#
#  ln1x == ln(1+x)
#  expx1 == exp(x)-1
#
#	Computed acccurately when x is very small
#
#			Gaston Gonnet (May 12, 2002)
#			Gaston Gonnet (Dec 07, 2004)
#
ln1x := proc( x:numeric )
local i;
if |x| > 0.125 then ln(1+x)
elif |x| > 0.01 then
     x - x^2/2 - sum( (-x)^i/i, i=3..18 )
else x - (0.5-(1/3+(-1/4+(1/5+(-1/6+(1/7-x/8)*x)*x)*x)*x)*x)*x^2
     fi
end:


expx1 := proc( x:numeric )
if |x| > 0.6931 then exp(x)-1
elif |x| > 0.0433217 then
     t := procname(x/16);
     to 4 do t := 2*t+t^2 od;
     t
else (1+(1+(1+(1+(1+(1+(1+x/8)*x/7)*x/6)*x/5)*x/4)*x/3)*x/2)*x fi
end: