1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUN-TIME COMPONENTS                         --
4--                                                                          --
5--            G N A T . M B B S _ D I S C R E T E _ R A N D O M             --
6--                                                                          --
7--                                 B o d y                                  --
8--                                                                          --
9--          Copyright (C) 1992-2018, Free Software Foundation, Inc.         --
10--                                                                          --
11-- GNAT is free software;  you can  redistribute it  and/or modify it under --
12-- terms of the  GNU General Public License as published  by the Free Soft- --
13-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
14-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
15-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
16-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
17--                                                                          --
18-- As a special exception under Section 7 of GPL version 3, you are granted --
19-- additional permissions described in the GCC Runtime Library Exception,   --
20-- version 3.1, as published by the Free Software Foundation.               --
21--                                                                          --
22-- You should have received a copy of the GNU General Public License and    --
23-- a copy of the GCC Runtime Library Exception along with this program;     --
24-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
25-- <http://www.gnu.org/licenses/>.                                          --
26--                                                                          --
27-- GNAT was originally developed  by the GNAT team at  New York University. --
28-- Extensive contributions were provided by Ada Core Technologies Inc.      --
29--                                                                          --
30------------------------------------------------------------------------------
31
32with Ada.Calendar;
33
34with Interfaces; use Interfaces;
35
36package body GNAT.MBBS_Discrete_Random is
37
38   package Calendar renames Ada.Calendar;
39
40   Fits_In_32_Bits : constant Boolean :=
41                       Rst'Size < 31
42                         or else (Rst'Size = 31
43                                  and then Rst'Pos (Rst'First) < 0);
44   --  This is set True if we do not need more than 32 bits in the result. If
45   --  we need 64-bits, we will only use the meaningful 48 bits of any 64-bit
46   --  number generated, since if more than 48 bits are required, we split the
47   --  computation into two separate parts, since the algorithm does not behave
48   --  above 48 bits.
49
50   --  The way this expression works is that obviously if the size is 31 bits,
51   --  it fits in 32 bits. In the 32-bit case, it fits in 32-bit signed if the
52   --  range has negative values. It is too conservative in the case that the
53   --  programmer has set a size greater than the default, e.g. a size of 33
54   --  for an integer type with a range of 1..10, but an over-conservative
55   --  result is OK. The important thing is that the value is only True if
56   --  we know the result will fit in 32-bits signed. If the value is False
57   --  when it could be True, the behavior will be correct, just a bit less
58   --  efficient than it could have been in some unusual cases.
59   --
60   --  One might assume that we could get a more accurate result by testing
61   --  the lower and upper bounds of the type Rst against the bounds of 32-bit
62   --  Integer. However, there is no easy way to do that. Why? Because in the
63   --  relatively rare case where this expression has to be evaluated at run
64   --  time rather than compile time (when the bounds are dynamic), we need a
65   --  type to use for the computation. But the possible range of upper bound
66   --  values for Rst (remembering the possibility of 64-bit modular types) is
67   --  from -2**63 to 2**64-1, and no run-time type has a big enough range.
68
69   -----------------------
70   -- Local Subprograms --
71   -----------------------
72
73   function Square_Mod_N (X, N : Int) return Int;
74   pragma Inline (Square_Mod_N);
75   --  Computes X**2 mod N avoiding intermediate overflow
76
77   -----------
78   -- Image --
79   -----------
80
81   function Image (Of_State : State) return String is
82   begin
83      return Int'Image (Of_State.X1) &
84             ','                     &
85             Int'Image (Of_State.X2) &
86             ','                     &
87             Int'Image (Of_State.Q);
88   end Image;
89
90   ------------
91   -- Random --
92   ------------
93
94   function Random (Gen : Generator) return Rst is
95      S    : State renames Gen.Writable.Self.Gen_State;
96      Temp : Int;
97      TF   : Flt;
98
99   begin
100      --  Check for flat range here, since we are typically run with checks
101      --  off, note that in practice, this condition will usually be static
102      --  so we will not actually generate any code for the normal case.
103
104      if Rst'Last < Rst'First then
105         raise Constraint_Error;
106      end if;
107
108      --  Continue with computation if non-flat range
109
110      S.X1 := Square_Mod_N (S.X1, S.P);
111      S.X2 := Square_Mod_N (S.X2, S.Q);
112      Temp := S.X2 - S.X1;
113
114      --  Following duplication is not an error, it is a loop unwinding
115
116      if Temp < 0 then
117         Temp := Temp + S.Q;
118      end if;
119
120      if Temp < 0 then
121         Temp := Temp + S.Q;
122      end if;
123
124      TF := Offs + (Flt (Temp) * Flt (S.P) + Flt (S.X1)) * S.Scl;
125
126      --  Pathological, but there do exist cases where the rounding implicit
127      --  in calculating the scale factor will cause rounding to 'Last + 1.
