1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT COMPILER COMPONENTS                         --
4--                                                                          --
5--                             E X P _ F I X D                              --
6--                                                                          --
7--                                 B o d y                                  --
8--                                                                          --
9--          Copyright (C) 1992-2014, 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.  See the GNU General Public License --
17-- for  more details.  You should have  received  a copy of the GNU General --
18-- Public License  distributed with GNAT; see file COPYING3.  If not, go to --
19-- http://www.gnu.org/licenses for a complete copy of the license.          --
20--                                                                          --
21-- GNAT was originally developed  by the GNAT team at  New York University. --
22-- Extensive contributions were provided by Ada Core Technologies Inc.      --
23--                                                                          --
24------------------------------------------------------------------------------
25
26with Atree;    use Atree;
27with Checks;   use Checks;
28with Einfo;    use Einfo;
29with Exp_Util; use Exp_Util;
30with Nlists;   use Nlists;
31with Nmake;    use Nmake;
32with Restrict; use Restrict;
33with Rident;   use Rident;
34with Rtsfind;  use Rtsfind;
35with Sem;      use Sem;
36with Sem_Eval; use Sem_Eval;
37with Sem_Res;  use Sem_Res;
38with Sem_Util; use Sem_Util;
39with Sinfo;    use Sinfo;
40with Stand;    use Stand;
41with Tbuild;   use Tbuild;
42with Uintp;    use Uintp;
43with Urealp;   use Urealp;
44
45package body Exp_Fixd is
46
47   -----------------------
48   -- Local Subprograms --
49   -----------------------
50
51   --  General note; in this unit, a number of routines are driven by the
52   --  types (Etype) of their operands. Since we are dealing with unanalyzed
53   --  expressions as they are constructed, the Etypes would not normally be
54   --  set, but the construction routines that we use in this unit do in fact
55   --  set the Etype values correctly. In addition, setting the Etype ensures
56   --  that the analyzer does not try to redetermine the type when the node
57   --  is analyzed (which would be wrong, since in the case where we set the
58   --  Treat_Fixed_As_Integer or Conversion_OK flags, it would think it was
59   --  still dealing with a normal fixed-point operation and mess it up).
60
61   function Build_Conversion
62     (N     : Node_Id;
63      Typ   : Entity_Id;
64      Expr  : Node_Id;
65      Rchk  : Boolean := False;
66      Trunc : Boolean := False) return Node_Id;
67   --  Build an expression that converts the expression Expr to type Typ,
68   --  taking the source location from Sloc (N). If the conversions involve
69   --  fixed-point types, then the Conversion_OK flag will be set so that the
70   --  resulting conversions do not get re-expanded. On return the resulting
71   --  node has its Etype set. If Rchk is set, then Do_Range_Check is set
72   --  in the resulting conversion node. If Trunc is set, then the
73   --  Float_Truncate flag is set on the conversion, which must be from
74   --  a floating-point type to an integer type.
75
76   function Build_Divide (N : Node_Id; L, R : Node_Id) return Node_Id;
77   --  Builds an N_Op_Divide node from the given left and right operand
78   --  expressions, using the source location from Sloc (N). The operands are
79   --  either both Universal_Real, in which case Build_Divide differs from
80   --  Make_Op_Divide only in that the Etype of the resulting node is set (to
81   --  Universal_Real), or they can be integer types. In this case the integer
82   --  types need not be the same, and Build_Divide converts the operand with
83   --  the smaller sized type to match the type of the other operand and sets
84   --  this as the result type. The Rounded_Result flag of the result in this
85   --  case is set from the Rounded_Result flag of node N. On return, the
86   --  resulting node is analyzed, and has its Etype set.
87
88   function Build_Double_Divide
89     (N       : Node_Id;
90      X, Y, Z : Node_Id) return Node_Id;
91   --  Returns a node corresponding to the value X/(Y*Z) using the source
92   --  location from Sloc (N). The division is rounded if the Rounded_Result
93   --  flag of N is set. The integer types of X, Y, Z may be different. On
94   --  return the resulting node is analyzed, and has its Etype set.
95
96   procedure Build_Double_Divide_Code
97     (N        : Node_Id;
98      X, Y, Z  : Node_Id;
99      Qnn, Rnn : out Entity_Id;
100      Code     : out List_Id);
101   --  Generates a sequence of code for determining the quotient and remainder
102   --  of the division X/(Y*Z), using the source location from Sloc (N).
