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Revision 42 - (show annotations) (download)
Fri Oct 14 01:50:00 2016 UTC (7 years, 9 months ago) by dashley
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Move shared source code to commonize.
1 // $Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_rats.c,v 1.10 2001/08/16 19:49:40 dtashley Exp $
2
3 //--------------------------------------------------------------------------------
4 //Copyright 2001 David T. Ashley
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569 //combination as such.
570 //
571 // 14. Revised Versions of this License.
572 //
573 // The Free Software Foundation may publish revised and/or new versions of
574 //the GNU General Public License from time to time. Such new versions will
575 //be similar in spirit to the present version, but may differ in detail to
576 //address new problems or concerns.
577 //
578 // Each version is given a distinguishing version number. If the
579 //Program specifies that a certain numbered version of the GNU General
580 //Public License "or any later version" applies to it, you have the
581 //option of following the terms and conditions either of that numbered
582 //version or of any later version published by the Free Software
583 //Foundation. If the Program does not specify a version number of the
584 //GNU General Public License, you may choose any version ever published
585 //by the Free Software Foundation.
586 //
587 // If the Program specifies that a proxy can decide which future
588 //versions of the GNU General Public License can be used, that proxy's
589 //public statement of acceptance of a version permanently authorizes you
590 //to choose that version for the Program.
591 //
592 // Later license versions may give you additional or different
593 //permissions. However, no additional obligations are imposed on any
594 //author or copyright holder as a result of your choosing to follow a
595 //later version.
596 //
597 // 15. Disclaimer of Warranty.
598 //
599 // THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
600 //APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
601 //HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
602 //OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
603 //THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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605 //IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
606 //ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
607 //
608 // 16. Limitation of Liability.
609 //
610 // IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
611 //WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
612 //THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
613 //GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
614 //USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
615 //DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
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617 //EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
618 //SUCH DAMAGES.
619 //
620 // 17. Interpretation of Sections 15 and 16.
621 //
622 // If the disclaimer of warranty and limitation of liability provided
623 //above cannot be given local legal effect according to their terms,
624 //reviewing courts shall apply local law that most closely approximates
625 //an absolute waiver of all civil liability in connection with the
626 //Program, unless a warranty or assumption of liability accompanies a
627 //copy of the Program in return for a fee.
628 //
629 // END OF TERMS AND CONDITIONS
630 //
631 // How to Apply These Terms to Your New Programs
632 //
633 // If you develop a new program, and you want it to be of the greatest
634 //possible use to the public, the best way to achieve this is to make it
635 //free software which everyone can redistribute and change under these terms.
636 //
637 // To do so, attach the following notices to the program. It is safest
638 //to attach them to the start of each source file to most effectively
639 //state the exclusion of warranty; and each file should have at least
640 //the "copyright" line and a pointer to where the full notice is found.
641 //
642 // <one line to give the program's name and a brief idea of what it does.>
643 // Copyright (C) <year> <name of author>
644 //
645 // This program is free software: you can redistribute it and/or modify
646 // it under the terms of the GNU General Public License as published by
647 // the Free Software Foundation, either version 3 of the License, or
648 // (at your option) any later version.
649 //
650 // This program is distributed in the hope that it will be useful,
651 // but WITHOUT ANY WARRANTY; without even the implied warranty of
652 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
653 // GNU General Public License for more details.
654 //
655 // You should have received a copy of the GNU General Public License
656 // along with this program. If not, see <http://www.gnu.org/licenses/>.
657 //
658 //Also add information on how to contact you by electronic and paper mail.
659 //
660 // If the program does terminal interaction, make it output a short
661 //notice like this when it starts in an interactive mode:
662 //
663 // <program> Copyright (C) <year> <name of author>
664 // This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
665 // This is free software, and you are welcome to redistribute it
666 // under certain conditions; type `show c' for details.
667 //
668 //The hypothetical commands `show w' and `show c' should show the appropriate
669 //parts of the General Public License. Of course, your program's commands
670 //might be different; for a GUI interface, you would use an "about box".
671 //
672 // You should also get your employer (if you work as a programmer) or school,
673 //if any, to sign a "copyright disclaimer" for the program, if necessary.
674 //For more information on this, and how to apply and follow the GNU GPL, see
675 //<http://www.gnu.org/licenses/>.
676 //
677 // The GNU General Public License does not permit incorporating your program
678 //into proprietary programs. If your program is a subroutine library, you
679 //may consider it more useful to permit linking proprietary applications with
680 //the library. If this is what you want to do, use the GNU Lesser General
681 //Public License instead of this License. But first, please read
682 //<http://www.gnu.org/philosophy/why-not-lgpl.html>.
683 //-------------------------------------------------------------------------------------------------
684 //--------------------------------------------------------------------------------
685 #define MODULE_GMP_RATS
686
687 #include <assert.h>
688 #include <stdio.h>
689 #include <string.h>
690
691 #include "bstrfunc.h"
692 #include "charfunc.h"
693 #include "gmp_ints.h"
694 #include "gmp_rats.h"
695
696 #if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
697 #include "ccmalloc.h"
698 #elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
699 #include "tclalloc.h"
700 #else
701 #include <malloc.h>
702 #endif
703
704
705 /******************************************************************/
706 /*** STATUS FUNCTIONS *******************************************/
707 /******************************************************************/
708 //Functions in this category provide information about rational
709 //numbers.
