long double __asinhl(long double x)
{
long double t,w;
int64_t hx,ix;
double xhi;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (hx, xhi);
ix = hx&0x7fffffffffffffffLL;
if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */
if(ix< 0x3c70000000000000LL) { /* |x|<2**-56 */
math_check_force_underflow (x);
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x4370000000000000LL) { /* |x| > 2**56 */
w = __ieee754_logl(fabsl(x))+ln2;
} else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */
t = fabs(x);
w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
} else { /* 2.0 >= |x| >= 2**-56 */
t = x*x;
w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
}
if(hx>0) return w; else return -w;
}
long double
__ieee754_acoshl(long double x)
{
long double t;
int64_t hx;
uint64_t lx;
double xhi, xlo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
EXTRACT_WORDS64 (lx, xlo);
if(hx<0x3ff0000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x41b0000000000000LL) { /* x > 2**28 */
if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */
} else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t));
}
}
long double
sqrtl(long double x) /* wrapper sqrtl */
{
#ifdef _IEEE_LIBM
return __ieee754_sqrtl(x);
#else
long double z;
z = __ieee754_sqrtl(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(x<0.0) {
return __kernel_standard(x,x,226); /* sqrtl(negative) */
} else
return z;
#endif
}
/* wrapper sqrtl */
long double
__sqrtl (long double x)
{
if (__builtin_expect (x < 0.0L, 0) && _LIB_VERSION != _IEEE_)
return __kernel_standard (x, x, 226); /* sqrt(negative) */
return __ieee754_sqrtl (x);
}
long double __asinhl(long double x)
{
long double t,w;
int64_t hx,ix;
GET_LDOUBLE_MSW64(hx,x);
ix = hx&0x7fffffffffffffffLL;
if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */
if(ix< 0x3e20000000000000LL) { /* |x|<2**-29 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x41b0000000000000LL) { /* |x| > 2**28 */
w = __ieee754_logl(fabs(x))+ln2;
} else if (ix>0x4000000000000000LL) { /* 2**28 > |x| > 2.0 */
t = fabs(x);
w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-29 */
t = x*x;
w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
}
if(hx>0) return w; else return -w;
}
long double
__ieee754_acoshl(long double x)
{
long double t;
u_int64_t lx;
int64_t hx;
GET_LDOUBLE_WORDS64(hx,lx,x);
if(hx<0x3fff000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
} else if(((hx-0x3fff000000000000LL)|lx)==0) {
return 0.0L; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_logl(2.0L*x-one/(x+__ieee754_sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
return __log1pl(t+__sqrtl(2.0L*t+t*t));
}
}
long double
__ieee754_asinl (long double x)
{
long double t, w, p, q, c, r, s;
int32_t ix, sign, flag;
ieee854_long_double_shape_type u;
flag = 0;
u.value = x;
sign = u.parts32.w0;
ix = sign & 0x7fffffff;
u.parts32.w0 = ix; /* |x| */
if (ix >= 0x3fff0000) /* |x|>= 1 */
{
if (ix == 0x3fff0000
&& (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0)
/* asin(1)=+-pi/2 with inexact */
return x * pio2_hi + x * pio2_lo;
return (x - x) / (x - x); /* asin(|x|>1) is NaN */
}
else if (ix < 0x3ffe0000) /* |x| < 0.5 */
{
if (ix < 0x3fc60000) /* |x| < 2**-57 */
{
if (huge + x > one)
return x; /* return x with inexact if x!=0 */
}
else
{
t = x * x;
/* Mark to use pS, qS later on. */
flag = 1;
}
}
else if (ix < 0x3ffe4000) /* 0.625 */
{
t = u.value - 0.5625;
p = ((((((((((rS10 * t
+ rS9) * t
+ rS8) * t
