inline T asymptotic_bessel_j_large_x_2(T v, T x)
{
// See A&S 9.2.19.
BOOST_MATH_STD_USING
// Get the phase and amplitude:
T ampl = asymptotic_bessel_amplitude(v, x);
T phase = asymptotic_bessel_phase_mx(v, x);
BOOST_MATH_INSTRUMENT_VARIABLE(ampl);
BOOST_MATH_INSTRUMENT_VARIABLE(phase);
//
// Calculate the sine of the phase, using
// sine/cosine addition rules to factor in
// the x - PI(v/2 + 1/4) term not added to the
// phase when we calculated it.
//
BOOST_MATH_INSTRUMENT_CODE(cos(phase));
BOOST_MATH_INSTRUMENT_CODE(cos(x));
BOOST_MATH_INSTRUMENT_CODE(sin(phase));
BOOST_MATH_INSTRUMENT_CODE(sin(x));
T cx = cos(x);
T sx = sin(x);
T ci = cos_pi(v / 2 + 0.25f);
T si = sin_pi(v / 2 + 0.25f);
T sin_phase = cos(phase) * (cx * ci + sx * si) - sin(phase) * (sx * ci - cx * si);
BOOST_MATH_INSTRUMENT_VARIABLE(sin_phase);
return sin_phase * ampl;
}
static npy_cdouble
rotate(npy_cdouble z, double v)
{
npy_cdouble w;
double c = cos_pi(v);
double s = sin_pi(v);
w.real = z.real*c - z.imag*s;
w.imag = z.real*s + z.imag*c;
return w;
}
static npy_cdouble
rotate_jy(npy_cdouble j, npy_cdouble y, double v)
{
npy_cdouble w;
double c = cos_pi(v);
double s = sin_pi(v);
w.real = j.real * c - y.real * s;
w.imag = j.imag * c - y.imag * s;
return w;
}
double
__ieee754_lgamma_r(double x, int *signgamp)
{
double t,y,z,nadj,p,p1,p2,p3,q,r,w;
int i,hx,lx,ix;
EXTRACT_WORDS(hx,lx,x);
/* purge off +-inf, NaN, +-0, and negative arguments */
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x*x;
if((ix|lx)==0) return one/zero;
if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
if(hx<0) {
*signgamp = -1;
return -__ieee754_log(-x);
} else return -__ieee754_log(x);
}
if(hx<0) {
if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
return one/zero;
t = sin_pi(x);
if(t==zero) return one/zero; /* -integer */
nadj = __ieee754_log(pi/fabs(t*x));
if(t<zero) *signgamp = -1;
x = -x;
}
/* purge off 1 and 2 */
if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
/* for x < 2.0 */
else if(ix<0x40000000) {
if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
r = -__ieee754_log(x);
if(ix>=0x3FE76944) {y = one-x; i= 0;}
else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
else {y = x; i=2;}
} else {
r = zero;
if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
else {y=x-one;i=2;}
}
switch(i) {
case 0:
z = y*y;
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
p = y*p1+p2;
r += (p-0.5*y); break;
case 1:
z = y*y;
w = z*y;
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
p = z*p1-(tt-w*(p2+y*p3));
r += (tf + p); break;
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
r += (-0.5*y + p1/p2);
}
}
else if(ix<0x40200000) { /* x < 8.0 */
i = (int)x;
t = zero;
y = x-(double)i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
r = half*y+p/q;
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
switch(i) {
