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double precision function d9ln2r (x)
c april 1978 edition. w. fullerton c3, los alamos scientific lab.
c
c evaluate dlog(1+x) from 2-nd order with relative error accuracy so
c that dlog(1+x) = x - x**2/2 + x**3*d9ln2r(x)
c
double precision x, xbig, xmax, xmin, ln21cs(50), ln22cs(37),
1 dcsevl, d1mach, dlog, dsqrt
external d1mach, dcsevl, initds
c
c series for ln21 on the interval -6.25000e-01 to 0.
c with weighted error 1.82e-32
c log weighted error 31.74
c significant figures required 31.00
c decimal places required 32.59
c
data ln21cs( 1) / +.1811196251 3478809875 8949530430 71 d+0 /
data ln21cs( 2) / -.1562712319 2872462669 6251555410 78 d+0 /
data ln21cs( 3) / +.2867630536 1557275209 5406271020 51 d-1 /
data ln21cs( 4) / -.5558699655 9481398781 1577251267 81 d-2 /
data ln21cs( 5) / +.1117897665 2299837657 3356662797 27 d-2 /
data ln21cs( 6) / -.2308050898 2327947182 2992795857 05 d-3 /
data ln21cs( 7) / +.4859885334 1100175874 6815580687 50 d-4 /
data ln21cs( 8) / -.1039012738 8903210765 5142426333 38 d-4 /
data ln21cs( 9) / +.2248456370 7390128494 6218049464 08 d-5 /
data ln21cs( 10) / -.4914059273 9266484875 3278025970 91 d-6 /
data ln21cs( 11) / +.1082825650 7077483336 6201529715 97 d-6 /
data ln21cs( 12) / -.2402587276 3420701435 9766754167 19 d-7 /
data ln21cs( 13) / +.5362460047 2708133762 9844432501 63 d-8 /
data ln21cs( 14) / -.1202995136 2138772264 6716464243 77 d-8 /
data ln21cs( 15) / +.2710788927 7591860785 6225516322 66 d-9 /
data ln21cs( 16) / -.6132356261 8319010068 7967284306 90 d-10 /
data ln21cs( 17) / +.1392085836 9159469857 4369085439 78 d-10 /
data ln21cs( 18) / -.3169930033 0223494015 2830572608 83 d-11 /
data ln21cs( 19) / +.7238375404 4307505335 2143261970 11 d-12 /
data ln21cs( 20) / -.1657001718 4764411391 4988055062 68 d-12 /
data ln21cs( 21) / +.3801842866 3117424257 3644226318 76 d-13 /
data ln21cs( 22) / -.8741118929 6972700259 7244298991 37 d-14 /
data ln21cs( 23) / +.2013561984 5055748302 1187510281 54 d-14 /
data ln21cs( 24) / -.4646445640 9033907031 1020081544 77 d-15 /
data ln21cs( 25) / +.1073928214 7018339453 4533385549 25 d-15 /
data ln21cs( 26) / -.2485853461 9937794755 5340218339 60 d-16 /
data ln21cs( 27) / +.5762019795 0800189813 8881426281 81 d-17 /
data ln21cs( 28) / -.1337306376 9804394701 4021999580 50 d-17 /
data ln21cs( 29) / +.3107465322 7331824966 5338071668 05 d-18 /
data ln21cs( 30) / -.7228810408 3040539906 9019579176 27 d-19 /
data ln21cs( 31) / +.1683378378 8037385103 3132581868 88 d-19 /
data ln21cs( 32) / -.3923946331 2069958052 5193727399 25 d-20 /
data ln21cs( 33) / +.9155146838 7536789746 3855286408 53 d-21 /
data ln21cs( 34) / -.2137889532 1320159520 9820958010 02 d-21 /
data ln21cs( 35) / +.4996450747 9047864699 8285645687 46 d-22 /
data ln21cs( 36) / -.1168624063 6080170135 3608061474 13 d-22 /
data ln21cs( 37) / +.2735312347 0391863775 6286867865 59 d-23 /
data ln21cs( 38) / -.6406802508 4792111965 0503458815 99 d-24 /
data ln21cs( 39) / +.1501629320 4334124162 9490719402 66 d-24 /
data ln21cs( 40) / -.3521737241 0398479759 4971450026 66 d-25 /
data ln21cs( 41) / +.8264390101 4814767012 4827333973 33 d-26 /
data ln21cs( 42) / -.1940493027 5943401918 0366178986 66 d-26 /
data ln21cs( 43) / +.4558788001 8841283562 4515884373 33 d-27 /
data ln21cs( 44) / -.1071549208 7545202154 3786250239 99 d-27 /
data ln21cs( 45) / +.2519940800 7927592978 0966741333 33 d-28 /
data ln21cs( 46) / -.5928908840 0120969341 7504768000 00 d-29 /
data ln21cs( 47) / +.1395586406 1057513058 2371532799 99 d-29 /
data ln21cs( 48) / -.3286457881 3478583431 4366975999 99 d-30 /
data ln21cs( 49) / +.7742496795 0478166247 2546986666 66 d-31 /
