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#define	BASE_NAME	trig
#include "dpml_ux.h"

#if !defined(MAKE_INCLUDE)
#   include STR(BUILD_FILE_NAME)
#endif

/* 
** OVERVIEW
** --------
**
** The implementation of the trig functions is based on four support routines:
** two common evaluation routine (one for sin/cos/sind/cosd and one for
** tan/cot/tand/cotd) together with two argument reduction routines, one for
** radian arguments and one for degree arguments.
** 
** There are various reduction schemes that can be used for trigonometric
** functions.  The polynomial evaluation routines require that the terms in
** the series decrease in magnitude.  For the trig functions, this implies
** that an argument reduction scheme should return a reduce argument with
** magnitude less than or equal to pi/4 is an appropriate choice.  In
** particular, we assume that for a given value, x, the argument reduction
** scheme (for both radian and degrees) produces two integers, I1 and I and an
** unpacked floating point result, z, such that
** 
** 	x = (2*pi)*I1 + I*(pi/2) + z, 	|z| <= pi/4
** 
**		NOTE: having the degree reduction return the reduced
**		argument in radian permits the use of only one set
**		of polynomial coefficient and simplifies the evaluation
**		logic.
**
** The value of I we will refer to as the quadrant bits and z as the reduced
** argument.  We assume also that argument reduction routines returns both I
** and z to its caller.  (I1 is never needed in the subsequent computations,
** so it is not returned.)
** 
** The following table gives an estimate of the number of terms in a polynomial
** and rational approximation for each of the basic trig functions.  For
** rational approximations the degree of the numerator and denominator are
** presented as an ordered pair.  The approximation is assumed to be good to
** 128 bits for |x| <= pi/4.  The values in this table were extrapolated from
** the tables given in Hart et. al.
** 
** 			   approximation form
** 			------------------------
** 	function	polynomial	rational
** 	--------	----------	--------
** 	sin		    12		 (6, 6)
** 	cos		    12		 (6, 6)
** 	tan		    29		 (7, 7)
** 
** So from the above table, it seems most efficient to evaluate sin and cos via
** polynomials and evaluate tangent via a rational approximation.  So we assume
** that for |x| <= pi/4, we have polynomials, S, C, P and Q such that
** 
** 		sin(x) ~ x*S(x^2)
** 		cos(x) ~ C(x^2)
** 		tan(x) ~ x*P(x^2)/Q(x^2)
** 		cot(x) ~ Q(x^2)/*[x*P(x^2)]
** 
** Now, for any argument, x, given its reduced argument, z, and its quadrant
** bits, I, we can evaluate sin, cos, tan and cot of x according to Table 1.
** ( For brevity we denote z*P(z^2) by p, Q(z^2) by q, etc):
** 
** 				   Quadrant bits, I
** 				----------------------------
** 		function	  0	  1	  2	  3
** 		--------	-----	-----	-----	-----
** 		sin		  s	  c	 -s	 -c
** 		cos		  c	 -s	 -c	  s
** 		tan		 p/q	-q/p	 p/q	-q/p
** 		cot		 q/p	-p/q	 q/p	-p/q
** 
** 				   Table 1
** 				   -------
** 
**
** REDUCTION INTERFACE:
** --------------------
** 
** As mentioned earlier, the overall design of the the trig routines is
** dependent on two routines to do argument reduction.  The prototype for 
** these functions is;
** 
** 		WORD
** 		__reduce(
** 		    _UX_FLOAT * unpacked_argument,
** 		    INT_64      octant,
** 		    _UX_FLOAT * reduced_argument
** 		    )
** 
** Assuming that 'unpacked_argument' points to a _UX_FLOAT data item with value
** x, then the semantics of the reduction routines are to compute integers I1
** and I, and a floating point value, z, such that
** 
** 	x + octant*(CYCLE/4) = (2*CYCLE)*I1 + (CYCLE/2) + z,  |z| < CYCLE/4
** 
** Note that performing the reduction on x + octant*(CYCLE/4), rather than x,
** not only allows us to deal with the <name>_vo entry points easily, it also
** permits easy use of the identities cos(x) = sin(x + CYCLE/2) and cot(x) = 
** tan(CYCLE/2) to consolidate the overall processing.
** 
** 
** 
** EVALUATION INTERFACE:
** ---------------------
** 
** The prototypes for each of the two evaluation routines is;
** 
** 	void
** 	__trig_evaluate(
** 	    UX_FLOAT * unpacked_argument,
** 	    WORD       octant,
** 	    U_WORD     function_code,
** 	    UX_FLOAT * unpacked_result
** 	    );
** 
** The evaluation routines need not know whether the evaluation is for degrees
** because the appropriate reduction is done based on the value of
** function_code.
*/ 

#if !defined(UX_RADIAN_REDUCE)
#    define UX_RADIAN_REDUCE		__INTERNAL_NAME(ux_radian_reduce__)
#endif

/*
** The radian reduction code is rather large and has a rather detailed
** explanation.  Consequently, its contained in a separate file and is
** included here.
*/

