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fvn_fnlib/e1.f
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function e1 (x)
c july 1977 edition. w. fullerton, c3, los alamos scientific lab.
dimension ae11cs(39), ae12cs(25), e11cs(19), e12cs(16),
1 ae13cs(25), ae14cs(26)
external csevl, inits, r1mach
c
c series for ae11 on the interval -1.00000d-01 to 0.
c with weighted error 1.76e-17
c log weighted error 16.75
c significant figures required 15.70
c decimal places required 17.55
c
data ae11cs( 1) / .1215032397 1606579e0 /
data ae11cs( 2) / -.0650887785 13550150e0 /
data ae11cs( 3) / .0048976513 57459670e0 /
data ae11cs( 4) / -.0006492378 43027216e0 /
data ae11cs( 5) / .0000938404 34587471e0 /
data ae11cs( 6) / .0000004202 36380882e0 /
data ae11cs( 7) / -.0000081133 74735904e0 /
data ae11cs( 8) / .0000028042 47688663e0 /
data ae11cs( 9) / .0000000564 87164441e0 /
data ae11cs(10) / -.0000003448 09174450e0 /
data ae11cs(11) / .0000000582 09273578e0 /
data ae11cs(12) / .0000000387 11426349e0 /
data ae11cs(13) / -.0000000124 53235014e0 /
data ae11cs(14) / -.0000000051 18504888e0 /
data ae11cs(15) / .0000000021 48771527e0 /
data ae11cs(16) / .0000000008 68459898e0 /
data ae11cs(17) / -.0000000003 43650105e0 /
data ae11cs(18) / -.0000000001 79796603e0 /
data ae11cs(19) / .0000000000 47442060e0 /
data ae11cs(20) / .0000000000 40423282e0 /
data ae11cs(21) / -.0000000000 03543928e0 /
data ae11cs(22) / -.0000000000 08853444e0 /
data ae11cs(23) / -.0000000000 00960151e0 /
data ae11cs(24) / .0000000000 01692921e0 /
data ae11cs(25) / .0000000000 00607990e0 /
data ae11cs(26) / -.0000000000 00224338e0 /
data ae11cs(27) / -.0000000000 00200327e0 /
data ae11cs(28) / -.0000000000 00006246e0 /
data ae11cs(29) / .0000000000 00045571e0 /
data ae11cs(30) / .0000000000 00016383e0 /
data ae11cs(31) / -.0000000000 00005561e0 /
data ae11cs(32) / -.0000000000 00006074e0 /
data ae11cs(33) / -.0000000000 00000862e0 /
data ae11cs(34) / .0000000000 00001223e0 /
data ae11cs(35) / .0000000000 00000716e0 /
data ae11cs(36) / -.0000000000 00000024e0 /
data ae11cs(37) / -.0000000000 00000201e0 /
data ae11cs(38) / -.0000000000 00000082e0 /
data ae11cs(39) / .0000000000 00000017e0 /
c
c series for ae12 on the interval -2.50000d-01 to -1.00000d-01
c with weighted error 5.83e-17
c log weighted error 16.23
c significant figures required 15.76
c decimal places required 16.93
c
data ae12cs( 1) / .5824174951 3472674e0 /
data ae12cs( 2) / -.1583488509 0578275e0 /
data ae12cs( 3) / -.0067642755 90323141e0 /
data ae12cs( 4) / .0051258439 50185725e0 /
data ae12cs( 5) / .0004352324 92169391e0 /
data ae12cs( 6) / -.0001436133 66305483e0 /
data ae12cs( 7) / -.0000418013 20556301e0 /
data ae12cs( 8) / -.0000027133 95758640e0 /
data ae12cs( 9) / .0000011513 81913647e0 /
data ae12cs(10) / .0000004206 50022012e0 /
data ae12cs(11) / .0000000665 81901391e0 /
data ae12cs(12) / .0000000006 62143777e0 /
data ae12cs(13) / -.0000000028 44104870e0 /
data ae12cs(14) / -.0000000009 40724197e0 /
data ae12cs(15) / -.0000000001 77476602e0 /
data ae12cs(16) / -.0000000000 15830222e0 /
data ae12cs(17) / .0000000000 02905732e0 /
data ae12cs(18) / .0000000000 01769356e0 /
