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//$Header: /cvsroot/esrg/sfesrg/esrgnxpj/sfnthcgi0304/subfunc_pfact_18.c,v 1.7 2003/07/01 03:46:58 dtashley Exp $
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//
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//********************************************************************************
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//Copyright (C) 2003 David T. Ashley
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//********************************************************************************
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//This program or source file is free software; you can redistribute it and/or
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//modify it under the terms of the GNU General Public License as published by
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//the Free Software Foundation; either version 2 of the License, or (at your
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//option) any later version.
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//
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//This program or source file is distributed in the hope that it will
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//be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
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//MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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//GNU General Public License for more details.
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//
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//You may have received a copy of the GNU General Public License
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//along with this program; if not, write to the Free Software
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//Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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//********************************************************************************
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//
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//This module attempts to factor an integer of up to 18 decimal
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//digits using a sieve method and subject to elapsed time constraints.
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//The constraint of "up to 18 digits"
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//is because that way trial divisors can stay in one unsigned
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//integer, which speeds the division. Additionally, there isn't
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//much use in trying to factor larger integers on a web page.
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//This subfunction is "parlor trivia" grade only.
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//
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//INPUT PARAMETERS
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//----------------
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//This subfunction accepts the following parameters, in order.
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//
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// (a) The number to factor.
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//
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// (b) The number of Miller-Rabin rounds to use when looking
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// at the probable primality of the original argument or of
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// residues.
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//
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// (c) The maximum time that should be allowed to elapse before the
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// program terminates (perhaps without finding factors).
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// This constraint is to protect the server capacity. (In the long
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// term, however, the web page may need to be removed--if too many
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// people use it, it will bring any server to a crawl.)
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//
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//OUTPUT RESULTS
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//--------------
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//The notation below gives the outputs of the program. In some cases, [i] notation
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//is used to indicate line numbers.
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//
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//[01] An overall success or failure code for the operation. Valid responses
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// are:
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// S : Success (for this subfunction, the only possible outcome).
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//
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//[02] The fully normalized first integer entered. This means it has been
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// stripped of all weird characters, etc., and also perhaps assigned
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// a default value if the original parameter wasn't acceptable.
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// This can be used by the PHP script to repopulate form boxes.
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//[03] The fully normalized second integer entered.
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//[04] The fully normalized second integer entered.
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//[05] The type of factor specified on the next line.
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// Possibilities are:
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// "P" : The factor is definitely prime.
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// "C" : The factor is definitely composite.
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// "p" : The factor is probably prime, established by
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// Miller-Rabin.
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//
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// Note that the "C" code can only appear if the utility has to give
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// up because it runs out of allowed time. This means that the input
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// number has not been fully factored or perhaps not factored at all.
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// The "C" code can only appear for the last factor or the only factor.
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//
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// The "p" code can also only appear for the last factor. This occurs when
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// either the original input argument is prime as established by
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// Miller-Rabin or else a division leaves a result that is similarly
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// established by Miller-Rabin.
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//[06] The factor itself.
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//[07] Its multiplicity.
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//[..] Lines 5-7 are repeated for as many factors as are located.
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//[..] The second-to-last line will contain "X".
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//[..] The last line will contain an "S".
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//
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//Note the following:
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// (a) Any valid output will contain at least 9 lines.
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// (b) Any valid output will have a number of lines divisible by 3.
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// (c) The number of factors found is (nlines - 6)/3 or alternately
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// nlines/3 - 2.
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// (d) What happened can be determined using the number of lines plus
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// the code of the last factor.
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//
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//The return value (exit code) from this subfunction is always 0.
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//
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#define MODULE_SUBFUNC_PFACT_18
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#include <assert.h>
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#include <ctype.h>
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#include <stddef.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <time.h>
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#include <gmp.h>
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#include "auxfuncs.h"
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#include "subfunc_pfact_18.h"
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#include "sieve_eratosthenes.h"
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int SUBFUNC_PFACT_18_main(int argc, char *argv[])
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{
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//The time snapshot against which we compare to see if we're over
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//time budget.