+ rS7) * t
+ rS6) * t
+ rS5) * t
+ rS4) * t
+ rS3) * t
+ rS2) * t
+ rS1) * t
+ rS0) * t;
q = ((((((((( t
+ sS9) * t
+ sS8) * t
+ sS7) * t
+ sS6) * t
+ sS5) * t
+ sS4) * t
+ sS3) * t
+ sS2) * t
+ sS1) * t
+ sS0;
t = asinr5625 + p / q;
if ((sign & 0x80000000) == 0)
return t;
else
return -t;
}
else
{
/* 1 > |x| >= 0.625 */
w = one - u.value;
t = w * 0.5;
}
p = (((((((((pS9 * t
+ pS8) * t
+ pS7) * t
+ pS6) * t
+ pS5) * t
+ pS4) * t
+ pS3) * t
+ pS2) * t
+ pS1) * t
+ pS0) * t;
q = (((((((( t
+ qS8) * t
+ qS7) * t
+ qS6) * t
+ qS5) * t
+ qS4) * t
+ qS3) * t
+ qS2) * t
+ qS1) * t
+ qS0;
if (flag) /* 2^-57 < |x| < 0.5 */
{
w = p / q;
return x + x * w;
}
s = __ieee754_sqrtl (t);
if (ix >= 0x3ffef333) /* |x| > 0.975 */
{
w = p / q;
t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
}
else
{
u.value = s;
u.parts32.w3 = 0;
u.parts32.w2 = 0;
w = u.value;
c = (t - w * w) / (s + w);
r = p / q;
p = 2.0 * s * r - (pio2_lo - 2.0 * c);
q = pio4_hi - 2.0 * w;
t = pio4_hi - (p - q);
}
if ((sign & 0x80000000) == 0)
return t;
else
return -t;
}
long double
__ieee754_y1l (long double x)
{
long double xx, xinv, z, p, q, c, s, cc, ss;
if (! __finitel (x))
{
if (x != x)
return x;
else
return 0.0L;
}
if (x <= 0.0L)
{
if (x < 0.0L)
return (zero / (zero * x));
return -HUGE_VALL + x;
}
xx = fabsl (x);
if (xx <= 2.0L)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = xx * neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
p = -TWOOPI / xx + p;
p = TWOOPI * __ieee754_logl (x) * __ieee754_j1l (x) + p;
return p;
}
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0L + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx);
return z;
}
__complex__ long double
__kernel_casinhl (__complex__ long double x, int adj)
{
__complex__ long double res;
long double rx, ix;
__complex__ long double y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsl (__real__ x);
ix = fabsl (__imag__ x);
if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
long double t = __real__ y;
__real__ y = __copysignl (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogl (y);
__real__ res += M_LN2l;
}
else if (rx >= 0.5L && ix < LDBL_EPSILON / 8.0L)
{
long double s = __ieee754_hypotl (1.0L, rx);
__real__ res = __ieee754_logl (rx + s);
if (adj)
__imag__ res = __ieee754_atan2l (s, __imag__ x);
else
__imag__ res = __ieee754_atan2l (ix, s);
}
else if (rx < LDBL_EPSILON / 8.0L && ix >= 1.5L)
{
long double s = __ieee754_sqrtl ((ix + 1.0L) * (ix - 1.0L));
__real__ res = __ieee754_logl (ix + s);
if (adj)
__imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
else
__imag__ res = __ieee754_atan2l (s, rx);
}
else if (ix > 1.0L && ix < 1.5L && rx < 0.5L)
{
if (rx < LDBL_EPSILON * LDBL_EPSILON)
{
long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
long double s = __ieee754_sqrtl (ix2m1);
__real__ res = __log1pl (2.0L * (ix2m1 + ix * s)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
else
__imag__ res = __ieee754_atan2l (s, rx);
}
else
{
long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
long double rx2 = rx * rx;
long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
long double d = __ieee754_sqrtl (ix2m1 * ix2m1 + f);
long double dp = d + ix2m1;
long double dm = f / dp;
long double r1 = __ieee754_sqrtl ((dm + rx2) / 2.0L);
long double r2 = rx * ix / r1;
__real__ res
= __log1pl (rx2 + dp + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx + r1, __copysignl (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
