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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__ */