// $Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_ralg.c,v 1.10 2002/01/27 17:58:15 dtashley Exp $
//--------------------------------------------------------------------------------
//Copyright 2001 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
//.
//-------------------------------------------------------------------------------------------------
//--------------------------------------------------------------------------------
#define MODULE_GMP_RALG
#include
#include
#include
#include
#include "fcmiof.h"
#include "gmp_ints.h"
#include "gmp_rats.h"
#include "gmp_ralg.h"
#include "intfunc.h"
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
#include "ccmalloc.h"
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
#include "tclalloc.h"
#else
/* Do nothing. */
#endif
/******************************************************************/
/*** INITIALIZATION AND DESTRUCTION FUNCTIONS *******************/
/******************************************************************/
//08/16/01: Visual inspection OK.
void GMP_RALG_cfdecomp_init(
GMP_RALG_cf_app_struct *decomp,
int *failure,
GMP_INTS_mpz_struct *num,
GMP_INTS_mpz_struct *den)
{
int loop_counter, i;
GMP_INTS_mpz_struct arb_temp1, arb_temp2;
//Eyeball the input parameters. The rest of the eyeballing
//will occur as functions are called to manipulate the
//numerator and denominator passed in.
assert(decomp != NULL);
assert(failure != NULL);
assert(num != NULL);
assert(den != NULL);
//Allocate space for temporary integers.
GMP_INTS_mpz_init(&arb_temp1);
GMP_INTS_mpz_init(&arb_temp2);
//Begin believing no failure.
*failure = 0;
//Initialize the copy of the numerator and denominator and
//copy these into the structure.
GMP_INTS_mpz_init(&(decomp->num));
GMP_INTS_mpz_copy(&(decomp->num), num);
GMP_INTS_mpz_init(&(decomp->den));
GMP_INTS_mpz_copy(&(decomp->den), den);
//Allocate the space for the first increment of the
//growable areas. We need to use different memory
//allocation functions depending on whether we're
//in a Tcl build or a DOS command-line utility
//build.
//Space for partial quotients.
decomp->a =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpAlloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#else
malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#endif
//Dividends.
decomp->dividend =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpAlloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#else
malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#endif
//Divisors.
decomp->divisor =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpAlloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#else
malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#endif
//Remainders.
decomp->remainder =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpAlloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#else
malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#endif
//Convergent numerators.
decomp->p =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpAlloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#else
malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#endif
//Convergent denominators.
decomp->q =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpAlloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#else
malloc(sizeof(GMP_INTS_mpz_struct) * GMP_RALG_CF_ALLOC_INCREMENT);
#endif
//Now the number of allocated slots is what we just allocated.
decomp->nallocd = GMP_RALG_CF_ALLOC_INCREMENT;
//The number of slots actually used is zero, to start with.
decomp->n = 0;
//There are a number of conditions that will lead to an error
//where we can't successfully form the continued fraction
//decomposition. These errors are:
// a)Either component is NAN.
// b)Zero denominator.
// c)Either component negative.
//In these cases, we'll pretend we got 0/1 for the number
//and set things accordingly, and we'll set the failure
//flag for the caller.
//
if (GMP_INTS_mpz_get_flags(num)
||
GMP_INTS_mpz_get_flags(den)
||
GMP_INTS_mpz_is_zero(den)
||
GMP_INTS_mpz_is_neg(num)
||
GMP_INTS_mpz_is_neg(den))
{
*failure = 1;
decomp->n = 1;
GMP_INTS_mpz_set_ui(&(decomp->num), 0);
GMP_INTS_mpz_set_ui(&(decomp->den), 1);
GMP_INTS_mpz_init(decomp->dividend);
GMP_INTS_mpz_set_ui(decomp->dividend, 0);
GMP_INTS_mpz_init(decomp->divisor);
GMP_INTS_mpz_set_ui(decomp->divisor, 1);
GMP_INTS_mpz_init(decomp->a);
GMP_INTS_mpz_set_ui(decomp->a, 0);
GMP_INTS_mpz_init(decomp->remainder);
GMP_INTS_mpz_set_ui(decomp->remainder, 0);
GMP_INTS_mpz_init(decomp->p);
GMP_INTS_mpz_set_ui(decomp->p, 0);
GMP_INTS_mpz_init(decomp->q);
GMP_INTS_mpz_set_ui(decomp->q, 1);
goto return_point;
}
//If we're here there are not any errors that we
//are willing to detect. We should be clear
//for a continued fraction decomposition.
loop_counter = 0;
do
{
//Increment the count of "rows", because we're
//about to add one.
decomp->n++;
//If we have used up all the space available
//for integers, we have to allocate more.
if (decomp->n > decomp->nallocd)
{
//We now have more allocated space.
decomp->nallocd += GMP_RALG_CF_ALLOC_INCREMENT;
//Be absolutely sure we have not made a greivous
//error.
assert(decomp->n <= decomp->nallocd);
//Space for dividends.
decomp->dividend =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_realloc(
decomp->dividend,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpRealloc((char *)decomp->dividend,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#else
realloc(decomp->dividend, sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#endif
//Space for divisors.
decomp->divisor =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_realloc(
decomp->divisor,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpRealloc((char *)decomp->divisor,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#else
realloc(decomp->divisor, sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#endif
//Space for partial quotients.
decomp->a =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_realloc(
decomp->a,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpRealloc((char *)decomp->a,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#else
realloc(decomp->a, sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#endif
//Space for remainders.
decomp->remainder =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_realloc(
decomp->remainder,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpRealloc((char *)decomp->remainder,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#else
realloc(decomp->remainder, sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#endif
//Space for partial quotient numerators.
decomp->p =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_realloc(
decomp->p,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpRealloc((char *)decomp->p,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#else
realloc(decomp->p, sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#endif
//Space for partial quotient denominators.
decomp->q =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_realloc(
decomp->q,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_INTS_mpz_struct *)
TclpRealloc((char *)decomp->q,
sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#else
realloc(decomp->q, sizeof(GMP_INTS_mpz_struct) * decomp->nallocd);
#endif
}
//At this point, we have enough space to do the next round of operations.
//Set up an index variable.
i = decomp->n - 1;
//Initialize all of the integers at this round.
GMP_INTS_mpz_init(decomp->dividend + i);
GMP_INTS_mpz_init(decomp->divisor + i);
GMP_INTS_mpz_init(decomp->a + i);
GMP_INTS_mpz_init(decomp->remainder + i);
GMP_INTS_mpz_init(decomp->p + i);
GMP_INTS_mpz_init(decomp->q + i);
//Perform the next round of continued fraction decomposition. This
//is standard stuff.
if (i==0)
{
//In the 0th round, we essentially perform initial assignments.
GMP_INTS_mpz_copy(decomp->dividend, &(decomp->num));
GMP_INTS_mpz_copy(decomp->divisor, &(decomp->den));
//Make the division to get quotient and remainder.
GMP_INTS_mpz_tdiv_qr(decomp->a, decomp->remainder, decomp->dividend, decomp->divisor);
//The convergents in the first round are always the quotient over 1.
GMP_INTS_mpz_copy(decomp->p, decomp->a);
GMP_INTS_mpz_set_ui(decomp->q, 1);
}
else if (i==1)
{
//In the 1st round, the only point of caution is that we have to
//consider p(k-2)/q(k-2) carefully.
GMP_INTS_mpz_copy(decomp->dividend + 1, decomp->divisor + 0);
GMP_INTS_mpz_copy(decomp->divisor + 1, decomp->remainder + 0);
//Make the division to get quotient and remainder.
GMP_INTS_mpz_tdiv_qr(decomp->a + 1,
decomp->remainder + 1,
decomp->dividend + 1,
decomp->divisor + 1);
//Need to compute the numerator of the convergent. This will be:
// a(1) p(0) + p(-1) = a(1)p(0) + 1.
GMP_INTS_mpz_mul(decomp->p + 1, decomp->a + 1, decomp->p + 0);
GMP_INTS_mpz_set_ui(&arb_temp1, 1);
GMP_INTS_mpz_add(decomp->p + 1, decomp->p + 1, &arb_temp1);
//Need to compute the denominator of the convergent. This will
//be a(1)q(0) + q(-1) = a(1) q(0) = a(1).
GMP_INTS_mpz_copy(decomp->q + 1, decomp->a + 1);
}
else
{
//In the general case, it is a simple formula.
//Rotate in the dividend and divisor from the previous round.
GMP_INTS_mpz_copy(decomp->dividend + i, decomp->divisor + i - 1);
GMP_INTS_mpz_copy(decomp->divisor + i, decomp->remainder + i - 1);
//Make the division to get quotient and remainder.