103   --  Entities of appropriate types are allocated for the quotient and
104   --  remainder and returned in Qnn and Rnn. The result is rounded if the
105   --  Rounded_Result flag of N is set. The Etype fields of Qnn and Rnn are
106   --  appropriately set on return.
107
108   function Build_Multiply (N : Node_Id; L, R : Node_Id) return Node_Id;
109   --  Builds an N_Op_Multiply node from the given left and right operand
110   --  expressions, using the source location from Sloc (N). The operands are
111   --  either both Universal_Real, in which case Build_Multiply differs from
112   --  Make_Op_Multiply only in that the Etype of the resulting node is set (to
113   --  Universal_Real), or they can be integer types. In this case the integer
114   --  types need not be the same, and Build_Multiply chooses a type long
115   --  enough to hold the product (i.e. twice the size of the longer of the two
116   --  operand types), and both operands are converted to this type. The Etype
117   --  of the result is also set to this value. However, the result can never
118   --  overflow Integer_64, so this is the largest type that is ever generated.
119   --  On return, the resulting node is analyzed and has its Etype set.
120
121   function Build_Rem (N : Node_Id; L, R : Node_Id) return Node_Id;
122   --  Builds an N_Op_Rem node from the given left and right operand
123   --  expressions, using the source location from Sloc (N). The operands are
124   --  both integer types, which need not be the same. Build_Rem converts the
125   --  operand with the smaller sized type to match the type of the other
126   --  operand and sets this as the result type. The result is never rounded
127   --  (rem operations cannot be rounded in any case). On return, the resulting
128   --  node is analyzed and has its Etype set.
129
130   function Build_Scaled_Divide
131     (N       : Node_Id;
132      X, Y, Z : Node_Id) return Node_Id;
133   --  Returns a node corresponding to the value X*Y/Z using the source
134   --  location from Sloc (N). The division is rounded if the Rounded_Result
135   --  flag of N is set. The integer types of X, Y, Z may be different. On
136   --  return the resulting node is analyzed and has is Etype set.
137
138   procedure Build_Scaled_Divide_Code
139     (N        : Node_Id;
140      X, Y, Z  : Node_Id;
141      Qnn, Rnn : out Entity_Id;
142      Code     : out List_Id);
143   --  Generates a sequence of code for determining the quotient and remainder
144   --  of the division X*Y/Z, using the source location from Sloc (N). Entities
145   --  of appropriate types are allocated for the quotient and remainder and
146   --  returned in Qnn and Rrr. The integer types for X, Y, Z may be different.
147   --  The division is rounded if the Rounded_Result flag of N is set. The
148   --  Etype fields of Qnn and Rnn are appropriately set on return.
149
150   procedure Do_Divide_Fixed_Fixed (N : Node_Id);
151   --  Handles expansion of divide for case of two fixed-point operands
152   --  (neither of them universal), with an integer or fixed-point result.
153   --  N is the N_Op_Divide node to be expanded.
154
155   procedure Do_Divide_Fixed_Universal (N : Node_Id);
156   --  Handles expansion of divide for case of a fixed-point operand divided
157   --  by a universal real operand, with an integer or fixed-point result. N
158   --  is the N_Op_Divide node to be expanded.
159
160   procedure Do_Divide_Universal_Fixed (N : Node_Id);
161   --  Handles expansion of divide for case of a universal real operand
162   --  divided by a fixed-point operand, with an integer or fixed-point
163   --  result. N is the N_Op_Divide node to be expanded.
164
165   procedure Do_Multiply_Fixed_Fixed (N : Node_Id);
166   --  Handles expansion of multiply for case of two fixed-point operands
167   --  (neither of them universal), with an integer or fixed-point result.
168   --  N is the N_Op_Multiply node to be expanded.
169
170   procedure Do_Multiply_Fixed_Universal (N : Node_Id; Left, Right : Node_Id);
171   --  Handles expansion of multiply for case of a fixed-point operand
172   --  multiplied by a universal real operand, with an integer or fixed-
173   --  point result. N is the N_Op_Multiply node to be expanded, and
174   --  Left, Right are the operands (which may have been switched).
175
176   procedure Expand_Convert_Fixed_Static (N : Node_Id);
177   --  This routine is called where the node N is a conversion of a literal
178   --  or other static expression of a fixed-point type to some other type.
179   --  In such cases, we simply rewrite the operand as a real literal and
180   --  reanalyze. This avoids problems which would otherwise result from
181   --  attempting to build and fold expressions involving constants.
