Like the GLSL interpolation qualifiers mentioned by Pavel Beliy, Direct3D (HLSL) has a limited set of Interpolation Modifiers
that you can set on each member of data structs or on any arguments that are passed to the pixel shader. See the remarks section of this MSDN page.
The set of supported modifiers is limited to linear, centroid, nointerpolation, noperspective and sample (see link for details).
Unfortunately, the wording of your question and comment seems to suggest you have a need for more detailed control over the interpolation technique used. For example, none of the will solve the need for renormalizing interpolated vectors.