710 //08/08/01: Visual inspection OK.
711 int GMP_RATS_mpq_is_nan(const GMP_RATS_mpq_struct *rn)
712 {
713 assert(rn != NULL);
714
715 //A rational number is NAN in one of two
716 //circumstances. If either of the integer components
717 //is NAN, or else if there is a zero denominator.
718 if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
719 {
720 return(1);
721 }
722 if (GMP_INTS_mpz_is_zero(&(rn->den)))
723 {
724 return(1);
725 }
726
727 //We're clean ...
728 return(0);
729 }
730
731
732 /******************************************************************/
733 /*** INITIALIZATION, CLEARING, AND SETTING FUNCTIONS ************/
734 /******************************************************************/
735 //08/07/01: Visual inspection OK.
736 void GMP_RATS_mpq_init(GMP_RATS_mpq_struct *arg)
737 {
738 //Eyeball the input parameter.
739 assert(arg != NULL);
740
741 //Initialize the numerator and denominator.
742 GMP_INTS_mpz_init(&(arg->num));
743 GMP_INTS_mpz_init(&(arg->den));
744
745 //Canonically, we must start off as 0/1--canonical zero.
746 GMP_INTS_mpz_set_ui(&(arg->num), 0);
747 GMP_INTS_mpz_set_ui(&(arg->den), 1);
748 }
749
750
751 //08/07/01: Visual inspection OK.
752 void GMP_RATS_mpq_clear(GMP_RATS_mpq_struct *arg)
753 {
754 //Eyeball the input parameter.
755 assert(arg != NULL);
756
757 //Clear the numerator and denominator. The called functions
758 //will check for NULL pointers and so forth.
759 GMP_INTS_mpz_clear(&(arg->num));
760 GMP_INTS_mpz_clear(&(arg->den));
761 }
762
763
764 //08/07/01: Visual inspection OK.
765 void GMP_RATS_mpq_set_si(GMP_RATS_mpq_struct *arg,
766 int num,
767 int den)
768 {
769 //Eyeball the input parameters.
770 assert(arg != NULL);
771
772 //Set the numerator and denominator.
773 GMP_INTS_mpz_set_si(&(arg->num), num);
774 GMP_INTS_mpz_set_si(&(arg->den), den);
775 }
776
777
778 //08/08/01: Visual inspection OK.
779 void GMP_RATS_mpq_copy( GMP_RATS_mpq_struct *dst,
780 const GMP_RATS_mpq_struct *src)
781 {
782 assert(dst != NULL);
783 assert(src != NULL);
784
785 GMP_INTS_mpz_copy(&(dst->num), &(src->num));
786 GMP_INTS_mpz_copy(&(dst->den), &(src->den));
787 }
788
789
790 //08/13/01: Visual inspection OK.
791 void GMP_RATS_mpq_swap( GMP_RATS_mpq_struct *a,
792 GMP_RATS_mpq_struct *b)
793 {
794 assert(a != NULL);
795 assert(b != NULL);
796
797 //Handle the swap by swapping integer components.
798 GMP_INTS_mpz_swap(&(a->num), &(b->num));
799 GMP_INTS_mpz_swap(&(a->den), &(b->den));
800 }
801
802
803 //08/13/01: Visual inspection OK.
804 void GMP_RATS_mpq_swap_components(GMP_RATS_mpq_struct *arg)
805 {
806 assert(arg != NULL);
807
808 GMP_INTS_mpz_swap(&(arg->num), &(arg->den));
809 }
810
811
812 //08/07/01: Visual inspection OK.
813 void GMP_RATS_mpq_set_complex_slash_sepd_rat_num(const char *s,
814 int *failure,
815 GMP_RATS_mpq_struct *rn)
816 {
817 char *slash_posn, *numerator, *denominator;
818 int s_len, numerator_len, denominator_len;
819 int i;
820
821 //Eyeball the input parameters.
822 assert(s != NULL);
823 assert(failure != NULL);
824 assert(rn != NULL);
825
826 //Start off believing there is no failure.
827 *failure = 0;
828
829 //Figure out if there is one and only one slash in the
830 //string. If this condition isn't met, we cannot
831 //go further.
832 slash_posn = strchr(s, '/');
833 if (!slash_posn)
834 {
835 *failure = 1;
836 return;
837 }
838 if (strchr(slash_posn + 1, '/')) //There is a second occurence.
839 {
840 *failure = 1;
841 return;
842 }
843
844 //At this point we have one and only one slash.
845 //Crack the string in two. We must do this because the
846 //input is a constant string. We are not allowed to touch it
847 //in the logical domain because of the "const" keyword. We can't
848 //do this in the physical domain because the debugger will nail
849 //us for it.
850 s_len = strlen(s);
851 numerator_len = slash_posn - s;
852 denominator_len = strlen(slash_posn + 1);
853 #if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
854 numerator = CCMALLOC_malloc(sizeof(char) * (numerator_len + 1));
855 denominator = CCMALLOC_malloc(sizeof(char) * (denominator_len + 1));
856 #elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
857 numerator = TclpAlloc(sizeof(char) * (numerator_len + 1));
858 denominator = TclpAlloc(sizeof(char) * (denominator_len + 1));
859 #else
860 numerator = malloc(sizeof(char) * (numerator_len + 1));
861 denominator = malloc(sizeof(char) * (denominator_len + 1));
862 #endif
863
864 assert(numerator != NULL);
865 assert(denominator != NULL);
866
867 for (i=0; i<numerator_len; i++)
868 {
869 numerator[i] = s[i];
870 }
871 numerator[numerator_len] = 0;
872
873 for (i=0; i<denominator_len; i++)
874 {
875 denominator[i] = s[slash_posn - s + 1 + i];
876 }
877 denominator[denominator_len] = 0;
878
879 //Try to parse out the numerator as an arbitrary integer.
