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eliax1996

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Dec 6th, 2023
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  1. class PartialLinearMapping:
  2.     range_start: int
  3.     width: int
  4.     destination_range_start: int
  5.  
  6.     def domain() -> Interval:
  7.         return Interval(self.range_start, self.range_start + self.width)
  8.  
  9.     def codomain() -> Interval:
  10.         return Interval(self.destination_range_start, self.destination_range_start + self.width)
  11.  
  12.     def last_included_number(self) -> int:
  13.         return self.range_start + self.width - 1
  14.  
  15.     def apply(num: int) -> int:
  16.         if num in range(self.range_start, self.range_start + self.width):
  17.             return num - self.range_start + self.destination_range_start
  18.         return num
  19.  
  20.     def unapply(num: int) -> int:
  21.         if num in range(self.destination_range_start, self.destination_range_start + self.width):
  22.             return num - self.destination_range_start + self.range_start
  23.         return num
  24.  
  25.  
  26. class Interval:
  27.     begin: int
  28.     end: int
  29.  
  30.     def __contains__(self, num):
  31.         return num in range(self.begin, end)
  32.  
  33.     def difference(self, other: Interval) -> list[Interval]:
  34.         # the other is bigger than us
  35.         if self.begin in other and self.end - 1 in other:
  36.             return []
  37.  
  38.         # the other is disjoint from us
  39.         if not (other.begin in self or other.end - 1 in self):
  40.             return [self]
  41.  
  42.         # the other is partial overlapped with us
  43.         if other.begin in self and other.end - 1 in self:
  44.             return [Interval(self.begin, other.begin), Interval(other.end, self.end)]
  45.  
  46.         if other.begin in self:
  47.             return Interval(self.begin, other.begin)
  48.         else:
  49.             return Interval(other.end, self.end)
  50.  
  51.     def intersection(self, other: Interval) -> Interval | None:
  52.         # the other is bigger than us
  53.         if self.begin in other and self.end - 1 in other:
  54.             return self
  55.  
  56.         # the other is disjoint from us
  57.         if not (other.begin in self or other.end - 1 in self):
  58.             return None
  59.  
  60.         # the other is partial overlapped with us
  61.         return Interval(max(self.begin, other.begin), min(self.end, other.end))
  62.  
  63.  
  64. def compose(
  65.     f: PartialLinearMapping,
  66.     g: PartialLinearMapping,
  67. ) -> tuple[list[PartialLinearMapping], list[PartialLinearMapping]]:
  68.     """
  69.    the left element is the old domain mapped in the new one
  70.    the right element is the new domain remaining from the partial function applied to the old one (basically its the non overlapping
  71.    domain of the second function with the codomain of the first)
  72.    """
  73.     f_o_g_domain = f.codomain().intersection(g.domain())
  74.    
  75.     # this is a list, we need to compute all the intervals that comes from here
  76.     f_minus_g = f.codomain().difference(g.domain())
  77.    
  78.     # this is uncomplete/wrong, I'm missing the
  79.     old_domain_mapped = list(
  80.         lambda x: x is None,
  81.         filter(
  82.             [
  83.                 PartialLinearMapping(
  84.                     f.range_start,
  85.                     f.unapply(f_o_g_domain.begin),
  86.                     f.destination_range_start
  87.                 ),
  88.                 PartialLinearMapping(
  89.                     f_o_g_domain.begin,
  90.                     f_o_g_domain.end,
  91.                     g.destination_range_start
  92.                 )
  93.             ]
  94.         )
  95.     )
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