defmodule Dspy.QuantumSuperposition do
  @moduledoc """
  Quantum Superposition of Thoughts - A perfect-exceeder reasoning modality.

  This module implements quantum-inspired reasoning where multiple contradictory
  solutions coexist in superposition until observation collapses them to optimal reality.

  Key quantum effects:
  - Superposition: Multiple solutions exist simultaneously
  - Entanglement: Solutions affect each other non-locally
  - Measurement: Observation collapses to optimal solution
  - Coherence: Maintains quantum state integrity
  """

  @behaviour Dspy.Module

  defstruct [
    :signature,
    :coherence_time,
    :superposition_states,
    :entanglement_matrix,
    :measurement_basis,
    :quantum_memory
  ]

  @type t :: %__MODULE__{
          signature: module(),
          coherence_time: pos_integer(),
          superposition_states: pos_integer(),
          entanglement_matrix: map(),
          measurement_basis: atom(),
          quantum_memory: map()
        }

  @doc """
  Create a new quantum superposition reasoning module.

  ## Options
  - `:coherence_time` - Time in ms to maintain quantum coherence (default: 1000)
  - `:superposition_states` - Number of simultaneous solution states (default: 8)
  - `:measurement_basis` - Basis for quantum measurement (:optimal, :random, :coherent)
  - `:entanglement_enabled` - Enable quantum entanglement between solutions
  """
  def new(signature, opts \\ []) do
    %__MODULE__{
      signature: signature,
      coherence_time: Keyword.get(opts, :coherence_time, 1000),
      superposition_states: Keyword.get(opts, :superposition_states, 8),
      entanglement_matrix: %{},
      measurement_basis: Keyword.get(opts, :measurement_basis, :optimal),
      quantum_memory: %{}
    }
  end

  @impl true
  def forward(module, inputs) do
    with {:ok, quantum_state} <- initialize_quantum_state(module, inputs),
         {:ok, superposition} <- generate_superposition(module, quantum_state),
         {:ok, entangled_states} <- apply_entanglement(module, superposition),
         {:ok, collapsed_solution} <- quantum_measurement(module, entangled_states) do
      prediction = %Dspy.Prediction{
        attrs: %{
          collapsed_solution: collapsed_solution.solution,
          superposition_trace: format_superposition_trace(superposition),
          entanglement_effects: format_entanglement_effects(entangled_states),
          quantum_coherence: calculate_coherence(superposition),
          measurement_outcome: collapsed_solution.measurement_data
        },
        completions: [],
        metadata: %{
          quantum_states: length(superposition.states),
          coherence_time: module.coherence_time,
          entanglement_strength: calculate_entanglement_strength(entangled_states)
        }
      }

      {:ok, prediction}
    else
      {:error, reason} -> {:error, reason}
    end
  end

  defp initialize_quantum_state(_module, inputs) do
    quantum_state = %{
      problem: inputs,
      wavefunction: generate_initial_wavefunction(),
      phase: :rand.uniform() * 2 * :math.pi(),
      coherence: 1.0,
      timestamp: System.monotonic_time(:millisecond)
    }

    {:ok, quantum_state}
  end

  defp generate_superposition(module, quantum_state) do
    # Generate multiple contradictory solution states simultaneously
    superposition_tasks =
      1..module.superposition_states
      |> Enum.map(fn state_id ->
        Task.async(fn ->
          generate_quantum_solution_state(module, quantum_state, state_id)
        end)
      end)

    solutions = Task.await_many(superposition_tasks, module.coherence_time)

    superposition = %{
      states: solutions,
      wavefunction: combine_wavefunctions(solutions),
      coherence_remaining: calculate_remaining_coherence(quantum_state),
      interference_patterns: detect_interference_patterns(solutions)
    }

    {:ok, superposition}
  end

  defp generate_quantum_solution_state(_module, quantum_state, state_id) do
    # Each state explores a different reasoning approach with quantum randomness
    reasoning_approach = select_quantum_approach(state_id)

    # Simulate quantum uncertainty in reasoning
    uncertainty_factor = :rand.uniform() * 0.3

    solution_content =
      generate_solution_with_approach(
        quantum_state.problem,
        reasoning_approach,
        uncertainty_factor
      )