#if !defined(MAKE_INCLUDE)
#   include "dpml_ux_radian_reduce.c"
#endif

/*
** UX_DEGREE_REDUCE performs argument reduction for degree arguments.  The
** reduction is performed in three phases:
**
**	(1) if |x| >= 2^141, reduce modulo 360 to a value less than 2^141
**	    by operating on the exponent field of x
**	(2) if |x| > 2^15, reduce modulo 360 to a value less that 2^15
**	    by operating on the integer portion of x
**	(3) if |x| < 2^15, compute I = nint(x/90) and the reduced argument
**	    as x - I*90
**
** The details of each of these phases is discussed in more detail in the
** code.
*/

#if !defined(UX_DEGREE_REDUCE)
#    define UX_DEGREE_REDUCE		__INTERNAL_NAME(ux_degree_reduce__)
#endif

static U_WORD
UX_DEGREE_REDUCE( UX_FLOAT * argument, WORD octant, UX_FLOAT * reduced_argument)
    {
    WORD cnt, digit_with_binary_pt, digit_num, w_tmp, quadrant;
    UX_SIGN_TYPE     sign;
    UX_EXPONENT_TYPE exponent, k;
    UX_FRACTION_DIGIT_TYPE current_digit, tmp_digit, sum_digit, borrow;


    sign = G_UX_SIGN(argument);
    exponent = G_UX_EXPONENT(argument);

    if (exponent > (UX_PRECISION + 14))
        {
        /*
        ** This is a very large argument.  We make use of the identity
        **
        **	8*(2^12)^(n+1) = 8*(136)^(n+1)	(mod 360)
        **	               = [8*(136)]*(136)^n
        **	               = (1088)*(136)^n
        **	               = 8*(136)^n	(mod 360)
        **
        ** Or employing induction, 8*(2^12)^n = 8 (mod 360)
        **
        ** If p is the precision of the data type, we begin by writing the
        ** input argument x as:
        **
        **	x = 2^n*f
        **	  = 2^(n-p)*(2^p*f)
        **	  = 2^(n-p)*F
        **
        ** where F = 2^p*f is an integer.  Now let k = floor((n - p - 3)/12)
        ** and r = n - p - 3 - 12*k.  Then
        **
        **	x = 2^(n-p)*F
        **	  = 2^(12k + r + 3)*F
        **	  = 8*2^(12k)]*(2^r*F)
        **	  = [8*(2^12)^k]*(2^r*F)
        **	  = 8*(2^r*F)			(mod 360)
        **	  = 2^(3 + r + p)*f
        **	  = 2^(n - 12*k)*f
        **
        ** So the approach is to find k and subtract 12*k from the exponent
        ** field.  This will reduce the input argument to a number less than
        ** 2^(p + 14)
        **
        ** One last note.  We don't actually do an integer divide to get
        ** k.  Rather we multiply n by an integer that is effectively the 
        ** reciprocal of 12.  This is easier to do if the exponent field
        ** is positive so we want to add a bias to the exponent that is
        ** divisible by 12 and that will force the exponent to be positive.
        ** We assume at this point that |exponent| < (1 << F_EXP_WIDTH).
        **
        ** Let the bias = 12*B, then
        **
        **		k = floor((n - p - 3)/12)
        **		  = floor((n - p - 3 + 12*B - 12*B)/12)
        **		  = floor((n - p - 3 + 12*B)/12 - B)
        **		  = floor((n - p - 3 + 12*B)/12) - B
        **		  = floor((n + (12*B - p - 3))/12) - B
        ** 
        ** 	==> n - 12*k = n - 12*[floor((n + (12*B - p - 3))/12) - B]
        ** 	             = n - 12*floor((n + (12*B - p - 3))/12) - 12*B
        */

#       define BIAS	(12*(((1 << F_EXP_WIDTH) + 11)/12))

        exponent += (BIAS - UX_PRECISION - 3);
        UMULH((UX_FRACTION_DIGIT_TYPE) exponent, RECIP_TWELVE, k);
        exponent = (exponent + (UX_PRECISION + 3)) - 12*k;
        P_UX_EXPONENT(argument, exponent);
        }