case 7: z *= (y+6.0); /* FALLTHRU */
case 6: z *= (y+5.0); /* FALLTHRU */
case 5: z *= (y+4.0); /* FALLTHRU */
case 4: z *= (y+3.0); /* FALLTHRU */
case 3: z *= (y+2.0); /* FALLTHRU */
r += __ieee754_log(z); break;
}
/* 8.0 <= x < 2**58 */
} else if (ix < 0x43900000) {
t = __ieee754_log(x);
z = one/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
r = (x-half)*(t-one)+w;
} else
/* 2**58 <= x <= inf */
r = x*(__ieee754_log(x)-one);
if(hx<0) r = nadj - r;
return r;
}
float __lgammaf_r(float x, int *signgamp)
{
union {float f; uint32_t i;} u = {x};
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
uint32_t ix;
int i,sign;
/* purge off +-inf, NaN, +-0, tiny and negative arguments */
*signgamp = 1;
sign = u.i>>31;
ix = u.i & 0x7fffffff;
if (ix >= 0x7f800000)
return x*x;
if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
if (sign) {
*signgamp = -1;
x = -x;
}
return -logf(x);
}
if (sign) {
x = -x;
t = sin_pi(x);
if (t == 0.0f) /* -integer */
return 1.0f/(x-x);
if (t > 0.0f)
*signgamp = -1;
else
t = -t;
nadj = logf(pi/(t*x));
}
/* purge off 1 and 2 */
if (ix == 0x3f800000 || ix == 0x40000000)
r = 0;
/* for x < 2.0 */
else if (ix < 0x40000000) {
if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
r = -logf(x);
if (ix >= 0x3f3b4a20) {
y = 1.0f - x;
i = 0;
} else if (ix >= 0x3e6d3308) {
y = x - (tc-1.0f);
i = 1;
} else {
y = x;
i = 2;
}
} else {
r = 0.0f;
if (ix >= 0x3fdda618) { /* [1.7316,2] */
y = 2.0f - x;
i = 0;
} else if (ix >= 0x3F9da620) { /* [1.23,1.73] */
y = x - tc;
i = 1;
} else {
y = x - 1.0f;
i = 2;
}
}
switch(i) {
case 0:
z = y*y;
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
p = y*p1+p2;
r += p - 0.5f*y;
break;
case 1:
z = y*y;
w = z*y;
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
p = z*p1-(tt-w*(p2+y*p3));
r += (tf + p);
break;
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
r += -0.5f*y + p1/p2;
}
} else if (ix < 0x41000000) { /* x < 8.0 */
i = (int)x;
y = x - (float)i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
r = 0.5f*y+p/q;
z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */
switch (i) {
case 7: z *= y + 6.0f; /* FALLTHRU */
case 6: z *= y + 5.0f; /* FALLTHRU */
case 5: z *= y + 4.0f; /* FALLTHRU */
case 4: z *= y + 3.0f; /* FALLTHRU */
case 3: z *= y + 2.0f; /* FALLTHRU */
r += logf(z);
break;
}
} else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */
t = logf(x);
z = 1.0f/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
r = (x-0.5f)*(t-1.0f)+w;
} else /* 2**58 <= x <= inf */
r = x*(logf(x)-1.0f);
if (sign)
r = nadj - r;
return r;
}
int test_main(int, char* [])
{
int i;
TEST_POLICY_SF(tgamma(3.0));
TEST_POLICY_SF(tgamma1pm1(0.25));
TEST_POLICY_SF(lgamma(50.0));
TEST_POLICY_SF(lgamma(50.0, &i));
TEST_POLICY_SF(digamma(12.0));
TEST_POLICY_SF(tgamma_ratio(12.0, 13.5));
TEST_POLICY_SF(tgamma_delta_ratio(100.0, 0.25));