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time_t time_snapshot;
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//Normalized first and second parameters (the integers).
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char *arg1;
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char *arg2;
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char *arg3;
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//Number of Miller-Rabin iterations to establish probable primality.
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int miller_rabin_iterations;
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//Maximum elapsed time allowed.
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int max_time;
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//Temporary iteration integers.
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int i;
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//Mask counter. Only check for timeout periodically, as calling the OS to get time
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//is presumed expensive.
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int mask_counter;
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//The current trial divisor.
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unsigned long trial_divisor, new_trial_divisor;
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//The current sieve table index.
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int sieve_table_index;
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//An exit flag kept to remember if we should bail the loop.
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int exit_flag;
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//The number to factor.
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mpz_t number_to_factor;
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//The square root limit. We only need to go that far.
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mpz_t square_root_limit;
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//The multiplicity of any factors we find.
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int multiplicity;
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//Initialize all of the GMP variables.
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mpz_init(number_to_factor);
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mpz_init(square_root_limit);
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//Grab a time snapshot.
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time_snapshot = time(NULL);
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//There must be an acceptable number of command-line arguments. If not,
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//abort the progam with phony data.
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if (argc != 5)
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{
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printf("S\n2\n25\n2\nC\n2\n2\nX\nS\n");
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return(0);
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}
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//Copy the command-line arguments to a safe place where we can manipulate them.
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//Leave 2 characters of space in case we assign a "0".
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arg1 = (char *)malloc((AUXFUNCS_size_t_max(1, strlen(argv[2])) + 1) * sizeof(char));
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arg2 = (char *)malloc((AUXFUNCS_size_t_max(1, strlen(argv[3])) + 1) * sizeof(char));
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arg3 = (char *)malloc((AUXFUNCS_size_t_max(1, strlen(argv[4])) + 1) * sizeof(char));
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if ((arg1 == NULL) || (arg2 == NULL) || (arg3 == NULL))
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{
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printf("S\n2\n25\n2\nC\n2\n2\nX\nS\n");
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return(0);
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}
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strcpy(arg1, argv[2]);
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strcpy(arg2, argv[3]);
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strcpy(arg3, argv[4]);
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//Strip all of the non-digit trash out of the arguments.
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AUXFUNCS_remove_non_digits(arg1);
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AUXFUNCS_remove_non_digits(arg2);
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AUXFUNCS_remove_non_digits(arg3);
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//Remove all leading zeros from arguments.
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AUXFUNCS_remove_leading_zeros(arg1);
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AUXFUNCS_remove_leading_zeros(arg2);
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AUXFUNCS_remove_leading_zeros(arg3);
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//If an argument is zero length, fill it in with 0.
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if (!strlen(arg1))
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strcpy(arg1, "0");
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if (!strlen(arg2))
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strcpy(arg2, "0");
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if (!strlen(arg3))
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strcpy(arg3, "0");
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//We are not allowed to have 0's in this function, so
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//abort on zeros. Also, we can't have 1 for a number to check,
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//as 1 can't be factored.
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if ((!strcmp(arg1, "0")) || (!strcmp(arg2, "0")) || (!strcmp(arg3, "0")) || (!strcmp(arg1, "1")))
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{
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printf("S\n2\n25\n2\nC\n2\n2\nX\nS\n");
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return(0);
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}
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//If the number to factor exceeds 18 digits, abort. Anything that has
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//18 or fewer digits is allowed.
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if (strlen(arg1) >18)
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{
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printf("S\n2\n25\n2\nC\n2\n2\nX\nS\n");
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return(0);
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}
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//Assign the number to factor. This is definitely a
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//GMP type.
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mpz_set_str(number_to_factor, arg1, 10);
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//Assign the number of Miller-Rabin repetitons to use, subject to an
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//absolute maximum of 1000 and minimum of 1.
