// $Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_rats.c,v 1.10 2001/08/16 19:49:40 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_RATS
#include
#include
#include
#include "bstrfunc.h"
#include "charfunc.h"
#include "gmp_ints.h"
#include "gmp_rats.h"
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
#include "ccmalloc.h"
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
#include "tclalloc.h"
#else
#include
#endif
/******************************************************************/
/*** STATUS FUNCTIONS *******************************************/
/******************************************************************/
//Functions in this category provide information about rational
//numbers.
//08/08/01: Visual inspection OK.
int GMP_RATS_mpq_is_nan(const GMP_RATS_mpq_struct *rn)
{
assert(rn != NULL);
//A rational number is NAN in one of two
//circumstances. If either of the integer components
//is NAN, or else if there is a zero denominator.
if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
{
return(1);
}
if (GMP_INTS_mpz_is_zero(&(rn->den)))
{
return(1);
}
//We're clean ...
return(0);
}
/******************************************************************/
/*** INITIALIZATION, CLEARING, AND SETTING FUNCTIONS ************/
/******************************************************************/
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_init(GMP_RATS_mpq_struct *arg)
{
//Eyeball the input parameter.
assert(arg != NULL);
//Initialize the numerator and denominator.
GMP_INTS_mpz_init(&(arg->num));
GMP_INTS_mpz_init(&(arg->den));
//Canonically, we must start off as 0/1--canonical zero.
GMP_INTS_mpz_set_ui(&(arg->num), 0);
GMP_INTS_mpz_set_ui(&(arg->den), 1);
}
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_clear(GMP_RATS_mpq_struct *arg)
{
//Eyeball the input parameter.
assert(arg != NULL);
//Clear the numerator and denominator. The called functions
//will check for NULL pointers and so forth.
GMP_INTS_mpz_clear(&(arg->num));
GMP_INTS_mpz_clear(&(arg->den));
}
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_set_si(GMP_RATS_mpq_struct *arg,
int num,
int den)
{
//Eyeball the input parameters.
assert(arg != NULL);
//Set the numerator and denominator.
GMP_INTS_mpz_set_si(&(arg->num), num);
GMP_INTS_mpz_set_si(&(arg->den), den);
}
//08/08/01: Visual inspection OK.
void GMP_RATS_mpq_copy( GMP_RATS_mpq_struct *dst,
const GMP_RATS_mpq_struct *src)
{
assert(dst != NULL);
assert(src != NULL);
GMP_INTS_mpz_copy(&(dst->num), &(src->num));
GMP_INTS_mpz_copy(&(dst->den), &(src->den));
}
//08/13/01: Visual inspection OK.
void GMP_RATS_mpq_swap( GMP_RATS_mpq_struct *a,
GMP_RATS_mpq_struct *b)
{
assert(a != NULL);
assert(b != NULL);
//Handle the swap by swapping integer components.
GMP_INTS_mpz_swap(&(a->num), &(b->num));
GMP_INTS_mpz_swap(&(a->den), &(b->den));
}
//08/13/01: Visual inspection OK.
void GMP_RATS_mpq_swap_components(GMP_RATS_mpq_struct *arg)
{
assert(arg != NULL);
GMP_INTS_mpz_swap(&(arg->num), &(arg->den));
}
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_set_complex_slash_sepd_rat_num(const char *s,
int *failure,
GMP_RATS_mpq_struct *rn)
{
char *slash_posn, *numerator, *denominator;
int s_len, numerator_len, denominator_len;
int i;
//Eyeball the input parameters.
assert(s != NULL);
assert(failure != NULL);
assert(rn != NULL);
//Start off believing there is no failure.
*failure = 0;
//Figure out if there is one and only one slash in the
//string. If this condition isn't met, we cannot
//go further.
slash_posn = strchr(s, '/');
if (!slash_posn)
{
*failure = 1;
return;
}
if (strchr(slash_posn + 1, '/')) //There is a second occurence.
{
*failure = 1;
return;
}
//At this point we have one and only one slash.
