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    * Redistributions of source code must retain the above copyright notice,
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      may be used to endorse or promote products derived from this software
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#include "dpml_ux.h"

#if (NUM_UX_FRACTION_DIGITS != 2)
#   error "Must have 64 bit integers"
#endif

/*
** MULTIPLY essentially computes the high 128 bits of the product of two
** unpacked x-float values.  The algorithm attempts to limit the number
** of integer multiplications performed.  The resulting product has roughly
** a 6 lsb error bound in the worst case.
*/

void
MULTIPLY(UX_FLOAT * x, UX_FLOAT *y, UX_FLOAT *z)
    {
    U_WORD x_hi, x_lo, y_hi, y_lo, z_hi, z_lo, p1, p2;

    x_hi = G_UX_MSD(x);
    y_hi = G_UX_MSD(y);

    z_lo = y_hi*x_hi;
        x_lo = G_UX_LSD(x);
        y_lo = G_UX_LSD(y);

    UMULH(y_hi, x_lo, p2);
        P_UX_SIGN(z, G_UX_SIGN(x) ^ G_UX_SIGN(y));
        P_UX_EXPONENT(z, G_UX_EXPONENT(x) + G_UX_EXPONENT(y));

    UMULH(y_lo, x_hi, p1);
        z_lo += p2;
        z_hi = (z_lo < p2);

    UMULH(y_hi, x_hi, p2);
        z_lo = z_lo + p1;
        z_hi += (z_lo < p1);

    P_UX_LSD(z, z_lo);
    z_hi = z_hi + p2;
    P_UX_MSD(z, z_hi);
    }


/*
** EXTENDED_MULTIPLY computes the exact 256 bit product of two unpacked
** x-float values. The result is stored in two unpacked x-float values
** containing the high and low 128 bits of the result
*/

void
EXTENDED_MULTIPLY(UX_FLOAT * x, UX_FLOAT * y, UX_FLOAT * hi, UX_FLOAT * lo)
    {
    UX_EXPONENT_TYPE exponent;
    UX_SIGN_TYPE     sign;
    UX_FRACTION_DIGIT_TYPE x_hi, x_lo, y_hi, y_lo, tmp_digit, carry, p1, p2;

    x_lo = G_UX_LSD(x);
    y_lo = G_UX_LSD(y);

    p1 = y_lo*x_lo;
        x_hi = G_UX_MSD(x);
        y_hi = G_UX_MSD(y);

    UMULH(y_lo, x_lo, tmp_digit);
        P_UX_LSD(lo, p1);
        sign = G_UX_SIGN(x) ^ G_UX_SIGN(y);
        exponent = G_UX_EXPONENT(x) + G_UX_EXPONENT(y);
        P_UX_SIGN(lo, sign);
        P_UX_EXPONENT(lo, exponent - 128);

    p1 = y_lo*x_hi;
        P_UX_SIGN(hi, sign);
        P_UX_EXPONENT(hi, exponent);

    p2 = y_hi*x_lo;
        P_UX_SIGN(lo, sign);
        P_UX_EXPONENT(lo, exponent - 128);
        tmp_digit += p1;
        carry = (tmp_digit < p1);

    p1 = x_hi*y_hi;
        tmp_digit += p2;
        carry += (tmp_digit < p2);
        P_UX_MSD(lo, tmp_digit);

    UMULH(y_hi, x_lo, p2);
        tmp_digit = p1 + carry;
        carry = (tmp_digit < p1);

    UMULH(y_lo, x_hi, p1);
        tmp_digit += p2;
        carry += (tmp_digit < p2);

    UMULH(y_hi, x_hi, p2);
        tmp_digit += p1;
        carry += (tmp_digit < p1);
        P_UX_LSD(hi, tmp_digit);

    tmp_digit = p2 + carry;
    P_UX_MSD(hi, tmp_digit);
    }

/*
** This routine divides two unpacked numbers:
**
**	o The 'flags' argument controls whether a FULL or HALF precision
**	  result is generated.
**	o If the pointer to one of the unpacked results is 0, then that
**	  argument is implicitly treated as being equal to 1.
**	o both argument pointers *CANNOT* be zero.
*
** A detailed description of the algorithm is presented in note 6.2 of the
** X_FLOAT notes conference.  Note that to the extent possible, the variable
** names in this routine were chosen to match the description in the design
** note.  In particular, upper case name imply 64 bit integer data types, while
** double precision values are denoted with lower case names.
*/

