erfcd2.h

Newlib 嵌入式 C库 标准实现代码

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/* PROLOG END TAG zYx                                              */
#ifdef __SPU__
#ifndef _ERFCD2_H_
#define _ERFCD2_H_	1

#include <spu_intrinsics.h>

#include "expd2.h"
#include "recipd2.h"
#include "divd2.h"
#include "erf_utils.h"

/*
 * FUNCTION
 *  vector double _erfcd2(vector double x)
 *
 * DESCRIPTION
 *  The erfcd2 function computes the complement error function of each element of x.
 *
 *  Accuracy Note: We would benefit from a rational approximation in the domain
 *  1.2 < x < 2.0 and also around x = 2.5.
 *
 *  C99 Special Cases:
 *  - erfc(+0) returns +1
 *  - erfc(-0) returns +1
 *  - erfc(+infinite) returns +0
 *  - erfc(-infinite) returns +2
 *
 *  Other Cases:
 *  - erfc(Nan) returns Nan
 *
 */

static __inline vector double _erfcd2(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_double2 onehalfd  = spu_splats(0.5);
  vec_double2 zerod     = spu_splats(0.0);
  vec_double2 oned      = spu_splats(1.0);
  vec_double2 twod      = spu_splats(2.0);
  vec_double2 sign_mask = spu_splats(-0.0);

  /* This is where we switch from near zero approx. */
  vec_float4 approx_point = spu_splats(1.71f);

  vec_double2 xabs, xsqu, xsign;
  vec_uint4 xhigh, xabshigh;
  vec_uint4 isnan, isneg;
  vec_double2 tresult, presult, result;

  xsign = spu_and(x, sign_mask);

  /* Force Denorms to 0 */
  x = spu_add(x, zerod);

  xabs = spu_andc(x, sign_mask);
  xsqu = spu_mul(x, x);

  /*
   * Use Taylor Series for x near 0
   * Preserve sign of x in result, since erf(-x) = -erf(x)
   * This approximation is for erf, so adjust for erfc.
   */
  TAYLOR_ERF(xabs, xsqu, tresult);
  tresult = spu_or(tresult, xsign);
  tresult = spu_sub(oned, tresult);

  /*
   * Now, use the Continued Fractions approximation away
   * from 0. If x < 0, use erfc(-x) = 2 - erfc(x)
   */
  CONTFRAC_ERFC(xabs, xsqu, presult);
  isneg = (vec_uint4)spu_shuffle(x, x, dup_even);
  isneg = spu_rlmaska(isneg, -32);
  presult = spu_sel(presult, spu_sub(twod, presult), (vec_ullong2)isneg);

  /*
   * Select the appropriate approximation.
   */
  vec_float4 xf = spu_roundtf(xabs);
  xf = spu_shuffle(xf, xf, dup_even);
  result = spu_sel(tresult, presult, (vec_ullong2)spu_cmpgt(xf, approx_point));

  /*
   * Special cases/errors.
   */
  xhigh = (vec_uint4)spu_shuffle(x, x, dup_even);
  xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);

  /* x = +/- infinite */
  result = spu_sel(result, zerod, (vec_ullong2)spu_cmpeq(xhigh, 0x7FF00000));
  result = spu_sel(result, twod,  (vec_ullong2)spu_cmpeq(xhigh, 0xFFF00000));

  /* x = nan, return x */
  isnan = spu_cmpgt(xabshigh, 0x7FF00000);
  result = spu_sel(result, x, (vec_ullong2)isnan);

  return result;
}

#endif /* _ERFCD2_H_ */
#endif /* __SPU__ */