import functools
import logging
import math
import operator
import sympy

from dataclasses import dataclass
from typing import Any, Callable, Dict, List, Optional, Set, Tuple, Type, Union

import torch
import torch.fx
import torch.fx.traceback as fx_traceback

from torch.fx.node import Argument, Target
from torch.utils._sympy.interp import sympy_interp

log = logging.getLogger(__name__)

try:
    import z3  # type: ignore[import]

    # Translation Validation for Dynamo guards
    # ========================================
    #
    # Checks whether optimizations applied to the collected guards are
    # valid. In other words, whether the guard function we actually run
    # does not have false positives (unsound).
    #
    # In order to do so, we build the guards using 2 different information
    # attached to each 'SymNode':
    #   1. SymPy expressions
    #   2. FX nodes
    #
    # SymPy expressions have implicit optimizations baked within itself,
    # which may have a few bugs. On the other hand, we build the FX graph
    # manually, with no optimizations enabled. This gives us access to
    # the "ground truth".
    #
    # We then convert into Z3 expressions both the SymPy expressions
    # (see [Note: SympyToZ3]) that reach 'ShapeEnv.produce_guards' function
    # and the FX nodes (see [Note: PopulateValidator]) that go through
    # 'ShapeEnv.evaluate_expr' function. Finally, we run the validation.
    # (see [Note: TranslationValidator])

    # Implementation of Python semantics as Z3 expressions.
    #
    # Z3 Real-Int theory has operators with semantics that differ that of
    # Python. Therefore, in order to get it right, we need to implement
    # the (Python) semantics we are relying on in Z3.
    @dataclass
    class Z3Ops:
        # Validator used for adding assertions as needed.
        # e.g. div(a, b) requires b != 0.
        validator: "TranslationValidator"

        # The 2 functions below are used for conditionally casting between
        # integer and reals.
        #
        # Returns a real expression from 'x'.
        @staticmethod
        def to_real(x: z3.ArithRef) -> z3.ArithRef:
            return x if x.is_real() else z3.ToReal(x)

        # Returns an integer expression from 'x'.
        @staticmethod
        def to_int(x: z3.ArithRef) -> z3.ArithRef:
            return x if x.is_int() else z3.ToInt(x)

        # Implements Python division semantics.
        def div(self, numerator: z3.ArithRef, denominator: z3.ArithRef) -> z3.ArithRef:
            self.validator.add_assertion(denominator != 0)  # type: ignore[arg-type]
            return Z3Ops.to_real(numerator) / Z3Ops.to_real(denominator)

        def floor(self, number: z3.ArithRef) -> z3.ArithRef:
            # Z3 ToInt function rounds a real number towards negative infinity.
            return Z3Ops.to_int(number)

        # Python semantics for 'FloorDiv' states that before applying the floor
        # function, the operands are converted to their common type.
        def floordiv(self, numerator: z3.ArithRef, denominator: z3.ArithRef) -> z3.ArithRef:
            cast_result_to_real = numerator.is_real() or denominator.is_real()
            result = Z3Ops.to_int(self.div(numerator, denominator))
            # Since the 'result' is already an integer, we just have to check
            # whether we should cast it to real.
            return Z3Ops.to_real(result) if cast_result_to_real else result

        def ceil(self, number: z3.ArithRef) -> z3.ArithRef:
            return z3.If(
                self.floor(number) < number,
                self.floor(number + 1),
                number
            )  # type: ignore[return-value]

        def max(self, a: z3.ArithRef, b: z3.ArithRef) -> z3.ArithRef:
            return z3.If(a > b, a, b)  # type: ignore[return-value]

        def min(self, a: z3.ArithRef, b: z3.ArithRef) -> z3.ArithRef:
            return z3.If(a < b, a, b)  # type: ignore[return-value]

        # Python semantics for 'Mod' is defined as: p % q = p - floordiv(p, q) * q
        # It should work with both integer and reals.
        def mod(self, p: z3.ArithRef, q: z3.ArithRef) -> z3.ArithRef:
            return p - self.floordiv(p, q) * q

        def pow(self, base: z3.ArithRef, exp: z3.ArithRef) -> z3.ArithRef:
            # Z3 can't handle complex numbers very well.
            self.validator.add_assertion(z3.Or(base != 0, exp > 0))  # type: ignore[arg-type]
            return base ** exp

        def sqrt(self, number: z3.ArithRef) -> z3.ArithRef:
            # Square-root:
            # 1. Only work with reals
            number = Z3Ops.to_real(number)
            # 2. The number should be positive or zero.
            #    Otherwise, Z3 returns 'unknown'.
            self.validator.add_assertion(number >= 0)
            return number ** 0.5