    %{
      id: state_id,
      approach: reasoning_approach,
      solution: solution_content,
      amplitude: :rand.uniform(),
      phase: :rand.uniform() * 2 * :math.pi(),
      uncertainty: uncertainty_factor,
      quantum_signature: generate_quantum_signature(solution_content)
    }
  end

  defp apply_entanglement(_module, superposition) do
    # Create quantum entanglement between solution states
    entangled_states =
      superposition.states
      |> Enum.map(fn state ->
        entangled_influences = calculate_entanglement_influences(state, superposition.states)

        Map.merge(state, %{
          entangled_with: entangled_influences,
          modified_amplitude: adjust_amplitude_for_entanglement(state, entangled_influences),
          non_local_effects: generate_non_local_effects(state, entangled_influences)
        })
      end)

    {:ok, entangled_states}
  end

  defp quantum_measurement(module, entangled_states) do
    # Collapse the quantum superposition to a single optimal solution
    case module.measurement_basis do
      :optimal -> measure_optimal_state(entangled_states)
      :random -> measure_random_state(entangled_states)
      :coherent -> measure_coherent_superposition(entangled_states)
    end
  end

  defp measure_optimal_state(entangled_states) do
    # Find state with highest quantum amplitude and coherence
    optimal_state =
      entangled_states
      |> Enum.max_by(fn state ->
        state.modified_amplitude * (1 - state.uncertainty) +
          calculate_entanglement_bonus(state)
      end)

    collapsed_solution = %{
      solution: synthesize_collapsed_solution(optimal_state, entangled_states),
      measurement_data: %{
        chosen_state: optimal_state.id,
        collapse_probability: optimal_state.modified_amplitude,
        quantum_number: optimal_state.quantum_signature
      }
    }

    {:ok, collapsed_solution}
  end

  defp measure_random_state(entangled_states) do
    # Probabilistic collapse based on quantum amplitudes
    total_amplitude = Enum.sum(Enum.map(entangled_states, & &1.modified_amplitude))
    random_point = :rand.uniform() * total_amplitude

    chosen_state = find_state_by_cumulative_probability(entangled_states, random_point)

    collapsed_solution = %{
      solution: synthesize_collapsed_solution(chosen_state, entangled_states),
      measurement_data: %{
        chosen_state: chosen_state.id,
        collapse_probability: chosen_state.modified_amplitude / total_amplitude,
        random_measurement: true
      }
    }

    {:ok, collapsed_solution}
  end

  defp measure_coherent_superposition(entangled_states) do
    # Maintain some superposition in the final answer
    coherent_solution = %{
      solution: synthesize_coherent_superposition(entangled_states),
      measurement_data: %{
        superposition_maintained: true,
        coherence_level: calculate_overall_coherence(entangled_states),
        quantum_interference: calculate_interference_effects(entangled_states)
      }
    }

    {:ok, coherent_solution}
  end

  # Helper functions for quantum operations

  defp generate_initial_wavefunction do
    # Simple quantum wavefunction representation
    %{
      real: :rand.uniform() * 2 - 1,
      imaginary: :rand.uniform() * 2 - 1,
      normalization: 1.0
    }
  end

  defp select_quantum_approach(state_id) do
    approaches = [
      :contradictory_synthesis,
      :paradox_embracing,
      :impossible_solutions,
      :reverse_causality,
      :non_classical_logic,
      :quantum_tunneling_reasoning,
      :superposition_maintaining,
      :entanglement_leveraging
    ]

    Enum.at(approaches, rem(state_id, length(approaches)))
  end

  defp generate_solution_with_approach(problem, approach, _uncertainty) do
    base_solution = generate_base_solution(problem)

    case approach do
      :contradictory_synthesis ->
        "Synthesizing contradictory aspects: #{base_solution} while simultaneously being its opposite through quantum superposition"

      :paradox_embracing ->
        "Embracing paradox: #{base_solution} achieves coherence by maintaining logical contradictions in quantum superposition"

      :impossible_solutions ->
        "Impossible solution pathway: #{base_solution} becomes possible through quantum tunneling across logical barriers"

      :reverse_causality ->
        "Retrocausal solution: #{base_solution} creates the conditions for its own necessity through temporal quantum effects"

      :non_classical_logic ->
        "Non-classical approach: #{base_solution} operates beyond binary logic through quantum many-valued truth states"

      :quantum_tunneling_reasoning ->
        "Tunneling solution: #{base_solution} bypasses classical reasoning barriers through quantum cognitive tunneling"

