In what "original CLAHE function"?
IPT's adapthisteq() follows roughly the same behavior as Karel Zuiderveld's original example from Graphics Gems IV.
While the parameter is called "normalized", it's clearly not in unit-scale. In other words, as ClipLimit is scaled [0 1] when using adapthisteq(), in this original example, it's on an interval of [1 numbins]. Doing it the way adapthisteq() does is convenient, since it decouples the two parameters from the user's perspective.
Part of the confusion may come from the apparent conflicting statements:
"higher values give more contrast" (large numbers give maximum contrast)
"A clip limit smaller than 1 results in standard AHE" (small numbers give maximum contrast)
The minimum sensible value for the clip limit is 1. If it's set to something less than 1, the given value will be discarded and the denormalized clip limit will be set to an arbitrarily large number (16384). That would be equivalent to setting the "normalized" clip limit to numbins (the maximum value), for tile sizes up to 128x128. So both statements are true.
There are other minor differences in parameter denormalization, but the parameter response is at least in the same direction.
