# auto-generated module by fonll_nc_nnlo package
# pylint: skip-file
# fmt: off
import numba as nb
import numpy as np
from eko.constants import CA as ca
from eko.constants import CF as cf
from eko.constants import TR as tr
from ..special.nielsen import nielsen
from ..special.zeta import zeta2, zeta3
[docs]
@nb.njit("f8(i8,i8,f8)", cache=True)
def wgplg(m,n,z):
return nielsen(m,n,z).real
[docs]
@nb.njit("f8(f8)", cache=True)
def clg1am0_a0(x):
res = tr * 16e0 * x * ( 1e0 - x )
return res
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@nb.njit("f8(f8)", cache=True)
def c2g1am0_aq(x):
res = tr * ( 4e0 - 8e0 * x + 8e0 * x**2 )
return res
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@nb.njit("f8(f8)", cache=True)
def c2g1am0_a0(x):
res = tr * ( ( 4e0 - 8e0 * x + 8e0 * x**2 ) * np.log( ( 1e0 - x ) / x ) - 4e0 + 32e0 * x - 32e0 * x**2 )
return res
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@nb.njit("f8(f8)", cache=True)
def clg2am0_af(x):
dlx=np.log(x)
dlm=np.log(1.0e0-x)
c1=64.0e0*x*(1.0e0-x)*dlm-128.0e0*x*dlx-32.0e0-160.0e0*x +544.0e0*x*x/3.0e0+32.0e0/x/3.0e0
res = tr * ca * c1
return res
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@nb.njit("f8(f8)", cache=True)
def clg2am0_aq(x):
dlx=np.log(x)
dlm=np.log(1.0e0-x)
a1=64.0e0*x*(1.0e0-x)*dlm-128.0e0*x*dlx-32.0e0-160.0e0*x +544.0e0*x*x/3.0e0+32.0e0/x/3.0e0
b1=32.0e0*x*dlx+16.0e0*(1.0e0-2.0e0*x*x+x)
res = tr * ( ca * a1 + cf * b1 )
return res
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@nb.njit("f8(f8)", cache=True)
def clg2am0_a0(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlm=np.log(1.0e0-x)
dlm2=dlm*dlm
dlp=np.log(1.0e0+x)
s11=wgplg(1,1,1.0e0-x)
s11m=wgplg(1,1,-x)
a2=96.0e0*x*dlx2+(64.0e0*x*x-192.0e0*x)*dlx*dlm+(32.0e0 -416.0e0*x*x+256.0e0*x)*dlx+32.0e0*x*(1.0e0-x)*dlm2+( -32.0e0+928.0e0*x*x/3.0e0-288.0e0*x+32.0e0/x/3.0e0)*dlm +64.0e0*x*x*zeta2-128.0e0*x*s11+64.0e0*x*(1.0e0+x)*(s11m +dlx*dlp)+32.0e0/3.0e0-1696*x*x/9.0e0+544.0e0*x/3.0e0 -32.0e0/x/9.0e0
b2=-(64.0e0*x*x*x/5.0e0+64.0e0*x/3.0e0)*dlx2+32.0e0*x *(s11+dlx*dlm)+(-208.0e0/15.0e0+192.0e0*x*x/5.0e0 -416.0e0*x/5.0e0-64.0e0/x/15.0e0)*dlx+(16.0e0-64.0e0*x*x +48.0e0*x)*dlm+(128.0e0*x*x*x/5.0e0-64.0e0*x/3.0e0)*zeta2 +(128.0e0*x*x*x/5.0e0-64.0e0*x/3.0e0+64.0e0/x/x/15.0e0) *(s11m+dlx*dlp)-256.0e0/15.0e0+672.0e0*x*x/5.0e0-608.0e0 *x/5.0e0+64.0e0/x/15.0e0
res = tr * ( ca * a2 + cf * b2 )
return res
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@nb.njit("f8(f8)", cache=True)