    if (exponent >= 16)
        {
        /*
        ** For a medium arguments, 2^15 < |x| < 2^142, we consider the fraction
        ** field of x as a sequence of digit.  The digits that are comprised
        ** entirely of "integer" bits are reduced modulo 360 using the 
        ** identity 8*2^12 = 8 (mod 360).
        **
        ** Begin by writing |x| = 2^n*f, with f in the interval [1/2, 1) and
        ** define s = (n - 15) % k, where k is the number of bits per fraction
        ** digit.  If there are 4 digits per UX_FLOAT, then the following
        ** diagram indicates the relationship between n, s and the binary point
        ** of x:
        **
        **                  |<---------- n - 15 -------->| 15 |<--
        **	            +-----------+-----------+-----------+-----------+
        **             f :  |     F1    |     F2    |    F3     |    F4     | 
        **	            +-----------+-----------+-----------+-----------+
        **	                                 -->|  s |<-- ^
        **                                                 binary pt
        **
        ** Suppose we now shift the bits of f, s bits to the left to get f'.
        ** Then the diagram would look like
        **
        **	                                 -->| 15 |<--
        **	+-----------+-----------+-----------+-----------+-----------+
        **  f': |     F0'   |     F1'   |     F2'   |     F3'   |    F4'    | 
        **	+-----------+-----------+-----------+-----------+-----------+
        **	                                         ^
        **                                            binary pt
        **
        ** and if we denote the number of digits per UX_FLOAT by N, then
        **
        **	x = 2^(n-s)*(F0' + F1'/K + F2'/K^2 + ... + F4'/K^N)
        **
        ** Now n - 15 - s is multiple of k, i.e. n - s = j*k + 15, so that
        ** 2^(n-s) = 2^(j*k+15) = 2^15*K^j and
        **
        **	x = 2^(n-s)*(F0' + F1'/K + F2'/K^2 + ... + FN'/K^N)
        **	  = 2^15*(K^j)*(F0' + F1'/K + F2'/K^2 + .... + FN'/K^N)
        **	  = 2^15*[F0'*K^j + F1'*K^(j-1) + ... + FN'/K^(j-N)]
        **	  = 2^15*A + 2^15*b
        **
        **	A = F0'*K^j + F1'*K^(j-1) + ... + Fj
        **	b = Fj+1'/K + ... + FN'/K^(N-j)
        **
        ** If we denote B = trunc(2^12*b) as B and b' = 2^15*b - 2^3*B, then
        **
        **	x = 2^15*A + 2^15*b
        **	  = 2^15*A + 2^3*B + b'
        **	  = 2^15*A + 2^3*B + b'
        **        = 8*(2^12*A + B) + b'
        **	  = 8*C + b'
        **
        ** Now let C_lo be the low 12 bits of C and C_hi be the remaining
        ** bits, then
        **
        **	8*C = 8*(C_lo + 2^12*C_hi)
        **	    = 8*(C_lo + 136*C_hi)	(mod 360)
        **	    = 8*C_lo + 8*136*C_hi)
        **	    = 8*C_lo + 8*C_hi)		(mod 360)
        **	    = 8*(C_lo + C_hi)
        **
        ** Thus we effectively reduced the value of 8*C by (almost) 12 bits
        ** modulo 360.  Obviously, we can iterate on this process until until
        ** we produce a value C' which is less that 2^12 and 8*C' = 8*C modulo
        ** 360.  In order to increase performance (and simplify the
        ** implementation) the actual code below doesn't do the reduction 12
        ** bits at a time initially.  Rather it first does the reduction 24 or
        ** 60 bits bits at a time (depending on the digit size), and then does
        ** 12 bit reduction on that result.
        **
        **	NOTE: In order to avoid copying the input argument to
        **	a work buffer and to simplify the logic, the follow code
        **	overlays the sign and exponent field of a UX_FLOAT type
        **	with an "extra" digit.
        */

#       if BITS_PER_UX_FRACTION_DIGIT_TYPE > (BITS_PER_UX_EXPONENT_TYPE + \
           BITS_PER_UX_SIGN_TYPE)
#           error "Need work buffer for this UX_FLOAT struct"
#       endif

        digit_with_binary_pt = exponent - 15;
        cnt = digit_with_binary_pt & (BITS_PER_UX_FRACTION_DIGIT_TYPE - 1);
        digit_with_binary_pt >>= __LOG2(BITS_PER_UX_FRACTION_DIGIT_TYPE);
        tmp_digit = 0;
        exponent -= cnt;

        if (cnt)
            { /* shift digit right (in memory) */
            w_tmp = BITS_PER_UX_FRACTION_DIGIT_TYPE - cnt;

            current_digit = G_UX_LSD(argument);
            P_UX_LSD(argument, current_digit << cnt);

#           if NUM_UX_FRACTION_DIGITS == 4

                tmp_digit = G_UX_FRACTION_DIGIT(argument, 2);
                P_UX_FRACTION_DIGIT(argument, 2,
                        (tmp_digit << cnt) | ( current_digit >> w_tmp));

                current_digit = G_UX_FRACTION_DIGIT(argument, 1);
                P_UX_FRACTION_DIGIT(argument, 1,
                        (current_digit << cnt) | ( tmpt_digit >> w_tmp));

#           endif

            tmp_digit = G_UX_MSD(argument);
            P_UX_MSD(argument,
                (tmp_digit << cnt) | ( current_digit >> w_tmp));
            tmp_digit >>= w_tmp;
            }
     /*   P_UX_FRACTION_DIGIT(argument, -1, tmp_digit); */
        /*
        ** Because of the compiler warning we are replacing the above
        ** line in the source.
        */

            *(&(((UX_FLOAT*)(argument))->fraction[0])-1) = tmp_digit;

        /*
        ** Extract B from the digit that contains the binary point
        */

        sum_digit = G_UX_FRACTION_DIGIT(argument, digit_with_binary_pt) >>
                      (BITS_PER_UX_FRACTION_DIGIT_TYPE - 12);

        /*
        ** Loop through the remaining integer digits and add them to B
        */

#       define MOD_360_BITS_PER_DIGIT (12*(BITS_PER_UX_FRACTION_DIGIT_TYPE/12))
#       define MOD_360_DIGIT_MASK     MAKE_MASK(MOD_360_BITS_PER_DIGIT, 0)

        digit_num = digit_with_binary_pt;
        cnt = 0;
        while (digit_num >= 0)
            {
            current_digit = G_UX_FRACTION_DIGIT(argument, --digit_num);
            P_UX_FRACTION_DIGIT(argument, digit_num, 0);
            if (cnt)
                {
                sum_digit += ((current_digit << cnt) & 0xfff);
                w_tmp = 12 - cnt;
                current_digit >>= w_tmp;
                cnt = -w_tmp;
                }

            sum_digit = (sum_digit + (current_digit & MOD_360_DIGIT_MASK))
                         + (current_digit >> MOD_360_BITS_PER_DIGIT);
            cnt += (BITS_PER_UX_FRACTION_DIGIT_TYPE - MOD_360_BITS_PER_DIGIT);
            }

