The API requirements can be found in any of the specs or extensions. Here is one: https://www.opengl.org/registry/specs/EXT/texture_filter_anisotropic.txt
All GPU vendors likely deviate from the spec because AF-quality used to be a part of many benchmarks. And current implementations will continue to keep on evolving as new workloads stress the existing approximations. Unfortunately, to know exactly what either does, you will need to be a part of one of the companies. But you can gauge the spectrum of possibilities from the following papers, listed in increasing order of quality and implementation cost:
Quoting from the spec:
Anisotropic texture filtering substantially changes Section 3.8.5.
Previously a single scale factor P was determined based on the
pixel's projection into texture space. Now two scale factors,
Px and Py, are computed.
Px = sqrt(dudx^2 + dvdx^2)
Py = sqrt(dudy^2 + dvdy^2)
Pmax = max(Px,Py)
Pmin = min(Px,Py)
N = min(ceil(Pmax/Pmin),maxAniso)
Lamda' = log2(Pmax/N)
where maxAniso is the smaller of the texture's value of
TEXTURE_MAX_ANISOTROPY_EXT or the implementation-defined value of
It is acceptable for implementation to round 'N' up to the nearest
supported sampling rate. For example an implementation may only
support power-of-two sampling rates.
It is also acceptable for an implementation to approximate the ideal
functions Px and Py with functions Fx and Fy subject to the following
1. Fx is continuous and monotonically increasing in |du/dx| and |dv/dx|.
Fy is continuous and monotonically increasing in |du/dy| and |dv/dy|.
2. max(|du/dx|,|dv/dx|} <= Fx <= |du/dx| + |dv/dx|.
max(|du/dy|,|dv/dy|} <= Fy <= |du/dy| + |dv/dy|.
Instead of a single sample, Tau, at (u,v,Lamda), 'N' locations in the mipmap
at LOD Lamda, are sampled within the texture footprint of the pixel.
Instead of a single sample, Tau, at (u,v,lambda), 'N' locations in
the mipmap at LOD Lamda are sampled within the texture footprint of
the pixel. This sum TauAniso is defined using the single sample Tau.
When the texture's value of TEXTURE_MAX_ANISOTROPHY_EXT is greater
than 1.0, use TauAniso instead of Tau to determine the fragment's
TauAniso = 1/N \ Tau(u(x - 1/2 + i/(N+1), y), v(x - 1/2 + i/(N+1), y)), Px > Py
TauAniso = 1/N \ Tau(u(x, y - 1/2 + i/(N+1)), v(x, y - 1/2 + i/(N+1))), Py >= Px
It is acceptable to approximate the u and v functions with equally spaced
samples in texture space at LOD Lamda:
TauAniso = 1/N \ Tau(u(x,y)+dudx(i/(N+1)-1/2), v(x,y)+dvdx(i/(N+1)-1/2)), Px > Py
TauAniso = 1/N \ Tau(u(x,y)+dudy(i/(N+1)-1/2), v(x,y)+dvdy(i/(N+1)-1/2)), Py >= Px
GL_EXT_texture_filter_anisotropicis very detailed. Maybe it might help you better understand the process. $\endgroup$