      :superposition_maintaining ->
        "Superposition solution: #{base_solution} maintains multiple simultaneous states without classical collapse"

      :entanglement_leveraging ->
        "Entangled solution: #{base_solution} leverages non-local quantum correlations for distributed problem solving"
    end
  end

  defp generate_base_solution(problem) do
    # Simplified solution generation for demonstration
    problem_text =
      case problem do
        %{quantum_problem: text} -> text
        %{problem: text} -> text
        text when is_binary(text) -> text
        _ -> "complex problem"
      end

    "Quantum-informed solution addressing: #{String.slice(problem_text, 0, 50)}..."
  end

  defp combine_wavefunctions(solutions) do
    # Combine quantum wavefunctions from multiple solutions
    total_real = Enum.sum(Enum.map(solutions, fn s -> :math.cos(s.phase) * s.amplitude end))
    total_imaginary = Enum.sum(Enum.map(solutions, fn s -> :math.sin(s.phase) * s.amplitude end))

    magnitude = :math.sqrt(total_real * total_real + total_imaginary * total_imaginary)

    %{
      real: total_real / magnitude,
      imaginary: total_imaginary / magnitude,
      magnitude: magnitude,
      phase: :math.atan2(total_imaginary, total_real)
    }
  end

  defp calculate_remaining_coherence(quantum_state) do
    time_elapsed = System.monotonic_time(:millisecond) - quantum_state.timestamp
    # Exponential coherence decay
    :math.exp(-time_elapsed / 1000.0)
  end

  defp detect_interference_patterns(solutions) do
    # Detect quantum interference between solution states
    solutions
    |> generate_pairs()
    |> Enum.map(fn [s1, s2] ->
      phase_difference = abs(s1.phase - s2.phase)
      amplitude_product = s1.amplitude * s2.amplitude

      interference_type =
        cond do
          phase_difference < :math.pi() / 4 -> :constructive
          phase_difference > 3 * :math.pi() / 4 -> :destructive
          true -> :partial
        end

      %{
        states: [s1.id, s2.id],
        type: interference_type,
        strength: amplitude_product * :math.cos(phase_difference)
      }
    end)
  end

  defp calculate_entanglement_influences(state, all_states) do
    all_states
    |> Enum.reject(fn s -> s.id == state.id end)
    |> Enum.map(fn other_state ->
      entanglement_strength = calculate_entanglement_strength_between(state, other_state)

      %{
        state_id: other_state.id,
        strength: entanglement_strength,
        influence_type: determine_influence_type(state, other_state)
      }
    end)
    |> Enum.filter(fn influence -> influence.strength > 0.1 end)
  end

  defp calculate_entanglement_strength_between(state1, state2) do
    # Calculate quantum entanglement strength between two states
    approach_similarity = if state1.approach == state2.approach, do: 0.8, else: 0.2
    phase_correlation = :math.cos(state1.phase - state2.phase)
    amplitude_resonance = :math.sqrt(state1.amplitude * state2.amplitude)

    (approach_similarity + abs(phase_correlation) + amplitude_resonance) / 3.0
  end

  defp determine_influence_type(state1, state2) do
    phase_diff = state1.phase - state2.phase

    cond do
      abs(phase_diff) < :math.pi() / 3 -> :reinforcing
      abs(phase_diff) > 2 * :math.pi() / 3 -> :opposing
      true -> :modulating
    end
  end

  defp adjust_amplitude_for_entanglement(state, entangled_influences) do
    adjustment_factor =
      entangled_influences
      |> Enum.reduce(0, fn influence, acc ->
        case influence.influence_type do
          :reinforcing -> acc + influence.strength * 0.2
          :opposing -> acc - influence.strength * 0.1
          :modulating -> acc + influence.strength * 0.05
        end
      end)

    max(0.1, min(1.0, state.amplitude + adjustment_factor))
  end

  defp generate_non_local_effects(_state, entangled_influences) do
    strong_influences = Enum.filter(entangled_influences, fn i -> i.strength > 0.5 end)

    if length(strong_influences) > 0 do
      "Non-local quantum correlations with states #{Enum.map(strong_influences, & &1.state_id)}"
    else
      "Minimal non-local effects"
    end
  end

  defp calculate_entanglement_bonus(state) do
    if Map.has_key?(state, :entangled_with) do
      length(state.entangled_with) * 0.1
    else
      0
    end
  end

  defp synthesize_collapsed_solution(chosen_state, _all_states) do
    # Synthesize final solution incorporating quantum effects
    base_solution = chosen_state.solution

    entanglement_info =
      if Map.has_key?(chosen_state, :entangled_with) do
        " Enhanced through quantum entanglement with #{length(chosen_state.entangled_with)} other solution states."
      else
        ""
      end

