// $Header: /cvsroot/esrg/sfesrg/esrgpcpj/cfbrapab/c_main.c,v 1.6 2002/01/27 17:58:15 dtashley Exp $
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//Copyright 2008 David T. Ashley
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// 17. Interpretation of Sections 15 and 16.
//
// If the disclaimer of warranty and limitation of liability provided
//above cannot be given local legal effect according to their terms,
//reviewing courts shall apply local law that most closely approximates
//an absolute waiver of all civil liability in connection with the
//Program, unless a warranty or assumption of liability accompanies a
//copy of the Program in return for a fee.
//
// END OF TERMS AND CONDITIONS
//
// How to Apply These Terms to Your New Programs
//
// If you develop a new program, and you want it to be of the greatest
//possible use to the public, the best way to achieve this is to make it
//free software which everyone can redistribute and change under these terms.
//
// To do so, attach the following notices to the program. It is safest
//to attach them to the start of each source file to most effectively
//state the exclusion of warranty; and each file should have at least
//the "copyright" line and a pointer to where the full notice is found.
//
//
// Copyright (C)
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see .
//
//Also add information on how to contact you by electronic and paper mail.
//
// If the program does terminal interaction, make it output a short
//notice like this when it starts in an interactive mode:
//
// Copyright (C)
// This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
// This is free software, and you are welcome to redistribute it
// under certain conditions; type `show c' for details.
//
//The hypothetical commands `show w' and `show c' should show the appropriate
//parts of the General Public License. Of course, your program's commands
//might be different; for a GUI interface, you would use an "about box".
//
// You should also get your employer (if you work as a programmer) or school,
//if any, to sign a "copyright disclaimer" for the program, if necessary.
//For more information on this, and how to apply and follow the GNU GPL, see
//.
//
// The GNU General Public License does not permit incorporating your program
//into proprietary programs. If your program is a subroutine library, you
//may consider it more useful to permit linking proprietary applications with
//the library. If this is what you want to do, use the GNU Lesser General
//Public License instead of this License. But first, please read
//.
//-------------------------------------------------------------------------------------------------
//--------------------------------------------------------------------------------
#include
#include
#include
#include
#include
#include
#include "bstrfunc.h"
#include "ccmalloc.h"
#include "ccmfatal.h"
#include "charfunc.h"
#include "cu_msgs.h"
#include "fcmiof.h"
#include "gmp_ints.h"
#include "gmp_rats.h"
#include "gmp_ralg.h"
#include "intfunc.h"
#define PNAME "cfbrapab"
#define PNAMEUC "CFBRAPAB"
const char *C_MAIN_cvcinfo(void)
{
return("$Header: /cvsroot/esrg/sfesrg/esrgpcpj/cfbrapab/c_main.c,v 1.6 2002/01/27 17:58:15 dtashley Exp $");
}
//This is a NULL-terminated table of pointers to functions
//which return version control strings for all of the files
//which make up the INTFAC program. This information would
//be helpful for debugging.
static const char *(*C_MAIN_vcinfoptrs[])(void) =
{
//This is the main module, should come first.
C_MAIN_cvcinfo,
//And now the others, in alphabetical order.
BSTRFUNC_hvcinfo,
BSTRFUNC_cvcinfo,
CCMALLOC_hvcinfo,
CCMALLOC_cvcinfo,
CCMFATAL_hvcinfo,
CCMFATAL_cvcinfo,
CHARFUNC_hvcinfo,
CHARFUNC_cvcinfo,
CU_MSGS_hvcinfo,
CU_MSGS_cvcinfo,
FCMIOF_hvcinfo,
FCMIOF_cvcinfo,
GMP_INTS_hvcinfo,
GMP_INTS_cvcinfo,
GMP_RALG_hvcinfo,
GMP_RALG_cvcinfo,
GMP_RATS_hvcinfo,
GMP_RATS_cvcinfo,
INTFUNC_hvcinfo,
INTFUNC_cvcinfo,
NULL
};
//This is the structure type used to hold information about all the
//command-line parameters.
//
struct CfbrapabCmainStruct
{
GMP_RATS_mpq_struct rn;
//The rational number specified on the command line.
//symmetry.
GMP_INTS_mpz_struct kmax;
//The value of KMAX specified on the command line. This must always
//be present.
int hmax_specified;
//TRUE if HMAX is specified in addition to KMAX. KMAX is mandatory
//in all cases.
GMP_INTS_mpz_struct hmax;
//The value of HMAX if it is specified. This is optional. This will be
//set to zero if it is not present on the command line.
int neversmaller_specified;
//TRUE if the -neversmaller option is specified on the command line.
int neverlarger_specified;
//TRUE if the -neverlarger option is specified on the command line.
int pred_specified;
//TRUE if the -pred option is specified on the command line.
int succ_specified;
//TRUE if the -succ option specified on the command line.
int n_specified;
//TRUE if the -n parameter is specified on the command line.
unsigned n;
//The value of n if it has been specified.
CU_MSGS_std_cmd_line_par_results_struct argblock;
//The block holding the options which are common across all
//of these command-line utilities.
};
//Processes the command-line parameters, and abstracts it to a
//the contents of a structure plus a failure flag.
static void process_command_line_args(struct CfbrapabCmainStruct *parblock,
int argc,
char* argv[])
{
int error_flag;
int first_dashed_parameter;
int i;
int recognized;
//Eyeball the input parameters.
assert(parblock != NULL);
assert(argc >= 1);
assert(argv != NULL);
//We have to have at least 3 total parameters. However, this is covered
//in main().
//Process the first parameter, which has to be the rational number we
//want to approximate. If there is a problem, give a helpful message
//and exit with an error code.
