newlib-cygwin/newlib/libm/machine/spu/headers/log2f4.h

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/* PROLOG END TAG zYx                                              */
#ifdef __SPU__

#ifndef _LOG2F4_H_
#define _LOG2F4_H_	1

#include <spu_intrinsics.h>

/*
 * FUNCTION
 *	vector float _log2f4(vector float x)
 *
 * DESCRIPTION
 *	The _log2f4 function computes log (base 2) on a vector if inputs 
 *      values x. The _log2f4 function is approximated as a polynomial of
 *      order 8 (C. Hastings, Jr, 1955).
 *
 *                   __8__
 *		     \
 *		      \ 
 *	log2f(1+x) =  /     Ci*x^i
 *                   /____
 *                    i=1
 *
 *	for x in the range 0.0 to 1.0
 *
 *	C1 =  1.4426898816672
 *	C2 = -0.72116591947498
 *	C3 =  0.47868480909345
 *	C4 = -0.34730547155299
 *	C5 =  0.24187369696082
 *	C6 = -0.13753123777116
 *	C7 =  0.052064690894143
 *	C8 = -0.0093104962134977
 *
 *	This function assumes that x is a non-zero positive value.
 *
 */
static __inline vector float _log2f4(vector float x)
{
  vector signed int exponent;
  vector float result;
  vector float x2, x4;
  vector float hi, lo;

  /* Extract the exponent from the input X. 
   */
  exponent = (vector signed int)spu_and(spu_rlmask((vector unsigned int)(x), -23), 0xFF);
  exponent = spu_add(exponent, -127);

  /* Compute the remainder after removing the exponent.
   */
  x = (vector float)spu_sub((vector signed int)(x), spu_sl(exponent, 23));

  /* Calculate the log2 of the remainder using the polynomial
   * approximation.
   */
  x = spu_sub(x, spu_splats(1.0f));

  /* 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 amd lo). 
   */
  x2 = spu_mul(x, x);
  x4 = spu_mul(x2, x2);

  hi = spu_madd(x, spu_splats(-0.0093104962134977f), spu_splats(0.052064690894143f));
  hi = spu_madd(x, hi, spu_splats(-0.13753123777116f));
  hi = spu_madd(x, hi, spu_splats( 0.24187369696082f));
  hi = spu_madd(x, hi, spu_splats(-0.34730547155299f));
  lo = spu_madd(x, spu_splats(0.47868480909345f), spu_splats(-0.72116591947498f));
  lo = spu_madd(x, lo, spu_splats(1.4426898816672f));
  lo = spu_mul(x, lo);
  result = spu_madd(x4, hi, lo);

  /* Add the exponent back into the result.
   */
  result = spu_add(result, spu_convtf(exponent, 0));
  
  return (result);
}

#endif /* _LOG2F4_H_ */
#endif /* __SPU__ */