41 lines
764 B
C
41 lines
764 B
C
#include "libm.h"
|
|
|
|
/* cosh(x) = (exp(x) + 1/exp(x))/2
|
|
* = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
|
|
* = 1 + x*x/2 + o(x^4)
|
|
*/
|
|
double cosh(double x)
|
|
{
|
|
union {double f; uint64_t i;} u = {.f = x};
|
|
uint32_t w;
|
|
double t;
|
|
|
|
/* |x| */
|
|
u.i &= (uint64_t)-1/2;
|
|
x = u.f;
|
|
w = u.i >> 32;
|
|
|
|
/* |x| < log(2) */
|
|
if (w < 0x3fe62e42) {
|
|
if (w < 0x3ff00000 - (26<<20)) {
|
|
/* raise inexact if x!=0 */
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
return 1;
|
|
}
|
|
t = expm1(x);
|
|
return 1 + t*t/(2*(1+t));
|
|
}
|
|
|
|
/* |x| < log(DBL_MAX) */
|
|
if (w < 0x40862e42) {
|
|
t = exp(x);
|
|
/* note: if x>log(0x1p26) then the 1/t is not needed */
|
|
return 0.5*(t + 1/t);
|
|
}
|
|
|
|
/* |x| > log(DBL_MAX) or nan */
|
|
/* note: the result is stored to handle overflow */
|
|
t = __expo2(x);
|
|
return t;
|
|
}
|