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1 | // $Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_ints.h,v 1.23 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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630 | // |

631 | // How to Apply These Terms to Your New Programs |

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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 | // |

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640 | //the "copyright" line and a pointer to where the full notice is found. |

641 | // |

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648 | // (at your option) any later version. |

649 | // |

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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 | /* |

686 | This software module is a careful adaptation of the integer functions |

687 | in the GNU MP library. |

688 | |

689 | By "adaptation" I mean the following: |

690 | |

691 | o Many of the macros and other constructs that affect readability |

692 | have been removed. This has been done for simplicity. |

693 | |

694 | o Only the needed functions (large integer and rational number |

695 | functions) have been included. This is for use in Dave Ashley's |

696 | set of tools. |

697 | |

698 | o The number of source modules has been dramatically reduced. |

699 | |

700 | o Assembly-language has been removed. Instead, at the lowest |

701 | level, the core is generic 'C' provided by GNU (this is |

702 | selected if processor=none is the processor chosen). This |

703 | certainly has an effect on speed, but I would rather sacrifice |

704 | quite a bit of speed and keep it simple (in one module). |

705 | |

706 | o The GNU MP library has been specifically ported for Microsoft |

707 | Visual C++ 6.0. In other words, its portability has been |

708 | deliberately destroyed. Do NOT try to use this on another |

709 | platform (or at least certainly do NOT contact me if you have |

710 | problems with this). |

711 | |

712 | o Certain other stylistic changes have been made. |

713 | |

714 | The GNU MP code is impressive, because it is so quick. However, |

715 | because many of the algorithms were so advanced, I couldn't |

716 | understand their basis. I would rather have a slower software |

717 | module that I can debug than a faster one that can't be |

718 | decisively debugged if necessary. |

719 | |

720 | This code can be optimized, if necessary, by reincorporating |

721 | GNU MP code without changing the interface. This would be |

722 | fairly easy to do. I would recommend proceeding in the following |

723 | order: |

724 | o Replacing the innards of some of the lower-level |

725 | functions with assembly-language (there may be usable |

726 | assembly-language in the GNU code). The lowest-level |

727 | multiplication function, for example, was noted to be |

728 | VERY inefficient (but correct!). |

729 | o Making algorithmic improvements in the higher-level |

730 | functions by reincorporating GNU code. These |

731 | algorithmic improvements were removed because |

732 | I couldn't understand them. For example, I could |

733 | not understand the advanced multiplication and |

734 | division algorithms. |

735 | |

736 | I decline to include the GNU public license statement which is |

737 | included with the GNU MP code, because this software has been |

738 | changed enough that it isn't quite the GNU MP code any longer. |

739 | However, this software module is still under the GNU public |

740 | license because it is included with Dave Ashley's tool set (The |

741 | Iju Tool Set). Additionally, although this software module has been |

742 | modified enough that it really is a separate effort, I would like to |

743 | acknowledge the tremendous job done by the GNU MP team. Certainly |

744 | I would not have undertaken a project of this complexity without |

745 | an existing template to work from--i.e. something successful already |

746 | in existence. The really hard work--a working and efficient design-- |

747 | was done by the GNU MP team, and my modifications, although substantial, |

748 | are trivial in comparison to the design work done by the GNU MP team. |

749 | |

750 | It should also be noted that this integer module is not a product |

751 | of GNU--I named it GNU_INTS because it is based on the GNU MP |

752 | library. The GNU MP library is faster and more sophisticated. This |

753 | is a pared down module to give some of the speed benefits of binary |

754 | arithmetic without too much extra complexity. Most of the |

755 | sophisticated algorithms used by the GNU MP library have been |

756 | removed. |

757 | |

758 | The basic abstraction implemented by this type of integer is that |

759 | any operation can be performed on integers, and NAN flags propagate. |

760 | However, once an integer has reached a NAN state, the tests (is_zero, etc.) |

761 | are unreliable. Generally, any client which uses these integers should |

762 | check errors before tests, but doesn't need to check them after each |

763 | calculation. I say "before" tests because otherwise an integer may reach |

764 | NAN and cause an infinite loop because a test will never become TRUE, etc. |

