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/* M. Beeson, for Mathpert */
/* macros, globals, and typedefs to go with arith.c */
/*
7.23.90 file created
1.27.95 last modified
2.15.95 added complexpowers field to aflag
history in arithh.his
*/
/*_____________________________________________________________________*/
/*  What kind of operations are performed by arith is controlled by
the parameter 'arithflag', as follows.  Note that arith ALWAYS evaluates
+, -, and / .  */

/* If new fields are added here, be sure that init_default_model initializes
them in model.c  */

typedef struct{
  unsigned
  fract:1,      /* evaluate arithmetic compound fractions? */
  varadd:1,     /* do addition and mult. on non-adjacent terms, e.g. a+3+x+4=a+7+x */
  intexp:1,     /* exponentiation with � integer exponents */
  negexp:1,     /* if zero, don't evaluate negative integer exponents */
  ratexp:1,     /*  exponentiation with rational exponents */
  roots:1,      /*  evaluate exact (integer and rational) roots */
  pure:1,       /*  if one, work only on terms that have a numerical value */
                /*  and STOP as soon as you find a term without numerical value */
  gcd:1,        /* evaluate 'gcd', 'mod', 'floor' */
  abs:1,        /* evaluate ABS */
  relop:1,      /* evaluate numerical inequalities and equalities
                   to true to false */
  factorial:1,  /* evaluate factorials and binomial coefficients */
  matrix:1,     /* use matrix arithmetic on matrices whose entries have values*/
                /* and evaluate determinants if possible */
  inverse:1,    /* evaluate matrix inverse if entries have values */
  functions:1,  /* evaluate exact values of functions when possible */
  sums:1,       /* evaluate indexed sums and products when possible */
  flt:1,        /* evaluate roots and powers as well as other functions to
                   double values using deval when exact value can't be found */
  complex:1,    /* use complex addition, multiplication, and subtraction. */
                 /* Note this affects the evaluation of roots and fractional
                    powers of negative numbers, eg. (-1)^(1/3) */
  complexpowers:1, /* also evaluate complex exponentials */
  comdenom:1,   /* if zero, don't add fractions unless they have the same denom */
  mod: 1;       /* if nonzero, perform arithmetic modulo 'modulus', which is
                   a static term in value.c.  Be sure to call set_modulus
                   before using this feature, as 'modulus' could be set in
                   one document and not in another.  */
}  aflag;       /* "arithmetic control flag " */

MEXPORT_POLYVAL void set_arithflag(aflag);
MEXPORT_POLYVAL aflag get_arithflag(void);   /* value.c   */
/*_____________________________________________________________________*/

/* The following macros work on terms representing positive or negative integers */
#define ODD(t)   ((NEGATIVE(t)) ? (INTDATA(ARG(0,t)) & 1) : (INTDATA(t) & 1))
#define EVEN(t)  !ODD(t)
/* The following two macros work on terms representing bignums */
#define BIGODD(t) ((NEGATIVE(t)) ? (BIGNUMDATA(ARG(0,t)).val[0] & 1) \
                                       : (BIGNUMDATA(t).val[0] & 1))
#define BIGEVEN(t)  !BIGODD(t)

/* The following macros works on positive integers or bignums */
#define ISODD(t)  (OBJECT(t) && ((TYPE(t)==INTEGER && (INTDATA(t) & 1)) || (TYPE(t)==BIGNUM && (BIGNUMDATA(t).val[0] & 1))))
#define ISEVEN(t) !ISODD(t)
extern unsigned doing_indexedsum;
extern long sumvar;

/* prototypes of public functions in arith.c, roots.c, some in pda.c */

MEXPORT_POLYVAL term conjugate(term);   /* compute complex conjugate of a number */
MEXPORT_ALGEBRA int arithmetic(term, term, term *, char *);  /* an operator callable from the menus */
MEXPORT_POLYVAL int value(term, term *);   /* arith using global variable arithflag */
MEXPORT_POLYVAL int arith(term, term *, aflag);   /* the main public function */
MEXPORT_POLYVAL long intgcd(long,long);
MEXPORT_POLYVAL long euclid(long,long,long *, long *);
MEXPORT_POLYVAL int gcd(term,term,term *);
MEXPORT_POLYVAL unsigned long fastexp(unsigned long, unsigned long ); /* doesn't detect overflow */
MEXPORT_POLYVAL int complexfastexp(term, term, unsigned, term *);
int lcm(term,term,term *, term *, term *);
int introot(unsigned long index, unsigned long arg, unsigned long *ans);
                     /* returns 1 if root(index,arg) isn't an integer */

/*  following public functions perform basic arithmetic operations on terms
    and return answers in fresh space: */
MEXPORT_POLYVAL int add( term, term, term *);  /* add two terms */
MEXPORT_POLYVAL int mult(term,term,term *);  /* add, mult, divide do not assume args are arithmetic */
MEXPORT_POLYVAL int divide(term,term,term *);  /* so that in future they can work on polynomials */
MEXPORT_POLYVAL int intdivide(term,term,term*,term*);  /* quo and rem for ints or bignums */
void negate(term, term*);     /* re-uses space  unlike add etc. */
MEXPORT_POLYVAL int tcompare(term x,term y, short *ans);
MEXPORT_POLYVAL int cadd( term, term, term *);  /* add two complex or real terms */
MEXPORT_POLYVAL int cmult(term,term,term *);  /* multiply two complex terms */
int cdivide(term,term,term *);  /* divide two complex terms */
void cnegate(term,term*);  /* negate a complex term */
int exponentiate(unsigned,term,term,term *);  /* assumes args are arithmetic expressions */

int take_root(term,term,term *);   /* assumes args are arithmetic expressions */
int take_complex_root(unsigned,term,term,term*);
MEXPORT_POLYVAL int eval_indexedsum(term,term *,aflag);  /* assumes upper and lower limits
                                      are arithmetic expressions */
int bitlength(unsigned long); /* how many bits to the right of and including the leftmost nonzero bit? */
MEXPORT_POLYVAL int tmod(term, term, term *);
int tfloor(term,term *);
MEXPORT_POLYVAL int factorial(term, term *);
MEXPORT_POLYVAL int binomial(term, term,term *);
     /* return -1 if x < y , 0 if x=y, or 1 if x > y */

void qr(unsigned,unsigned,unsigned *, unsigned *);
void lqr(long, long, long *, long *);
MEXPORT_ALGEBRA int factor_gaussian_integer(term, unsigned *, term *);
MEXPORT_POLYVAL int tmodexp(term m, term u, term x, term *ans);   /*  compute u^x mod m */
MEXPORT_POLYVAL long intmodexp(unsigned long m, long a, unsigned long b); /* a^b mod m */
MEXPORT_ALGEBRA int nsquarefree(term);   /* return 1 if apparently squarefree, 0 if not */
MEXPORT_ALGEBRA int rootfree(term,unsigned);  /* free of n-th roots?                    */
MEXPORT_POLYVAL void parts(term, term *, term *);  /* arith.c */