def c2g2am0_aqf(x):
dlx=np.log(x)
dlm=np.log(1.0e0-x)
c1=-248.0e0*x*x/3.0e0+64.0e0*x+8.0e0+32.0e0/x/3.0e0 +(32.0e0*x*x-32.0e0*x+16.0e0)*dlm+(64.0e0*x+16.0e0)*dlx
res = tr * ca * c1
return res
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@nb.njit("f8(f8)", cache=True)
def c2g2am0_af(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlm=np.log(1.0e0-x)
dlm2=dlm*dlm
s11=wgplg(1,1,1.0e0-x)
c2=(-16.0e0+32.0e0*x-32.0e0*x*x)*zeta2+1124.0e0*x*x/3.0e0 -968.0e0*x/3.0e0-172.0e0/3.0e0+16.0e0/x/3.0e0+(16.0e0 -32.0e0*x+32.0e0*x*x)*dlm2-(8.0e0+32.0e0*x)*dlx2+(248.0e0 *x*x/3.0e0-256.0e0*x-8.0e0)*dlx+(32.0e0/x/3.0e0-8.0e0 +192.0e0*x-632.0e0*x*x/3.0e0)*dlm+(96.0e0*x-32.0e0*x*x) *dlx*dlm+(64.0e0*x+16.0e0)*s11
res = tr * ca * c2
return res
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@nb.njit("f8(f8)", cache=True)
def c2g2am0_aq2(x):
dlx=np.log(x)
dlm=np.log(1.0e0-x)
a1=16.0e0/x/3.0e0-124.0e0*x*x/3.0e0+32.0e0*x+4.0e0 +(16.0e0*x*x-16.0e0*x+8.0e0)*dlm+(32.0e0*x+8.0e0)*dlx
b1=-2.0e0+8.0e0*x+(16.0e0*x*x-16.0e0*x+8.0e0)*dlm +(-16.0e0*x*x+8.0e0*x-4.0e0)*dlx
res = tr * ( ca * a1 + cf * b1 )
return res
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@nb.njit("f8(f8)", cache=True)
def c2g2am0_aq(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlm=np.log(1.0e0-x)
dlm2=dlm*dlm
dlp=np.log(1.0e0+x)
s111mx=wgplg(1,1,1.0e0-x)
s11mx=wgplg(1,1,-x)
a2=-(16.0e0+32.0e0*x*x)*zeta2+1628.0e0*x*x/9.0e0 -368.0e0*x/3.0e0-220.0e0/3.0e0+208.0e0/x/9.0e0 +(16.0e0*x*x-16.0e0*x+8.0e0)*dlm2-(48.0e0*x+16.0e0) *dlx2+(-536.0e0*x*x/3.0e0+160.0e0*x-8.0e0+32.0e0/x/3.0e0) *dlm+(200.0e0*x*x-192.0e0*x)*dlx+(96.0e0*x-32.0e0*x*x) *dlx*dlm+(64.0e0*x+16.0e0)*s111mx-(32.0e0*x*x+32.0e0*x+16.0e0) *(s11mx+dlx*dlp)
b2=(-64.0e0*x*x+64.0e0*x-32.0e0)*zeta2+16.0e0*x*x-68.0e0*x +36.0e0+(32.0e0*x*x-32.0e0*x+16.0e0)*dlm2+(32.0e0*x*x -16.0e0*x+8.0e0)*dlx2+(-80.0e0*x*x+96.0e0*x-28.0e0)*dlm +(80.0e0*x*x-48.0e0*x+8.0e0)*dlx+(-64.0e0*x*x+48.0e0*x -24.0e0)*dlx*dlm+(8.0e0-16.0e0*x)*s111mx
res = tr * ( ca * a2 + cf * b2 )
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2g2am0_a0(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlx3=dlx2*dlx
dlm=np.log(1.0e0-x)
dlm2=dlm*dlm
dlm3=dlm2*dlm
dlp=np.log(1.0e0+x)
dlp2=dlp*dlp
s11=wgplg(1,1,1.0e0-x)
s121mx=wgplg(1,2,1.0e0-x)
s12mx=wgplg(1,2,-x)
s211mx=wgplg(2,1,1.0e0-x)
s21mx=wgplg(2,1,-x)
s111mx=wgplg(1,1,1.0e0-x)
s11mx=wgplg(1,1,-x)
z=(1.0e0-x)/(1.0e0+x)
s21z=wgplg(2,1,z)
s21mz=wgplg(2,1,-z)