880 //If this can't be done, it is an immediate failure.
881 GMP_INTS_mpz_set_general_int(&(rn->num),
882 failure,
883 numerator);
884 if (*failure)
885 {
886 *failure = 1; //Clamp to 1, don't know what non-zero value
887 //was there.
888 goto ret_pt;
889 }
890
891 //Try to parse out the denominator.
892 GMP_INTS_mpz_set_general_int(&(rn->den),
893 failure,
894 denominator);
895 if (*failure)
896 {
897 *failure = 1; //Clamp to 1, don't know what non-zero value
898 //was there.
899 goto ret_pt;
900 }
901
902 //At this point, we have both a numerator and denominator.
903 //Clean up and return.
904 ret_pt:
905 #if defined(APP_TYPE_SIMPLE_DOS_CONSOLE)
906 CCMALLOC_free(numerator);
907 CCMALLOC_free(denominator);
908 #elif defined(APP_TYPE_IJUSCRIPTER_IJUCONSOLE)
909 TclpFree(numerator);
910 TclpFree(denominator);
911 #else
912 free(numerator);
913 free(denominator);
914 #endif
915 }
916
917
918 //08/07/01: Visual inspection OK.
919 void GMP_RATS_mpq_set_sci_not_rat_num(const char *s,
920 int *failure,
921 GMP_RATS_mpq_struct *rn)
922 {
923 int parse_failure;
924 //Return code from the floating point parsing
925 //function.
926 char mant_sign;
927 //Sign character, if any, from the mantissa,
928 //or N otherwise.
929 size_t mant_bdp;
930 //The index to the start of the mantissa before
931 //the decimal point.
932 size_t mant_bdp_len;
933 //The length of the mantissa before the decimal
934 //point. Zero means not defined, i.e. that
935 //no characters were parsed and interpreted as
936 //that part of a floating point number.
937 size_t mant_adp;
938 size_t mant_adp_len;
939 //Similar fields for after the decimal point.
940 char exp_sign;
941 //Sign of the exponent, if any, or N otherwise.
942 size_t exp;
943 size_t exp_len;
944 //Similar fields as to the mantissa, but for the
945 //exponent.
946 size_t si;
947 //Iteration variable.
948 int exponent_val;
949 //The value of the exponent. We can't accept
950 //an exponent outside the range of a 24-bit
951 //signed integer. The 24-bit limit is arbitrary.
952 //For one thing, it gives room to detect overflow
953 //as are adding and multiplying by 10.
954
955 //Eyeball the input parameters.
956 assert(s != NULL);
957 assert(failure != NULL);
958 assert(rn != NULL);
959 //Subcomponents of the rational number will be checked as
960 //we make integer calls, if we're in debug mode.
961
962 //Start off believing no failure.
963 *failure = 0;
964
965 //Set the output to 0/1. This is the default case for some
966 //steps below.
967 GMP_RATS_mpq_set_si(rn, 0, 1);
968
969 //Attempt to parse the number as a general number
970 //in scientific notation.
971 BSTRFUNC_parse_gen_sci_not_num(s,
972 &parse_failure,
973 &mant_sign,
974 &mant_bdp,
975 &mant_bdp_len,
976 &mant_adp,
977 &mant_adp_len,
978 &exp_sign,
979 &exp,
980 &exp_len);
981
982 //If it wouldn't parse as a general number, can't go further.
983 if (parse_failure)
984 {
985 *failure = 1;
986 return;
987 }
988 else
989 {
990 //The number parsed out. The general strategy is to form a rational number
991 //consisting of the mantissa, with the decimal point shifted fully right, over
992 //a denominator of 1. From there, we process the exponent and combine it with
993 //the number of characters after the decimal point to form a virtual exponent.
994 //If the exponent is positive, we multiply the numerator by the power of 10.
995 //If the exponent is negative, we multiply the denominator by that power of 10.
996
997 //We want to trim the trailing zeros off of the portion of the mantissa after the
998 //decimal point. We only need to back up indices, no need to make copies, etc.
999 //Note that it is possible that there are only zeros, in which case we'll end
1000 //up with a length of zero.
1001 while ((mant_adp_len > 0) && (s[mant_adp + mant_adp_len - 1]=='0'))
1002 mant_adp_len--;
1003
1004 //Trim the leading zeros off of the portion of the mantissa before the
1005 //decimal point. Note that it is possible that there is only a zero,
1006 //so we may trim it down to nothing.
1007 while ((mant_bdp_len > 0) && (s[mant_bdp]=='0'))
1008 {
1009 mant_bdp++;
1010 mant_bdp_len--;
1011 }
1012
1013 //If we have only zeros in the mantissa, both before the
1014 //decimal point and after, then we return 0.
1015 if ((mant_bdp_len + mant_adp_len) == 0)
1016 {
1017 *failure = 0;
1018 return;
1019 }
1020
1021 //Convert the numerator to an integer which represents the
1022 //part before the mantissa and the part after the mantissa
1023 //concatenated as an integer. We could call a function to do
1024 //this, but the function is not really any better in algorithm.
