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I am using the ARM NEON vrsqrteq intrinsic to calculate the approximate reciprocal square root of a vector of floats. I would like to know the accuracy of that approximation.

However I can't find any documentation that provides this. The Neon programmers' guide simply states that the vrsqrteq intrinsic finds the approximate reciprocal square root but does not say a word about the accuracy.

For AVX for example, Intel provides the maximum relative error for the _mm256_rsqrt_ps intrinsic in the Intel Intrinsics Guide.

Is there somewhere something similar for ARM NEON intrinsics? I'm guessing the accuracy of the vrsqrteq intrinsic is different on different processors, but is there maybe a guaranteed minimal accuracy?

I also have the same situation for the vrecpeq intrinsic.

jonicho
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    The precise algorithm is given in the Architecture Reference Manual. I didn't see error bounds given, but presumably one could derive them. But the idea seems to be that it is the initial iterate for Newton-Raphson approximation, and you're meant to follow it by iterating `vrsqrts` until you converge to any desired accuracy. – Nate Eldredge Nov 15 '22 at 07:05
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    ARM's Programmer's Guides are informal documentation meant to give you a general overview of the instruction set. For the full formal details, you are supposed to refer to the Architecture Reference Manual. – Nate Eldredge Nov 15 '22 at 07:06

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