data ln21cs( 50) / -.1824773566 7260887638 1252266666 66 d-31 /
c
c series for ln22 on the interval 0. to 8.12500e-01
c with weighted error 6.10e-32
c log weighted error 31.21
c significant figures required 30.32
c decimal places required 32.00
c
data ln22cs( 1) / -.2224253253 5020460829 8601522355 2 d+0 /
data ln22cs( 2) / -.6104710010 8078623986 8010475576 4 d-1 /
data ln22cs( 3) / +.7427235009 7503945905 1962975572 9 d-2 /
data ln22cs( 4) / -.9335018261 6369705656 1277960639 7 d-3 /
data ln22cs( 5) / +.1200499076 8726012833 5073128735 9 d-3 /
data ln22cs( 6) / -.1570472295 2820041128 2335260824 3 d-4 /
data ln22cs( 7) / +.2081874781 0512710960 5078359275 9 d-5 /
data ln22cs( 8) / -.2789195577 6467136540 5721305137 5 d-6 /
data ln22cs( 9) / +.3769355823 7601320584 2289513544 7 d-7 /
data ln22cs( 10) / -.5130902896 5277112582 4058993800 3 d-8 /
data ln22cs( 11) / +.7027141178 1506947382 0621821539 2 d-9 /
data ln22cs( 12) / -.9674859550 1343423892 4397200513 7 d-10 /
data ln22cs( 13) / +.1338104645 9248873065 8849644974 8 d-10 /
data ln22cs( 14) / -.1858102603 5340639816 2845384659 1 d-11 /
data ln22cs( 15) / +.2589294422 5279197493 0860012307 0 d-12 /
data ln22cs( 16) / -.3619568316 1415886744 6602538217 2 d-13 /
data ln22cs( 17) / +.5074037398 0166230880 0685891739 6 d-14 /
data ln22cs( 18) / -.7131012977 0311273027 0093874892 7 d-15 /
data ln22cs( 19) / +.1004490328 5545674818 5338678412 6 d-15 /
data ln22cs( 20) / -.1417906532 1840257919 0440507528 5 d-16 /
data ln22cs( 21) / +.2005297034 7433261178 9108639607 4 d-17 /
data ln22cs( 22) / -.2840996662 3398033053 6539671756 7 d-18 /
data ln22cs( 23) / +.4031469883 9690798995 9987866282 6 d-19 /
data ln22cs( 24) / -.5729325241 8322073204 5549895679 9 d-20 /
data ln22cs( 25) / +.8153488253 8900106758 4892873386 6 d-21 /
data ln22cs( 26) / -.1161825588 5497217876 0602746879 9 d-21 /
data ln22cs( 27) / +.1657516611 6625383436 5933977599 9 d-22 /
data ln22cs( 28) / -.2367336704 7108051901 1401728000 0 d-23 /
data ln22cs( 29) / +.3384670367 9755213860 7656959999 9 d-24 /
data ln22cs( 30) / -.4843940829 2157182042 9639679999 9 d-25 /
data ln22cs( 31) / +.6938759162 5142737186 7613866666 6 d-26 /
data ln22cs( 32) / -.9948142607 0314365719 2379733333 3 d-27 /
data ln22cs( 33) / +.1427440611 2116986106 3475200000 0 d-27 /
data ln22cs( 34) / -.2049794721 8982349115 6650666666 6 d-28 /
data ln22cs( 35) / +.2945648756 4013622228 8554666666 6 d-29 /
data ln22cs( 36) / -.4235973185 1849570276 6933333333 3 d-30 /
data ln22cs( 37) / +.6095532614 0038320401 0666666666 6 d-31 /
c
data ntln21, ntln22, xmin, xbig, xmax / 2*0, 3*0.d0 /
c
if (ntln21.ne.0) go to 10
eps = d1mach(3)
ntln21 = initds (ln21cs, 50, 0.1*eps)
ntln22 = initds (ln22cs, 37, 0.1*eps)
c
xmin = -1.0d0 + dsqrt(d1mach(4))
sqeps = sqrt (eps)
xmax = 8.0/sqeps
xmax = xmax - (dble(eps)*xmax**2 - 2.d0*dlog(xmax))
1 / (2.d0*dble(eps)*xmax)
xbig = 6.0/sqrt(sqeps)
xbig = xbig - (dble(sqeps)*xbig**2 - 2.d0*dlog(xbig))
1 / (2.d0*dble(sqeps)*xbig)
c
10 if (x.lt.(-.625d0) .or. x.gt.0.8125d0) go to 20
c
if (x.lt.0.0d0) d9ln2r = 0.375d0 + dcsevl (16.d0*x/5.d0+1.d0,
1 ln21cs, ntln21)
if (x.ge.0.0d0) d9ln2r = 0.375d0 + dcsevl (32.d0*x/13.d0-1.d0,
1 ln22cs, ntln22)
return
c
20 if (x.lt.xmin) call seteru (
1 57hd9ln2r answer lt half precision because x is too near -1,
2 57, 1, 1)
if (x.gt.xmax) call seteru (
1 51hd9ln2r no precision in answer because x is too big, 51,
2 3, 2)
if (x.gt.xbig) call seteru (
1 53hd9ln2r answer lt half precision because x is too big, 53,
2 2, 1)
c
d9ln2r = (dlog(1.d0+x) - x*(1.d0 - 0.5d0*x)) / x**3
return
c
end
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