a31=dlx3*(16.0e0/3.0e0+16.0e0*x)+ dlx2*dlm*(-8.0e0+16.0e0*x*x-64.0e0*x)+ dlx2*dlp*(12.0e0+32.0e0*x*x+24.0e0*x)+ dlx2*(-114.0e0*x*x+184.0e0*x)+ dlx*dlm2*(-16.0e0*x*x+48.0e0*x)+ dlx*dlm*dlp*(-16.0e0-32.0e0*x*x-32.0e0*x)+ dlx*dlm*(16.0e0+292.0e0*x*x-288.0e0*x)+ dlx*dlp2*(8.0e0+16.0e0*x)
a32=dlx*dlp*(-48.0e0+208.0e0*x*x/3.0e0+16.0e0*x- 32.0e0/x/3.0e0)+ dlx*zeta2*(-16.0e0+32.0e0*x*x-160.0e0*x)+ dlx*s111mx*(+32.0e0*x)+ dlx*s11mx*(24.0e0+32.0e0*x*x+48.0e0*x)+ dlx*(292.0e0/3.0e0-5780.0e0*x*x/9.0e0+332.0e0*x)+ dlm2*(-6.0e0-214.0e0*x*x/3.0e0+64.0e0*x+16.0e0/x/3.0e0)+ zeta2*dlm*(-40.0e0-64.0e0*x*x+48.0e0*x)
a33=dlm*s111mx*(16.0e0+64.0e0*x)+ dlm*s11mx*(-16.0e0-32.0e0*x*x-32.0e0*x)+ dlm*(-112.0e0/3.0e0+2996.0e0*x*x/9.0e0-860.0e0*x/3.0e0 +208.0e0/x/9.0e0)+ zeta2*dlp*(8.0e0+16.0e0*x)+ dlp*s11mx*(16.0e0+32.0e0*x)+ s21mz*(-16.0e0-32.0e0*x*x-32.0e0*x)+ s21z*(16.0e0+32.0e0*x*x+32.0e0*x)
a34=zeta2*(-4.0e0+796.0e0*x*x/3.0e0-208.0e0*x-32.0e0/x)+ zeta3*(-12.0e0-8.0e0*x*x-56.0e0*x)+ s111mx*(20.0e0+80.0e0*x*x/3.0e0-64.0e0*x+64.0e0/x/3.0e0)+ s211mx*(-16.0e0-128.0e0*x)+ s121mx*(40.0e0+144.0e0*x)+ s11mx*(-48.0e0+208.0e0*x*x/3.0e0+16.0e0*x-32.0e0/x/3.0e0)+ s21mx*(-24.0e0-48.0e0*x)+ s12mx*(16.0e0+32.0e0*x)+80.0e0/x/9.0e0+ 466.0e0/9.0e0-878.0e0*x*x/9.0e0+260.0e0*x/9.0e0
a3=a31+a32+a33+a34
b31=dlx3*(-8.0e0/3.0e0-32.0e0*x*x/3.0e0+16.0e0*x/3.0e0)+ dlx2*dlm*(16.0e0+48.0e0*x*x-32.0e0*x)+ dlx2*dlp*(16.0e0+16.0e0*x*x+32.0e0*x)+ dlx2*(-4.0e0-96.0e0*x*x*x/5.0e0-52.0e0*x*x+8.0e0*x/3.0e0)+ dlx*dlm2*(-20.0e0-48.0e0*x*x+40.0e0*x)+ dlx*dlm*(24.0e0+168.0e0*x*x-160.0e0*x)+ dlx*dlp2*(-32.0e0-32.0e0*x*x-64.0e0*x)+ dlx*dlp*(96.0e0+192.0e0*x*x*x/5.0e0+128.0e0*x/3.0e0)
b32=16.0e0*dlx*dlp/x/x/15.0e0-16.0e0*dlx/x/15.0e0+ dlx*zeta2*(32.0e0+64.0e0*x*x-64.0e0*x)+ dlx*s111mx*(32.0e0*x*x)+ dlx*s11mx*(-32.0e0-32.0e0*x*x+64.0e0*x)+ dlx*(-712.0e0/15.0e0-672.0e0*x*x/5.0e0+136.0e0*x/5.0e0)+ dlm3*(8.0e0+16.0e0*x*x-16.0e0*x)+ dlm2*(-22.0e0-84.0e0*x*x+88.0e0*x)+ zeta2*dlm*(-32.0e0*x*x)
b33=dlm*s111mx*(8.0e0-16.0e0*x)+ dlm*(28.0e0+96.0e0*x*x-132.0e0*x)+ zeta2*dlp*(-32.0e0-32.0e0*x*x-64.0e0*x)+ dlp*s11mx*(-64.0e0-64.0e0*x*x-128.0e0*x)+ zeta2*(48.0e0+192.0e0*x*x*x/5.0e0+104.0e0*x*x- 208.0e0*x/3.0e0)+ zeta3*(112.0e0+192.0e0*x*x-96.0e0*x)
b34=s111mx*(-24.0e0+64.0e0*x*x-48.0e0*x)+ s211mx*(-24.0e0-32.0e0*x*x+48.0e0*x)+ s121mx*(-32.0e0+64.0e0*x)+ s11mx*(96.0e0+192.0e0*x*x*x/5.0e0+128.0e0*x/3.0e0)+ 16.0e0*s11mx/x/x/15.0e0+16.0e0/x/15.0e0+ s21mx*(96.0e0+96.0e0*x*x-64.0e0*x)+ s12mx*(-64.0e0-64.0e0*x*x-128.0e0*x)- 904.0e0/15.0e0+328.0e0*x*x/5.0e0+68.0e0*x/5.0e0
