from __future__ import annotations

import copy
from fractions import Fraction
from typing import Any

SCHEMA_VERSION = 2
MAX_INTEGER = (1 << 63) - 1
NOTE_TYPES = ('maxima', 'long', 'breve', 'whole', 'half', 'quarter', 'eighth', '16th', '32nd', '64th', '128th', '256th', '512th', '1024th')
TYPE_LENGTHS = {name: Fraction(32, 2 ** index) for index, name in enumerate(NOTE_TYPES)}
NATURAL = {'c': 0, 'd': 2, 'e': 4, 'f': 5, 'g': 7, 'a': 9, 'b': 11}
LETTERS = 'cdefgab'
MODE_STEPS = {'major': 0, 'ionian': 0, 'dorian': 1, 'phrygian': 2, 'lydian': 3, 'mixolydian': 4, 'minor': 5, 'aeolian': 5, 'locrian': 6}


def rational(value: Fraction | int) -> dict[str, int]:
  value = Fraction(value)
  if abs(value.numerator) > MAX_INTEGER or value.denominator > MAX_INTEGER:
    raise ValueError('musical time exceeds the supported 64-bit rational range')
  return {'numerator': value.numerator, 'denominator': value.denominator}


def fraction(value: Any) -> Fraction:
  if not isinstance(value, dict) or set(value) != {'numerator', 'denominator'}:
    raise ValueError('musical time must be a numerator/denominator object')
  n, d = value['numerator'], value['denominator']
  if type(n) is not int or type(d) is not int or d <= 0 or abs(n) > MAX_INTEGER or d > MAX_INTEGER:
    raise ValueError('invalid musical time')
  result = Fraction(n, d)
  if rational(result) != value:
    raise ValueError('musical time must be reduced')
  return result


def written_length(written: dict) -> Fraction:
  kind, dots = written['type'], written.get('dots', 0)
  if kind not in TYPE_LENGTHS or type(dots) is not int or not 0 <= dots <= 16:
    raise ValueError('invalid written duration or augmentation-dot count (maximum 16)')
  return TYPE_LENGTHS[kind] * (2 - Fraction(1, 2 ** dots))


def written_for(length: Fraction) -> dict:
  for name, base in TYPE_LENGTHS.items():
    for dots in range(17):
      if length == base * (2 - Fraction(1, 2 ** dots)):
        return {'type': name, 'dots': dots}
  # Generated rational spans need an explicit time modification, not rounded ticks.
  base = next((name for name, size in TYPE_LENGTHS.items() if size <= length), '1024th')
  return {'type': base, 'dots': 0, 'ratio': rational(length / TYPE_LENGTHS[base])}


def metric_length(written: dict) -> Fraction:
  ratio = fraction(written.get('ratio', rational(1)))
  if ratio <= 0:
    raise ValueError('written duration ratio must be positive')
  if 'normal' in written:
    written_length(written['normal'])
  return written_length(written) * ratio


def pitch_number(pitch: dict) -> int:
  letter = pitch['letter'].lower()
  alter, octave = pitch.get('alter', 0), pitch['octave']
  if letter not in NATURAL or type(alter) is not int or type(octave) is not int or not -3 <= alter <= 3 or not -4 <= octave <= 16:
    raise ValueError('invalid spelled pitch')
  return 12 * (octave + 1) + NATURAL[letter] + alter


def pitch_name(pitch: dict) -> str:
  alter = pitch.get('alter', 0)
  return pitch['letter'].upper() + ('#' * alter if alter > 0 else 'b' * -alter)


def parse_pitch_name(name: str) -> dict:
  if not name or name[0].lower() not in NATURAL or any(c not in '#b' for c in name[1:]):
    raise ValueError(f'invalid pitch name: {name!r}')
  return {'letter': name[0].lower(), 'alter': name[1:].count('#') - name[1:].count('b')}


def key_from_fifths(fifths: int, mode: str = 'major') -> dict:
  if mode not in MODE_STEPS and mode != 'none':
    raise ValueError(f'unsupported mode: {mode}')
  if not -14 <= fifths <= 14:
    raise ValueError('key signatures support up to fourteen fifths in either direction')
  degree = fifths * 4 + MODE_STEPS.get(mode, 0)
  letter = LETTERS[degree % 7]
  signature = [0] * 7
  order = 'fcgdaeb' if fifths > 0 else 'beadgcf'
  for i in range(abs(fifths)):
    signature[LETTERS.index(order[i % 7])] += 1 if fifths > 0 else -1
  tonic = {'letter': letter, 'alter': signature[LETTERS.index(letter)]}
  return {'fifths': fifths, 'mode': mode, 'tonic': tonic if mode != 'none' else None, 'alterations': signature}