1025 //We can do it ourselves.
1026 GMP_INTS_mpz_set_ui(&(rn->num), 0);
1027 for (si = 0; si < mant_bdp_len; si++)
1028 {
1029 int val;
1030
1031 GMP_INTS_mpz_mul_si(&(rn->num), &(rn->num), 10);
1032 val = CHARFUNC_digit_to_val(s[mant_bdp + si]);
1033 if (val >= 0)
1034 GMP_INTS_mpz_add_ui(&(rn->num), &(rn->num), val);
1035 }
1036 for (si = 0; si < mant_adp_len; si++)
1037 {
1038 int val;
1039
1040 GMP_INTS_mpz_mul_si(&(rn->num), &(rn->num), 10);
1041 val = CHARFUNC_digit_to_val(s[mant_adp + si]);
1042 if (val >= 0)
1043 GMP_INTS_mpz_add_ui(&(rn->num), &(rn->num), val);
1044 }
1045
1046 //The numerator should now have an integer which is
1047 //The absolute value of the mantissa. Process the possible
1048 //sign.
1049 if (mant_sign == '-')
1050 GMP_INTS_mpz_negate(&(rn->num));
1051
1052 //We now need to form a value from the exponent, if any.
1053 //First, tackle the exponent. Process the
1054 //exponent into a signed integer. We have to
1055 //balk at anything outside of 24 bits. The
1056 //procedure used automatically handles
1057 //leading zeros correctly.
1058 exponent_val = 0;
1059 for (si=exp; si<(exp+exp_len); si++)
1060 {
1061 int val;
1062
1063 val = CHARFUNC_digit_to_val(s[si]);
1064
1065 assert(val >= 0 && val <= 9);
1066
1067 exponent_val *= 10;
1068 exponent_val += val;
1069
1070 if (((exp_sign=='-') && (exponent_val>8388608))
1071 ||
1072 ((exp_sign != '-') && (exponent_val>8388607)))
1073 {
1074 *failure = 1;
1075 return;
1076 }
1077 }
1078
1079 //If we're here, the exponent has been computed and
1080 //is within 24 bits. However, we need to adjust for
1081 //the sign.
1082 if (exp_sign == '-')
1083 exponent_val = -exponent_val;
1084
1085 //We need to adjust the exponent for the number of digits
1086 //after the decimal point.
1087 exponent_val -= mant_adp_len;
1088
1089 //Again, clip for size.
1090 if ((exponent_val < -8388608) || (exponent_val > 8388607))
1091 {
1092 *failure = 1;
1093 return;
1094 }
1095
1096 //There are two cases to consider. If the exponent
1097 //is positive, we need to multiply the numerator
1098 //by 10 exponentiated to the power of the exponent.
1099 //If the exponent is negative, we need to do the
1100 //same thing to the denominator. If the exponent
1101 //is negative, we don't need to do anything.
1102 if (exponent_val > 0)
1103 {
1104 GMP_INTS_mpz_struct k10, k10_exponentiated;
1105
1106 GMP_INTS_mpz_init(&k10);
1107 GMP_INTS_mpz_init(&k10_exponentiated);
1108
1109 GMP_INTS_mpz_set_ui(&k10, 10);
1110
1111 GMP_INTS_mpz_pow_ui(&k10_exponentiated, &k10, exponent_val);
1112
1113 GMP_INTS_mpz_mul(&(rn->num), &(rn->num), &k10_exponentiated);
1114
1115 GMP_INTS_mpz_clear(&k10);
1116 GMP_INTS_mpz_clear(&k10_exponentiated);
1117
1118 *failure = 0;
1119
1120 if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
1121 *failure = 1;
1122
1123 return;
1124 }
1125 else if (exponent_val < 0)
1126 {
1127 GMP_INTS_mpz_struct k10, k10_exponentiated;
1128
1129 GMP_INTS_mpz_init(&k10);
1130 GMP_INTS_mpz_init(&k10_exponentiated);
1131
1132 GMP_INTS_mpz_set_ui(&k10, 10);
1133
1134 GMP_INTS_mpz_pow_ui(&k10_exponentiated, &k10, -exponent_val);
1135
1136 GMP_INTS_mpz_mul(&(rn->den), &(rn->den), &k10_exponentiated);
1137
1138 GMP_INTS_mpz_clear(&k10);
1139 GMP_INTS_mpz_clear(&k10_exponentiated);
1140
1141 *failure = 0;
1142
1143 if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
1144 *failure = 1;
1145
1146 return;
1147 }
1148 }
1149 }
1150
1151
1152 //08/07/01: Visual inspection OK.
1153 void GMP_RATS_mpq_set_all_format_rat_num(const char *s,
1154 int *failure,
1155 GMP_RATS_mpq_struct *rn)
1156 {
1157 //Eyeball the input parameters.
1158 assert(s != NULL);
1159 assert(failure != NULL);
1160 assert(rn != NULL);
1161
1162 //Assume no failure.
1163 *failure = 0;
1164
1165 //Try in order to parse as integers with slash then
1166 //as number in scientific notation.
1167 GMP_RATS_mpq_set_complex_slash_sepd_rat_num(s,
1168 failure,
1169 rn);
1170 if (!*failure)
1171 return;
1172
1173 GMP_RATS_mpq_set_sci_not_rat_num(s,
1174 failure,
1175 rn);
1176
1177 if (*failure)
1178 *failure = 1; //Clamp output.
