[WIP] Kokkos ParsedFunction

[NamjaeChoi]

Refs #30655.

You are very welcome to check this out and test the function parser to find corner cases. It reports Abstract Syntax Tree (AST) of the expression and its Reverse Polish Notation (RPN) to be used on GPUs. For example:

[parsed]
  type = KokkosParsedFunction
  expression = 'if( (-1+2*3) > 6, sin(0), cos(0) ) + 1 / 2'
[]

Abstract Syntax Tree (AST) of KokkosParsedFunction parsed:

Binary (+)
  Call (
    Callee:
      Identifier (if)
    Arguments:
      Binary (>)
        Binary (+)
          Unary (-)
            Number (1)
          Binary (*)
            Number (2)
            Number (3)
        Number (6)
      Call (
        Callee:
          Identifier (sin)
        Arguments:
          Number (0)
      )
      Call (
        Callee:
          Identifier (cos)
        Arguments:
          Number (0)
      )
  )
  Binary (/)
    Number (1)
    Number (2)

Reverse Polish Notation (RPN) of KokkosParsedFunction parsed:

1.000000 - 2.000000 3.000000 * + 6.000000 > 0.000000 sin 0.000000 cos if 1.000000 2.000000 / +

Error handling examples:

*** ERROR ***
Kokkos parsed function error: expected ')'.
if( (-1+2*3) > 6, sin(0), cos(0) + 1 / 2
                                       ^

*** ERROR ***
Kokkos parsed function error: extra ')'.
if( (-1+2*3) > 6, sin(0), cos(0) )) + 1 / 2
                                  ^

*** ERROR ***
Kokkos parsed function error: invalid function call syntax.
if( (-1+2*3) > 6, sin(0), 42(0) ) + 1 / 2
                           ^

*** ERROR ***
Kokkos parsed function error: unsupported function 'foo'.
if( (-1+2*3) > 6, sin(0), foo(0) ) + 1 / 2
                            ^

*** ERROR ***
Kokkos parsed function error: if() expects 3 argument(s).
if( (-1+2*3) > 6, sin(0)) + 1 / 2
 ^

*** ERROR ***
Kokkos parsed function error: unexpected character ';'.
if( (-1+2*3) > 6, sin(0), cos(0) ); + 1 / 2
                                  ^

*** ERROR ***
Kokkos parsed function error: expected an expression.
if( (-1+2*3) > 6, sin(0), cos(0) ) ++ 1 / 2
                                    ^

*** ERROR ***
Kokkos parsed function error: variable name 'log' is reserved for function.
if( (-1+2*3) > 6, sin(0), cos(0) ) + log / 2
                                       ^

[dschwen]

I suggest using the PEG parser already shipped with MOOSE to parse the functions.

[dschwen]

Alternatively you can use FParser (and get algebraic optimization) and access the tape and transform that into GPU operations.

[dschwen]

Here is an example for a GPU function parser (that generates torch compute graphs):

https://github.com/idaholab/marlin/blob/devel/include/utils/MarlinExpressionParser.h
https://github.com/idaholab/marlin/blob/devel/src/utils/MarlinExpressionParser.C

and uses peg::parser (grammar is at the bottom of the .h file).

[NamjaeChoi]

access the tape

How do I access the tape? Using FParser will be probably better for consistency.