newlib-cygwin/newlib/libm/machine/spu/headers/exp2f.h

/*
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  International Business Machines Corporation,
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    * Neither the names of the copyright holders nor the names of their
  contributors may be used to endorse or promote products derived from this
  software without specific prior written permission.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
  IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
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*/
#ifndef _EXP2F_H_
#define _EXP2F_H_	1

#ifndef M_LN2
#define M_LN2	0.69314718055994530942	/* ln(2) */
#endif /* M_LN2 */

/*
 * FUNCTION
 *	float _exp2f(float x)
 *
 * DESCRIPTION
 *	_exp2f computes 2 raised to the input x. Computation is
 *	performed by observing the 2^(a+b) = 2^a * 2^b.
 *	We decompose x into a and b (above) by letting.
 *	a = ceil(x), b = x - a;
 *
 *	2^a is easilty computed by placing a into the exponent
 *	or a floating point number whose mantissa is all zeros.
 *
 *	2^b is computed using the following polynomial approximation.
 *	(C. Hastings, Jr, 1955).
 *
 *             __7__
 *	       \
 *		\
 *	2^x =   /     Ci*x^i
 *             /____
 *              i=0
 *
 *	for x in the range 0.0 to 1.0
 *
 *	C0 =  1.0
 *	C1 = -0.9999999995
 *	C2 =  0.4999999206
 *	C3 = -0.1666653019
 *	C4 =  0.0416573475
 *	C5 = -0.0083013598
 *	C6 =  0.0013298820
 *	C7 = -0.0001413161
 *
 */
static __inline float _exp2f(float x)
{
  union {
    float f;
    unsigned int ui;
  } bias, exp_int, exp_frac;
  unsigned int overflow, underflow;
  int ix;
  float frac, frac2, frac4;
  float hi, lo;

  /* Break in the input x into two parts ceil(x), x - ceil(x).
   */
  bias.f = x;
  bias.ui = ~(unsigned int)((signed)(bias.ui) >> 31) & 0x3F7FFFFF;
  ix = (int)(x + bias.f);
  frac = (float)ix - x;
  frac *= (float)(M_LN2);

  exp_int.ui  = (ix + 127) << 23;

  overflow  = (ix > 128)  ? 0x7FFFFFFF : 0x0;
  underflow = (ix < -127) ? 0xFFFFFFFF : 0x0;

  /* 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).
   */
  frac2 = frac  * frac;
  frac4 = frac2 * frac2;
  hi = -0.0001413161f * frac + 0.0013298820f;
  hi =             hi * frac - 0.0083013598f;
  hi =             hi * frac + 0.0416573475f;
  lo = -0.1666653019f * frac + 0.4999999206f;
  lo =             lo * frac - 0.9999999995f;
  lo =             lo * frac + 1.0f;
  exp_frac.f =     hi * frac4 + lo;

  ix += exp_frac.ui >> 23;
  exp_frac.f *= exp_int.f;

  exp_frac.ui = (exp_frac.ui | overflow) & ~underflow;

  return (exp_frac.f);
}

#endif /* _EXP2F_H_ */