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use std;
use num::complex::Complex;
pub trait Li2<T> {
fn li2(&self) -> T;
}
impl Li2<f64> for f64 {
fn li2(&self) -> f64 {
let pi = 3.1415926535897932384626433832795;
let pi2 = pi*pi;
let pi3 = pi2/3.;
let pi6 = pi2/6.;
let coeffs = [0.42996693560813697, 0.40975987533077105,
-0.01858843665014592, 0.00145751084062268,-0.00014304184442340,
0.00001588415541880,-0.00000190784959387, 0.00000024195180854,
-0.00000003193341274, 0.00000000434545063,-0.00000000060578480,
0.00000000008612098,-0.00000000001244332, 0.00000000000182256,
-0.00000000000027007, 0.00000000000004042,-0.00000000000000610,
0.00000000000000093,-0.00000000000000014, 0.00000000000000002];
if *self == 1.0 {
pi6
} else if *self == -1.0 {
-pi2/12.
} else {
let t = -*self;
let (y, s, a) = if t <= -2.0 {
let b1 = (-t).ln();
let b2 = (1.0 + 1.0/t).ln();
(-1.0/(1.0 + t), 1.0, -pi3 + 0.5*(b1*b1 - b2*b2))
} else if t < -1.0 {
let a = (-t).ln();
(-1.0 - t, -1.0, -pi6 + a*(a + (1.0 + 1.0/t).ln()))
} else if t <= -0.5 {
let a = (-t).ln();
(-(1.0 + t)/t, 1.0, -pi6 + a*(-0.5*a + (1.0 + t).ln()))
} else if t < 0.0 {
let b1 = (1.0 + t).ln();
(-t/(1.0 + t), -1.0, 0.5*b1*b1)
} else if t <= 1.0 {
(t, 1.0, 0.)
} else {
let b1 = t.ln();
(1.0/t, -1.0, pi6 + 0.5*b1*b1)
};
let h = y+y - 1.0;
let alfa = h+h;
let mut b0 = 0.0;
let mut b1 = 0.0;
let mut b2 = 0.0;
for c in coeffs.iter().rev() {
b0 = c + alfa*b1 - b2;
b2 = b1;
b1 = b0;
}
-(s*(b0 - h*b2) + a)
}
}
}
impl Li2<Complex<f64>> for Complex<f64> {
fn li2(&self) -> Complex<f64> {
let pi = 3.1415926535897932384626433832795;
let bf = [
- 1./4.,
1./36.,
- 1./36.0e2,
1./21168.0e1,
- 1./108864.0e2,
1./52690176.0e1,
- 4.0647616451442255268059093862919666745470571274397078e-11,
8.9216910204564525552179873167527488515142836130490451e-13,
- 1.9939295860721075687236443477937897056306947496538801e-14,
4.5189800296199181916504765528555932283968190144666184e-16,
- 1.0356517612181247014483411542218656665960912381686505e-17,
2.3952186210261867457402837430009803816789490019429743e-19,
- 5.5817858743250093362830745056254199055670546676443981e-21,
1.3091507554183212858123073991865923017498498387833038e-22,
- 3.0874198024267402932422797648664624315955652561327457e-24,
7.315975652702203420357905609252148591033401063690875e-26,
- 1.7408456572340007409890551477597025453408414217542713e-27,
4.1576356446138997196178996207752266734882541595115639e-29,
- 9.9621484882846221031940067024558388498548600173944888e-31,
2.3940344248961653005211679878937495629342791569329158e-32,
];
let rz = self.re;
let iz = self.im;
let az = self.norm();
if iz == 0. {
if rz <= 1. {
return Complex::new(rz.li2(), 0.0)
} else {
return Complex::new(rz.li2(), -pi*rz.ln())
}
} else if az < std::f64::EPSILON {
return *self;
}
let (cy, cz, jsgn, ipi12) = if rz <= 0.5 {
if az > 1. {
(-0.5 * sqr((-self).ln()), -(1. - 1. / self).ln(), -1., -2.)
} else {
(Complex::new(0.,0.), -(1. - self).ln(), 1., 0.)
}
} else {
if az <= (2.0*rz).sqrt() {
let l = -(self).ln();
(l * (1. - self).ln(), l, -1., 2.)
} else {
(-0.5 * sqr((-self).ln()), -(1. - 1. / self).ln(), -1., -2.)
}
};
let cz2 = sqr(cz);
let sum =
cz +
cz2 * (bf[0] +
cz * (bf[1] +
cz2 * (bf[2] +
cz2 * (bf[3] +
cz2 * (bf[4] +
cz2 * (bf[5] +
cz2 * (bf[6] +
cz2 * (bf[7] +
cz2 * (bf[8] +
cz2 * (bf[9] +
cz2 * (bf[10] +
cz2 * (bf[11] +
cz2 * (bf[12] +
cz2 * (bf[13] +
cz2 * (bf[14] +
cz2 * (bf[15] +
cz2 * (bf[16] +
cz2 * (bf[17] +
cz2 * (bf[18] +
cz2 * (bf[19]))))))))))))))))))));
jsgn * sum + cy + ipi12 * pi * pi / 12.
}
}
fn sqr(x: Complex<f64>) -> Complex<f64> { x*x }