long double cosl(long double x)
{
union ldshape u = {x};
unsigned n;
long double y[2], hi, lo;
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
x = u.f;
if (x < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG)
/* raise inexact if x!=0 */
return 1.0 + x;
return __cosl(x, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
return __cosl(hi, lo);
case 1:
return -__sinl(hi, lo, 1);
case 2:
return -__cosl(hi, lo);
case 3:
default:
return __sinl(hi, lo, 1);
}
}
long double sinl(long double x)
{
union ldshape u = {x};
unsigned n;
long double y[2], hi, lo;
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
if (u.f < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f);
return x;
}
return __sinl(x, 0.0, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
return __sinl(hi, lo, 1);
case 1:
return __cosl(hi, lo);
case 2:
return -__sinl(hi, lo, 1);
case 3:
default:
return -__cosl(hi, lo);
}
}
void
_CDTOD(d_complex_t *ret_val,
d_complex_t x,
_f_real16 *r)
{
_f_real16 __atan2l(_f_real16 ax, _f_real16 bx);
_f_real16 __cosl(_f_real16 ax);
_f_real16 __expl(_f_real16 ax);
_f_real16 __logl(_f_real16 ax);
_f_real16 __sinl(_f_real16 ax);
_f_real16 _CDABS(d_complex_t z);
_f_real16 y = *r;
_f_real16 one;
_f_real16 two;
if (x.real == (_f_real16) 0.0 && x.imag == (_f_real16) 0.0) {
if (y == (_f_real16) 0.0) {
ret_val->real = _DBL_NaN;
ret_val->imag = _DBL_NaN;
}
else {
ret_val->real = (_f_real16) 0.0;
ret_val->imag = (_f_real16) 0.0;
}
return;
}
one = y * __atan2l(x.imag, x.real);
two = y * __logl(_CDABS(x));
ret_val->real = __expl(two) * __cosl(one);
ret_val->imag = __expl(two) * __sinl(one);
}
void
_CDTOCD(d_complex_t *ret_val,
d_complex_t x,
d_complex_t y)
{
_f_real16 __atan2l(_f_real16 ax, _f_real16 bx);
_f_real16 __cosl(_f_real16 ax);
_f_real16 __expl(_f_real16 ax);
_f_real16 __logl(_f_real16 ax);
_f_real16 __sinl(_f_real16 ax);
_f_real16 __sqrtl(_f_real16 ax);
_f_real16 a;
_f_real16 b;
_f_real16 c;
_f_real16 d;
_f_real16 one;
_f_real16 two;
REGISTER_16 realx;
REGISTER_16 imagx;
_f_real16 loglabsx, atn2l, expltwo;
if (x.real == 0.0 && x.imag == 0.0) {
if (y.real == 0.0 && y.imag == 0.0) {
ret_val->real = _DBL_NaN;
ret_val->imag = _DBL_NaN;
}
else {
ret_val->real = (_f_real16) 0.0;
ret_val->imag = (_f_real16) 0.0;
}
return;
}
realx.f = x.real;
imagx.f = x.imag;
a = x.real;
b = x.imag;
c = y.real;
d = y.imag;
/* clear sign bit */
realx.ui[0] &= ~IEEE_128_64_SIGN_BIT;
imagx.ui[0] &= ~IEEE_128_64_SIGN_BIT;
atn2l = __atan2l(b,a);
if (realx.f > imagx.f)
loglabsx = __logl(realx.f *
__sqrtl(1.0 + (imagx.f/realx.f) * (imagx.f/realx.f)));
else
loglabsx = __logl(imagx.f *
__sqrtl(1.0 + (realx.f/imagx.f) * (realx.f/imagx.f)));
one = d * loglabsx + c * atn2l;
two = c * loglabsx - d * atn2l;
expltwo = __expl(two);
ret_val->real = expltwo * __cosl(one);
ret_val->imag = expltwo * __sinl(one);
}
void
_CDEXP(d_complex_t *ret_val,
d_complex_t z )
{
_f_real16 __expl(_f_real16 x);
_f_real16 __cosl(_f_real16 x);
_f_real16 __sinl(_f_real16 x);
ret_val->real = __expl(z.real) * __cosl(z.imag);
ret_val->imag = __expl(z.real) * __sinl(z.imag);
}
void sincosl(long double x, long double *sin, long double *cos)
{
union IEEEl2bits u;
unsigned n;
long double y[2], s, c;
u.e = x;
u.bits.sign = 0;
/* x = nan or inf */
if (u.bits.exp == 0x7fff) {
*sin = *cos = x - x;
return;
}
/* |x| < (double)pi/4 */
if (u.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (u.bits.exp < 0x3fff - 64) {
/* raise underflow if subnormal */
if (u.bits.exp == 0) FORCE_EVAL(x*0x1p-120f);
*sin = x;
/* raise inexact if x!=0 */
*cos = 1.0 + x;
return;
}
*sin = __sinl(x, 0, 0);
*cos = __cosl(x, 0);
return;
}
n = __rem_pio2l(x, y);
s = __sinl(y[0], y[1], 1);
c = __cosl(y[0], y[1]);
switch (n & 3) {
case 0:
*sin = s;
*cos = c;
break;
case 1:
*sin = c;
*cos = -s;
break;
case 2:
*sin = -s;
*cos = -c;
break;
case 3:
default:
*sin = -c;
*cos = s;
break;
}
}
void sincosl(long double x, long double *sin, long double *cos)
{
union IEEEl2bits u;
int n;
long double y[2], s, c;
u.e = x;
u.bits.sign = 0;
/* x = +-0 or subnormal */
if (!u.bits.exp) {
*sin = x;
*cos = 1.0;
return;
}
/* x = nan or inf */