182
183   function Fpt_Value (N : Node_Id) return Node_Id;
184   --  Given an operand of fixed-point operation, return an expression that
185   --  represents the corresponding Universal_Real value. The expression
186   --  can be of integer type, floating-point type, or fixed-point type.
187   --  The expression returned is neither analyzed and resolved. The Etype
188   --  of the result is properly set (to Universal_Real).
189
190   function Integer_Literal
191     (N        : Node_Id;
192      V        : Uint;
193      Negative : Boolean := False) return Node_Id;
194   --  Given a non-negative universal integer value, build a typed integer
195   --  literal node, using the smallest applicable standard integer type. If
196   --  and only if Negative is true a negative literal is built. If V exceeds
197   --  2**63-1, the largest value allowed for perfect result set scaling
198   --  factors (see RM G.2.3(22)), then Empty is returned. The node N provides
199   --  the Sloc value for the constructed literal. The Etype of the resulting
200   --  literal is correctly set, and it is marked as analyzed.
201
202   function Real_Literal (N : Node_Id; V : Ureal) return Node_Id;
203   --  Build a real literal node from the given value, the Etype of the
204   --  returned node is set to Universal_Real, since all floating-point
205   --  arithmetic operations that we construct use Universal_Real
206
207   function Rounded_Result_Set (N : Node_Id) return Boolean;
208   --  Returns True if N is a node that contains the Rounded_Result flag
209   --  and if the flag is true or the target type is an integer type.
210
211   procedure Set_Result
212     (N     : Node_Id;
213      Expr  : Node_Id;
214      Rchk  : Boolean := False;
215      Trunc : Boolean := False);
216   --  N is the node for the current conversion, division or multiplication
217   --  operation, and Expr is an expression representing the result. Expr may
218   --  be of floating-point or integer type. If the operation result is fixed-
219   --  point, then the value of Expr is in units of small of the result type
220   --  (i.e. small's have already been dealt with). The result of the call is
221   --  to replace N by an appropriate conversion to the result type, dealing
222   --  with rounding for the decimal types case. The node is then analyzed and
223   --  resolved using the result type. If Rchk or Trunc are True, then
224   --  respectively Do_Range_Check and Float_Truncate are set in the
225   --  resulting conversion.
226
227   ----------------------
228   -- Build_Conversion --
229   ----------------------
230
231   function Build_Conversion
232     (N     : Node_Id;
233      Typ   : Entity_Id;
234      Expr  : Node_Id;
235      Rchk  : Boolean := False;
236      Trunc : Boolean := False) return Node_Id
237   is
238      Loc    : constant Source_Ptr := Sloc (N);
239      Result : Node_Id;
240      Rcheck : Boolean := Rchk;
241
242   begin
243      --  A special case, if the expression is an integer literal and the
244      --  target type is an integer type, then just retype the integer
245      --  literal to the desired target type. Don't do this if we need
246      --  a range check.
247
248      if Nkind (Expr) = N_Integer_Literal
249        and then Is_Integer_Type (Typ)
250        and then not Rchk
251      then
252         Result := Expr;
253
254      --  Cases where we end up with a conversion. Note that we do not use the
255      --  Convert_To abstraction here, since we may be decorating the resulting
256      --  conversion with Rounded_Result and/or Conversion_OK, so we want the
257      --  conversion node present, even if it appears to be redundant.
258
259      else
260         --  Remove inner conversion if both inner and outer conversions are
261         --  to integer types, since the inner one serves no purpose (except
262         --  perhaps to set rounding, so we preserve the Rounded_Result flag)
263         --  and also we preserve the range check flag on the inner operand
264
265         if Is_Integer_Type (Typ)
266           and then Is_Integer_Type (Etype (Expr))
267           and then Nkind (Expr) = N_Type_Conversion
268         then
269            Result :=
270              Make_Type_Conversion (Loc,
271                Subtype_Mark => New_Occurrence_Of (Typ, Loc),
272                Expression   => Expression (Expr));
273            Set_Rounded_Result (Result, Rounded_Result_Set (Expr));
274            Rcheck := Rcheck or Do_Range_Check (Expr);
275
276         --  For all other cases, a simple type conversion will work
277
278         else
279            Result :=
280              Make_Type_Conversion (Loc,
281                Subtype_Mark => New_Occurrence_Of (Typ, Loc),
282                Expression   => Expr);
283
284            Set_Float_Truncate (Result, Trunc);
285         end if;
286
287         --  Set Conversion_OK if either result or expression type is a
288         --  fixed-point type, since from a semantic point of view, we are
289         --  treating fixed-point values as integers at this stage.