#define _D_POW_2(n)	((double) ((U_WORD)1 << n))

#define       TWO_POW_62  (_D_POW_2(62))
#define       TWO_POW_124 (TWO_POW_62*TWO_POW_62)
#define RECIP_TWO_POW_16  (1./_D_POW_2(16))
#define RECIP_TWO_POW_60  (1./_D_POW_2(60))
#define RECIP_TWO_POW_184 (4./(TWO_POW_124 * TWO_POW_62 ))


static const UX_FLOAT __ux_one__ = { 0, 1, ((U_WORD) 1 << 63), 0 };
	
void
DIVIDE( UX_FLOAT * aPtr, UX_FLOAT * bPtr, U_WORD flags, UX_FLOAT * cPtr)
    {
    UX_EXPONENT_TYPE exponent;

    UX_FRACTION_DIGIT_TYPE A1, A2, B1, B2, Q1, Q2, S, R, P00, P01, P11,
                           N0, N1, N2, C1, mask, E;
    D_TYPE r, b_hi, b_lo, r_hi, r_lo, a_hi, a_lo, a, q_hi, q_lo;

    /*
    ** for performance reasons, pre-load some of the interesting items even
    ** though we might not actually use them.  Specifically, by loading B1
    ** and B2 before the normalization check allows the compiler to better
    ** schedule the code after the check.
    */

    bPtr = (bPtr == 0) ? (UX_FLOAT *)&__ux_one__ : bPtr;	
    aPtr = (aPtr == 0) ? (UX_FLOAT *)&__ux_one__ : aPtr;
    B1 = G_UX_MSD(bPtr);
    B2 = G_UX_LSD(bPtr);

    if (bPtr == &__ux_one__)
        {
        UX_COPY(aPtr, cPtr);
        return;
        }

    /*
    ** If b isn't normalized, then the whole algorithm falls apart.  So make
    ** sure that b is normalized.
    */

    if ((UX_SIGNED_FRACTION_DIGIT_TYPE) B1 >= 0)
        {
        NORMALIZE(bPtr);
        B1 = G_UX_MSD(bPtr);
        B2 = G_UX_LSD(bPtr);
        }

    /*
    ** The first step is to estimate 1/b in double precsion to more then 70
    ** bits. This is done by getting an initial estimate to 1/b and use a 
    ** variation of Newton's iteration to improve the accuracy.  The basic
    ** approach is
    **
    **		b'    = high 53 bits of b
    **		b_hi' = high 26 bits of b
    **		b_lo' = bits 27 through 80 of b
    **
    **		r'    = 1/b'
    **		r_hi' = high 26 bits of r
    **		r_lo' = [ (1 - b_hi'*r_hi') - b_lo'*r_hi'] * r'
    **
    ** However, there is certain amount of weird scaling of the values that
    ** takes place to deal with the integer to float conversion and subsequent
    ** uses of the results.
    **
    ** Note that the two macros below are used to convert *signed* integers
    ** to and from double precision.  We use signed conversions because they
    ** are generally faster than unsigned conversions.
    */

#   define TO_DOUBLE(a) ((double) ((UX_SIGNED_FRACTION_DIGIT_TYPE) (a)))
#   define TO_DIGIT(a)  ((UX_SIGNED_FRACTION_DIGIT_TYPE) (a))

    r = TWO_POW_124 / TO_DOUBLE( B1 >> 1 );

        /*
        ** While the divide is going on, we can compute all sorts of stuff
        */

        mask = MAKE_MASK( 38, 0 );

        b_hi = TO_DOUBLE((B1 & ~mask) >> 1);
        b_lo = RECIP_TWO_POW_16 * TO_DOUBLE(((B1 & mask) << 15) | (B2 >> 49));

        A1 = G_UX_MSD(aPtr);
        A2 = G_UX_LSD(aPtr);

        P_UX_SIGN(    cPtr, G_UX_SIGN(aPtr) ^ G_UX_SIGN(bPtr) );
        exponent = G_UX_EXPONENT(aPtr) - G_UX_EXPONENT(bPtr);

    /*
    ** Get the high part of r as both an integer and a floating point value.
    ** In the process, bias r_hi downward to insure that r_lo is positive.
    ** (See the design note for details.)
    */

    R = TO_DIGIT( r );
    R = (R - (5 << 8)) & ~MAKE_MASK( 36, 0 );
    r_hi = TO_DOUBLE(R);

