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/* PROLOG END TAG zYx                                              */

#ifdef __SPU__

#ifndef _LGAMMAD2_H_

#define _LGAMMAD2_H_    1

#include <spu_intrinsics.h>

#include "divd2.h"

#include "recipd2.h"

#include "logd2.h"

#include "sind2.h"

#include "truncd2.h"

/*

 * FUNCTION

 *      vector double _lgammad2(vector double x) - Natural Log of Gamma Function

 *

 * DESCRIPTION

 *      _lgammad2 calculates the natural logarithm of the absolute value of the gamma

 *      function for the corresponding elements of the input vector.

 *

 * C99 Special Cases:

 *      lgamma(0) returns +infinite

 *      lgamma(1) returns +0

 *      lgamma(2) returns +0

 *      lgamma(negative integer) returns +infinite

 *      lgamma(+infinite) returns +infinite

 *      lgamma(-infinite) returns +infinite

 *

 * Other Cases:

 *  lgamma(Nan) returns Nan

 *  lgamma(Denorm) treated as lgamma(0) and returns +infinite

 *

 */

#define PI                  3.1415926535897932384626433832795028841971693993751058209749445923078164

#define HALFLOG2PI          9.1893853320467274178032973640561763986139747363778341281715154048276570E-1

#define EULER_MASCHERONI    0.5772156649015328606065

/*

 * Zeta constants for Maclaurin approx. near zero

 */

#define ZETA_02_DIV_02       8.2246703342411321823620758332301E-1

#define ZETA_03_DIV_03      -4.0068563438653142846657938717048E-1

#define ZETA_04_DIV_04       2.7058080842778454787900092413529E-1

#define ZETA_05_DIV_05      -2.0738555102867398526627309729141E-1

#define ZETA_06_DIV_06       1.6955717699740818995241965496515E-1

/*

 *  More Maclaurin coefficients

 */

/*

#define ZETA_07_DIV_07      -1.4404989676884611811997107854997E-1

#define ZETA_08_DIV_08       1.2550966952474304242233565481358E-1

#define ZETA_09_DIV_09      -1.1133426586956469049087252991471E-1

#define ZETA_10_DIV_10       1.0009945751278180853371459589003E-1

#define ZETA_11_DIV_11      -9.0954017145829042232609298411497E-2

#define ZETA_12_DIV_12       8.3353840546109004024886499837312E-2

#define ZETA_13_DIV_13      -7.6932516411352191472827064348181E-2

#define ZETA_14_DIV_14       7.1432946295361336059232753221795E-2

#define ZETA_15_DIV_15      -6.6668705882420468032903448567376E-2

#define ZETA_16_DIV_16       6.2500955141213040741983285717977E-2

#define ZETA_17_DIV_17      -5.8823978658684582338957270605504E-2

#define ZETA_18_DIV_18       5.5555767627403611102214247869146E-2

#define ZETA_19_DIV_19      -5.2631679379616660733627666155673E-2

#define ZETA_20_DIV_20       5.0000047698101693639805657601934E-2

 */

/*

 * Coefficients for Stirling's Series for Lgamma()

 */

#define STIRLING_01    8.3333333333333333333333333333333333333333333333333333333333333333333333E-2

#define STIRLING_02   -2.7777777777777777777777777777777777777777777777777777777777777777777778E-3

#define STIRLING_03    7.9365079365079365079365079365079365079365079365079365079365079365079365E-4

#define STIRLING_04   -5.9523809523809523809523809523809523809523809523809523809523809523809524E-4

#define STIRLING_05    8.4175084175084175084175084175084175084175084175084175084175084175084175E-4

#define STIRLING_06   -1.9175269175269175269175269175269175269175269175269175269175269175269175E-3

#define STIRLING_07    6.4102564102564102564102564102564102564102564102564102564102564102564103E-3

#define STIRLING_08   -2.9550653594771241830065359477124183006535947712418300653594771241830065E-2

#define STIRLING_09    1.7964437236883057316493849001588939669435025472177174963552672531000704E-1

#define STIRLING_10   -1.3924322169059011164274322169059011164274322169059011164274322169059011E0

#define STIRLING_11    1.3402864044168391994478951000690131124913733609385783298826777087646653E1

#define STIRLING_12   -1.5684828462600201730636513245208897382810426288687158252375643679991506E2

