------------------------------------------------------------------------------ -- -- -- GNAT RUN-TIME COMPONENTS -- -- -- -- G N A T . M B B S _ D I S C R E T E _ R A N D O M -- -- -- -- B o d y -- -- -- -- Copyright (C) 1992-2017, 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 -- -- . -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ with Ada.Calendar; with Interfaces; use Interfaces; package body GNAT.MBBS_Discrete_Random is package Calendar renames Ada.Calendar; Fits_In_32_Bits : constant Boolean := Rst'Size < 31 or else (Rst'Size = 31 and then Rst'Pos (Rst'First) < 0); -- This is set True if we do not need more than 32 bits in the result. If -- we need 64-bits, we will only use the meaningful 48 bits of any 64-bit -- number generated, since if more than 48 bits are required, we split the -- computation into two separate parts, since the algorithm does not behave -- above 48 bits. -- The way this expression works is that obviously if the size is 31 bits, -- it fits in 32 bits. In the 32-bit case, it fits in 32-bit signed if the -- range has negative values. It is too conservative in the case that the -- programmer has set a size greater than the default, e.g. a size of 33 -- for an integer type with a range of 1..10, but an over-conservative -- result is OK. The important thing is that the value is only True if -- we know the result will fit in 32-bits signed. If the value is False -- when it could be True, the behavior will be correct, just a bit less -- efficient than it could have been in some unusual cases. -- -- One might assume that we could get a more accurate result by testing -- the lower and upper bounds of the type Rst against the bounds of 32-bit -- Integer. However, there is no easy way to do that. Why? Because in the -- relatively rare case where this expression has to be evaluated at run -- time rather than compile time (when the bounds are dynamic), we need a -- type to use for the computation. But the possible range of upper bound -- values for Rst (remembering the possibility of 64-bit modular types) is -- from -2**63 to 2**64-1, and no run-time type has a big enough range. ----------------------- -- Local Subprograms -- ----------------------- function Square_Mod_N (X, N : Int) return Int; pragma Inline (Square_Mod_N); -- Computes X**2 mod N avoiding intermediate overflow ----------- -- Image -- ----------- function Image (Of_State : State) return String is begin return Int'Image (Of_State.X1) & ',' & Int'Image (Of_State.X2) & ',' & Int'Image (Of_State.Q); end Image; ------------ -- Random -- ------------ function Random (Gen : Generator) return Rst is S : State renames Gen.Writable.Self.Gen_State; Temp : Int; TF : Flt; begin -- Check for flat range here, since we are typically run with checks -- off, note that in practice, this condition will usually be static -- so we will not actually generate any code for the normal case. if Rst'Last < Rst'First then raise Constraint_Error; end if; -- Continue with computation if non-flat range S.X1 := Square_Mod_N (S.X1, S.P); S.X2 := Square_Mod_N (S.X2, S.Q); Temp := S.X2 - S.X1; -- Following duplication is not an error, it is a loop unwinding if Temp < 0 then Temp := Temp + S.Q; end if; if Temp < 0 then Temp := Temp + S.Q; end if; TF := Offs + (Flt (Temp) * Flt (S.P) + Flt (S.X1)) * S.Scl; -- Pathological, but there do exist cases where the rounding implicit -- in calculating the scale factor will cause rounding to 'Last + 1. -- In those cases, returning 'First results in the least bias. if TF >= Flt (Rst'Pos (Rst'Last)) + 0.5 then return Rst'First; elsif not Fits_In_32_Bits then return Rst'Val (Interfaces.Integer_64 (TF)); else return Rst'Val (Int (TF)); end if; end Random; ----------- -- Reset -- ----------- procedure Reset (Gen : Generator; Initiator : Integer) is S : State renames Gen.Writable.Self.Gen_State; X1, X2 : Int; begin X1 := 2 + Int (Initiator) mod (K1 - 3); X2 := 2 + Int (Initiator) mod (K2 - 3); for J in 1 .. 5 loop X1 := Square_Mod_N (X1, K1); X2 := Square_Mod_N (X2, K2); end loop; -- Eliminate effects of small Initiators S := (X1 => X1, X2 => X2, P => K1, Q => K2, FP => K1F, Scl => Scal); end Reset; ----------- -- Reset -- ----------- procedure Reset (Gen : Generator) is S : State renames Gen.Writable.Self.Gen_State; Now : constant Calendar.Time := Calendar.Clock; X1 : Int; X2 : Int; begin X1 := Int (Calendar.Year (Now)) * 12 * 31 + Int (Calendar.Month (Now) * 31) + Int (Calendar.Day (Now)); X2 := Int (Calendar.Seconds (Now) * Duration (1000.0)); X1 := 2 + X1 mod (K1 - 3); X2 := 2 + X2 mod (K2 - 3); -- Eliminate visible effects of same day starts for J in 1 .. 5 loop X1 := Square_Mod_N (X1, K1); X2 := Square_Mod_N (X2, K2); end loop; S := (X1 => X1, X2 => X2, P => K1, Q => K2, FP => K1F, Scl => Scal); end Reset; ----------- -- Reset -- ----------- procedure Reset (Gen : Generator; From_State : State) is begin Gen.Writable.Self.Gen_State := From_State; end Reset; ---------- -- Save -- ---------- procedure Save (Gen : Generator; To_State : out State) is begin To_State := Gen.Gen_State; end Save; ------------------ -- Square_Mod_N -- ------------------ function Square_Mod_N (X, N : Int) return Int is begin return Int ((Integer_64 (X) ** 2) mod (Integer_64 (N))); end Square_Mod_N; ----------- -- Value -- ----------- function Value (Coded_State : String) return State is Last : constant Natural := Coded_State'Last; Start : Positive := Coded_State'First; Stop : Positive := Coded_State'First; Outs : State; begin while Stop <= Last and then Coded_State (Stop) /= ',' loop Stop := Stop + 1; end loop; if Stop > Last then raise Constraint_Error; end if; Outs.X1 := Int'Value (Coded_State (Start .. Stop - 1)); Start := Stop + 1; loop Stop := Stop + 1; exit when Stop > Last or else Coded_State (Stop) = ','; end loop; if Stop > Last then raise Constraint_Error; end if; Outs.X2 := Int'Value (Coded_State (Start .. Stop - 1)); Outs.Q := Int'Value (Coded_State (Stop + 1 .. Last)); Outs.P := Outs.Q * 2 + 1; Outs.FP := Flt (Outs.P); Outs.Scl := (RstL - RstF + 1.0) / (Flt (Outs.P) * Flt (Outs.Q)); -- Now do *some* sanity checks if Outs.Q < 31 or else Outs.X1 not in 2 .. Outs.P - 1 or else Outs.X2 not in 2 .. Outs.Q - 1 then raise Constraint_Error; end if; return Outs; end Value; end GNAT.MBBS_Discrete_Random;