tanh.c raw

   1  #include "libm.h"
   2  
   3  /* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
   4   *         = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
   5   *         = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
   6   */
   7  double tanh(double x)
   8  {
   9  	union {double f; uint64_t i;} u = {.f = x};
  10  	uint32_t w;
  11  	int sign;
  12  	double_t t;
  13  
  14  	/* x = |x| */
  15  	sign = u.i >> 63;
  16  	u.i &= (uint64_t)-1/2;
  17  	x = u.f;
  18  	w = u.i >> 32;
  19  
  20  	if (w > 0x3fe193ea) {
  21  		/* |x| > log(3)/2 ~= 0.5493 or nan */
  22  		if (w > 0x40340000) {
  23  			/* |x| > 20 or nan */
  24  			/* note: this branch avoids raising overflow */
  25  			t = 1 - 0/x;
  26  		} else {
  27  			t = expm1(2*x);
  28  			t = 1 - 2/(t+2);
  29  		}
  30  	} else if (w > 0x3fd058ae) {
  31  		/* |x| > log(5/3)/2 ~= 0.2554 */
  32  		t = expm1(2*x);
  33  		t = t/(t+2);
  34  	} else if (w >= 0x00100000) {
  35  		/* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
  36  		t = expm1(-2*x);
  37  		t = -t/(t+2);
  38  	} else {
  39  		/* |x| is subnormal */
  40  		/* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
  41  		FORCE_EVAL((float)x);
  42  		t = x;
  43  	}
  44  	return sign ? -t : t;
  45  }
  46