1179 }
1180
1181
1182 /******************************************************************/
1183 /*** NORMALIZATION FUNCTIONS ************************************/
1184 /******************************************************************/
1185 //08/07/01: Visual inspection OK.
1186 void GMP_RATS_mpq_normalize_sign(GMP_RATS_mpq_struct *rn)
1187 {
1188 //Eyeball the input.
1189 assert(rn != NULL);
1190
1191 if (GMP_INTS_mpz_is_neg(&rn->num) && GMP_INTS_mpz_is_neg(&rn->den))
1192 {
1193 //Both negative, can negate both, this leaves both positive,
1194 //which is the normalized form for a positive rational
1195 //number.
1196 GMP_INTS_mpz_negate(&rn->num);
1197 GMP_INTS_mpz_negate(&rn->den);
1198 }
1199 else if (!GMP_INTS_mpz_is_neg(&rn->num) && GMP_INTS_mpz_is_neg(&rn->den))
1200 {
1201 //Denominator neg, numerator non-neg, can negate both. This
1202 //will leave numerator neg, denominator pos, which is
1203 //normalized form for negative rational number.
1204 GMP_INTS_mpz_negate(&rn->num);
1205 GMP_INTS_mpz_negate(&rn->den);
1206 }
1207 }
1208
1209
1210 //08/07/01: Visual inspection OK.
1211 void GMP_RATS_mpq_normalize(GMP_RATS_mpq_struct *rn)
1212 {
1213 //Eyeball the input.
1214 assert(rn != NULL);
1215
1216 //Cover some special cases. If either component has flags
1217 //set, don't even touch it.
1218 if (GMP_INTS_mpz_get_flags(&(rn->num)) || GMP_INTS_mpz_get_flags(&(rn->den)))
1219 {
1220 return;
1221 }
1222 //If the denominator is zero, normalize it to 1/0, the canonical
1223 //for for an illegal rational number.
1224 else if (GMP_INTS_mpz_is_zero(&(rn->den)))
1225 {
1226 GMP_RATS_mpq_set_si(rn, 1, 0);
1227 return;
1228 }
1229 //If the numerator is zero, convert the number to the canonical
1230 //form for zero of 0/1.
1231 else if (GMP_INTS_mpz_is_zero(&(rn->num)))
1232 {
1233 GMP_RATS_mpq_set_si(rn, 0, 1);
1234 return;
1235 }
1236 else
1237 {
1238 int num_is_neg;
1239 int den_is_neg;
1240 GMP_INTS_mpz_struct gcd, quotient, remainder;
1241
1242 //Allocate space for the integers used.
1243 GMP_INTS_mpz_init(&gcd);
1244 GMP_INTS_mpz_init(&quotient);
1245 GMP_INTS_mpz_init(&remainder);
1246
1247 //This is the most normal case, where we need to
1248 //look at reducing the numerator and denominator.
1249 //One way to do it would be to obtain the g.c.d.
1250 //and divide this out, and this is the route
1251 //we'll take. However, must grab out the sign.
1252 if (GMP_INTS_mpz_is_neg(&(rn->num)))
1253 {
1254 num_is_neg = 1;
1255 GMP_INTS_mpz_negate(&(rn->num));
1256 }
1257 else
1258 {
1259 num_is_neg = 0;
1260 }
1261
1262 if (GMP_INTS_mpz_is_neg(&(rn->den)))
1263 {
1264 den_is_neg = 1;
1265 GMP_INTS_mpz_negate(&(rn->den));
1266 }
1267 else
1268 {
1269 den_is_neg = 0;
1270 }
1271
1272 //Calculate the GCD.
1273 GMP_INTS_mpz_gcd(&gcd, &(rn->num), &(rn->den));
1274
1275 //Divide the numerator by the GCD and store it
1276 //back.
1277 GMP_INTS_mpz_tdiv_qr(&quotient, &remainder,
1278 &(rn->num), &gcd);
1279 GMP_INTS_mpz_copy(&(rn->num), &quotient);
1280
1281 //Divide the denominator by the GCD and store it
1282 //back.
1283 GMP_INTS_mpz_tdiv_qr(&quotient, &remainder,
1284 &(rn->den), &gcd);
1285 GMP_INTS_mpz_copy(&(rn->den), &quotient);
1286
1287 //We now need to adjust the sign. Both the
1288 //numerator and denominator are definitely
1289 //positive. Need to make the numerator
1290 //negative if either but not both of the
1291 //original signs were negative.
1292 if ((num_is_neg && !den_is_neg) || (!num_is_neg && den_is_neg))
1293 {
1294 GMP_INTS_mpz_negate(&(rn->num));
1295 }
1296
1297 //Deallocate space for the integers used.
1298 GMP_INTS_mpz_clear(&gcd);
1299 GMP_INTS_mpz_clear(&quotient);
1300 GMP_INTS_mpz_clear(&remainder);
1301
1302 return;
1303 }
1304 }
1305
1306
1307 /******************************************************************/
1308 /*** ARITHMETIC FUNCTIONS ***************************************/
1309 /******************************************************************/
1310 //08/08/01: Visual inspection OK.