    /*
    ** At this point we have:
    **
    ** 		r    = 2^61 * r'
    **		r_hi = 2^61 * r_hi'
    **		b_hi = 2^63 * b_hi'
    **		b_lo = 2^63 * b_lo'
    **
    ** so that
    **
    **		2*r_lo' = [ (2^124 - b_hi*r_hi) - b_lo*r_hi ] * (r/2^184)
    */

    r_lo = D_GROUP(D_GROUP((TWO_POW_124) - b_hi*r_hi) - (b_lo*r_hi)) * (RECIP_TWO_POW_184*r);

    /*
    ** Now that we have 1/b ~ r_hi' + r_lo' (scaling notwithstanding), we can
    ** compute an approximation to q = a/b = a*(1/b), where the product is
    ** performed in high and low pieces:
    **
    **		q = (a_hi' + a_lo') * (r_hi' + r_lo')
    **		  = a_hi' * r_hi' + [ a_lo' * r_hi' + (a_hi' + a_lo') * r_lo' ]
    **		  = a_hi' * r_hi' + [ a_lo' * r_hi' + a' * r_lo' ]
    **		  = q_hi' + q_lo'
    **
    ** Note that in the above, we want to insure that a' ~ a_hi' + a_lo' is
    ** less than the actual value of a to insure that the computed value of
    ** q is less that 2.
    */

    a    = TO_DOUBLE( (A1 >> 11) << 10 );
    a_hi = TO_DOUBLE( (A1 & ~mask) >> 1);
    a_lo = RECIP_TWO_POW_16 * TO_DOUBLE(((A1 & mask) << 15) | (A2 >> 49));

    r_hi = RECIP_TWO_POW_60 * r_hi;
    q_hi = a_hi*r_hi;
    q_lo = a_lo*r_hi + a*r_lo;

    /*
    ** With the above conversions and computations we have
    **
    **		a    = 2^63*a'
    **		a_hi = 2^63*a_hi'
    **		a_lo = 2^63*a_lo'
    **		r_hi = 2*r_hi'
    **		r_lo = 2*r_lo'
    **		q_hi = 2^64 * q_hi'
    **		q_lo = 2^64 * q_lo'
    **
    ** We would like to convert the high 65 bits of q_hi + q_lo into integers,
    ** S' and Q1'.  Note that converting q_hi to an integer can cause an
    ** overflow.  However since q_hi contains only 52 significant bits, we
    ** can convert .25 * q_hi instead which won't overflow.
    */

    Q1 = TO_DIGIT(.25 * q_hi);
    E  = TO_DIGIT( q_lo );

    S = ( Q1 >> 62 );
    Q1 = (4*Q1) + E;
    S += (Q1 < E);
    Q2 = 0;

    if (flags == HALF_PRECISION) goto pack_it;

    /*
    ** While we're at it, compute an integer approximation to 1/b.  I.e. get
    ** and integer R such that R/2^63 ~ 1/b.
    **
    **		 R = 2^63 * (r_hi' + r_lo' )
    **		   = 2^63 * r_hi' + 2^63 * r_lo'
    **		   = 2^63 * r_hi' + 2^62 * r_lo
    **
    ** Recall that in the original computation of r_hi, we previously computed
    ** the integer value R as 2^61*r_hi', so that we can now compute
    ** 
    **		R <-- 4*R + 2^62 * r_lo 
    **
    ** Note that for b very close to 1/2, R will be 2^64 which can't be 
    ** represented in 64 bits.  In this case, we take R = 2^64 - 1 which is
    ** close enough and can be represented in 64 bits.
    */

    R = (R << 2) + TO_DIGIT( TWO_POW_62*r_lo );
    R = ( R == 0 ) ? ( (UX_SIGNED_FRACTION_DIGIT_TYPE) -1 ) : R;

    /*
    ** Using S and Q1 as the current guess for the high 65 bits of the result
    ** compute the remainder:
    **
    **             +----------+----------+
    **             |    A1    |    A2    |                2^128*(2^64*A1 + A2)
    **             +----------+----------+
    **
    **             +----------+----------+
    **             |    B1    |    B2    |              s'*2^128*(2^64*B1 + B2)
    **             +----------+----------+
    **             |       Q1'*B1        |                2^128*Q1'*B1
    **             +----------+----------+----------+
    **                        |       Q1'*B2        |      2^64*Q1'*B2
    **                        +----------+----------+
    **
    **  +----------+----------+----------+----------+
    **  |    N0'   |    N1'   |   N2'    |   N3'    |
    **  +----------+----------+----------+----------+
    **
    ** Start by summing all the products into N0:N1:N2:N3
    **
    **		NOTE: for performance reasons, we don't actually
    **		compute N3'
    */

    mask = -S;

