The math is internally represented as a tree for display and editing. Most of the performance critical code is the numeric evaluation when graphing. For that, the math is compiled to a linear byte code which vastly improves locality of reference and is an opportunity to apply optimizations such as common subexpression elimination and loop invariant code motion.
I hadn't followed the link in article originally to get to https://mobile.twitter.com/RonAvitzur/status/146102321572409.... So literally the process of parsing the expression and producing the byte code is the performance challenge now? Or is it also walking the bytecode to do anything?
My basic question would be: why not go back to flex/bison/yacc/whatever via C-FFI? (But I think it would still be bad, since you'll want to get to a Swift data structure for your ops and those will still have the Arc issues)
That thread describes me working through performance issues in the initial port eight months ago. Those cases perform adequately now. Parsing is not a bottleneck. Walking the bytecode remains a performance hotspot, as that is where all the numeric calculations occur, but no more or less so comparing the C++ and Swift implementations.
I did investigate maintaining the flex/bison parser, since its generated state machine C code is more robust than my handwritten recursive descent parser when presented with pathological input. However, as you say, since I need a Swift data structure in the end, there is little to be gained and a lot of complication bridging via a C-FFI.
Yes, the numeric evaluation is vectorized via the Accelerate Framework's vForce and vDSP APIs. That is a significant performance improvement. The numeric evaluation remains a hotspot with vectorization, as that is where the app does most of its work.
Can you say more about the parse tree impact on performance?
Is the expression left in a tree form and effectively "interpreted" from the AST for all points? Is that the critical path?