    # Lifts a callable to be used in Z3.
    #
    # This function replaces the given 'op' by a function that:
    #
    #   1. Lifts the arguments into Z3 (i.e. make them inhabitants of Z3)
    #
    #   2. Calls an operation that corresponds to 'op', but works with Z3
    #      inhabitants (left as is if it works as is)
    def z3op(op: Callable, validator: "TranslationValidator") -> Callable:
        from torch.fx.experimental.symbolic_shapes import sym_sqrt

        # Operations that have booleans as their argument.
        # This is needed because the argument of some FX nodes were
        # literal integers, instead of booleans. So, whenever this flag
        # is set, we also convert ints to booleans.
        boolean_ops = {operator.not_, operator.and_, operator.or_}
        as_bool = op in boolean_ops

        # Lifts the function into 'z3.ExprRef' domain.
        def lift(func):
            def wrap(a) -> z3.ExprRef:
                if isinstance(a, (z3.ArithRef, z3.BoolRef)):
                    return a
                # Convert it into a Z3 value, if it is some of the supported
                # types below.
                if isinstance(a, bool) or (as_bool and isinstance(a, int)):
                    return z3.BoolVal(bool(a))
                if isinstance(a, (int, sympy.Integer)):
                    return z3.IntVal(int(a))
                if isinstance(a, (float, sympy.Float)):
                    return z3.RealVal(float(a))
                raise ValueError(f"can't lift type: {type(a)}")

            @functools.wraps(func)
            def wrapper(*args):
                # Lifts the arguments into a list of Z3 inhabitants.
                wrapped_args = (wrap(a) for a in args)
                # Run the function on the Z3 expressions.
                return func(*wrapped_args)

            return wrapper

        ops = Z3Ops(validator)
        replacement_map = {
            # Operator module.
            operator.not_: lift(z3.Not),
            operator.and_: lift(z3.And),
            operator.or_: lift(z3.Or),
            operator.floordiv: lift(ops.floordiv),
            operator.truediv: lift(ops.div),
            operator.mod: lift(ops.mod),

            # Math module.
            math.ceil: lift(ops.ceil),
            math.floor: lift(ops.floor),

            # Torch module.
            torch.sym_float: lift(ops.to_real),
            torch.sym_max: lift(ops.max),
            torch.sym_min: lift(ops.min),
            sym_sqrt: lift(ops.sqrt),
            # Not lifted because we only use this function as a
            # marker for adding the expression as validator input.
            torch._assert: torch._assert,
        }
        return replacement_map[op] if op in replacement_map else lift(op)

    # Processes an FX graph, populating the given validator.
    #
    # [Note: PopulateValidator]
    # This class walks through each node in the FX graph, translating
    # them into the Z3 world.
    #
    # Then, whenever it finds an 'torch._assert' call_function operation,
    # it adds the Z3 expression corresponding to the argument as validator
    # input.
    class PopulateValidator(torch.fx.Interpreter):
        def __init__(self, graph: torch.fx.Graph, validator: "TranslationValidator"):
            # Reference to the translation validator.
            self.validator = validator

            # Build the graph module and call `Interpreter` constructor.
            module = torch.fx.GraphModule(root={}, graph=graph)
            super().__init__(module, garbage_collect_values=True)

        def placeholder(self, target: Target, args: Tuple[Argument, ...], kwargs: Dict[str, Any]) -> Any:
            symbol = fx_traceback.get_current_meta()["symbol"]
            return self.validator.z3var(symbol)

        def call_function(self, target: Target, args: Tuple[Argument, ...], kwargs: Dict[str, Any]) -> Any:
            if target != torch._assert:
                # Actually runs the node target function (which is already
                # lifted) with its arguments.
                return super().call_function(target, args, kwargs)
            # Adds the Z3 expression corresponding to the first argument
            # as a validator input.
            assert len(args) == 1, f"expected 1 argument on assertion. Got: {len(args)} "
            self.validator.add_source_expr(args[0])  # type: ignore[arg-type]

