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)?
Getting a division that is always correctly rounded is going to be hard. I can't prove it's impossible, though. > 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 You don't need the table. This is the "magic" approximation to 1/sqrt(x) described at http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf: float invSqrt(float x) { float xhalf = 0.5f*x; union { float x; int i; } u; u.x = x; u.i = 0x5f3759df - (u.i >> 1); x = u.x * (1.5f - xhalf * u.x * u.x); return x; } Square that, and you've got a good approximation to 1/x. Two goes through Newton/Raphson gets you float, three gets you double. This may be faster, depending on the target. Andrew.
