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That's great and all, but nobody needs a 32-bit anything in 2018. This undergraduate paper provides a magic number and associated error bound for 64-bit doubles: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
That's great and all, but nobody needs a 32-bit anything in 2018. This undergraduate paper provides a magic number and associated error bound for 64-bit doubles: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
Tell us more about this strange "2018" place!
That's great and all, but nobody needs a 32-bit anything in 2018. This undergraduate paper provides a magic number and associated error bound for 64-bit doubles: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
That's great and all, but nobody needs a 32-bit anything in 2018. This undergraduate paper provides a magic number and associated error bound for 64-bit doubles: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
That's not really accurate. Even in cases were 32 bit and 64 bit operations are equally fast on the CPU, 32 bit values still take up half the memory. For many workloads, the limiting factor is cache space. So, if you can use 32 but values, you can get much better performance for those workloads.
That's great and all, but nobody needs a 32-bit anything in 2018. This undergraduate paper provides a magic number and associated error bound for 64-bit doubles: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
Lots of ML and AI applications are using ever-smaller precisions. Half and even quarter-precision floats are able to maximize efficiency of the various CPU/GPU ALUs.
It is worth noting that with AVX-512, Intel has introduced a native inverse sqrt approximation (VRSQRT14).
It is worth noting that with AVX-512, Intel has introduced a native inverse sqrt approximation (VRSQRT14).
It is worth noting that with AVX-512, Intel has introduced a native inverse sqrt approximation (VRSQRT14).
How does that perform in comparison?
That's great and all, but nobody needs a 32-bit anything in 2018. This undergraduate paper provides a magic number and associated error bound for 64-bit doubles: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
https://www.wired.com/1997/01/did-gates-really-say-640k-is-e...
That's great and all, but nobody needs a 32-bit anything in 2018. This undergraduate paper provides a magic number and associated error bound for 64-bit doubles: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
Even scientific calculation would be fine with 32 bit floats, but average floating point error due to representation creeps with ON (iirc) over N multiplications, so you have to use 64 bit for many scientific applications to get satisfactory results after a million or a trillion multiplications.
If your algorithm is not stable then even 64-bit won't help you.
Compare Euler vs Verlet - https://en.wikipedia.org/wiki/Verlet_integration