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| | #include "libm.h"
/* sinh(x) = (exp(x) - 1/exp(x))/2
* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
* = x + x^3/6 + o(x^5)
*/
double sinh(double x)
{
union {double f; uint64_t i;} u = {.f = x};
uint32_t w;
double t, h, absx;
h = 0.5;
if (u.i >> 63)
h = -h;
/* |x| */
u.i &= (uint64_t)-1/2;
absx = u.f;
w = u.i >> 32;
/* |x| < log(DBL_MAX) */
if (w < 0x40862e42) {
t = expm1(absx);
if (w < 0x3ff00000) {
if (w < 0x3ff00000 - (26<<20))
/* note: inexact and underflow are raised by expm1 */
/* note: this branch avoids spurious underflow */
return x;
return h*(2*t - t*t/(t+1));
}
/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
return h*(t + t/(t+1));
}
/* |x| > log(DBL_MAX) or nan */
/* note: the result is stored to handle overflow */
t = __expo2(absx, 2*h);
return t;
}
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