#define STIRLING_13    2.1931033333333333333333333333333333333333333333333333333333333333333333E3

#define STIRLING_14   -3.6108771253724989357173265219242230736483610046828437633035334184759472E4

#define STIRLING_15    6.9147226885131306710839525077567346755333407168779805042318946657100161E5

/*

 *  More Stirling's coefficients

 */

/*

#define STIRLING_16   -1.5238221539407416192283364958886780518659076533839342188488298545224541E7

#define STIRLING_17    3.8290075139141414141414141414141414141414141414141414141414141414141414E8

#define STIRLING_18   -1.0882266035784391089015149165525105374729434879810819660443720594096534E10

#define STIRLING_19    3.4732028376500225225225225225225225225225225225225225225225225225225225E11

#define STIRLING_20   -1.2369602142269274454251710349271324881080978641954251710349271324881081E13

#define STIRLING_21    4.8878806479307933507581516251802290210847053890567382180703629532735764E14

*/

static __inline vector double _lgammad2(vector double x)

{

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

  vec_uchar16 dup_odd   = ((vec_uchar16) { 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 });

  vec_uchar16 swap_word = ((vec_uchar16) { 4,5,6,7, 0,1,2,3, 12,13,14,15,  8, 9,10,11  });

  vec_double2 infinited = (vec_double2)spu_splats(0x7FF0000000000000ull);

  vec_double2 zerod     = spu_splats(0.0);

  vec_double2 oned      = spu_splats(1.0);

  vec_double2 twod      = spu_splats(2.0);

  vec_double2 pi        = spu_splats(PI);

  vec_double2 sign_maskd = spu_splats(-0.0);

  /* This is where we switch from near zero approx. */

  vec_float4 zero_switch = spu_splats(0.001f);

  vec_float4 shift_switch = spu_splats(6.0f);

  vec_float4 xf;

  vec_double2 inv_x, inv_xsqu;

  vec_double2 xtrunc, xstirling;

  vec_double2 sum, xabs;

  vec_uint4 xhigh, xlow, xthigh, xtlow;

  vec_uint4 x1, isnaninf, isnposint, iszero, isint, isneg, isshifted, is1, is2;

  vec_double2 result, stresult, shresult, mresult, nresult;

  /* Force Denorms to 0 */

  x = spu_add(x, zerod);

  xabs = spu_andc(x, sign_maskd);

  xf = spu_roundtf(xabs);

  xf = spu_shuffle(xf, xf, dup_even);

  /*

   * For 0 < x <= 0.001.

   * Approximation Near Zero

   *

   * Use Maclaurin Expansion of lgamma()

   *

   * lgamma(z) = -ln(z) - z * EulerMascheroni + Sum[(-1)^n * z^n * Zeta(n)/n]

   */

  mresult = spu_madd(xabs, spu_splats(ZETA_06_DIV_06), spu_splats(ZETA_05_DIV_05));

  mresult = spu_madd(xabs, mresult, spu_splats(ZETA_04_DIV_04));

  mresult = spu_madd(xabs, mresult, spu_splats(ZETA_03_DIV_03));

  mresult = spu_madd(xabs, mresult, spu_splats(ZETA_02_DIV_02));

  mresult = spu_mul(xabs, spu_mul(xabs, mresult));

  mresult = spu_sub(mresult, spu_add(_logd2(xabs), spu_mul(xabs, spu_splats(EULER_MASCHERONI))));

  /*

   * For 0.001 < x <= 6.0, we are going to push value

   * out to an area where Stirling's approximation is

   * accurate. Let's use a constant of 6.

   *

   * Use the recurrence relation:

   *    lgamma(x + 1) = ln(x) + lgamma(x)

   *

   * Note that we shift x here, before Stirling's calculation,

   * then after Stirling's, we adjust the result.

   *

   */

  isshifted = spu_cmpgt(shift_switch, xf);

  xstirling = spu_sel(xabs, spu_add(xabs, spu_splats(6.0)), (vec_ullong2)isshifted);

  inv_x    = _recipd2(xstirling);

  inv_xsqu = spu_mul(inv_x, inv_x);

  /*

   * For 6.0 < x < infinite

   *

   * Use Stirling's Series.

   *

   *              1                    1                1      1        1

   * lgamma(x) = --- ln (2*pi) + (z - ---) ln(x) - x + --- - ----- + ------ ...

