Why doesn't x**y%z work like pow(x, y, z) if y is negative?

Question

I have these values for x, y and z:

x = 1402709587326125487755933770599785022011554878478352915458023572822263891029946822919389113025226898265
y = -1653150172609560595889587008271025520100868674290063537844119789327420377094035018771640253912456367085
z = 5223965736281209292468836459168070829492174759961935620654434528517414151878323192140113927287012325803

pow(x,y,z) returns 6996453002252837241098775666312149651703153544682991747419581607713 (like it needs to be according to the RSA-assignment)

x**y%z should do the same, but returns 0.0 Can someone explain why? I'm guessing it has something to do with the negative y.

I get `ValueError: pow() 2nd argument cannot be negative when 3rd argument specified` on python 3.6.13 — jkr, Jan 11 '22 at 15:00
Does this answer your question? [Negative power in modular pow()](https://stackoverflow.com/questions/34119110/negative-power-in-modular-pow) — Renat, Jan 11 '22 at 15:00
`x**y` is a *fraction*, which is a *floating point value* below `5.562684646268003E-309` - mimimum possible magnitude for `double`, - so you have `x ** y == 0.0` — Dmitry Bychenko, Jan 11 '22 at 15:01
Note that using `pow` to compute modular inverses requires Python>=3.8. — Brian61354270, Jan 11 '22 at 15:02
@KellyBundy - because the OP has a negative exponent, and that causes an error when also using a mod value. — jkr, Jan 13 '22 at 16:35
@jakub Only because you're using an old Python version. Why are you telling us that? — Kelly Bundy, Jan 15 '22 at 02:33

score 3 · Accepted Answer · answered Jan 11 '22 at 15:09

When you compute

x ** y % z

you do it in two steps: (x ** y) % z. The very first step

x ** y

returns floating point fraction which is by far below 5.562684646268003E-309 (which is the minimum possible magnitude for double). So, x ** y == 0.0 and, finally, 0 % z == 0

Why doesn't x**y%z work like pow(x, y, z) if y is negative?

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