    # Translates SymPy expressions into Z3 expressions.
    #
    # [Note: SympyToZ3]
    # At the time of the translation, all free variables present in the
    # SymPy expression being translated must be already mapped to a Z3
    # integer variable.
    class SympyToZ3:
        OPERATOR_HANDLES = {"add", "mul", "eq", "ne", "lt", "gt", "le", "ge"}

        def __init__(
                self,
                validator: "TranslationValidator",
        ) -> None:
            self._validator = validator
            self._ops = Z3Ops(self._validator)

        def constant(self, value: Any, dtype: torch.dtype) -> z3.ExprRef:
            if dtype is torch.int64:
                return z3.IntVal(value)
            if dtype is torch.double:
                return z3.RealVal(value)
            if dtype is torch.bool:
                return z3.BoolVal(value)
            raise ValueError(f"unsupported dtype (SympyToZ3): {dtype}")

        def truediv(self, numerator: z3.ArithRef, denominator: z3.ArithRef) -> z3.ArithRef:
            return self._ops.div(numerator, denominator)

        def floordiv(self, numerator: z3.ArithRef, denominator: z3.ArithRef) -> z3.ArithRef:
            return self._ops.floordiv(numerator, denominator)

        def div(self, numerator: z3.ArithRef, denominator: z3.ArithRef) -> z3.ArithRef:
            return self._ops.floordiv(numerator, denominator)

        def pow(self, base: z3.ArithRef, exp: z3.ArithRef) -> z3.ArithRef:
            return self._ops.pow(base, exp)

        def mod(self, p: z3.ArithRef, q: z3.ArithRef) -> z3.ArithRef:
            return self._ops.mod(p, q)

        def __getattr__(self, name: str) -> Any:
            REPLACEMENT = {
                "and_": z3.And,
                "or_": z3.Or,
                "not_": z3.Not,
                "floor": self._ops.floor,
                "ceil": self._ops.ceil,
            }

            if name in REPLACEMENT:
                return REPLACEMENT[name]
            if name in self.OPERATOR_HANDLES:
                return getattr(operator, name)
            raise AttributeError(f"unhandled operator: {name}")

        def run(self, expr: sympy.Basic) -> z3.ExprRef:
            return sympy_interp(self, self._validator.symbols, expr)  # type: ignore[arg-type]

    # Dynamo guards translation validator.
    #
    # [Note: TranslationValidator]
    # Verifies whether the guards issued by 'ShapeEnv.produce_guards' are sound.
    # That is: whether those (target) guards only yield TRUE whenever the original,
    # unoptimized, (source) guards yield TRUE.
    #
    # More concretely, given 'source' and 'target' guard expressions, we wish to
    # check whether the following expression holds:
    #
    # Not(And(source)) AND And(target)
    #
    # i.e. whether there is an assignment of the free variables where the opposite
    # happens: target is TRUE, but source is FALSE.
    class TranslationValidator:
        def __init__(self) -> None:
            # Mapping of SymPy symbols to Z3 variables.
            self.symbols: Dict[sympy.Symbol, z3.ExprRef] = {}

            # Set of source Z3 expressions.
            # They represent the generated guards without any kind of
            # simplification or transformation.
            self._source_exprs: Set[z3.BoolRef] = set()

            # Set of target Z3 expressions.
            # They represent the actual checked guards at runtime. They might
            # be simplified or transformed versions of the source guards.
            self._target_exprs: Set[z3.BoolRef] = set()

            # Set of Z3 expressions representing assertions over both the
            # source and target expressions.
            self._assertions: Set[z3.BoolRef] = set()

        # Retrieves the corresponding Z3 variable.
        def z3var(self, symbol: sympy.Symbol) -> z3.ExprRef:
            assert symbol in self.symbols, f"Z3 variable not found for: {symbol}"
            return self.symbols[symbol]

        # Create a variable in Z3 of 'type' for 'symbol', if it doesn't already exists.
        def add_var(self, symbol: sympy.Symbol, type: Type) -> z3.ExprRef:
            if symbol in self.symbols:
                return self.symbols[symbol]

            if type is int:
                var = z3.Int(symbol.name)

