Andrew Haley wrote: > Paolo Bonzini wrote: >>> I'd like to implement something similar for MaverickCrunch, using the >>> integer 32-bit MAC functions, but there is no reciprocal estimate >>> function on the MaverickCrunch. I guess a lookup table could be >>> implemented, but how many entries will need to be generated, and how >>> accurate will it have to be IEEE754 compliant (in the swdiv routine)? >> I think sh does something like that. It is quite a mess, as it has half >> a dozen ways to implement division. >> >> The idea is to use integer arithmetic to compute the right exponent, and >> the lookup table to estimate the mantissa. I used something like this >> for square root: >> >> 1) shift the entire FP number by 1 to the right (logical right shift) >> 2) sum 0x20000000 so that the exponent is still offset by 64 >> 3) extract the 8 bits from 14 to 22 and look them up in a 256-entry, >> 32-bit table >> 4) sum the value (as a 32-bit integer!) with the content of the table >> 5) perform 2 Newton-Raphson iterations as necessary > > To avoid the lookup table, calculate > > x = (a/2) + (8^(1/4) - 1)^2 > > which gives relative errors less than 0.036 over the range 1/2 <= a <= 2 > at a cost of one shift and one addition. The errors after 1,2,3, and 4 > iterations of Heron's rule are 0.64E-3, 0.204E-6, 0.211E-13, and 0.222E-27. > > So, this requires one more iteration but avoids the use of a table and the > corresponding memory hit. > > Source: Computer Approximations, Hart et al.
Sorry, a context switch: this is for sqrt, not division. Brain fade. Andrew.
