github.com/afumu/libc@v0.0.6/musl/src/math/tanh.c (about)

     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  }