1311 void GMP_RATS_mpq_add( GMP_RATS_mpq_struct *result,
1312 const GMP_RATS_mpq_struct *arg1,
1313 const GMP_RATS_mpq_struct *arg2)
1314 {
1315 GMP_RATS_mpq_struct rv;
1316 GMP_INTS_mpz_struct temp;
1317
1318 //Eyeball the input parameters.
1319 assert(result != NULL);
1320 assert(arg1 != NULL);
1321 assert(arg2 != NULL);
1322
1323 //Generally speaking, we do not want to require that
1324 //the arguments and the result be distinct, as this is
1325 //too much of a restriction on the caller. The approach
1326 //taken, somewhat wasteful, is to allocate a place for
1327 //the return value.
1328 //
1329 //For addition, if we are adding a/b and c/d, the
1330 //result is necessarily algebraically
1331 //(ad + cb)/bd.
1332 //
1333 //If either rational number in the input is invalid,
1334 //flag the result as invalid.
1335 if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
1336 {
1337 GMP_RATS_mpq_set_si(result, 1, 0);
1338 }
1339 else
1340 {
1341 //Both rational numbers are OK. Can simply stage the
1342 //result by the algebraic identity and then
1343 //normalize it. Only need one temporary variable.
1344 //
1345 //Initialize the rational number that we will use to
1346 //hold return value in case it is the same as one
1347 //or both of the arguments.
1348 GMP_RATS_mpq_init(&rv);
1349
1350 //Initialize the temporary integer.
1351 GMP_INTS_mpz_init(&temp);
1352
1353 //numerator = a * d
1354 GMP_INTS_mpz_mul(&(rv.num), &(arg1->num), &(arg2->den));
1355
1356 //temp = c * b
1357 GMP_INTS_mpz_mul(&temp, &(arg2->num), &(arg1->den));
1358
1359 //numerator = a * d + c * b
1360 GMP_INTS_mpz_add(&(rv.num), &(rv.num), &temp);
1361
1362 //denominator = b * d
1363 GMP_INTS_mpz_mul(&(rv.den), &(arg1->den), &(arg2->den));
1364
1365 //Copy the temporary result to the actual return value.
1366 //Had to wait until now in case result was the same
1367 //as either or both args.
1368 GMP_RATS_mpq_copy(result, &rv);
1369
1370 //Normalize the result.
1371 GMP_RATS_mpq_normalize(result);
1372
1373 //Free dynamic memory.
1374 GMP_RATS_mpq_clear(&rv);
1375 GMP_INTS_mpz_clear(&temp);
1376 }
1377 }
1378
1379
1380 //08/08/01: Visual inspection OK.
1381 void GMP_RATS_mpq_sub( GMP_RATS_mpq_struct *result,
1382 const GMP_RATS_mpq_struct *arg1,
1383 const GMP_RATS_mpq_struct *arg2)
1384 {
1385 GMP_RATS_mpq_struct negated_arg_2;
1386
1387 //Eyeball the input parameters.
1388 assert(result != NULL);
1389 assert(arg1 != NULL);
1390 assert(arg2 != NULL);
1391
1392 //For the subtract function, we could do it directly,
1393 //but might as well just define it recursively
1394 //in terms of add. We can't modify the inputs,
1395 //so copy the second off and negate it. All error
1396 //flags and so forth will propagate automatically.
1397 //
1398 //Allocate space for the negated arg 2.
1399 GMP_RATS_mpq_init(&negated_arg_2);
1400
1401 //Copy from the original.
1402 GMP_RATS_mpq_copy(&negated_arg_2, arg2);
1403
1404 //Negate the copy. Negating the numerator will
1405 //do it.
1406 GMP_INTS_mpz_negate(&(negated_arg_2.num));
1407
1408 //Make the add, which now is really a subtract.
1409 GMP_RATS_mpq_add(result, arg1, &negated_arg_2);
1410
1411 //Destroy the temporary variable.
1412 GMP_RATS_mpq_clear(&negated_arg_2);
1413 }
1414
1415
1416 //08/16/01: Visual inspection OK.
1417 void GMP_RATS_mpq_mul( GMP_RATS_mpq_struct *result,
1418 const GMP_RATS_mpq_struct *arg1,
1419 const GMP_RATS_mpq_struct *arg2)
1420 {
1421 //Eyeball the input parameters.
1422 assert(result != NULL);
1423 assert(arg1 != NULL);
1424 assert(arg2 != NULL);
1425
1426 //If either rational number in the input is invalid,
1427 //flag the result as invalid.
1428 if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
1429 {
1430 GMP_RATS_mpq_set_si(result, 1, 0);
1431 }
1432 else
1433 {
1434 //Rational number multiplication is a simple matter.
1435 //Just multiply components. Don't need to worry
1436 //about rational numbers overlapping, as numerator
1437 //operations and denominator operations are separate.
1438 GMP_INTS_mpz_mul(&(result->num),
1439 &(arg1->num),
1440 &(arg2->num));
1441 GMP_INTS_mpz_mul(&(result->den),
1442 &(arg1->den),
1443 &(arg2->den));
1444
1445 //Normalize it.
1446 GMP_RATS_mpq_normalize(result);
1447 }
1448 }
1449
1450
1451 //08/16/01: Visual inspection OK.
1452 void GMP_RATS_mpq_div( GMP_RATS_mpq_struct *result,
1453 const GMP_RATS_mpq_struct *arg1,
1454 const GMP_RATS_mpq_struct *arg2)
1455 {
1456 GMP_RATS_mpq_struct rv;
1457
1458 //Eyeball the input parameters.