GMP_INTS_mpz_tdiv_qr(decomp->a + i,
decomp->remainder + i,
decomp->dividend + i,
decomp->divisor + i);
//Need to compute the numerator of the convergent. This will be:
// p(i) = a(i)p(i-1) + p(i-2)
GMP_INTS_mpz_mul(decomp->p + i, decomp->a + i, decomp->p + i - 1);
GMP_INTS_mpz_add(decomp->p + i, decomp->p + i, decomp->p + i - 2);
//Need to compute the numerator of the convergent. This will be:
// q(i) = q(i)q(i-1) + q(i-2)
GMP_INTS_mpz_mul(decomp->q + i, decomp->a + i, decomp->q + i - 1);
GMP_INTS_mpz_add(decomp->q + i, decomp->q + i, decomp->q + i - 2);
}
loop_counter++;
} while(!GMP_INTS_mpz_is_zero(decomp->remainder + decomp->n - 1) && loop_counter < 100000);
//In debug builds, be sure we did not terminate based on the loop counter.
assert(loop_counter != 100000);
return_point:
//Deallocate space for temporary integers.
GMP_INTS_mpz_clear(&arb_temp1);
GMP_INTS_mpz_clear(&arb_temp2);
}
//08/16/01: Visual inspection OK.
void GMP_RALG_cfdecomp_destroy(
GMP_RALG_cf_app_struct *decomp
)
{
int i;
//Eyeball the input parameters. Other eyeballing
//will be done as integers are destroyed.
assert(decomp != NULL);
//First, destroy the things that are bound directly
//to the record.
GMP_INTS_mpz_clear(&(decomp->num));
GMP_INTS_mpz_clear(&(decomp->den));
//Now, destroy every integer which is allocated.
for (i=0; i < decomp->n; i++)
{
GMP_INTS_mpz_clear(decomp->dividend + i);
GMP_INTS_mpz_clear(decomp->divisor + i);
GMP_INTS_mpz_clear(decomp->a + i);
GMP_INTS_mpz_clear(decomp->remainder + i);
GMP_INTS_mpz_clear(decomp->p + i);
GMP_INTS_mpz_clear(decomp->q + i);
}
//Now, destroy the arrays of integers.
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(decomp->dividend);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)decomp->dividend);
#else
free(decomp->dividend);
#endif
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(decomp->divisor);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)decomp->divisor);
#else
free(decomp->divisor);
#endif
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(decomp->a);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)decomp->a);
#else
free(decomp->a);
#endif
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(decomp->remainder);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)decomp->remainder);
#else
free(decomp->remainder);
#endif
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(decomp->p);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)decomp->p);
#else
free(decomp->p);
#endif
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(decomp->q);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)decomp->q);
#else
free(decomp->q);
#endif
}
/******************************************************************/
/*** FORMATTED OUTPUT FUNCTIONS *********************************/
/******************************************************************/
//08/16/01: Visual inspection OK.
void GMP_RALG_cfdecomp_emit(
FILE *s,
char *banner,
GMP_RALG_cf_app_struct *decomp,
int nf,
int dap,
const GMP_INTS_mpz_struct *dap_denominator)
{
int i;
GMP_INTS_mpz_struct arb_temp, arb_quotient, arb_remainder;
//Eyeball the input parameters. The banner is allowed to
//be null, so can't check that.
assert(s != NULL);
assert(decomp != NULL);
//Allocate our temporary integers.
GMP_INTS_mpz_init(&arb_temp);
GMP_INTS_mpz_init(&arb_quotient);
GMP_INTS_mpz_init(&arb_remainder);
//If banner requested and noformat option not used.
if (banner && !nf)
{
FCMIOF_stream_bannerheading(s, banner, 1);
}
//Dump the input numerator.
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
&(decomp->num),
"Input Numerator");
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, &(decomp->num));
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
//Dump the input denominator.
if (!nf)
{
GMP_INTS_mpz_long_int_format_to_stream(s,
&(decomp->den),
"Input Denominator");
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, &(decomp->den));
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
for (i=0; in; i++)
{
char strbuf[100];
//Buffer to prepare description.
//Print out the dividend at each round.
if (!nf)
{
sprintf(strbuf, "dividend(%d)", i);
GMP_INTS_mpz_long_int_format_to_stream(s,
decomp->dividend + i,
strbuf);
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, decomp->dividend+i);
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
//Print out the divisor at each round.
if (!nf)
{
sprintf(strbuf, "divisor(%d)", i);
GMP_INTS_mpz_long_int_format_to_stream(s,
decomp->divisor + i,
strbuf);
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, decomp->divisor+i);
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
//Print out partial quotient at each round.
if (!nf)
{
sprintf(strbuf, "a(%d)", i);
GMP_INTS_mpz_long_int_format_to_stream(s,
decomp->a + i,
strbuf);
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, decomp->a+i);
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
//It doesn't make any sense to print out the
//remainder, because this becomes the divisor
//for the next round. It is just wasted output
//lines.
//Print out the convergent numerator at
//each round.
if (!nf)
{
sprintf(strbuf, "p(%d)", i);
GMP_INTS_mpz_long_int_format_to_stream(s,
decomp->p + i,
strbuf);
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, decomp->p+i);
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
//Print out the convergent denominator at
//each round.
if (!nf)
{
sprintf(strbuf, "q(%d)", i);
GMP_INTS_mpz_long_int_format_to_stream(s,
decomp->q + i,
strbuf);
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, decomp->q+i);
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
if (dap)
{
//Calculate the DAP numerator
GMP_INTS_mpz_mul(&arb_temp, dap_denominator, decomp->p + i);
GMP_INTS_mpz_tdiv_qr(&arb_quotient, &arb_remainder,
&arb_temp, decomp->q + i);
//Print DAP numerator.
if (!nf)
{
sprintf(strbuf, "dap_h(%d)", i);
GMP_INTS_mpz_long_int_format_to_stream(s,
&arb_quotient,
strbuf);
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, &arb_quotient);
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
//Print DAP denominator.
if (!nf)
{
sprintf(strbuf, "dap_k(%d)", i);
GMP_INTS_mpz_long_int_format_to_stream(s,
dap_denominator,
strbuf);
}
else
{
GMP_INTS_mpz_arb_int_raw_to_stream(s, dap_denominator);
fprintf(s, "\n");
}
//Separator if not in unformatted mode.
if (!nf)
FCMIOF_stream_hline(s);
}
}
//Deallocate our temporary integers.
GMP_INTS_mpz_clear(&arb_temp);
GMP_INTS_mpz_clear(&arb_quotient);
GMP_INTS_mpz_clear(&arb_remainder);
}
/******************************************************************/
/*** FAREY SERIES PREDECESSOR AND SUCCESSOR FUNCTIONS ***********/
/******************************************************************/
//08/16/01: Visual inspection OK.
void GMP_RALG_farey_predecessor(
GMP_RATS_mpq_struct *result,
const GMP_RATS_mpq_struct *plus_two,
const GMP_RATS_mpq_struct *plus_one,
const GMP_INTS_mpz_struct *N)
{
GMP_RATS_mpq_struct result_copy;
//Used to hold return value in case the result
//is the same as either of the input arguments.
GMP_INTS_mpz_struct temp1, temp2, floor_func;
//Temporary integers.
assert(result != NULL);
assert(plus_two != NULL);
assert(plus_one != NULL);
assert(N != NULL);
//Initialize the variables used.
GMP_RATS_mpq_init(&result_copy);
GMP_INTS_mpz_init(&temp1);
GMP_INTS_mpz_init(&temp2);
GMP_INTS_mpz_init(&floor_func);
//Numerator of the term in the floor function.
GMP_INTS_mpz_add(&temp1, &(plus_two->den), N);
//Term in the floor function. This is used to
//calculate both numerator and denominator, so we save it.
GMP_INTS_mpz_tdiv_qr(&floor_func, &temp2, &temp1, &(plus_one->den));
//Product of result of floor function and numerator--now
//forming the numerator of the output.
GMP_INTS_mpz_mul(&temp2, &floor_func, &(plus_one->num));
//Final result assigned to numerator.
GMP_INTS_mpz_sub(&(result_copy.num), &temp2, &(plus_two->num));
//Product of result of floor function and denominator--now
//forming the denominator of the output.
GMP_INTS_mpz_mul(&temp2, &floor_func, &(plus_one->den));
//Final result assigned to denominator.
GMP_INTS_mpz_sub(&(result_copy.den), &temp2, &(plus_two->den));
//Copy the result to the object owned by the caller.
GMP_RATS_mpq_copy(result, &result_copy);
//Deallocate dynamic memory.
GMP_RATS_mpq_clear(&result_copy);
GMP_INTS_mpz_clear(&temp1);
GMP_INTS_mpz_clear(&temp2);
GMP_INTS_mpz_clear(&floor_func);
}
//08/16/01: Visual inspection OK.
void GMP_RALG_farey_successor(
GMP_RATS_mpq_struct *result,
const GMP_RATS_mpq_struct *minus_two,
const GMP_RATS_mpq_struct *minus_one,
const GMP_INTS_mpz_struct *N)
{
GMP_RATS_mpq_struct result_copy;
//Used to hold return value in case the result
//is the same as either of the input arguments.
GMP_INTS_mpz_struct temp1, temp2, floor_func;
//Temporary integers.
assert(result != NULL);
assert(minus_two != NULL);
assert(minus_one != NULL);
assert(N != NULL);
//Initialize the variables used.
