_Float128
__tanhl (_Float128 x)
{
_Float128 t, z;
uint32_t jx, ix;
ieee854_long_double_shape_type u;
/* Words of |x|. */
u.value = x;
jx = u.parts32.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.parts32.w0 = ix; /* Absolute value of x. */
if (ix >= 0x3fff0000)
{ /* |x| >= 1 */
t = __expm1l (two * u.value);
z = one - two / (t + two);
}
else
{
t = __expm1l (-two * u.value);
z = -t / (t + two);
}
/* |x| > 40, return +-1 */
}
else
{
z = one - tiny; /* raised inexact flag */
}
return (jx & 0x80000000) ? -z : z;
}
long double __tanhl(long double x)
{
long double t,z;
int64_t jx,ix;
double xhi;
/* High word of |x|. */
xhi = ldbl_high (x);
EXTRACT_WORDS64 (jx, xhi);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
/* |x| < 40 */
if (ix < 0x4044000000000000LL) { /* |x|<40 */
if (ix == 0)
return x; /* x == +-0 */
if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
{
math_check_force_underflow (x);
return x; /* tanh(small) = small */
}
if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */
t = __expm1l(two*fabsl(x));
z = one - two/(t+two);
} else {
t = __expm1l(-two*fabsl(x));
z= -t/(t+two);
}
/* |x| > 40, return +-1 */
} else {
z = one - tiny; /* raised inexact flag */
}
return (jx>=0)? z: -z;
}
long double
__ieee754_sinhl (long double x)
{
long double t, w, h;
u_int32_t jx, ix;
ieee854_long_double_shape_type u;
/* Words of |x|. */
u.value = x;
jx = u.parts32.w0;
ix = jx & 0x7fffffff;
/* x is INF or NaN */
if (ix >= 0x7fff0000)
return x + x;
h = 0.5;
if (jx & 0x80000000)
h = -h;
/* Absolute value of x. */
u.parts32.w0 = ix;
/* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
if (ix <= 0x40044000)
{
if (ix < 0x3fc60000) /* |x| < 2^-57 */
if (shuge + x > one)
return x; /* sinh(tiny) = tiny with inexact */
t = __expm1l (u.value);
if (ix < 0x3fff0000)
return h * (2.0 * 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 * __ieee754_expl (u.value);
/* |x| in [log(maxdouble), overflowthreshold]
Overflow threshold is log(2 * maxdouble). */
if (u.value <= ovf_thresh)
{
w = __ieee754_expl (0.5 * u.value);
t = h * w;
return t * w;
}
/* |x| > overflowthreshold, sinhl(x) overflow */
return x * shuge;
}
long double
__ieee754_sinhl(long double x)
{
long double t,w,h;
u_int32_t jx,ix,i0,i1;
/* Words of |x|. */
GET_LDOUBLE_WORDS(jx,i0,i1,x);
ix = jx&0x7fff;
/* x is INF or NaN */
if(__builtin_expect(ix==0x7fff, 0)) return x+x;
h = 0.5;
if (jx & 0x8000) h = -h;
/* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
if (ix<0x3fdf) { /* |x|<2**-32 */
if (fabsl (x) < LDBL_MIN)
{
long double force_underflow = x * x;
math_force_eval (force_underflow);
}
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
}
t = __expm1l(fabsl(x));
if(ix<0x3fff) return h*(2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}
/* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
return h*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthreshold] */
if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0
|| (i0 == 0xb174ddc0
&& i1 <= 0x31aec0ea)))) {
w = __ieee754_expl(0.5*fabsl(x));
t = h*w;
return t*w;
}
/* |x| > overflowthreshold, sinhl(x) overflow */
return x*shuge;
}
long double
__ieee754_sinhl(long double x)
{
long double t,w,h;
int64_t ix,jx;
double xhi;
/* High word of |x|. */
xhi = ldbl_high (x);
EXTRACT_WORDS64 (jx, xhi);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) return x+x;
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x4044000000000000LL) { /* |x|<40 */
if (ix<0x3c90000000000000LL) { /* |x|<2**-54 */
math_check_force_underflow (x);
if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
}
t = __expm1l(fabsl(x));
if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
w = t/(t+one);
return h*(t+w);
}
/* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= 0x408633ce8fb9f87eLL) {
w = __ieee754_expl(0.5*fabsl(x));
t = h*w;
return t*w;
}
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
long double
__ieee754_coshl (long double x)
{
long double t,w;
int64_t ix;
/* High word of |x|. */
GET_LDOUBLE_MSW64(ix,x);
ix &= 0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) return x*x;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e42fefa39efLL) {
t = __expm1l(fabsl(x));
w = one+t;
if (ix<0x3c80000000000000LL) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x4036000000000000LL) {
t = __ieee754_expl(fabsl(x));
return half*t+half/t;
}
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix < 0x408633ce8fb9f87dLL) {
w = __ieee754_expl(half*fabsl(x));
t = half*w;
return t*w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
static long double
gammal_positive (long double x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5L)
{
*exp2_adj = 0;
return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5L)
{
*exp2_adj = 0;
return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam));
}
else if (x < 12.5L)
{
/* Adjust into the range for using exp (lgamma). */
*exp2_adj = 0;
long double n = __ceill (x - 1.5L);
long double x_adj = x - n;
long double eps;
long double prod = __gamma_productl (x_adj, 0, n, &eps);
return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam))
* prod * (1.0L + eps));
}
else
{
long double eps = 0;
long double x_eps = 0;
long double x_adj = x;
long double prod = 1;
if (x < 24.0L)
{
/* Adjust into the range for applying Stirling's
approximation. */
long double n = __ceill (24.0L - x);
x_adj = x + n;
x_eps = (x - (x_adj - n));
prod = __gamma_productl (x_adj - n, x_eps, n, &eps);
}
/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
starting by computing pow (X_ADJ, X_ADJ) with a power of 2
factored out. */
long double exp_adj = -eps;
long double x_adj_int = __roundl (x_adj);
long double x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
long double x_adj_mant = __frexpl (x_adj, &x_adj_log2);
if (x_adj_mant < M_SQRT1_2l)
{
x_adj_log2--;
x_adj_mant *= 2.0L;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
long double ret = (__ieee754_powl (x_adj_mant, x_adj)
* __ieee754_exp2l (x_adj_log2 * x_adj_frac)
* __ieee754_expl (-x_adj)
* __ieee754_sqrtl (2 * M_PIl / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logl (x_adj);
long double bsum = gamma_coeff[NCOEFF - 1];
long double x_adj2 = x_adj * x_adj;
for (size_t i = 1; i <= NCOEFF - 1; i++)
bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
exp_adj += bsum / x_adj;
return ret + ret * __expm1l (exp_adj);
}
}