290
291         if Is_Fixed_Point_Type (Typ)
292           or else Is_Fixed_Point_Type (Etype (Expression (Result)))
293         then
294            Set_Conversion_OK (Result);
295         end if;
296
297         --  Set Do_Range_Check if either it was requested by the caller,
298         --  or if an eliminated inner conversion had a range check.
299
300         if Rcheck then
301            Enable_Range_Check (Result);
302         else
303            Set_Do_Range_Check (Result, False);
304         end if;
305      end if;
306
307      Set_Etype (Result, Typ);
308      return Result;
309   end Build_Conversion;
310
311   ------------------
312   -- Build_Divide --
313   ------------------
314
315   function Build_Divide (N : Node_Id; L, R : Node_Id) return Node_Id is
316      Loc         : constant Source_Ptr := Sloc (N);
317      Left_Type   : constant Entity_Id  := Base_Type (Etype (L));
318      Right_Type  : constant Entity_Id  := Base_Type (Etype (R));
319      Result_Type : Entity_Id;
320      Rnode       : Node_Id;
321
322   begin
323      --  Deal with floating-point case first
324
325      if Is_Floating_Point_Type (Left_Type) then
326         pragma Assert (Left_Type = Universal_Real);
327         pragma Assert (Right_Type = Universal_Real);
328
329         Rnode := Make_Op_Divide (Loc, L, R);
330         Result_Type := Universal_Real;
331
332      --  Integer and fixed-point cases
333
334      else
335         --  An optimization. If the right operand is the literal 1, then we
336         --  can just return the left hand operand. Putting the optimization
337         --  here allows us to omit the check at the call site.
338
339         if Nkind (R) = N_Integer_Literal and then Intval (R) = 1 then
340            return L;
341         end if;
342
343         --  If left and right types are the same, no conversion needed
344
345         if Left_Type = Right_Type then
346            Result_Type := Left_Type;
347            Rnode :=
348              Make_Op_Divide (Loc,
349                Left_Opnd  => L,
350                Right_Opnd => R);
351
352         --  Use left type if it is the larger of the two
353
354         elsif Esize (Left_Type) >= Esize (Right_Type) then
355            Result_Type := Left_Type;
356            Rnode :=
357              Make_Op_Divide (Loc,
358                Left_Opnd  => L,
359                Right_Opnd => Build_Conversion (N, Left_Type, R));
360
361         --  Otherwise right type is larger of the two, us it
362
363         else
364            Result_Type := Right_Type;
365            Rnode :=
366              Make_Op_Divide (Loc,
367                Left_Opnd => Build_Conversion (N, Right_Type, L),
368                Right_Opnd => R);
369         end if;
370      end if;
371
372      --  We now have a divide node built with Result_Type set. First
373      --  set Etype of result, as required for all Build_xxx routines
374
375      Set_Etype (Rnode, Base_Type (Result_Type));
376
377      --  Set Treat_Fixed_As_Integer if operation on fixed-point type
378      --  since this is a literal arithmetic operation, to be performed
379      --  by Gigi without any consideration of small values.
380
381      if Is_Fixed_Point_Type (Result_Type) then
382         Set_Treat_Fixed_As_Integer (Rnode);
383      end if;
384
385      --  The result is rounded if the target of the operation is decimal
386      --  and Rounded_Result is set, or if the target of the operation
387      --  is an integer type.
388
389      if Is_Integer_Type (Etype (N))
390        or else Rounded_Result_Set (N)
391      then
392         Set_Rounded_Result (Rnode);
393      end if;
394
395      return Rnode;
396   end Build_Divide;
397
398   -------------------------
399   -- Build_Double_Divide --
400   -------------------------
401
402   function Build_Double_Divide
403     (N       : Node_Id;
404      X, Y, Z : Node_Id) return Node_Id
405   is
406      Y_Size : constant Int := UI_To_Int (Esize (Etype (Y)));
407      Z_Size : constant Int := UI_To_Int (Esize (Etype (Z)));
408      Expr   : Node_Id;
409
410   begin
411      --  If denominator fits in 64 bits, we can build the operations directly
412      --  without causing any intermediate overflow, so that's what we do.