        /*
        ** For 64 bit digits, at this point sum_digit can have five 12 bit
        ** "digits" plus a carry "digit" for a total of six.  So it is
        ** more efficient to compress sum_digit 24 bits at a time rather than
        ** 12 bits at a time.
        */

#       if (BITS_PER_UX_FRACTION_DIGIT_TYPE == 64)

            sum_digit = (sum_digit & 0xffffff) + ((sum_digit >> 24) & 0xffffff)
                          + ((sum_digit >> 48) & 0xffffff);

#       endif

        /*
        ** At this point sum_digit may contain two 12 bit "digits" plus a
        ** carry "digit".  So we recurse (at most twice) to reduce it to 12
        ** bits modulo 360.
        */

        while ((tmp_digit = (sum_digit >> 12)))
            sum_digit = (sum_digit & 0xfff) + tmp_digit;

        /*
        ** Now put the reduced integer into the original fraction field,
        ** normalize the result, and calculate the exponent value.
        */

        current_digit = G_UX_FRACTION_DIGIT(argument, digit_with_binary_pt);
        current_digit &= MAKE_MASK(BITS_PER_UX_FRACTION_DIGIT_TYPE - 12, 0);
        current_digit |= (sum_digit << (BITS_PER_UX_FRACTION_DIGIT_TYPE - 12));
        P_UX_FRACTION_DIGIT(argument, digit_with_binary_pt, current_digit);
        P_UX_EXPONENT(argument, exponent);

        exponent -= NORMALIZE(argument);
        }


    /*
    ** At this point |x| < 2^15 so that if I = nint(x/90), I < 2^9 and 
    ** I*90 requires at most 15 significant bits.  This means that we
    ** can reduce x by working only with its most significant digit.
    **
    ** Let F be the high k bits of the fraction of x, where k is the number
    ** of bits per fraction digit and K = 2^k.  Further, let R an k-1 bit
    ** integer such that 1/90 ~ R/(32*K).  (I.e. R is the high bits of 1/90
    ** unnormalized by one bit.)  We can now write x = 2^n*(F + e)/K and 
    ** 1/90 = (R + d)/(32*K), where |e| < 1 and |d| < 1/2.  Consequently
    ** we have:
    **
    **		x/90 = (2^n*f)*(1/90)
    **		     = 2^n*[(F + e)/K]*[(R + d)/(32*K)]
    **		     = 2^(n-5)*(F*R + e*R + d*F + e*d)/K^2
    **		     = 2^(n-5)*(K*hi(F*R) + lo(F*R) + e*R + d*F + e*d)/K^2
    **
    ** Now K*hi(F*R) > K^2/8 and | lo(F*R) + e*R + d*F + e*d | < 2K and
    ** so the relative error in neglecting lo(F*R) + e*R + d*F + e*d is less
    ** that one part in 2^(k-4).  Since k is at least 32, the relative error
    ** is very small.  We have then
    **
    **		x/90 = 2^(n-5)*[K*hi(F*R) + lo(F*R) + e*R + d*F + e*d]/K^2
    **		     ~ 2^(n-5)*hi(F*R)/K
    */

    w_tmp = exponent - 5;
    P_UX_SIGN(argument, 0);
    current_digit = G_UX_MSD(argument);

    if (w_tmp > 0)
        { UMULH( current_digit, MSD_OF_RECIP_90, tmp_digit); }
    else
        { /* I = 0 */
        w_tmp = 1;
        tmp_digit = 0;
        }

    /* I ~ x/90, "add in octant" and round to nearest integer */

    cnt = BITS_PER_UX_FRACTION_DIGIT_TYPE - w_tmp;
    tmp_digit = (tmp_digit + ((octant & 1) << (cnt - 1)) +
                        SET_BIT(cnt - 1)) & ~MAKE_MASK(cnt, 0);

    /* Get quadrant bits and adjust for sign of the argument */

    quadrant = (tmp_digit >> cnt);
    quadrant = (sign) ? -quadrant : quadrant;
    quadrant += (octant >> 1);

    /* now subtract I*90 from x */

#   define MSD_OF_NINETY	(((UX_FRACTION_DIGIT_TYPE) 45) << \
				(BITS_PER_UX_FRACTION_DIGIT_TYPE - 6))

    UMULH(tmp_digit, MSD_OF_NINETY, tmp_digit);
    tmp_digit = (current_digit >> 2) - tmp_digit;
    current_digit = (current_digit & 3) | (4*tmp_digit);
    if (((UX_SIGNED_FRACTION_DIGIT_TYPE) tmp_digit) < 0)
        {
        sign ^= UX_SIGN_BIT;

        sum_digit = G_UX_LSD(argument);
        tmp_digit = -sum_digit;
        borrow = (sum_digit != 0);
        P_UX_LSD(argument, tmp_digit);

#       if ( NUM_UX_FRACTION_DIGITS == 4)

            sum_digit = G_UX_FRACTION_DIGIT(argument, 2);
            tmp_digit = - (sum_digit + borrow);
            borrow = (sum_digit != 0) | borrow;
            P_UX_FRACTION_DIGIT(argument, 2, tmp_digit);

            sum_digit = G_UX_FRACTION_DIGIT(argument, 1);
            tmp_digit = - (sum_digit + borrow);
            borrow = (sum_digit != 0) | borrow;
            P_UX_FRACTION_DIGIT(argument, 1, tmp_digit);

