Linear-log -> asinh(x) Its linear for small values and log for large. It also has the advantage that it is continuous and smooth. (Obviously asinh is not very

Linear-log -> asinh(x) Its linear for small values and log for large. It also has the advantage that it is continuous and smooth. (Obviously asinh is not very useful for allocation) I first thought of it while pondering an amp that would best use the limited dynamic range of a (analog) recording media. Thats what I do in my free time. I later realized that asinh(f(x)) is a great substitute for log space when plotting. It preserves the sign and the small value details while compressing large values. Unfortunately no one os familiar with this mapping. EDIT: from apeheele's comment below I noticed I made a mistake and its not tanh, but asinh that is linear for small x and logarithmic for large c.