GMP_RATS_mpq_init(&result_copy);
GMP_INTS_mpz_init(&temp1);
GMP_INTS_mpz_init(&temp2);
GMP_INTS_mpz_init(&floor_func);
//Numerator of the term in the floor function.
GMP_INTS_mpz_add(&temp1, &(minus_two->den), N);
//Term in the floor function. This is used to
//calculate both numerator and denominator, so we save it.
GMP_INTS_mpz_tdiv_qr(&floor_func, &temp2, &temp1, &(minus_one->den));
//Product of result of floor function and numerator--now
//forming the numerator of the output.
GMP_INTS_mpz_mul(&temp2, &floor_func, &(minus_one->num));
//Final result assigned to numerator.
GMP_INTS_mpz_sub(&(result_copy.num), &temp2, &(minus_two->num));
//Product of result of floor function and denominator--now
//forming the denominator of the output.
GMP_INTS_mpz_mul(&temp2, &floor_func, &(minus_one->den));
//Final result assigned to denominator.
GMP_INTS_mpz_sub(&(result_copy.den), &temp2, &(minus_two->den));
//Copy the result to the object owned by the caller.
GMP_RATS_mpq_copy(result, &result_copy);
//Deallocate dynamic memory.
GMP_RATS_mpq_clear(&result_copy);
GMP_INTS_mpz_clear(&temp1);
GMP_INTS_mpz_clear(&temp2);
GMP_INTS_mpz_clear(&floor_func);
}
//08/16/01: Visual inspection OK.
void GMP_RALG_enclosing_farey_neighbors(
const GMP_RATS_mpq_struct *rn_in,
const GMP_INTS_mpz_struct *N,
const GMP_RALG_cf_app_struct *cf_rep,
int *equality,
GMP_RATS_mpq_struct *left,
GMP_RATS_mpq_struct *right)
{
GMP_RATS_mpq_struct rn_abs;
//Absolute value of rational number supplied.
GMP_RATS_mpq_struct previous_convergent;
//Convergent before the one that has the denominator
//not exceeding the order of the series. Need to fudge
//a little bit because don't have -1-th order convergents
//tabulated.
GMP_RATS_mpq_struct other_neighbor;
//The other neighbor besides the highest-order convergent
//without denominator too large.
GMP_INTS_mpz_struct temp1, temp2, temp3, temp4;
//Temporary integers.
int ho_conv;
//Index of highest-ordered convergent that does not have
//denominator too large.
//Eyeball the parameters.
assert(rn_in != NULL);
assert(N != NULL);
assert(cf_rep != NULL);
assert(equality != NULL);
assert(left != NULL);
assert(right != NULL);
//Allocate dynamic variables.
GMP_RATS_mpq_init(&rn_abs);
GMP_RATS_mpq_init(&previous_convergent);
GMP_RATS_mpq_init(&other_neighbor);
GMP_INTS_mpz_init(&temp1);
GMP_INTS_mpz_init(&temp2);
GMP_INTS_mpz_init(&temp3);
GMP_INTS_mpz_init(&temp4);
//Zero is a troublesome case, because it requires us to
//cross signs. Split this case out explicitly.
if (GMP_INTS_mpz_is_zero(&(rn_in->num)))
{
*equality = 1; //0/1 a member of Farey series of any order.
GMP_INTS_mpz_set_si(&(left->num), -1);
GMP_INTS_mpz_copy(&(left->den), N);
GMP_INTS_mpz_set_si(&(right->num), 1);
GMP_INTS_mpz_copy(&(right->den), N);
}
else
{
//Make a copy of the rational number in. As a condition of
//using this function, it must be normalized, but it still
//may be negative. Our strategy is to treat the number as
//positive, find the neighbors, then if it was negative
//complement and re-order the neighbors. In other words,
//find neighbors to a negative number by symmetry, not
//by forming the CF representation of a negative number.
//Also, we can't touch the input parameter.
GMP_RATS_mpq_copy(&rn_abs, rn_in);
GMP_INTS_mpz_abs(&(rn_abs.num));
//Find the index of the highest-ordered convergent
//with a denominator not exceeding the denominator of
//the rational number supplied. The zero'th order
//convergent has a denominator of 1, so that one
//at least is safe.
//Assign either the "left" or right
//neighbor to be the highest-ordered
//convergent with a denominator not exceeding the
//denominator of the rational number input. I say
//"either" because the properties of convergents let
//us know based on the oddness or evenness of the order
//which side it is on.
ho_conv = 0;
while (((ho_conv + 1) < cf_rep->n) && (GMP_INTS_mpz_cmp(cf_rep->q + ho_conv + 1, N) <= 0))
{
#if 0
//Some questions about this loop--debugging output.
printf("ho_conv : %d\n", ho_conv);
GMP_INTS_mpz_long_int_format_to_stream(stdout,
cf_rep->q + ho_conv + 1,
"decomp_den");
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(rn_abs.den),
"rn_in_den");
printf("Compare result: %d\n\n", GMP_INTS_mpz_cmp(cf_rep->q + ho_conv + 1, &(rn_abs.den)));
#endif
ho_conv++;
}
if (INTFUNC_is_even(ho_conv))
{
GMP_INTS_mpz_copy(&(left->num), cf_rep->p + ho_conv);
GMP_INTS_mpz_copy(&(left->den), cf_rep->q + ho_conv);
}
else
{
GMP_INTS_mpz_copy(&(right->num), cf_rep->p + ho_conv);
GMP_INTS_mpz_copy(&(right->den), cf_rep->q + ho_conv);
}
//Now, we need to calculate the other neighbor based
//on the standard formula. This is a little tricky
//because we don't have the -1-th order convergents
//tabulated so we have to fudge a little bit.
if (ho_conv == 0)
{
GMP_RATS_mpq_set_si(&previous_convergent, 1, 0);
}
else
{
GMP_INTS_mpz_copy(&(previous_convergent.num), cf_rep->p + ho_conv - 1);
GMP_INTS_mpz_copy(&(previous_convergent.den), cf_rep->q + ho_conv - 1);
}
//Calculate the other neighbor according to the standard
//formula.
GMP_INTS_mpz_sub(&temp1, N, &(previous_convergent.den));
GMP_INTS_mpz_tdiv_qr(&temp2, &temp3, &temp1, cf_rep->q + ho_conv);
//temp2 now contains term from floor() function in formula.
GMP_INTS_mpz_mul(&temp1, &temp2, cf_rep->p + ho_conv);
GMP_INTS_mpz_add(&(other_neighbor.num), &temp1, &(previous_convergent.num));
GMP_INTS_mpz_mul(&temp1, &temp2, cf_rep->q + ho_conv);
GMP_INTS_mpz_add(&(other_neighbor.den), &temp1, &(previous_convergent.den));
//Copy the other neighbor into the right slot.
if (INTFUNC_is_even(ho_conv))
{
GMP_RATS_mpq_copy(right, &other_neighbor);
}
else
{
GMP_RATS_mpq_copy(left, &other_neighbor);
}
//Set the equality flag. We have equality if and only
//if the denominator of the rational number is less than
//or equal to N.
if (GMP_INTS_mpz_cmp(&(rn_abs.den), N) <= 0)
{
*equality = 1;
}
else
{
*equality = 0;
}
//In the event of equality, we don't really have the true
//neighbors. If the final convergent is even-ordered,
//the left needs to be replaced. If the final convergent
//is odd-ordered, the right needs to be replaced.
if (*equality)
{
if (INTFUNC_is_even(ho_conv))
{
//Left needs to be replaced.
GMP_RALG_farey_predecessor(
left,
right,
&rn_abs,
N);
}
else
{
//Right needs to be replaced.
GMP_RALG_farey_successor(
right,
left,
&rn_abs,
N);
}
}
//OK, we should be all done. The final catch is that if
//the number supplied was negative, we need to invert
//and re-order the neighbors.
if (GMP_INTS_mpz_is_neg(&(rn_in->num)))
{
GMP_RATS_mpq_swap(left, right);
GMP_INTS_mpz_negate(&(left->num));
GMP_INTS_mpz_negate(&(right->num));
}
} //End if (rn==0) else clause
//Deallocate dynamic variables.
GMP_RATS_mpq_clear(&rn_abs);
GMP_RATS_mpq_clear(&previous_convergent);
GMP_RATS_mpq_clear(&other_neighbor);
GMP_INTS_mpz_clear(&temp1);
GMP_INTS_mpz_clear(&temp2);
GMP_INTS_mpz_clear(&temp3);
GMP_INTS_mpz_clear(&temp4);
}
//08/16/01: Visual inspection OK. Did not fully inspect the
//iterative part of this function. Unit testing will be
//careful, expect that to catch any anomalies.
void GMP_RALG_consecutive_fab_terms(
const GMP_RATS_mpq_struct *rn_in,
const GMP_INTS_mpz_struct *kmax,
const GMP_INTS_mpz_struct *hmax,
int n_left_in,
int n_right_in,
GMP_RALG_fab_neighbor_collection_struct *result
)
{
int error_flag, equality_flag;
char *estring_kmax_neg = "KMAX is zero, negative, or NAN.";
char *estring_hmax_neg = "HMAX is negative or NAN.";
char *estring_general = "Unspecified general error in GMP_RALG_consecutive_fab_terms().";
GMP_RATS_mpq_struct q_temp1, q_temp2, q_temp3, q_temp4,
left_neighbor, right_neighbor,
left_neighbor_abs, right_neighbor_abs,
hmax_over_one_neg, corner_point_neg,
abs_norm_recip_rn;
//Eyeball input parameters.
assert(rn_in != NULL);
assert(kmax != NULL);
assert(n_left_in >= 0);
assert(n_left_in <= 0x00FFFFFF);
assert(n_right_in >= 0);
assert(n_right_in <= 0x00FFFFFF);
assert(result != NULL);
//Allocate all of the dynamic memory we'll need for this function. It will be
//released at the end.
