I am trying to implement the “fast inverse square root” algorithm in Julia: function rsqrt(x::Float32) xₛ = x int32 = reinterpret(UInt32, xₛ) int32 = 0x5f3759df - int32 >> 1 xₛ = reinterpret(Float32, int32) xₛ *= 1.5f0 - x * 0.5f0 * xₛ^2 return xₛ end But the result is defi…

The C code gives the same answer, I don’t think this is an exact algorithm(?). $ cat main.c #include <stdio.h> float Q_rsqrt( float number ) { long i; float x2, y; const float threehalfs = 1.5F; x2 = number * 0.5F; y = number; i = * ( long * ) &y…

[image] singularitti: But the result is definitely not right: It’s pretty close? julia> rsqrt(9.0f0) 0.3329532f0 julia> 1/sqrt(9) 0.3333333333333333 And if you do another Newton iteration you get closer.

Yeah, it is not an exact algorithm. Sorry, I was somehow comparing it with sqrt. My mistake.

By coincidence I was implementing the same algorithm 5 days ago :smiley: function fast_sqrt(y::Float32) x2 = y * 0.5f0 i = reinterpret(Int32, y) i = 0x5f3759df - (i >> 1) y = reinterpret(Float32, i) y = y * (1.5f0 - x2 * y * y) return y end

I was going to make it a package . I am surprised that Julia does not have this function built in? julia> @macroexpand @fastmath 1.0f0 / sqrt(2.0f0) :(Base.FastMath.div_fast(1.0f0, Base.FastMath.sqrt_fast(2.0f0))) julia> @macroexpand @fastmath inv(sqrt(2.0f0)) :(Base.FastMath.inv_fast(Base.FastMath…

I mean it’s only an approximation and if you compare performance: using BenchmarkTools function fast_sqrt(y::Float32) x2 = y * 0.5f0 i = reinterpret(Int32, y) i = 0x5f3759df - (i >> 1) y = reinterpret(Float32, i) y = y * (1.5f0 - x2 * y^2) return y end function compare_in…

I think the speed difference was much more drastic on older hardware.

Also x86 has a dedicated instruction for this that is more accurate (14 bits) and faster. RSQRTSS — Compute Reciprocal of Square Root of Scalar Single-Precision Floating-Point Value

Would maybe be reasonable to expose this. The only trouble is what to do on non-x86 hardware. You’d want a software implementation of that instruction that’s as accurate but not too slow.

Yeah, but it would be really interesting to have this smart trick somewhere. And we can have it for Float64 (it’s easy), 128 bits floating numbers (implemented by MultiFloats.jl , etc… It would not be easy for me to do this by myself.

How to convert the binary form of a float to an integer, and vice versa?

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How to convert the binary form of a float to an integer, and vice versa?

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