What's the inverse of a square root?
- Thread starter K.I.L.E.R
- Start date
x*x
I didn't come up with that statement. I just replaced the value of 'x' with my grandmother, err I mean '9999.99'.
You must have a very short attention span if you leave out the first half of a statement that is less than 30 characters in length.
Blazkowicz
Legend
x^(-1/2)
Dunno I would think that the inverse of x is 1/x, so the inverse of sqrt(x) is 1/sqrt(x).
(Never too sure when it comes to english wording of maths, but in french it's definetly that.)
This makes sense since there's a RSQRT "ASM" instruction...
(Reciprocal SQuareRooT)
(BTW, noticed there are 2 FastInvSqrt articles on Beyond3D ? ;p)
(Never too sure when it comes to english wording of maths, but in french it's definetly that.)
This makes sense since there's a RSQRT "ASM" instruction...
(Reciprocal SQuareRooT)
(BTW, noticed there are 2 FastInvSqrt articles on Beyond3D ? ;p)
Except the Reciprocal is the "Multiplicative Inverse". So RSQRT is the Multiplicative Inverse of Sqrt and in normal plain old maths the Multiplicative Inverse is x^-1 so RSQRT is (sqrt(x))^-1 = 1/sqrt(x).
Clearly one would only expect the inverse and multpilicative inverse to be the same is when we are talking about multiplication. Our german speaking friend has it down pat. I'm actually suprised we are having this issue.
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According to 'calc.exe' the 'Inv' (Inverse) of 'x^2' is a square root so hense the Inverse of a square root is square. 
Of course one shouldn't use ambiguous terms such as inverse square root if they mean reciprocal square root.
Of course one shouldn't use ambiguous terms such as inverse square root if they mean reciprocal square root.
ShootMyMonkey
Veteran
We have these sorts of issues not because of any mathematical reason but because semantics is so ambiguous and the written word is low bandwidth. Hence why someone can think of "inverse square root" and "the inverse of the square root function" as the same thing even though the former is a (not entirely proper) term describing multiplicative inverses.
For instance, if referring to the "inverse of f(x) = x", then the inverse is just g(x) = x, since that makes g(f(x)) = f(x) = x... but referring to the "inverse of x" has a different implied meaning.
Hence, we can show that English is creation of cruel devils. Q.E.D.
"x>=0 is not necessary"
Yes it really is, I insist you specify an appropriate domain!
Here is the definition in pedant mode:
given a function f(x) and some domain X, the inverse function exists iff
for every x is an element of X
f^-1 (f(x)) = f (f^-1(x)) = x
take X to be R. x^2 is defined over all of R, sqrt(x) is otoh most certainly not. Thus, over R, sqrt(x) has NO inverse function.
If you replace that domain of definition with the algebraic completion C, then it most certainly does exist.
Yes it really is, I insist you specify an appropriate domain!
Here is the definition in pedant mode:
given a function f(x) and some domain X, the inverse function exists iff
for every x is an element of X
f^-1 (f(x)) = f (f^-1(x)) = x
take X to be R. x^2 is defined over all of R, sqrt(x) is otoh most certainly not. Thus, over R, sqrt(x) has NO inverse function.
If you replace that domain of definition with the algebraic completion C, then it most certainly does exist.