#       endif

        current_digit = - (current_digit + borrow);
        }
    P_UX_MSD(argument, current_digit);
    NORMALIZE(argument);

    /* Last by not least, convert to radians */

    MULTIPLY(argument, UX_PI_OVER_180, reduced_argument);
    UX_TOGGLE_SIGN(reduced_argument, sign);

    return quadrant;
    }

/*
** UX_SINCOS is the common evaluation routine for all of the sin/cos and
** sind/cosd entry points.  UX_SINCOS invokes the appropriate reduction
** routine (radian or degrees) and then performs 1 or 2 polynomial evaluation
** on the reduced argument to get the result (or results, for sincos and
** sincosd)
*/

#define ODD_POLY_FLAGS		SQUARE_TERM | ALTERNATE_SIGN | POST_MULTIPLY
#define EVEN_POLY_FLAGS		SQUARE_TERM | ALTERNATE_SIGN

#define SIN_POLY_FLAGS		NUMERATOR_FLAGS( ODD_POLY_FLAGS )
#define COS_POLY_FLAGS		DENOMINATOR_FLAGS( EVEN_POLY_FLAGS )

WORD
UX_SINCOS(
  UX_FLOAT * unpacked_argument,
  WORD       octant,
  WORD       function_code,
  UX_FLOAT * unpacked_result)
    {
    WORD quadrant, poly_type;
    UX_FLOAT reduced_argument;
    U_WORD (* reduce)( UX_FLOAT *, WORD, UX_FLOAT *);

    /* Get the quadrant bits and the reduced argument */

    reduce = (function_code & DEGREE) ? UX_DEGREE_REDUCE : UX_RADIAN_REDUCE;
    quadrant = reduce( unpacked_argument, octant, &reduced_argument );
    function_code &= ~DEGREE;

    /*
    ** Select the polynomial coefficients and the form of the 
    ** polynomial based on the quadrant the reduced argument
    ** lies in.  NOTE: the difference between the sin and cos
    ** has been accounted for in the value of octant.
    */

    if ( SINCOS_FUNC == function_code )
        {
        poly_type = SIN_POLY_FLAGS | COS_POLY_FLAGS | NO_DIVIDE;

        /* Adjust location of sin/cos polynomials */
        poly_type |= ( (quadrant & 1) ? SWAP : NULL );
        }
    else if (quadrant & 1)
        /* We need to evaluate C(x^2) */
        poly_type = SKIP | COS_POLY_FLAGS;
    else 
        /* We need to evaluate x*S(x^2) */
        poly_type = SKIP | SIN_POLY_FLAGS;

    /*
    ** Evaluate the polynomial and set the sign based on the quadrant
    */

    EVALUATE_RATIONAL(
        &reduced_argument,
        SINCOS_COEF_ARRAY,
        SINCOS_COEF_ARRAY_DEGREE,
        poly_type,
        unpacked_result);

    if (quadrant & 2)
        UX_TOGGLE_SIGN(&unpacked_result[0], UX_SIGN_BIT);

    /*
    ** If this is a sincos entry point, set the sign on the second
    ** result
    */

    if ((SINCOS_FUNC == function_code) && ((quadrant + 1) & 2))
        UX_TOGGLE_SIGN(&unpacked_result[1], UX_SIGN_BIT);
  
    return 0; /* No error conditions for sin/cos */
    }


/*
** UX_TANCOT is the common evaluation routine fo tan, cot, tand and cotd.
** UX_TANCOT invokes the appropriate reduction routine (radian or degrees) and
** then computes tan or cot as the ratio of two polynomials
**
** An important difference between UX_TANCOT and UX_SINCOS is that for the
** tand/cotd routines, the reduced argument may be zero.  Depending on the
** quadrant bits, the correct result would then be either 0 or +/- Inf.   The
** common tan/cot evaluation routine detects the +/- Inf case and returns an
** unpacked result with its exponent field set to a large positive value,
** denoted by UX_INFINITY_EXPONENT.
*/

#if !defined(UX_TANCOT)
#   define UX_TANCOT		__INTERNAL_NAME(ux_tancot__)
#endif

static WORD
UX_TANCOT(
  UX_FLOAT * unpacked_argument,
  WORD       octant,
  WORD       function_code,
  UX_FLOAT * unpacked_result)
    {
    WORD quadrant, div_flag;
    UX_FLOAT reduced_argument;
    U_WORD (* reduce)(UX_FLOAT *, WORD, UX_FLOAT *);

    /*
    ** Get the quadrant bits and the reduced argument, check for
    ** zero and process accordingly.
    */

    reduce = (function_code & DEGREE) ? UX_DEGREE_REDUCE : UX_RADIAN_REDUCE;
    quadrant = reduce( unpacked_argument, octant, &reduced_argument );
    div_flag = ((quadrant + (function_code >> 3)) & 1) ? SWAP : 0;

    if (0 == G_UX_MSD(&reduced_argument))
        { /* reduced argument is zero */
        UX_SET_SIGN_EXP_MSD(unpacked_result, 0, UX_ZERO_EXPONENT, 0);
	if ( div_flag /* == SWAP */ )
            {
            P_UX_EXPONENT(unpacked_result, UX_INFINITY_EXPONENT);
            P_UX_MSD(unpacked_result, UX_MSB);
            }
        return (function_code & TAN_FUNC) ?
           TAND_ODD_MULTIPLE_OF_90 : COTD_MULTIPLE_OF_180;
        }