//Crack the string in two. We must do this because the
//input is a constant string. We are not allowed to touch it
//in the logical domain because of the "const" keyword. We can't
//do this in the physical domain because the debugger will nail
//us for it.
s_len = strlen(s);
numerator_len = slash_posn - s;
denominator_len = strlen(slash_posn + 1);
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
numerator = CCMALLOC_malloc(sizeof(char) * (numerator_len + 1));
denominator = CCMALLOC_malloc(sizeof(char) * (denominator_len + 1));
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
numerator = TclpAlloc(sizeof(char) * (numerator_len + 1));
denominator = TclpAlloc(sizeof(char) * (denominator_len + 1));
#else
numerator = malloc(sizeof(char) * (numerator_len + 1));
denominator = malloc(sizeof(char) * (denominator_len + 1));
#endif
assert(numerator != NULL);
assert(denominator != NULL);
for (i=0; inum),
failure,
numerator);
if (*failure)
{
*failure = 1; //Clamp to 1, don't know what non-zero value
//was there.
goto ret_pt;
}
//Try to parse out the denominator.
GMP_INTS_mpz_set_general_int(&(rn->den),
failure,
denominator);
if (*failure)
{
*failure = 1; //Clamp to 1, don't know what non-zero value
//was there.
goto ret_pt;
}
//At this point, we have both a numerator and denominator.
//Clean up and return.
ret_pt:
#if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
CCMALLOC_free(numerator);
CCMALLOC_free(denominator);
#elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
TclpFree(numerator);
TclpFree(denominator);
#else
free(numerator);
free(denominator);
#endif
}
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_set_sci_not_rat_num(const char *s,
int *failure,
GMP_RATS_mpq_struct *rn)
{
int parse_failure;
//Return code from the floating point parsing
//function.
char mant_sign;
//Sign character, if any, from the mantissa,
//or N otherwise.
size_t mant_bdp;
//The index to the start of the mantissa before
//the decimal point.
size_t mant_bdp_len;
//The length of the mantissa before the decimal
//point. Zero means not defined, i.e. that
//no characters were parsed and interpreted as
//that part of a floating point number.
size_t mant_adp;
size_t mant_adp_len;
//Similar fields for after the decimal point.
char exp_sign;
//Sign of the exponent, if any, or N otherwise.
size_t exp;
size_t exp_len;
//Similar fields as to the mantissa, but for the
//exponent.
size_t si;
//Iteration variable.
int exponent_val;
//The value of the exponent. We can't accept
//an exponent outside the range of a 24-bit
//signed integer. The 24-bit limit is arbitrary.
//For one thing, it gives room to detect overflow
//as are adding and multiplying by 10.
//Eyeball the input parameters.
assert(s != NULL);
assert(failure != NULL);
assert(rn != NULL);
//Subcomponents of the rational number will be checked as
//we make integer calls, if we're in debug mode.
//Start off believing no failure.
*failure = 0;
//Set the output to 0/1. This is the default case for some
//steps below.
GMP_RATS_mpq_set_si(rn, 0, 1);
//Attempt to parse the number as a general number
//in scientific notation.
BSTRFUNC_parse_gen_sci_not_num(s,
&parse_failure,
&mant_sign,
&mant_bdp,
&mant_bdp_len,
&mant_adp,
&mant_adp_len,
&exp_sign,
&exp,
&exp_len);
//If it wouldn't parse as a general number, can't go further.
if (parse_failure)
{
*failure = 1;
return;
}
else
{
//The number parsed out. The general strategy is to form a rational number
//consisting of the mantissa, with the decimal point shifted fully right, over
//a denominator of 1. From there, we process the exponent and combine it with
//the number of characters after the decimal point to form a virtual exponent.
//If the exponent is positive, we multiply the numerator by the power of 10.
//If the exponent is negative, we multiply the denominator by that power of 10.
//We want to trim the trailing zeros off of the portion of the mantissa after the
//decimal point. We only need to back up indices, no need to make copies, etc.