413
414      if Int'Max (Y_Size, Z_Size) <= 32 then
415         return
416           Build_Divide (N, X, Build_Multiply (N, Y, Z));
417
418      --  Otherwise we use the runtime routine
419
420      --    [Qnn : Interfaces.Integer_64,
421      --     Rnn : Interfaces.Integer_64;
422      --     Double_Divide (X, Y, Z, Qnn, Rnn, Round);
423      --     Qnn]
424
425      else
426         declare
427            Loc  : constant Source_Ptr := Sloc (N);
428            Qnn  : Entity_Id;
429            Rnn  : Entity_Id;
430            Code : List_Id;
431
432            pragma Warnings (Off, Rnn);
433
434         begin
435            Build_Double_Divide_Code (N, X, Y, Z, Qnn, Rnn, Code);
436            Insert_Actions (N, Code);
437            Expr := New_Occurrence_Of (Qnn, Loc);
438
439            --  Set type of result in case used elsewhere (see note at start)
440
441            Set_Etype (Expr, Etype (Qnn));
442
443            --  Set result as analyzed (see note at start on build routines)
444
445            return Expr;
446         end;
447      end if;
448   end Build_Double_Divide;
449
450   ------------------------------
451   -- Build_Double_Divide_Code --
452   ------------------------------
453
454   --  If the denominator can be computed in 64-bits, we build
455
456   --    [Nnn : constant typ := typ (X);
457   --     Dnn : constant typ := typ (Y) * typ (Z)
458   --     Qnn : constant typ := Nnn / Dnn;
459   --     Rnn : constant typ := Nnn / Dnn;
460
461   --  If the numerator cannot be computed in 64 bits, we build
462
463   --    [Qnn : typ;
464   --     Rnn : typ;
465   --     Double_Divide (X, Y, Z, Qnn, Rnn, Round);]
466
467   procedure Build_Double_Divide_Code
468     (N        : Node_Id;
469      X, Y, Z  : Node_Id;
470      Qnn, Rnn : out Entity_Id;
471      Code     : out List_Id)
472   is
473      Loc    : constant Source_Ptr := Sloc (N);
474
475      X_Size : constant Int := UI_To_Int (Esize (Etype (X)));
476      Y_Size : constant Int := UI_To_Int (Esize (Etype (Y)));
477      Z_Size : constant Int := UI_To_Int (Esize (Etype (Z)));
478
479      QR_Siz : Int;
480      QR_Typ : Entity_Id;
481
482      Nnn : Entity_Id;
483      Dnn : Entity_Id;
484
485      Quo : Node_Id;
486      Rnd : Entity_Id;
487
488   begin
489      --  Find type that will allow computation of numerator
490
491      QR_Siz := Int'Max (X_Size, 2 * Int'Max (Y_Size, Z_Size));
492
493      if QR_Siz <= 16 then
494         QR_Typ := Standard_Integer_16;
495      elsif QR_Siz <= 32 then
496         QR_Typ := Standard_Integer_32;
497      elsif QR_Siz <= 64 then
498         QR_Typ := Standard_Integer_64;
499
500      --  For more than 64, bits, we use the 64-bit integer defined in
501      --  Interfaces, so that it can be handled by the runtime routine
502
503      else
504         QR_Typ := RTE (RE_Integer_64);
505      end if;
506
507      --  Define quotient and remainder, and set their Etypes, so
508      --  that they can be picked up by Build_xxx routines.
509
510      Qnn := Make_Temporary (Loc, 'S');
511      Rnn := Make_Temporary (Loc, 'R');
512
513      Set_Etype (Qnn, QR_Typ);
514      Set_Etype (Rnn, QR_Typ);
515
516      --  Case that we can compute the denominator in 64 bits
517
518      if QR_Siz <= 64 then
519
520         --  Create temporaries for numerator and denominator and set Etypes,
521         --  so that New_Occurrence_Of picks them up for Build_xxx calls.