TEST_POLICY_SF(factorial<double>(8));
TEST_POLICY_SF(unchecked_factorial<double>(3));
TEST_POLICY_SF(double_factorial<double>(5));
TEST_POLICY_SF(rising_factorial(20.5, 5));
TEST_POLICY_SF(falling_factorial(10.2, 7));
TEST_POLICY_SF(tgamma(12.0, 13.0));
TEST_POLICY_SF(tgamma_lower(12.0, 13.0));
TEST_POLICY_SF(gamma_p(12.0, 13.0));
TEST_POLICY_SF(gamma_q(12.0, 15.0));
TEST_POLICY_SF(gamma_p_inv(12.0, 0.25));
TEST_POLICY_SF(gamma_q_inv(15.0, 0.25));
TEST_POLICY_SF(gamma_p_inva(12.0, 0.25));
TEST_POLICY_SF(gamma_q_inva(12.0, 0.25));
TEST_POLICY_SF(erf(2.5));
TEST_POLICY_SF(erfc(2.5));
TEST_POLICY_SF(erf_inv(0.25));
TEST_POLICY_SF(erfc_inv(0.25));
TEST_POLICY_SF(beta(12.0, 15.0));
TEST_POLICY_SF(beta(12.0, 15.0, 0.25));
TEST_POLICY_SF(betac(12.0, 15.0, 0.25));
TEST_POLICY_SF(ibeta(12.0, 15.0, 0.25));
TEST_POLICY_SF(ibetac(12.0, 15.0, 0.25));
TEST_POLICY_SF(ibeta_inv(12.0, 15.0, 0.25));
TEST_POLICY_SF(ibetac_inv(12.0, 15.0, 0.25));
TEST_POLICY_SF(ibeta_inva(12.0, 0.75, 0.25));
TEST_POLICY_SF(ibetac_inva(12.0, 0.75, 0.25));
TEST_POLICY_SF(ibeta_invb(12.0, 0.75, 0.25));
TEST_POLICY_SF(ibetac_invb(12.0, 0.75, 0.25));
TEST_POLICY_SF(gamma_p_derivative(12.0, 15.0));
TEST_POLICY_SF(ibeta_derivative(12.0, 15.75, 0.25));
TEST_POLICY_SF(fpclassify(12.0));
TEST_POLICY_SF(isfinite(12.0));
TEST_POLICY_SF(isnormal(12.0));
TEST_POLICY_SF(isnan(12.0));
TEST_POLICY_SF(isinf(12.0));
TEST_POLICY_SF(log1p(0.0025));
TEST_POLICY_SF(expm1(0.0025));
TEST_POLICY_SF(cbrt(30.0));
TEST_POLICY_SF(sqrt1pm1(0.0025));
TEST_POLICY_SF(powm1(1.0025, 12.0));
TEST_POLICY_SF(legendre_p(5, 0.75));
TEST_POLICY_SF(legendre_p(7, 3, 0.75));
TEST_POLICY_SF(legendre_q(5, 0.75));
TEST_POLICY_SF(legendre_next(2, 0.25, 12.0, 5.0));
TEST_POLICY_SF(legendre_next(2, 2, 0.25, 12.0, 5.0));
TEST_POLICY_SF(laguerre(5, 12.2));
TEST_POLICY_SF(laguerre(7, 3, 5.0));
TEST_POLICY_SF(laguerre_next(2, 5.0, 12.0, 5.0));
TEST_POLICY_SF(laguerre_next(5, 3, 5.0, 20.0, 10.0));
TEST_POLICY_SF(hermite(1, 2.0));
TEST_POLICY_SF(hermite_next(2, 2.0, 3.0, 2.0));
TEST_POLICY_SF(spherical_harmonic_r(5, 4, 0.75, 0.25));
TEST_POLICY_SF(spherical_harmonic_i(5, 4, 0.75, 0.25));
TEST_POLICY_SF(ellint_1(0.25));
TEST_POLICY_SF(ellint_1(0.25, 0.75));
TEST_POLICY_SF(ellint_2(0.25));
TEST_POLICY_SF(ellint_2(0.25, 0.75));
TEST_POLICY_SF(ellint_3(0.25, 0.75));
TEST_POLICY_SF(ellint_3(0.25, 0.125, 0.75));
TEST_POLICY_SF(ellint_rc(3.0, 5.0));
TEST_POLICY_SF(ellint_rd(2.0, 3.0, 4.0));
TEST_POLICY_SF(ellint_rf(2.0, 3.0, 4.0));
TEST_POLICY_SF(ellint_rj(2.0, 3.0, 5.0, 0.25));
TEST_POLICY_SF(hypot(5.0, 3.0));
TEST_POLICY_SF(sinc_pi(3.0));
TEST_POLICY_SF(sinhc_pi(2.0));
TEST_POLICY_SF(asinh(12.0));
TEST_POLICY_SF(acosh(5.0));
TEST_POLICY_SF(atanh(0.75));
TEST_POLICY_SF(sin_pi(5.0));
TEST_POLICY_SF(cos_pi(6.0));
TEST_POLICY_SF(cyl_neumann(2.0, 5.0));
TEST_POLICY_SF(cyl_neumann(2, 5.0));