    UMULH( Q1, B2, P11 );
    P01 = Q1 * B1;
    UMULH( Q1, B1, P00 );

    N2 = B2 & mask;	/* N2/N1 = B2/B1 if S = 1, 0 otherwise */
    N1 = B1 & mask;

    N2 += P11;
    C1 =  (N2 < P11);
    N2 += P01;
    C1 += (N2 < P01);

    N1 += P00;
    N0 =  (N1 < P00);
    N1 += C1;
    N0 += (N1 < C1);

    /* Subtract the sum from A1:A2 */

    N0 = -N0;
    C1 = (A2 < N2);
    N2 = A2 - N2;
    N0 -= (A1 < N1);
    N1 = A1 - N1;
    N0 -= (N1 < C1);
    N1 -= C1;

    /*
    ** Since the original estimate to S:Q1 was good to more then 70 bits, the
    ** current value of S:Q1 can be off by at most one.  By looking at the
    ** values of N0 and N1, we can determine an adjustment, E, to S:Q1.
    ** With the adjusted S:Q1 we know that N0 = N1 = 0, so we only need to
    ** adjust N2.
    */

    E = (N0 | (N1 != 0));
    mask = (E == 0) ? B1 : N0;
    N2 = N2 - (mask ^ B1);

    /*
    ** Using R/2^63 ~ 1/b and the adjusted N2, compute an approximation to Q2
    ** Note that if Q2 has it's high bit set, then the original value of E was
    ** one too low.
    */

    UMULH( R, N2, Q2 );

    E += ( ( (UX_SIGNED_FRACTION_DIGIT_TYPE) Q2 ) < 0);
    Q2 = 2*Q2 + ((A1 | A2) != 0);	/* Make sure 0/b is zero */

    /* Adjust S and Q1 using the final value of E */

    Q1 += E;
    S  =  S + (((UX_SIGNED_FRACTION_DIGIT_TYPE) E) >> 63) + (Q1 < E);

    /* Last but not least, pack it */

pack_it:

    P_UX_MSD(     cPtr,        (S << 63) | (Q1 >> S) );
    P_UX_LSD(     cPtr, ((Q1 & S) << 63) | (Q2 >> S) );
    P_UX_EXPONENT(cPtr, exponent + S);

    return;
    }

    
/*
**
** The following two routines evaluate polynomials, P(x), via Horner's
** scheme for positive x:
**
**		s(k) <-- c(k) +/- x*s(k+1)  for k = n-1, ..., 0
**
** where the c(k)'s are the polynomial coefficients and	s(n) = c(n). The
** arguments to these routines (not in order) are
**
**	x		a pointer to the unpacked bits of x
**	cnt		the degree of the polynomial
**	coef		A pointer to pairs of quadwords specifying the hi/lo
**			bits of the coefficient.  We assume the coefficients
**			are stored reverse order: c(n) to c(0)
**	shift		cnt*(x->exp) - This is passed in rather than computed
**			here sense on the calling side, cnt is a known
**			constant, so the multiply can be done by shifts and
**			adds rather than a real integer multiply.
**	p		a pointer to the unpacked result.
**
** The routines return the high bits of the result.
**
** IMPORTANT ASSUMPTIONS:
** ######################
**
**	o This routine assumes that the terms of the polynomial are decreasing.
**	  I.e. that c(k) > x*s(k+1) for all k.
**
**	o shift = cnt*(x->exp), so that if shift is decremented by x->exp
**	  each time cnt decremented, then shift will become 0 before cnt
**	  becomes negative.
*/

static void
__eval_pos_poly(UX_FLOAT * x, WORD shift, FIXED_128 * coef, WORD cnt,
  UX_FLOAT * p)
    {
    UX_FRACTION_DIGIT_TYPE c_hi, c_lo, s_hi, s_lo, p1, p2;
    UX_FRACTION_DIGIT_TYPE x_hi, x_lo, carry;
    UX_EXPONENT_TYPE exponent;
    WORD shift_inc;