    /*
    ** Evaluate z*P(z^2) and and Q(z^2) and perform the appropriate
    ** division.  Set the sign bit according to the quadrant.
    */

    EVALUATE_RATIONAL(
        &reduced_argument,
        TANCOT_COEF_ARRAY,
        TANCOT_COEF_ARRAY_DEGREE,
        NUMERATOR_FLAGS( SQUARE_TERM | ALTERNATE_SIGN | POST_MULTIPLY) |
          DENOMINATOR_FLAGS( SQUARE_TERM | ALTERNATE_SIGN) | div_flag,
        unpacked_result);

    if (quadrant & 1)
        UX_TOGGLE_SIGN(unpacked_result, UX_SIGN_BIT);

    return G_UX_SIGN(unpacked_result) ? COTD_NEG_OVERFLOW : COTD_POS_OVERFLOW;
    }

/*
** Each of the of trig routines call a common routine C_UX_TRIG, to unpack the
** input argument and then dispatch the result to UX_SINCOS or UX_TANCOT
** evaluation routine. For sincos and sincosd entry points, if the return
** value is written by the unpack routine, the common routine must take care
** to write the second result.
*/

#if !defined(C_UX_TRIG)
#   define C_UX_TRIG		__INTERNAL_NAME(C_ux_trig__)
#endif

#define F_C_NAN_OR_INF_MASK	(SET_BIT(F_C_INF) | SET_BIT(F_C_NAN))

static void
C_UX_TRIG(
  _X_FLOAT * packed_argument,
  WORD octant,
  WORD function_code,
  U_WORD const * class_to_action_map,
  WORD underflow_error,
  _X_FLOAT * packed_result
  OPT_EXCEPTION_INFO_DECLARATION )
    {
    _X_FLOAT *second_value;
    WORD fp_class, overflow_error;
    UX_FLOAT unpacked_result[3], unpacked_argument;
    WORD (* trig_eval)( UX_FLOAT *, WORD, WORD, UX_FLOAT *);

    trig_eval = (SINCOS_FUNC & function_code) ? UX_SINCOS : UX_TANCOT;

    fp_class = UNPACK(
        packed_argument,
        &unpacked_argument,
        class_to_action_map,
        packed_result
        OPT_EXCEPTION_INFO_ARGUMENT );

   if (0 > fp_class)
        { /* If this is a SINCOS evaluation, write second result */

        if (SINCOS_FUNC == (function_code & ~DEGREE))
            {
            second_value =
                ((1 << F_C_BASE_CLASS(fp_class)) & F_C_NAN_OR_INF_MASK) ?
                &packed_result[0] : (_X_FLOAT *) _X_ONE;
            _X_COPY(second_value, &packed_result[1]);
            }
        return;
        }

    overflow_error = trig_eval(
        &unpacked_argument,
        octant,
	function_code,
        unpacked_result);

    PACK(
        unpacked_result,
        packed_result,
        underflow_error,
        overflow_error
        OPT_EXCEPTION_INFO_ARGUMENT );

    if (SINCOS_FUNC == (function_code & ~DEGREE))
        { /* pack second result for sincos evaluations */
        PACK(
            unpacked_result + 1,
            packed_result + 1,
            NOT_USED,
            NOT_USED
            OPT_EXCEPTION_INFO_ARGUMENT );
        }
    }

/*
** The following 6 entry points implement the user level x-float sin/cos and
** sind/cosd functions
*/

#define TRIG_ENTRY(oct, code, map, under)				 \
        X_X_PROTO(F_ENTRY_NAME, packed_result, packed_argument)          \
	    {								 \
	    EXCEPTION_INFO_DECL				                 \
            DECLARE_X_FLOAT(packed_result)                               \
									 \
	    INIT_EXCEPTION_INFO;					 \
	    C_UX_TRIG(							 \
            PASS_ARG_X_FLOAT(packed_argument),               \
	        oct, code, map, under,					 \
            PASS_RET_X_FLOAT(packed_result)              \
	        OPT_EXCEPTION_INFO);					 \
            RETURN_X_FLOAT(packed_result);                               \
	    }

#
#define TRIG_ENTRY_RR(oct, code, map, under)                 \
        RR_X_PROTO(F_ENTRY_NAME, packed_result1, packed_result2, packed_argument)          \
        {                                \
        EXCEPTION_INFO_DECL                              \
        _X_FLOAT packed_result[2];                               \
                                     \
        INIT_EXCEPTION_INFO;                     \
        C_UX_TRIG(                           \
            PASS_ARG_X_FLOAT(packed_argument),               \
            oct, code, map, under,                   \
            packed_result /*PASS_RET_X_FLOAT(packed_result)*/                \
            OPT_EXCEPTION_INFO);                     \
        *packed_result1 = packed_result[0];                              \
        *packed_result2 = packed_result[1];                              \
        }


#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_SIN_NAME
	TRIG_ENTRY(0, SIN_FUNC, SIN_CLASS_TO_ACTION_MAP, NOT_USED)