GMP_RATS_mpq_init(&(parblock->rn));
GMP_RATS_mpq_set_all_format_rat_num( argv[1],
&error_flag,
&(parblock->rn));
//If there was a parse error, announce and abort.
if (error_flag || GMP_RATS_mpq_is_nan(&(parblock->rn)))
{
printf("\"%s\" is not a properly formatted rational number.\n", argv[1]);
exit(4);
}
//Normalize the rational number specified as input. It is allowed to
//be negative.
GMP_RATS_mpq_normalize(&(parblock->rn));
//The next item has to be a number, it has to be
//an integer, it has to be positive, and it
//is KMAX. Parse out that. If there are any
//errors, abort.
GMP_INTS_mpz_init(&(parblock->kmax));
GMP_INTS_mpz_set_general_int(&(parblock->kmax), &error_flag, argv[2]);
if (error_flag || GMP_INTS_mpz_is_zero(&(parblock->kmax)) || GMP_INTS_mpz_is_neg(&(parblock->kmax)))
{
printf("\"%s\" is not a properly formatted positive integer.\n", argv[2]);
exit(4);
}
//Unconditionally allocate space for hmax.
GMP_INTS_mpz_init(&(parblock->hmax));
//If there is a third parameter, it can be two things. It can
//be either HMAX, or it can be the start of the parameters
//with dashes. First, let's decide which case applies.
if (argc <= 3)
{
first_dashed_parameter = 3;
parblock->hmax_specified = 0;
}
else
{
if (argv[3][0] == '-')
{
first_dashed_parameter = 3;
parblock->hmax_specified = 0;
}
else
{
first_dashed_parameter = 4;
parblock->hmax_specified = 1;
GMP_INTS_mpz_set_general_int(&(parblock->hmax), &error_flag, argv[3]);
if (error_flag || GMP_INTS_mpz_is_zero(&(parblock->hmax)) || GMP_INTS_mpz_is_neg(&(parblock->hmax)))
{
printf("\"%s\" is not a properly formatted positive integer.\n", argv[3]);
exit(4);
}
}
}
//Loop through the remaining parameters, trying to process each
//one either as a parameter specific to this program or else
//as a general parameter.
//
//Initialize the internal general parameter block.
CU_MSGS_cmd_line_par_results_struct_create(&(parblock->argblock));
parblock->neversmaller_specified = 0;
parblock->neverlarger_specified = 0;
parblock->pred_specified = 0;
parblock->succ_specified = 0;
parblock->n_specified = 0;
parblock->n = 0;
for (i=first_dashed_parameter; ineversmaller_specified = 1;
}
else if (!strcmp("-neverlarger", argv[i]))
{
parblock->neverlarger_specified = 1;
}
else if (!strcmp("-pred", argv[i]))
{
parblock->pred_specified = 1;
}
else if (!strcmp("-succ", argv[i]))
{
parblock->succ_specified = 1;
}
else if (!strcmp("-n", argv[i]))
{
parblock->n_specified = 1;
//To go along with -n, we have to have a next parameter.
if (i == (argc-1))
{
printf("The \"-n\" parameter must include a following count.\n");
exit(4);
}
//Bump i to index to next par.
i++;
//Try to parse this as a UINT24. It must be that.
GMP_INTS_mpz_parse_into_uint32(&(parblock->n), &error_flag, argv[i]);
//If it couldn't be parsed as an integer, flunk it.
if (error_flag)
{
printf("\"%s\" is not a valid unsigned integer or exceeds 24 bits.\n", argv[i]);
exit(4);
}
//If it is too large, flunk it.
if (parblock->n > 0x00FFFFFF)
{
printf("\"%s\" is an unsigned integer but exceeds 24 bits.\n", argv[i]);
exit(4);
}
//OK, we're cool ...
}
else
{
//Two possibilities left. Either general parameter, or else unrecognized.
CU_MSGS_cmd_line_par_results_struct_process_arg(&(parblock->argblock),
argv[i],
&recognized);
if (!recognized)
{
printf("\"%s\" is not a recognized command-line parameter.\n", argv[i]);
exit(4);
}
//Was picked up as general parameter.
}
}
//Congeal our thoughts on the "general" command-line parameters. No errors possible
//here.
CU_MSGS_cmd_line_par_results_struct_finalize(&(parblock->argblock));
//printf("Boo.\n");
//printf("neverlarger %d succ %d\n", parblock->neverlarger_specified, parblock->succ_specified);
//Look for mutually exclusive options among the program-specific parameters.
if (
(parblock->neversmaller_specified && (parblock->neverlarger_specified || parblock->pred_specified || parblock->succ_specified|| parblock->n_specified))
||
(parblock->neverlarger_specified && (parblock->pred_specified || parblock->succ_specified || parblock->n_specified))
||
(parblock->pred_specified && (parblock->succ_specified|| parblock->n_specified))
||
(parblock->succ_specified && parblock->n_specified)
)
{
printf("The \"-neversmaller\", \"-neverlarger\", \"-pred\", \"-succ\", and \"-n\" options are\nmutually exclusive.\n");
exit(4);
}
//OK, we're clean, all pars in order.
}
//Releases the dynamic memory associated with the parameter block.
static void release_command_line_args(struct CfbrapabCmainStruct *parblock)
{
assert(parblock != NULL);
//This function is superfluous, since in a command-line utility it doesn't really
//matter if everything is released. But, here goes.