765 | */ |

766 | |

767 | #ifndef GMP_INTS_H_INCLUDED |

768 | #define GMP_INTS_H_INCLUDED |

769 | |

770 | #ifdef MODULE_GMP_INTS |

771 | #define DECMOD_GMP_INTS |

772 | #else |

773 | #define DECMOD_GMP_INTS extern |

774 | #endif |

775 | |

776 | typedef unsigned long int GMP_INTS_limb_t; |

777 | //The fundamental data type for representing integers in binary |

778 | //form. For MSVC++, this is a 32-bit type. This data type |

779 | //is not normally needed publicly. |

780 | #define GMP_INTS_BITS_PER_LIMB (32) |

781 | //This is the number of bits that each limb is assumed to hold. |

782 | //There is an explicit function in the interface to check this, |

783 | //in case anything changes with future versions of MSVC++. |

784 | //This software module is NOT meant to be portable, or even |

785 | //particularly quick. It is meant to be verifiable and |

786 | //testable instead. |

787 | typedef long int GMP_INTS_limb_signed_t; |

788 | //Signed version of above. |

789 | typedef GMP_INTS_limb_t * GMP_INTS_limb_ptr; |

790 | //Pointer to a limb (or, more characteristically, to an array |

791 | //of limbs). |

792 | typedef const GMP_INTS_limb_t * GMP_INTS_limb_srcptr; |

793 | //Constant pointer used as the source pointer for copies |

794 | //and other operations. |

795 | typedef long int GMP_INTS_size_t; |

796 | //Used for representing the size of things to this module |

797 | typedef long int GMP_INTS_exp_t; |

798 | //Used for representing exponent. Assumed to be large enough |

799 | //for this. |

800 | |

801 | //Below is fundamental structure which holds an arbitrary-size |

802 | //integer. |

803 | typedef struct |

804 | { |

805 | int flags; |

806 | //Bit-flags as to the condition of the |

807 | //integer. The bitflags defined so far |

808 | //are designed to be mutually exclusive, |

809 | //and are listed below. At the same time, |

810 | //we need to define the "official" strings |

811 | //for these bit flags. |

812 | #define GMP_INTS_EF_INTOVF_POS (1) |

813 | #define GMP_INTS_EF_INTOVF_POS_STRING \ |

814 | "GMP_INTS_EF_INTOVF_POS" |

815 | //The integer has become too large |

816 | //growing in a positive direction. |

817 | //No further arithmetic will be |

818 | //performed on it. |

819 | #define GMP_INTS_EF_INTOVF_NEG (2) |

820 | #define GMP_INTS_EF_INTOVF_NEG_STRING \ |

821 | "GMP_INTS_EF_INTOVF_NEG" |

822 | //The integer has become too large |

823 | //growing in a negative direction. |

824 | //No further arithmetic will be |

825 | //performed on it. |

826 | #define GMP_INTS_EF_INTOVF_TAINT_POS (4) |

827 | #define GMP_INTS_EF_INTOVF_TAINT_POS_STRING \ |

828 | "GMP_INTS_EF_INTOVF_TAINT_POS" |

829 | //The integer has been arithmetically |

830 | //combined with an integer that has |

831 | //overflowed in the positive direction. |

832 | //This integer is thus considered tainted |

833 | //and no further arithmetic will be |

834 | //performed on it. |

835 | #define GMP_INTS_EF_INTOVF_TAINT_NEG (8) |

836 | #define GMP_INTS_EF_INTOVF_TAINT_NEG_STRING \ |

837 | "GMP_INTS_EF_INTOVF_TAINT_NEG" |

838 | //The integer has been arithmetically |

839 | //combined with an integer that has |

840 | //overflowed in the negative direction. |

841 | //This integer is thus considered tainted |

842 | //and no further arithmetic will be |

843 | //performed on it. |

844 | //The flags above will prevent arithmetic |

845 | //on an integer and will taint any integer |

846 | //that comes into contact with it as the |

847 | //result of an operation. These flags are |

848 | //cleared only by an assignment operation |

849 | //of any kind. |

850 | // |

851 | //The next logical questions are: |

852 | // o Why do we want to make a size |

853 | // limit on integers, anyway? |

854 | // o How big is too big? |

855 | // |

856 | //We want a limit because this software module |

857 | //will be used in programs that should be |

858 | //reliable. Allowing arbitrarily large results |

859 | //would invite users to break the software. |

860 | //It would also make testing impossible, because |

861 | //the module could not be tested out to its |

862 | //limits. Assigning limits means that testing |

863 | //can be performed to the limits. Also, there |

864 | //are certain constructs in the software that |

865 | //may break at high limits, such as _alloca(). |

866 | // |

867 | //The question of how large is too large is a |

868 | //harder question. Arbitrarily, let's decide |

869 | //that we want the equivalent of integers with |

870 | //100,000 decimal digits, which is about |

871 | //332,224 bits, or 10,382 limbs. (By the way |

872 | //this limit can always be raised later, but |

873 | //the important point is that it exists and |

874 | //is tested to). Any integer with more limbs |

875 | //than this is considered illegal. |

876 | #define GMP_INTS_MAXIMUM_LIMBS_PER_INT (10382) |

877 | int n_allocd; /* Number of limbs allocated and pointed |

878 | to by the limbs field. This gives the |

879 | number allocated (i.e. physically |

880 | allocated), but the next field tells how |

881 | many are used. Memory is never shrunk |

882 | automatically by this software module |

883 | (per the wise GNU MP design), so this |

884 | number does not ever automatically |

885 | decrease. */ |

886 | int size; /* abs(size) is the number of limbs the |

887 | last field points to. If _mp_size is |

888 | negative this is a negative number. This |

889 | will be zero if the integer is zero. */ |

890 | GMP_INTS_limb_t *limbs; |

891 | /* Pointer to the limbs. The first field |

892 | of the structure (above) tells how many |

893 | spots are allocated, and the second |

894 | field (above) tells how many are used. |

895 | Numbers are stored least-significant |

896 | limbs first. */ |

897 | } GMP_INTS_mpz_struct; |

898 | |

899 | |

900 | /* Wrappers for non-stack memory allocation function to be used |

901 | ** by integer, rational number, and integer and rational number |

902 | ** algorithm functions. These must be public because they are |

903 | ** used by the other modules that deal with integers and rational |

904 | ** numbers. |

905 | */ |

906 | DECMOD_GMP_INTS void *GMP_INTS_malloc( size_t size ); |

907 | DECMOD_GMP_INTS void *GMP_INTS_calloc( size_t num, size_t size ); |

908 | DECMOD_GMP_INTS void *GMP_INTS_realloc( void *memblock, size_t size ); |

909 | DECMOD_GMP_INTS void *GMP_INTS_realloc_w_size( void *memblock, |

910 | size_t old_size, |

911 | size_t size ); |

912 | DECMOD_GMP_INTS void GMP_INTS_free( void *memblock ); |

913 | DECMOD_GMP_INTS void GMP_INTS_free_w_size( void *memblock, size_t size ); |

