interpolation.h

Every varispeed thing in audio is this: a tape effect, a pitch shifter, a sampler transposing, a chorus whose delay is moving, a session running at a rate the material was not recorded at. The SDK could already do the whole- buffer case (resample.h) and the sampler had a Catmull-Rom reader welded into it, and there was nothing in between: nothing that takes a STREAM, block after block, remembering what it had from last time.

That memory is the entire difficulty. An interpolator needs samples on both sides of the point it is reading, and at a block boundary the ones on the left belong to the previous call. Get that wrong and the result is a click every block, at exactly the block rate, which people diagnose as anything except an interpolator.

Four points about the kernels, since choosing between them is the reason there is more than one:

Zero-order hold  no cost, no delay, and audible aliasing. Real use: a
                 control signal, or a deliberate lo-fi effect.
Linear           a lowpass whose corner moves with the fraction, which is
                 why a linearly-interpolated delay sounds duller as it
                 sweeps.
Catmull-Rom      four points, C1 continuous, passes through its points.
Lagrange (3rd)   four points, the polynomial that fits them exactly.
Windowed sinc    what the maths actually says, at the cost of a table and
                 a wide window; the only one whose error keeps falling as
                 you spend more on it.

Every kernel declares its LATENCY, in samples, and the test measures that rather than believing it. A latency that is documented and wrong is worse than one that is undocumented, because the host compensates by it.