__expo2.c raw

   1  #include "libm.h"
   2  
   3  /* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */
   4  static const int k = 2043;
   5  static const double kln2 = 0x1.62066151add8bp+10;
   6  
   7  /* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */
   8  double __expo2(double x, double sign)
   9  {
  10  	double scale;
  11  
  12  	/* note that k is odd and scale*scale overflows */
  13  	INSERT_WORDS(scale, (uint32_t)(0x3ff + k/2) << 20, 0);
  14  	/* exp(x - k ln2) * 2**(k-1) */
  15  	/* in directed rounding correct sign before rounding or overflow is important */
  16  	return exp(x - kln2) * (sign * scale) * scale;
  17  }
  18