914 | |

915 | /******************************************************************/ |

916 | /*** PORTABILITY CHECK FUNCTIONS *******************************/ |

917 | /******************************************************************/ |

918 | //Because there is the risk that Microsoft Visual C++ might |

919 | //change in the future, the following function can be called |

920 | //to see if the assumptions about data sizes are valid. This |

921 | //function returns TRUE if there is a problem, or FALSE |

922 | //otherwise. |

923 | DECMOD_GMP_INTS int GMP_INTS_data_sizes_are_wrong(void); |

924 | |

925 | |

926 | /******************************************************************/ |

927 | /*** ERROR STRING IDENTIFICATION AND PROCESSING FUNCTIONS *******/ |

928 | /******************************************************************/ |

929 | //These functions are provided because some clients may deal |

930 | //only with symbolic representations (Tcl/Tk, for example). |

931 | // |

932 | //Attempts to identify the passed string as one of the error |

933 | //strings sanctioned by this module. Returns -1 if not a match |

934 | //or else the following values. |

935 | // 0: GMP_INTS_EF_INTOVF_POS |

936 | // 1: GMP_INTS_EF_INTOVF_NEG |

937 | // 2: GMP_INTS_EF_INTOVF_TAINT_POS |

938 | // 3: GMP_INTS_EF_INTOVF_TAINT_NEG |

939 | DECMOD_GMP_INTS |

940 | int GMP_INTS_identify_nan_string(const char *s); |

941 | |

942 | //Returns the sanctioned string for the nan value indicated. |

943 | //Integers that may be passed are the same as the |

944 | //indices above. No parameter except 0-3 is allowed. |

945 | DECMOD_GMP_INTS |

946 | const char *GMP_INTS_supply_nan_string(int idx); |

947 | |

948 | /******************************************************************/ |

949 | /*** DEBUG PRINTING FUNCTIONS **********************************/ |

950 | /******************************************************************/ |

951 | //These functions are for printing out integers and limbs |

952 | //and groups of limbs for unit testing and debugging. |

953 | // |

954 | //Prints out a group of limbs, preceded by a description. |

955 | //n may be 0 and/or the lg pointer supplied may be NULL. |

956 | DECMOD_GMP_INTS |

957 | void GMP_INTS_print_limb_group(FILE *stream, |

958 | GMP_INTS_limb_srcptr lg, |

959 | GMP_INTS_size_t n, |

960 | char *desc); |

961 | //Prints an entire integer for diagnosis. |

962 | DECMOD_GMP_INTS |

963 | void GMP_INTS_mpz_print_int(FILE *stream, |

964 | const GMP_INTS_mpz_struct *arg, |

965 | char *desc); |

966 | |

967 | /****************************************************************/ |

968 | /*** MACRO REPLACEMENTS *************************************/ |

969 | /****************************************************************/ |

970 | //The functions here are macros that have been replaced and |

971 | //made functions for clarity. Speed was sacrificed for clarity. |

972 | DECMOD_GMP_INTS |

973 | int GMP_INTS_mpz_get_flags(const GMP_INTS_mpz_struct *arg); |

974 | //Allows a caller to obtain the flags of an integer. |

975 | //A non-zero value indicates trouble. To figure out which |

976 | //trouble, compare against the bit constants defined |

977 | //with the "flags" field of the structure type, above. |

978 | DECMOD_GMP_INTS GMP_INTS_size_t GMP_INTS_abs_of_size_t(GMP_INTS_size_t arg); |

979 | //Returns the absolute value of one of the size arguments used |

980 | //to indicate number of limbs. This function is useful |

981 | //because integers natively stored with a negative size |

982 | //for negative arguments, so the absolute value gives the |

983 | //number of limbs consumed. |

984 | DECMOD_GMP_INTS int GMP_INTS_mpz_sgn(const GMP_INTS_mpz_struct *arg); |

985 | //Returns -1 if integer is negative, 0 if it is zero, |

986 | //or 1 if it is positive. |

987 | DECMOD_GMP_INTS int GMP_INTS_mpz_is_neg(const GMP_INTS_mpz_struct *arg); |

988 | DECMOD_GMP_INTS int GMP_INTS_mpz_is_zero(const GMP_INTS_mpz_struct *arg); |

989 | DECMOD_GMP_INTS int GMP_INTS_mpz_is_pos(const GMP_INTS_mpz_struct *arg); |

990 | //These functions return 1 if the condition is met, or 0 |

991 | //otherwise. |

992 | DECMOD_GMP_INTS int GMP_INTS_mpz_is_odd(const GMP_INTS_mpz_struct *arg); |

993 | //Returns 1 if the integer is odd, or 0 if it is even. |

994 | DECMOD_GMP_INTS int GMP_INTS_mpz_is_even(const GMP_INTS_mpz_struct *arg); |