b3=b31+b32+b33+b34
res = tr * ( ca * a3 + cf * b3 )
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def clps2am0_af(x):
dlx=np.log(x)
c1=32.0e0/3.0e0/x+64.0e0*x*x/3.0e0 -32.0e0-32.0e0*x*dlx
res = cf * tr * c1
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def clps2am0_aq(x):
dlx=np.log(x)
a1=-32.0e0*x*dlx-32.0e0+64.0e0*x*x/3.0e0+32.0e0/x/3.0e0
res = cf * tr * a1
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def clps2am0_a0(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlm=np.log(1.0e0-x)
spx=wgplg(1,1,1.0e0-x)
a2=32.0e0*x*(dlx2-dlx*dlm-spx)+(-32.0e0+64.0e0*x*x/3.0e0 +32.0e0/x/3.0e0)*dlm+(32.0e0-64.0e0*x*x-32.0e0*x)*dlx +32.0e0/3.0e0+320.0e0*x*x/9.0e0-128.0e0*x/3.0e0 -32.0e0/x/9.0e0
res = cf * tr * a2
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ps2am0_aqf(x):
dlx=np.log(x)
c1=-32.0e0*x*x/3.0e0-8.0e0*x+8.0e0+32.0e0/x/3.0e0 +16.0e0*(1.0e0+x)*dlx
res = cf * tr * c1
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ps2am0_af(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlm=np.log(1.0e0-x)
spx=wgplg(1,1,1.0e0-x)
c2=128.0e0*x*x/3.0e0+16.0e0*x/3.0e0-160.0e0/3.0e0 +16.0e0/x/3.0e0+8.0e0*(1.0e0+x)*(-dlx2+2.0e0*dlx*dlm +2.0e0*spx)+(-32.0e0*x*x/3.0e0-8.0e0*x+8.0e0+32.0e0/x/3.0e0) *dlm+(32.0e0*x*x/3.0e0-40.0e0*x-8.0e0)*dlx
res = cf * tr * c2
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ps2am0_aq2(x):
dlx=np.log(x)
a1=-16.0e0*x*x/3.0e0-4.0e0*x+4.0e0+16.0e0/x/3.0e0 +8.0e0*(1.0e0+x)*dlx
res = cf * tr * a1
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ps2am0_aq(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlm=np.log(1.0e0-x)
s11=wgplg(1,1,1.0e0-x)
a2=-64.0e0*x*x/9.0e0+160.0e0*x/3.0e0-208.0e0/3.0e0 +208.0e0/x/9.0e0+32.0e0*x*x*dlx+16.0e0*(1.0e0+x)*(-dlx2+dlx*dlm +s11)+(-32.0e0*x*x/3.0e0-8.0e0*x+8.0e0+32.0e0/x/3.0e0) *dlm
res = cf * tr * a2
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ps2am0_a0(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlx3=dlx*dlx2
dlm=np.log(1.0e0-x)
dlm2=dlm*dlm
dlp=np.log(1.0e0+x)
s11=wgplg(1,1,1.0e0-x)
s12=wgplg(1,2,1.0e0-x)
s21=wgplg(2,1,1.0e0-x)
s11m=wgplg(1,1,-x)
a3=(1.0e0+x)*(16.0e0*dlx3/3.0e0-16.0e0*dlx2*dlm+8.0e0 *dlx*dlm2-32.0e0*zeta2*dlx+16.0e0*dlm*s11+32.0e0*s12 -16.0e0*s21)+(40.0e0*x-16.0e0*x*x)*dlx2+32.0e0*x*x*dlx *dlm+(280.0e0/3.0e0-704.0e0*x*x/9.0e0-88.0e0*x)*dlx +(4.0e0-16.0e0*x*x/3.0e0-4.0e0*x+16.0e0/x/3.0e0)*dlm2 +(-208.0e0/3.0e0-64.0e0*x*x/9.0e0+160.0e0*x/3.0e0 +208.0e0/x/9.0e0)*dlm+(-16.0e0+64.0e0*x*x/3.0e0-16.0e0*x -32.0e0/x)*zeta2+(16.0e0-16.0e0*x+64.0e0/x/3.0e0 +32.0e0*x*x/3.0e0)*s11+(-32.0e0-32.0e0*x*x/3.0e0-32.0e0 *x-32.0e0/x/3.0e0)*(s11m+dlx*dlp)+304.0e0/9.0e0+832.0e0 *x*x/9.0e0-1216.0e0*x/9.0e0+80.0e0/x/9.0e0
