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fvn_fnlib/dasinh.f
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double precision function dasinh (x)
c june 1977 edition. w. fullerton, c3, los alamos scientific lab.
double precision x, asnhcs(39), aln2, sqeps, xmax, y,
1 dcsevl, d1mach, dlog, dsqrt
external d1mach, dcsevl, initds
c
c series for asnh on the interval 0. to 1.00000e+00
c with weighted error 2.26e-32
c log weighted error 31.65
c significant figures required 30.59
c decimal places required 32.44
c
data asnhcs( 1) / -.1282003991 1738186343 3721273592 68 d+0 /
data asnhcs( 2) / -.5881176118 9951767565 2117571383 62 d-1 /
data asnhcs( 3) / +.4727465432 2124815640 7252497560 29 d-2 /
data asnhcs( 4) / -.4938363162 6536172101 3601747902 73 d-3 /
data asnhcs( 5) / +.5850620705 8557412287 4948352593 21 d-4 /
data asnhcs( 6) / -.7466998328 9313681354 7550692171 88 d-5 /
data asnhcs( 7) / +.1001169358 3558199265 9661920158 12 d-5 /
data asnhcs( 8) / -.1390354385 8708333608 6164722588 86 d-6 /
data asnhcs( 9) / +.1982316948 3172793547 3173602371 48 d-7 /
data asnhcs( 10) / -.2884746841 7848843612 7472728003 17 d-8 /
data asnhcs( 11) / +.4267296546 7159937953 4575149959 07 d-9 /
data asnhcs( 12) / -.6397608465 4366357868 7526323096 81 d-10 /
data asnhcs( 13) / +.9699168608 9064704147 8782931311 79 d-11 /
data asnhcs( 14) / -.1484427697 2043770830 2466583656 96 d-11 /
data asnhcs( 15) / +.2290373793 9027447988 0401843789 83 d-12 /
data asnhcs( 16) / -.3558839513 2732645159 9789426513 10 d-13 /
data asnhcs( 17) / +.5563969408 0056789953 3745390885 54 d-14 /
data asnhcs( 18) / -.8746250959 9624678045 6665935201 62 d-15 /
data asnhcs( 19) / +.1381524884 4526692155 8688022981 29 d-15 /
data asnhcs( 20) / -.2191668828 2900363984 9551422641 49 d-16 /
data asnhcs( 21) / +.3490465852 4827565638 3139237068 80 d-17 /
data asnhcs( 22) / -.5578578840 0895742439 6301570321 06 d-18 /
data asnhcs( 23) / +.8944514661 7134012551 0508827989 33 d-19 /
data asnhcs( 24) / -.1438342634 6571317305 5518452394 66 d-19 /
data asnhcs( 25) / +.2319181187 2169963036 3261446826 66 d-20 /
data asnhcs( 26) / -.3748700795 3314343674 5706045439 99 d-21 /
data asnhcs( 27) / +.6073210982 2064279404 5492428800 00 d-22 /
data asnhcs( 28) / -.9859940276 4633583177 3701734400 00 d-23 /
data asnhcs( 29) / +.1603921745 2788496315 2326382933 33 d-23 /
data asnhcs( 30) / -.2613884735 0287686596 7161343999 99 d-24 /
data asnhcs( 31) / +.4267084960 6857390833 3581653333 33 d-25 /
data asnhcs( 32) / -.6977021703 9185243299 7307733333 33 d-26 /
data asnhcs( 33) / +.1142508833 6806858659 8126933333 33 d-26 /
data asnhcs( 34) / -.1873529207 8860968933 0210133333 33 d-27 /
data asnhcs( 35) / +.3076358441 4464922794 0659200000 00 d-28 /
data asnhcs( 36) / -.5057736403 1639824787 0463999999 99 d-29 /
data asnhcs( 37) / +.8325075471 2689142224 2133333333 33 d-30 /
data asnhcs( 38) / -.1371845728 2501044163 9253333333 33 d-30 /
data asnhcs( 39) / +.2262986842 6552784104 1066666666 66 d-31 /
c
data aln2 / 0.6931471805 5994530941 7232121458 18d0 /
data nterms, xmax, sqeps / 0, 2*0.d0 /
c
if (nterms.ne.0) go to 10
nterms = initds (asnhcs, 39, 0.1*sngl(d1mach(3)) )
sqeps = dsqrt (d1mach(3))
xmax = 1.0d0/sqeps
c
10 y = dabs(x)
if (y.gt.1.0d0) go to 20
c
dasinh = x
if (y.gt.sqeps) dasinh = x*(1.0d0 + dcsevl (2.d0*x*x-1.d0,
1 asnhcs, nterms) )
return
20 if (y.lt.xmax) dasinh = dlog (y + dsqrt(y*y+1.d0) )
if (y.ge.xmax) dasinh = aln2 + dlog(y)
dasinh = dsign (dasinh, x)
return
c
end
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