Modules/_math.c

   1 /* Definitions of some C99 math library functions, for those platforms
   2    that don't implement these functions already. */
   3
   4 #include <float.h>
   5 #include <math.h>
   6
   7 /* Mathematically, expm1(x) = exp(x) - 1.  The expm1 function is designed
   8    to avoid the significant loss of precision that arises from direct
   9    evaluation of the expression exp(x) - 1, for x near 0. */
  10
  11 double
  12 _Py_expm1(double x)
  13 {
  14     /* For abs(x) >= log(2), it's safe to evaluate exp(x) - 1 directly; this
  15        also works fine for infinities and nans.
  16
  17        For smaller x, we can use a method due to Kahan that achieves close to
  18        full accuracy.
  19     */
  20
  21     if (fabs(x) < 0.7) {
  22         double u;
  23         u = exp(x);
  24         if (u == 1.0)
  25             return x;
  26         else
  27             return (u - 1.0) * x / log(u);
  28     }
  29     else
  30         return exp(x) - 1.0;
  31 }