Predict cheaply, correct strictly

Synthetic English narration.

Two precisions, different roles
FP32 supplies the share warm start. FP64 handles correction, final residual checks, prices, output, exits and moments.

Build a warm start
The predictor runs at most sixteen rounds, with a looser tolerance. It only prepares a guess; the FP64 checks decide whether the answer is accepted.

Correct the guess in FP64
Convert the predicted shares to FP64, normalize them, then apply the original correction rule. If the prediction is unusable, restore the original FP64 initialization.

Check the returned answer
Recompute the residual of the returned shares. Check it, the residual when the solver stopped, the number of updates, and that every value is finite.

Keep the final accuracy
The predictor may change the iteration path. Keep the final accuracy, check every economic result, and measure speed only after those checks pass.