GMP_RATS_mpq_init(&q_temp1);
GMP_RATS_mpq_init(&q_temp2);
GMP_RATS_mpq_init(&q_temp3);
GMP_RATS_mpq_init(&q_temp4);
GMP_RATS_mpq_init(&left_neighbor);
GMP_RATS_mpq_init(&right_neighbor);
GMP_RATS_mpq_init(&left_neighbor_abs);
GMP_RATS_mpq_init(&right_neighbor_abs);
GMP_RATS_mpq_init(&hmax_over_one_neg);
GMP_RATS_mpq_init(&corner_point_neg);
GMP_RATS_mpq_init(&abs_norm_recip_rn);
//Zero out the result block. This is the easiest way to give many variables
//default values of 0, FALSE, and NULL.
memset(result, 0, sizeof(GMP_RALG_fab_neighbor_collection_struct));
//Allocate all integer and rational number structures in the result block.
GMP_RATS_mpq_init(&(result->rn_in));
GMP_INTS_mpz_init(&(result->kmax_in));
GMP_INTS_mpz_init(&(result->hmax_in));
GMP_RATS_mpq_init(&(result->hmax_over_one));
GMP_RATS_mpq_init(&(result->corner_point));
GMP_RATS_mpq_init(&(result->corner_point_minus_one));
GMP_RATS_mpq_init(&(result->corner_point_plus_one));
GMP_RATS_mpq_init(&(result->norm_rn));
GMP_RATS_mpq_init(&(result->abs_norm_rn));
//Fill in the rational number, exactly as passed.
GMP_RATS_mpq_copy(&(result->rn_in), rn_in);
//Fill in the number of left and right neighbors that the caller wants.
//However, let's of course say nothing less than zero and nothing more
//than 10000 neighbors on either side.
result->n_left_in = INTFUNC_min(INTFUNC_max(0, n_left_in), 10000);
result->n_right_in = INTFUNC_min(INTFUNC_max(0, n_right_in), 10000);
//Fill in the value of KMAX, exactly as passed. If it is not at least
//the value of 1 or if error flags, croak.
GMP_INTS_mpz_copy(&(result->kmax_in), kmax);
if (GMP_INTS_mpz_get_flags(kmax) || GMP_INTS_mpz_is_zero(kmax) || GMP_INTS_mpz_is_neg(kmax))
{
result->error =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(char) * (strlen(estring_kmax_neg) + 1));
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpAlloc(sizeof(char) * (strlen(estring_kmax_neg) + 1));
#else
malloc(sizeof(char) * (strlen(estring_kmax_neg) + 1));
#endif
strcpy(result->error, estring_kmax_neg);
goto return_point;
}
//Decide whether the caller intends to use HMAX. Neg is error, but zero
//is a signal that don't intend to use.
if (hmax)
{
GMP_INTS_mpz_copy(&(result->hmax_in), hmax);
if (GMP_INTS_mpz_get_flags(hmax) || GMP_INTS_mpz_is_neg(hmax))
{
result->error =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(char) * (strlen(estring_hmax_neg) + 1));
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpAlloc(sizeof(char) * (strlen(estring_hmax_neg) + 1));
#else
malloc(sizeof(char) * (strlen(estring_hmax_neg) + 1));
#endif
strcpy(result->error, estring_hmax_neg);
goto return_point;
}
else if (GMP_INTS_mpz_is_pos(hmax))
{
result->hmax_supplied = 1;
}
}
//If HMAX has been supplied, assign and normalize the
//corner point.
if (result->hmax_supplied)
{
GMP_INTS_mpz_copy(&(result->corner_point.num), &(result->hmax_in));
GMP_INTS_mpz_copy(&(result->corner_point.den), &(result->kmax_in));
GMP_RATS_mpq_normalize(&(result->corner_point));
}
//If HMAX has been supplied, we want to get the continued
//fraction representation of both the corner point and its
//reciprocal. This is because we're going to need to
//find its adjacent points so we can easily crawl
//around a rectangular region of the integer lattice.
if (result->hmax_supplied)
{
//CF representation of corner point.
GMP_RALG_cfdecomp_init(&(result->corner_point_cf_rep),
&error_flag,
&(result->corner_point.num),
&(result->corner_point.den));
result->corner_point_cf_rep_formed = 1;
//If there was an error forming the CF representation
//of the corner point, bail out.
if (error_flag)
{
result->error =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(char) * (strlen(estring_general) + 1));
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpAlloc(sizeof(char) * (strlen(estring_general) + 1));
#else
malloc(sizeof(char) * (strlen(estring_general) + 1));
#endif
strcpy(result->error, estring_general);
goto return_point;
}
//CF representation of reciprocal of corner point.
GMP_RALG_cfdecomp_init(&(result->corner_point_recip_cf_rep),
&error_flag,
&(result->corner_point.den),
&(result->corner_point.num));
result->corner_point_recip_cf_rep_formed = 1;
//If there was an error forming the CF representation
//of the reciprocal of the corner point, bail out.
if (error_flag)
{
result->error =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(char) * (strlen(estring_general) + 1));
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpAlloc(sizeof(char) * (strlen(estring_general) + 1));
#else
malloc(sizeof(char) * (strlen(estring_general) + 1));
#endif
strcpy(result->error, estring_general);
goto return_point;
}
}
//Normalize the rational number supplied.
GMP_RATS_mpq_copy(&(result->norm_rn), rn_in);
GMP_RATS_mpq_normalize(&(result->norm_rn));
//Form the absolute value of the normalized
//version, and set the neg flag.
GMP_RATS_mpq_copy(&(result->abs_norm_rn),&(result->norm_rn));
if (GMP_INTS_mpz_is_neg(&(result->abs_norm_rn.num)))
{
GMP_INTS_mpz_negate(&(result->abs_norm_rn.num));
result->rn_is_neg = 1;
}
//Form the continued fraction representation of the
//absolute value of the rational number supplied.
//This is always required, because we cannot get any
//neighbors without it.
GMP_RALG_cfdecomp_init(&(result->rn_abs_cf_rep),
&error_flag,
&(result->abs_norm_rn.num),
&(result->abs_norm_rn.den));
result->rn_abs_cf_rep_formed = 1;
//If there was an error forming the CF representation
//of the absolute value of rational number supplied, bail out.
if (error_flag)
{
result->error =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(char) * (strlen(estring_general) + 1));
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpAlloc(sizeof(char) * (strlen(estring_general) + 1));
#else
malloc(sizeof(char) * (strlen(estring_general) + 1));
#endif
strcpy(result->error, estring_general);
goto return_point;
}
//Set the equality flag. The rational number supplied is
//in the series of interest if and only if, in its normalized
//form, K <= KMAX, and if HMAX was supplied, H <= HMAX.
if (GMP_INTS_mpz_cmp(&(result->abs_norm_rn.den), kmax) <= 0)
{
if (result->hmax_supplied)
{
if (GMP_INTS_mpz_cmp(&(result->abs_norm_rn.num), hmax) <= 0)
{
result->equality = 1;
}
else
{
result->equality = 0;
}
}
else
{
result->equality = 1;
}
}
else
{
result->equality = 0;
}
//The final cause of error is if the rational number
//supplied is outside the interval [-HMAX/1, HMAX/1].
//In such cases, simply refuse to calculate
//any approximations. This error can only occur
//if HMAX is specified. If only KMAX is specified,
//this error cannot occur.
if (result->hmax_supplied)
{
//Form the rational number HMAX/1. We will use it for
//a comparison.
GMP_INTS_mpz_copy(&(result->hmax_over_one.num), hmax);
GMP_INTS_mpz_set_ui(&(result->hmax_over_one.den), 1);
//If the comparison shows that the absolute value of
//the rational number in is larger than HMAX over 1,
//then declare an error.
if (GMP_RATS_mpq_cmp(&(result->abs_norm_rn),&(result->hmax_over_one),NULL) > 0)
{
result->error =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(char) * (strlen(estring_general) + 1));
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpAlloc(sizeof(char) * (strlen(estring_general) + 1));
#else
malloc(sizeof(char) * (strlen(estring_general) + 1));
#endif
strcpy(result->error, estring_general);
goto return_point;
}
}
//If we're here, we're very much clean. The only thing
//that could go wrong is an overflow.
