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_lgammal_r (long double x, int *signgamp)
{
long double p, q, w, z, nx;
int i, nn;
*signgamp = 1;
if (! __finitel (x))
return x * x;
if (x == 0.0L)
{
if (__signbitl (x))
*signgamp = -1;
}
if (x < 0.0L)
{
q = -x;
p = __floorl (q);
if (p == q)
return (one / (p - p));
i = p;
if ((i & 1) == 0)
*signgamp = -1;
else
*signgamp = 1;
if (q < 0x1p-120L)
return -__logl (q);
z = q - p;
if (z > 0.5L)
{
p += 1.0L;
z = p - q;
}
z = q * __sinl (PIL * z);
w = __ieee754_lgammal_r (q, &i);
z = __logl (PIL / z) - w;
return (z);
}
if (x < 13.5L)
{
p = 0.0L;
nx = __floorl (x + 0.5L);
nn = nx;
switch (nn)
{
case 0:
/* log gamma (x + 1) = log(x) + log gamma(x) */
if (x < 0x1p-120L)
return -__logl (x);
else if (x <= 0.125)
{
p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1);
}
else if (x <= 0.375)
{
z = x - 0.25L;
p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
p += lgam1r25b;
p += lgam1r25a;
}
else if (x <= 0.625)
{
z = x + (1.0L - x0a);
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
else if (x <= 0.875)
{
z = x - 0.75L;
p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
p += lgam1r75b;
p += lgam1r75a;
}
else
{
z = x - 1.0L;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
p = p - __logl (x);
break;
case 1:
if (x < 0.875L)
{
if (x <= 0.625)
{
z = x + (1.0L - x0a);
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
else if (x <= 0.875)
{
z = x - 0.75L;
p = z * neval (z, RN1r75, NRN1r75)
/ deval (z, RD1r75, NRD1r75);
p += lgam1r75b;
p += lgam1r75a;
}
else
{
z = x - 1.0L;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
p = p - __logl (x);
}
else if (x < 1.0L)
{
z = x - 1.0L;
p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9);
}
else if (x == 1.0L)
p = 0.0L;
else if (x <= 1.125L)
{
z = x - 1.0L;
p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1);
}
else if (x <= 1.375)
{
z = x - 1.25L;
p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
p += lgam1r25b;
p += lgam1r25a;
}
else
{
/* 1.375 <= x+x0 <= 1.625 */
z = x - x0a;
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
break;
case 2:
if (x < 1.625L)
{
z = x - x0a;
z = z - x0b;
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
p = p * z * z;
p = p + y0b;
p = p + y0a;
}
else if (x < 1.875L)
{
z = x - 1.75L;
p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
p += lgam1r75b;
p += lgam1r75a;
}
else if (x == 2.0L)
p = 0.0L;
else if (x < 2.375L)
{
z = x - 2.0L;
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
}
else
{
z = x - 2.5L;
p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
p += lgam2r5b;
p += lgam2r5a;
}
break;
case 3:
if (x < 2.75)
{
z = x - 2.5L;
p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
p += lgam2r5b;
p += lgam2r5a;
}
else
{
z = x - 3.0L;
p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3);
p += lgam3b;
p += lgam3a;
}
break;
case 4:
z = x - 4.0L;
p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4);
p += lgam4b;
p += lgam4a;
break;
case 5:
z = x - 5.0L;
p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5);
p += lgam5b;
p += lgam5a;
break;
case 6:
z = x - 6.0L;
p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6);
p += lgam6b;
p += lgam6a;
break;
case 7:
z = x - 7.0L;
p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7);
p += lgam7b;
p += lgam7a;
break;
case 8:
z = x - 8.0L;
p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8);
p += lgam8b;
p += lgam8a;
break;
case 9:
z = x - 9.0L;
p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9);
p += lgam9b;
p += lgam9a;
break;
case 10:
z = x - 10.0L;
p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10);
p += lgam10b;
p += lgam10a;
break;
case 11:
z = x - 11.0L;
p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11);
p += lgam11b;
p += lgam11a;
break;
case 12:
z = x - 12.0L;
p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12);
p += lgam12b;
p += lgam12a;
break;
case 13:
z = x - 13.0L;
p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13);
p += lgam13b;
p += lgam13a;
break;
}
return p;
}
if (x > MAXLGM)
return (*signgamp * huge * huge);
q = ls2pi - x;
q = (x - 0.5L) * __logl (x) + q;
if (x > 1.0e18L)
return (q);
p = 1.0L / (x * x);
q += neval (p, RASY, NRASY) / x;
return (q);
}
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;
}
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);
}
}
