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Bilinear filtering shader artifacts

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Hello,
I implemented a very basic bilinear interpolation pixel shader in glsl.
It's fine for the most part. Except when I zoom in on my texture, and depending where I am in it, I'm seeing weird lines showing a miscalculation...

I read upon it, it appears it's due to a quad misalignment with the screen...
My scene is 2D, there's a quad, one texture is applied on it...that's it...

I am confused though about what to do, it seems one solution is a half a pixel shift...
but is it for texture coordinates? quad coordinates?

None of what I tried seems to work...

Thanks for any help.

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