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| | #include "libm.h"
/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
* = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
* = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
*/
double tanh(double x)
{
union {double f; uint64_t i;} u = {.f = x};
uint32_t w;
int sign;
double_t t;
/* x = |x| */
sign = u.i >> 63;
u.i &= (uint64_t)-1/2;
x = u.f;
w = u.i >> 32;
if (w > 0x3fe193ea) {
/* |x| > log(3)/2 ~= 0.5493 or nan */
if (w > 0x40340000) {
/* |x| > 20 or nan */
/* note: this branch avoids raising overflow */
t = 1 - 0/x;
} else {
t = expm1(2*x);
t = 1 - 2/(t+2);
}
} else if (w > 0x3fd058ae) {
/* |x| > log(5/3)/2 ~= 0.2554 */
t = expm1(2*x);
t = t/(t+2);
} else if (w >= 0x00100000) {
/* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
t = expm1(-2*x);
t = -t/(t+2);
} else {
/* |x| is subnormal */
/* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
FORCE_EVAL(x*x);
t = x;
}
return sign ? -t : t;
}
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