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

/*
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  International Business Machines Corporation,
  Sony Computer Entertainment, Incorporated,
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  contributors may be used to endorse or promote products derived from this
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  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
  IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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*/
#ifndef _ATANF_H_
#define _ATANF_H_	1

#ifndef M_PI_2
#define M_PI_2		1.5707963267949f
#endif /* M_PI_2 */

/*
 * FUNCTION
 *	float _atanf(float x)
 *
 * DESCRIPTION
 *	_atanf computes the arc tangent of the value x; that is the value
 *	whose tangent is x.
 *
 *	_atanf returns the arc tangent 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 Laboratiry, 1955).
 *                __8__
 *		  \
 *		   \
 *	atanf(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 float _atanf(float x)
{
  float xabs;
  float bias;
  float x2, x3, x4, x8, x9;
  float hi, lo;
  float result;

  bias = 0.0f;
  xabs = (x < 0.0f) ? -x : x;

  if (xabs >= 1.0f) {
    bias = M_PI_2;
    if (x < 0.0f) {
      bias = -bias;
    }
    x = -1.0f / x;
  }
  /* 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 += x;

  x2 = x * x;
  x3 = x2 * x;
  x4 = x2 * x2;
  x8 = x4 * x4;
  x9 = x8 * x;
  hi =  0.0028662257f * x2 - 0.0161657367f;
  hi =             hi * x2 + 0.0429096138f;
  hi =             hi * x2 - 0.0752896400f;
  hi =             hi * x2 + 0.1065626393f;
  lo = -0.1420889944f * x2 + 0.1999355085f;
  lo =             lo * x2 - 0.3333314528f;
  lo =             lo * x3 + bias;

  result = hi * x9 + lo;

  return (result);
}

#endif /* _ATANF_H_ */