function bie (x) c july 1977 edition. w. fullerton, c3, los alamos scientific lab. c c evaluate bi(x) for x .le. 0 and bi(x)*exp(-zeta) where c zeta = 2/3 * x**(3/2) for x .ge. 0.0 c dimension bifcs(9), bigcs(8), bif2cs(10), big2cs(10), bipcs(24), 1 bip2cs(29) external csevl, exp, inits, r1mach, sin, sqrt c c series for bif on the interval -1.00000d+00 to 1.00000d+00 c with weighted error 1.88e-19 c log weighted error 18.72 c significant figures required 17.74 c decimal places required 19.20 c data bif cs( 1) / -.0167302164 7198664948e0 / data bif cs( 2) / .1025233583 424944561e0 / data bif cs( 3) / .0017083092 5073815165e0 / data bif cs( 4) / .0000118625 4546774468e0 / data bif cs( 5) / .0000000449 3290701779e0 / data bif cs( 6) / .0000000001 0698207143e0 / data bif cs( 7) / .0000000000 0017480643e0 / data bif cs( 8) / .0000000000 0000020810e0 / data bif cs( 9) / .0000000000 0000000018e0 / c c series for big on the interval -1.00000d+00 to 1.00000d+00 c with weighted error 2.61e-17 c log weighted error 16.58 c significant figures required 15.17 c decimal places required 17.03 c data big cs( 1) / .0224662232 4857452e0 / data big cs( 2) / .0373647754 5301955e0 / data big cs( 3) / .0004447621 8957212e0 / data big cs( 4) / .0000024708 0756363e0 / data big cs( 5) / .0000000079 1913533e0 / data big cs( 6) / .0000000000 1649807e0 / data big cs( 7) / .0000000000 0002411e0 / data big cs( 8) / .0000000000 0000002e0 / c c series for bif2 on the interval 1.00000d+00 to 8.00000d+00 c with weighted error 1.11e-17 c log weighted error 16.95 c approx significant figures required 16.5 c decimal places required 17.45 c data bif2cs( 1) / 0.0998457269 3816041e0 / data bif2cs( 2) / .4786249778 63005538e0 / data bif2cs( 3) / .0251552119 604330118e0 / data bif2cs( 4) / .0005820693 885232645e0 / data bif2cs( 5) / .0000074997 659644377e0 / data bif2cs( 6) / .0000000613 460287034e0 / data bif2cs( 7) / .0000000003 462753885e0 / data bif2cs( 8) / .0000000000 014288910e0 / data bif2cs( 9) / .0000000000 000044962e0 / data bif2cs(10) / .0000000000 000000111e0 / c c series for big2 on the interval 1.00000d+00 to 8.00000d+00 c with weighted error 1.19e-18 c log weighted error 17.92 c approx significant figures required 17.2 c decimal places required 18.42 c data big2cs( 1) / .0333056621 45514340e0 / data big2cs( 2) / .1613092151 23197068e0 / data big2cs( 3) / .0063190073 096134286e0 / data big2cs( 4) / .0001187904 568162517e0 / data big2cs( 5) / .0000013045 345886200e0 / data big2cs( 6) / .0000000093 741259955e0 / data big2cs( 7) / .0000000000 474580188e0 / data big2cs( 8) / .0000000000 001783107e0 / data big2cs( 9) / .0000000000 000005167e0 / data big2cs(10) / .0000000000 000000011e0 / c c series for bip on the interval 1.25000d-01 to 3.53553d-01 c with weighted error 1.91e-17 c log weighted error 16.72 c significant figures required 15.35 c decimal places required 17.41 c data bip cs( 1) / -.0832204747 7943447e0 / data bip cs( 2) / .0114611892 7371174e0 / data bip cs( 3) / .0004289644 0718911e0 / data bip cs( 4) / -.0001490663 9379950e0 / data bip cs( 5) / -.0000130765 9726787e0 / data bip cs( 6) / .0000063275 9839610e0 / data bip cs( 7) / -.0000004222 6696982e0 / data bip cs( 8) / -.0000001914 7186298e0 / data bip cs( 9) / .0000000645 3106284e0 / data bip cs(10) / -.0000000078 4485467e0 / data bip cs(11) / -.0000000009 6077216e0 / data bip cs(12) / .0000000007 0004713e0 / data bip cs(13) / -.0000000001 7731789e0 / data bip cs(14) / .0000000000 2272089e0 / data bip cs(15) / .0000000000 0165404e0 / data bip cs(16) / -.0000000000 0185171e0 / data bip cs(17) / .0000000000 0059576e0 / data bip cs(18) / -.0000000000 0012194e0 / data bip cs(19) / .0000000000 0001334e0 / data bip cs(20) / .0000000000 0000172e0 / data bip cs(21) / -.0000000000 0000145e0 / data bip cs(22) / .0000000000 0000049e0 / data bip cs(23) / -.0000000000 0000011e0 / data bip cs(24) / .0000000000 0000001e0 / c c series for bip2 on the interval 0. to 1.25000d-01 c with weighted error 1.05e-18 c log weighted error 17.98 c significant figures required 16.74 c decimal places required 18.71 c data bip2cs( 1) / -.1135967375 85988679e0 / data bip2cs( 2) / .0041381473 947881595e0 / data bip2cs( 3) / .0001353470 622119332e0 / data bip2cs( 4) / .0000104273 166530153e0 / data bip2cs( 5) / .0000013474 954767849e0 / data bip2cs( 6) / .0000001696 537405438e0 / data bip2cs( 7) / -.0000000100 965008656e0 / data bip2cs( 8) / -.0000000167 291194937e0 / data bip2cs( 9) / -.0000000045 815364485e0 / data bip2cs(10) / .0000000003 736681366e0 / data bip2cs(11) / .0000000005 766930320e0 / data bip2cs(12) / .0000000000 621812650e0 / data bip2cs(13) / -.0000000000 632941202e0 / data bip2cs(14) / -.0000000000 149150479e0 / data bip2cs(15) / .0000000000 078896213e0 / data bip2cs(16) / .0000000000 024960513e0 / data bip2cs(17) / -.0000000000 012130075e0 / data bip2cs(18) / -.0000000000 003740493e0 / data bip2cs(19) / .0000000000 002237727e0 / data bip2cs(20) / .0000000000 000474902e0 / data bip2cs(21) / -.0000000000 000452616e0 / data bip2cs(22) / -.0000000000 000030172e0 / data bip2cs(23) / .0000000000 000091058e0 / data bip2cs(24) / -.0000000000 000009814e0 / data bip2cs(25) / -.0000000000 000016429e0 / data bip2cs(26) / .0000000000 000005533e0 / data bip2cs(27) / .0000000000 000002175e0 / data bip2cs(28) / -.0000000000 000001737e0 / data bip2cs(29) / -.0000000000 000000010e0 / c data atr / 8.750690570 8484345 e0 / c atr = 16.0/(sqrt(8.)-1.) and btr = -(sqrt(8.)+1.)/(sqrt(8.)-1.) data btr / -2.093836321 356054 e0 / c data nbif, nbig, nbif2, nbig2, nbip, nbip2 / 6*0 / data x3sml, x32sml, xbig / 3*0.0 / c if (nbif.ne.0) go to 10 eta = 0.1*r1mach(3) nbif = inits (bifcs, 9, eta) nbig = inits (bigcs, 8, eta) nbif2 = inits (bif2cs, 10, eta) nbig2 = inits (big2cs, 10, eta) nbip = inits (bipcs , 24, eta) nbip2 = inits (bip2cs, 29, eta) c x3sml = eta**0.3333 x32sml = 1.3104*x3sml**2 xbig = r1mach(2)**0.6666 c 10 if (x.ge.(-1.0)) go to 20 call r9aimp (x, xm, theta) bie = xm * sin(theta) return c 20 if (x.gt.1.0) go to 30 z = 0.0 if (abs(x).gt.x3sml) z = x**3 bie = 0.625 + csevl (z, bifcs, nbif) + x*(0.4375 + 1 csevl (z, bigcs, nbig)) if (x.gt.x32sml) bie = bie * exp(-2.0*x*sqrt(x)/3.0) return c 30 if (x.gt.2.0) go to 40 z = (2.0*x**3 - 9.0) / 7.0 bie = exp(-2.0*x*sqrt(x)/3.0) * (1.125 + csevl (z, bif2cs, nbif2) 1 + x*(0.625 + csevl (z, big2cs, nbig2)) ) return c 40 if (x.gt.4.0) go to 50 sqrtx = sqrt(x) z = atr/(x*sqrtx) + btr bie = (0.625 + csevl (z, bipcs, nbip)) / sqrt(sqrtx) return c 50 sqrtx = sqrt(x) z = -1.0 if (x.lt.xbig) z = 16.0/(x*sqrtx) - 1.0 bie = (0.625 + csevl (z, bip2cs, nbip2))/sqrt(sqrtx) return c end