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circuitpython/lib/libm_dbl/cosh.c

40 lines
764 B

#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;
}