995 | //Returns 1 if the integer is even, or 0 if it is odd. |

996 | DECMOD_GMP_INTS void GMP_INTS_mpz_negate(GMP_INTS_mpz_struct *arg); |

997 | //Negates the number (changes the sign). |

998 | DECMOD_GMP_INTS |

999 | void GMP_INTS_mpn_normalize(GMP_INTS_limb_ptr limb_array, |

1000 | GMP_INTS_size_t *idx); |

1001 | //Adjusts an index downward to bypass any most significant |

1002 | //zero limbs. This was a macro in the GNU implementation. |

1003 | //This is for when the size of a result is overestimated |

1004 | //(the most pessimistic estimates must be made when |

1005 | //allocating memory before an operation). |

1006 | DECMOD_GMP_INTS |

1007 | void GMP_INTS_mpn_copy_limbs(GMP_INTS_limb_ptr dest, |

1008 | GMP_INTS_limb_srcptr src, |

1009 | GMP_INTS_size_t n); |

1010 | //Copies limbs from source to destination. This |

1011 | //function replaces a macro that was present in the |

1012 | //GNU code. Again, clarity over speed. |

1013 | /****************************************************************/ |

1014 | /*** LOW-LEVEL ARITHMETIC FUNCTIONS *************************/ |

1015 | /****************************************************************/ |

1016 | //Gives the flags of a result integer as a function of the |

1017 | //flags of its two operands. If the function requires only |

1018 | //one operand, just use zero as the second parameter and the |

1019 | //result will be correct. Handles tainting. |

1020 | DECMOD_GMP_INTS |

1021 | int GMP_INTS_two_op_flags_map(int flags1, int flags2); |

1022 | |

1023 | //Adds the single limb s2_limb to the array of limbs s1, |

1024 | //processing carries, and copies the result to the location |

1025 | //res_ptr. res_ptr is assumed to be [at least] the same size |

1026 | //as s1. From the design, s1 and res_ptr may be the |

1027 | //same set of locations. The |

1028 | //result is 1 if there was a carry out of the final limb or |

1029 | //0 otherwise. |

1030 | DECMOD_GMP_INTS |

1031 | GMP_INTS_limb_t GMP_INTS_mpn_add_1 (GMP_INTS_limb_ptr res_ptr, |

1032 | GMP_INTS_limb_srcptr s1_ptr, |

1033 | GMP_INTS_size_t s1_size, |

1034 | GMP_INTS_limb_t s2_limb); |

1035 | |

1036 | //Very similar to the addition function. Counts on the single |

1037 | //limb that is being subtracted being not enough to roll over the |

1038 | //integer that is being subtracted from. No harm if this is done |

1039 | //(it just obeys 2-s complement rules) but this was probably not |

1040 | //the intent. From the design, s1 and res_ptr may |

1041 | //be the same set of locations. The |

1042 | //result is 1 if there was a borrow out of the final limb or |

1043 | //0 otherwise. |

1044 | DECMOD_GMP_INTS |

1045 | GMP_INTS_limb_t GMP_INTS_mpn_sub_1(GMP_INTS_limb_ptr res_ptr, |

1046 | GMP_INTS_limb_srcptr s1_ptr, |

1047 | GMP_INTS_size_t s1_size, |

1048 | GMP_INTS_limb_t s2_limb); |

1049 | |

1050 | //Multiplies a limb by a group of limbs. The return value is |

1051 | //the unsigned overflow out of the "top", which may be up to |

1052 | //one limb large (i.e. it is more than just a carry, it has |

1053 | //a value besides 0 and 1). |

1054 | DECMOD_GMP_INTS |

1055 | GMP_INTS_limb_t GMP_INTS_mpn_mul_1(GMP_INTS_limb_ptr res_ptr, |

1056 | GMP_INTS_limb_srcptr s1_ptr, |

1057 | GMP_INTS_size_t s1_size, |

1058 | GMP_INTS_limb_t s2_limb); |

1059 | |

1060 | //Adds together two groups of limbs of same size. The result |

1061 | //may be the same location as one or both of the two |

1062 | //operands. |

1063 | DECMOD_GMP_INTS |

1064 | GMP_INTS_limb_t GMP_INTS_mpn_add_n(GMP_INTS_limb_ptr res_ptr, |

1065 | GMP_INTS_limb_srcptr s1_ptr, |

1066 | GMP_INTS_limb_srcptr s2_ptr, |

1067 | GMP_INTS_size_t size); |

1068 | |

1069 | //This function makes the mapping: |

1070 | // res_ptr = res_ptr + s2_limb * s1_ptr |

1071 | //From the design, it appears that it is alright if |

1072 | //res_ptr and s1_ptr are the same area. The return |

1073 | //value is the excess that that should exist one limb |

1074 | //above the MSL of res_ptr (i.e. it is more than a carry, it |

1075 | //may be larger than one). |

1076 | DECMOD_GMP_INTS |

1077 | GMP_INTS_limb_t GMP_INTS_mpn_addmul_1(GMP_INTS_limb_ptr res_ptr, |

1078 | GMP_INTS_limb_srcptr s1_ptr, |

1079 | GMP_INTS_size_t s1_size, |

1080 | GMP_INTS_limb_t s2_limb); |

1081 | |

1082 | //This function adds in general two natural numbers. Numbers must |

1083 | //be arranged so that S2 takes no more limbs than S1, i.e. |

1084 | //LIMBS(s1) >= LIMBS(s2). Memory must be allocated, and there must |

1085 | //be space for the result. Not clear from the design if memory |

1086 | //areas can be coincident, but suspect can. |

1087 | DECMOD_GMP_INTS |

1088 | GMP_INTS_limb_t GMP_INTS_mpn_add(GMP_INTS_limb_ptr res_ptr, |

1089 | GMP_INTS_limb_srcptr s1_ptr, |

1090 | GMP_INTS_size_t s1_size, |

1091 | GMP_INTS_limb_srcptr s2_ptr, |

1092 | GMP_INTS_size_t s2_size); |

1093 | |

1094 | //Subtracts two same-size operands. They may be coincident in |

1095 | //memory. |

1096 | DECMOD_GMP_INTS |

1097 | GMP_INTS_limb_t GMP_INTS_mpn_sub_n(GMP_INTS_limb_ptr res_ptr, |

1098 | GMP_INTS_limb_srcptr s1_ptr, |

1099 | GMP_INTS_limb_srcptr s2_ptr, |

1100 | GMP_INTS_size_t size); |

1101 | |

1102 | //This function subtracts in general two natural numbers. Numbers must |

1103 | //be arranged so that S2 takes no more limbs than S1, i.e. |

1104 | //LIMBS(s1) >= LIMBS(s2). Memory must be allocated, and there must |

1105 | //be space for the result. Not clear from the design if memory |

1106 | //areas can be coincident. Result is S1-S2. |

1107 | DECMOD_GMP_INTS |

1108 | GMP_INTS_limb_t GMP_INTS_mpn_sub (GMP_INTS_limb_ptr res_ptr, |

1109 | GMP_INTS_limb_srcptr s1_ptr, |

1110 | GMP_INTS_size_t s1_size, |

1111 | GMP_INTS_limb_srcptr s2_ptr, |

1112 | GMP_INTS_size_t s2_size); |

1113 | |

1114 | //Shifts UP of size USIZE left by CNT. CNT must be less than the number |

1115 | //of bits per limb, which is at this time 32. "wp" and "up" may be |

1116 | //coincident. Zero count is not allowed. Value returned is the bits shifted |

1117 | //out the left. |

1118 | DECMOD_GMP_INTS |

1119 | GMP_INTS_limb_t GMP_INTS_mpn_lshift(GMP_INTS_limb_ptr wp, |

1120 | GMP_INTS_limb_srcptr up, |

1121 | GMP_INTS_size_t usize, |

1122 | unsigned int cnt); |

1123 | |

1124 | //Shifts UP of size USIZE right by CNT. CNT must be less than the number |

1125 | //of bits per limb, which is at this time 32. "wp" and "up" may be |

1126 | //coincident. Zero count is not allowed. Value returned is the bits shifted |