CU_MSGS_cmd_line_par_results_struct_destroy(&(parblock->argblock));
GMP_RATS_mpq_clear(&(parblock->rn));
GMP_INTS_mpz_clear(&(parblock->kmax));
GMP_INTS_mpz_clear(&(parblock->hmax));
}
//Prints out a single rational number in the format endorsed
//by this program. This often includes DAP information
//and difference information. It is assumed that the
//previous information is terminated by a horizontal line,
//and this function terminates with a horizontal line.
static void CMAIN_print_app_in_std_form(FILE *s,
int index,
GMP_RATS_mpq_struct *rn,
GMP_RATS_mpq_struct *approx,
int nf,
int show_diff,
int show_dap,
GMP_INTS_mpz_struct *dap_den)
{
char sbuf[250];
GMP_RATS_mpq_struct diff, q_temp1;
GMP_INTS_mpz_struct z_temp1, quotient, remainder;
//Eyeball the input parameters.
assert(s != NULL);
assert(rn != NULL);
assert(approx != NULL);
assert(dap_den != NULL);
//Allocate.
GMP_RATS_mpq_init(&diff);
GMP_RATS_mpq_init(&q_temp1);
GMP_INTS_mpz_init(&z_temp1);
GMP_INTS_mpz_init("ient);
GMP_INTS_mpz_init(&remainder);
//Print out the approximation numerator.
sprintf(sbuf, "approx_num(%d)", index);
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
&(approx->num),
sbuf);
}
else
{
int nreserved;
char *p;
fprintf(s, "%d\n", index);
nreserved = GMP_INTS_mpz_size_in_base_10(&(approx->num));
p = CCMALLOC_malloc(sizeof(char) * nreserved);
GMP_INTS_mpz_to_string(p, &(approx->num));
fprintf(s, "%s\n", p);
CCMALLOC_free(p);
}
if (!nf)
FCMIOF_hline();
//Print out the approximation denominator.
sprintf(sbuf, "approx_den(%d)", index);
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
&(approx->den),
sbuf);
}
else
{
int nreserved;
char *p;
nreserved = GMP_INTS_mpz_size_in_base_10(&(approx->den));
p = CCMALLOC_malloc(sizeof(char) * nreserved);
GMP_INTS_mpz_to_string(p, &(approx->den));
fprintf(s, "%s\n", p);
CCMALLOC_free(p);
}
if (!nf)
FCMIOF_hline();
//If the "dap" flag is set, calculate and display decimal equivalent of the
//approximation.
if (show_dap)
{
//Make the calculation for decimal approximation.
GMP_RATS_mpq_copy(&q_temp1, approx);
GMP_RATS_mpq_normalize(&q_temp1);
GMP_INTS_mpz_mul(&z_temp1, dap_den, &q_temp1.num);
GMP_INTS_mpz_tdiv_qr("ient, &remainder,
&z_temp1, &q_temp1.den);
sprintf(sbuf, "dap_num(%d)", index);
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
&(quotient),
sbuf);
}
else
{
int nreserved;
char *p;
nreserved = GMP_INTS_mpz_size_in_base_10(&(quotient));
p = CCMALLOC_malloc(sizeof(char) * nreserved);
GMP_INTS_mpz_to_string(p, &(quotient));
fprintf(s, "%s\n", p);
CCMALLOC_free(p);
}
if (!nf)
FCMIOF_hline();
//Print out the approximation denominator.
sprintf(sbuf, "dap_den(%d)", index);
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
dap_den,
sbuf);
}
else
{
int nreserved;
char *p;
nreserved = GMP_INTS_mpz_size_in_base_10(dap_den);
p = CCMALLOC_malloc(sizeof(char) * nreserved);
GMP_INTS_mpz_to_string(p, dap_den);
fprintf(s, "%s\n", p);
CCMALLOC_free(p);
}
if (!nf)
FCMIOF_hline();
}
//If the "diff" flag is set, calculate and display the rational difference.
if (show_diff)
{
GMP_RATS_mpq_sub(&diff, approx, rn);
GMP_RATS_mpq_normalize(&diff);
sprintf(sbuf, "error_num(%d)", index);
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
&(diff.num),
sbuf);
}
else
{
int nreserved;
char *p;
nreserved = GMP_INTS_mpz_size_in_base_10(&(diff.num));
p = CCMALLOC_malloc(sizeof(char) * nreserved);
GMP_INTS_mpz_to_string(p, &(diff.num));
fprintf(s, "%s\n", p);
CCMALLOC_free(p);
}
if (!nf)
FCMIOF_hline();
//Print out the approximation denominator.
sprintf(sbuf, "error_den(%d)", index);
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
&(diff.den),
sbuf);
}
else
{
int nreserved;
char *p;
nreserved = GMP_INTS_mpz_size_in_base_10(&(diff.den));
p = CCMALLOC_malloc(sizeof(char) * nreserved);
GMP_INTS_mpz_to_string(p, &(diff.den));
fprintf(s, "%s\n", p);
CCMALLOC_free(p);
}
if (!nf)
FCMIOF_hline();
}
//Deallocate.
GMP_RATS_mpq_clear(&diff);
GMP_RATS_mpq_clear(&q_temp1);
GMP_INTS_mpz_clear(&z_temp1);
GMP_INTS_mpz_clear("ient);
GMP_INTS_mpz_clear(&remainder);
}
//Handles the classic case of finding the closest
//neighbor(s).
static int CMAIN_classic_closest_neighbor(struct CfbrapabCmainStruct *parblock)
{
int rv = 0;
GMP_RATS_mpq_struct hmax_over_one, hmax_over_kmax, rn_in_abs;
GMP_INTS_mpz_struct dap_denominator;
GMP_RALG_cf_app_struct cf_decomp;
GMP_RALG_fab_neighbor_collection_struct neighbor_data;
int error_flag;
//Allocate all dynamic memory.
