atanf4.h

Newlib 嵌入式 C库 标准实现代码

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#ifdef __SPU__

#ifndef _ATANF4_H_
#define _ATANF4_H_	1

#include <spu_intrinsics.h>

#include "simdmath.h"
#include "recipf4.h"

/*
 * FUNCTION
 *	vector float _atanf4(vector float x)
 *
 * DESCRIPTION
 *	The _atanf4 function computes the arc tangent of a vector of values x; 
 *      that is the values whose tangent is x.
 *
 *	The _atanf4 function returns the arc tangents in radians and the value 
 *      is mathematically defined to be in the range -PI/2 to PI/2.
 *
 *	The arc tangent function is computed using a polynomial approximation
 *	(B. Carlson, M. Goldstein, Los Alamos Scientific Laboratory, 1955).
 *                __8__
 *		  \
 *		   \ 
 *	atan(x) =  /    Ci*x^(2*i+1)
 *                /____
 *                 i=0
 *
 *	for x in the range -1 to 1. The remaining regions are defined to be:
 *
 *	[1, infinity]   :  PI/2 + atanf(-1/x)
 *	[-infinity, -1] : -PI/2 + atanf(-1/x)
 *
 */
static __inline vector float _atanf4(vector float x)
{
  vector float bias;
  vector float x2, x3, x4, x8, x9;
  vector float hi, lo;
  vector float result;
  vector float inv_x;
  vector unsigned int sign;
  vector unsigned int select;

  sign = spu_sl(spu_rlmask((vector unsigned int)x, -31), 31);
  inv_x = _recipf4(x);
  inv_x = (vector float)spu_xor((vector unsigned int)inv_x, spu_splats(0x80000000));

  select = (vector unsigned int)spu_cmpabsgt(x, spu_splats(1.0f));
  bias = (vector float)spu_or(sign, (vector unsigned int)(spu_splats((float)SM_PI_2)));
  bias = (vector float)spu_and((vector unsigned int)bias, select);

  x = spu_sel(x, inv_x, select);

  /* Instruction counts can be reduced if the polynomial was
   * computed entirely from nested (dependent) fma's. However, 
   * to reduce the number of pipeline stalls, the polygon is evaluated 
   * in two halves(hi and lo).
   */
  bias = spu_add(bias, x);
  x2 = spu_mul(x, x);
  x3 = spu_mul(x2, x);
  x4 = spu_mul(x2, x2);
  x8 = spu_mul(x4, x4);
  x9 = spu_mul(x8, x);
  hi = spu_madd(spu_splats(0.0028662257f), x2, spu_splats(-0.0161657367f));
  hi = spu_madd(hi, x2, spu_splats(0.0429096138f));
  hi = spu_madd(hi, x2, spu_splats(-0.0752896400f));
  hi = spu_madd(hi, x2, spu_splats(0.1065626393f));
  lo = spu_madd(spu_splats(-0.1420889944f), x2, spu_splats(0.1999355085f));
  lo = spu_madd(lo, x2, spu_splats(-0.3333314528f));
  lo = spu_madd(lo, x3, bias);
  
  result = spu_madd(hi, x9, lo);

  return (result);
}

#endif /* _ATANF4_H_ */
#endif /* __SPU__ */