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miller_rabin_iterations = 25;
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if (strlen(arg2) > 3)
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{
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miller_rabin_iterations = 1000;
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}
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else
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{
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sscanf(arg2, "%d", &miller_rabin_iterations);
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if (miller_rabin_iterations < 1)
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miller_rabin_iterations = 1;
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}
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//Assign the maximum time allowed, subject to a maximum of 1000 and minimum of 3.
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if (strlen(arg3) > 3)
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{
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max_time = 1000;
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}
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else
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{
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sscanf(arg3, "%d", &max_time);
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if (max_time < 3)
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max_time = 3;
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}
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//Output the header information before beginning the search.
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printf("S\n");
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mpz_out_str(stdout, 10, number_to_factor);
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printf("\n");
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printf("%d\n", miller_rabin_iterations);
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printf("%d\n", max_time);
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//Loop through the list of divisors we should try before starting the sieve.
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//This won't possibly exceed our time, so do it.
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for (i=0; i<SIEVE_ERATOSTHENES_N_SIEVE_FACTORS; i++)
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{
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multiplicity = 0;
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//printf("Trial divisor: %d\n", SIEVE_ERATOSTHENES_sieve_factors[i]);
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//Factor out all occurrences that we can.
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while (mpz_divisible_ui_p(number_to_factor, SIEVE_ERATOSTHENES_sieve_factors[i]))
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{
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mpz_divexact_ui(number_to_factor, number_to_factor, SIEVE_ERATOSTHENES_sieve_factors[i]);
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multiplicity++;
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}
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//Now output the information record to the stdout if we could factor it.
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if (multiplicity)
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{
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printf("P\n");
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printf("%u\n", SIEVE_ERATOSTHENES_sieve_factors[i]);
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printf("%d\n", multiplicity);
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}
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}
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//Gear up for tabulated operation as we sieve.
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new_trial_divisor = trial_divisor = SIEVE_ERATOSTHENES_FIRST_TRIAL_DIVISOR;
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sieve_table_index = SIEVE_ERATOSTHENES_FIRST_SIEVE_INDEX;
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mask_counter = 0;
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//Set the exit flag initially. One thing that could have
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//caused us to be ready to exit already is if we brought the
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//number to factor down to 1. We check this now because
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//otherwise only check it when have factored something out and
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//seive loop would run indefinitely if didn't do this.
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exit_flag = 0;
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if (!mpz_cmp_ui(number_to_factor, 1))
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exit_flag = 1;
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//Effectively, we may have broken down the number to factor
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//with just a few operations. So, effectively, we are
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//starting afresh here. We only need to proceed to the
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//square root of the current number to factor (not the
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//original one.
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mpz_sqrt(square_root_limit, number_to_factor);
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//If the last value from the numbers to try before we start
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//the sieve is already past the square root limit, then whatever
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//remains is definitely prime, and we can exit.
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if (mpz_cmp_ui(square_root_limit, SIEVE_ERATOSTHENES_sieve_factors[SIEVE_ERATOSTHENES_N_SIEVE_FACTORS - 1]) <= 0)
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{
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| 303 |
if (mpz_cmp_ui(number_to_factor, 1))
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{
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exit_flag = 1;
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printf("P\n");
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mpz_out_str(stdout, 10, number_to_factor);
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printf("\n");
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printf("1\n");
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goto done;
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}
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}
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//If Miller-Rabin says that the remaining number is probably prime, that is good
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//enough.
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if (mpz_probab_prime_p(number_to_factor, miller_rabin_iterations) == 1)
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{
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exit_flag = 1;
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printf("p\n");
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mpz_out_str(stdout, 10, number_to_factor);
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printf("\n");
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printf("1\n");
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goto done;
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}
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//Loop entry condition.
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multiplicity = 0;
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| 328 |
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//This is the main loop. We only check for elapsed time
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//infrequently.