1459 assert(result != NULL);
1460 assert(arg1 != NULL);
1461 assert(arg2 != NULL);
1462
1463 //If either rational number in the input is invalid,
1464 //flag the result as invalid.
1465 if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
1466 {
1467 GMP_RATS_mpq_set_si(result, 1, 0);
1468 }
1469 else
1470 {
1471 //Rational number division is a simple matter.
1472 //Just multiply components. We do need to worry
1473 //about rational numbers overlapping, so must
1474 //make a copy of the return value. If denominator
1475 //of return value is zero, it is NAN, but caller
1476 //should detect this.
1477 //
1478 //Allocate return value.
1479 GMP_RATS_mpq_init(&rv);
1480
1481 //Calculate quotient.
1482 GMP_INTS_mpz_mul(&(rv.num),
1483 &(arg1->num),
1484 &(arg2->den));
1485 GMP_INTS_mpz_mul(&(rv.den),
1486 &(arg1->den),
1487 &(arg2->num));
1488
1489 //Normalize quotient.
1490 GMP_RATS_mpq_normalize(&rv);
1491
1492 //Copy to its destination.
1493 GMP_RATS_mpq_copy(result, &rv);
1494
1495 //Deallocate temporary return value.
1496 GMP_RATS_mpq_clear(&rv);
1497 }
1498 }
1499
1500
1501 /******************************************************************/
1502 /*** COMPARISON FUNCTIONS ***************************************/
1503 /******************************************************************/
1504 //08/16/01: Visual inspection OK.
1505 int GMP_RATS_mpq_cmp(const GMP_RATS_mpq_struct *arg1,
1506 const GMP_RATS_mpq_struct *arg2,
1507 int *failure)
1508 {
1509 int arg1_sgn;
1510 int arg2_sgn;
1511 int rv, failure_rv;
1512 GMP_INTS_mpz_struct prod1, prod2;
1513
1514 //Eyeball the input parameters. Note that the third
1515 //parameter may be NULL.
1516 assert(arg1 != NULL);
1517 assert(arg2 != NULL);
1518
1519 //If either of the input arguments are NAN, we
1520 //cannot compare arguments. We return 0, and it
1521 //depends on the caller whether it is important
1522 //that the comparison is bogus.
1523 if (GMP_RATS_mpq_is_nan(arg1) || GMP_RATS_mpq_is_nan(arg2))
1524 {
1525 if (failure != NULL)
1526 *failure = 1;
1527 return(0);
1528 }
1529
1530 //Calculate the sign of the left argument. The encoding
1531 //we'll use is -1 means negative, 0 means zero, and
1532 //1 means positive.
1533 if (GMP_INTS_mpz_is_zero(&(arg1->num)))
1534 {
1535 arg1_sgn = 0;
1536 }
1537 else if (GMP_INTS_mpz_is_neg(&(arg1->num)) && GMP_INTS_mpz_is_neg(&(arg1->den)))
1538 {
1539 arg1_sgn = 1;
1540 }
1541 else if (GMP_INTS_mpz_is_neg(&(arg1->num)) && GMP_INTS_mpz_is_pos(&(arg1->den)))
1542 {
1543 arg1_sgn = -1;
1544 }
1545 else if (GMP_INTS_mpz_is_pos(&(arg1->num)) && GMP_INTS_mpz_is_neg(&(arg1->den)))
1546 {
1547 arg1_sgn = -1;
1548 }
1549 else if (GMP_INTS_mpz_is_pos(&(arg1->num)) && GMP_INTS_mpz_is_pos(&(arg1->den)))
1550 {
1551 arg1_sgn = 1;
1552 }
1553
1554 //Calculate the sign of the right argument. The encoding
1555 //we'll use is -1 means negative, 0 means zero, and
1556 //1 means positive.
1557 if (GMP_INTS_mpz_is_zero(&(arg2->num)))
1558 {
1559 arg2_sgn = 0;
1560 }
1561 else if (GMP_INTS_mpz_is_neg(&(arg2->num)) && GMP_INTS_mpz_is_neg(&(arg2->den)))
1562 {
1563 arg2_sgn = 1;
1564 }
1565 else if (GMP_INTS_mpz_is_neg(&(arg2->num)) && GMP_INTS_mpz_is_pos(&(arg2->den)))
1566 {
1567 arg2_sgn = -1;
1568 }
1569 else if (GMP_INTS_mpz_is_pos(&(arg2->num)) && GMP_INTS_mpz_is_neg(&(arg2->den)))
1570 {
1571 arg2_sgn = -1;
1572 }
1573 else if (GMP_INTS_mpz_is_pos(&(arg2->num)) && GMP_INTS_mpz_is_pos(&(arg2->den)))
1574 {
1575 arg2_sgn = 1;
1576 }
1577
1578 //OK, can handle some simple cases where the signs of the
1579 //operands are different or both are zero.
