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1 dashley 25 // $Header: /cvsroot/esrg/sfesrg/esrgpcpj/shared/c_datd/gmp_ints.h,v 1.23 2001/08/16 19:49:40 dtashley Exp $
3     //--------------------------------------------------------------------------------
4     //Copyright 2001 David T. Ashley
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683     //-------------------------------------------------------------------------------------------------
684     //--------------------------------------------------------------------------------
685     /*
686     This software module is a careful adaptation of the integer functions
687     in the GNU MP library.
689     By "adaptation" I mean the following:
691     o Many of the macros and other constructs that affect readability
692     have been removed. This has been done for simplicity.
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.
698     o The number of source modules has been dramatically reduced.
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).
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).
712     o Certain other stylistic changes have been made.
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.
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.
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.
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.
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     */
767     #ifndef GMP_INTS_H_INCLUDED
768     #define GMP_INTS_H_INCLUDED
770     #ifdef MODULE_GMP_INTS
771     #define DECMOD_GMP_INTS
772     #else
773     #define DECMOD_GMP_INTS extern
774     #endif
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.
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)
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)
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)
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)
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;
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 );
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);
926     /******************************************************************/
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
940     int GMP_INTS_identify_nan_string(const char *s);
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.
946     const char *GMP_INTS_supply_nan_string(int idx);
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.
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.
963     void GMP_INTS_mpz_print_int(FILE *stream,
964     const GMP_INTS_mpz_struct *arg,
965     char *desc);
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.
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).
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).
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.
1021     int GMP_INTS_two_op_flags_map(int flags1, int flags2);
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.
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);
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.
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);
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).
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);
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.
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);
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).
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);
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.
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);
1094     //Subtracts two same-size operands. They may be coincident in
1095     //memory.
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);
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.
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);
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.
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);
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.
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);
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.
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);
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.
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);
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.
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).
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);
1176     /******************************************************************/
1177     /*** LIMB SPACE REALLOCATION FUNCTIONS *************************/
1178     /******************************************************************/
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.
1184     /******************************************************************/
1186     /******************************************************************/
1187     //Allocate space for an integer and sets it to zero.
1188     //This must be the first call made.
1190     void GMP_INTS_mpz_init (GMP_INTS_mpz_struct *x);
1192     //Deallocates space for an integer. This must be the
1193     //final call made.
1195     void GMP_INTS_mpz_clear (GMP_INTS_mpz_struct *x);
1198     /******************************************************************/
1199     /*** PUBLIC ASSIGNMENT FUNCTIONS *******************************/
1200     /******************************************************************/
1201     //Copies from one integer to another. Must both be allocated and \
1202     //not be the same variable.
1204     void GMP_INTS_mpz_copy( GMP_INTS_mpz_struct *dst,
1205     const GMP_INTS_mpz_struct *src);
1207     //Assigns the integer to be the value of an unsigned long.
1209     void GMP_INTS_mpz_set_ui (GMP_INTS_mpz_struct *dest,
1210     unsigned long int val);
1212     //Assigns the integer to be the value of a signed long.
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.
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);
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);
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);
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.
1253     void GMP_INTS_mpz_swap(GMP_INTS_mpz_struct *a,
1254     GMP_INTS_mpz_struct *b);
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.
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);
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);
1272     //Subtracts two aribtrary integers to produce an arbitrary
1273     //result. The result space must be initialized already.
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);
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);
1285     //Multiplies two arbitrary integers to produce an arbitrary
1286     //result. The result space must be initialized already.
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);
1292     //Multiplies the arbitrary integer by a C-native signed
1293     //long.
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.
1301     void GMP_INTS_mpz_mul_ui ( GMP_INTS_mpz_struct *w,
1302     const GMP_INTS_mpz_struct *u,
1303     unsigned long int v);
1305     //Divides integers.
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);
1312     //Calculates the factorial. All values <=1 result in a
1313     //value of 1.
1315     void GMP_INTS_mpz_fac_ui(GMP_INTS_mpz_struct *result,
1316     unsigned long int n);
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.
1322     void GMP_INTS_mpz_pow_ui( GMP_INTS_mpz_struct *result,
1323     const GMP_INTS_mpz_struct *base,
1324     unsigned exponent);
1326     //Takes the absolute value of the arbitrary integer passed.
1328     void GMP_INTS_mpz_abs(GMP_INTS_mpz_struct *arg);
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.
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);
1341     /******************************************************************/
1342     /*** PUBLIC CONVERSION AND OUTPUT FUNCTIONS ********************/
1343     /******************************************************************/
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.
1350     int GMP_INTS_mpz_size_in_base_10(const GMP_INTS_mpz_struct *arg);
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.
1358     void GMP_INTS_mpz_to_string(char *out,
1359     const GMP_INTS_mpz_struct *in);
1361     //Prints the integer passed to the stream in a long-hand
1362     //format.
1364     void GMP_INTS_mpz_long_int_format_to_stream(FILE *s,
1365     const GMP_INTS_mpz_struct *i,
1366     const char *desc);
1368     //Prints the integer raw to a stream--just digits, no extra chars.
1370     void GMP_INTS_mpz_arb_int_raw_to_stream(FILE *s,
1371     const GMP_INTS_mpz_struct *i);
1373     /******************************************************************/
1374     /*** COMPARISON AND SIZING FUNCTIONS ***************************/
1375     /******************************************************************/
1376     //Returns 1 if arbitrary integer will fit in an unsigned integer,
1377     //or 0 otherwise.
1379     int GMP_INTS_mpz_fits_uint_p (const GMP_INTS_mpz_struct *src);
1381     //Returns 1 if arbitrary integer will fit in a signed integer,
1382     //or 0 otherwise.
1384     int GMP_INTS_mpz_fits_sint_p (const GMP_INTS_mpz_struct *src);
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.
1391     unsigned GMP_INTS_mpz_get_limb_zero(const GMP_INTS_mpz_struct *src);
1393     //Returnes neg value if u<v, 0 if u==v, and 1 if u>v.
1395     int GMP_INTS_mpz_cmp (const GMP_INTS_mpz_struct *u,
1396     const GMP_INTS_mpz_struct *v);
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.
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.
1408     int GMP_INTS_mpz_cmp_si (const GMP_INTS_mpz_struct *u,
1409     signed long int v_digit);
1411     //Compares the absolute value of two arbitrary integers.
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.
1418     int GMP_INTS_mpz_cmpabs_ui(const GMP_INTS_mpz_struct *u,
1419     unsigned long int v_digit);
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);
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 $")
1432     #endif /* GMP_INTS_H_INCLUDED */
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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