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| 331 |
while (!exit_flag)
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{
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//Replace the trial divisor.
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trial_divisor = new_trial_divisor;
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| 336 |
//printf("Trial divisor: %d\n", trial_divisor);
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| 337 |
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| 338 |
//Factor out all occurrences that we can of the trial divisor, if we can.
|
| 339 |
while (mpz_divisible_ui_p(number_to_factor, trial_divisor))
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| 340 |
{
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| 341 |
mpz_divexact_ui(number_to_factor, number_to_factor, trial_divisor);
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| 342 |
multiplicity++;
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| 343 |
}
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| 344 |
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| 345 |
//Now output the information record to the stdout if we could factor it.
|
| 346 |
if (multiplicity)
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| 347 |
{
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| 348 |
printf("P\n");
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| 349 |
printf("%u\n", trial_divisor);
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| 350 |
printf("%d\n", multiplicity);
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| 351 |
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| 352 |
//We need to calculate a new square root bound.
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| 353 |
mpz_sqrt(square_root_limit, number_to_factor);
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| 354 |
|
| 355 |
//If we are over the square root bound, the remaining number to factor
|
| 356 |
//is prime and we should exit.
|
| 357 |
if (mpz_cmp_ui(square_root_limit, trial_divisor) <= 0)
|
| 358 |
exit_flag = 1;
|
| 359 |
|
| 360 |
//Are we over the time bound? We might has well check here,
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| 361 |
//because finding prime factors is rare.
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| 362 |
if ((time(NULL) - time_snapshot) > max_time)
|
| 363 |
exit_flag = 1;
|
| 364 |
|
| 365 |
//Does the Miller-Rabin test say that the remaining number
|
| 366 |
//is with near perfect certainty prime?
|
| 367 |
if (mpz_probab_prime_p(number_to_factor, miller_rabin_iterations) >= 1)
|
| 368 |
exit_flag = 1;
|
| 369 |
|
| 370 |
//Is the remaining number "1", indicating we've factored it fully?
|
| 371 |
if (!mpz_cmp_ui(number_to_factor, 1))
|
| 372 |
exit_flag = 1;
|
| 373 |
|
| 374 |
//Set multiplicity to zero again so don't re-enter until successful
|
| 375 |
//division again.
|
| 376 |
multiplicity = 0;
|
| 377 |
}
|
| 378 |
|
| 379 |
//Advance to our next trial divisor.
|
| 380 |
new_trial_divisor = trial_divisor + SIEVE_ERATOSTHENES_sieve[sieve_table_index];
|
| 381 |
|
| 382 |
//If the new is < the old, we've rolled over. This means an exit is necessary.
|
| 383 |
if (new_trial_divisor < trial_divisor)
|
| 384 |
exit_flag = 1;
|
| 385 |
|
| 386 |
//Advance the sieve index.
|
| 387 |
sieve_table_index = (sieve_table_index + 1) % SIEVE_ERATOSTHENES_N_SIEVE;
|
| 388 |
|
| 389 |
//This is our only chance to check for termination conditions that
|
| 390 |
//don't come about from a successful division. But we don't do
|
| 391 |
//this often.
|
| 392 |
mask_counter++;
|
| 393 |
if (!(mask_counter & 0xFFFFF))
|
| 394 |
{
|
| 395 |
//First, have we exceeded the square root bound?
|
| 396 |
if (mpz_cmp_ui(square_root_limit, trial_divisor) <= 0)
|
| 397 |
exit_flag = 1;
|
| 398 |
//Second, are we over the time budget?
|
| 399 |
if ((time(NULL) - time_snapshot) > max_time)
|
| 400 |
exit_flag = 1;
|
| 401 |
}
|
| 402 |
}
|
| 403 |
|
| 404 |
//If we've made it out of the loop, there are a variety of reasons for that.
|
| 405 |
//Find the right one and close up.
