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

-- -- | |

-- 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) 1992-2021, 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. -- | |

-- -- | |

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

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; |