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cabal test gives:

Preprocessing test suite 'test' for dvda-0.4...

TestMain.hs:9:8:
    Could not find module ‘Dvda.Tests.Unary’
    Use -v to see a list of the files searched for.

There are some O[n^2] operations which could be O[log(n)] if Data.Map or Data.IntMap was used, like the use of elem to see if an expression is repeated.

GNode may use Ord for topsort already, so change to sortBy

there's a runtime exception hiding in there right now

Complicated because it's easy to get NaN or Infinity, or errors related to TInt overflows.

Current tests are on a restricted subset that will hopefully show some errors. That subset should be grown.

Current tests are on scalars only, need to implement tensors.

Need to implement symbolic variables/substitution tests.

This can all be done automatically with the type system

Capability to specify expressions as "atomic" and generate code once, treat as atomic function like Sin or Multiply. For stuff like rk4 - would generate function that takes in primal and perturbations, outputs primal and perturbations - possible to do this with reverse sensitivities?

• simplification rules
• compare AD with complex step
• compare AD with Numeric.AD

Is it possible to implement l'hopital's rule and a limit function, and then derive formulas for differentiation - perhaps may be easier with complex step?

The simplification pruneZeros can work on integer 0 just as well as Zero. This will make other simplifications easier as well.

Instead of maintaining numeric values with lists use some sort of unboxed array.

It would also be nice to use Repa to apply functions natively, instead of zipWith/map.

It'll be interesting to see if this can be made faster than the c backend

replace "error" with Dvda.Errror (error) which prints some standard exception with maybe some fun ascii text

this isn't hard, just low priority

Now that callNative is implemented, it would be great to have simple operators like diff and grad and so on that can be used on your own pure functions to get a derivative. (This will be handy for testing, hint hint :)

If I do CSE right now, I think some nodes are hashed (many) more times than one. If I want hashing, I should probably use something like data HashedExpr a = HashedExpr (Expr a) Int and hash greedily

• trig: cos(0) = 1, cos(pi) = -1, etc
• sanity checks: 1/0 = error, log(0) = error, etc
• logBase a b
  | a == b = 1
  | otherwise = logBase a b
• a / b
  | b == 0 = error "blah"
  | a == b = 1
  | otherwise = a / b
• ~= algebraically equal operator (commutative simplifying version of (==))
• Neg (Neg a) = a
• cancel out terms e.g. 4/16 --> 1/4

• code generation / compilation / dynamic linking
  • c or fortran?
  • vanilla blas for tensors?
  • parallelism?
• runtime backends
  • repa and hmatrix for tensor types
  • DPH or other parallelism strategy
• profiling code extremely important

Can this be done in a lightweight manner? Must it be integrated into SourceType?

Give symbolic variables their own data type so that functions with symbolic inputs or outputs don't have to pass (Expr a) with runtime error checking.

It's necessary for the ease of use of DVDA to allow expressions to be created from operations on Symbolic types through functional dependencies.

Right now it's just for loops

commutative is already in there

the hash of EBinary Mul x y may be different than the hash of of EBinary Mul x ERef even if ERef is a reference to y

RankNTypes were used to generalize safeBinaryConstruct/safeUnaryConstruct, but I duplicated these functions for Num/Fractional/Floating.

Would this exploit laziness and safe a lot of duplicated and/or unneeded evaluation?

They would be equivalent already except for Add/Sub.

Fix this after (Sub a b) is replaced with (Add a (Neg b))

here's how to reproduce.....

Perform runtime check when toFunction is called asserting that all inputs are present. Warn if too many inputs are present?