GMP_RATS_mpq_init(&hmax_over_one);
GMP_RATS_mpq_init(&hmax_over_kmax);
GMP_INTS_mpz_init(&dap_denominator);
GMP_RATS_mpq_init(&rn_in_abs);
//Set the DAP denominator to 1e108.
GMP_INTS_mpz_set_general_int(&dap_denominator,
&error_flag,
"1e108");
//By convention, we will not mess with anything with an
//absolute value greater than HMAX/1. If such a condition exists, puke out.
//Form up the value of HMAX/1 if HMAX was specified.
if (parblock->hmax_specified)
{
GMP_INTS_mpz_copy(&(hmax_over_one.num), &(parblock->hmax));
GMP_INTS_mpz_set_ui(&(hmax_over_one.den), 1);
GMP_RATS_mpq_copy(&rn_in_abs, &(parblock->rn));
GMP_INTS_mpz_abs(&(rn_in_abs.num));
if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_one, NULL) > 0)
{
printf("The magnitude of the number supplied exceeds HMAX/1, and hence the number\n"
"has no neighbors in the series of interest. Calculation cannot continue.\n");
exit(4);
}
}
//If the "verbose" option is specified, we want to give the continued fraction
//partial quotients and convergents of either the number to approximate,
//its reciprocal, or none of the above, as appropriate; and give a bit more
//information, in addition.
if (parblock->argblock.verbose)
{
if (parblock->hmax_specified)
{
//Stuff HMAX/KMAX. This is necessary for comparison.
GMP_INTS_mpz_copy(&(hmax_over_kmax.num), &(parblock->hmax));
GMP_INTS_mpz_copy(&(hmax_over_kmax.den), &(parblock->kmax));
}
if (!(parblock->hmax_specified) || (GMP_RATS_mpq_cmp(&(parblock->rn), &hmax_over_kmax, NULL) < 0))
{
//Either HMAX was not specified or else we are below the corner point on the
//integer lattice. Get the continued fraction representation of the number
//rather than its reciprocal.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.num), &(rn_in_abs.den));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Rep Of Abs Value Of Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
else if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_kmax, NULL) == 0)
{
//In this case, the rational number specified is exactly the same in
//magnitude as HMAX/KMAX. I am inclined to suppress the CF decomp.
printf("Rational number specified is HMAX/KMAX. CF decomp not provided.\n");
}
else
{
//The number specified is beyond the corner point. It is appropriate to
//provide the decomposition of the reciprocal rather than of the number
//itself.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.den), &(rn_in_abs.num));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Rep Of Reciprocal Of Abs Value Of Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
} //End if verbose.
//Do all the work to get the neighbors of the number passed.
GMP_RALG_consecutive_fab_terms(
&(parblock->rn),
&(parblock->kmax),
(parblock->hmax_specified) ? (&(parblock->hmax)) : (NULL),
1,
1,
&neighbor_data);
//Print the neighbor data block for debugging.
#if 0
GMP_RALG_consecutive_fab_terms_result_dump(stdout, &neighbor_data);
#endif
//There are four possibilities at this point.
// a)Attempting to find the rational neighbors generated an error.
// b)The rational number specified was already in the series of interest,
// in which case we will use it.
// c)The left neighbor is closer or in a tie we want to choose it.
// d)The right neighbor is closer or in a tie we want to choose it.
if (neighbor_data.error)
{
//
printf("Internal error: %s\n", neighbor_data.error);
}
else if (neighbor_data.equality)
{
CMAIN_print_app_in_std_form(stdout,
0,
&(neighbor_data.rn_in),
&(neighbor_data.rn_in),
parblock->argblock.noformat,
0,
1,
&dap_denominator);
}
else
{
GMP_RATS_mpq_struct left_neighbor, right_neighbor,
left_diff, right_diff,
left_abs, right_abs;
int error_cmp;
int mag_cmp;
GMP_RATS_mpq_init(&left_neighbor);
GMP_RATS_mpq_init(&right_neighbor);
GMP_RATS_mpq_init(&left_diff);
GMP_RATS_mpq_init(&right_diff);
GMP_RATS_mpq_init(&left_abs);
GMP_RATS_mpq_init(&right_abs);
//Snatch the left neighbor.
if (neighbor_data.n_left_out)
{
GMP_RATS_mpq_copy(&left_neighbor, &(neighbor_data.lefts[0].neighbor));
}
//Snatch the right neighbor.
if (neighbor_data.n_right_out)
{
GMP_RATS_mpq_copy(&right_neighbor, &(neighbor_data.rights[0].neighbor));
}
//Calculate the differences, take their absolute
//values.
GMP_RATS_mpq_sub(&left_diff, &left_neighbor, &(neighbor_data.rn_in));
GMP_RATS_mpq_sub(&right_diff, &right_neighbor, &(neighbor_data.rn_in));
GMP_RATS_mpq_normalize(&left_diff);
GMP_RATS_mpq_normalize(&right_diff);
GMP_INTS_mpz_abs(&(left_diff.num));
GMP_INTS_mpz_abs(&(right_diff.num));
//Now that the differences are calculated, take the
//absolute values of the neighbors themselves.
//We will use this to break ties.