}
}
else if (ix == 1.0L && rx < 0.5L)
{
if (rx < LDBL_EPSILON / 8.0L)
{
__real__ res = __log1pl (2.0L * (rx + __ieee754_sqrtl (rx))) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (__ieee754_sqrtl (rx),
__copysignl (1.0L, __imag__ x));
else
__imag__ res = __ieee754_atan2l (1.0L, __ieee754_sqrtl (rx));
}
else
{
long double d = rx * __ieee754_sqrtl (4.0L + rx * rx);
long double s1 = __ieee754_sqrtl ((d + rx * rx) / 2.0L);
long double s2 = __ieee754_sqrtl ((d - rx * rx) / 2.0L);
__real__ res = __log1pl (rx * rx + d + 2.0L * (rx * s1 + s2)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx + s1,
__copysignl (1.0L + s2,
__imag__ x));
else
__imag__ res = __ieee754_atan2l (1.0L + s2, rx + s1);
}
}
else if (ix < 1.0L && rx < 0.5L)
{
if (ix >= LDBL_EPSILON)
{
if (rx < LDBL_EPSILON * LDBL_EPSILON)
{
long double onemix2 = (1.0L + ix) * (1.0L - ix);
long double s = __ieee754_sqrtl (onemix2);
__real__ res = __log1pl (2.0L * rx / s) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (s, __imag__ x);
else
__imag__ res = __ieee754_atan2l (ix, s);
}
else
{
long double onemix2 = (1.0L + ix) * (1.0L - ix);
long double rx2 = rx * rx;
long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
long double d = __ieee754_sqrtl (onemix2 * onemix2 + f);
long double dp = d + onemix2;
long double dm = f / dp;
long double r1 = __ieee754_sqrtl ((dp + rx2) / 2.0L);
long double r2 = rx * ix / r1;
__real__ res
= __log1pl (rx2 + dm + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx + r1,
__copysignl (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
}
}
else
{
long double s = __ieee754_hypotl (1.0L, rx);
__real__ res = __log1pl (2.0L * rx * (rx + s)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (s, __imag__ x);
else
__imag__ res = __ieee754_atan2l (ix, s);
}
if (__real__ res < LDBL_MIN)
{
volatile long double force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0L;
__imag__ y = 2.0L * rx * ix;
y = __csqrtl (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
long double t = __real__ y;
__real__ y = __copysignl (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogl (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = __copysignl (__real__ res, __real__ x);
__imag__ res = __copysignl (__imag__ res, (adj ? 1.0L : __imag__ x));
return res;
}
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);
}
}
_Float128
__ieee754_y0l(_Float128 x)
{
_Float128 xx, xinv, z, p, q, c, s, cc, ss;
if (! isfinite (x))
{
if (x != x)
return x + x;
else
return 0;
}
if (x <= 0)
{
if (x < 0)
return (zero / (zero * x));
return -HUGE_VALL + x;
}
xx = fabsl (x);
if (xx <= 0x1p-57)
return U0 + TWOOPI * __ieee754_logl (x);
if (xx <= 2)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
p = TWOOPI * __ieee754_logl (x) * __ieee754_j0l (x) + p;
return p;
}
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (x, &s, &c);
ss = s - c;
cc = s + c;
if (xx <= LDBL_MAX / 2)
{
z = -__cosl (x + x);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
}
if (xx > L(0x1p256))
return ONEOSQPI * ss / __ieee754_sqrtl (x);
xinv = 1 / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1 + z * p;
q = z * xinv * q;
q = q - L(0.125) * xinv;
z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x);
return z;
}
long double __ieee754_hypotl(long double x, long double y)
{
long double a,b,t1,t2,y1,y2,w;
u_int32_t j,k,ea,eb;
GET_LDOUBLE_EXP(ea,x);
ea &= 0x7fff;
GET_LDOUBLE_EXP(eb,y);
eb &= 0x7fff;
if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
