Fixed-Point Blockset

Conclusion

The number of Y data points follows the expected pattern. For the same worst case error, unrestricted spacing (uneven) requires the fewest data points, and power of two spaced breakpoints requires the most. However, the implementation for the evenly spaced and the power of two cases does not need the breakpoints in the generated code. This reduces their data ROM requirements by a half. As a result, the evenly spaced case actually uses less data ROM than the unevenly spaced case. Also, the power of two case requires only slightly more ROM than the uneven case. Changing the worst case error can change these rankings. Nonetheless, when you compare data ROM usage, you should always take into account the fact that the evenly spaced and power of two spaced cases do not require their breakpoints in ROM.

The effort of determining where the current input is relative to the breakpoints strongly favors the evenly spaced and power of two spaced cases. With uneven spacing, you use a binary search method that loops up to log2(N) times. With even and power of two spacing, you can determine the location with the execution of one line of C code. But you cannot decide the relative advantages of power of two versus evenly spaced without detailed knowledge of the hardware and the C compiler.

The effort of calculating the interpolation favors the power of two case, which uses a bitwise AND operation and a shift to replace a subtraction and a division. The amount of advantage provided by this depends on the specific hardware, but you would expect an advantage in code size, speed, and also in accuracy. The evenly space case calculates the interpolation with a minor improvement in efficiency over the unevenly spaced case.

Interpolation

Function Reference