TEST_POLICY_SF(cyl_bessel_j(2.0, 5.0));
TEST_POLICY_SF(cyl_bessel_j(2, 5.0));
TEST_POLICY_SF(cyl_bessel_i(3.0, 5.0));
TEST_POLICY_SF(cyl_bessel_i(3, 5.0));
TEST_POLICY_SF(cyl_bessel_k(3.0, 5.0));
TEST_POLICY_SF(cyl_bessel_k(3, 5.0));
TEST_POLICY_SF(sph_bessel(3, 5.0));
TEST_POLICY_SF(sph_bessel(3, 5));
TEST_POLICY_SF(sph_neumann(3, 5.0));
TEST_POLICY_SF(sph_neumann(3, 5));
return 0;
}
//------------------------------------------------------------------------------
double Cmath::__ieee754_lgamma_r( double x, int* signgamp )
{
static const double zero = 0.00000000000000000000e+00;
static const double half= 5.00000000000000000000e-01; // 0x3FE00000, 0x00000000
static const double one = 1.00000000000000000000e+00; // 0x3FF00000, 0x00000000
static const double pi = 3.14159265358979311600e+00; // 0x400921FB, 0x54442D18
static const double a0 = 7.72156649015328655494e-02; // 0x3FB3C467, 0xE37DB0C8
static const double a1 = 3.22467033424113591611e-01; // 0x3FD4A34C, 0xC4A60FAD
static const double a2 = 6.73523010531292681824e-02; // 0x3FB13E00, 0x1A5562A7
static const double a3 = 2.05808084325167332806e-02; // 0x3F951322, 0xAC92547B
static const double a4 = 7.38555086081402883957e-03; // 0x3F7E404F, 0xB68FEFE8
static const double a5 = 2.89051383673415629091e-03; // 0x3F67ADD8, 0xCCB7926B
static const double a6 = 1.19270763183362067845e-03; // 0x3F538A94, 0x116F3F5D
static const double a7 = 5.10069792153511336608e-04; // 0x3F40B6C6, 0x89B99C00
static const double a8 = 2.20862790713908385557e-04; // 0x3F2CF2EC, 0xED10E54D
static const double a9 = 1.08011567247583939954e-04; // 0x3F1C5088, 0x987DFB07
static const double a10 = 2.52144565451257326939e-05; // 0x3EFA7074, 0x428CFA52
static const double a11 = 4.48640949618915160150e-05; // 0x3F07858E, 0x90A45837
static const double tc = 1.46163214496836224576e+00; // 0x3FF762D8, 0x6356BE3F
static const double tf = -1.21486290535849611461e-01; // 0xBFBF19B9, 0xBCC38A42
static const double tt = -3.63867699703950536541e-18; // 0xBC50C7CA, 0xA48A971F
static const double t0 = 4.83836122723810047042e-01; // 0x3FDEF72B, 0xC8EE38A2
static const double t1 = -1.47587722994593911752e-01; // 0xBFC2E427, 0x8DC6C509
static const double t2 = 6.46249402391333854778e-02; // 0x3FB08B42, 0x94D5419B
static const double t3 = -3.27885410759859649565e-02; // 0xBFA0C9A8, 0xDF35B713
static const double t4 = 1.79706750811820387126e-02; // 0x3F9266E7, 0x970AF9EC
static const double t5 = -1.03142241298341437450e-02; // 0xBF851F9F, 0xBA91EC6A
static const double t6 = 6.10053870246291332635e-03; // 0x3F78FCE0, 0xE370E344
static const double t7 = -3.68452016781138256760e-03; // 0xBF6E2EFF, 0xB3E914D7
static const double t8 = 2.25964780900612472250e-03; // 0x3F6282D3, 0x2E15C915
static const double t9 = -1.40346469989232843813e-03; // 0xBF56FE8E, 0xBF2D1AF1