    "#{base_solution}#{entanglement_info} Quantum measurement selected this solution with probability #{Float.round(chosen_state.modified_amplitude, 3)}."
  end

  defp find_state_by_cumulative_probability(states, target) do
    {chosen_state, _} =
      states
      |> Enum.reduce({nil, 0}, fn state, {current, cumulative} ->
        new_cumulative = cumulative + state.modified_amplitude

        if new_cumulative >= target and is_nil(current) do
          {state, new_cumulative}
        else
          {current, new_cumulative}
        end
      end)

    chosen_state || List.last(states)
  end

  defp synthesize_coherent_superposition(entangled_states) do
    # Maintain quantum superposition in the final answer
    solution_components =
      entangled_states
      |> Enum.map(fn state ->
        "#{state.solution} (amplitude: #{Float.round(state.modified_amplitude, 2)})"
      end)
      |> Enum.join(" ⟷ ")

    "Coherent quantum superposition: #{solution_components}. All solutions exist simultaneously until further observation."
  end

  defp calculate_overall_coherence(entangled_states) do
    total_amplitude = Enum.sum(Enum.map(entangled_states, & &1.modified_amplitude))
    variance = calculate_amplitude_variance(entangled_states)

    total_amplitude / (1 + variance)
  end

  defp calculate_interference_effects(entangled_states) do
    interferences = detect_interference_patterns(entangled_states)

    constructive_count = Enum.count(interferences, fn i -> i.type == :constructive end)
    destructive_count = Enum.count(interferences, fn i -> i.type == :destructive end)

    "Constructive: #{constructive_count}, Destructive: #{destructive_count}"
  end

  # Formatting functions for output

  defp format_superposition_trace(superposition) do
    state_info =
      superposition.states
      |> Enum.map(fn state ->
        "State #{state.id} (#{state.approach}): amplitude #{Float.round(state.amplitude, 3)}"
      end)
      |> Enum.join("; ")

    "Quantum superposition with #{length(superposition.states)} states: #{state_info}"
  end

  defp format_entanglement_effects(entangled_states) do
    entanglement_pairs =
      entangled_states
      |> Enum.flat_map(fn state ->
        if Map.has_key?(state, :entangled_with) do
          Enum.map(state.entangled_with, fn e -> "#{state.id}↔#{e.state_id}" end)
        else
          []
        end
      end)
      |> Enum.uniq()

    "Quantum entanglement pairs: #{Enum.join(entanglement_pairs, ", ")}"
  end

  defp calculate_coherence(superposition) do
    Float.round(superposition.coherence_remaining, 3)
  end

  defp calculate_entanglement_strength(entangled_states) do
    total_entanglements =
      entangled_states
      |> Enum.map(fn state ->
        if Map.has_key?(state, :entangled_with) do
          Enum.sum(Enum.map(state.entangled_with, & &1.strength))
        else
          0
        end
      end)
      |> Enum.sum()

    Float.round(total_entanglements / length(entangled_states), 3)
  end

  defp calculate_amplitude_variance(states) do
    amplitudes = Enum.map(states, & &1.modified_amplitude)
    mean = Enum.sum(amplitudes) / length(amplitudes)

    variance =
      amplitudes
      |> Enum.map(fn amp -> :math.pow(amp - mean, 2) end)
      |> Enum.sum()
      |> Kernel./(length(amplitudes))

    variance
  end

  defp generate_quantum_signature(solution_content) do
    # Generate a quantum signature for the solution
    hash = :crypto.hash(:sha256, solution_content)
    Integer.to_string(Base.encode16(hash) |> String.slice(0, 8) |> String.to_integer(16), 36)
  end

  defp generate_pairs([]), do: []
  defp generate_pairs([_]), do: []

  defp generate_pairs([h | t]) do
    pairs = Enum.map(t, fn x -> [h, x] end)
    pairs ++ generate_pairs(t)
  end
end
