(12C) log1p function

[Albert Chan]

Using relation again: atanh(sin(z)) = asinh(tan(z))
Assume x positive, but close to 0

atanh( 1-x ) = asinh( (1-x) / √(2x-x²) )
atanh( x-1 ) = -atanh( 1-x )

Example, x = 1.2345678e-9, using Casio FX-115MS, showing internal digits:

atanh( 1-x ) = atanh(0.999999998766) = 10.6030760457

asinh( (1-x) / √(2x-x²) ) = asinh(20124.612604) = 10.6028460338 (all digits correct)

Edit: another way, also very good: atanh( 1-x ) = ½ ln(2/x - 1)