static const double t10 = 8.81081882437654011382e-04; // 0x3F4CDF0C, 0xEF61A8E9
static const double t11 = -5.38595305356740546715e-04; // 0xBF41A610, 0x9C73E0EC
static const double t12 = 3.15632070903625950361e-04; // 0x3F34AF6D, 0x6C0EBBF7
static const double t13 = -3.12754168375120860518e-04; // 0xBF347F24, 0xECC38C38
static const double t14 = 3.35529192635519073543e-04; // 0x3F35FD3E, 0xE8C2D3F4
static const double u0 = -7.72156649015328655494e-02; // 0xBFB3C467, 0xE37DB0C8
static const double u1 = 6.32827064025093366517e-01; // 0x3FE4401E, 0x8B005DFF
static const double u2 = 1.45492250137234768737e+00; // 0x3FF7475C, 0xD119BD6F
static const double u3 = 9.77717527963372745603e-01; // 0x3FEF4976, 0x44EA8450
static const double u4 = 2.28963728064692451092e-01; // 0x3FCD4EAE, 0xF6010924
static const double u5 = 1.33810918536787660377e-02; // 0x3F8B678B, 0xBF2BAB09
static const double v1 = 2.45597793713041134822e+00; // 0x4003A5D7, 0xC2BD619C
static const double v2 = 2.12848976379893395361e+00; // 0x40010725, 0xA42B18F5
static const double v3 = 7.69285150456672783825e-01; // 0x3FE89DFB, 0xE45050AF
static const double v4 = 1.04222645593369134254e-01; // 0x3FBAAE55, 0xD6537C88
static const double v5 = 3.21709242282423911810e-03; // 0x3F6A5ABB, 0x57D0CF61
static const double s0 = -7.72156649015328655494e-02; // 0xBFB3C467, 0xE37DB0C8
static const double s1 = 2.14982415960608852501e-01; // 0x3FCB848B, 0x36E20878
static const double s2 = 3.25778796408930981787e-01; // 0x3FD4D98F, 0x4F139F59
static const double s3 = 1.46350472652464452805e-01; // 0x3FC2BB9C, 0xBEE5F2F7
static const double s4 = 2.66422703033638609560e-02; // 0x3F9B481C, 0x7E939961
static const double s5 = 1.84028451407337715652e-03; // 0x3F5E26B6, 0x7368F239
static const double s6 = 3.19475326584100867617e-05; // 0x3F00BFEC, 0xDD17E945
static const double r1 = 1.39200533467621045958e+00; // 0x3FF645A7, 0x62C4AB74
static const double r2 = 7.21935547567138069525e-01; // 0x3FE71A18, 0x93D3DCDC
static const double r3 = 1.71933865632803078993e-01; // 0x3FC601ED, 0xCCFBDF27
static const double r4 = 1.86459191715652901344e-02; // 0x3F9317EA, 0x742ED475
static const double r5 = 7.77942496381893596434e-04; // 0x3F497DDA, 0xCA41A95B
static const double r6 = 7.32668430744625636189e-06; // 0x3EDEBAF7, 0xA5B38140
static const double w0 = 4.18938533204672725052e-01; // 0x3FDACFE3, 0x90C97D69
static const double w1 = 8.33333333333329678849e-02; // 0x3FB55555, 0x5555553B
static const double w2 = -2.77777777728775536470e-03; // 0xBF66C16C, 0x16B02E5C
static const double w3 = 7.93650558643019558500e-04; // 0x3F4A019F, 0x98CF38B6
static const double w4 = -5.95187557450339963135e-04; // 0xBF4380CB, 0x8C0FE741
static const double w5 = 8.36339918996282139126e-04; // 0x3F4B67BA, 0x4CDAD5D1
static const double w6 = -1.63092934096575273989e-03; // 0xBF5AB89D, 0x0B9E43E4