    /* Initialize internal copies and accumulators */

    x_hi = G_UX_MSD(x);
    x_lo = G_UX_LSD(x);
    shift_inc = G_UX_EXPONENT(x);
    s_lo = s_hi = 0;


    /*
    ** If the shift count is >= 128, than this product won't contribute to
    ** the final product.  Skip over all of the coefficients that correspond
    ** to large shifts
    */

    if (shift < 128) goto p_check_shift_64_to_127;

    p_shift_ge_128:
        shift += shift_inc;
        coef++;
        cnt--;
        if (shift >= 128) goto p_shift_ge_128;
//printf("Eval_pos_poly, shift=%lld !!\n",shift);

    /*
    ** Each time through this loop, c_hi = 0.  Since we assume that c(k) >
    ** x*s(k+1), if there is a carry out on the sum s(k) = c(k) + x*s(k*1),
    ** then the shift count for the next iteration must be less than 64.
    ** Consequently, we need only worry about the carry out from the sum
    ** when we leave this loop.  That means each time we enter the top of
    ** the loop, both c_hi and s_hi = 0;
    */

    p_check_shift_64_to_127:
        if (shift < 64) goto p_check_shift_1_to_63;

    /*
    ** Depending on the size of shift_inc and the rate at which the
    ** coefficients decrease, several of the next Horner's scheme iterations
    ** will yield zero results, so there is no need to do the multiply.
    ** Since multiplies are likely to be expensive, we check for this case
    ** and skip over them.
    */

    if (s_lo) goto p_shift_64_to_127;

    p_shift_64_to_127_zero_loop:
        s_lo = coef->digits[1] >> (shift - 64);
 	//printf("s_lo, sh, sh_inc, c: %llx, %llx, %llx, %llx (%llx)\n",s_lo,shift, shift_inc,coef->digits[1],coef->digits[0]);
       shift += shift_inc;
        coef++;
        cnt--;
        if (shift < 64) goto p_check_shift_1_to_63;
        if (s_lo == 0) goto p_shift_64_to_127_zero_loop;

    /*
    ** s_lo is no longer zero, so do the multiply and accumulate the
    ** products.
    */

p_shift_64_to_127:
		//printf("s_lo,x_hi,p1: %llx, %llx, %llx\n",s_lo,x_hi,p1);
        UMULH(s_lo, x_hi, p1);
		//printf("s_lo,x_hi,p1: %llx, %llx, %llx\n",s_lo,x_hi,p1);
            c_lo = coef->digits[1] >> (shift - 64);
            shift += shift_inc;
            coef++;
            cnt--;
        s_lo = c_lo + p1;
        if (shift >= 64) goto p_shift_64_to_127;

    /* Set carry out from last add */
    s_hi = (s_lo < p1);
        
    /* 
    ** When shift = 0, the complementary shift is 64.  ANSI C does not
    ** specify the result of a shift by 64, so we need to handle this as
    ** a special case.
    */

    p_check_shift_1_to_63:
        exponent = 0;
        if (shift == 0) goto p_shift_eq_0;

    /*
    ** Depending on the size of shift_inc and the rate at which the
    ** coefficients decrease, several of the next Horner's scheme iterations
    ** will yield zero results for s_hi, so there is no need to do the
    ** multiplies associated with s_hi.  Since multiplies are likely to be
    ** expensive, we check for this case and skip over them.
    */

    if (s_hi) goto p_shift_1_to_63;

    p_shift_1_to_63_zero_loop:
        UMULH(s_lo, x_hi, p1);
            c_hi = coef->digits[1];
            c_lo = coef->digits[0];
            c_lo = (c_lo >> shift) | (c_hi << (64 - shift));
            s_hi = c_hi >> shift;
            shift += shift_inc;
            coef++;
            cnt--;
        s_lo = c_lo + p1;
        s_hi += (s_lo < p1);
        if (shift == 0) goto p_shift_eq_0;
        if (s_hi == 0) goto p_shift_1_to_63_zero_loop;

    p_shift_1_to_63:

    while (cnt >= 0)
        {
        p1 = s_hi*x_hi;
            c_hi = coef->digits[1];
            c_lo = coef->digits[0];
            c_lo = (c_lo >> shift) | (c_hi << (64 - shift));
            c_hi >>= shift;

        UMULH(s_hi, x_lo, p2);
            c_lo += p1;
            carry = (c_lo < p1);
            cnt--;

        UMULH(s_lo, x_hi, p1);
            c_lo += p2;
            carry += (c_lo < p2);
            shift += shift_inc;

