__float128
tanhq (__float128 x)
{
__float128 t, z;
uint32_t jx, ix;
ieee854_float128 u;
/* Words of |x|. */
u.value = x;
jx = u.words32.w0;
ix = jx & 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7fff0000)
{
/* for NaN it's not important which branch: tanhl(NaN) = NaN */
if (jx & 0x80000000)
return one / x - one; /* tanhl(-inf)= -1; */
else
return one / x + one; /* tanhl(+inf)=+1 */
}
/* |x| < 40 */
if (ix < 0x40044000)
{
if (u.value == 0)
return x; /* x == +- 0 */
if (ix < 0x3fc60000) /* |x| < 2^-57 */
{
math_check_force_underflow (x);
return x * (one + tiny); /* tanh(small) = small */
}
u.words32.w0 = ix; /* Absolute value of x. */
if (ix >= 0x3fff0000)
{ /* |x| >= 1 */
t = expm1q (two * u.value);
z = one - two / (t + two);
}
else
{
t = expm1q (-two * u.value);
z = -t / (t + two);
}
/* |x| > 40, return +-1 */
}
else
{
z = one - tiny; /* raised inexact flag */
}
return (jx & 0x80000000) ? -z : z;
}
__float128
sinhq (__float128 x)
{
__float128 t, w, h;
uint32_t jx, ix;
ieee854_float128 u;
/* Words of |x|. */
u.value = x;
jx = u.words32.w0;
ix = jx & 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7fff0000)
return x + x;
h = 0.5Q;
if (jx & 0x80000000)
h = -h;
/* Absolute value of x. */
u.words32.w0 = ix;
/* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
if (ix <= 0x40044000)
{
if (ix < 0x3fc60000) /* |x| < 2^-57 */
{
math_check_force_underflow (x);
if (shuge + x > one)
return x; /* sinh(tiny) = tiny with inexact */
}
t = expm1q (u.value);
if (ix < 0x3fff0000)
return h * (2.0Q * t - t * t / (t + one));
return h * (t + t / (t + one));
}
/* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
if (ix <= 0x400c62e3) /* 11356.375 */
return h * expq (u.value);
/* |x| in [log(maxdouble), overflowthreshold]
Overflow threshold is log(2 * maxdouble). */
if (u.value <= ovf_thresh)
{
w = expq (0.5Q * u.value);
t = h * w;
return t * w;
}
/* |x| > overflowthreshold, sinhq(x) overflow */
return x * shuge;
}
__float128
coshq (__float128 x)
{
__float128 t, w;
int32_t ex;
ieee854_float128 u;
u.value = x;
ex = u.words32.w0 & 0x7fffffff;
/* Absolute value of x. */
u.words32.w0 = ex;
/* x is INF or NaN */
if (ex >= 0x7fff0000)
return x * x;
/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expq(|x|)) */
if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
{
t = expm1q (u.value);
w = one + t;
if (ex < 0x3fb80000) /* |x| < 2^-116 */
return w; /* cosh(tiny) = 1 */
return one + (t * t) / (w + w);
}
/* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
if (ex < 0x40044000)
{
t = expq (u.value);
return half * t + half / t;
}
/* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
if (ex <= 0x400c62e3) /* 11356.375 */
return half * expq (u.value);
/* |x| in [log(maxdouble), overflowthresold] */
if (u.value <= ovf_thresh)
{
w = expq (half * u.value);
t = half * w;
return t * w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge * huge;
}