GMP_RATS_mpq_normalize(&left_neighbor);
GMP_RATS_mpq_normalize(&right_neighbor);
GMP_INTS_mpz_abs(&(left_neighbor.num));
GMP_INTS_mpz_abs(&(right_neighbor.num));
//Compare the relative differences and magnitudes.
error_cmp = GMP_RATS_mpq_cmp(&left_diff, &right_diff, NULL);
mag_cmp = GMP_RATS_mpq_cmp(&left_neighbor, &right_neighbor, NULL);
//Figure out which to present as the best approximation and
//do it.
if (!(parblock->neversmaller_specified) &&
((parblock->neverlarger_specified) || (error_cmp < 0) || ((error_cmp == 0) && (mag_cmp < 0))))
{
CMAIN_print_app_in_std_form(stdout,
-1,
&(neighbor_data.rn_in),
&(neighbor_data.lefts[0].neighbor),
parblock->argblock.noformat,
1,
1,
&dap_denominator);
}
else
{
CMAIN_print_app_in_std_form(stdout,
1,
&(neighbor_data.rn_in),
&(neighbor_data.rights[0].neighbor),
parblock->argblock.noformat,
1,
1,
&dap_denominator);
}
//Deallocate.
GMP_RATS_mpq_clear(&left_neighbor);
GMP_RATS_mpq_clear(&right_neighbor);
GMP_RATS_mpq_clear(&left_diff);
GMP_RATS_mpq_clear(&right_diff);
GMP_RATS_mpq_clear(&left_abs);
GMP_RATS_mpq_clear(&right_abs);
}
//Deallocate all dynamic memory.
GMP_RALG_consecutive_fab_terms_result_free(&neighbor_data);
GMP_RATS_mpq_clear(&hmax_over_one);
GMP_RATS_mpq_clear(&hmax_over_kmax);
GMP_INTS_mpz_clear(&dap_denominator);
GMP_RATS_mpq_clear(&rn_in_abs);
return(rv);
}
//Handles the case of finding multiple neighbors.
static int CMAIN_multiple_neighbor(struct CfbrapabCmainStruct *parblock)
{
int rv = 0;
GMP_RATS_mpq_struct hmax_over_one, hmax_over_kmax, rn_in_abs;
GMP_INTS_mpz_struct dap_denominator;
GMP_RALG_cf_app_struct cf_decomp;
GMP_RALG_fab_neighbor_collection_struct neighbor_data;
int error_flag;
int i;
//Allocate all dynamic memory.
GMP_RATS_mpq_init(&hmax_over_one);
GMP_RATS_mpq_init(&hmax_over_kmax);
GMP_INTS_mpz_init(&dap_denominator);
GMP_RATS_mpq_init(&rn_in_abs);
//Set the DAP denominator to 1e108.
GMP_INTS_mpz_set_general_int(&dap_denominator,
&error_flag,
"1e108");
//By convention, we will not mess with anything with an
//absolute value greater than HMAX/1. If such a condition exists, puke out.
//Form up the value of HMAX/1 if HMAX was specified.
if (parblock->hmax_specified)
{
GMP_INTS_mpz_copy(&(hmax_over_one.num), &(parblock->hmax));
GMP_INTS_mpz_set_ui(&(hmax_over_one.den), 1);
GMP_RATS_mpq_copy(&rn_in_abs, &(parblock->rn));
GMP_INTS_mpz_abs(&(rn_in_abs.num));
if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_one, NULL) > 0)
{
printf("The magnitude of the number supplied exceeds HMAX/1, and hence the number\n"
"has no neighbors in the series of interest. Calculation cannot continue.\n");
exit(4);
}
}
//If the "verbose" option is specified, we want to give the continued fraction
//partial quotients and convergents of either the number to approximate,
//its reciprocal, or none of the above, as appropriate; and give a bit more
//information, in addition.
if (parblock->argblock.verbose)
{
if (parblock->hmax_specified)
{
//Stuff HMAX/KMAX. This is necessary for comparison.
GMP_INTS_mpz_copy(&(hmax_over_kmax.num), &(parblock->hmax));
GMP_INTS_mpz_copy(&(hmax_over_kmax.den), &(parblock->kmax));
}
if (!(parblock->hmax_specified) || (GMP_RATS_mpq_cmp(&(parblock->rn), &hmax_over_kmax, NULL) < 0))
{
//Either HMAX was not specified or else we are below the corner point on the
//integer lattice. Get the continued fraction representation of the number
//rather than its reciprocal.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.num), &(rn_in_abs.den));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Representation Of Absolute Value Of Rational Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
else if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_kmax, NULL) == 0)
{
//In this case, the rational number specified is exactly the same in
//magnitude as HMAX/KMAX. I am inclined to suppress the CF decomp.
printf("Rational number specified is HMAX/KMAX. CF decomp not provided.\n");
}
else
{
//The number specified is beyond the corner point. It is appropriate to
//provide the decomposition of the reciprocal rather than of the number
//itself.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.den), &(rn_in_abs.num));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Representation Of Reciprocal Of Absolute Value Of Rational Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
} //End if verbose.
//Do all the work to get the neighbors of the number passed.
GMP_RALG_consecutive_fab_terms(
&(parblock->rn),
&(parblock->kmax),
(parblock->hmax_specified) ? (&(parblock->hmax)) : (NULL),
parblock->n,
parblock->n,
&neighbor_data);
//Print the neighbor data block for debugging.
#if 0
GMP_RALG_consecutive_fab_terms_result_dump(stdout, &neighbor_data);
#endif
//Loop through, printing out the left neighbors in order.
for (i = neighbor_data.n_left_out - 1; i >= 0; i--)
{
CMAIN_print_app_in_std_form(stdout,
-(i + 1),
&(neighbor_data.rn_in),
&(neighbor_data.lefts[i].neighbor),
parblock->argblock.noformat,
1,
1,
&dap_denominator);
}
//If the number itself appears in the series of interest, spit that out.
if (neighbor_data.equality)
{
CMAIN_print_app_in_std_form(stdout,
0,
&(neighbor_data.rn_in),
&(neighbor_data.norm_rn),
parblock->argblock.noformat,
1,
1,
&dap_denominator);
}
//Loop through, printing out the right neighbors in order.
for (i = 0; i < neighbor_data.n_right_out; i++)
{
CMAIN_print_app_in_std_form(stdout,
i+1,
&(neighbor_data.rn_in),
&(neighbor_data.rights[i].neighbor),
parblock->argblock.noformat,
1,
1,
&dap_denominator);
}
//Deallocate all dynamic memory.
