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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 |

5 | //------------------------------------------------------------------------------------------------- |

6 | //This source code and any program in which it is compiled/used is provided under the GNU GENERAL |

7 | //PUBLIC LICENSE, Version 3, full license text below. |

8 | //------------------------------------------------------------------------------------------------- |

9 | // GNU GENERAL PUBLIC LICENSE |

10 | // Version 3, 29 June 2007 |

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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("ient); |

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("ient, &remainder, |

1278 | &(rn->num), &gcd); |

1279 | GMP_INTS_mpz_copy(&(rn->num), "ient); |

1280 | |

1281 | //Divide the denominator by the GCD and store it |

1282 | //back. |

1283 | GMP_INTS_mpz_tdiv_qr("ient, &remainder, |

1284 | &(rn->den), &gcd); |

1285 | GMP_INTS_mpz_copy(&(rn->den), "ient); |

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("ient); |

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. |

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