newlib-cygwin/newlib/libm/machine/spu/headers/recipd2.h

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/* PROLOG END TAG zYx                                              */
#ifdef __SPU__

#ifndef _RECIPD2_H_
#define _RECIPD2_H_		1

#include <spu_intrinsics.h>


/*
 * FUNCTION
 *	vector double _recipd2(vector double value)
 * 
 * DESCRIPTION
 * 	The _recipd2 function inverts "value" and returns the result. 
 *      Computation is performed using the single precision reciprocal 
 *      estimate and interpolate instructions to produce a 12 accurate 
 *      estimate.
 *
 *	One (1) iteration of a Newton-Raphson is performed to improve 
 *	accuracy to single precision floating point. Two additional double 
 *	precision iterations are  needed to achieve a full double
 *	preicision result.
 *
 *	The Newton-Raphson iteration is of the form:
 *		X[i+1] = X[i] * (2.0 - b*X[i]) 
 * 	where b is the input value to be inverted
 *
 */ 
static __inline vector double _recipd2(vector double value_d)
{
  vector unsigned long long zero     = (vector unsigned long long) { 0x0000000000000000ULL, 0x0000000000000000ULL };
  vector unsigned long long expmask  = (vector unsigned long long) { 0x7FF0000000000000ULL, 0x7FF0000000000000ULL };
  vector unsigned long long signmask = (vector unsigned long long) { 0x8000000000000000ULL, 0x8000000000000000ULL };
  vector float  x0;
  vector float  value;
  vector float  two   = spu_splats(2.0f);
  vector double two_d = spu_splats(2.0);
  vector double x1, x2, x3;
  vector double bias;

  /* Bias the divisor to correct for double precision floating
   * point exponents that are out of single precision range.
   */
  bias = spu_xor(spu_and(value_d, (vector double)expmask), (vector double)expmask);
  value = spu_roundtf(spu_mul(value_d, bias));
  x0 = spu_re(value);
  x1 = spu_extend(spu_mul(x0, spu_nmsub(value, x0, two)));
  x1 = spu_mul(x1, bias);
  x2 = spu_mul(x1, spu_nmsub(value_d, x1, two_d));
  x3 = spu_mul(x2, spu_nmsub(value_d, x2, two_d));

  /* Handle input = +/- infinity or +/-0. */
  vec_double2 xabs = spu_andc(value_d, (vec_double2)signmask);
  vec_ullong2 zeroinf = spu_or(spu_cmpeq(xabs, (vec_double2)expmask),
                               spu_cmpeq(xabs, (vec_double2)zero));
  x3 = spu_sel(x3, spu_xor(value_d, (vector double)expmask), zeroinf);

  return (x3);
}

#endif /* _RECIPD2_H_ */
#endif /* __SPU__ */