data ae12cs(19) / .0000000000 00492735e0 /
data ae12cs(20) / .0000000000 00093709e0 /
data ae12cs(21) / .0000000000 00010707e0 /
data ae12cs(22) / -.0000000000 00000537e0 /
data ae12cs(23) / -.0000000000 00000716e0 /
data ae12cs(24) / -.0000000000 00000244e0 /
data ae12cs(25) / -.0000000000 00000058e0 /
c
c series for e11 on the interval -4.00000d+00 to -1.00000d+00
c with weighted error 1.08e-18
c log weighted error 17.97
c significant figures required 19.02
c decimal places required 18.61
c
data e11 cs( 1) / -16.1134616555 71494026e0 /
data e11 cs( 2) / 7.7940727787 426802769e0 /
data e11 cs( 3) / -1.9554058188 631419507e0 /
data e11 cs( 4) / .3733729386 6277945612e0 /
data e11 cs( 5) / -.0569250319 1092901938e0 /
data e11 cs( 6) / .0072110777 6966009185e0 /
data e11 cs( 7) / -.0007810490 1449841593e0 /
data e11 cs( 8) / .0000738809 3356262168e0 /
data e11 cs( 9) / -.0000062028 6187580820e0 /
data e11 cs(10) / .0000004681 6002303176e0 /
data e11 cs(11) / -.0000000320 9288853329e0 /
data e11 cs(12) / .0000000020 1519974874e0 /
data e11 cs(13) / -.0000000001 1673686816e0 /
data e11 cs(14) / .0000000000 0627627066e0 /
data e11 cs(15) / -.0000000000 0031481541e0 /
data e11 cs(16) / .0000000000 0001479904e0 /
data e11 cs(17) / -.0000000000 0000065457e0 /
data e11 cs(18) / .0000000000 0000002733e0 /
data e11 cs(19) / -.0000000000 0000000108e0 /
c
c series for e12 on the interval -1.00000d+00 to 1.00000d+00
c with weighted error 3.15e-18
c log weighted error 17.50
c approx significant figures required 15.8
c decimal places required 18.10
c
data e12 cs( 1) / -0.0373902147 92202795e0 /
data e12 cs( 2) / 0.0427239860 62209577e0 /
data e12 cs( 3) / -.1303182079 849700544e0 /
data e12 cs( 4) / .0144191240 2469889073e0 /
data e12 cs( 5) / -.0013461707 8051068022e0 /
data e12 cs( 6) / .0001073102 9253063780e0 /
data e12 cs( 7) / -.0000074299 9951611943e0 /
data e12 cs( 8) / .0000004537 7325690753e0 /
data e12 cs( 9) / -.0000000247 6417211390e0 /
data e12 cs(10) / .0000000012 2076581374e0 /
data e12 cs(11) / -.0000000000 5485141480e0 /
data e12 cs(12) / .0000000000 0226362142e0 /
data e12 cs(13) / -.0000000000 0008635897e0 /
data e12 cs(14) / .0000000000 0000306291e0 /
data e12 cs(15) / -.0000000000 0000010148e0 /
data e12 cs(16) / .0000000000 0000000315e0 /
c
c series for ae13 on the interval 2.50000d-01 to 1.00000d+00
c with weighted error 2.34e-17
c log weighted error 16.63
c significant figures required 16.14
c decimal places required 17.33
c
data ae13cs( 1) / -.6057732466 4060346e0 /
data ae13cs( 2) / -.1125352434 8366090e0 /
data ae13cs( 3) / .0134322662 47902779e0 /
data ae13cs( 4) / -.0019268451 87381145e0 /
data ae13cs( 5) / .0003091183 37720603e0 /
data ae13cs( 6) / -.0000535641 32129618e0 /
data ae13cs( 7) / .0000098278 12880247e0 /
data ae13cs( 8) / -.0000018853 68984916e0 /
data ae13cs( 9) / .0000003749 43193568e0 /
data ae13cs(10) / -.0000000768 23455870e0 /
data ae13cs(11) / .0000000161 43270567e0 /
data ae13cs(12) / -.0000000034 66802211e0 /
data ae13cs(13) / .0000000007 58754209e0 /
data ae13cs(14) / -.0000000001 68864333e0 /
data ae13cs(15) / .0000000000 38145706e0 /