GMP_RALG_consecutive_fab_terms_result_free(&neighbor_data);
GMP_RATS_mpq_clear(&hmax_over_one);
GMP_RATS_mpq_clear(&hmax_over_kmax);
GMP_INTS_mpz_clear(&dap_denominator);
GMP_RATS_mpq_clear(&rn_in_abs);
return(rv);
}
//Handles the case of finding the predecessor.
int CMAIN_predecessor(struct CfbrapabCmainStruct *parblock)
{
int rv = 0;
GMP_RATS_mpq_struct hmax_over_one, hmax_over_kmax, rn_in_abs;
GMP_INTS_mpz_struct dap_denominator;
GMP_RALG_cf_app_struct cf_decomp;
GMP_RALG_fab_neighbor_collection_struct neighbor_data;
int error_flag;
//Allocate all dynamic memory.
GMP_RATS_mpq_init(&hmax_over_one);
GMP_RATS_mpq_init(&hmax_over_kmax);
GMP_INTS_mpz_init(&dap_denominator);
GMP_RATS_mpq_init(&rn_in_abs);
//Set the DAP denominator to 1e108.
GMP_INTS_mpz_set_general_int(&dap_denominator,
&error_flag,
"1e108");
//By convention, we will not mess with anything with an
//absolute value greater than HMAX/1. If such a condition exists, puke out.
//Form up the value of HMAX/1 if HMAX was specified.
if (parblock->hmax_specified)
{
GMP_INTS_mpz_copy(&(hmax_over_one.num), &(parblock->hmax));
GMP_INTS_mpz_set_ui(&(hmax_over_one.den), 1);
GMP_RATS_mpq_copy(&rn_in_abs, &(parblock->rn));
GMP_INTS_mpz_abs(&(rn_in_abs.num));
if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_one, NULL) > 0)
{
printf("The magnitude of the number supplied exceeds HMAX/1, and hence the number\n"
"has no neighbors in the series of interest. Calculation cannot continue.\n");
exit(4);
}
}
//If the "verbose" option is specified, we want to give the continued fraction
//partial quotients and convergents of either the number to approximate,
//its reciprocal, or none of the above, as appropriate; and give a bit more
//information, in addition.
if (parblock->argblock.verbose)
{
if (parblock->hmax_specified)
{
//Stuff HMAX/KMAX. This is necessary for comparison.
GMP_INTS_mpz_copy(&(hmax_over_kmax.num), &(parblock->hmax));
GMP_INTS_mpz_copy(&(hmax_over_kmax.den), &(parblock->kmax));
}
if (!(parblock->hmax_specified) || (GMP_RATS_mpq_cmp(&(parblock->rn), &hmax_over_kmax, NULL) < 0))
{
//Either HMAX was not specified or else we are below the corner point on the
//integer lattice. Get the continued fraction representation of the number
//rather than its reciprocal.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.num), &(rn_in_abs.den));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Representation Of Absolute Value Of Rational Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
else if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_kmax, NULL) == 0)
{
//In this case, the rational number specified is exactly the same in
//magnitude as HMAX/KMAX. I am inclined to suppress the CF decomp.
printf("Rational number specified is HMAX/KMAX. CF decomp not provided.\n");
}
else
{
//The number specified is beyond the corner point. It is appropriate to
//provide the decomposition of the reciprocal rather than of the number
//itself.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.den), &(rn_in_abs.num));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Representation Of Reciprocal Of Absolute Value Of Rational Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
} //End if verbose.
//Do all the work to get the neighbors of the number passed.
GMP_RALG_consecutive_fab_terms(
&(parblock->rn),
&(parblock->kmax),
(parblock->hmax_specified) ? (&(parblock->hmax)) : (NULL),
1,
0,
&neighbor_data);
//Print the neighbor data block for debugging.
#if 0
GMP_RALG_consecutive_fab_terms_result_dump(stdout, &neighbor_data);
#endif
//Print the neighbor on the left, if it exists.
if (neighbor_data.n_left_out)
{
CMAIN_print_app_in_std_form(stdout,
-1,
&(neighbor_data.rn_in),
&(neighbor_data.lefts[0].neighbor),
parblock->argblock.noformat,
0,
0,
&dap_denominator);
}
//Deallocate all dynamic memory.
GMP_RALG_consecutive_fab_terms_result_free(&neighbor_data);
GMP_RATS_mpq_clear(&hmax_over_one);
GMP_RATS_mpq_clear(&hmax_over_kmax);
GMP_INTS_mpz_clear(&dap_denominator);
GMP_RATS_mpq_clear(&rn_in_abs);
return(rv);
}
//Handles the case of finding the successor.
int CMAIN_successor(struct CfbrapabCmainStruct *parblock)
{
int rv = 0;
GMP_RATS_mpq_struct hmax_over_one, hmax_over_kmax, rn_in_abs;
GMP_INTS_mpz_struct dap_denominator;
GMP_RALG_cf_app_struct cf_decomp;
GMP_RALG_fab_neighbor_collection_struct neighbor_data;
int error_flag;
//Allocate all dynamic memory.
GMP_RATS_mpq_init(&hmax_over_one);
GMP_RATS_mpq_init(&hmax_over_kmax);
GMP_INTS_mpz_init(&dap_denominator);
GMP_RATS_mpq_init(&rn_in_abs);
//Set the DAP denominator to 1e108.