//Allocate space for the left and right arrays of
//neighbors.
if (result->n_left_in)
{
result->lefts =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_RALG_fab_neighbor_struct) * result->n_left_in);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_RALG_fab_neighbor_struct *)
TclpAlloc(sizeof(GMP_RALG_fab_neighbor_struct) * result->n_left_in);
#else
malloc(sizeof(GMP_RALG_fab_neighbor_struct) * result->n_left_in);
#endif
}
if (result->n_right_in)
{
result->rights =
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_malloc(sizeof(GMP_RALG_fab_neighbor_struct) * result->n_right_in);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
(GMP_RALG_fab_neighbor_struct *)
TclpAlloc(sizeof(GMP_RALG_fab_neighbor_struct) * result->n_right_in);
#else
malloc(sizeof(GMP_RALG_fab_neighbor_struct) * result->n_right_in);
#endif
}
//If the rational number supplied is above the corner
//point, we want to form the continued fraction representation
//of its reciprocal.
if (result->hmax_supplied)
{
if (GMP_RATS_mpq_cmp(&(result->abs_norm_rn),&(result->corner_point),NULL) > 0)
{
GMP_RALG_cfdecomp_init(&(result->rn_abs_recip_cf_rep),
&error_flag,
&(result->abs_norm_rn.den),
&(result->abs_norm_rn.num));
result->rn_abs_recip_cf_rep_formed = 1;
}
}
//If HMAX has been supplied, we want to calculate the points just below and above
//the corner point. The reason we want to do this is because we need to gracefully
//"round the corner" in either direction.
//
//Calculate the point just to the left of the corner point.
if (result->hmax_supplied)
{
GMP_RALG_enclosing_farey_neighbors(
&(result->corner_point),
&(result->kmax_in),
&(result->corner_point_cf_rep),
&equality_flag,
&(result->corner_point_minus_one),
&(q_temp1)
);
}
//Calculate the point just to the right of the corner point. This is
//where HMAX is the dominant constraint. We need to find the left
//Farey neighbor to the reciprocal of the corner point in the Farey
//series of order HMAX, then take its reciprocal. There is the possibility
//if KMAX=1 that this point will have a denominator of zero, but we
//will accept that as a number here, since we should never hit it,
//as it will be beyond HMAX/1.
if (result->hmax_supplied)
{
GMP_RATS_mpq_copy(&q_temp1, &(result->corner_point));
GMP_INTS_mpz_swap(&(q_temp1.num), &(q_temp1.den));
GMP_RALG_enclosing_farey_neighbors(
&q_temp1,
&(result->hmax_in),
&(result->corner_point_recip_cf_rep),
&equality_flag,
&(result->corner_point_plus_one),
&(q_temp2)
);
GMP_INTS_mpz_swap(&(result->corner_point_plus_one.num), &(result->corner_point_plus_one.den));
}
//Calculate the complement of HMAX/1. Nothing that we generate can go beyond
//this to the south.
if (result->hmax_supplied)
{
GMP_RATS_mpq_copy(&(hmax_over_one_neg), &(result->hmax_over_one));
GMP_INTS_mpz_negate(&(hmax_over_one_neg.num));
}
//Also calculate the complement of HMAX/KMAX.
if (result->hmax_supplied)
{
GMP_RATS_mpq_copy(&(corner_point_neg), &(result->corner_point));
GMP_INTS_mpz_negate(&(corner_point_neg.num));
}
//Form the reciprocal of the absolute value of the normalized value of
//the rational number in.
GMP_RATS_mpq_copy(&abs_norm_recip_rn, &(result->abs_norm_rn));
GMP_RATS_mpq_swap_components(&abs_norm_recip_rn);
//OK, now we get down to brass tacks. Iterate first to get the
//left neighbors. The ordinary complexity of this is also compounded
//by the fact that we must handle negative numbers as well--everything
//from -HMAX/1 to HMAX/1.
//
//PSEUDO-CODE:
// a)If the rational number to approximate is <= -HMAX/1 or there are no
// left neighbors requested, terminate with no neighbors on the left.
//
// b)Find the right neighbor of the rational number supplied.
//
// c)Find the left neighbor of the rational number supplied.
//
// d)While (queued_count < count)
//
// e)Queue the left neighbor, queued_count++
//
// f)If (queued_count >= count), break.
//
// g)If (left_neighbor <= -HMAX/1), break
//
// h)Advance the frame one to the left.
//
//**************************************************************************
// a)If the rational number to approximate is <= -HMAX/1 or there are no
// left neighbors requested, terminate with no neighbors on the left.
//**************************************************************************
if ((result->hmax_supplied && GMP_RATS_mpq_cmp(&(result->norm_rn), &hmax_over_one_neg, NULL) <= 0)
|| (n_left_in <= 0))
goto done_with_left_neighbors;
//**************************************************************************
// b)Find the right neighbor of the rational number supplied.
//**************************************************************************
// c)Find the left neighbor of the rational number supplied.
//**************************************************************************
if (!result->hmax_supplied)
{
//In this case, the notion of corner point is meaningless, because
//there is no constraint on H. We can just go on our merry way. Get
//the two neighbors.
GMP_RALG_enclosing_farey_neighbors(
&(result->norm_rn),
&(result->kmax_in),
&(result->rn_abs_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//The enclosing Farey neighbor function is prohibited from identifying the
//rational number itself as a Farey term. If the number is in the Farey
//series, we must replace the right neighbor, otherwise we cannot apply
//the standard recursive formulas.
if (equality_flag)
{
GMP_RATS_mpq_copy(&right_neighbor, &(result->norm_rn));
}
}
else if (GMP_RATS_mpq_cmp(&(result->norm_rn), &corner_point_neg, NULL) < 0)
{
//The rational number specified is negative and below the negative corner point.
//This means that HMAX is the dominant constraint. We need to find the
//neighbors in the Farey series of order HMAX, then reorder and invert, etc.
GMP_RALG_enclosing_farey_neighbors(
&abs_norm_recip_rn,
&(result->hmax_in),
&(result->rn_abs_recip_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//Again, if the number specified was already in the series of interest,
//we need to swap in the right neighbor.
if (equality_flag)
{
GMP_RATS_mpq_copy(&right_neighbor, &abs_norm_recip_rn);
}
//Take the reciprocal of both neighbors, which will put them out of order,
//then negate them, which will put them back in order.
GMP_RATS_mpq_swap_components(&left_neighbor);
GMP_INTS_mpz_negate(&(left_neighbor.num));
GMP_RATS_mpq_swap_components(&right_neighbor);
GMP_INTS_mpz_negate(&(right_neighbor.num));
}
else if (GMP_RATS_mpq_cmp(&(result->norm_rn), &corner_point_neg, NULL) == 0)
{
//The rational number specified is the negative corner point. In this case
//Because we can never return the corner point itself as a left neighbor,
//we need to set the left value to be the negative of one past, and the right
//to be the negative of the corner point.
GMP_RATS_mpq_copy(&left_neighbor, &(result->corner_point_plus_one));
GMP_INTS_mpz_negate(&(left_neighbor.num));
GMP_RATS_mpq_copy(&right_neighbor, &(result->corner_point));
GMP_INTS_mpz_negate(&(right_neighbor.num));
}
else if ((GMP_RATS_mpq_cmp(&(result->norm_rn), &corner_point_neg, NULL) > 0)
&&
(GMP_RATS_mpq_cmp(&(result->norm_rn), &(result->corner_point), NULL) < 0))
{
//The rational number specified is in the area dominated by the KMAX constraint
//between -HMAX/KMAX and HMAX/KMAX. The ordinary Farey neighbor function will
//handle this correctly. Again, we need to adjust the output if the number
//is already formable, because the Farey neighbor function is prohibited from
//returning the number itself as a neighbor.
GMP_RALG_enclosing_farey_neighbors(
&(result->norm_rn),
&(result->kmax_in),
&(result->rn_abs_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//The enclosing Farey neighbor function is prohibited from identifying the
//rational number itself as a Farey term. If the number is in the Farey
//series, we must replace the right neighbor, otherwise we cannot apply
//the standard recursive formulas.
if (equality_flag)
{
GMP_RATS_mpq_copy(&right_neighbor, &(result->norm_rn));
}
}
else if (GMP_RATS_mpq_cmp(&(result->norm_rn), &(result->corner_point), NULL) == 0)
{
//The rational number specified is the corner point. In this case
//because we can never return the corner point itself as a left neighbor,
//we need to set the left value to be one before, and the right
//to be the corner point.
GMP_RATS_mpq_copy(&left_neighbor, &(result->corner_point_minus_one));
GMP_RATS_mpq_copy(&right_neighbor, &(result->corner_point));
}
else
{
//The only possibility left is that the number is positive and above the
//corner point where HMAX is the dominant constraint.
