long double
cbrtl(long double x) {
long double s, t, r, w, y;
double dx, dy;
int *py = (int *) &dy;
int n, m, m3, sx;
if (!finitel(x))
return (x + x);
if (iszerol(x))
return (x);
sx = signbitl(x);
x = fabsl(x);
n = ilogbl(x);
m = n / 3;
m3 = m + m + m;
y = scalbnl(x, -m3);
dx = (double) y;
dy = cbrt(dx);
py[1 - n0] += 2;
if (py[1 - n0] == 0)
py[n0] += 1;
/* one step newton iteration to 113 bits with error < 0.667ulps */
t = (long double) dy;
t = scalbnl(t, m);
s = t * t;
r = x / s;
w = t + t;
r = (r - t) / (w + r);
t += t * r;
return (sx == 0 ? t : -t);
}
long double
log10l(long double x) {
long double y, z;
enum fp_direction_type rd;
int n;
if (!finitel(x))
return (x + fabsl(x)); /* x is +-INF or NaN */
else if (x > zero) {
n = ilogbl(x);
if (n < 0)
n += 1;
rd = __swapRD(fp_nearest);
y = n;
x = scalbnl(x, -n);
z = y * log10_2lo + ivln10 * logl(x);
z += y * log10_2hi;
if (rd != fp_nearest)
(void) __swapRD(rd);
return (z);
} else if (x == zero) /* -INF */
return (-one / zero);
else /* x <0 , return NaN */
return (zero / zero);
}
long double
tanhl(long double x) {
long double t, y, z;
int signx;
#ifndef lint
volatile long double dummy;
#endif
if (isnanl(x))
return (x + x); /* x is NaN */
signx = signbitl(x);
t = fabsl(x);
z = one;
if (t <= threshold) {
if (t > one)
z = one - two / (expm1l(t + t) + two);
else if (t > small) {
y = expm1l(-t - t);
z = -y / (y + two);
} else {
#ifndef lint
dummy = t + big;
/* inexact if t != 0 */
#endif
return (x);
}
} else if (!finitel(t))
return (copysignl(one, x));
else
return (signx ? -z + small * small : z - small * small);
return (signx ? -z : z);
}
long double
floorl(long double x) {
long double t;
if (!finitel(x))
return (x + x);
t = rintl(x);
if (t <= x)
return (t); /* already floor(x) */
else /* x < t case: return t-1 */
return (copysignl(t - qone, x));
}
long double
ceill(long double x) {
long double t;
if (!finitel(x))
return (x + x);
t = rintl(x);
if (t >= x) /* already ceil(x) */
return (t);
else /* t < x case: return t+1 */
return (copysignl(t + qone, x));
}
long double
aintl(long double x) {
long double t, w;
if (!finitel(x))
return (x + x);
w = fabsl(x);
t = rintl(w);
if (t <= w)
return (copysignl(t, x)); /* NaN or already aint(|x|) */
else /* |t|>|x| case */
return (copysignl(t - qone, x)); /* |t-1|*sign(x) */
}
long double
sinhl(long double x)
{
long double r, t;
if (!finitel(x))
return (x + x); /* x is INF or NaN */
r = fabsl(x);
if (r < lnovft) {
t = expm1l(r);
r = copysignl((t + t / (one + t)) * half, x);
} else {
r = copysignl(expl((r - lnovft) - lnovlo), x);
r = scalbnl(r, 16383);
}
return (r);
}
long double
anintl(long double x) {
long double t, w, z;
if (!finitel(x))
return (x + x);
w = fabsl(x);
t = rintl(w);
if (t == w)
return (copysignl(t, x));
z = t - w;
if (z > qhalf)
t = t - qone;
else if (z <= qmhalf)
t = t + qone;
return (copysignl(t, x));
}
void
sincosl(long double x, long double *s, long double *c) {
long double y[2], z = 0.0L;
int n, ix;
#if defined(__i386) || defined(__amd64)
int *px = (int *) &x;