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_COS_NAME
	TRIG_ENTRY(2, COS_FUNC, COS_CLASS_TO_ACTION_MAP, NOT_USED)

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_SINCOS_NAME
    TRIG_ENTRY_RR(0, SINCOS_FUNC, SINCOS_CLASS_TO_ACTION_MAP, NOT_USED)


#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_SIND_NAME
	TRIG_ENTRY(0, SIND_FUNC, SIND_CLASS_TO_ACTION_MAP, SIND_UNDERFLOW)

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_COSD_NAME
	TRIG_ENTRY(2, COSD_FUNC, COSD_CLASS_TO_ACTION_MAP, NOT_USED)

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_SINCOSD_NAME
    TRIG_ENTRY_RR(0, SINCOSD_FUNC, SINCOSD_CLASS_TO_ACTION_MAP, SIND_UNDERFLOW)


/*
** The following 4 entry points implement the user level x-float tan/cot and
** tand/cotd functions
*/

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_TAN_NAME
	TRIG_ENTRY(0, TAN_FUNC, TAN_CLASS_TO_ACTION_MAP, NOT_USED)

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_COT_NAME
	TRIG_ENTRY(0, COT_FUNC, COT_CLASS_TO_ACTION_MAP, NOT_USED)

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_TAND_NAME
	TRIG_ENTRY(0, TAND_FUNC, TAND_CLASS_TO_ACTION_MAP, TAND_UNDERFLOW)

#undef  F_ENTRY_NAME
#define F_ENTRY_NAME F_COTD_NAME
	TRIG_ENTRY(0, COTD_FUNC, COTD_CLASS_TO_ACTION_MAP, NOT_USED)


#if defined(MAKE_INCLUDE)

    @divert -append divertText

    precision = ceil(UX_PRECISION/8) + 4;

#   undef TABLE_NAME

    START_TABLE;

    TABLE_COMMENT("sin class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "SIN_CLASS_TO_ACTION_MAP\t");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(6) +
	      CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     2) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     2) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     0) );

    TABLE_COMMENT("cos class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "COS_CLASS_TO_ACTION_MAP\t");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(5) +
	      CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     3) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     3) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_VALUE,     1) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_VALUE,     1) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     1) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     1) );

    TABLE_COMMENT("sincos class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "SINCOS_CLASS_TO_ACTION_MAP");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(4) +
              CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     4) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     4) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     0) );

    TABLE_COMMENT("sind class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "SIND_CLASS_TO_ACTION_MAP");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(3) +
	      CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     5) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     5) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_UNPACKED,  0) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_UNPACKED,  0) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     0) );

    TABLE_COMMENT("cosd class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "COSD_CLASS_TO_ACTION_MAP");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(2) +
	      CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     6) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     6) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_VALUE,     1) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_VALUE,     1) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     1) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     1) );

    TABLE_COMMENT("sincosd class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "SINCOSD_CLASS_TO_ACTION_MAP");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(1) +
              CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     7) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     7) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_UNPACKED,  0) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_UNPACKED,  0) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     0) );

    TABLE_COMMENT("Data for the above mappings");

        PRINT_U_TBL_ITEM( /* data 1 */                 ONE);
        PRINT_U_TBL_ITEM( /* data 2 */     SIN_OF_INFINITY);
        PRINT_U_TBL_ITEM( /* data 3 */     COS_OF_INFINITY);
        PRINT_U_TBL_ITEM( /* data 4 */  SINCOS_OF_INFINITY);
        PRINT_U_TBL_ITEM( /* data 5 */    SIND_OF_INFINITY);
        PRINT_U_TBL_ITEM( /* data 6 */    COSD_OF_INFINITY);
        PRINT_U_TBL_ITEM( /* data 7 */ SINCOSD_OF_INFINITY);

    TABLE_COMMENT("tan class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "TAN_CLASS_TO_ACTION_MAP\t");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(1) +
              CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     0) );
        PRINT_U_TBL_ITEM( /* data 1 */ TAN_OF_INFINITY);

    TABLE_COMMENT("tand class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "TAND_CLASS_TO_ACTION_MAP");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(1) +
              CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_VALUE,     0) );
        PRINT_U_TBL_ITEM( /* data 1 */ TAND_OF_INFINITY);


    TABLE_COMMENT("cot class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "COT_CLASS_TO_ACTION_MAP\t");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(1) +
              CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_UNPACKED,  0) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_UNPACKED,  0) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_ERROR,     2) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_ERROR,     3) );
        PRINT_U_TBL_ITEM( /* data 1 */ COT_OF_INFINITY);
        PRINT_U_TBL_ITEM( /* data 2 */     COT_OF_ZERO);
        PRINT_U_TBL_ITEM( /* data 3 */ COT_OF_NEG_ZERO);