|
| 406 |
if (!mpz_cmp_ui(number_to_factor, 1))
|
| 407 |
{
|
| 408 |
//We divided the number down to 1. There is nothing further to do.
|
| 409 |
}
|
| 410 |
else if (mpz_cmp_ui(square_root_limit, trial_divisor) <= 0)
|
| 411 |
{
|
| 412 |
//We are at or over the square root limit. The remaining number is definitely prime.
|
| 413 |
printf("P\n");
|
| 414 |
mpz_out_str(stdout, 10, number_to_factor);
|
| 415 |
printf("\n");
|
| 416 |
printf("1\n");
|
| 417 |
}
|
| 418 |
else if (mpz_probab_prime_p(number_to_factor, miller_rabin_iterations) == 0)
|
| 419 |
{
|
| 420 |
//Miller-Rabin says the remaining number is definitely composite.
|
| 421 |
printf("C\n");
|
| 422 |
mpz_out_str(stdout, 10, number_to_factor);
|
| 423 |
printf("\n");
|
| 424 |
printf("1\n");
|
| 425 |
}
|
| 426 |
else if (mpz_probab_prime_p(number_to_factor, miller_rabin_iterations) == 1)
|
| 427 |
{
|
| 428 |
//Miller-Rabin says the remaining number is probably prime.
|
| 429 |
printf("p\n");
|
| 430 |
mpz_out_str(stdout, 10, number_to_factor);
|
| 431 |
printf("\n");
|
| 432 |
printf("1\n");
|
| 433 |
}
|
| 434 |
else if (mpz_probab_prime_p(number_to_factor, miller_rabin_iterations) == 2)
|
| 435 |
{
|
| 436 |
//Miller-Rabin says the remaining number is definitely prime.
|
| 437 |
printf("P\n");
|
| 438 |
mpz_out_str(stdout, 10, number_to_factor);
|
| 439 |
printf("\n");
|
| 440 |
printf("1\n");
|
| 441 |
}
|
| 442 |
|
| 443 |
//Output the invariant footer information.
|
| 444 |
done:
|
| 445 |
printf("X\n");
|
| 446 |
printf("S\n");
|
| 447 |
|
| 448 |
//Always return 0.
|
| 449 |
return(0);
|
| 450 |
}
|
| 451 |
|
| 452 |
//********************************************************************************
|
| 453 |
// $Log: subfunc_pfact_18.c,v $
|
| 454 |
// Revision 1.7 2003/07/01 03:46:58 dtashley
|
| 455 |
// Edits towards working continued fraction best rational approximation
|
| 456 |
// functionality.
|
| 457 |
//
|
| 458 |
// Revision 1.6 2003/04/17 20:02:05 dtashley
|
| 459 |
// License text for the GPL added. All source files are now under the GPL,
|
| 460 |
// after some discussion on the GMP list.
|
| 461 |
//
|
| 462 |
// Revision 1.5 2003/04/16 07:22:37 dtashley
|
| 463 |
// All checks completed.
|
| 464 |
//
|
| 465 |
// Revision 1.4 2003/04/16 07:02:06 dtashley
|
| 466 |
// Spelling of Greek name corrected to Eratosthenes from incorrect Erastothenes.
|
| 467 |
//
|
| 468 |
// Revision 1.3 2003/04/16 06:49:21 dtashley
|
| 469 |
// Edits.
|
| 470 |
//
|
| 471 |
// Revision 1.2 2003/04/16 03:25:15 dtashley
|
| 472 |
// Seems to be working correctly. Only a careful proofreading and some
|
| 473 |
// testing remain.
|
| 474 |
//
|
| 475 |
// Revision 1.1 2003/04/15 23:54:58 dtashley
|
| 476 |
// Initial checkin.
|
| 477 |
//********************************************************************************
|
| 478 |
// End of SUBFUNC_PFACT_18.C.
|
| 479 |
//********************************************************************************
|
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