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fvn_fnlib/psi.f
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function psi (x)
c april 1977 version. w. fullerton, c3, los alamos scientific lab.
dimension psics(23), apsics(16)
external cot, csevl, inits, r1mach
c
c series for psi on the interval 0. to 1.00000d+00
c with weighted error 2.03e-17
c log weighted error 16.69
c significant figures required 16.39
c decimal places required 17.37
c
data psi cs( 1) / -.0380570808 35217922e0 /
data psi cs( 2) / .4914153930 2938713e0 /
data psi cs( 3) / -.0568157478 21244730e0 /
data psi cs( 4) / .0083578212 25914313e0 /
data psi cs( 5) / -.0013332328 57994342e0 /
data psi cs( 6) / .0002203132 87069308e0 /
data psi cs( 7) / -.0000370402 38178456e0 /
data psi cs( 8) / .0000062837 93654854e0 /
data psi cs( 9) / -.0000010712 63908506e0 /
data psi cs(10) / .0000001831 28394654e0 /
data psi cs(11) / -.0000000313 53509361e0 /
data psi cs(12) / .0000000053 72808776e0 /
data psi cs(13) / -.0000000009 21168141e0 /
data psi cs(14) / .0000000001 57981265e0 /
data psi cs(15) / -.0000000000 27098646e0 /
data psi cs(16) / .0000000000 04648722e0 /
data psi cs(17) / -.0000000000 00797527e0 /
data psi cs(18) / .0000000000 00136827e0 /
data psi cs(19) / -.0000000000 00023475e0 /
data psi cs(20) / .0000000000 00004027e0 /
data psi cs(21) / -.0000000000 00000691e0 /
data psi cs(22) / .0000000000 00000118e0 /
data psi cs(23) / -.0000000000 00000020e0 /
c
c series for apsi on the interval 0. to 2.50000d-01
c with weighted error 5.54e-17
c log weighted error 16.26
c significant figures required 14.42
c decimal places required 16.86
c
data apsics( 1) / -.0204749044 678185e0 /
data apsics( 2) / -.0101801271 534859e0 /
data apsics( 3) / .0000559718 725387e0 /
data apsics( 4) / -.0000012917 176570e0 /
data apsics( 5) / .0000000572 858606e0 /
data apsics( 6) / -.0000000038 213539e0 /
data apsics( 7) / .0000000003 397434e0 /
data apsics( 8) / -.0000000000 374838e0 /
data apsics( 9) / .0000000000 048990e0 /
data apsics(10) / -.0000000000 007344e0 /
data apsics(11) / .0000000000 001233e0 /
data apsics(12) / -.0000000000 000228e0 /
data apsics(13) / .0000000000 000045e0 /
data apsics(14) / -.0000000000 000009e0 /
data apsics(15) / .0000000000 000002e0 /
data apsics(16) / -.0000000000 000000e0 /
c
data pi / 3.1415926535 8979324e0/
data ntpsi, ntapsi, xbig, dxrel /0, 0, 0., 0./
c
if (ntpsi.ne.0) go to 10
ntpsi = inits (psics, 23, 0.1*r1mach(3))
ntapsi = inits (apsics, 16, 0.1*r1mach(3))
c
xbig = 1.0/sqrt(r1mach(3))
dxrel = sqrt (r1mach(4))
c
10 y = abs(x)
if (y.ge.2.0) go to 30
c
c psi(x) for -2. .le. x .le. 2.
c
n = x
if (x.lt.0.) n = n - 1
y = x - float(n)
n = n - 1
psi = csevl (2.*y-1., psics, ntpsi)
if (n.eq.0) return
c
n = -n
if (x.eq.0.) call seteru (14hpsi x is 0, 14, 2, 2)
if (x.lt.0. .and. x+float(n-2).eq.0.) call seteru (
1 31hpsi x is a negative integer, 31, 3, 2)
if (x.lt.(-0.5) .and. abs((x-aint(x-0.5))/x).lt.dxrel) call seteru
1 (68hpsi answer lt half precision because x too near negative
1 integer, 68, 1, 1)
c
do 20 i=1,n
psi = psi - 1.0/(x+float(i-1))
20 continue
return
c
c psi(x) for abs(x) .ge. 2.
c
30 aux = 0.
if (y.lt.xbig) aux = csevl (8./y**2-1., apsics, ntapsi)
if (x.lt.0.) psi = alog(abs(x)) - 0.5/x + aux - pi*cot(pi*x)
if (x.gt.0.) psi = alog(x) - 0.5/x + aux
return
c
end
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