//Note that it is possible that there are only zeros, in which case we'll end
//up with a length of zero.
while ((mant_adp_len > 0) && (s[mant_adp + mant_adp_len - 1]=='0'))
mant_adp_len--;
//Trim the leading zeros off of the portion of the mantissa before the
//decimal point. Note that it is possible that there is only a zero,
//so we may trim it down to nothing.
while ((mant_bdp_len > 0) && (s[mant_bdp]=='0'))
{
mant_bdp++;
mant_bdp_len--;
}
//If we have only zeros in the mantissa, both before the
//decimal point and after, then we return 0.
if ((mant_bdp_len + mant_adp_len) == 0)
{
*failure = 0;
return;
}
//Convert the numerator to an integer which represents the
//part before the mantissa and the part after the mantissa
//concatenated as an integer. We could call a function to do
//this, but the function is not really any better in algorithm.
//We can do it ourselves.
GMP_INTS_mpz_set_ui(&(rn->num), 0);
for (si = 0; si < mant_bdp_len; si++)
{
int val;
GMP_INTS_mpz_mul_si(&(rn->num), &(rn->num), 10);
val = CHARFUNC_digit_to_val(s[mant_bdp + si]);
if (val >= 0)
GMP_INTS_mpz_add_ui(&(rn->num), &(rn->num), val);
}
for (si = 0; si < mant_adp_len; si++)
{
int val;
GMP_INTS_mpz_mul_si(&(rn->num), &(rn->num), 10);
val = CHARFUNC_digit_to_val(s[mant_adp + si]);
if (val >= 0)
GMP_INTS_mpz_add_ui(&(rn->num), &(rn->num), val);
}
//The numerator should now have an integer which is
//The absolute value of the mantissa. Process the possible
//sign.
if (mant_sign == '-')
GMP_INTS_mpz_negate(&(rn->num));
//We now need to form a value from the exponent, if any.
//First, tackle the exponent. Process the
//exponent into a signed integer. We have to
//balk at anything outside of 24 bits. The
//procedure used automatically handles
//leading zeros correctly.
exponent_val = 0;
for (si=exp; si<(exp+exp_len); si++)
{
int val;
val = CHARFUNC_digit_to_val(s[si]);
assert(val >= 0 && val <= 9);
exponent_val *= 10;
exponent_val += val;
if (((exp_sign=='-') && (exponent_val>8388608))
||
((exp_sign != '-') && (exponent_val>8388607)))
{
*failure = 1;
return;
}
}
//If we're here, the exponent has been computed and
//is within 24 bits. However, we need to adjust for
//the sign.
if (exp_sign == '-')
exponent_val = -exponent_val;
//We need to adjust the exponent for the number of digits
//after the decimal point.
exponent_val -= mant_adp_len;
//Again, clip for size.
if ((exponent_val < -8388608) || (exponent_val > 8388607))
{
*failure = 1;
return;
}
//There are two cases to consider. If the exponent
//is positive, we need to multiply the numerator
//by 10 exponentiated to the power of the exponent.
//If the exponent is negative, we need to do the
//same thing to the denominator. If the exponent
//is negative, we don't need to do anything.
if (exponent_val > 0)
{
GMP_INTS_mpz_struct k10, k10_exponentiated;
GMP_INTS_mpz_init(&k10);
GMP_INTS_mpz_init(&k10_exponentiated);
GMP_INTS_mpz_set_ui(&k10, 10);
GMP_INTS_mpz_pow_ui(&k10_exponentiated, &k10, exponent_val);
GMP_INTS_mpz_mul(&(rn->num), &(rn->num), &k10_exponentiated);
GMP_INTS_mpz_clear(&k10);
GMP_INTS_mpz_clear(&k10_exponentiated);
*failure = 0;
if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
*failure = 1;
return;
}
else if (exponent_val < 0)
{
GMP_INTS_mpz_struct k10, k10_exponentiated;
GMP_INTS_mpz_init(&k10);
GMP_INTS_mpz_init(&k10_exponentiated);
GMP_INTS_mpz_set_ui(&k10, 10);
GMP_INTS_mpz_pow_ui(&k10_exponentiated, &k10, -exponent_val);
GMP_INTS_mpz_mul(&(rn->den), &(rn->den), &k10_exponentiated);
GMP_INTS_mpz_clear(&k10);
GMP_INTS_mpz_clear(&k10_exponentiated);
*failure = 0;
if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
*failure = 1;
return;
}
}
}
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_set_all_format_rat_num(const char *s,
int *failure,
GMP_RATS_mpq_struct *rn)
{
//Eyeball the input parameters.
assert(s != NULL);
assert(failure != NULL);
assert(rn != NULL);
//Assume no failure.
