func Lngamma_sgn_sing(N int, eps float64, lng *Result, sgn *float64) error {
if eps == 0.0 {
lng.val = 0.0
lng.err = 0.0
*sgn = 0.0
return err.EDOM
} else if N == 1 {
/* calculate series for
* g = eps gamma(-1+eps) + 1 + eps/2 (1+3eps)/(1-eps^2)
* double-precision for |eps| < 0.02
*/
c0 := 0.07721566490153286061
c1 := 0.08815966957356030521
c2 := -0.00436125434555340577
c3 := 0.01391065882004640689
c4 := -0.00409427227680839100
c5 := 0.00275661310191541584
c6 := -0.00124162645565305019
c7 := 0.00065267976121802783
c8 := -0.00032205261682710437
c9 := 0.00016229131039545456
g5 := c5 + eps*(c6+eps*(c7+eps*(c8+eps*c9)))
g := eps * (c0 + eps*(c1+eps*(c2+eps*(c3+eps*(c4+eps*g5)))))
/* calculate eps gamma(-1+eps), a negative quantity */
gam_e := g - 1.0 - 0.5*eps*(1.0+3.0*eps)/(1.0-eps*eps)
lng.val = math.Log(math.Abs(gam_e) / math.Abs(eps))
lng.err = 2.0 * gsl.DBL_EPSILON * math.Abs(lng.val)
if eps > 0.0 {
*sgn = -1.0
} else {
*sgn = 1.0
}
return err.SUCCESS
}
var g float64
/* series for sin(Pi(N+1-eps))/(Pi eps) modulo the sign
* double-precision for |eps| < 0.02
*/
cs1 := -1.6449340668482264365
cs2 := 0.8117424252833536436
cs3 := -0.1907518241220842137
cs4 := 0.0261478478176548005
cs5 := -0.0023460810354558236
e2 := eps * eps
sin_ser := 1.0 + e2*(cs1+e2*(cs2+e2*(cs3+e2*(cs4+e2*cs5))))
/* calculate series for ln(gamma(1+N-eps))
* double-precision for |eps| < 0.02
*/
aeps := math.Abs(eps)
var c1, c2, c3, c4, c5, c6, c7, lng_ser float64
var c0, psi_0, psi_1, psi_2, psi_3, psi_4, psi_5, psi_6 *Result
psi_2.val = 0.0
psi_3.val = 0.0
psi_4.val = 0.0
psi_5.val = 0.0
psi_6.val = 0.0
Lnfact_e(N, c0)
Psi_int_e(N+1, psi_0)
Psi_1_int_e(N+1, psi_1)
switch {
case aeps > 0.00001:
Psi_n_e(2, float64(N)+1.0, psi_2)
case aeps > 0.0002:
Psi_n_e(3, float64(N)+1.0, psi_3)
case aeps > 0.001:
Psi_n_e(4, float64(N)+1.0, psi_4)
case aeps > 0.005:
Psi_n_e(5, float64(N)+1.0, psi_5)
case aeps > 0.01:
Psi_n_e(6, float64(N)+1.0, psi_6)
}
c1 = psi_0.val
c2 = psi_1.val / 2.0
c3 = psi_2.val / 6.0
c4 = psi_3.val / 24.0
c5 = psi_4.val / 120.0
c6 = psi_5.val / 720.0
c7 = psi_6.val / 5040.0
lng_ser = c0.val - eps*(c1-eps*(c2-eps*(c3-eps*(c4-eps*(c5-eps*(c6-eps*c7))))))
/* calculate
* g = ln(|eps gamma(-N+eps)|)
* = -ln(gamma(1+N-eps)) + ln(|eps Pi/sin(Pi(N+1+eps))|)
*/
g = -lng_ser - math.Log(sin_ser)
lng.val = g - math.Log(math.Abs(eps))
lng.err = c0.err + 2.0*gsl.DBL_EPSILON*(math.Abs(g)+math.Abs(lng.val))
if eps > 0.0 {
*sgn = 1.0
} else {
*sgn = -1.0
}
if gsl.IsOdd(N) {
*sgn *= -1.0
} else {
*sgn *= 1.0
}
return err.SUCCESS
}
func Exprel_n_CF(N int, x float64, result *Result) error {
RECUR_BIG := gsl.SQRT_DBL_MAX
maxiter := 5000
n := 1
Anm2 := 1.0
Bnm2 := 0.0
Anm1 := 0.0
Bnm1 := 1.0
a1 := 1.0
b1 := 1.0
a2 := -x
b2 := float64(N) + 1.0
var an, bn, old_fn, del float64
An := b1*Anm1 + a1*Anm2 /* A1 */
Bn := b1*Bnm1 + a1*Bnm2 /* B1 */
/* One explicit step, before we get to the main pattern. */
n++
Anm2 = Anm1
Bnm2 = Bnm1
Anm1 = An
Bnm1 = Bn
An = b2*Anm1 + a2*Anm2 /* A2 */
Bn = b2*Bnm1 + a2*Bnm2 /* B2 */
fn := An / Bn
for n < maxiter {
n++
Anm2 = Anm1
Bnm2 = Bnm1
Anm1 = An
Bnm1 = Bn
if gsl.IsOdd(n) {
an = (float64(n-1) / 2.0) * x
} else {
an = -(float64(N) + (float64(n) / 2) - 1.0) * x
}
bn = float64(N + n - 1)
An = bn*Anm1 + an*Anm2
Bn = bn*Bnm1 + an*Bnm2
if math.Abs(An) > RECUR_BIG || math.Abs(Bn) > RECUR_BIG {
An /= RECUR_BIG
Bn /= RECUR_BIG
Anm1 /= RECUR_BIG
Bnm1 /= RECUR_BIG
Anm2 /= RECUR_BIG
Bnm2 /= RECUR_BIG
}
old_fn = fn
fn = An / Bn
del = old_fn / fn
if math.Abs(del-1.0) < 2.0*gsl.DBL_EPSILON {
break
}
}
result.val = fn
result.err = 2.0 * (float64(n) + 1.0) * gsl.DBL_EPSILON * math.Abs(fn)
if n == maxiter {
return err.EMAXITER
}
return err.SUCCESS
}