#endif
/* trig(Inf or NaN) is NaN */
if (!finitel(x)) {
*s = *c = x - x;
return;
}
/* High word of x. */
#if defined(__i386) || defined(__amd64)
XTOI(px, ix);
#else
ix = *(int *) &x;
#endif
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3ffe9220)
*s = __k_sincosl(x, z, c);
/* argument reduction needed */
else {
n = __rem_pio2l(x, y);
switch (n & 3) {
case 0:
*s = __k_sincosl(y[0], y[1], c);
break;
case 1:
*c = -__k_sincosl(y[0], y[1], s);
break;
case 2:
*s = -__k_sincosl(y[0], y[1], c);
*c = -*c;
break;
case 3:
*c = __k_sincosl(y[0], y[1], s);
*s = -*s;
}
}
}
long double
coshl(long double x) {
long double t, w;
w = fabsl(x);
if (!finitel(w))
return (w + w); /* x is INF or NaN */
if (w < thr1) {
t = w < tinyl ? w : expm1l(w);
w = one + t;
if (w != one)
w = one + (t * t) / (w + w);
return (w);
} else if (w < thr2) {
t = expl(w);
return (half * (t + one / t));
} else if (w <= lnovftL)
return (half * expl(w));
else {
return (scalbnl(expl((w - MEP1 * ln2hi) - MEP1 * ln2lo), ME));
}
}
long double
coshl(long double x) {
long double w, t;
w = fabsl(x);
if (!finitel(w))
return (w + w); /* x is INF or NaN */
if (w < thr1) {
if (w < tinyl)
return (one + w); /* inexact+directed rounding */
t = expm1l(w);
w = one + t;
w = one + (t * t) / (w + w);
return (w);
}
if (w < thr2) {
t = expl(w);
return (half * (t + one / t));
}
if (w <= lnovft)
return (half * expl(w));
return (scalbnl(expl((w - lnovft) - lnovlo), 16383));
}
long double
atan2l(long double y, long double x) {
long double t, z;
int k, m, signy, signx;
if (x != x || y != y)
return (x + y); /* return NaN if x or y is NAN */
signy = signbitl(y);
signx = signbitl(x);
if (x == one)
return (atanl(y));
m = signy + signx + signx;
/* when y = 0 */
if (y == zero)
switch (m) {
case 0:
return (y); /* atan(+0,+anything) */
case 1:
return (y); /* atan(-0,+anything) */
case 2:
return (PI + tiny); /* atan(+0,-anything) */
case 3:
return (-PI - tiny); /* atan(-0,-anything) */
}
/* when x = 0 */
if (x == zero)
return (signy == 1 ? -PIo2 - tiny : PIo2 + tiny);
/* when x is INF */
if (!finitel(x))
if (!finitel(y)) {
switch (m) {
case 0:
return (PIo4 + tiny); /* atan(+INF,+INF) */
case 1:
return (-PIo4 - tiny); /* atan(-INF,+INF) */
case 2:
return (PI3o4 + tiny); /* atan(+INF,-INF) */
case 3:
return (-PI3o4 - tiny); /* atan(-INF,-INF) */
}
} else {
switch (m) {
case 0:
return (zero); /* atan(+...,+INF) */
case 1:
return (-zero); /* atan(-...,+INF) */
case 2:
return (PI + tiny); /* atan(+...,-INF) */
case 3:
return (-PI - tiny); /* atan(-...,-INF) */
}
}
/* when y is INF */
if (!finitel(y))
return (signy == 1 ? -PIo2 - tiny : PIo2 + tiny);
/* compute y/x */
x = fabsl(x);
y = fabsl(y);
t = PI_lo;
k = (ilogbl(y) - ilogbl(x));
if (k > 120)
z = PIo2 + half * t;
else if (m > 1 && k < -120)
z = zero;
else
z = atanl(y / x);
switch (m) {
case 0:
return (z); /* atan(+,+) */
case 1:
return (-z); /* atan(-,+) */
case 2:
return (PI - (z - t)); /* atan(+,-) */
case 3:
return ((z - t) - PI); /* atan(-,-) */
}
/* NOTREACHED */
}