .TP .B $ARIRC Location of the optional configuration file. .SH SEE ALSO .BR emacs (1) .P More information on how to use \fBaribas\fR can be found in \fI/usr/share/doc/aribas\fR. .P The \fBaribas\fR home page is http://www.mathematik.uni-muenchen.de/~forster/sw/aribas.html .\"------------------------------------------------------------- .SH BUGS Bug reports should be sent by email to forster@mathematik.uni-muenchen.de .SH AUTHOR Otto Forster is the author of the aribas program. This man page was compiled by Ralf Treinen from the aribas documentation for the Debian package of aribas, and supplemented by the author.