k=0;
if(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */
if(ea == 0x7fff) { /* Inf or NaN */
u_int32_t exp __attribute__ ((unused));
u_int32_t high,low;
w = a+b; /* for sNaN */
GET_LDOUBLE_WORDS(exp,high,low,a);
if(((high&0x7fffffff)|low)==0) w = a;
GET_LDOUBLE_WORDS(exp,high,low,b);
if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ea -= 0x2580; eb -= 0x2580; k += 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
if(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */
if(eb == 0) { /* subnormal b or 0 */
u_int32_t exp __attribute__ ((unused));
u_int32_t high,low;
GET_LDOUBLE_WORDS(exp,high,low,b);
if((high|low)==0) return a;
SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
GET_LDOUBLE_EXP (ea, a);
GET_LDOUBLE_EXP (eb, b);
if (eb > ea)
{
t1 = a;
a = b;
b = t1;
j = ea;
ea = eb;
eb = j;
}
} else { /* scale a and b by 2^9600 */
ea += 0x2580; /* a *= 2^9600 */
eb += 0x2580; /* b *= 2^9600 */
k -= 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
u_int32_t high;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea,high,0);
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
u_int32_t high;
GET_LDOUBLE_MSW(high,b);
a = a+a;
SET_LDOUBLE_WORDS(y1,eb,high,0);
y2 = b - y1;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea+1,high,0);
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int32_t exp;
t1 = 1.0;
GET_LDOUBLE_EXP(exp,t1);
SET_LDOUBLE_EXP(t1,exp+k);
w *= t1;
math_check_force_underflow_nonneg (w);
return w;
} else return w;
}
long double
__ieee754_j0l (long double x)
{
long double xx, xinv, z, p, q, c, s, cc, ss;
if (! isfinite (x))
{
if (x != x)
return x;
else
return 0.0L;
}
if (x == 0.0L)
return 1.0L;
xx = fabsl (x);
if (xx <= 2.0L)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = z * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
p -= 0.25L * z;
p += 1.0L;
return p;
}
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = s - c;
cc = s + c;
if (xx <= LDBL_MAX / 2.0L)
{
z = -__cosl (xx + xx);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
}
if (xx > 0x1p256L)
return ONEOSQPI * cc / __ieee754_sqrtl (xx);
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0L + z * p;
q = z * xinv * q;
q = q - 0.125L * xinv;
z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
return z;
}
__complex__ long double
__csqrtl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nanl ("") : 0;
__imag__ res = __copysignl (HUGE_VALL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nanl ("") : __copysignl (0.0, __imag__ x));
}
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else
{
if (__builtin_expect (icls == FP_ZERO, 0))
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysignl (__ieee754_sqrtl (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabsl (__ieee754_sqrtl (__real__ x));
__imag__ res = __copysignl (0.0, __imag__ x);
}
}
else if (__builtin_expect (rcls == FP_ZERO, 0))
{
long double r = __ieee754_sqrtl (0.5 * fabsl (__imag__ x));
__real__ res = r;
__imag__ res = __copysignl (r, __imag__ x);
}
else
{
long double d, r, s;
d = __ieee754_hypotl (__real__ x, __imag__ x);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
r = __ieee754_sqrtl (0.5L * d + 0.5L * __real__ x);
s = (0.5L * __imag__ x) / r;
}
else
{
s = __ieee754_sqrtl (0.5L * d - 0.5L * __real__ x);
r = fabsl ((0.5L * __imag__ x) / s);
}
__real__ res = r;
__imag__ res = __copysignl (s, __imag__ x);
}
}
return res;
}
long double
