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While testing the exp function we noticed some errors at the specified magnitude. Within this range the exp function returns the input value +1 as an output. We chose to run a test of 1m exponentially spaced values in the ranges [-2^-27,-2^-32] and [2^-32,2^-27] which showed 7603 and 3912 results with an error of >=0.5 ULP (compared with MPFR in 128 bit) with the highest being 0.56 ULP and 0.53 ULP. It's easy to fix by changing the magnitude at which the input value +1 is returned from <2^-28 to <2^-32 and using the polynomial instead. This reduces the number of results with an error of >=0.5 ULP to 485 and 479 in above tests, all of which are exactly 0.5 ULP. As we were already checking on exp we also took a look at expf. For expf the magnitude where the input value +1 is returned can be increased from <2^-28 to <2^-23 without accuracy loss for a slight performance improvement. To ensure this was the correct value we tested all values in the ranges [-2^-17,-2^-28] and [2^-28,2^-17] (~92.3m values each).
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