   *              2                    2               12x   360x^3  1260x^5

   *

   * Taking 10 terms of the sum gives good results for x > 6.0

   *

   */

  sum = spu_madd(inv_xsqu, spu_splats(STIRLING_15), spu_splats(STIRLING_14));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_13));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_12));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_11));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_10));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_09));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_08));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_07));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_06));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_05));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_04));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_03));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_02));

  sum = spu_madd(sum, inv_xsqu, spu_splats(STIRLING_01));

  sum = spu_mul(sum, inv_x);

  stresult = spu_madd(spu_sub(xstirling, spu_splats(0.5)), _logd2(xstirling), spu_splats(HALFLOG2PI));

  stresult = spu_sub(stresult, xstirling);

  stresult = spu_add(stresult, sum);

  /*

   * Adjust result if we shifted x into Stirling range.

   *

   * lgamma(x) = lgamma(x + n) - ln(x(x+1)(x+2)...(x+n-1)

   *

   */

  shresult = spu_mul(xabs, spu_add(xabs, spu_splats(1.0)));

  shresult = spu_mul(shresult, spu_add(xabs, spu_splats(2.0)));

  shresult = spu_mul(shresult, spu_add(xabs, spu_splats(3.0)));

  shresult = spu_mul(shresult, spu_add(xabs, spu_splats(4.0)));

  shresult = spu_mul(shresult, spu_add(xabs, spu_splats(5.0)));

  shresult = _logd2(shresult);

  shresult = spu_sub(stresult, shresult);

  stresult = spu_sel(stresult, shresult, (vec_ullong2)isshifted);

  /*

   * Select either Maclaurin or Stirling result before Negative X calc.

   */

  xf = spu_shuffle(xf, xf, dup_even);

  vec_uint4 useStirlings = spu_cmpgt(xf, zero_switch);

  result = spu_sel(mresult, stresult, (vec_ullong2)useStirlings);

  /*

   * Approximation for Negative X

   *

   * Use reflection relation

   *

   * gamma(x) * gamma(-x) = -pi/(x sin(pi x))

   *

   * lgamma(x) = log(pi/(-x sin(pi x))) - lgamma(-x)

   *

   */

  nresult = spu_mul(x, _sind2(spu_mul(x, pi)));

  nresult = spu_andc(nresult, sign_maskd);

  nresult = _logd2(_divd2(pi, nresult));

  nresult = spu_sub(nresult, result);

  /*

   * Select between the negative or positive x approximations.

   */

  isneg = (vec_uint4)spu_shuffle(x, x, dup_even);

  isneg = spu_rlmaska(isneg, -32);

  result = spu_sel(result, nresult, (vec_ullong2)isneg);

  /*

   * Finally, special cases/errors.

   */

  xhigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);

  xlow  = (vec_uint4)spu_shuffle(xabs, xabs, dup_odd);

  /* x = zero, return infinite */

  x1 = spu_or(xhigh, xlow);

  iszero = spu_cmpeq(x1, 0);

  /* x = negative integer, return infinite */

  xtrunc = _truncd2(xabs);

  xthigh = (vec_uint4)spu_shuffle(xtrunc, xtrunc, dup_even);

  xtlow  = (vec_uint4)spu_shuffle(xtrunc, xtrunc, dup_odd);

  isint = spu_and(spu_cmpeq(xthigh, xhigh), spu_cmpeq(xtlow, xlow));

  isnposint = spu_or(spu_and(isint, isneg), iszero);

  result = spu_sel(result, infinited, (vec_ullong2)isnposint);

  /* x = 1.0 or 2.0, return 0.0 */

  is1 = spu_cmpeq((vec_uint4)x, (vec_uint4)oned);

  is1 = spu_and(is1, spu_shuffle(is1, is1, swap_word));

  is2 = spu_cmpeq((vec_uint4)x, (vec_uint4)twod);

  is2 = spu_and(is2, spu_shuffle(is2, is2, swap_word));

  result = spu_sel(result, zerod, (vec_ullong2)spu_or(is1,is2));

  /* x = +/- infinite or nan, return |x| */

  isnaninf = spu_cmpgt(xhigh, 0x7FEFFFFF);

  result = spu_sel(result, xabs, (vec_ullong2)isnaninf);

  return result;

}

#endif /* _LGAMMAD2_H_ */

#endif /* __SPU__ */