        UMULH(s_hi, x_hi, p2);
            s_lo = c_lo + p1;
            carry += (s_lo < p1);
            c_hi += carry;
            carry = (c_hi < carry);
            coef++;

        s_hi = c_hi + p2;
        carry += (s_hi < p2);
        if (carry)
            {
            s_lo = (s_lo >> 1) | (s_hi << 63);
            s_hi = (s_hi >> 1) | SET_BIT(63);
            shift++;
            exponent++;
            }
        if (shift == 0) break;
        }


    p_shift_eq_0:

    while (cnt >= 0)
        {
        p1 = s_hi*x_hi;
            c_hi = coef->digits[1];
            c_lo = coef->digits[0];

        UMULH(s_hi, x_lo, p2);
            c_lo += p1;
            carry = (c_lo < p1);
            cnt--;

        UMULH(s_lo, x_hi, p1);
            c_lo += p2;
            carry += (c_lo < p2);

        UMULH(s_hi, x_hi, p2);
            s_lo = c_lo + p1;
            carry += (s_lo < p1);
            c_hi += carry;
            carry = (c_hi < carry);
            coef++;

        s_hi = c_hi + p2;
        carry += (s_hi < p2);
        if (carry)
            {
            s_lo = (s_lo >> 1) | (s_hi << 63);
            s_hi = (s_hi >> 1) | SET_BIT(63);
            shift = 1;
            exponent++;
            if (cnt >= 0)
                goto p_shift_1_to_63;
            }
        }
        
    P_UX_LSD(p, s_lo);
    P_UX_MSD(p, s_hi);
    P_UX_EXPONENT(p, exponent);
    P_UX_SIGN(p, 0);
    }

static void
__eval_neg_poly(UX_FLOAT * x, WORD shift, FIXED_128 * coef, WORD cnt,
  UX_FLOAT * p)
    {
    UX_FRACTION_DIGIT_TYPE c_hi, c_lo, s_hi, s_lo, p1, p2, tmp;
    UX_FRACTION_DIGIT_TYPE x_hi, x_lo;
    WORD shift_inc;

    x_hi = G_UX_MSD(x);
    x_lo = G_UX_LSD(x);
    shift_inc = G_UX_EXPONENT(x);

    s_lo = s_hi = 0;
    if (shift < 128) goto n_check_shift_64_to_127;

    /* Skip over all the big shifts */

    n_shift_ge_128:
        shift += shift_inc;
        coef++;
        cnt--;
        if (shift >= 128) goto n_shift_ge_128;

    /*
     * Each time through this loop, c_hi = 0.  Since we assume that c(k) >
     * x*s(k+1), s(k) = c(k) - x*s(k*1) < c(k).  Consequently, there is
     * no borrow from the computation of s(k) into it high 64 bits.
     * That means each time we enter the top of the loop, both c_hi and
     * s_hi = 0;
     */

    n_check_shift_64_to_127:
        if (shift < 64) goto n_check_shift_1_to_63;

    /*
     * Depending on the size of shift_inc and the rate at which the
     * coefficients decrease, several of the next Horner's scheme iterations
     * will yield zero results, so there is no need to do the multiply.
     * Since multiplies are likely to be expensive, we check for this case
     * and skip over them.
     */

    if (s_lo) goto n_shift_64_to_127;

    n_shift_64_to_127_zero_loop:
        s_lo = coef->digits[1] >> (shift - 64);
        shift += shift_inc;
        coef++;
        cnt--;
        if (shift < 64) goto n_check_shift_1_to_63;
        if (s_lo == 0) goto n_shift_64_to_127_zero_loop;

    /*
     * s_lo is no longer zero, so do the multiply and accumulate the
     * products.
     */

    n_shift_64_to_127:
        UMULH(s_lo, x_hi, p1);
            c_lo = coef->digits[1] >> (shift - 64);
            shift += shift_inc;
            coef++;
            cnt--;
        s_lo = c_lo - p1;
        if (shift >= 64) goto n_shift_64_to_127;

    /* 
     * When shift = 0, the complementary shift is 64.  ANSI C does not
     * specify the result of a shift by 64, so we need to handle this as
     * a special case.
     */

    n_check_shift_1_to_63:
        if (shift == 0) goto n_shift_eq_0;

