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fvn_fnlib/aid.f
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function aid (x)
c july 1980 edition. w. fullerton, bell labs.
c
c evaluate the derivative of the airy function ai(x).
c
dimension aifcs(8), aigcs(9)
external aide, csevl, inits, r1mach
c
c series for aif on the interval -1.00000e+00 to 1.00000e+00
c with weighted error 5.22e-18
c log weighted error 17.28
c significant figures required 16.01
c decimal places required 17.73
c
data aifcs( 1) / 0.1052746122 6531408809 e0/
data aifcs( 2) / 0.0118361362 8152997844 e0/
data aifcs( 3) / 0.0001232810 4173225664 e0/
data aifcs( 4) / 0.0000006226 1225638140 e0/
data aifcs( 5) / 0.0000000018 5298887844 e0/
data aifcs( 6) / 0.0000000000 0363328873 e0/
data aifcs( 7) / 0.0000000000 0000504622 e0/
data aifcs( 8) / 0.0000000000 0000000522 e0/
c
c series for aig on the interval -1.00000e+00 to 1.00000e+00
c with weighted error 3.14e-19
c log weighted error 18.50
c significant figures required 17.44
c decimal places required 18.98
c
data aigcs( 1) / 0.0212338781 5091866685 2e0/
data aigcs( 2) / 0.0863159303 3521440675 2e0/
data aigcs( 3) / 0.0017975947 2038323135 8e0/
data aigcs( 4) / 0.0000142654 9987555069 3e0/
data aigcs( 5) / 0.0000000594 3799528368 3e0/
data aigcs( 6) / 0.0000000001 5240336647 9e0/
data aigcs( 7) / 0.0000000000 0026458766 0e0/
data aigcs( 8) / 0.0000000000 0000033156 2e0/
data aigcs( 9) / 0.0000000000 0000000031 4e0/
c
data naif, naig, x2sml, x3sml / 2*0, 2*0.0 /
c
if (naif.ne.0) go to 10
naif = inits (aifcs, 8, 0.1*r1mach(3))
naig = inits (aigcs, 9, 0.1*r1mach(3))
c
x3sml = r1mach(3)**0.3334
x2sml = sqrt(r1mach(3))
c
10 if (x.ge.(-1.0)) go to 20
call r9admp (x, xn, phi)
aid = xn * cos(phi)
return
c
20 if (x.gt.1.0) go to 30
x3 = 0.0
if (abs(x).gt.x3sml) x3 = x**3
x2 = 0.0
if (abs(x).gt.x2sml) x2 = x*x
aid = (x2*(0.125 + csevl (x3, aifcs, naif)) -
1 csevl (x3, aigcs, naig)) - 0.25
return
c
30 aid = aide(x) * exp(-2.0*x*sqrt(x)/3.0)
return
c
end
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