1127 | //out the right. |

1128 | DECMOD_GMP_INTS |

1129 | GMP_INTS_limb_t GMP_INTS_mpn_rshift (GMP_INTS_limb_ptr wp, |

1130 | GMP_INTS_limb_srcptr up, |

1131 | GMP_INTS_size_t usize, |

1132 | unsigned int cnt); |

1133 | |

1134 | //Compares two natural numbers of same size and returns the expected |

1135 | //1 iff op1 > op2, -1 if op1 < op2, or 0 if they are equal. Leading |

1136 | //zero limbs are alright and do not affect the result. |

1137 | DECMOD_GMP_INTS |

1138 | int GMP_INTS_mpn_cmp (GMP_INTS_limb_srcptr op1_ptr, |

1139 | GMP_INTS_limb_srcptr op2_ptr, |

1140 | GMP_INTS_size_t size); |

1141 | |

1142 | //This is the basic multiplication of two natural numbers, each of |

1143 | //which may occuply many limbs. In the |

1144 | //original GNU MP code, there were several algorithms which could |

1145 | //be selected, depending on the size of the operands and other |

1146 | //factors. This was the most basic case--the basic longhand |

1147 | //multiplication. The code has been pared so that this is the |

1148 | //only case. |

1149 | DECMOD_GMP_INTS |

1150 | void GMP_INTS_mpn_mul_basecase (GMP_INTS_limb_ptr prodp, |

1151 | GMP_INTS_limb_srcptr up, |

1152 | GMP_INTS_size_t usize, |

1153 | GMP_INTS_limb_srcptr vp, |

1154 | GMP_INTS_size_t vsize); |

1155 | |

1156 | //This is the basic multiplication of two natural numbers. In the old |

1157 | //GNU MP code, one of several algorithms would be selected. The code |

1158 | //has been pared down so that this is just a passthrough to |

1159 | //GMP_INTS_mpn_mul_basecase(). Only the simplest multiplication |

1160 | //algorithm is used at this point. |

1161 | DECMOD_GMP_INTS |

1162 | void GMP_INTS_mpn_mul_n (GMP_INTS_limb_ptr p, |

1163 | GMP_INTS_limb_srcptr a, |

1164 | GMP_INTS_limb_srcptr b, |

1165 | GMP_INTS_size_t n); |

1166 | //Multiplication of two natural numbers. Value returned is the most |

1167 | //significant limb of the array of predicted size un+vn, rather than |

1168 | //the spillover (this is unlike most functions). |

1169 | DECMOD_GMP_INTS |

1170 | GMP_INTS_limb_t GMP_INTS_mpn_mul(GMP_INTS_limb_ptr prodp, |

1171 | GMP_INTS_limb_srcptr up, |

1172 | GMP_INTS_size_t un, |

1173 | GMP_INTS_limb_srcptr vp, |

1174 | GMP_INTS_size_t vn); |

1175 | |

1176 | /******************************************************************/ |

1177 | /*** LIMB SPACE REALLOCATION FUNCTIONS *************************/ |

1178 | /******************************************************************/ |

1179 | DECMOD_GMP_INTS |

1180 | void *GMP_INTS_mpz_realloc (GMP_INTS_mpz_struct *m, |

1181 | GMP_INTS_size_t new_size); |

1182 | //Changes the number of limbs allocated. |

1183 | |

1184 | /******************************************************************/ |

1185 | /*** PUBLIC INITIALIZATION AND MEMORY MANAGEMENT FUNCTIONS *****/ |

1186 | /******************************************************************/ |

1187 | //Allocate space for an integer and sets it to zero. |

1188 | //This must be the first call made. |

1189 | DECMOD_GMP_INTS |

1190 | void GMP_INTS_mpz_init (GMP_INTS_mpz_struct *x); |

1191 | |

1192 | //Deallocates space for an integer. This must be the |

1193 | //final call made. |

1194 | DECMOD_GMP_INTS |

1195 | void GMP_INTS_mpz_clear (GMP_INTS_mpz_struct *x); |

1196 | |

1197 | |

1198 | /******************************************************************/ |

1199 | /*** PUBLIC ASSIGNMENT FUNCTIONS *******************************/ |

1200 | /******************************************************************/ |

1201 | //Copies from one integer to another. Must both be allocated and \ |

1202 | //not be the same variable. |

1203 | DECMOD_GMP_INTS |

1204 | void GMP_INTS_mpz_copy( GMP_INTS_mpz_struct *dst, |

1205 | const GMP_INTS_mpz_struct *src); |

1206 | |

1207 | //Assigns the integer to be the value of an unsigned long. |

1208 | DECMOD_GMP_INTS |

1209 | void GMP_INTS_mpz_set_ui (GMP_INTS_mpz_struct *dest, |

1210 | unsigned long int val); |

1211 | |

1212 | //Assigns the integer to be the value of a signed long. |

1213 | DECMOD_GMP_INTS |

1214 | void GMP_INTS_mpz_set_si (GMP_INTS_mpz_struct *dest, |

1215 | signed long int val); |

1216 | //Assigns the integer to be the value of a simple string |

1217 | //(simple = no E notation). Only form handled is |

1218 | // [-]digits. |

1219 | //Other forms will not cause catastrophic failure but might |

1220 | //not behave as expected. |

1221 | DECMOD_GMP_INTS |

1222 | void GMP_INTS_mpz_set_simple_char_str(GMP_INTS_mpz_struct *z, |

1223 | const char *s); |

1224 | //Assigns an arbitary integer to be a number with E notation. |

1225 | //*failure set non-zero if can't parse or set. Number must |

1226 | //be pure integer--no lost precison when scientific notation |

