That paper was never formally published (that I can track down anyhow) but note it has both regular and reciprocal square root versions (the latter on the way to computing a square root) as well as in...
That paper was concerned with doubles and getting the initial approximation to slightly under 8 bits was sufficient to get a correctly rounded double sqrt within 3 iterations.
Tweaking the magic value to get rid of the initial LUT altogether is reasonable for float32, for the correctly rounded float64 sqrt-from-rsqrt they cared about it would've needed an extra iter which they tried to avoid.
Tweaking the magic value to get rid of the initial LUT altogether is reasonable for float32, for the correctly rounded float64 sqrt-from-rsqrt they cared about it would've needed an extra iter which they tried to avoid.
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