1580 if ((arg1_sgn == 0) && (arg2_sgn == 0))
1581 {
1582 if (failure != NULL)
1583 *failure = 0;
1584 return(0);
1585 }
1586 else if ((arg1_sgn == -1) && (arg2_sgn > -1))
1587 {
1588 if (failure != NULL)
1589 *failure = 0;
1590 return(-1);
1591 }
1592 else if ((arg1_sgn == 0) && (arg2_sgn < 0))
1593 {
1594 if (failure != NULL)
1595 *failure = 0;
1596 return(1);
1597 }
1598 else if ((arg1_sgn == 0) && (arg2_sgn > 0))
1599 {
1600 if (failure != NULL)
1601 *failure = 0;
1602 return(-1);
1603 }
1604 else if ((arg1_sgn == 1) && (arg2_sgn < 1))
1605 {
1606 if (failure != NULL)
1607 *failure = 0;
1608 return(1);
1609 }
1610
1611 //OK at this point, we cannot make a simple determination
1612 //as to the relative ordering. The signs of arg1 and
1613 //arg2 are both the same, either both positive or both
1614 //negative. We have to do a multiplication to sort
1615 //it out.
1616 //
1617 //Allocate the two integers to hold multiplication
1618 //results.
1619 GMP_INTS_mpz_init(&prod1);
1620 GMP_INTS_mpz_init(&prod2);
1621
1622 //Cross-multiply to get relative magnitudes.
1623 GMP_INTS_mpz_mul(&prod1, &(arg1->num), &(arg2->den));
1624 GMP_INTS_mpz_mul(&prod2, &(arg1->den), &(arg2->num));
1625
1626 //Take absolute values.
1627 GMP_INTS_mpz_abs(&prod1);
1628 GMP_INTS_mpz_abs(&prod2);
1629
1630 //If we overflowed either multiplication and generated
1631 //a NAN, we cannot complete the compare.
1632 if (GMP_INTS_mpz_get_flags(&prod1) || GMP_INTS_mpz_get_flags(&prod2))
1633 {
1634 failure_rv = 1;
1635 rv = 0;
1636 }
1637 //If both rational numbers were effectively positive, we can
1638 //use the relative ordering of the products as the relative
1639 //ordering of the rational numbers.
1640 else if (arg1_sgn == 1)
1641 {
1642 //Compare the integers.
1643 rv = GMP_INTS_mpz_cmp(&prod1, &prod2);
1644
1645 //Clamp the return value.
1646 if (rv < 0)
1647 rv = -1;
1648 else if (rv == 0)
1649 rv = 0;
1650 else if (rv > 0)
1651 rv = 1;
1652
1653 //There was no error.
1654 failure_rv = 0;
1655 }
1656 else
1657 {
1658 //The only case that *should* allow us to be here is
1659 //if the sign of both numbers is neg.
1660 assert(arg1_sgn == -1);
1661
1662 //Compare the integers.
1663 rv = GMP_INTS_mpz_cmp(&prod1, &prod2);
1664
1665 //Invert and clamp the return value.
1666 if (rv < 0)
1667 rv = 1;
1668 else if (rv == 0)
1669 rv = 0;
1670 else if (rv > 0)
1671 rv = -1;
1672
1673 //There was no error.
1674 failure_rv = 0;
1675 }
1676
1677 //Deallocate the two integers.
1678 GMP_INTS_mpz_clear(&prod1);
1679 GMP_INTS_mpz_clear(&prod2);
1680
1681 //Return the return values.
1682 if (failure != NULL)
1683 *failure = failure_rv;
1684 return(rv);
1685 }
1686
1687
1688 /******************************************************************/
1689 /*** VERSION CONTROL REPORTING FUNCTIONS ************************/
1690 /******************************************************************/
1691 //08/07/01: Visual inspection OK.
1692 const char *GMP_RATS_cvcinfo(void)
1693 {
1694 return("$Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_rats.c,v 1.10 2001/08/16 19:49:40 dtashley Exp $");
1695 }
1696
1697
1698 //08/07/01: Visual inspection OK.
1699 const char *GMP_RATS_hvcinfo(void)
1700 {
1701 return(GMP_RATS_H_VERSION);
1702 }
1703
1704
1705 //**************************************************************************
1706 // $Log: gmp_rats.c,v $
1707 // Revision 1.10 2001/08/16 19:49:40 dtashley
1708 // Beginning to prepare for v1.05 release.
1709 //
1710 // Revision 1.9 2001/08/15 06:56:05 dtashley
1711 // Substantial progress. Safety check-in.
1712 //
1713 // Revision 1.8 2001/08/12 10:20:58 dtashley
1714 // Safety check-in. Substantial progress.
1715 //
1716 // Revision 1.7 2001/08/10 00:53:59 dtashley
1717 // Completion of basic rational number arithmetic utilities and extensions.
1718 //
1719 // Revision 1.6 2001/08/08 02:16:51 dtashley
1720 // Completion of RNRED utility and ARBINT RNRED Tcl extension.
1721 //
1722 // Revision 1.5 2001/08/07 10:42:48 dtashley
1723 // Completion of CFRATNUM extensions and DOS command-line utility.
1724 //
1725 // Revision 1.4 2001/07/13 21:02:20 dtashley
1726 // Version control reporting changes.
1727 //
1728 // Revision 1.3 2001/07/13 20:44:42 dtashley
1729 // Changes, CVS keyword expansion test.
1730 //
1731 // Revision 1.2 2001/07/13 00:57:08 dtashley
1732 // Safety check-in. Substantial progress on port.
1733 //
1734 // Revision 1.1 2001/07/12 05:42:06 dtashley
1735 // Initial checkin.
1736 //
1737 //**************************************************************************
1738 // End of GMP_RATS.C.

dashley@gmail.com
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