data ae13cs(16) / -.0000000000 08733026e0 /
data ae13cs(17) / .0000000000 02023672e0 /
data ae13cs(18) / -.0000000000 00474132e0 /
data ae13cs(19) / .0000000000 00112211e0 /
data ae13cs(20) / -.0000000000 00026804e0 /
data ae13cs(21) / .0000000000 00006457e0 /
data ae13cs(22) / -.0000000000 00001568e0 /
data ae13cs(23) / .0000000000 00000383e0 /
data ae13cs(24) / -.0000000000 00000094e0 /
data ae13cs(25) / .0000000000 00000023e0 /
c
c series for ae14 on the interval 0. to 2.50000d-01
c with weighted error 5.41e-17
c log weighted error 16.27
c significant figures required 15.38
c decimal places required 16.97
c
data ae14cs( 1) / -.1892918000 753017e0 /
data ae14cs( 2) / -.0864811785 5259871e0 /
data ae14cs( 3) / .0072241015 4374659e0 /
data ae14cs( 4) / -.0008097559 4575573e0 /
data ae14cs( 5) / .0001099913 4432661e0 /
data ae14cs( 6) / -.0000171733 2998937e0 /
data ae14cs( 7) / .0000029856 2751447e0 /
data ae14cs( 8) / -.0000005659 6491457e0 /
data ae14cs( 9) / .0000001152 6808397e0 /
data ae14cs(10) / -.0000000249 5030440e0 /
data ae14cs(11) / .0000000056 9232420e0 /
data ae14cs(12) / -.0000000013 5995766e0 /
data ae14cs(13) / .0000000003 3846628e0 /
data ae14cs(14) / -.0000000000 8737853e0 /
data ae14cs(15) / .0000000000 2331588e0 /
data ae14cs(16) / -.0000000000 0641148e0 /
data ae14cs(17) / .0000000000 0181224e0 /
data ae14cs(18) / -.0000000000 0052538e0 /
data ae14cs(19) / .0000000000 0015592e0 /
data ae14cs(20) / -.0000000000 0004729e0 /
data ae14cs(21) / .0000000000 0001463e0 /
data ae14cs(22) / -.0000000000 0000461e0 /
data ae14cs(23) / .0000000000 0000148e0 /
data ae14cs(24) / -.0000000000 0000048e0 /
data ae14cs(25) / .0000000000 0000016e0 /
data ae14cs(26) / -.0000000000 0000005e0 /
c
data ntae11, ntae12, nte11, nte12, ntae13, ntae14 /6*0/
data xmax /0./
c
if (ntae11.ne.0) go to 10
eta = 0.1*r1mach(3)
ntae11 = inits (ae11cs, 39, eta)
ntae12 = inits (ae12cs, 25, eta)
nte11 = inits (e11cs, 19, eta)
nte12 = inits (e12cs, 16, eta)
ntae13 = inits (ae13cs, 25, eta)
ntae14 = inits (ae14cs, 26, eta)
c
xmax = -alog (r1mach(1))
xmax = xmax - alog(xmax)
c
10 if (x.gt.(-10.)) go to 20
c
c e1(x) = -ei(-x) for x .le. -10.
c
e1 = exp(-x)/x * (1.+csevl (20./x+1., ae11cs, ntae11))
return
c
20 if (x.gt.(-4.0)) go to 30
c
c e1(x) = -ei(-x) for -10. .lt. x .le. -4.
c
e1 = exp(-x)/x * (1.+csevl ((40./x+7.)/3., ae12cs, ntae12))
return
c
30 if (x.gt.(-1.0)) go to 40
c
c e1(x) = -ei(-x) for -4. .lt. x .le. -1.
c
e1 = -alog(abs(x)) + csevl ((2.*x+5.)/3., e11cs, nte11)
return
c
40 if (x.gt.1.) go to 50
if (x.eq.0.) call seteru (14he1 x is 0, 14, 2, 2)
c
c e1(x) = -ei(-x) for -1. .lt. x .le. 1., x .ne. 0.
c
e1 = (-alog(abs(x)) - 0.6875 + x) + csevl (x, e12cs, nte12)
return
c
50 if (x.gt.4.) go to 60
c
c e1(x) = -ei(-x) for 1. .lt. x .le. 4.
c
e1 = exp(-x)/x * (1.+csevl ((8./x-5.)/3., ae13cs, ntae13))
return
c
60 if (x.gt.xmax) go to 70
c
c e1(x) = -ei(-x) for 4. .lt. x .le. xmax
c
e1 = exp(-x)/x * (1. + csevl (8./x-1., ae14cs, ntae14))
return
c
c e1(x) = -ei(-x) for x .gt. xmax
c
70 call seteru (30he1 x so big e1 underflows, 30, 1, 0)
e1 = 0.
return
c
end
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