expm1d2.h

Newlib 嵌入式 C库 标准实现代码

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/* PROLOG END TAG zYx                                              */
#ifdef __SPU__

#ifndef _EXPM1D2_H_
#define _EXPM1D2_H_	1

#include <spu_intrinsics.h>

#include "expd2.h"
#include "divd2.h"

#define EXPM1_P0 0.0000000000000000000000000e+00
#define EXPM1_P1 1.0000000000000000000000000e+00
#define EXPM1_P2 9.7234232565378004697204117e-04
#define EXPM1_P3 3.3328278237299953368211192e-02
#define EXPM1_P4 3.1156225044634678993365345e-05
#define EXPM1_P5 2.1352206553343212164751408e-04
#define EXPM1_P6 1.6975135794626144795757452e-07
#define EXPM1_P7 2.7686287801334994383131629e-07
#define EXPM1_P8 1.1186114936216450015354379e-10

#define EXPM1_Q0 1.0000000000000000000000000e+00
#define EXPM1_Q1 -4.9902765767434620336473472e-01
#define EXPM1_Q2 1.1617544040780639069687652e-01
#define EXPM1_Q3 -1.6551954366467523660499950e-02
#define EXPM1_Q4 1.5864115838972218334307351e-03
#define EXPM1_Q5 -1.0534540477401370666288988e-04
#define EXPM1_Q6 4.7650003993592160620959043e-06
#define EXPM1_Q7 -1.3529198871087017840776265e-07
#define EXPM1_Q8 1.8635779407675460757658020e-09

/*
 * FUNCTION
 *	vector double _expm1d2(vector double x)
 *
 * DESCRIPTION
 *	_expm1d2 computes the exponential - 1 for each element
 *	of the input vector x.
 *
 *	This function is intended to return accurate values, even
 *	where exp(x) - 1 would normally produce bad results due to
 *	floating-point cancellation errors.
 *
 */

static __inline vector double _expm1d2(vector double x) 
{
  vector double oned  = spu_splats(1.0);
  vector double range = spu_splats(1.0625);
  vector unsigned long long use_exp;
  vector double pr, qr;
  vector double eresult;
  vector double rresult;
  vector double result;

  /* Compiler Bug. Replace xbug with x when spu_cmp*() doesn't 
   * modify it's arguments! */
  volatile vector double xbug = x;
  use_exp = spu_cmpabsgt(xbug, range);

  /*
   * Calculate directly using exp(x) - 1
   */
  eresult = spu_sub(_expd2(x), oned);

  /*
   * For x in [-1.0625,1.0625], use a rational approximation.
   * The madd's are interleaved to reduce dependency stalls. Looks
   * like gcc is smart enough to do this on it's own... but why
   * take the chance.
   */
  pr = spu_madd(x, spu_splats(EXPM1_P8), spu_splats(EXPM1_P7));
  qr = spu_madd(x, spu_splats(EXPM1_Q8), spu_splats(EXPM1_Q7));
  pr = spu_madd(pr, x, spu_splats(EXPM1_P6));
  qr = spu_madd(qr, x, spu_splats(EXPM1_Q6));
  pr = spu_madd(pr, x, spu_splats(EXPM1_P5));
  qr = spu_madd(qr, x, spu_splats(EXPM1_Q5));
  pr = spu_madd(pr, x, spu_splats(EXPM1_P4));
  qr = spu_madd(qr, x, spu_splats(EXPM1_Q4));
  pr = spu_madd(pr, x, spu_splats(EXPM1_P3));
  qr = spu_madd(qr, x, spu_splats(EXPM1_Q3));
  pr = spu_madd(pr, x, spu_splats(EXPM1_P2));
  qr = spu_madd(qr, x, spu_splats(EXPM1_Q2));
  pr = spu_madd(pr, x, spu_splats(EXPM1_P1));
  qr = spu_madd(qr, x, spu_splats(EXPM1_Q1));
  pr = spu_madd(pr, x, spu_splats(EXPM1_P0));
  qr = spu_madd(qr, x, spu_splats(EXPM1_Q0));
  rresult = _divd2(pr, qr);

  /*
   * Select either direct calculation or rational approximation.
   */
  result = spu_sel(rresult, eresult, use_exp);

  return result;
}

#endif /* _EXPM1D2_H_ */
#endif /* __SPU__ */