GMP_RALG_enclosing_farey_neighbors(
&abs_norm_recip_rn,
&(result->hmax_in),
&(result->rn_abs_recip_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//Again, if the number specified was already in the series of interest,
//we need to swap in the neighbor. This time, however, it must be the
//left neighbor because taking the reciprocals will reverse the order.
if (equality_flag)
{
GMP_RATS_mpq_copy(&left_neighbor, &abs_norm_recip_rn);
}
//Take the reciprocal of both neighbors, which will put them out of order,
//then swap them, which will put them back in order.
GMP_RATS_mpq_swap_components(&left_neighbor);
GMP_RATS_mpq_swap_components(&right_neighbor);
GMP_RATS_mpq_swap(&left_neighbor, &right_neighbor);
}
#if 0
//Print out the left neighbor and right neighbor determined, for debugging.
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(left_neighbor.num),
"left_neigh_num");
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(left_neighbor.den),
"left_neigh_den");
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(right_neighbor.num),
"right_neigh_num");
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(right_neighbor.den),
"right_neigh_den");
#endif
//**************************************************************************
// d)While (queued_count < count)
//**************************************************************************
while (result->n_left_out < result->n_left_in)
{
//**************************************************************************
// e)Queue the left neighbor, queued_count++
//**************************************************************************
(result->lefts + result->n_left_out)->index = -(result->n_left_out + 1);
GMP_RATS_mpq_init(&((result->lefts + result->n_left_out)->neighbor));
GMP_RATS_mpq_copy(&((result->lefts + result->n_left_out)->neighbor), &left_neighbor);
(result->n_left_out)++;
//**************************************************************************
// f)If (queued_count >= count), break.
//**************************************************************************
//By the way, this step is to save unnecessary contortions once we've met
//the quota.
if (result->n_left_out >= result->n_left_in)
break;
//**************************************************************************
// g)If (left_neighbor <= -HMAX/1), break
//**************************************************************************
//This breaks us when we've queued the most negative number we can--can't go
//further. This only applies for cases where KMAX is also specified.
if (result->hmax_supplied
&&
GMP_RATS_mpq_cmp(&left_neighbor, &hmax_over_one_neg, NULL) <= 0)
break;
//**************************************************************************
// h)Advance the frame one to the left.
//**************************************************************************
//Advancing one frame to the left is a complicated affair, requiring several
//subcases. We break it up into regions which are best visualized using
//a graph of the integer lattice with dots for each rational number.
if (!(result->hmax_supplied))
{
//This is the case where we're are looking only in the
//Farey series.
if (GMP_INTS_mpz_is_pos(&left_neighbor.num))
{
//In this case, the left neighbor and right neighbor
//are both positive, and we can apply the standard
//formulas.
GMP_RALG_farey_predecessor(&q_temp1,
&right_neighbor,
&left_neighbor,
&(result->kmax_in));
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &q_temp1);
}
else if (GMP_INTS_mpz_is_zero(&left_neighbor.num))
{
//In this case, we are making the transition from positive
//to negative.
GMP_INTS_mpz_set_si(&(left_neighbor.num), -1);
GMP_INTS_mpz_copy(&(left_neighbor.den), &(result->kmax_in));
GMP_RATS_mpq_set_si(&right_neighbor, 0, 1);
}
else
{
//Here, we are purely negative and decreasing. Need to negate
//the numbers, find successor, then negate.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_INTS_mpz_abs(&(q_temp1.num));
GMP_INTS_mpz_abs(&(q_temp2.num));
GMP_RALG_farey_successor(&q_temp3,
&q_temp2,
&q_temp1,
&(result->kmax_in));
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &q_temp3);
GMP_INTS_mpz_negate(&(left_neighbor.num));
}
}
else if (GMP_RATS_mpq_cmp(&left_neighbor, &(result->corner_point), NULL) > 0)
{
//We are above the top corner point. In this case HMAX is the dominant
//constraint, and we find our food by taking reciprocals and applying
//the standard relationships in the Farey series of order HMAX.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_RATS_mpq_swap_components(&q_temp1);
GMP_RATS_mpq_swap_components(&q_temp2);
GMP_RALG_farey_successor(&q_temp3,
&q_temp2,
&q_temp1,
&(result->hmax_in));
GMP_RATS_mpq_swap_components(&q_temp3);
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &q_temp3);
}
else if (GMP_RATS_mpq_cmp(&left_neighbor, &(result->corner_point), NULL) == 0)
{
//We are precisely at the corner point. This is where we round the corner.
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &(result->corner_point_minus_one));
}
else if (GMP_INTS_mpz_is_pos(&left_neighbor.num))
{
//In this region we are going straight down the Farey series.
GMP_RALG_farey_predecessor(&q_temp1,
&right_neighbor,
&left_neighbor,
&(result->kmax_in));
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &q_temp1);
}
else if (GMP_INTS_mpz_is_zero(&left_neighbor.num))
{
//In this case, we are making the transition from positive
//to negative.
GMP_INTS_mpz_set_si(&(left_neighbor.num), -1);
GMP_INTS_mpz_copy(&(left_neighbor.den), &(result->kmax_in));
GMP_RATS_mpq_set_si(&right_neighbor, 0, 1);
}
else if (GMP_RATS_mpq_cmp(&left_neighbor, &corner_point_neg, NULL) > 0)
{
//Here, we are purely negative and decreasing. Need to negate
//the numbers, find successor, then negate.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_INTS_mpz_abs(&(q_temp1.num));
GMP_INTS_mpz_abs(&(q_temp2.num));
GMP_RALG_farey_successor(&q_temp3,
&q_temp2,
&q_temp1,
&(result->kmax_in));
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &q_temp3);
GMP_INTS_mpz_negate(&(left_neighbor.num));
}
else if (GMP_RATS_mpq_cmp(&left_neighbor, &corner_point_neg, NULL) == 0)
{
//This is where we are rounding the negative corner.
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &(result->corner_point_plus_one));
GMP_INTS_mpz_negate(&(left_neighbor.num));
}
else
{
//Here we're going in the negative direction along the "bottom" of the
//rectangle.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_INTS_mpz_abs(&(q_temp1.num));
GMP_INTS_mpz_abs(&(q_temp2.num));
GMP_RATS_mpq_swap_components(&q_temp1);
GMP_RATS_mpq_swap_components(&q_temp2);
GMP_RALG_farey_predecessor(&q_temp3,
&q_temp2,
&q_temp1,
&(result->hmax_in));
GMP_RATS_mpq_swap_components(&q_temp3);
GMP_INTS_mpz_negate(&(q_temp3.num));
GMP_RATS_mpq_copy(&right_neighbor, &left_neighbor);
GMP_RATS_mpq_copy(&left_neighbor, &q_temp3);
}
}
done_with_left_neighbors: ;
//**************************************************************************
// a)If the rational number to approximate is >= HMAX/1 or there are no
// right neighbors requested, terminate with no neighbors on the right.
//**************************************************************************
if ((result->hmax_supplied && GMP_RATS_mpq_cmp(&(result->norm_rn), &(result->hmax_over_one), NULL) >= 0)
|| (n_right_in <= 0))
goto done_with_right_neighbors;
//**************************************************************************
// b)Find the right neighbor of the rational number supplied.
//**************************************************************************
// c)Find the left neighbor of the rational number supplied.
//**************************************************************************
if (!result->hmax_supplied)
{
//In this case, the notion of corner point is meaningless, because
//there is no constraint on H. We can just go on our merry way. Get
//the two neighbors.
GMP_RALG_enclosing_farey_neighbors(
&(result->norm_rn),
&(result->kmax_in),
&(result->rn_abs_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//The enclosing Farey neighbor function is prohibited from identifying the
//rational number itself as a Farey term. If the number is in the Farey
//series, we must replace the left neighbor, otherwise we cannot apply
//the standard recursive formulas.
if (equality_flag)
{
GMP_RATS_mpq_copy(&left_neighbor, &(result->norm_rn));
}
}
else if (GMP_RATS_mpq_cmp(&(result->norm_rn), &corner_point_neg, NULL) < 0)
{
//The rational number specified is negative and below the negative corner point.
//This means that HMAX is the dominant constraint. We need to find the
//neighbors in the Farey series of order HMAX, then reorder and invert, etc.
GMP_RALG_enclosing_farey_neighbors(
&abs_norm_recip_rn,
&(result->hmax_in),
&(result->rn_abs_recip_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//Again, if the number specified was already in the series of interest,
//we need to swap in the left neighbor.
if (equality_flag)
{
GMP_RATS_mpq_copy(&left_neighbor, &abs_norm_recip_rn);
}
//Take the reciprocal of both neighbors, which will put them out of order,
//then negate them, which will put them back in order.
GMP_RATS_mpq_swap_components(&left_neighbor);
GMP_INTS_mpz_negate(&(left_neighbor.num));
GMP_RATS_mpq_swap_components(&right_neighbor);
GMP_INTS_mpz_negate(&(right_neighbor.num));
}
else if (GMP_RATS_mpq_cmp(&(result->norm_rn), &corner_point_neg, NULL) == 0)
{
//The rational number specified is the negative corner point. In this case
//Because we can never return the corner point itself as a left neighbor,
//we need to set the right value to be the negative of one before, and the left
//to be the negative of the corner point.