GMP_INTS_mpz_set_general_int(&dap_denominator,
&error_flag,
"1e108");
//By convention, we will not mess with anything with an
//absolute value greater than HMAX/1. If such a condition exists, puke out.
//Form up the value of HMAX/1 if HMAX was specified.
if (parblock->hmax_specified)
{
GMP_INTS_mpz_copy(&(hmax_over_one.num), &(parblock->hmax));
GMP_INTS_mpz_set_ui(&(hmax_over_one.den), 1);
GMP_RATS_mpq_copy(&rn_in_abs, &(parblock->rn));
GMP_INTS_mpz_abs(&(rn_in_abs.num));
if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_one, NULL) > 0)
{
printf("The magnitude of the number supplied exceeds HMAX/1, and hence the number\n"
"has no neighbors in the series of interest. Calculation cannot continue.\n");
exit(4);
}
}
//If the "verbose" option is specified, we want to give the continued fraction
//partial quotients and convergents of either the number to approximate,
//its reciprocal, or none of the above, as appropriate; and give a bit more
//information, in addition.
if (parblock->argblock.verbose)
{
if (parblock->hmax_specified)
{
//Stuff HMAX/KMAX. This is necessary for comparison.
GMP_INTS_mpz_copy(&(hmax_over_kmax.num), &(parblock->hmax));
GMP_INTS_mpz_copy(&(hmax_over_kmax.den), &(parblock->kmax));
}
if (!(parblock->hmax_specified) || (GMP_RATS_mpq_cmp(&(parblock->rn), &hmax_over_kmax, NULL) < 0))
{
//Either HMAX was not specified or else we are below the corner point on the
//integer lattice. Get the continued fraction representation of the number
//rather than its reciprocal.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.num), &(rn_in_abs.den));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Representation Of Absolute Value Of Rational Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
else if (GMP_RATS_mpq_cmp(&(rn_in_abs), &hmax_over_kmax, NULL) == 0)
{
//In this case, the rational number specified is exactly the same in
//magnitude as HMAX/KMAX. I am inclined to suppress the CF decomp.
printf("Rational number specified is HMAX/KMAX. CF decomp not provided.\n");
}
else
{
//The number specified is beyond the corner point. It is appropriate to
//provide the decomposition of the reciprocal rather than of the number
//itself.
GMP_RALG_cfdecomp_init(&cf_decomp, &error_flag, &(rn_in_abs.den), &(rn_in_abs.num));
//Print out the continued fraction decomposition of the rational number.
GMP_RALG_cfdecomp_emit(stdout,
"CF Representation Of Reciprocal Of Absolute Value Of Rational Number Specified",
&cf_decomp,
0,
1,
&dap_denominator);
//Destroy the decomposition--free the memory.
GMP_RALG_cfdecomp_destroy(&cf_decomp);
}
} //End if verbose.
//Do all the work to get the neighbors of the number passed.
GMP_RALG_consecutive_fab_terms(
&(parblock->rn),
&(parblock->kmax),
(parblock->hmax_specified) ? (&(parblock->hmax)) : (NULL),
0,
1,
&neighbor_data);
//Print the neighbor data block for debugging.
#if 0
GMP_RALG_consecutive_fab_terms_result_dump(stdout, &neighbor_data);
#endif
//Print the neighbor on the right, if it exists.
if (neighbor_data.n_right_out)
{
CMAIN_print_app_in_std_form(stdout,
-1,
&(neighbor_data.rn_in),
&(neighbor_data.rights[0].neighbor),
parblock->argblock.noformat,
0,
0,
&dap_denominator);
}
//Deallocate all dynamic memory.
GMP_RALG_consecutive_fab_terms_result_free(&neighbor_data);
GMP_RATS_mpq_clear(&hmax_over_one);
GMP_RATS_mpq_clear(&hmax_over_kmax);
GMP_INTS_mpz_clear(&dap_denominator);
GMP_RATS_mpq_clear(&rn_in_abs);
return(rv);
}
int c_main(int argc, char* argv[])
{
int rv=0;
struct CfbrapabCmainStruct parblock;
if (argc==2 && !strcmp(argv[1], "-help"))
{
FCMIOF_hline();
printf("DESCRIPTION\n");
printf(" This utility calculates best rational approximations of the form h/k\n");
printf(" under the constraint k <= KMAX (i.e. in the Farey series of order KMAX),\n");
printf(" or under the constraints k <= KMAX and h <= HMAX (i.e. in a rectangular\n");
printf(" region of the integer lattice). This utility uses continued fraction\n");
printf(" algorithms presented in the accompanying book \"A Practitioner's Guide\n");
printf(" ...\", and this book (a work in progress) should be consulted both as a\n");
printf(" reference to the algorithms and a reference for this utility. All\n");
printf(" rational numbers calculated are in lowest terms. This utility will\n");
printf(" operate on negative numbers, but all results are produced by symmetry\n");
printf(" (the continued fraction representation of negative numbers is NOT\n");
printf(" calculated). The default operation of this utility is to calculated the\n");
printf(" closest rational number in the series of interest. If the rational\n");
printf(" number supplied is equidistant between two formable rational numbers in\n");
printf(" the series of interest, the neighbor smaller in magnitude is returned. If\n");
printf(" the rational number supplied is already formable, it is returned in lowest\n");
printf(" terms. If the rational number supplied does not have neighbors (i.e. it\n");
printf(" is larger than HMAX/1), an error is generated.\n");
printf("\n");
printf("USAGE\n");
printf(" cfbrapab srn urn_kmax [options]\n");
printf(" cfbrapab srn urn_kmax urn_hmax [options]\n");
printf(" cfbrapab -help\n");
printf("\n");
printf("OPTIONS\n");
printf(" -neversmaller, -neverlarger\n");
printf(" The -neversmaller option will prohibit this utility from choosing a\n");
printf(" rational approximation which is smaller than the rational number\n");
printf(" supplied. Thus, this option will force the utility to choose the right\n");
printf(" neighbor rather than the left, regardless of relative distance. The\n");
printf(" behavior if the rational number supplied is formable under the \n");
printf(" constraints is unchanged. The -neverlarger option is analogous.\n");
printf(" These options cannot be used with -n, -pred, or -succ.\n");
printf(" -pred, -succ\n");
printf(" Will cause the utility to find the predecessor or successor in the\n");
printf(" series of interest to the rational number supplied (in the event the\n");
printf(" number supplied is already formable under the constraints). For\n");
printf(" numbers not already formable under the constraints, the left or right\n");
printf(" formable neighbor will be returned. Supplying a rational number that\n");
printf(" does not have a predecessor or successor (i.e. < 0/1 or > HMAX/1) will\n");
printf(" generate an error. These options cannot be used with -neversmaller,\n");
printf(" -neverlarger, or -n.\n");
CU_MSGS_std_options(stdout, PNAME);
FCMIOF_hline();
CU_MSGS_toolset_info_msg(stdout, PNAME);
FCMIOF_hline();
}
else if (argc < 3)
{
CU_MSGS_too_few_args_msg(stdout, PNAME);
rv = 4;
goto ret_pt;
}
else
{
//In this branch, we must have an invocation of the form
// cfbrapab SRN KMAX
//or
// cfbrapab SRN KMAX HMAX
//
//Call the function to collect all the command-line parameters.