def key_label(key: dict) -> str:
  if not key.get('tonic'):
    return 'No key'
  label = pitch_name(key['tonic'])
  return label if key['mode'] in ('major', 'ionian') else label + ' ' + key['mode']


def meter_length(meter: dict) -> Fraction:
  return sum((Fraction(sum(group['beats']) * 4, group['unit']) for group in meter.get('groups', [])), Fraction())


def meter_label(meter: dict) -> str:
  if meter.get('unmetered'):
    return 'senza misura'
  return '+'.join('+'.join(map(str, group['beats'])) + '/' + str(group['unit']) for group in meter['groups'])


def beat_lengths(meter: dict) -> list[Fraction]:
  result = []
  for group in meter.get('groups', []):
    beats, unit = group['beats'], group['unit']
    if len(beats) > 1:
      result.extend(Fraction(b * 4, unit) for b in beats)
    elif beats[0] > 3 and beats[0] % 3 == 0 and unit >= 8:
      result.extend([Fraction(12, unit)] * (beats[0] // 3))
    else:
      result.extend([Fraction(4, unit)] * beats[0])
  return result


def validate_meter(meter: dict) -> None:
  groups = meter.get('groups', [])
  if not groups and not meter.get('unmetered'):
    raise ValueError('meter requires beat groups or senza misura')
  for group in groups:
    if type(group['unit']) is not int or not 0 < group['unit'] <= 4096 or not group['beats']:
      raise ValueError('meter unit must be between 1 and 4096 with nonempty beats')
    if any(type(b) is not int or not 0 < b <= 1024 for b in group['beats']):
      raise ValueError('meter count must be between 1 and 1024')


def make_event(identifier: str, onset: Fraction, duration: Fraction, kind: str, pitches: list[dict] | None = None, written: dict | None = None) -> dict:
  if duration <= 0:
    raise ValueError('generated event duration must be positive')
  notation = written or written_for(duration)
  event = {'id': identifier, 'kind': kind, 'onset': rational(onset), 'duration': rational(duration), 'written': notation, 'hidden': False, 'pitches': []}
  for i, p in enumerate(pitches or []):
    event['pitches'].append({**copy.deepcopy(p), 'id': f'{identifier}-p{i+1}', 'duration': rational(duration), 'written': copy.deepcopy(notation)})
  return event


def validate_document(document: dict) -> None:
  if document.get('schema_version') != SCHEMA_VERSION:
    raise ValueError('unsupported score schema; regenerate score assets with the current generator')
  staves = document.get('staves', [])
  if len(staves) != 1:
    raise ValueError('exactly one staff is currently supported')
  ids: set[str] = set()
  events: dict[str, dict] = {}
  tones: dict[str, tuple[dict, Fraction, Fraction]] = {}
  absolute = Fraction()
  for measure in staves[0]['measures']:
    length = fraction(measure['duration'])
    if length <= 0:
      raise ValueError('measure duration must be positive')
    voices = measure.get('voices', [])
    if len(voices) != 1:
      raise ValueError('exactly one rhythmic voice is currently supported')
    previous_end = Fraction()
    for note in voices[0]['notes']:
      if not note['id'] or note['id'] in ids:
        raise ValueError(f'duplicate event ID: {note["id"]}')
      ids.add(note['id'])
      events[note['id']] = note
      onset, duration = fraction(note['onset']), fraction(note['duration'])
      if onset < 0 or duration < 0 or onset + duration > length:
        raise ValueError(f'event outside measure: {note["id"]}')
      if note['kind'] not in ('note', 'rest', 'spacer'):
        raise ValueError('invalid event kind')
      if not note.get('grace'):
        if duration == 0 or onset < previous_end:
          raise ValueError('overlapping events in one rhythmic voice')
        previous_end = onset + duration
      elif duration != 0:
        raise ValueError('grace notes must not advance metric time')
      expected = metric_length(note['written'])
      if not note.get('grace') and not note.get('measure_rest') and duration != expected:
        raise ValueError('metric and written event durations disagree')
      if note['kind'] != 'note' and note.get('pitches'):
        raise ValueError('rests and spacers cannot contain pitches')
      if note['kind'] == 'note' and not note.get('pitches') and note.get('notehead') != 'slash':
        raise ValueError('pitched event requires at least one pitch')
      for p in note.get('pitches', []):
        pitch_number(p)
        pd = fraction(p['duration'])
        if pd < 0 or (pd == 0 and not note.get('grace')) or pd > duration or not p['id'] or p['id'] in tones:
          raise ValueError('invalid chord-tone duration or duplicate ID')
        if not note.get('grace') and pd != metric_length(p['written']):
          raise ValueError('metric and written chord-tone durations disagree')
        tones[p['id']] = (p, absolute + onset, pd)
    for harmony in measure.get('harmonies', []):
      if not 0 <= fraction(harmony['onset']) < length:
        raise ValueError('harmony outside measure')
    for change in measure.get('attributes', []):
      if not 0 <= fraction(change['onset']) < length:
        raise ValueError('attribute change outside measure')
    for state in [measure, *measure.get('attributes', [])]:
      if 'meter' in state:
        validate_meter(state['meter'])
      if 'key' in state and (len(state['key']['alterations']) != 7 or any(type(a) is not int or not -3 <= a <= 3 for a in state['key']['alterations'])):
        raise ValueError('key alterations must contain seven integers from -3 through 3')
      if 'clef' in state and (state['clef']['sign'] not in ('G','F','C') or not 1 <= state['clef']['line'] <= 5 or not -3 <= state['clef']['octave_change'] <= 3):
        raise ValueError('invalid pitched clef')
    absolute += length
  for identifier, (p, start, duration) in tones.items():
    if target := p.get('tie_to'):
      if target not in tones:
        raise ValueError(f'dangling tie: {identifier} -> {target}')
      other, next_start, _ = tones[target]
      if other.get('tie_from') != identifier or pitch_number(p) != pitch_number(other) or next_start != start + duration:
        raise ValueError(f'invalid tie: {identifier} -> {target}')
    if source := p.get('tie_from'):
      if source not in tones or tones[source][0].get('tie_to') != identifier:
        raise ValueError(f'dangling incoming tie: {identifier}')
  span_ids = set()
  event_order = {identifier:index for index, identifier in enumerate(events)}
  for span in staves[0].get('tuplets', []):
    if not span['id'] or span['id'] in span_ids or span['start'] not in ids or span['end'] not in ids or not 0 < span['note_count'] <= 1000000 or not 0 < span['space_count'] <= 1000000 or not 0 <= span['depth'] <= 16:
      raise ValueError('invalid tuplet span')
    members = [n['id'] for n in events.values() if span['id'] in n.get('tuplet_ids', [])]
    if not members or members[0] != span['start'] or members[-1] != span['end'] or event_order[span['start']] > event_order[span['end']]:
      raise ValueError('tuplet endpoints disagree with member events')
    if span.get('bracket', 'auto') not in ('yes','no','auto') or span.get('show_number','actual') not in ('none','actual','both'):
      raise ValueError('invalid tuplet appearance')
    span_ids.add(span['id'])
  for note in events.values():
    if any(t not in span_ids for t in note.get('tuplet_ids', [])):
      raise ValueError('event refers to an unknown tuplet')
    if tremolo := note.get('tremolo'):
      if tremolo['type'] not in ('single','start','stop') or type(tremolo['marks']) is not int or not 0 <= tremolo['marks'] <= 8:
        raise ValueError('invalid measured tremolo')
      if tremolo['type'] in ('start','stop'):
        other = events.get(tremolo.get('partner'))
        expected_type = 'stop' if tremolo['type'] == 'start' else 'start'
        if not other or other.get('tremolo',{}).get('partner') != note['id'] or other['tremolo']['type'] != expected_type or other['tremolo']['marks'] != tremolo['marks']:
          raise ValueError('invalid paired tremolo')
  for span in staves[0].get('octave_shifts', []):
    if not 0 <= fraction(span['start']) < fraction(span['end']) <= absolute or not -3 <= span['octaves'] <= 3:
      raise ValueError('invalid octave-shift span')