GMP_RATS_mpq_copy(&left_neighbor, &(result->corner_point));
GMP_INTS_mpz_negate(&(left_neighbor.num));
GMP_RATS_mpq_copy(&right_neighbor, &(result->corner_point_minus_one));
GMP_INTS_mpz_negate(&(right_neighbor.num));
}
else if ((GMP_RATS_mpq_cmp(&(result->norm_rn), &corner_point_neg, NULL) > 0)
&&
(GMP_RATS_mpq_cmp(&(result->norm_rn), &(result->corner_point), NULL) < 0))
{
//The rational number specified is in the area dominated by the KMAX constraint
//between -HMAX/KMAX and HMAX/KMAX. The ordinary Farey neighbor function will
//handle this correctly. Again, we need to adjust the output if the number
//is already formable, because the Farey neighbor function is prohibited from
//returning the number itself as a neighbor.
GMP_RALG_enclosing_farey_neighbors(
&(result->norm_rn),
&(result->kmax_in),
&(result->rn_abs_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//The enclosing Farey neighbor function is prohibited from identifying the
//rational number itself as a Farey term. If the number is in the Farey
//series, we must replace the left neighbor, otherwise we cannot apply
//the standard recursive formulas.
if (equality_flag)
{
GMP_RATS_mpq_copy(&left_neighbor, &(result->norm_rn));
}
}
else if (GMP_RATS_mpq_cmp(&(result->norm_rn), &(result->corner_point), NULL) == 0)
{
//The rational number specified is the positive corner point. In this case.
//because we can never return the corner point itself as a right neighbor,
//we need to set the right value to be one after, and the left
//to be the corner point.
GMP_RATS_mpq_copy(&left_neighbor, &(result->corner_point));
GMP_RATS_mpq_copy(&right_neighbor, &(result->corner_point_plus_one));
}
else
{
//The only possibility left is that the number is positive and at or above the
//corner point where HMAX is the dominant constraint.
GMP_RALG_enclosing_farey_neighbors(
&abs_norm_recip_rn,
&(result->hmax_in),
&(result->rn_abs_recip_cf_rep),
&equality_flag,
&left_neighbor,
&right_neighbor
);
//Again, if the number specified was already in the series of interest,
//we need to swap in the neighbor. This time, however, it must be the
//right neighbor because taking the reciprocals will reverse the order.
if (equality_flag)
{
GMP_RATS_mpq_copy(&right_neighbor, &abs_norm_recip_rn);
}
//Take the reciprocal of both neighbors, which will put them out of order,
//then swap them, which will put them back in order.
GMP_RATS_mpq_swap_components(&left_neighbor);
GMP_RATS_mpq_swap_components(&right_neighbor);
GMP_RATS_mpq_swap(&left_neighbor, &right_neighbor);
}
#if 0
//Print out the left neighbor and right neighbor determined, for debugging.
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(left_neighbor.num),
"left_neigh_num");
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(left_neighbor.den),
"left_neigh_den");
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(right_neighbor.num),
"right_neigh_num");
GMP_INTS_mpz_long_int_format_to_stream(stdout,
&(right_neighbor.den),
"right_neigh_den");
#endif
//**************************************************************************
// d)While (queued_count < count)
//**************************************************************************
while (result->n_right_out < result->n_right_in)
{
//**************************************************************************
// e)Queue the right neighbor, queued_count++
//**************************************************************************
(result->rights + result->n_right_out)->index = (result->n_right_out + 1);
GMP_RATS_mpq_init(&((result->rights + result->n_right_out)->neighbor));
GMP_RATS_mpq_copy(&((result->rights + result->n_right_out)->neighbor), &right_neighbor);
(result->n_right_out)++;
//**************************************************************************
// f)If (queued_count >= count), break.
//**************************************************************************
//By the way, this step is to save unnecessary contortions once we've met
//the quota.
if (result->n_right_out >= result->n_right_in)
break;
//**************************************************************************
// g)If (right_neighbor >= HMAX/1), break
//**************************************************************************
//This breaks us when we've queued the most positive number we can--can't go
//further. This only applies for cases where KMAX is also specified.
if (result->hmax_supplied
&&
GMP_RATS_mpq_cmp(&right_neighbor, &(result->hmax_over_one), NULL) >= 0)
break;
//**************************************************************************
// h)Advance the frame one to the right.
//**************************************************************************
//Advancing one frame to the right is a complicated affair, requiring several
//subcases. We break it up into regions which are best visualized using
//a graph of the integer lattice with dots for each rational number.
if (!(result->hmax_supplied))
{
//This is the case where we're are looking only in the
//Farey series.
if (GMP_INTS_mpz_is_neg(&right_neighbor.num))
{
//Neg and increasing towards zero. Can handle by symmetry.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_INTS_mpz_abs(&(q_temp1.num));
GMP_INTS_mpz_abs(&(q_temp2.num));
GMP_RALG_farey_predecessor(&q_temp3,
&q_temp1,
&q_temp2,
&(result->kmax_in));
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &q_temp3);
GMP_INTS_mpz_negate(&(right_neighbor.num));
}
else if (GMP_INTS_mpz_is_zero(&right_neighbor.num))
{
//Right term just hit zero and are increasing.
//Left will become 0/1, right becomes 1/KMAX.
GMP_RATS_mpq_set_si(&left_neighbor, 0, 1);
GMP_INTS_mpz_set_si(&(right_neighbor.num), 1);
GMP_INTS_mpz_copy(&(right_neighbor.den), &(result->kmax_in));
}
else
{
//Are above zero and increasing. Can use standard Farey
//successor formula.
GMP_RALG_farey_successor(&q_temp1,
&left_neighbor,
&right_neighbor,
&(result->kmax_in));
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &q_temp1);
}
}
else if (GMP_RATS_mpq_cmp(&right_neighbor, &corner_point_neg, NULL) < 0)
{
//We are below the negative corner point and moving towards
//zero, with HMAX the dominant constraint. We can proceed by
//symmetry, producing a Farey successor and negating and inverting.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_INTS_mpz_abs(&(q_temp1.num));
GMP_INTS_mpz_abs(&(q_temp2.num));
GMP_RATS_mpq_swap_components(&q_temp1);
GMP_RATS_mpq_swap_components(&q_temp2);
GMP_RALG_farey_successor(&q_temp3,
&q_temp1,
&q_temp2,
&(result->hmax_in));
GMP_RATS_mpq_swap_components(&q_temp3);
GMP_INTS_mpz_negate(&(q_temp3.num));
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &q_temp3);
}
else if (GMP_RATS_mpq_cmp(&right_neighbor, &corner_point_neg, NULL) == 0)
{
//We are at the bottom negative corner point and need to "round the corner".
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &(result->corner_point_minus_one));
GMP_INTS_mpz_negate(&(right_neighbor.num));
}
else if (GMP_INTS_mpz_is_neg(&right_neighbor.num))
{
//In this region we are going straight up the Farey series approaching
//zero. Need to negate to use standard relationships.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_INTS_mpz_abs(&(q_temp1.num));
GMP_INTS_mpz_abs(&(q_temp2.num));
GMP_RALG_farey_predecessor(&q_temp3,
&q_temp1,
&q_temp2,
&(result->kmax_in));
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &q_temp3);
GMP_INTS_mpz_negate(&(right_neighbor.num));
}
else if (GMP_INTS_mpz_is_zero(&right_neighbor.num))
{
//Zero crossover.
GMP_RATS_mpq_set_si(&left_neighbor, 0, 1);
GMP_INTS_mpz_set_si(&(right_neighbor.num), 1);
GMP_INTS_mpz_copy(&(right_neighbor.den), &(result->kmax_in));
}
else if (GMP_RATS_mpq_cmp(&right_neighbor, &(result->corner_point), NULL) < 0)
{
//Below corner point. Standard relationship applies.
GMP_RALG_farey_successor(&q_temp1,
&left_neighbor,
&right_neighbor,
&(result->kmax_in));
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &q_temp1);
}
else if (GMP_RATS_mpq_cmp(&right_neighbor, &(result->corner_point), NULL) == 0)
{
//At the positive corner point.
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &(result->corner_point_plus_one));
}
else
{
//Above the positive corner point and heading for HMAX/1.