//This function takes care of error processing, as well. If there
//is an error of any kind, the function will simply abort and
//supply the right return error code of 4.
process_command_line_args(&parblock,
argc,
argv);
//If the debug option was set, emit the debugging information.
if (parblock.argblock.debug)
{
FCMIOF_hline();
CU_MSGS_emit_vcinfo_from_ptr_table(stdout,C_MAIN_vcinfoptrs,PNAMEUC);
}
//Emit the opening horizontal line iff the -nf option isn't set.
if (!(parblock.argblock.noformat))
FCMIOF_hline();
//Print out a major mode message to indicate what we are trying to do.
if (!(parblock.argblock.noformat))
{
if (!parblock.neversmaller_specified && !parblock.neverlarger_specified && !parblock.pred_specified && !parblock.succ_specified)
{
printf("MAJOR MODE: Finding closest rational number(s) under the constraints.\n");
}
else if (parblock.neversmaller_specified)
{
printf("MAJOR MODE: Finding closest rational number with magnitude not smaller under\n the constraints.\n");
}
else if (parblock.neverlarger_specified)
{
printf("MAJOR MODE: Finding closest rational number with magnitude not larger under\n the constraints.\n");
}
else if (parblock.pred_specified)
{
printf("MAJOR MODE: Finding predecessor under the constraints.\n");
}
else if (parblock.succ_specified)
{
printf("MAJOR MODE: Finding successor under the constraints.\n");
}
else
{
assert(0);
}
FCMIOF_hline();
}
//Echo back the command-line parameters.
if (!(parblock.argblock.noformat))
{
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(parblock.rn.num),
"RI_IN Numerator");
FCMIOF_hline();
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(parblock.rn.den),
"RI_IN Denominator");
FCMIOF_hline();
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(parblock.kmax),
"K_MAX");
FCMIOF_hline();
if (parblock.hmax_specified)
{
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(parblock.hmax),
"H_MAX");
FCMIOF_hline();
}
if (parblock.n_specified)
{
GMP_INTS_mpz_struct temp24;
GMP_INTS_mpz_init(&temp24);
GMP_INTS_mpz_set_ui(&temp24, parblock.n);
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&temp24,
"Number Of Neighbors");
FCMIOF_hline();
GMP_INTS_mpz_clear(&temp24);
}
}
//We need to split now into distinct cases
//depending on the command-line parameters. We will
//then hack out solutions for each case.
if (!parblock.pred_specified && !parblock.succ_specified && !parblock.n_specified)
{
//Classic closest neighbor case.
rv = CMAIN_classic_closest_neighbor(&parblock);
}
else if (parblock.n_specified)
{
//Classic multiple neighbor case.
rv = CMAIN_multiple_neighbor(&parblock);
}
else if (parblock.pred_specified)
{
rv = CMAIN_predecessor(&parblock);
}
else if (parblock.succ_specified)
{
rv = CMAIN_successor(&parblock);
}
else
{
assert(0);
}
//Emit the closing horizontal line iff the -nf option isn't set.
//if (!(parblock.argblock.noformat))
// FCMIOF_hline();
//Release all dynamic memory.
release_command_line_args(&parblock);
}
ret_pt:
return(rv);
}
//**************************************************************************
// $Log: c_main.c,v $
// Revision 1.6 2002/01/27 17:58:15 dtashley
// CRC32, other programs modified to work under new directory structure.
//
// Revision 1.5 2001/08/16 19:49:36 dtashley
// Beginning to prepare for v1.05 release.
//
// Revision 1.4 2001/08/15 06:55:59 dtashley
// Substantial progress. Safety check-in.
//
// Revision 1.3 2001/08/12 10:20:58 dtashley
// Safety check-in. Substantial progress.
//
// Revision 1.2 2001/07/26 03:53:17 dtashley
// Utilities that are under constructions stubbed to announce this,
// batch build file enhanced.
//
// Revision 1.1 2001/07/23 08:53:17 dtashley
// Initial check-in.
//
//**************************************************************************
// End of C_MAIN.C.