522
523         Nnn := Make_Temporary (Loc, 'N');
524         Dnn := Make_Temporary (Loc, 'D');
525
526         Set_Etype (Nnn, QR_Typ);
527         Set_Etype (Dnn, QR_Typ);
528
529         Code := New_List (
530           Make_Object_Declaration (Loc,
531             Defining_Identifier => Nnn,
532             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
533             Constant_Present    => True,
534             Expression => Build_Conversion (N, QR_Typ, X)),
535
536           Make_Object_Declaration (Loc,
537             Defining_Identifier => Dnn,
538             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
539             Constant_Present    => True,
540             Expression =>
541               Build_Multiply (N,
542                 Build_Conversion (N, QR_Typ, Y),
543                 Build_Conversion (N, QR_Typ, Z))));
544
545         Quo :=
546           Build_Divide (N,
547             New_Occurrence_Of (Nnn, Loc),
548             New_Occurrence_Of (Dnn, Loc));
549
550         Set_Rounded_Result (Quo, Rounded_Result_Set (N));
551
552         Append_To (Code,
553           Make_Object_Declaration (Loc,
554             Defining_Identifier => Qnn,
555             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
556             Constant_Present    => True,
557             Expression          => Quo));
558
559         Append_To (Code,
560           Make_Object_Declaration (Loc,
561             Defining_Identifier => Rnn,
562             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
563             Constant_Present    => True,
564             Expression =>
565               Build_Rem (N,
566                 New_Occurrence_Of (Nnn, Loc),
567                 New_Occurrence_Of (Dnn, Loc))));
568
569      --  Case where denominator does not fit in 64 bits, so we have to
570      --  call the runtime routine to compute the quotient and remainder
571
572      else
573         Rnd := Boolean_Literals (Rounded_Result_Set (N));
574
575         Code := New_List (
576           Make_Object_Declaration (Loc,
577             Defining_Identifier => Qnn,
578             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc)),
579
580           Make_Object_Declaration (Loc,
581             Defining_Identifier => Rnn,
582             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc)),
583
584           Make_Procedure_Call_Statement (Loc,
585             Name => New_Occurrence_Of (RTE (RE_Double_Divide), Loc),
586             Parameter_Associations => New_List (
587               Build_Conversion (N, QR_Typ, X),
588               Build_Conversion (N, QR_Typ, Y),
589               Build_Conversion (N, QR_Typ, Z),
590               New_Occurrence_Of (Qnn, Loc),
591               New_Occurrence_Of (Rnn, Loc),
592               New_Occurrence_Of (Rnd, Loc))));
593      end if;
594   end Build_Double_Divide_Code;
595
596   --------------------
597   -- Build_Multiply --
598   --------------------
599
600   function Build_Multiply (N : Node_Id; L, R : Node_Id) return Node_Id is
601      Loc         : constant Source_Ptr := Sloc (N);
602      Left_Type   : constant Entity_Id  := Etype (L);
603      Right_Type  : constant Entity_Id  := Etype (R);
604      Left_Size   : Int;
605      Right_Size  : Int;
606      Rsize       : Int;
607      Result_Type : Entity_Id;
608      Rnode       : Node_Id;
609
610   begin
611      --  Deal with floating-point case first
612
613      if Is_Floating_Point_Type (Left_Type) then
614         pragma Assert (Left_Type = Universal_Real);
615         pragma Assert (Right_Type = Universal_Real);
616
617         Result_Type := Universal_Real;
618         Rnode := Make_Op_Multiply (Loc, L, R);
619
620      --  Integer and fixed-point cases
621
622      else
623         --  An optimization. If the right operand is the literal 1, then we
624         --  can just return the left hand operand. Putting the optimization
625         --  here allows us to omit the check at the call site. Similarly, if
626         --  the left operand is the integer 1 we can return the right operand.
627
628         if Nkind (R) = N_Integer_Literal and then Intval (R) = 1 then
629            return L;
630         elsif Nkind (L) = N_Integer_Literal and then Intval (L) = 1 then
631            return R;
632         end if;
633
634         --  Otherwise we need to figure out the correct result type size
635         --  First figure out the effective sizes of the operands. Normally
636         --  the effective size of an operand is the RM_Size of the operand.
637         --  But a special case arises with operands whose size is known at
638         --  compile time. In this case, we can use the actual value of the
639         --  operand to get its size if it would fit signed in 8 or 16 bits.
640
641         Left_Size := UI_To_Int (RM_Size (Left_Type));
642
643         if Compile_Time_Known_Value (L) then
644            declare
645               Val : constant Uint := Expr_Value (L);
646            begin
647               if Val < Int'(2 ** 7) then
648                  Left_Size := 8;
649               elsif Val < Int'(2 ** 15) then
650                  Left_Size := 16;
651               end if;
652            end;
653         end if;
654
655         Right_Size := UI_To_Int (RM_Size (Right_Type));
656
657         if Compile_Time_Known_Value (R) then
658            declare
659               Val : constant Uint := Expr_Value (R);
660            begin
661               if Val <= Int'(2 ** 7) then
662                  Right_Size := 8;
663               elsif Val <= Int'(2 ** 15) then
664                  Right_Size := 16;
665               end if;
666            end;
667         end if;
668
669         --  Now the result size must be at least twice the longer of
670         --  the two sizes, to accommodate all possible results.