    /*
     * Depending on the size of shift_inc and the rate at which the
     * coefficients decrease, several of the next Horner's scheme iterations
     * will yield zero results for s_hi, so there is no need to do the
     * multiplies associated with s_hi.  Since multiplies are likely to be
     * expensive, we check for this case and skip over them.
     */

    if (s_hi) goto n_shift_1_to_63;

    n_shift_1_to_63_zero_loop:
        UMULH(s_lo, x_hi, p1);
            c_hi = coef->digits[1];
            c_lo = coef->digits[0];
            c_lo = (c_lo >> shift) | (c_hi << (64 - shift));
            s_hi = (c_hi >> shift);
            shift += shift_inc;
            coef++;
            cnt--;
        s_lo = c_lo - p1;
        s_hi -= (s_lo > c_lo);
        if (shift == 0) goto n_shift_eq_0;
        if (s_hi == 0) goto n_shift_1_to_63_zero_loop;

    n_shift_1_to_63:
        p1 = s_hi*x_hi;
            c_hi = coef->digits[1];
            c_lo = coef->digits[0];
            c_lo = (c_lo >> shift) | (c_hi << (64 - shift));
            c_hi >>= shift;

        UMULH(s_hi, x_lo, p2);
            tmp = c_lo - p1;
            c_hi -= (tmp > c_lo);
            cnt--;

        UMULH(s_lo, x_hi, p1);
            c_lo = tmp - p2;
            c_hi -= (c_lo > tmp);
            shift += shift_inc;

        UMULH(s_hi, x_hi, p2);
            s_lo = c_lo - p1;
            c_hi -= (s_lo > c_lo);
            coef++;

        s_hi = c_hi - p2;
        if (shift) goto n_shift_1_to_63;


    n_shift_eq_0:

    while (cnt >= 0)
        {
        p1 = s_hi*x_hi;
            c_hi = coef->digits[1];
            c_lo = coef->digits[0];

        UMULH(s_hi, x_lo, p2);
            tmp = c_lo - p1;
            c_hi -= (tmp > c_lo);
            cnt--;

        UMULH(s_lo, x_hi, p1);
            c_lo = tmp - p2;
            c_hi -= (c_lo > tmp);

        UMULH(s_hi, x_hi, p2);
            s_lo = c_lo - p1;
            c_hi -= (s_lo > c_lo);
            coef++;

        s_hi = c_hi - p2;
        }
    P_UX_LSD(p, s_lo);
    P_UX_MSD(p, s_hi);
    P_UX_EXPONENT(p, 0);
    P_UX_SIGN(p, 0);
    }


/*
** EVALUATE_RATIONAL is a driver routine for the two polynomial evaluation
** routines.  Even though it is architecture and word size independent, it
** is included in this file to increase "locality".
**
** EVALUATE_RATIONAL generally computes a rational approximation, however,
** by specifying the appropriate set of flags, one, or two polynomial
** evaluation can be performed.
**
** The following flags are used to independently control the "form" of the
** numerator and denominator polynomials:
**
**		SQUARE_TERM
**		ALTERNATE_SIGN
**		POST_MULTIPLY
**		STANDARD
**
** The following flags control whether or not a rational approximation is
** performed and what form it has:
**
**		SWAP
**		SKIP
**		NO_DIVIDE
**
** If the SKIP flag is specified in conjunction with the flags for either
** the numerator or denominator being zero, only one part of a rational
** will be evaluated.
*/

#define EITHER(n)	   (DENOMINATOR_FLAGS(n) | NUMERATOR_FLAGS(n))
#define NUMERATOR_MASK	   NUMERATOR_FLAGS(MAKE_MASK(NUM_DEN_FIELD_WIDTH, 0))
#define DENOMINATOR_MASK   DENOMINATOR_FLAGS(MAKE_MASK(NUM_DEN_FIELD_WIDTH, 0))

#define UPDATE_COEF_PTR(c,d)	(c) = ((FIXED_128 *)((char *) (c) + (d)))
#define G_EXPONENT(c)		((UX_EXPONENT_TYPE) ((WORD *) (c))[-1])


void
EVALUATE_RATIONAL(
  UX_FLOAT  * argument,
  FIXED_128 * coefficients,
  U_WORD      degree,
  U_WORD      flags,
  UX_FLOAT  * result)
    {
    WORD tmp;
    WORD sign, shift, byte_length, poly_shift;
    UX_EXPONENT_TYPE exponent;
    UX_FLOAT * first_result, *second_result, arg_squared, *poly_arg;
    void (* poly_func)(UX_FLOAT *, WORD, FIXED_128 *, WORD, UX_FLOAT *);

