__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;
}
int main()
{
__float128 f = -2.0Q;
f = fabsq(f);
f = expq(f);
return 0;
}
__complex128
cexpq (__complex128 z)
{
__float128 a, b;
__complex128 v;
a = REALPART (z);
b = IMAGPART (z);
COMPLEX_ASSIGN (v, cosq (b), sinq (b));
return expq (a) * v;
}
GFC_REAL_16
erfc_scaled_r16 (GFC_REAL_16 x)
{
if (x < -106.566990228185312813205074546585730Q)
{
return __builtin_infq();
}
if (x < 12)
{
/* Compute directly as ERFC_SCALED(x) = ERFC(x) * EXP(X**2).
This is not perfect, but much better than netlib. */
return erfcq(x) * expq(x * x);
}
else
{
/* Calculate ERFC_SCALED(x) using a power series in 1/x:
ERFC_SCALED(x) = 1 / (x * sqrt(pi))
* (1 + Sum_n (-1)**n * (1 * 3 * 5 * ... * (2n-1))
/ (2 * x**2)**n)
*/
GFC_REAL_16 sum = 0, oldsum;
GFC_REAL_16 inv2x2 = 1 / (2 * x * x);
GFC_REAL_16 fac = 1;
int n = 1;
while (n < 200)
{
fac *= - (2*n - 1) * inv2x2;
oldsum = sum;
sum += fac;
if (sum == oldsum)
break;
n++;
}
return (1 + sum) / x * (M_2_SQRTPIq / 2);
}
}
inline void eval_exp(float128_backend& result, const float128_backend& arg)
{
result.value() = expq(arg.value());
}
__float128 weight(__float128 t) {
if(t<=0.Q || t>=1.Q) {
return 0.Q;
}
return expq((1.Q)/(t*(t-1.Q)));
}
__float128
expm1q (__float128 x)
{
__float128 px, qx, xx;
int32_t ix, sign;
ieee854_float128 u;
int k;
/* Detect infinity and NaN. */
u.value = x;
ix = u.words32.w0;
sign = ix & 0x80000000;
ix &= 0x7fffffff;
if (!sign && ix >= 0x40060000)
{
/* If num is positive and exp >= 6 use plain exp. */
return expq (x);
}
if (ix >= 0x7fff0000)
{
/* Infinity. */
if (((ix & 0xffff) | u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
{
if (sign)
return -1.0Q;
else
return x;
}
/* NaN. No invalid exception. */
return x;
}
/* expm1(+- 0) = +- 0. */
if ((ix == 0) && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
return x;
/* Overflow. */
if (x > maxlog)
{
errno = ERANGE;
return (HUGE_VALQ * HUGE_VALQ);
}
/* Minimum value. */
if (x < minarg)
return (4.0/HUGE_VALQ - 1.0Q);
/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
xx = C1 + C2; /* ln 2. */
px = floorq (0.5 + x / xx);
k = px;
/* remainder times ln 2 */
x -= px * C1;
x -= px * C2;
/* Approximate exp(remainder ln 2). */
px = (((((((P7 * x
+ P6) * x
+ P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x;
qx = (((((((x
+ Q7) * x
+ Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
xx = x * x;
qx = x + (0.5 * xx + xx * px / qx);
/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
We have qx = exp(remainder ln 2) - 1, so
exp(x) - 1 = 2^k (qx + 1) - 1
= 2^k qx + 2^k - 1. */
px = ldexpq (1.0Q, k);
x = px * qx + (px - 1.0);
return x;
}
double weight(double t) {
if(t<=0 || t>=1) { return 0; }
return expq((1)/(t*(t-1)));
//return t*(1-t);
}
__complex128
ctanhq (__complex128 x)
{
__complex128 res;
if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
{
if (__quadmath_isinf_nsq (__real__ x))
{
__real__ res = copysignq (1.0Q, __real__ x);
__imag__ res = copysignq (0.0Q, __imag__ x);
}
else if (__imag__ x == 0.0Q)
{
res = x;
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
#ifdef HAVE_FENV_H
if (__quadmath_isinf_nsq (__imag__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
__float128 sinix, cosix;
__float128 den;
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
int icls = fpclassifyq (__imag__ x);
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
{
sincosq (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0Q;
}
if (fabsq (__real__ x) > t)
{
/* Avoid intermediate overflow when the imaginary part of
the result may be subnormal. Ignoring negligible terms,
the real part is +/- 1, the imaginary part is
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
__float128 exp_2t = expq (2 * t);
__real__ res = copysignq (1.0, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsq (__real__ x);
__real__ x -= t;
__imag__ res /= exp_2t;
if (__real__ x > t)
{
/* Underflow (original real part of x has absolute value
> 2t). */
__imag__ res /= exp_2t;
}
else
__imag__ res /= expq (2 * __real__ x);
}
else
{
__float128 sinhrx, coshrx;
if (fabsq (__real__ x) > FLT128_MIN)
{
sinhrx = sinhq (__real__ x);
coshrx = coshq (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0Q;
}
if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
}
}
return res;
}