long double
sinhl(long double x)
{
long double hi,lo,x2,x4;
double dx2,s;
int16_t ix,jx;
GET_LDBL_EXPSIGN(jx,x);
ix = jx&0x7fff;
/* x is INF or NaN */
if(ix>=0x7fff) return x+x;
ENTERI();
s = 1;
if (jx<0) s = -1;
/* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */
if (ix<0x4005) { /* |x|<64 */
if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x|<TINY */
if(shuge+x>1) RETURNI(x); /* sinh(tiny) = tiny with inexact */
if (ix<0x3fff) { /* |x|<1 */
x2 = x*x;
#if LDBL_MANT_DIG == 64
x4 = x2*x2;
RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) +
((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x);
#elif LDBL_MANT_DIG == 113
dx2 = x2;
RETURNI(((((((((((S25*dx2 + S23)*dx2 +
S21)*x2 + S19)*x2 +
S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 +
S5)* (x2*x*x2) +
S3*(x2*x) + x);
#endif
}
k_hexpl(fabsl(x), &hi, &lo);
RETURNI(s*(lo - 0.25/(hi + lo) + hi));
}
/* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */
if (fabsl(x) <= o_threshold)
RETURNI(s*hexpl(fabsl(x)));
/* |x| > o_threshold, sinh(x) overflow */
return x*shuge;
}
long double
coshl(long double x)
{
long double hi,lo,x2,x4;
#if LDBL_MANT_DIG == 113
double dx2;
#endif
uint16_t ix;
GET_LDBL_EXPSIGN(ix,x);
ix &= 0x7fff;
/* x is INF or NaN */
if(ix>=0x7fff) return x*x;
ENTERI();
/* |x| < 1, return 1 or c(x) */
if(ix<0x3fff) {
if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */
RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */
x2 = x*x;
#if LDBL_MANT_DIG == 64
x4 = x2*x2;
RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
#elif LDBL_MANT_DIG == 113
dx2 = x2;
RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
C20)*x2 + C18)*x2 +
C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
C4)*(x2*x2) + C2*x2 + 1);
#endif
}
/* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
if (ix < 0x4005) {
k_hexpl(fabsl(x), &hi, &lo);
RETURNI(lo + 0.25/(hi + lo) + hi);
}
/* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
if (fabsl(x) <= o_threshold)
RETURNI(hexpl(fabsl(x)));
/* |x| > o_threshold, cosh(x) overflow */
RETURNI(huge*huge);
}
long double
tanhl(long double x)
{
long double hi,lo,s,x2,x4,z;
double dx2;
int16_t jx,ix;
GET_LDBL_EXPSIGN(jx,x);
ix = jx&0x7fff;
/* x is INF or NaN */
if(ix>=0x7fff) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
ENTERI();
/* |x| < 40 */
if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */
if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */
/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
}
if (ix<0x3ffd) { /* |x|<0.25 */
x2 = x*x;
#if LDBL_MANT_DIG == 64
x4 = x2*x2;
RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
T3*(x2*x) + x);
#elif LDBL_MANT_DIG == 113
dx2 = x2;
#if 0
RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
(x2*x*x2) +
T3*(x2*x) + x);
#else
long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
(x2*x*x2);
RETURNI(q + T3*(x2*x) + x);
#endif
#endif
}
k_hexpl(2*fabsl(x), &hi, &lo);
if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */
z = divl(hi, lo, -0.5, hi, lo, 0.5);
else
z = one - one/(lo+0.5+hi);
/* |x| >= 40, return +-1 */
} else {
z = one - tiny; /* raise inexact flag */
}
s = 1;
if (jx<0) s = -1;
RETURNI(s*z);
}