    /* Scale argument and squared it if its needed */

    sign = flags;
    UX_INCR_EXPONENT(argument, G_SCALE(flags));
    if (flags & EITHER(SQUARE_TERM))
        {
        poly_arg = &arg_squared;
        MULTIPLY(argument, argument, &arg_squared);
        }
    else
        {
        poly_arg = argument;
        tmp = G_UX_SIGN(argument) ? EITHER(ALTERNATE_SIGN) : 0;
        sign = flags ^ tmp;
        }

    /* Start calculation of shift parameter. */

    NORMALIZE(poly_arg);
    exponent = G_UX_EXPONENT(poly_arg);
    P_UX_EXPONENT(poly_arg, exponent);
    shift = -degree*exponent;
    byte_length = (degree + 1)*sizeof(FIXED_128) + sizeof(WORD);

    /* allocate locations for 1st and 2nd result */

    tmp = (((flags & SWAP) == 0) || (flags & SKIP)) ? 0 : 1;
    first_result  = result + tmp;
    second_result = result + 1 - tmp;

    if (NUMERATOR_MASK & flags)
        {
//printf("NUMERATOR_MASK !!\n");
        poly_func =  (ALTERNATE_SIGN & sign) ? __eval_neg_poly :
            __eval_pos_poly;

        first_result = (DENOMINATOR_MASK & flags) ? first_result : result;

        poly_func(
            poly_arg,
            shift,
	    coefficients,
	    degree,
	    first_result);
 		//printf("f_result= (%x %x) %llx %llx\n",first_result->sign,first_result->exponent,first_result->fraction[0],first_result->fraction[1]);

 //printf("fl & NUMERATOR_FLAGS(POST_MULTIPLY) = %llx (%llx)\n", flags & NUMERATOR_FLAGS(POST_MULTIPLY), flags); 
        if (flags & NUMERATOR_FLAGS(POST_MULTIPLY))
            MULTIPLY(argument, first_result, first_result);
 		//printf("result..= (%x %x) %llx %llx\n",result->sign,result->exponent,result->fraction[0],result->fraction[1]);

        UPDATE_COEF_PTR(coefficients, byte_length);
        UX_INCR_EXPONENT(first_result, G_EXPONENT(coefficients));
        }
    else
        {
        second_result = result;
        flags |= NO_DIVIDE;
        if ( flags & SKIP )
            UPDATE_COEF_PTR(coefficients, byte_length);
        }


    if (DENOMINATOR_MASK & flags)
        {
 //printf("DENOMINATOR_MASK !!\n");
       poly_func = ( DENOMINATOR_FLAGS(ALTERNATE_SIGN) & sign ) ?
            __eval_neg_poly : __eval_pos_poly;

        poly_func(
            poly_arg,
            shift,
	    coefficients,
	    degree,
	    second_result);

        if (flags & DENOMINATOR_FLAGS(POST_MULTIPLY))
            MULTIPLY(argument, second_result, second_result);

        UPDATE_COEF_PTR(coefficients, byte_length);
        UX_INCR_EXPONENT(second_result, G_EXPONENT(coefficients));

        if ( flags & SKIP )
            /* Numerator was skipped, we're done */
            return;
        }
    else
        {
        flags |= NO_DIVIDE;
        if ( flags & SKIP )
            UPDATE_COEF_PTR(coefficients, byte_length);
        }

 //printf("fl & NO_DIV = %llx\n", flags & NO_DIVIDE);
 		//printf("result0= (%x %x) %llx %llx\n",result->sign,result->exponent,result->fraction[0],result->fraction[1]);

    if ((flags & NO_DIVIDE) == 0)
        DIVIDE(result, result + 1, FULL_PRECISION, result);
    }


#if 0
U_INT_64 __umulh( U_INT_64 i, U_INT_64 j ) {
    U_INT_64 k;
        {
	U_INT_64 iLo, iHi, jLo, jHi, p0, p1, p2; 
        iLo = __LO(i); iHi = __HI(i);
        jLo = __LO(j); jHi = __HI(j);
	p0  = iLo * jLo;
	p1  = (iLo * jHi);
	p2  = (iHi * jLo) + __HI(p0) + __LO(p1);\
        k   = (iHi * jHi) + __HI(p1) + __HI(p2);
	}
    return k;
}
#endif