__ieee754_hypotl(long double x, long double y)
{
long double a,b,t1,t2,y1,y2,w;
int64_t j,k,ha,hb;
GET_LDOUBLE_MSW64(ha,x);
ha &= 0x7fffffffffffffffLL;
GET_LDOUBLE_MSW64(hb,y);
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_LDOUBLE_MSW64(a,ha); /* a <- |a| */
SET_LDOUBLE_MSW64(b,hb); /* b <- |b| */
if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
k=0;
if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
u_int64_t low;
w = a+b; /* for sNaN */
GET_LDOUBLE_LSW64(low,a);
if(((ha&0xffffffffffffLL)|low)==0) w = a;
GET_LDOUBLE_LSW64(low,b);
if(((hb^0x7fff000000000000LL)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ha -= 0x2580000000000000LL;
hb -= 0x2580000000000000LL; k += 9600;
SET_LDOUBLE_MSW64(a,ha);
SET_LDOUBLE_MSW64(b,hb);
}
if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
u_int64_t low;
GET_LDOUBLE_LSW64(low,b);
if((hb|low)==0) return a;
t1=0;
SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
GET_LDOUBLE_MSW64 (ha, a);
GET_LDOUBLE_MSW64 (hb, b);
if (hb > ha)
{
t1 = a;
a = b;
b = t1;
j = ha;
ha = hb;
hb = j;
}
} else { /* scale a and b by 2^9600 */
ha += 0x2580000000000000LL; /* a *= 2^9600 */
hb += 0x2580000000000000LL; /* b *= 2^9600 */
k -= 9600;
SET_LDOUBLE_MSW64(a,ha);
SET_LDOUBLE_MSW64(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
SET_LDOUBLE_MSW64(t1,ha);
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
SET_LDOUBLE_MSW64(y1,hb);
y2 = b - y1;
t1 = 0;
SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL);
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int64_t high;
t1 = 1.0L;
GET_LDOUBLE_MSW64(high,t1);
SET_LDOUBLE_MSW64(t1,high+(k<<48));
return t1*w;
} else return w;
}
long double
__ieee754_j1l (long double x)
{
long double xx, xinv, z, p, q, c, s, cc, ss;
if (! isfinite (x))
{
if (x != x)
return x;
else
return 0.0L;
}
if (x == 0.0L)
return x;
xx = fabsl (x);
if (xx <= 0x1p-58L)
{
long double ret = x * 0.5L;
if (fabsl (ret) < LDBL_MIN)
{
long double force_underflow = ret * ret;
math_force_eval (force_underflow);
}
return ret;
}
if (xx <= 2.0L)
{
/* 0 <= x <= 2 */
z = xx * xx;
p = xx * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
p += 0.5L * xx;
if (x < 0)
p = -p;
return p;
}
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
if (xx <= LDBL_MAX / 2.0L)
{
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
}
if (xx > 0x1p256L)
{
z = ONEOSQPI * cc / __ieee754_sqrtl (xx);
if (x < 0)
z = -z;
return z;
}
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
{
if (xinv <= 0.125)
{
if (xinv <= 0.0625)
{
p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
}
else
{
p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
}
}
else if (xinv <= 0.1875)
{
p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
}
else
{
p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
}
} /* .25 */
else /* if (xinv <= 0.5) */
{
if (xinv <= 0.375)
{
if (xinv <= 0.3125)
{
p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
}
else
{
p = neval (z, P2r7_3r2N, NP2r7_3r2N)
/ deval (z, P2r7_3r2D, NP2r7_3r2D);
q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
/ deval (z, Q2r7_3r2D, NQ2r7_3r2D);
}
}
else if (xinv <= 0.4375)
{
p = neval (z, P2r3_2r7N, NP2r3_2r7N)
/ deval (z, P2r3_2r7D, NP2r3_2r7D);
q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
/ deval (z, Q2r3_2r7D, NQ2r3_2r7D);
}
else
{
p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
}
}
p = 1.0L + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
if (x < 0)
z = -z;
return z;
}
