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//$Header$ |
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//******************************************************************************** |
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//Copyright (c) 2003, 2018 David T. Ashley. |
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//******************************************************************************** |
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//This file is part of "arith_large_cgi", a program that is designed to be |
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//invoked by a PHP script as part of serving a web page that performs |
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//calculations involving large integers. (A secondary compiled program is |
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//used because a compiled program can perform certain calculation-intensive |
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//tasks far more efficiently than a PHP script.) This program is provided by |
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//David T. Ashley (dashley@gmail.com) under the MIT License (reproduced |
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//immediately below). |
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//******************************************************************************** |
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//Permission is hereby granted, free of charge, to any person obtaining a copy |
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//of this software and associated documentation files (the "Software"), to deal |
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//in the Software without restriction, including without limitation the rights |
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//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
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//copies of the Software, and to permit persons to whom the Software is |
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//furnished to do so, subject to the following conditions: |
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// |
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//The above copyright notice and this permission notice shall be included in all |
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//copies or substantial portions of the Software. |
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// |
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//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
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//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
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//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
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//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
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//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
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//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
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//SOFTWARE. |
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//******************************************************************************** |
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//This module is the GCD subfunction of a general-purpose CGI-BIN program to support |
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//number theory demonstration applications. |
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// |
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//INPUT PARAMETERS |
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//---------------- |
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//The subfunction accepts two parameters, the integers whose GCD is to be |
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//calculated. There is substantial tolerance for invalid characters. |
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//Naturally, the integers should be positive. |
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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. |
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// EP1A : The first integer could not be parsed, which means it is ill-formatted. |
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// EP1B : The first integer was zero or negative. |
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// EP2A : The second integer could not be parsed, which means it is ill-formatted. |
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// EP2B : The second integer was zero or negative. |
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// EQ : Other or unspecified error. |
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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. This can be used by the |
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// PHP script to repopulate the form boxes. |
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//[03] The fully normalized second integer entered. |
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// |
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//In the event that the status code indicates error, no further lines |
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//will be written. |
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// |
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//[04] The round number of the application of Euclid's algorithm, starting |
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// at "1". |
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//[05] "a". |
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//[06] "b". |
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//[07] a div b. |
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//[08] a mod b. |
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//[09] ... repeating sequence, starting back at [4] and repeating until a |
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// zero remainder. |
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//[..] The GCD of the two integers. This will be positive and |
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// contain no commas or extraneous characters. |
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//[..] "S", indicating success. |
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// |
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//Note that as per the definition above, any valid non-error output from |
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//this program will contain a number of lines which is a multiple of 5. |
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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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|
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#define MODULE_SUBFUNC_GCD |
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|
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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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|
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#include <gmp.h> |
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|
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#include "auxfuncs.h" |
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#include "subfunc_gcd.h" |
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|
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int SUBFUNC_GCD_main(int argc, char *argv[]) |
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{ |
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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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|
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//GMP types to maintain the algorithm. |
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int round; |
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mpz_t alg_a, alg_b, alg_adivb, alg_amodb; |
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|
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//There must be an acceptable number of command-line arguments. |
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if (argc != 4) |
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{ |
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printf("EQ\n0\n0\n"); |
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return(0); |
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} |
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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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if ((arg1 == NULL) || (arg2 == NULL)) |
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{ |
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printf("EQ\n%s\n%s\n", argv[2], argv[3]); |
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exit(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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|
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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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|
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//Remove all leading zeros from both arguments. |
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AUXFUNCS_remove_leading_zeros(arg1); |
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AUXFUNCS_remove_leading_zeros(arg2); |
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|
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//If either 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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|
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//If either argument exceeds 1000 digits, abort. |
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if ((strlen(arg1)>1000) || (strlen(arg2) > 1000)) |
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{ |
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printf("EQ\n0\n0\n"); |
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return(0); |
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} |
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|
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//If either argument is zero, abort. |
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if (!strcmp(arg1, "0")) |
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{ |
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printf("EP1B\n0\n0\n"); |
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return(0); |
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} |
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if (!strcmp(arg2, "0")) |
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{ |
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printf("EP2B\n0\n0\n"); |
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return(0); |
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} |
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|
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//Initialize all of the GMP variables. |
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mpz_init(alg_a); |
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mpz_init(alg_b); |
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mpz_init(alg_adivb); |
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mpz_init(alg_amodb); |
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|
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//Assign a and b to initial values. |
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mpz_set_str(alg_a, arg1, 10); |
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mpz_set_str(alg_b, arg2, 10); |
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|
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//We assume at this point that we will be successful. Output |
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//the header stuff. |
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printf("S\n"); |
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mpz_out_str(stdout, 10, alg_a); |
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printf("\n"); |
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mpz_out_str(stdout, 10, alg_b); |
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printf("\n"); |
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|
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//We require as an initial condition that a >= b. Make |
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//that happen. |
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if (mpz_cmp(alg_a, alg_b) < 0) |
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{ |
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mpz_swap(alg_a, alg_b); |
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} |
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|
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//To make the algorithm cleaner, we preload for the first |
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//assignment. |
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mpz_set(alg_amodb, alg_b); |
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mpz_set(alg_b, alg_a); |
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|
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//Now begin the algorithm proper. |
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round = 0; |
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do |
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{ |
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//We are at next round. |
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round++; |
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|
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//Values for this round inherited from the last one. |
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mpz_set(alg_a, alg_b); |
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mpz_set(alg_b, alg_amodb); |
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|
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//Calculate the quotient and remainder. |
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mpz_fdiv_qr(alg_adivb, alg_amodb, alg_a, alg_b); |
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|
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//Output all the data from the round. |
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printf("%d\n", round); |
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mpz_out_str(stdout, 10, alg_a); |
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printf("\n"); |
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mpz_out_str(stdout, 10, alg_b); |
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printf("\n"); |
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mpz_out_str(stdout, 10, alg_adivb); |
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printf("\n"); |
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mpz_out_str(stdout, 10, alg_amodb); |
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printf("\n"); |
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} |
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while((round < 2000) && (mpz_sgn(alg_amodb) > 0)); |
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|
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//The GCD canonically will be the last non-zero remainder. |
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mpz_out_str(stdout, 10, alg_b); |
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printf("\n"); |
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|
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//Finally, we output the trailing "S". |
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printf("S\n"); |
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|
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return(0); |
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} |
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|
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//******************************************************************************** |
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// End of SUBFUNC_GCD.C. |
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//******************************************************************************** |
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