    TABLE_COMMENT("cotd class-to-action-mapping");
    PRINT_CLASS_TO_ACTION_TBL_DEF( "COTD_CLASS_TO_ACTION_MAP");
    PRINT_64_TBL_ITEM( CLASS_TO_ACTION_DISP(1) +
              CLASS_TO_ACTION( F_C_SIG_NAN,    RETURN_QUIET_NAN, 0) +
              CLASS_TO_ACTION( F_C_QUIET_NAN,  RETURN_VALUE,     0) +
              CLASS_TO_ACTION( F_C_POS_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_NEG_INF,    RETURN_ERROR,     1) +
              CLASS_TO_ACTION( F_C_POS_DENORM, RETURN_ERROR,     2) +
              CLASS_TO_ACTION( F_C_NEG_DENORM, RETURN_ERROR,     3) +
              CLASS_TO_ACTION( F_C_POS_ZERO,   RETURN_ERROR,     4) +
              CLASS_TO_ACTION( F_C_NEG_ZERO ,  RETURN_ERROR,     5) );
        PRINT_U_TBL_ITEM( /* data 1 */  COTD_OF_INFINITY);
        PRINT_U_TBL_ITEM( /* data 2 */ COTD_POS_OVERFLOW);
        PRINT_U_TBL_ITEM( /* data 3 */ COTD_NEG_OVERFLOW);
        PRINT_U_TBL_ITEM( /* data 4 */      COTD_OF_ZERO);
        PRINT_U_TBL_ITEM( /* data 5 */  COTD_OF_NEG_ZERO);

    TABLE_COMMENT("Unpacked constants pi/180");
    PRINT_UX_TBL_ADEF_ITEM( "UX_PI_OVER_180\t\t",  pi/180);

    TABLE_COMMENT("Packed constants 1");
    PRINT_F_TBL_ADEF_ITEM( "_X_ONE\t\t\t",  1);

    /*
    ** Now we compute the "high" digit of 1/90 and 1/12.  For 1/12, we would
    ** to compute and integer R, such that trunc(E/12) = UMULH(R*E).  We
    ** state without proof here that if the number of bits per digit is
    ** 2*k + d, where d = 0 or 1, then N = 2^(2*k+d) + 2^(3-d) is divisible
    ** by 12 and taking R = N/12 gives the appropriate result.
    */

    PRINT_UX_FRACTION_DIGIT_TBL_VDEF_ITEM( "MSD_OF_RECIP_90\t\t", 
        nint(bldexp(1/90, BITS_PER_UX_FRACTION_DIGIT_TYPE + 5)));

    PRINT_UX_FRACTION_DIGIT_TBL_VDEF_ITEM( "RECIP_TWELVE\t\t", 
        ceil(bldexp(1/12, BITS_PER_UX_FRACTION_DIGIT_TYPE)));

    /*
    ** Now generate coefficients for computing sin.
    */

    function __sin(x)
        {
        if (x == 0)
            return 1;
        else
            return sin(x)/x;
        }

    save_precision = precision;
    precision = ceil(UX_PRECISION/8) + 8;

    max_arg = pi/4;

    remes(REMES_FIND_POLYNOMIAL + REMES_RELATIVE_WEIGHT + REMES_SQUARE_ARG,
           0, max_arg, __sin, UX_PRECISION, &sin_degree, &ux_rational_coefs);

    /*
    ** Now generate coefficients for computing cos and add them to the
    ** ux_rational coefficient array so that they can be accessed by the
    ** rational evaluation routine.
    */

    function __cos(x) { return cos(x); }

    remes(REMES_FIND_POLYNOMIAL + REMES_RELATIVE_WEIGHT + REMES_SQUARE_ARG,
           0, max_arg, __cos, UX_PRECISION, &cos_degree, &dummy_coefs);

    precision = save_precision;

    k = sin_degree + 1;
    for (i = 0; i <= cos_degree; i++)
        ux_rational_coefs[k++] = dummy_coefs[i];

    TABLE_COMMENT("Fixed point coefficients for sin and cos evaluation");
    PRINT_FIXED_128_TBL_ADEF("SINCOS_COEF_ARRAY\t");
    degree = print_ux_rational_coefs(sin_degree, cos_degree, 0);
    PRINT_WORD_DEF("SINCOS_COEF_ARRAY_DEGREE", degree );

    /*
    ** Last but not least, get the rational coefficients for tan/cot
    */

    function __tan(x)
        {
        if (x == 0)
            return 1;
        else
            return tan(x)/x;
        }

    save_precision = precision;
    precision = ceil(UX_PRECISION/8) + 8;

    max_arg = pi/4;

    remes(REMES_FIND_RATIONAL + REMES_RELATIVE_WEIGHT + REMES_SQUARE_ARG,
        0, max_arg, __tan, UX_PRECISION, &num_degree, &den_degree,
        &ux_rational_coefs);

    precision = save_precision;

    TABLE_COMMENT("Fixed point coefficients for tan and cot evaluation");
    PRINT_FIXED_128_TBL_ADEF("TANCOT_COEF_ARRAY\t");
    degree = print_ux_rational_coefs(num_degree, den_degree, 0);
    PRINT_WORD_DEF("TANCOT_COEF_ARRAY_DEGREE", degree );

    TABLE_COMMENT("Unpacked value of pi/4");
    PRINT_UX_TBL_ADEF_ITEM( "UX_PI_OVER_FOUR", pi/4);

    END_TABLE;

    @end_divert
    @eval my $tableText;						\
          my $outText    = MphocEval( GetStream( "divertText" ) );	\
          my $defineText = Egrep( "#define", $outText, \$tableText );	\
             $outText    = "$tableText\n\n$defineText";			\
          my $headerText = GetHeaderText( STR(BUILD_FILE_NAME),         \
                           "Definitions and constants trigonometric " .	\
                              "routines", __FILE__ );			\
             print "$headerText\n\n$outText\n";
#endif