671
672         Rsize := 2 * Int'Max (Left_Size, Right_Size);
673
674         if Rsize <= 8 then
675            Result_Type := Standard_Integer_8;
676
677         elsif Rsize <= 16 then
678            Result_Type := Standard_Integer_16;
679
680         elsif Rsize <= 32 then
681            Result_Type := Standard_Integer_32;
682
683         else
684            Result_Type := Standard_Integer_64;
685         end if;
686
687         Rnode :=
688            Make_Op_Multiply (Loc,
689              Left_Opnd  => Build_Conversion (N, Result_Type, L),
690              Right_Opnd => Build_Conversion (N, Result_Type, R));
691      end if;
692
693      --  We now have a multiply node built with Result_Type set. First
694      --  set Etype of result, as required for all Build_xxx routines
695
696      Set_Etype (Rnode, Base_Type (Result_Type));
697
698      --  Set Treat_Fixed_As_Integer if operation on fixed-point type
699      --  since this is a literal arithmetic operation, to be performed
700      --  by Gigi without any consideration of small values.
701
702      if Is_Fixed_Point_Type (Result_Type) then
703         Set_Treat_Fixed_As_Integer (Rnode);
704      end if;
705
706      return Rnode;
707   end Build_Multiply;
708
709   ---------------
710   -- Build_Rem --
711   ---------------
712
713   function Build_Rem (N : Node_Id; L, R : Node_Id) return Node_Id is
714      Loc         : constant Source_Ptr := Sloc (N);
715      Left_Type   : constant Entity_Id  := Etype (L);
716      Right_Type  : constant Entity_Id  := Etype (R);
717      Result_Type : Entity_Id;
718      Rnode       : Node_Id;
719
720   begin
721      if Left_Type = Right_Type then
722         Result_Type := Left_Type;
723         Rnode :=
724           Make_Op_Rem (Loc,
725             Left_Opnd  => L,
726             Right_Opnd => R);
727
728      --  If left size is larger, we do the remainder operation using the
729      --  size of the left type (i.e. the larger of the two integer types).
730
731      elsif Esize (Left_Type) >= Esize (Right_Type) then
732         Result_Type := Left_Type;
733         Rnode :=
734           Make_Op_Rem (Loc,
735             Left_Opnd  => L,
736             Right_Opnd => Build_Conversion (N, Left_Type, R));
737
738      --  Similarly, if the right size is larger, we do the remainder
739      --  operation using the right type.
740
741      else
742         Result_Type := Right_Type;
743         Rnode :=
744           Make_Op_Rem (Loc,
745             Left_Opnd => Build_Conversion (N, Right_Type, L),
746             Right_Opnd => R);
747      end if;
748
749      --  We now have an N_Op_Rem node built with Result_Type set. First
750      --  set Etype of result, as required for all Build_xxx routines
751
752      Set_Etype (Rnode, Base_Type (Result_Type));
753
754      --  Set Treat_Fixed_As_Integer if operation on fixed-point type
755      --  since this is a literal arithmetic operation, to be performed
756      --  by Gigi without any consideration of small values.
757
758      if Is_Fixed_Point_Type (Result_Type) then
759         Set_Treat_Fixed_As_Integer (Rnode);
760      end if;
761
762      --  One more check. We did the rem operation using the larger of the
763      --  two types, which is reasonable. However, in the case where the
764      --  two types have unequal sizes, it is impossible for the result of
765      --  a remainder operation to be larger than the smaller of the two
766      --  types, so we can put a conversion round the result to keep the
767      --  evolving operation size as small as possible.
768
769      if Esize (Left_Type) >= Esize (Right_Type) then
770         Rnode := Build_Conversion (N, Right_Type, Rnode);
771      elsif Esize (Right_Type) >= Esize (Left_Type) then
772         Rnode := Build_Conversion (N, Left_Type, Rnode);
773      end if;
774
775      return Rnode;
776   end Build_Rem;
777
778   -------------------------
779   -- Build_Scaled_Divide --
780   -------------------------
781
782   function Build_Scaled_Divide
783     (N       : Node_Id;
784      X, Y, Z : Node_Id) return Node_Id
785   is
786      X_Size : constant Int := UI_To_Int (Esize (Etype (X)));
787      Y_Size : constant Int := UI_To_Int (Esize (Etype (Y)));
788      Expr   : Node_Id;
789
790   begin
791      --  If numerator fits in 64 bits, we can build the operations directly
792      --  without causing any intermediate overflow, so that's what we do.