double t, y, z, nadj, p, p1, p2, p3, q, r, w;
Cmp_signed__int32 i, hx, lx, ix;
extract_words( hx, lx, x );
// purge off +-inf, NaN, +-0, and negative arguments
*signgamp = 1;
ix = hx & 0x7fffffff;
if( ix >= 0x7ff00000 )
{
return x * x;
}
if( ( ix | lx ) == 0 )
{
return one / zero;
}
if( ix < 0x3b900000 )
{
// |x|<2**-70, return -log(|x|)
if( hx < 0 )
{
*signgamp = -1;
return -__ieee754_log( -x );
}
else
{
return -__ieee754_log( x );
}
}
if( hx < 0 )
{
if( ix >= 0x43300000 ) // |x|>=2**52, must be -integer
{
return one / zero;
}
t = sin_pi( x );
if( t == zero )
{
return one / zero; // -integer
}
nadj = __ieee754_log( pi / fabs( t * x ) );
if( t < zero )
{
*signgamp = -1;
}
x = -x;
}
// purge off 1 and 2
if( ( ( ( ix - 0x3ff00000 ) | lx ) == 0 ) || ( ( ( ix - 0x40000000 ) | lx ) == 0 ) )
{
r = 0;
}// for x < 2.0
else if( ix < 0x40000000 )
{
if( ix <= 0x3feccccc )
{
// lgamma(x) = lgamma(x+1)-log(x)
r = -__ieee754_log( x );
if( ix >= 0x3FE76944 )
{
y = one - x;
i = 0;
}
else if( ix >= 0x3FCDA661 )
{
y = x - ( tc - one );
i = 1;
}
else
{
y = x;
i = 2;
}
}
else
{
r = zero;
if( ix >= 0x3FFBB4C3 )
{
y = 2.0 - x;
i = 0;
} // [1.7316,2]
else if( ix >= 0x3FF3B4C4 )
{
y = x - tc;
i = 1;
} // [1.23,1.73]
else
{
y = x - one;
i = 2;
}
}
switch( i )
{
case 0:
z = y * y;
p1 = a0 + z * ( a2 + z * ( a4 + z * ( a6 + z * ( a8 + z * a10 ) ) ) );
p2 = z * ( a1 + z * ( a3 + z * ( a5 + z * ( a7 + z * ( a9 + z * a11 ) ) ) ) );
p = y * p1 + p2;
r += ( p - 0.5 * y );
break;
case 1:
z = y * y;
w = z * y;
p1 = t0 + w * ( t3 + w * ( t6 + w * ( t9 + w * t12 ) ) ); // parallel comp
p2 = t1 + w * ( t4 + w * ( t7 + w * ( t10 + w * t13 ) ) );
p3 = t2 + w * ( t5 + w * ( t8 + w * ( t11 + w * t14 ) ) );
p = z * p1 - ( tt - w * ( p2 + y * p3 ) );
r += ( tf + p );
break;
case 2:
p1 = y * ( u0 + y * ( u1 + y * ( u2 + y * ( u3 + y * ( u4 + y * u5 ) ) ) ) );
p2 = one + y * ( v1 + y * ( v2 + y * ( v3 + y * ( v4 + y * v5 ) ) ) );
r += ( -0.5 * y + p1 / p2 );
}
}
else if( ix < 0x40200000 )
{
// x < 8.0
i = (Cmp_signed__int32)x;
t = zero;
y = x - (double)i;
p = y * ( s0 + y * ( s1 + y * ( s2 + y * ( s3 + y * ( s4 + y * ( s5 + y * s6 ) ) ) ) ) );
q = one + y * ( r1 + y * ( r2 + y * ( r3 + y * ( r4 + y * ( r5 + y * r6 ) ) ) ) );
r = half * y + p / q;
z = one; // lgamma(1+s) = log(s) + lgamma(s)
switch( i )
{
case 7: z *= ( y + 6.0 ); // FALLTHRU
case 6: z *= ( y + 5.0 ); // FALLTHRU
case 5: z *= ( y + 4.0 ); // FALLTHRU
case 4: z *= ( y + 3.0 ); // FALLTHRU
case 3: z *= ( y + 2.0 ); // FALLTHRU
r += __ieee754_log( z );
break;
}
// 8.0 <= x < 2**58
}
else if( ix < 0x43900000 )
{
t = __ieee754_log( x );
z = one / x;
y = z * z;
w = w0 + z * ( w1 + y * ( w2 + y * ( w3 + y * ( w4 + y * ( w5 + y * w6 ) ) ) ) );
r = ( x - half ) * ( t - one ) + w;
}
else
{
// 2**58 <= x <= inf
r = x * ( __ieee754_log( x ) - one );
}
if( hx < 0 )
{
r = nadj - r;
}
return r;
}