1227 | //is processed. |

1228 | void GMP_INTS_mpz_set_sci_not_num(GMP_INTS_mpz_struct *z, |

1229 | int *failure, |

1230 | const char *s); |

1231 | |

1232 | //Attempts to parse an integer using the following three |

1233 | //formats: a)simple integer, b)simple integer with commas, |

1234 | //c)integer in scientific notation. Returns the value of |

1235 | //the integer if parse successful, or 0 and a failure flag |

1236 | //otherwise. |

1237 | void GMP_INTS_mpz_set_general_int(GMP_INTS_mpz_struct *z, |

1238 | int *failure, |

1239 | const char *s); |

1240 | |

1241 | //Attempts to parse an integer as either a simple integer, |

1242 | //an integer with commas, or a number in scientific notation |

1243 | //into a UINT32. If the number cannot be parsed into that, |

1244 | //the result is zero and failure is true. |

1245 | void GMP_INTS_mpz_parse_into_uint32(unsigned *result, |

1246 | int *failure, |

1247 | char *s); |

1248 | |

1249 | //Swaps a and b. What this does is a swap of the area |

1250 | //pointed to (i.e. the control block). Pointers held in |

1251 | //these blocks are therefore automatically swapped. |

1252 | DECMOD_GMP_INTS |

1253 | void GMP_INTS_mpz_swap(GMP_INTS_mpz_struct *a, |

1254 | GMP_INTS_mpz_struct *b); |

1255 | |

1256 | /****************************************************************/ |

1257 | /*** PUBLIC INTEGER ARITHMETIC FUNCTIONS ********************/ |

1258 | /****************************************************************/ |

1259 | //Adds two arbitrary integers to produce an arbitrary result. |

1260 | //The result space must be initialized already. |

1261 | DECMOD_GMP_INTS |

1262 | void GMP_INTS_mpz_add ( GMP_INTS_mpz_struct *w, |

1263 | const GMP_INTS_mpz_struct *u, |

1264 | const GMP_INTS_mpz_struct *v); |

1265 | |

1266 | //Adds the integer v to u and produces w. u and w must be |

1267 | //be created already. |

1268 | void GMP_INTS_mpz_add_ui ( GMP_INTS_mpz_struct *w, |

1269 | const GMP_INTS_mpz_struct *u, |

1270 | unsigned long int v); |

1271 | |

1272 | //Subtracts two aribtrary integers to produce an arbitrary |

1273 | //result. The result space must be initialized already. |

1274 | DECMOD_GMP_INTS |

1275 | void GMP_INTS_mpz_sub ( GMP_INTS_mpz_struct *w, |

1276 | const GMP_INTS_mpz_struct *u, |

1277 | const GMP_INTS_mpz_struct *v); |

1278 | |

1279 | //Subtracts the integer v from u to produce w. u and w must |

1280 | //be created already. |

1281 | void GMP_INTS_mpz_sub_ui ( GMP_INTS_mpz_struct *w, |

1282 | const GMP_INTS_mpz_struct *u, |

1283 | unsigned long int v); |

1284 | |

1285 | //Multiplies two arbitrary integers to produce an arbitrary |

1286 | //result. The result space must be initialized already. |

1287 | DECMOD_GMP_INTS |

1288 | void GMP_INTS_mpz_mul ( GMP_INTS_mpz_struct *w, |

1289 | const GMP_INTS_mpz_struct *u, |

1290 | const GMP_INTS_mpz_struct *v); |

1291 | |

1292 | //Multiplies the arbitrary integer by a C-native signed |

1293 | //long. |

1294 | DECMOD_GMP_INTS |

1295 | void GMP_INTS_mpz_mul_si ( GMP_INTS_mpz_struct *w, |

1296 | const GMP_INTS_mpz_struct *u, |

1297 | long int v); |

1298 | //Multiplies the arbitrary integer by a C-native unsigned |

1299 | //long. |

1300 | DECMOD_GMP_INTS |

1301 | void GMP_INTS_mpz_mul_ui ( GMP_INTS_mpz_struct *w, |

1302 | const GMP_INTS_mpz_struct *u, |

1303 | unsigned long int v); |

1304 | |

1305 | //Divides integers. |

1306 | DECMOD_GMP_INTS |

1307 | void GMP_INTS_mpz_tdiv_qr ( GMP_INTS_mpz_struct *quot, |

1308 | GMP_INTS_mpz_struct *rem, |

1309 | const GMP_INTS_mpz_struct *num, |

1310 | const GMP_INTS_mpz_struct *den); |

1311 | |

1312 | //Calculates the factorial. All values <=1 result in a |

1313 | //value of 1. |

1314 | DECMOD_GMP_INTS |

1315 | void GMP_INTS_mpz_fac_ui(GMP_INTS_mpz_struct *result, |

1316 | unsigned long int n); |

1317 | |

1318 | //Exponentiates a base to an exponent. 0^0=1, N^0=1. The algorithm |

1319 | //used is successive squaring and multiplying. Not the MOST efficient, |

1320 | //but OK. The result and the base must be different variables. |

1321 | DECMOD_GMP_INTS |

1322 | void GMP_INTS_mpz_pow_ui( GMP_INTS_mpz_struct *result, |

1323 | const GMP_INTS_mpz_struct *base, |

1324 | unsigned exponent); |

1325 | |

1326 | //Takes the absolute value of the arbitrary integer passed. |

1327 | DECMOD_GMP_INTS |

1328 | void GMP_INTS_mpz_abs(GMP_INTS_mpz_struct *arg); |

1329 | |

1330 | //Calculates the gcd() of the two arguments. If either argument is zero, the |

1331 | //result is automatically 1. If either argument is negative, its absolute |

1332 | //value is used. The two input pointers may not be the same, because doing |

1333 | //that is senseless--it would become a copy operation, because gcd(x,x) = x. |

