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/* PROLOG END TAG zYx                                              */

#ifdef __SPU__

#ifndef _EXPD2_H_

#define _EXPD2_H_       1

#include <spu_intrinsics.h>

#include "floord2.h"

#define LOG2E 1.4426950408889634073599     // 1/log(2) 

/*

 * FUNCTION

 *      vector double _expd2(vector double x)

 *

 * DESCRIPTION

 *      _expd2 computes e raised to the input x for

 *      each of the element of the double word vector.

 *

 * Calculation is performed by reducing the input argument

 * to within a managable range, and then computing the power

 * series to the 11th degree.

 *

 * Range reduction is performed using the property:

 *

 *      exp(x) = 2^n * exp(r)

 *

 * Values for "n" and "r" are determined such that:

 *

 *       x = n * ln(2) + r, |r| <= ln(2)/2

 *

 *       n = floor(  (x/ln(2)) + 1/2  )

 *       r = x - (n * ln(2))

 *

 * To enhance the precision for "r", computation is performed

 * using a two part representation of ln(2).

 *

 * Once the input is reduced, the power series is computed:

 *

 *                    __12_

 *                    \

 *       exp(x) = 1 +  \   (x^i)/i!

 *                     /

 *                    /____

 *                     i=2

 *

 * The resulting value is scaled by 2^n and returned.

 *

 */

static __inline vector double _expd2(vector double x)

{

  //  log(2) in extended machine representable precision

  vec_double2 ln2_hi = spu_splats(6.9314575195312500E-1);  // 3FE62E4000000000

  vec_double2 ln2_lo = spu_splats(1.4286068203094172E-6);  // 3EB7F7D1CF79ABCA

  //  coefficients for the power series

  // vec_double2 f01 = spu_splats(1.00000000000000000000E0);  // 1/(1!)

  vec_double2 f02 = spu_splats(5.00000000000000000000E-1); // 1/(2!)

  vec_double2 f03 = spu_splats(1.66666666666666666667E-1); // 1/(3!)

  vec_double2 f04 = spu_splats(4.16666666666666666667E-2); // 1/(4!)

  vec_double2 f05 = spu_splats(8.33333333333333333333E-3); // 1/(5!)

  vec_double2 f06 = spu_splats(1.38888888888888888889E-3); // 1/(6!)

  vec_double2 f07 = spu_splats(1.98412698412698412698E-4); // 1/(7!)

  vec_double2 f08 = spu_splats(2.48015873015873015873E-5); // 1/(8!)

  vec_double2 f09 = spu_splats(2.75573192239858906526E-6); // 1/(9!)

  vec_double2 f10 = spu_splats(2.75573192239858906526E-7); // 1/(10!)

  vec_double2 f11 = spu_splats(2.50521083854417187751E-8); // 1/(11!)

  vec_double2 f12 = spu_splats(2.08767569878680989792E-9); // 1/(12!)

  //  rx = floor(1/2 + x/log(2))  

  vec_double2 rx = _floord2(spu_madd(x,spu_splats(LOG2E),spu_splats(0.5)));

  // extract the exponent of reduction

  vec_int4 exp = spu_convts(spu_roundtf(rx),0);

  // reduce the input to within [ -ln(2)/2 ... ln(2)/2 ]

  vec_double2 r;

  r = spu_nmsub(rx,ln2_hi,x);

  r = spu_nmsub(rx,ln2_lo,r);

  vec_double2 result;

  vec_double2 r2 = spu_mul(r,r);

  //  Use Horner's method on the power series

  /*  result = ((((c12*x + c11)*x + c10)*x + c9)*x + c8)*x + c7)*x + c6)*x^6 +

              ((((((c5*x + c4)*x + c3)*x + c2)*x + c1)*x + c0

  */

#ifdef __SPU_EDP__

  vec_double2 p1, p2, r4, r6;

  p1 = spu_madd(f12, r, f11);

  p2 = spu_madd(f05, r, f04);

  r4 = spu_mul(r2, r2);

  p1 = spu_madd(p1, r, f10);

  p2 = spu_madd(p2, r, f03);

  p1 = spu_madd(p1, r, f09);

  p2 = spu_madd(p2, r, f02);

  p1 = spu_madd(p1, r, f08);

  r6 = spu_mul(r2, r4);

  p1 = spu_madd(p1, r, f07);

  p2 = spu_madd(p2, r2, r);

  p1 = spu_madd(p1, r, f06);

  result = spu_madd(r6, p1, p2);

  result = spu_add(result, spu_splats(1.0));

#else

  result = spu_madd(r,f12,f11);

  result = spu_madd(result,r,f10);

  result = spu_madd(result,r,f09);

  result = spu_madd(result,r,f08);

  result = spu_madd(result,r,f07);

  result = spu_madd(result,r,f06);

  result = spu_madd(result,r,f05);

  result = spu_madd(result,r,f04);

  result = spu_madd(result,r,f03);

  result = spu_madd(result,r,f02);

  result = spu_madd(result,r2,r);

  result = spu_add(result,spu_splats(1.0));

#endif  /* __SPU_EDP__ */

  //  Scale the result - basically a call to ldexpd2()

  vec_int4 e1, e2;

  vec_int4 min = spu_splats(-2044);

  vec_int4 max = spu_splats(2046);

  vec_uint4 cmp_min, cmp_max;

  vec_uint4 shift = (vec_uint4) { 20, 32, 20, 32 };

  vec_double2 f1, f2;

  /* Clamp the specified exponent to the range -2044 to 2046.

   */

  cmp_min = spu_cmpgt(exp, min);

  cmp_max = spu_cmpgt(exp, max);

  exp = spu_sel(min, exp, cmp_min);

  exp = spu_sel(exp, max, cmp_max);

  /* Generate the factors f1 = 2^e1 and f2 = 2^e2

   */

  e1 = spu_rlmaska(exp, -1);

  e2 = spu_sub(exp, e1);

  f1 = (vec_double2)spu_sl(spu_add(e1, 1023), shift);

  f2 = (vec_double2)spu_sl(spu_add(e2, 1023), shift);

  /* Compute the product x * 2^e1 * 2^e2

   */

  result = spu_mul(spu_mul(result, f1), f2);

  return result;

}

#endif /* _EXPD2_H_ */

#endif /* __SPU__ */