Posted by Roy Hughes at 17:06 on 2012 Sep 23
Graham,thanks for the PP presentation, I wasnt there so it has been a very good read. It prompted me to revisit posts earlier in this thread about 32 bit floating point TIFF files.In an earlier life (pre-retirement) I worked in the city writing back office systems where microscopic rates of interest were applied to astronomical sums of money (not mine!) and spent a lot of time investigating the accuracy (or otherwise) of floating point numbers.Floating point numbers are always saved Normalised (i.e. no leading zeroes) so any any loss of accuracy is at the low end of the number. The normal IEEE representation as used in the math co-processor in your PC has the general format [8 bit unsigned exponent, sign bit, 23 bit mantissa]. The exponent is implicitly scaled giving a range -127 to +127. The first binary digit of the mantissa is omitted (as by definition it will always be 1) and the next 23 bits stored. The 32 bit floating point TIFF format follows this standard (if the document issued by Adobe in 1992 is to be believed) and therefore the accuracy is 24 rather than 23 bits (7.225 decimal places).The final precision when holding integer numbers in floating point would vary according to the size of the number being represented, a fully saturated pixel would lose accuracy (but only at the 1 part in 16 million odd end, where it really would not matter) but not magnitude. At the other end of the scale a single 1 bit value would have 23 spurious binary places of accuracy.I can see that the software manipulating the numbers could need 32 bit integer working registers but 32 bit TIFF files should work quite acceptably for storing images.Have I missed something here?. Over to you.Roy