GMP_RATS_mpq_copy(&q_temp1, &left_neighbor);
GMP_RATS_mpq_copy(&q_temp2, &right_neighbor);
GMP_RATS_mpq_swap_components(&q_temp1);
GMP_RATS_mpq_swap_components(&q_temp2);
GMP_RALG_farey_predecessor(&q_temp3,
&q_temp1,
&q_temp2,
&(result->hmax_in));
GMP_RATS_mpq_swap_components(&q_temp3);
GMP_RATS_mpq_copy(&left_neighbor, &right_neighbor);
GMP_RATS_mpq_copy(&right_neighbor, &q_temp3);
}
}
done_with_right_neighbors: ;
//This is a single return point so we catch all the dynamic memory
//deallocation.
return_point:
GMP_RATS_mpq_clear(&q_temp1);
GMP_RATS_mpq_clear(&q_temp2);
GMP_RATS_mpq_clear(&q_temp3);
GMP_RATS_mpq_clear(&q_temp4);
GMP_RATS_mpq_clear(&left_neighbor);
GMP_RATS_mpq_clear(&right_neighbor);
GMP_RATS_mpq_clear(&left_neighbor_abs);
GMP_RATS_mpq_clear(&right_neighbor_abs);
GMP_RATS_mpq_clear(&hmax_over_one_neg);
GMP_RATS_mpq_clear(&corner_point_neg);
GMP_RATS_mpq_clear(&abs_norm_recip_rn);
}
//08/16/01: Visual inspection OK.
void GMP_RALG_consecutive_fab_terms_result_free(
GMP_RALG_fab_neighbor_collection_struct *arg
)
{
int i;
//Eyeball the input.
assert(arg != NULL);
//Deallocate all rational numbers and integers that MUST be allocated, i.e. they are
//never conditional.
GMP_RATS_mpq_clear(&(arg->rn_in));
GMP_INTS_mpz_clear(&(arg->kmax_in));
GMP_INTS_mpz_clear(&(arg->hmax_in));
GMP_RATS_mpq_clear(&(arg->hmax_over_one));
GMP_RATS_mpq_clear(&(arg->corner_point));
GMP_RATS_mpq_clear(&(arg->corner_point_minus_one));
GMP_RATS_mpq_clear(&(arg->corner_point_plus_one));
GMP_RATS_mpq_clear(&(arg->norm_rn));
GMP_RATS_mpq_clear(&(arg->abs_norm_rn));
//Destroy any continued fraction representations that were
//formed.
if (arg->rn_abs_cf_rep_formed)
{
GMP_RALG_cfdecomp_destroy(&(arg->rn_abs_cf_rep));
}
if (arg->rn_abs_recip_cf_rep_formed)
{
GMP_RALG_cfdecomp_destroy(&(arg->rn_abs_recip_cf_rep));
}
if(arg->corner_point_cf_rep_formed)
{
GMP_RALG_cfdecomp_destroy(&(arg->corner_point_cf_rep));
}
if(arg->corner_point_recip_cf_rep_formed)
{
GMP_RALG_cfdecomp_destroy(&(arg->corner_point_recip_cf_rep));
}
//Walk through the lefts, freeing up any allocated rational numbers.
for (i=0; i < arg->n_left_out; i++)
{
GMP_RATS_mpq_clear(&(arg->lefts[i].neighbor));
}
//Walk through the rights, freeing up any allocated rational numbers.
for (i=0; i < arg->n_right_out; i++)
{
GMP_RATS_mpq_clear(&(arg->rights[i].neighbor));
}
//Deallocate any area assigned for lefts.
if (arg->lefts)
{
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(arg->lefts);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)arg->lefts);
#else
free(arg->lefts);
#endif
arg->lefts = NULL;
}
//Deallocate any area assigned for rights.
if (arg->rights)
{
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(arg->rights);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree((char *)arg->rights);
#else
free(arg->rights);
#endif
arg->rights = NULL;
}
}
//08/16/01: Visual inspection OK.
void GMP_RALG_consecutive_fab_terms_result_dump(
FILE *s,
GMP_RALG_fab_neighbor_collection_struct *arg
)
{
int i;
char buf[250];
//Eyeball the input parameters.
assert(s != NULL);
assert(arg != NULL);
//Announce intent.
FCMIOF_stream_bannerheading(s,
"Emitting Neighbor Decomp For Analysis",
1);
//Dump the fields, in order.
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->rn_in.num),
"rn_in_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->rn_in.den),
"rn_in_den");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->kmax_in),
"kmax_in");
fprintf(s, " hmax_supplied: %12d\n", arg->hmax_supplied);
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->hmax_in),
"hmax_in");
if (arg->error)
{
fprintf(s, " error: %s\n", arg->error);
}
else
{
fprintf(s, " error: NULL\n");
}
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->corner_point.num),
"corner_point_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->corner_point.den),
"corner_point_den");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->corner_point_minus_one.num),
"cor_pt_minus_one_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->corner_point_minus_one.den),
"cor_pt_minus_one_den");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->corner_point_plus_one.num),
"cor_pt_plus_one_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->corner_point_plus_one.den),
"cor_pt_plus_one_den");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->hmax_over_one.num),
"hmax/1_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->hmax_over_one.den),
"hmax/1_den");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->norm_rn.num),
"norm_rn_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->norm_rn.den),
"norm_rn_den");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->abs_norm_rn.num),
"abs_norm_rn_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->abs_norm_rn.den),
"abs_norm_rn_den");
fprintf(s, " rn_is_neg: %12d\n", arg->rn_is_neg);
fprintf(s, " n_left_in: %12d\n", arg->n_left_in);
fprintf(s, " n_right_in: %12d\n", arg->n_right_in);
fprintf(s, "rn_abs_cf_rep_formed: %12d\n", arg->rn_abs_cf_rep_formed);
if (arg->rn_abs_cf_rep_formed)
{
GMP_RALG_cfdecomp_emit(s, "Abs Of RN In CF Decomp", &(arg->rn_abs_cf_rep), 0, 0, NULL);
}
fprintf(s, "rn_abs_recip_cf_rep_formed: %12d\n", arg->rn_abs_recip_cf_rep_formed);
if (arg->rn_abs_recip_cf_rep_formed)
{
GMP_RALG_cfdecomp_emit(s, "Abs Of Recip Of RN In CF Decomp", &(arg->rn_abs_recip_cf_rep), 0, 0, NULL);
}
fprintf(s, "corner_point_cf_rep_formed: %12d\n", arg->corner_point_cf_rep_formed);
if (arg->corner_point_cf_rep_formed)
{
GMP_RALG_cfdecomp_emit(s, "Corner Point CF Decomp", &(arg->corner_point_cf_rep), 0, 0, NULL);
}
fprintf(s, "cor_pt_recip_cf_rep_formed: %12d\n", arg->corner_point_recip_cf_rep_formed);
if (arg->corner_point_recip_cf_rep_formed)
{
GMP_RALG_cfdecomp_emit(s, "Corner Point Recip CF Decomp", &(arg->corner_point_recip_cf_rep), 0, 0, NULL);
}
fprintf(s, " equality: %12d\n", arg->equality);
fprintf(s, " n_left_out: %12d\n", arg->n_left_out);
fprintf(s, " n_right_out: %12d\n", arg->n_right_out);
for (i=0; i < arg->n_left_out; i++)
{
sprintf(buf, "Contents Of Left Neighbor Array [%d]", i);
FCMIOF_stream_bannerheading(s,
buf,
0);
fprintf(s, " index: %12d\n", arg->lefts[i].index);
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->lefts[i].neighbor.num),
"neighbor_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->lefts[i].neighbor.den),
"neighbor_den");
}
for (i=0; i < arg->n_right_out; i++)
{
sprintf(buf, "Contents Of Right Neighbor Array [%d]", i);
FCMIOF_stream_bannerheading(s,
buf,
0);
fprintf(s, " index: %12d\n", arg->rights[i].index);
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->rights[i].neighbor.num),
"neighbor_num");
GMP_INTS_mpz_long_int_format_to_stream(s,
&(arg->rights[i].neighbor.den),
"neighbor_den");
}
FCMIOF_stream_hline(s);
}
/******************************************************************/
/*** VERSION CONTROL REPORTING FUNCTIONS ************************/
/******************************************************************/
//08/16/01: Visual inspection OK.
const char *GMP_RALG_cvcinfo(void)
{
return("$Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_ralg.c,v 1.10 2002/01/27 17:58:15 dtashley Exp $");
}
//08/16/01: Visual inspection OK.
const char *GMP_RALG_hvcinfo(void)
{
return(GMP_RALG_H_VERSION);
}
//**************************************************************************
// $Log: gmp_ralg.c,v $
// Revision 1.10 2002/01/27 17:58:15 dtashley
// CRC32, other programs modified to work under new directory structure.
//
// Revision 1.9 2001/08/18 18:33:13 dtashley
// Preparing for release of v1.05.
//
// Revision 1.8 2001/08/16 19:49:40 dtashley
// Beginning to prepare for v1.05 release.
//
// Revision 1.7 2001/08/15 06:56:05 dtashley
// Substantial progress. Safety check-in.
//
// Revision 1.6 2001/08/12 10:20:58 dtashley
// Safety check-in. Substantial progress.
//
// Revision 1.5 2001/08/07 10:42:48 dtashley
// Completion of CFRATNUM extensions and DOS command-line utility.
//
// Revision 1.4 2001/07/13 21:02:20 dtashley
// Version control reporting changes.
//
// Revision 1.3 2001/07/13 20:44:42 dtashley
// Changes, CVS keyword expansion test.
//
// Revision 1.2 2001/07/13 00:57:08 dtashley
// Safety check-in. Substantial progress on port.
//
// Revision 1.1 2001/07/12 05:42:06 dtashley
// Initial checkin.
//
//**************************************************************************
// End of GMP_RALG.C.