Color space conversion errors with ProPhoto RGB — 15 bits

Now let’s look at ProPhotoRGB conversion errors with 15-bit quantization.  I took all 16+ million colors in sRGB and converted them to PPRGB and back, quantizing to 15-bits per color plane after each conversion. The conversions themselves were performed algorithmically (no tables involved) with double precision floating point, and have errors on the order of 10^-14 CIELab DeltaE.  I looked at the CIELab DeltaE errors after each iteration:

If we take all the colors available  in an 8-bit representation of PPRGB, convert them to 15bits per color plane, thence to Lab and back, quantizing to 15 bits after eadh conversion this is what we see:

In the past tests, 16 bit results have had half the error of 15-bit ones. Assuming that continues, in a 15 or 16-bit editing environment, it doesn’t look like there’s anything to be worried about in performing repeated conversions between sRGB and PPRGB, as long as the conversion algorithms themselves are written so that the internal calculations are accurate.