res = cf * tr * a3
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def clns2am0_aq(x):
res = 16e0 * cf * tr * x / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def clns2am0_a0(x):
res = 16e0 * cf * tr * ( x * np.log( 1e0 - x ) - 2e0 * x * np.log(x) - 25e0 * x / 6e0 + 1e0 ) / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2am0_aq2(x):
b1=(-1e0-x)*2.0e0
res = 2e0 * cf * tr * b1 / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2am0_aq(x):
dlx=np.log(x)
dlm=np.log(1.0e0-x)
a1=((-8.0e0*(1.0e0+x*x)*dlx/(1.0e0-x)+13.0e0*x+1.0e0) + (-1e0-x)*(4.0e0*dlm-29.0e0/3.0e0))
res = 2e0 * cf * tr * a1 / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2am0_a0(x):
dlx=np.log(x)
dlx2=dlx*dlx
dlm=np.log(1.0e0-x)
dlm2=dlm*dlm
spx=wgplg(1,1,1.0e0-x)
a2=(1.0e0+13.0e0*x)*dlm-(3.0e0+23.0e0*x)*dlx+29.0e0/6.0e0 -295.0e0*x/6.0e0+(1.0e0+x*x)*(-4.0e0*spx-8.0e0*dlx *dlm+6.0e0*dlx2+67.0e0*dlx/3.0e0)/(1.0e0-x)
b2=(-1e0-x)*(-4.0e0*zeta2+2.0e0*dlm2 -29.0e0*dlm/3.0e0+359e0/18.0e0)
res = 2e0 * cf * tr * ( a2 + b2 ) / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2bm0_aq2(x):
z = 2e0 / ( 1e0 - x )
res = z * 4e0 * cf * tr / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2bm0_aq(x):
dlm = np.log( 1e0 - x )
z = 2e0 / ( 1e0 - x )
res = z * 2e0 * cf * tr * ( 4e0 * dlm - 29e0 / 3e0 ) / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2bm0_a0(x):
dlm = np.log( 1e0 - x )
dlm2 = dlm * dlm
z = 2e0 / ( 1e0 - x )
res = z * 2e0 * cf * tr * ( - 4e0 * zeta2 + 2e0 * dlm2 - 29e0 * dlm / 3e0 + 359e0 / 18e0 ) / 3e0
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2cm0_aq2(x):
dlm = np.log( 1e0 - x )
res = 8e0 * cf * tr * dlm / 3e0 + 2e0 * cf * tr
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2cm0_aq(x):
dlm = np.log( 1e0 - x )
dlm2 = dlm * dlm
res = 4e0 * cf * tr * ( 2e0 * dlm2 - 29e0 * dlm / 3e0 ) / 3e0 - cf * tr * ( 32e0 * zeta2 / 3e0 + 38e0 / 3e0 )
return res
[docs]
@nb.njit("f8(f8)", cache=True)
def c2ns2cm0_a0(x):
dlm = np.log( 1e0 - x )
dlm2 = dlm * dlm
dlm3 = dlm2 * dlm
res = 4e0 * cf * tr * ( - 4e0 * zeta2 * dlm + 2e0 * dlm3 / 3e0 - 29e0 * dlm2 / 6e0 + 359e0 * dlm / 18e0 ) / 3e0 + cf * tr * ( 268e0 * zeta2 / 9e0 + 265e0 / 9e0 )
return res