                # If 'symbol' is positive (SymPy assumption), we have to
                # convey it to Z3 as well.
                if symbol.is_positive:  # type: ignore[attr-defined]
                    self._target_exprs.add(var > 0)
            elif type is float:
                var = z3.Real(symbol.name)
            elif type is bool:
                var = z3.Bool(symbol.name)
            else:
                raise RuntimeError(f"unsupported type for Z3 variable: {type}")

            self.symbols[symbol] = var
            return var

        # Checks whether all symbols were already added.
        def _check_freesymbols(self, e: sympy.Basic) -> None:
            for s in e.free_symbols:
                assert isinstance(s, sympy.Symbol)
                # Call 'z3var' just to check whether there's already a
                # Z3 variable corresponding to 's'.
                self.z3var(s)


        def to_z3_boolean_expr(self, e: sympy.Basic) -> z3.BoolRef:
            z3expr = SympyToZ3(self).run(e)
            assert isinstance(z3expr, z3.BoolRef), f"expected boolean expression. Got: {z3expr}"
            return z3expr

        def add_source_expr(self, e: z3.BoolRef) -> None:
            self._source_exprs.add(e)

        def add_target_expr(self, e: sympy.Expr) -> None:
            self._check_freesymbols(e)
            self._target_exprs.add(self.to_z3_boolean_expr(e))

        def add_assertion(self, e: Union[z3.BoolRef, sympy.Basic]) -> None:
            if isinstance(e, sympy.Basic):
                self._check_freesymbols(e)
                ref = self.to_z3_boolean_expr(e)
            else:
                ref = e
            assert isinstance(ref, z3.BoolRef)
            self._assertions.add(ref)

        # The result of a validation run.
        @dataclass
        class Result:
            success: bool

            # Mapping of the name of each free variable to the value assigned to it.
            model: Optional[z3.ModelRef] = None

            # List of the source expressions that failed due to the assignment.
            failed_source_expr: Optional[List[z3.BoolRef]] = None

        def validate(self) -> "TranslationValidator.Result":
            from torch._dynamo.utils import dynamo_timed

            if len(self._source_exprs) == 0 or len(self._target_exprs) == 0:
                # If there are no source/target expressions, there's nothing we really
                # wish to prove. So, we just return.
                return self.Result(success=True)

            # Here, we use "QF_NRA" logic for the solver:
            #   "Quantifier-free Non-linear Real Arithmetic".
            #
            # Most of the guards expressions have:
            #   1. arithmetic between integer and reals
            #   2. no quantifiers
            #   3. potentially non-linear.
            #
            # Although there's also "QF_NIRA" (mixed integer-real arithmetic),
            # "QF_NRA" seems to work better on 'dynamo/test_dynamic_shapes.py'.
            solver = z3.SolverFor("QF_NRA")
            # Set a timeout for finding a solution.
            solver.set(timeout=translation_validator_timeout())

            # Add all the assertions to the solver.
            for assertion in self._assertions:
                solver.add(assertion)

            # "Is there any case where it's TRUE for the target expressions,
            #  but FALSE for the source expressions?"
            solver.add(z3.Not(z3.And(*self._source_exprs)))
            solver.add(*self._target_exprs)

            log.debug("translation validation: start")
            r = dynamo_timed()(solver.check)()
            if r == z3.sat:
                # Target expressions are unsound.
                # Log the found model and the source expressions that failed.
                model = solver.model()
                return self.Result(
                    success=False,
                    model=model,
                    failed_source_expr=[inp for inp in self._source_exprs if not model.evaluate(inp)],
                )
            else:
                if r == z3.unknown:
                    # Could not find a solution. It didn't fail, but it also
                    # didn't succeed. Canceling the validation execution (keyboard
                    # interrupt) also gets to this branch.
                    log.warning("translation validation: could not validate: got z3.unknown")
                else:
                    # Target expressions are sound.
                    assert r == z3.unsat
                    log.debug("translation validation: success")
                return self.Result(success=True)
except ImportError:
    _HAS_Z3 = False
else:
    _HAS_Z3 = True


def translation_validator_enabled() -> bool:
    from torch._dynamo import config
    assert _HAS_Z3 or not config.translation_validation, (
        "translation validation requires Z3 package. Please, either install "
        "z3-solver or disable translation validation."
    )
    return config.translation_validation

def translation_validator_timeout() -> int:
    from torch._dynamo import config
    return config.translation_validation_timeout