*failure = 0;
//Try in order to parse as integers with slash then
//as number in scientific notation.
GMP_RATS_mpq_set_complex_slash_sepd_rat_num(s,
failure,
rn);
if (!*failure)
return;
GMP_RATS_mpq_set_sci_not_rat_num(s,
failure,
rn);
if (*failure)
*failure = 1; //Clamp output.
}
/******************************************************************/
/*** NORMALIZATION FUNCTIONS ************************************/
/******************************************************************/
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_normalize_sign(GMP_RATS_mpq_struct *rn)
{
//Eyeball the input.
assert(rn != NULL);
if (GMP_INTS_mpz_is_neg(&rn->num) && GMP_INTS_mpz_is_neg(&rn->den))
{
//Both negative, can negate both, this leaves both positive,
//which is the normalized form for a positive rational
//number.
GMP_INTS_mpz_negate(&rn->num);
GMP_INTS_mpz_negate(&rn->den);
}
else if (!GMP_INTS_mpz_is_neg(&rn->num) && GMP_INTS_mpz_is_neg(&rn->den))
{
//Denominator neg, numerator non-neg, can negate both. This
//will leave numerator neg, denominator pos, which is
//normalized form for negative rational number.
GMP_INTS_mpz_negate(&rn->num);
GMP_INTS_mpz_negate(&rn->den);
}
}
//08/07/01: Visual inspection OK.
void GMP_RATS_mpq_normalize(GMP_RATS_mpq_struct *rn)
{
//Eyeball the input.
assert(rn != NULL);
//Cover some special cases. If either component has flags
//set, don't even touch it.
if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
{
return;
}
//If the denominator is zero, normalize it to 1/0, the canonical
//for for an illegal rational number.
else if (GMP_INTS_mpz_is_zero(&(rn->den)))
{
GMP_RATS_mpq_set_si(rn, 1, 0);
return;
}
//If the numerator is zero, convert the number to the canonical
//form for zero of 0/1.
else if (GMP_INTS_mpz_is_zero(&(rn->num)))
{
GMP_RATS_mpq_set_si(rn, 0, 1);
return;
}
else
{
int num_is_neg;
int den_is_neg;
GMP_INTS_mpz_struct gcd, quotient, remainder;
//Allocate space for the integers used.
GMP_INTS_mpz_init(&gcd);
GMP_INTS_mpz_init("ient);
GMP_INTS_mpz_init(&remainder);
//This is the most normal case, where we need to
//look at reducing the numerator and denominator.
//One way to do it would be to obtain the g.c.d.
//and divide this out, and this is the route
//we'll take. However, must grab out the sign.
if (GMP_INTS_mpz_is_neg(&(rn->num)))
{
num_is_neg = 1;
GMP_INTS_mpz_negate(&(rn->num));
}
else
{
num_is_neg = 0;
}
if (GMP_INTS_mpz_is_neg(&(rn->den)))
{
den_is_neg = 1;
GMP_INTS_mpz_negate(&(rn->den));
}
else
{
den_is_neg = 0;
}
//Calculate the GCD.
GMP_INTS_mpz_gcd(&gcd, &(rn->num), &(rn->den));
//Divide the numerator by the GCD and store it
//back.
GMP_INTS_mpz_tdiv_qr("ient, &remainder,
&(rn->num), &gcd);
GMP_INTS_mpz_copy(&(rn->num), "ient);
//Divide the denominator by the GCD and store it
//back.
GMP_INTS_mpz_tdiv_qr("ient, &remainder,
&(rn->den), &gcd);
GMP_INTS_mpz_copy(&(rn->den), "ient);
//We now need to adjust the sign. Both the
//numerator and denominator are definitely
//positive. Need to make the numerator
//negative if either but not both of the
//original signs were negative.
if ((num_is_neg && !den_is_neg) || (!num_is_neg && den_is_neg))
{
GMP_INTS_mpz_negate(&(rn->num));
}
//Deallocate space for the integers used.
