| ------------------------------------------------------------------------------ |

| -- -- |

| -- GNAT RUN-TIME COMPONENTS -- |

| -- -- |

| -- S Y S T E M . E X P _ M O D -- |

| -- -- |

| -- S p e c -- |

| -- -- |

| -- Copyright (C) 1992-2014, Free Software Foundation, Inc. -- |

| -- -- |

| -- GNAT is free software; you can redistribute it and/or modify it under -- |

| -- terms of the GNU General Public License as published by the Free Soft- -- |

| -- ware Foundation; either version 3, or (at your option) any later ver- -- |

| -- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- |

| -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- |

| -- or FITNESS FOR A PARTICULAR PURPOSE. -- |

| -- -- |

| -- As a special exception under Section 7 of GPL version 3, you are granted -- |

| -- additional permissions described in the GCC Runtime Library Exception, -- |

| -- version 3.1, as published by the Free Software Foundation. -- |

| -- -- |

| -- You should have received a copy of the GNU General Public License and -- |

| -- a copy of the GCC Runtime Library Exception along with this program; -- |

| -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see -- |

| -- <http://www.gnu.org/licenses/>. -- |

| -- -- |

| -- GNAT was originally developed by the GNAT team at New York University. -- |

| -- Extensive contributions were provided by Ada Core Technologies Inc. -- |

| -- -- |

| ------------------------------------------------------------------------------ |

| |

| -- This function performs exponentiation of a modular type with non-binary |

| -- modulus values. Arithmetic is done in Long_Long_Unsigned, with explicit |

| -- accounting for the modulus value which is passed as the second argument. |

| -- Note that 1 is a binary modulus (2**0), so the compiler should not (and |

| -- will not) call this function with Modulus equal to 1. |

| |

| with System.Unsigned_Types; |

| |

| package System.Exp_Mod is |

| pragma Pure; |

| use type System.Unsigned_Types.Unsigned; |

| |

| subtype Power_Of_2 is System.Unsigned_Types.Unsigned with |

| Dynamic_Predicate => |

| Power_Of_2 /= 0 and then (Power_Of_2 and (Power_Of_2 - 1)) = 0; |

| |

| function Exp_Modular |

| (Left : System.Unsigned_Types.Unsigned; |

| Modulus : System.Unsigned_Types.Unsigned; |

| Right : Natural) return System.Unsigned_Types.Unsigned |

| with |

| Pre => Modulus /= 0 and then Modulus not in Power_Of_2, |

| Post => Exp_Modular'Result = Left ** Right mod Modulus; |

| |

| end System.Exp_Mod; |