if (u.bits.exp == 0x7fff) {
*sin = *cos = x - x;
return;
}
/* |x| < pi/4 */
if (u.e < M_PI_4) {
*sin = __sinl(x, 0, 0);
*cos = __cosl(x, 0);
return;
}
n = __rem_pio2l(x, y);
s = __sinl(y[0], y[1], 1);
c = __cosl(y[0], y[1]);
switch (n & 3) {
case 0:
*sin = s;
*cos = c;
break;
case 1:
*sin = c;
*cos = -s;
break;
case 2:
*sin = -s;
*cos = -c;
break;
case 3:
default:
*sin = -c;
*cos = s;
break;
}
}
static long double
lg_cospi (long double x)
{
if (x <= 0.25L)
return __cosl (M_PIl * x);
else
return __sinl (M_PIl * (0.5L - x));
}
long double cosl(long double x)
{
union IEEEl2bits z;
unsigned n;
long double y[2];
long double hi, lo;
z.e = x;
z.bits.sign = 0;
/* If x = NaN or Inf, then cos(x) = NaN. */
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64)
/* raise inexact if x!=0 */
return 1.0 + x;
return __cosl(z.e, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
hi = __cosl(hi, lo);
break;
case 1:
hi = -__sinl(hi, lo, 1);
break;
case 2:
hi = -__cosl(hi, lo);
break;
case 3:
hi = __sinl(hi, lo, 1);
break;
}
return hi;
}
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;
}
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
int64_t hx;
u_int64_t lx;
long double ret;
GET_LDOUBLE_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (hx < 0 && (u_int64_t) hx < 0xffff000000000000ULL && __rintl (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (hx == 0xffff000000000000ULL && lx == 0)
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if ((hx & 0x7fff000000000000ULL) == 0x7fff000000000000ULL)
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (x >= 1756.0L)
{
/* Overflow. */
*signgamp = 0;
return LDBL_MAX * LDBL_MAX;
}
else
{
SET_RESTORE_ROUNDL (FE_TONEAREST);
if (x > 0.0L)
{
*signgamp = 0;
int exp2_adj;
ret = gammal_positive (x, &exp2_adj);
ret = __scalbnl (ret, exp2_adj);
}
else if (x >= -LDBL_EPSILON / 4.0L)
{
*signgamp = 0;
ret = 1.0L / x;
}
else
{
long double tx = __truncl (x);
*signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1;
if (x <= -1775.0L)
/* Underflow. */
ret = LDBL_MIN * LDBL_MIN;
else
{
long double frac = tx - x;
if (frac > 0.5L)
frac = 1.0L - frac;
long double sinpix = (frac <= 0.25L
? __sinl (M_PIl * frac)
: __cosl (M_PIl * (0.5L - frac)));
int exp2_adj;
ret = M_PIl / (-x * sinpix
* gammal_positive (-x, &exp2_adj));
ret = __scalbnl (ret, -exp2_adj);
}
}
}
if (isinf (ret) && x != 0)
{
if (*signgamp < 0)
return -(-__copysignl (LDBL_MAX, ret) * LDBL_MAX);
else
return __copysignl (LDBL_MAX, ret) * LDBL_MAX;
}
else if (ret == 0)
{
if (*signgamp < 0)
return -(-__copysignl (LDBL_MIN, ret) * LDBL_MIN);
else
return __copysignl (LDBL_MIN, ret) * LDBL_MIN;
}
else
return ret;
}
_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_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;
}
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;
}
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
u_int32_t es, hx, lx;
GET_LDOUBLE_WORDS (es, hx, lx, x);
if (__glibc_unlikely (((es & 0x7fff) | hx | lx) == 0))
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (__glibc_unlikely (es == 0xffffffff && ((hx & 0x7fffffff) | lx) == 0))
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if (__glibc_unlikely ((es & 0x7fff) == 0x7fff))
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (__builtin_expect ((es & 0x8000) != 0, 0) && __rintl (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (x >= 1756.0L)
{
/* Overflow. */
*signgamp = 0;
return LDBL_MAX * LDBL_MAX;
}
else if (x > 0.0L)
{
*signgamp = 0;
int exp2_adj;
long double ret = gammal_positive (x, &exp2_adj);
return __scalbnl (ret, exp2_adj);
}
else if (x >= -LDBL_EPSILON / 4.0L)
{
*signgamp = 0;
return 1.0f / x;
}
else
{
long double tx = __truncl (x);
*signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1;
if (x <= -1766.0L)
/* Underflow. */
return LDBL_MIN * LDBL_MIN;
long double frac = tx - x;
if (frac > 0.5L)
frac = 1.0L - frac;
long double sinpix = (frac <= 0.25L
? __sinl (M_PIl * frac)
: __cosl (M_PIl * (0.5L - frac)));
int exp2_adj;
long double ret = M_PIl / (-x * sinpix
* gammal_positive (-x, &exp2_adj));
return __scalbnl (ret, -exp2_adj);
}
}