GMP_INTS_mpz_clear(&gcd);
GMP_INTS_mpz_clear("ient);
GMP_INTS_mpz_clear(&remainder);
return;
}
}
/******************************************************************/
/*** ARITHMETIC FUNCTIONS ***************************************/
/******************************************************************/
//08/08/01: Visual inspection OK.
void GMP_RATS_mpq_add( GMP_RATS_mpq_struct *result,
const GMP_RATS_mpq_struct *arg1,
const GMP_RATS_mpq_struct *arg2)
{
GMP_RATS_mpq_struct rv;
GMP_INTS_mpz_struct temp;
//Eyeball the input parameters.
assert(result != NULL);
assert(arg1 != NULL);
assert(arg2 != NULL);
//Generally speaking, we do not want to require that
//the arguments and the result be distinct, as this is
//too much of a restriction on the caller. The approach
//taken, somewhat wasteful, is to allocate a place for
//the return value.
//
//For addition, if we are adding a/b and c/d, the
//result is necessarily algebraically
//(ad + cb)/bd.
//
//If either rational number in the input is invalid,
//flag the result as invalid.
if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
{
GMP_RATS_mpq_set_si(result, 1, 0);
}
else
{
//Both rational numbers are OK. Can simply stage the
//result by the algebraic identity and then
//normalize it. Only need one temporary variable.
//
//Initialize the rational number that we will use to
//hold return value in case it is the same as one
//or both of the arguments.
GMP_RATS_mpq_init(&rv);
//Initialize the temporary integer.
GMP_INTS_mpz_init(&temp);
//numerator = a * d
GMP_INTS_mpz_mul(&(rv.num), &(arg1->num), &(arg2->den));
//temp = c * b
GMP_INTS_mpz_mul(&temp, &(arg2->num), &(arg1->den));
//numerator = a * d + c * b
GMP_INTS_mpz_add(&(rv.num), &(rv.num), &temp);
//denominator = b * d
GMP_INTS_mpz_mul(&(rv.den), &(arg1->den), &(arg2->den));
//Copy the temporary result to the actual return value.
//Had to wait until now in case result was the same
//as either or both args.
GMP_RATS_mpq_copy(result, &rv);
//Normalize the result.
GMP_RATS_mpq_normalize(result);
//Free dynamic memory.
GMP_RATS_mpq_clear(&rv);
GMP_INTS_mpz_clear(&temp);
}
}
//08/08/01: Visual inspection OK.
void GMP_RATS_mpq_sub( GMP_RATS_mpq_struct *result,
const GMP_RATS_mpq_struct *arg1,
const GMP_RATS_mpq_struct *arg2)
{
GMP_RATS_mpq_struct negated_arg_2;
//Eyeball the input parameters.
assert(result != NULL);
assert(arg1 != NULL);
assert(arg2 != NULL);
//For the subtract function, we could do it directly,
//but might as well just define it recursively
//in terms of add. We can't modify the inputs,
//so copy the second off and negate it. All error
//flags and so forth will propagate automatically.
//
//Allocate space for the negated arg 2.
GMP_RATS_mpq_init(&negated_arg_2);
//Copy from the original.
GMP_RATS_mpq_copy(&negated_arg_2, arg2);
//Negate the copy. Negating the numerator will
//do it.
GMP_INTS_mpz_negate(&(negated_arg_2.num));
//Make the add, which now is really a subtract.
GMP_RATS_mpq_add(result, arg1, &negated_arg_2);
//Destroy the temporary variable.
GMP_RATS_mpq_clear(&negated_arg_2);
}
//08/16/01: Visual inspection OK.
void GMP_RATS_mpq_mul( GMP_RATS_mpq_struct *result,
const GMP_RATS_mpq_struct *arg1,
const GMP_RATS_mpq_struct *arg2)
{
//Eyeball the input parameters.
assert(result != NULL);
assert(arg1 != NULL);
assert(arg2 != NULL);
//If either rational number in the input is invalid,
//flag the result as invalid.
if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
{
GMP_RATS_mpq_set_si(result, 1, 0);
}
else
{
//Rational number multiplication is a simple matter.
//Just multiply components. Don't need to worry
//about rational numbers overlapping, as numerator
//operations and denominator operations are separate.
