I am guessing that your polynomial constant A is 131.29 (as in the original formula and in the scaled version in the table) not 133.29 (as in the table and the scaling factor calculation).
(By the way, using a superscript for squaring would seem to be clearer than using x2. I am guessing that this was a conversion to html issue.)
It would slightly simplify your equations for determining the required number of bits to simply use 'log'--for the quotient of two logs, the base does not matter. (I also thought the base was presented as a subscript rather than a superscript, but that may be a cultural difference.)
It seems that a high result multiplier would be more desirable than a full precision (doubled precision result) or low result multiplier. I.e., one tends to care about the most significant bits. (Since a normalized FP multiply uses the high result, I would guess that FPGAs support such.)
Also with multiplication (and division) shifts can be done before the operation or after the operation as long as the multiplier will not lose necessary precision. (When one operand is a constant, this can allow one to avoid shifting.)
Blog Doing Math in FPGAs Tom Burke 23 comments For a recent project, I explored doing "real" (that is, non-integer) math on a Spartan 3 FPGA. FPGAs, by their nature, do integer math. That is, there's no floating-point ...