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/* PROLOG END TAG zYx                                              */

#ifdef __SPU__

#ifndef _ACOSD2_H_

#define _ACOSD2_H_      1

#include "simdmath.h"

#include <spu_intrinsics.h>

#include "sqrtd2.h"

#include "divd2.h"

/*

 * FUNCTION

 *      vector double _acosd2(vector double x)

 *

 * DESCRIPTION

 *      Compute the arc cosine of the vector of double precision elements

 *      specified by x, returning the resulting angles in radians. The input

 *      elements are to be in the closed interval [-1, 1]. Values outside

 *      this range result in a invalid operation execption being latched in

 *      the FPSCR register and a NAN is returned.

 *

 *      The basic algorithm computes the arc cosine using PI/2 - asind2(x).

 *      However, as |x| approaches 1, there is a cancellation error in

 *      subtracting asind2(x) from PI/2, so we simplify the evaluation

 *      instead of layering acosd2 on top of asind2.

 *

 *      This yields the basic algorithm of:

 *

 *         absx = (x < 0.0) ? -x : x;

 *

 *         if (absx > 0.5) {

 *           if (x < 0) {

 *             addend = SM_PI;

 *             multiplier = -2.0;

 *           } else {

 *             addend = 0.0;

 *             multiplier = 2.0;

 *           }

 *

 *           x = sqrt(-0.5 * absx + 0.5);

 *         } else {

 *           addend = SM_PI_2;

 *           multiplier = -1.0;

 *         }

 *

 *          x2 = x * x;

 *          x3 = x2 * x;

 *

 *          p = ((((P5 * x2 + P4)*x2 + P3)*x2 + P2)*x2 + P1)*x2 + P0;

 *

 *          q = ((((Q5 * x2 + Q4)*x2 + Q3)*x2 + Q2)*x2 + Q1)*x2 + Q0;;

 *

 *          pq = p / q;

 *

 *          result = (x3*pq + x)*multiplier - addend;

 *

 *      Where P5-P0 and Q5-Q0 are the polynomial coeficients. See asind2

 *      for additional details.

 */

static __inline vector double _acosd2(vector double x)

{

  vec_uint4   x_gt_half, x_eq_half;

  vec_double2 x_neg;                    // input x is negative

  vec_double2 x_abs;                    // absolute value of x

  vec_double2 x_trans;                  // transformed x when |x| > 0.5

  vec_double2 x2, x3;                   // x squared and x cubed, respectively.

  vec_double2 result;

  vec_double2 multiplier, addend;

  vec_double2 p, q, pq;

  vec_double2 half = spu_splats(0.5);

  vec_double2 sign = (vec_double2)spu_splats(0x8000000000000000ULL);

  vec_uchar16 splat_hi = ((vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11});

  // Compute the absolute value of x

  x_abs = spu_andc(x, sign);

  // Perform transformation for the case where |x| > 0.5. We rely on

  // sqrtd2 producing a NAN is |x| > 1.0.

  x_trans = _sqrtd2(spu_nmsub(x_abs, half, half));

  // Determine the correct addend and multiplier.

  x_neg = (vec_double2)spu_rlmaska((vec_int4)spu_shuffle(x, x, splat_hi), -31);

  x_gt_half = spu_cmpgt((vec_uint4)x_abs, (vec_uint4)half);

  x_eq_half = spu_cmpeq((vec_uint4)x_abs, (vec_uint4)half);

  x_gt_half = spu_or(x_gt_half, spu_and(x_eq_half, spu_rlqwbyte(x_gt_half, 4)));

  x_gt_half = spu_shuffle(x_gt_half, x_gt_half, splat_hi);

  addend = spu_sel(spu_splats(SM_PI_2), spu_and(spu_splats(SM_PI), x_neg), (vec_ullong2)x_gt_half);

  multiplier = spu_sel(spu_splats(-1.0), spu_sel(spu_splats(2.0), x, (vec_ullong2)sign), (vec_ullong2)x_gt_half);

  // Select whether to use the x or the transformed x for the polygon evaluation.

  // if |x| > 0.5 use x_trans

  // else         use x

  x = spu_sel(x, x_trans, (vec_ullong2)x_gt_half);

  // Compute the polynomials.

  x2 = spu_mul(x, x);

  x3 = spu_mul(x2, x);

  p = spu_madd(spu_splats(0.004253011369004428248960), x2, spu_splats(-0.6019598008014123785661));

  p = spu_madd(p, x2, spu_splats(5.444622390564711410273));

  p = spu_madd(p, x2, spu_splats(-16.26247967210700244449));

  p = spu_madd(p, x2, spu_splats(19.56261983317594739197));

  p = spu_madd(p, x2, spu_splats(-8.198089802484824371615));

  q = spu_add(x2, spu_splats(-14.74091372988853791896));

  q = spu_madd(q, x2, spu_splats(70.49610280856842141659));

  q = spu_madd(q, x2, spu_splats(-147.1791292232726029859));

  q = spu_madd(q, x2, spu_splats(139.5105614657485689735));

  q = spu_madd(q, x2, spu_splats(-49.18853881490881290097));

  // Compute the rational solution p/q and final multiplication and addend 

  // correction.

  pq = _divd2(p, q);

  result = spu_madd(spu_madd(x3, pq, x), multiplier, addend);

  return (result);

}

#endif /* _ACOSD2_H_ */

#endif /* __SPU__ */