GMP_INTS_mpz_mul(&(result->num),
&(arg1->num),
&(arg2->num));
GMP_INTS_mpz_mul(&(result->den),
&(arg1->den),
&(arg2->den));
//Normalize it.
GMP_RATS_mpq_normalize(result);
}
}
//08/16/01: Visual inspection OK.
void GMP_RATS_mpq_div( GMP_RATS_mpq_struct *result,
const GMP_RATS_mpq_struct *arg1,
const GMP_RATS_mpq_struct *arg2)
{
GMP_RATS_mpq_struct rv;
//Eyeball the input parameters.
assert(result != NULL);
assert(arg1 != NULL);
assert(arg2 != NULL);
//If either rational number in the input is invalid,
//flag the result as invalid.
if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
{
GMP_RATS_mpq_set_si(result, 1, 0);
}
else
{
//Rational number division is a simple matter.
//Just multiply components. We do need to worry
//about rational numbers overlapping, so must
//make a copy of the return value. If denominator
//of return value is zero, it is NAN, but caller
//should detect this.
//
//Allocate return value.
GMP_RATS_mpq_init(&rv);
//Calculate quotient.
GMP_INTS_mpz_mul(&(rv.num),
&(arg1->num),
&(arg2->den));
GMP_INTS_mpz_mul(&(rv.den),
&(arg1->den),
&(arg2->num));
//Normalize quotient.
GMP_RATS_mpq_normalize(&rv);
//Copy to its destination.
GMP_RATS_mpq_copy(result, &rv);
//Deallocate temporary return value.
GMP_RATS_mpq_clear(&rv);
}
}
/******************************************************************/
/*** COMPARISON FUNCTIONS ***************************************/
/******************************************************************/
//08/16/01: Visual inspection OK.
int GMP_RATS_mpq_cmp(const GMP_RATS_mpq_struct *arg1,
const GMP_RATS_mpq_struct *arg2,
int *failure)
{
int arg1_sgn;
int arg2_sgn;
int rv, failure_rv;
GMP_INTS_mpz_struct prod1, prod2;
//Eyeball the input parameters. Note that the third
//parameter may be NULL.
assert(arg1 != NULL);
assert(arg2 != NULL);
//If either of the input arguments are NAN, we
//cannot compare arguments. We return 0, and it
//depends on the caller whether it is important
//that the comparison is bogus.
if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
{
if (failure != NULL)
*failure = 1;
return(0);
}
//Calculate the sign of the left argument. The encoding
//we'll use is -1 means negative, 0 means zero, and
//1 means positive.
if (GMP_INTS_mpz_is_zero(&(arg1->num)))
{
arg1_sgn = 0;
}
else if (GMP_INTS_mpz_is_neg(&(arg1->num)) && GMP_INTS_mpz_is_neg(&(arg1->den)))
{
arg1_sgn = 1;
}
else if (GMP_INTS_mpz_is_neg(&(arg1->num)) && GMP_INTS_mpz_is_pos(&(arg1->den)))
{
arg1_sgn = -1;
}
else if (GMP_INTS_mpz_is_pos(&(arg1->num)) && GMP_INTS_mpz_is_neg(&(arg1->den)))
{
arg1_sgn = -1;
}
else if (GMP_INTS_mpz_is_pos(&(arg1->num)) && GMP_INTS_mpz_is_pos(&(arg1->den)))
{
arg1_sgn = 1;
}
//Calculate the sign of the right argument. The encoding
//we'll use is -1 means negative, 0 means zero, and
//1 means positive.
if (GMP_INTS_mpz_is_zero(&(arg2->num)))
{
arg2_sgn = 0;
}
else if (GMP_INTS_mpz_is_neg(&(arg2->num)) && GMP_INTS_mpz_is_neg(&(arg2->den)))
{
arg2_sgn = 1;
}
else if (GMP_INTS_mpz_is_neg(&(arg2->num)) && GMP_INTS_mpz_is_pos(&(arg2->den)))
{
arg2_sgn = -1;
}
else if (GMP_INTS_mpz_is_pos(&(arg2->num)) && GMP_INTS_mpz_is_neg(&(arg2->den)))
{
arg2_sgn = -1;
}
else if (GMP_INTS_mpz_is_pos(&(arg2->num)) && GMP_INTS_mpz_is_pos(&(arg2->den)))
{
arg2_sgn = 1;
}
//OK, can handle some simple cases where the signs of the
//operands are different or both are zero.