128      --  In those cases, returning 'First results in the least bias.
129
130      if TF >= Flt (Rst'Pos (Rst'Last)) + 0.5 then
131         return Rst'First;
132
133      elsif not Fits_In_32_Bits then
134         return Rst'Val (Interfaces.Integer_64 (TF));
135
136      else
137         return Rst'Val (Int (TF));
138      end if;
139   end Random;
140
141   -----------
142   -- Reset --
143   -----------
144
145   procedure Reset (Gen : Generator; Initiator : Integer) is
146      S      : State renames Gen.Writable.Self.Gen_State;
147      X1, X2 : Int;
148
149   begin
150      X1 := 2 + Int (Initiator) mod (K1 - 3);
151      X2 := 2 + Int (Initiator) mod (K2 - 3);
152
153      for J in 1 .. 5 loop
154         X1 := Square_Mod_N (X1, K1);
155         X2 := Square_Mod_N (X2, K2);
156      end loop;
157
158      --  Eliminate effects of small Initiators
159
160      S :=
161        (X1  => X1,
162         X2  => X2,
163         P   => K1,
164         Q   => K2,
165         FP  => K1F,
166         Scl => Scal);
167   end Reset;
168
169   -----------
170   -- Reset --
171   -----------
172
173   procedure Reset (Gen : Generator) is
174      S    : State renames Gen.Writable.Self.Gen_State;
175      Now  : constant Calendar.Time := Calendar.Clock;
176      X1   : Int;
177      X2   : Int;
178
179   begin
180      X1 := Int (Calendar.Year    (Now)) * 12 * 31 +
181            Int (Calendar.Month   (Now) * 31)      +
182            Int (Calendar.Day     (Now));
183
184      X2 := Int (Calendar.Seconds (Now) * Duration (1000.0));
185
186      X1 := 2 + X1 mod (K1 - 3);
187      X2 := 2 + X2 mod (K2 - 3);
188
189      --  Eliminate visible effects of same day starts
190
191      for J in 1 .. 5 loop
192         X1 := Square_Mod_N (X1, K1);
193         X2 := Square_Mod_N (X2, K2);
194      end loop;
195
196      S :=
197        (X1  => X1,
198         X2  => X2,
199         P   => K1,
200         Q   => K2,
201         FP  => K1F,
202         Scl => Scal);
203
204   end Reset;
205
206   -----------
207   -- Reset --
208   -----------
209
210   procedure Reset (Gen : Generator; From_State : State) is
211   begin
212      Gen.Writable.Self.Gen_State := From_State;
213   end Reset;
214
215   ----------
216   -- Save --
217   ----------
218
219   procedure Save (Gen : Generator; To_State : out State) is
220   begin
221      To_State := Gen.Gen_State;
222   end Save;
223
224   ------------------
225   -- Square_Mod_N --
226   ------------------
227
228   function Square_Mod_N (X, N : Int) return Int is
229   begin
230      return Int ((Integer_64 (X) ** 2) mod (Integer_64 (N)));
231   end Square_Mod_N;
232
233   -----------
234   -- Value --
235   -----------
236
237   function Value (Coded_State : String) return State is
238      Last  : constant Natural := Coded_State'Last;
239      Start : Positive := Coded_State'First;
240      Stop  : Positive := Coded_State'First;
241      Outs  : State;
242
243   begin
244      while Stop <= Last and then Coded_State (Stop) /= ',' loop
245         Stop := Stop + 1;
246      end loop;
247
248      if Stop > Last then
249         raise Constraint_Error;
250      end if;
251
252      Outs.X1 := Int'Value (Coded_State (Start .. Stop - 1));
253      Start := Stop + 1;
254
255      loop
256         Stop := Stop + 1;
257         exit when Stop > Last or else Coded_State (Stop) = ',';
258      end loop;
259
260      if Stop > Last then
261         raise Constraint_Error;
262      end if;
263
264      Outs.X2  := Int'Value (Coded_State (Start .. Stop - 1));
265      Outs.Q   := Int'Value (Coded_State (Stop + 1 .. Last));
266      Outs.P   := Outs.Q * 2 + 1;
267      Outs.FP  := Flt (Outs.P);
268      Outs.Scl := (RstL - RstF + 1.0) / (Flt (Outs.P) * Flt (Outs.Q));
269
270      --  Now do *some* sanity checks
271
272      if Outs.Q < 31
273        or else Outs.X1 not in 2 .. Outs.P - 1
274        or else Outs.X2 not in 2 .. Outs.Q - 1
275      then
276         raise Constraint_Error;
277      end if;
278
279      return Outs;
280   end Value;
281
282end GNAT.MBBS_Discrete_Random;
283