Function k1_small 

pub(crate) fn k1_small(x: f64) -> DoubleDouble

Rational approximant for f(x) := BesselK(1, x) - Log(x)*BesselI(1, x) - 1/x

Generated by Wolfram Mathematica:

<<FunctionApproximations`
ClearAll["Global`*"]
f[x_]:=(BesselK[1,x]-Log[x]BesselI[1,x]-1/x)/x
g[z_]:=f[Sqrt[z]]
{err,approx}=MiniMaxApproximation[g[z],{z,{0.0000000000001,1},5,4},WorkingPrecision->60]
poly=Numerator[approx][[1]];
coeffs=CoefficientList[poly,z];
TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50},ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]
poly=Denominator[approx][[1]];
coeffs=CoefficientList[poly,z];
TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50},ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]