## lustrec / doc / integer_division.org @ 58d610e1

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Integer division in LustreC |
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* Issue |

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Integer division / and associated modulo mod |

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a = (a / b) * b + (a mod b) |

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Division between two integers can be interpreted in different ways |

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- a C like division where sign(a mod b) = sign a |

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- a euclidean division where 0 <= a mod b < |b| |

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In both cases they satisfy the above equation. |

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Kind model-checker or Horn encoding assumes the mathematical definition, ie. the |

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euclidean division, while lustreC or the Verimag compiler rely on the C |

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definition. |

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In the following we deonote by div_C/mod_C and div_M/mod_M the functions in C |

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and math, respectively. |

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As an example -4 div_C 3 = -1 while -4 div_M 3 = 2 |

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Some properties: |

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- we have a div_M b = a div_C b when a = b * k |

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- we have a mod_C b = 0 \equiv a mod_M b = 0. |

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* From C to Euclidian |

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a mod_M b = (a mod_C b) + (a mod_C b < 0 ? abs(b) : 0) |

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a div_M b = (a - (a mod_M b)) div_C b |

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= (a - ((a mod_C b) + (a mod_C b < 0 ? abs(b) : 0))) div_C b |

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* From Euclidian to C |

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a mod_C b = a mod_M b - ((a mod_M b <> 0 && a <= 0) ? abs(b) : 0) |

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a div_C b = (a - (a mod_C b)) div_M b |

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= (a mod_M b <> 0 && a <= 0)?((a - a mod_M b + abs(b)) div_M b) :((a - a mod_M b) div_M b) |