tFloat Ugci(tFloat s1, tFloat s2, tFloat q, tFloat pu, tFloat pl, tFloat Fs)
{
if(pu<pl)
return Fs*fabsq(s1-s2)/(powq(q,pu)-1.0q);
else
return Fs*fabsq(s1-s2)/(powq(q,pl)-1.0q);
}
tFloat Residual(int n, tFloat *T, tFloat **eq)
{
tFloat r = 0.0q;
r += fabsq(eq[0][2]*T[1] + eq[0][2] - eq[0][0]*T[0]);
for(int i=1; i<n-1; i++)
r += fabsq(eq[i][1]*T[i-1] + eq[i][2]*T[i+1] + eq[i][2] - eq[i][0]*T[i]);
r+= fabsq(eq[n-1][1]*T[n-2] + eq[n-1][2] - eq[n-1][0]*T[n-1]);
return r;
}
int main()
{
__float128 f = -2.0Q;
f = fabsq(f);
return 0;
}
/* Square root algorithm from glibc. */
__complex128
csqrtq (__complex128 z)
{
__float128 re = REALPART(z), im = IMAGPART(z);
__complex128 v;
if (im == 0)
{
if (re < 0)
{
COMPLEX_ASSIGN (v, 0, copysignq (sqrtq (-re), im));
}
else
{
COMPLEX_ASSIGN (v, fabsq (sqrtq (re)), copysignq (0, im));
}
}
else if (re == 0)
{
__float128 r = sqrtq (0.5 * fabsq (im));
COMPLEX_ASSIGN (v, r, copysignq (r, im));
}
else
{
__float128 d = hypotq (re, im);
__float128 r, s;
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (re > 0)
r = sqrtq (0.5 * d + 0.5 * re), s = (0.5 * im) / r;
else
s = sqrtq (0.5 * d - 0.5 * re), r = fabsq ((0.5 * im) / s);
COMPLEX_ASSIGN (v, r, copysignq (s, im));
}
return v;
}
inline __float128 abs( __float128 x )
{
return fabsq( x );
}
inline void eval_fabs(float128_backend& result, const float128_backend& arg)
{
result.value() = fabsq(arg.value());
}
__float128
log2q (__float128 x)
{
__float128 z;
__float128 y;
int e;
int64_t hx, lx;
/* Test for domain */
GET_FLT128_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
return (-1.0Q / fabsq (x)); /* log2l(+-0)=-inf */
if (hx < 0)
return (x - x) / (x - x);
if (hx >= 0x7fff000000000000LL)
return (x + x);
if (x == 1.0Q)
return 0.0Q;
/* separate mantissa from exponent */
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = frexpq (x, &e);
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if ((e > 2) || (e < -2))
{
if (x < SQRTH)
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5Q;
y = 0.5Q * z + 0.5Q;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5Q;
z -= 0.5Q;
y = 0.5Q * x + 0.5Q;
}
x = z / y;
z = x * x;
y = x * (z * neval (z, R, 5) / deval (z, S, 5));
goto done;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH)
{
e -= 1;
x = 2.0 * x - 1.0Q; /* 2x - 1 */
}
else
{
x = x - 1.0Q;
}
z = x * x;
y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
y = y - 0.5 * z;
done:
/* Multiply log of fraction by log2(e)
* and base 2 exponent by 1
*/
z = y * LOG2EA;
z += x * LOG2EA;
z += y;
z += x;
z += e;
return (z);
}
__float128
remquoq (__float128 x, __float128 y, int *quo)
{
int64_t hx,hy;
uint64_t sx,lx,ly,qs;
int cquo;
GET_FLT128_WORDS64 (hx, lx, x);
GET_FLT128_WORDS64 (hy, ly, y);
sx = hx & 0x8000000000000000ULL;
qs = sx ^ (hy & 0x8000000000000000ULL);
hy &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* Purge off exception values. */
if ((hy | ly) == 0)
return (x * y) / (x * y); /* y = 0 */
if ((hx >= 0x7fff000000000000LL) /* x not finite */
|| ((hy >= 0x7fff000000000000LL) /* y is NaN */
&& (((hy - 0x7fff000000000000LL) | ly) != 0)))
return (x * y) / (x * y);
if (hy <= 0x7ffbffffffffffffLL)
