asinh.f
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function asinh (x)
c april 1977 edition. w. fullerton, c3, los alamos scientific lab.
dimension asnhcs(20)
external csevl, inits, r1mach
data aln2 /0.6931471805 5994530942e0/
c
c series for asnh on the interval 0. to 1.00000d+00
c with weighted error 2.19e-17
c log weighted error 16.66
c significant figures required 15.60
c decimal places required 17.31
c
data asnhcs( 1) / -.1282003991 1738186e0 /
data asnhcs( 2) / -.0588117611 89951768e0 /
data asnhcs( 3) / .0047274654 32212481e0 /
data asnhcs( 4) / -.0004938363 16265361e0 /
data asnhcs( 5) / .0000585062 07058557e0 /
data asnhcs( 6) / -.0000074669 98328931e0 /
data asnhcs( 7) / .0000010011 69358355e0 /
data asnhcs( 8) / -.0000001390 35438587e0 /
data asnhcs( 9) / .0000000198 23169483e0 /
data asnhcs(10) / -.0000000028 84746841e0 /
data asnhcs(11) / .0000000004 26729654e0 /
data asnhcs(12) / -.0000000000 63976084e0 /
data asnhcs(13) / .0000000000 09699168e0 /
data asnhcs(14) / -.0000000000 01484427e0 /
data asnhcs(15) / .0000000000 00229037e0 /
data asnhcs(16) / -.0000000000 00035588e0 /
data asnhcs(17) / .0000000000 00005563e0 /
data asnhcs(18) / -.0000000000 00000874e0 /
data asnhcs(19) / .0000000000 00000138e0 /
data asnhcs(20) / -.0000000000 00000021e0 /
c
data nterms, xmax, sqeps /0, 0., 0./
c
if (nterms.ne.0) go to 10
nterms = inits (asnhcs, 20, 0.1*r1mach(3))
sqeps = sqrt (r1mach(3))
xmax = 1.0/sqeps
c
10 y = abs(x)
if (y.gt.1.0) go to 20
c
asinh = x
if (y.gt.sqeps) asinh = x*(1.0 + csevl (2.*x*x-1., asnhcs,nterms))
return
c
20 if (y.lt.xmax) asinh = alog (y + sqrt(y**2+1.))
if (y.ge.xmax) asinh = aln2 + alog(y)
asinh = sign (asinh, x)
c
return
end