1334 | //However, the result may be the same as either of the two inputs. |

1335 | DECMOD_GMP_INTS |

1336 | void GMP_INTS_mpz_gcd(GMP_INTS_mpz_struct *result, |

1337 | const GMP_INTS_mpz_struct *arg1, |

1338 | const GMP_INTS_mpz_struct *arg2); |

1339 | |

1340 | |

1341 | /******************************************************************/ |

1342 | /*** PUBLIC CONVERSION AND OUTPUT FUNCTIONS ********************/ |

1343 | /******************************************************************/ |

1344 | |

1345 | //Get an upper bound on the number of characters required for |

1346 | //representing an integer, including minus sign and commas, |

1347 | //Terminating zero, etc. This is just a little wasteful, but |

1348 | //will always reserve enough memory. |

1349 | DECMOD_GMP_INTS |

1350 | int GMP_INTS_mpz_size_in_base_10(const GMP_INTS_mpz_struct *arg); |

1351 | |

1352 | //Convert from integer to string. Commas must be |

1353 | //added separately, and there is enough space reserved for |

1354 | //them. This function is only warrantied not to overflow |

1355 | //a buffer allocated using the function above as a sizing |

1356 | //guide. |

1357 | DECMOD_GMP_INTS |

1358 | void GMP_INTS_mpz_to_string(char *out, |

1359 | const GMP_INTS_mpz_struct *in); |

1360 | |

1361 | //Prints the integer passed to the stream in a long-hand |

1362 | //format. |

1363 | DECMOD_GMP_INTS |

1364 | void GMP_INTS_mpz_long_int_format_to_stream(FILE *s, |

1365 | const GMP_INTS_mpz_struct *i, |

1366 | const char *desc); |

1367 | |

1368 | //Prints the integer raw to a stream--just digits, no extra chars. |

1369 | DECMOD_GMP_INTS |

1370 | void GMP_INTS_mpz_arb_int_raw_to_stream(FILE *s, |

1371 | const GMP_INTS_mpz_struct *i); |

1372 | |

1373 | /******************************************************************/ |

1374 | /*** COMPARISON AND SIZING FUNCTIONS ***************************/ |

1375 | /******************************************************************/ |

1376 | //Returns 1 if arbitrary integer will fit in an unsigned integer, |

1377 | //or 0 otherwise. |

1378 | DECMOD_GMP_INTS |

1379 | int GMP_INTS_mpz_fits_uint_p (const GMP_INTS_mpz_struct *src); |

1380 | |

1381 | //Returns 1 if arbitrary integer will fit in a signed integer, |

1382 | //or 0 otherwise. |

1383 | DECMOD_GMP_INTS |

1384 | int GMP_INTS_mpz_fits_sint_p (const GMP_INTS_mpz_struct *src); |

1385 | |

1386 | //Retrieves an unsigned version of limb zero from the number, |

1387 | //or will return zero if the number is zero. This is the |

1388 | //officially sanctioned way to get the value if it fits in |

1389 | //an unsigned. |

1390 | DECMOD_GMP_INTS |

1391 | unsigned GMP_INTS_mpz_get_limb_zero(const GMP_INTS_mpz_struct *src); |

1392 | |

1393 | //Returnes neg value if u<v, 0 if u==v, and 1 if u>v. |

1394 | DECMOD_GMP_INTS |

1395 | int GMP_INTS_mpz_cmp (const GMP_INTS_mpz_struct *u, |

1396 | const GMP_INTS_mpz_struct *v); |

1397 | |

1398 | //Compares an arbitrary integer to an unsigned long |

1399 | //and returns relative ordering, <0 if u < v, 0 if u==v, |

1400 | //and >0 if u > v. |

1401 | DECMOD_GMP_INTS |

1402 | int GMP_INTS_mpz_cmp_ui (const GMP_INTS_mpz_struct *u, |

1403 | unsigned long int v_digit); |

1404 | //Compares arbitrary integer to a signed long |

1405 | //and returns relative ordering, <0 if u<v, 0 if u==v, |

1406 | //and >0 if u>v. |

1407 | DECMOD_GMP_INTS |

1408 | int GMP_INTS_mpz_cmp_si (const GMP_INTS_mpz_struct *u, |

1409 | signed long int v_digit); |

1410 | |

1411 | //Compares the absolute value of two arbitrary integers. |

1412 | DECMOD_GMP_INTS |

1413 | int GMP_INTS_mpz_cmpabs (const GMP_INTS_mpz_struct *u, |

1414 | const GMP_INTS_mpz_struct *v); |

1415 | //Compares the absolute value of an arbitrary integer and |

1416 | //an unsigned long. |

1417 | DECMOD_GMP_INTS |

1418 | int GMP_INTS_mpz_cmpabs_ui(const GMP_INTS_mpz_struct *u, |

1419 | unsigned long int v_digit); |

1420 | |

1421 | /****************************************************************/ |

1422 | /*** VERSION CONTROL REPORTING FUNCTIONS ********************/ |