x = fmodq (x, 8 * y); /* now x < 8y */
if (((hx - hy) | (lx - ly)) == 0)
{
*quo = qs ? -1 : 1;
return zero * x;
}
x = fabsq (x);
y = fabsq (y);
cquo = 0;
if (hy <= 0x7ffcffffffffffffLL && x >= 4 * y)
{
x -= 4 * y;
cquo += 4;
}
if (hy <= 0x7ffdffffffffffffLL && x >= 2 * y)
{
x -= 2 * y;
cquo += 2;
}
if (hy < 0x0002000000000000LL)
{
if (x + x > y)
{
x -= y;
++cquo;
if (x + x >= y)
{
x -= y;
++cquo;
}
}
}
else
{
__float128 y_half = 0.5Q * y;
if (x > y_half)
{
x -= y;
++cquo;
if (x >= y_half)
{
x -= y;
++cquo;
}
}
}
*quo = qs ? -cquo : cquo;
/* Ensure correct sign of zero result in round-downward mode. */
if (x == 0.0Q)
x = 0.0Q;
if (sx)
x = -x;
return x;
}
__complex128
cacoshq (__complex128 x)
{
__complex128 res;
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)
{
if (icls == QUADFP_INFINITE)
{
__real__ res = HUGE_VALQ;
if (rcls == QUADFP_NAN)
__imag__ res = nanq ("");
else
__imag__ res = copysignq ((rcls == QUADFP_INFINITE
? (__real__ x < 0.0
? M_PIq - M_PI_4q : M_PI_4q)
: M_PI_2q), __imag__ x);
}
else if (rcls == QUADFP_INFINITE)
{
__real__ res = HUGE_VALQ;
if (icls >= QUADFP_ZERO)
__imag__ res = copysignq (signbitq (__real__ x) ? M_PIq : 0.0,
__imag__ x);
else
__imag__ res = nanq ("");
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
}
}
else if (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)
{
__real__ res = 0.0;
__imag__ res = copysignq (M_PI_2q, __imag__ x);
}
/* The factor 16 is just a guess. */
else if (16.0Q * fabsq (__imag__ x) < fabsq (__real__ x))
{
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0Q * clogq (csqrtq ((x + 1.0Q) / 2.0Q)
+ csqrtq ((x - 1.0Q) / 2.0Q));
if (signbitq (__real__ res))
__real__ res = 0.0Q;
}
else
{
__complex128 y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = csqrtq (y);
if (signbitq (x))
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = clogq (y);
}
return res;
}
__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;
}
static __float128
__quadmath_kernel_tanq (__float128 x, __float128 y, int iy)
{
__float128 z, r, v, w, s;
int32_t ix, sign = 1;
ieee854_float128 u, u1;
u.value = x;
ix = u.words32.w0 & 0x7fffffff;
if (ix < 0x3fc60000) /* x < 2**-57 */
{
if ((int) x == 0)
{ /* generate inexact */
if ((ix | u.words32.w1 | u.words32.w2 | u.words32.w3
| (iy + 1)) == 0)
return one / fabsq (x);
else
return (iy == 1) ? x : -one / x;
}
}
if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */
{
if ((u.words32.w0 & 0x80000000) != 0)
{
x = -x;
y = -y;
sign = -1;
}
else
sign = 1;
z = pio4hi - x;
w = pio4lo - y;
x = z + w;
y = 0.0;
}
z = x * x;
r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
r = r / v;
s = z * x;
r = y + z * (s * r + y);
r += TH * s;
w = x + r;
if (ix >= 0x3ffe5942)
{
v = (__float128) iy;
w = (v - 2.0Q * (x - (w * w / (w + v) - r)));
if (sign < 0)
w = -w;
return w;
}
if (iy == 1)
return w;
else
{ /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
u1.value = w;
u1.words32.w2 = 0;
u1.words32.w3 = 0;
v = r - (u1.value - x); /* u1+v = r+x */
z = -1.0 / w;
u.value = z;
u.words32.w2 = 0;
u.words32.w3 = 0;
s = 1.0 + u.value * u1.value;
return u.value + z * (s + u.value * v);
}
}