if ((arg1_sgn == 0) && (arg2_sgn == 0))
{
if (failure != NULL)
*failure = 0;
return(0);
}
else if ((arg1_sgn == -1) && (arg2_sgn > -1))
{
if (failure != NULL)
*failure = 0;
return(-1);
}
else if ((arg1_sgn == 0) && (arg2_sgn < 0))
{
if (failure != NULL)
*failure = 0;
return(1);
}
else if ((arg1_sgn == 0) && (arg2_sgn > 0))
{
if (failure != NULL)
*failure = 0;
return(-1);
}
else if ((arg1_sgn == 1) && (arg2_sgn < 1))
{
if (failure != NULL)
*failure = 0;
return(1);
}
//OK at this point, we cannot make a simple determination
//as to the relative ordering. The signs of arg1 and
//arg2 are both the same, either both positive or both
//negative. We have to do a multiplication to sort
//it out.
//
//Allocate the two integers to hold multiplication
//results.
GMP_INTS_mpz_init(&prod1);
GMP_INTS_mpz_init(&prod2);
//Cross-multiply to get relative magnitudes.
GMP_INTS_mpz_mul(&prod1, &(arg1->num), &(arg2->den));
GMP_INTS_mpz_mul(&prod2, &(arg1->den), &(arg2->num));
//Take absolute values.
GMP_INTS_mpz_abs(&prod1);
GMP_INTS_mpz_abs(&prod2);
//If we overflowed either multiplication and generated
//a NAN, we cannot complete the compare.
if (GMP_INTS_mpz_get_flags(&prod1) || GMP_INTS_mpz_get_flags(&prod2))
{
failure_rv = 1;
rv = 0;
}
//If both rational numbers were effectively positive, we can
//use the relative ordering of the products as the relative
//ordering of the rational numbers.
else if (arg1_sgn == 1)
{
//Compare the integers.
rv = GMP_INTS_mpz_cmp(&prod1, &prod2);
//Clamp the return value.
if (rv < 0)
rv = -1;
else if (rv == 0)
rv = 0;
else if (rv > 0)
rv = 1;
//There was no error.
failure_rv = 0;
}
else
{
//The only case that *should* allow us to be here is
//if the sign of both numbers is neg.
assert(arg1_sgn == -1);
//Compare the integers.
rv = GMP_INTS_mpz_cmp(&prod1, &prod2);
//Invert and clamp the return value.
if (rv < 0)
rv = 1;
else if (rv == 0)
rv = 0;
else if (rv > 0)
rv = -1;
//There was no error.
failure_rv = 0;
}
//Deallocate the two integers.
GMP_INTS_mpz_clear(&prod1);
GMP_INTS_mpz_clear(&prod2);
//Return the return values.
if (failure != NULL)
*failure = failure_rv;
return(rv);
}
/******************************************************************/
/*** VERSION CONTROL REPORTING FUNCTIONS ************************/
/******************************************************************/
//08/07/01: Visual inspection OK.
const char *GMP_RATS_cvcinfo(void)
{
return("$Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_rats.c,v 1.10 2001/08/16 19:49:40 dtashley Exp $");
}
//08/07/01: Visual inspection OK.
const char *GMP_RATS_hvcinfo(void)
{
return(GMP_RATS_H_VERSION);
}
//**************************************************************************
// $Log: gmp_rats.c,v $
// Revision 1.10 2001/08/16 19:49:40 dtashley
// Beginning to prepare for v1.05 release.
//
// Revision 1.9 2001/08/15 06:56:05 dtashley
// Substantial progress. Safety check-in.
//
// Revision 1.8 2001/08/12 10:20:58 dtashley
// Safety check-in. Substantial progress.
//
// Revision 1.7 2001/08/10 00:53:59 dtashley
// Completion of basic rational number arithmetic utilities and extensions.
//
// Revision 1.6 2001/08/08 02:16:51 dtashley
// Completion of RNRED utility and ARBINT RNRED Tcl extension.
//
// 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_RATS.C.