1423 | /****************************************************************/ |

1424 | DECMOD_GMP_INTS const char *GMP_INTS_cvcinfo(void); |

1425 | DECMOD_GMP_INTS const char *GMP_INTS_hvcinfo(void); |

1426 | |

1427 | /* Preprocessor string to allow the H-file version to be |

1428 | ** compiled into the C-file. |

1429 | */ |

1430 | #define GMP_INTS_H_VERSION ("$Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_ints.h,v 1.23 2001/08/16 19:49:40 dtashley Exp $") |

1431 | |

1432 | #endif /* GMP_INTS_H_INCLUDED */ |

1433 | |

1434 | |

1435 | //************************************************************************** |

1436 | // $Log: gmp_ints.h,v $ |

1437 | // Revision 1.23 2001/08/16 19:49:40 dtashley |

1438 | // Beginning to prepare for v1.05 release. |

1439 | // |

1440 | // Revision 1.22 2001/08/15 06:56:05 dtashley |

1441 | // Substantial progress. Safety check-in. |

1442 | // |

1443 | // Revision 1.21 2001/08/07 10:42:48 dtashley |

1444 | // Completion of CFRATNUM extensions and DOS command-line utility. |

1445 | // |

1446 | // Revision 1.20 2001/07/30 02:51:18 dtashley |

1447 | // INTGCD extension and command-line utility finished up. |

1448 | // |

1449 | // Revision 1.19 2001/07/29 07:18:22 dtashley |

1450 | // Completion of ARBINT INTFAC extension. |

1451 | // |

1452 | // Revision 1.18 2001/07/25 23:40:02 dtashley |

1453 | // Completion of INTFAC program, many changes to handling of large |

1454 | // integers. |

1455 | // |

1456 | // Revision 1.17 2001/07/21 03:32:44 dtashley |

1457 | // Addition of several files. |

1458 | // |

1459 | // Revision 1.16 2001/07/21 01:39:01 dtashley |

1460 | // Safety check-in. Major function to output an integer as rows of digits |

1461 | // has been completed. This was the last major function that needed to be |

1462 | // completed before useful command-line utilities can be constructed. |

1463 | // |

1464 | // Revision 1.15 2001/07/19 20:06:03 dtashley |

1465 | // Division finished. String formatting functions underway. Safety check-in. |

1466 | // |

1467 | // Revision 1.14 2001/07/18 21:53:09 dtashley |

1468 | // Division function finished and passes preliminary tests. Safety check-in. |

1469 | // |

1470 | // Revision 1.13 2001/07/17 22:30:14 dtashley |

1471 | // Safety check-in. Division function under construction. |

1472 | // |

1473 | // Revision 1.12 2001/07/16 17:46:46 dtashley |

1474 | // Multiplication finished, and only indirectly unit-tested. More detailed unit |

1475 | // test must follow, but expect no problems. |

1476 | // |

1477 | // Revision 1.11 2001/07/16 00:28:22 dtashley |

1478 | // Safety check-in. Addition and subtraction functions finished. |

1479 | // |

1480 | // Revision 1.10 2001/07/15 06:40:10 dtashley |

1481 | // Adaptation of GNU arbitrary-size integer package integrated into IjuScripter |

1482 | // and IjuConsole. |

1483 | // |

1484 | // Revision 1.9 2001/07/15 00:59:52 dtashley |

1485 | // Safety check-in. Commit before working on laptop. |

1486 | // |

1487 | // Revision 1.8 2001/07/14 07:03:37 dtashley |

1488 | // Safety check-in. Modifications and progress. |

1489 | // |

1490 | // Revision 1.7 2001/07/14 02:05:02 dtashley |

1491 | // Safety check-in. Almost ready for first unit-testing. |

1492 | // |

1493 | // Revision 1.6 2001/07/13 21:02:20 dtashley |

1494 | // Version control reporting changes. |

1495 | // |

1496 | // Revision 1.5 2001/07/13 18:17:16 dtashley |

1497 | // Safety check-in. Additionally, new files added. |

1498 | // |

1499 | // Revision 1.4 2001/07/13 06:54:57 dtashley |

1500 | // Safety check-in. Substantial progress and modifications. |

1501 | // |

1502 | // Revision 1.3 2001/07/13 00:57:08 dtashley |

1503 | // Safety check-in. Substantial progress on port. |

1504 | // |

1505 | // Revision 1.2 2001/07/12 06:44:12 dtashley |

1506 | // Safety check-in. |

1507 | // |

1508 | // Revision 1.1 2001/07/12 05:07:02 dtashley |

1509 | // Initial checkin. |

1510 | // |

1511 | //************************************************************************** |

1512 | // End of GMP_INTS.H. |

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