793
794      if Int'Max (X_Size, Y_Size) <= 32 then
795         return
796           Build_Divide (N, Build_Multiply (N, X, Y), Z);
797
798      --  Otherwise we use the runtime routine
799
800      --    [Qnn : Integer_64,
801      --     Rnn : Integer_64;
802      --     Scaled_Divide (X, Y, Z, Qnn, Rnn, Round);
803      --     Qnn]
804
805      else
806         declare
807            Loc  : constant Source_Ptr := Sloc (N);
808            Qnn  : Entity_Id;
809            Rnn  : Entity_Id;
810            Code : List_Id;
811
812            pragma Warnings (Off, Rnn);
813
814         begin
815            Build_Scaled_Divide_Code (N, X, Y, Z, Qnn, Rnn, Code);
816            Insert_Actions (N, Code);
817            Expr := New_Occurrence_Of (Qnn, Loc);
818
819            --  Set type of result in case used elsewhere (see note at start)
820
821            Set_Etype (Expr, Etype (Qnn));
822            return Expr;
823         end;
824      end if;
825   end Build_Scaled_Divide;
826
827   ------------------------------
828   -- Build_Scaled_Divide_Code --
829   ------------------------------
830
831   --  If the numerator can be computed in 64-bits, we build
832
833   --    [Nnn : constant typ := typ (X) * typ (Y);
834   --     Dnn : constant typ := typ (Z)
835   --     Qnn : constant typ := Nnn / Dnn;
836   --     Rnn : constant typ := Nnn / Dnn;
837
838   --  If the numerator cannot be computed in 64 bits, we build
839
840   --    [Qnn : Interfaces.Integer_64;
841   --     Rnn : Interfaces.Integer_64;
842   --     Scaled_Divide (X, Y, Z, Qnn, Rnn, Round);]
843
844   procedure Build_Scaled_Divide_Code
845     (N        : Node_Id;
846      X, Y, Z  : Node_Id;
847      Qnn, Rnn : out Entity_Id;
848      Code     : out List_Id)
849   is
850      Loc    : constant Source_Ptr := Sloc (N);
851
852      X_Size : constant Int := UI_To_Int (Esize (Etype (X)));
853      Y_Size : constant Int := UI_To_Int (Esize (Etype (Y)));
854      Z_Size : constant Int := UI_To_Int (Esize (Etype (Z)));
855
856      QR_Siz : Int;
857      QR_Typ : Entity_Id;
858
859      Nnn : Entity_Id;
860      Dnn : Entity_Id;
861
862      Quo : Node_Id;
863      Rnd : Entity_Id;
864
865   begin
866      --  Find type that will allow computation of numerator
867
868      QR_Siz := Int'Max (X_Size, 2 * Int'Max (Y_Size, Z_Size));
869
870      if QR_Siz <= 16 then
871         QR_Typ := Standard_Integer_16;
872      elsif QR_Siz <= 32 then
873         QR_Typ := Standard_Integer_32;
874      elsif QR_Siz <= 64 then
875         QR_Typ := Standard_Integer_64;
876
877      --  For more than 64, bits, we use the 64-bit integer defined in
878      --  Interfaces, so that it can be handled by the runtime routine
879
880      else
881         QR_Typ := RTE (RE_Integer_64);
882      end if;
883
884      --  Define quotient and remainder, and set their Etypes, so
885      --  that they can be picked up by Build_xxx routines.
886
887      Qnn := Make_Temporary (Loc, 'S');
888      Rnn := Make_Temporary (Loc, 'R');
889
890      Set_Etype (Qnn, QR_Typ);
891      Set_Etype (Rnn, QR_Typ);
892
893      --  Case that we can compute the numerator in 64 bits
894
895      if QR_Siz <= 64 then
896         Nnn := Make_Temporary (Loc, 'N');
897         Dnn := Make_Temporary (Loc, 'D');
898
899         --  Set Etypes, so that they can be picked up by New_Occurrence_Of
900
901         Set_Etype (Nnn, QR_Typ);
902         Set_Etype (Dnn, QR_Typ);
903
904         Code := New_List (
905           Make_Object_Declaration (Loc,
906             Defining_Identifier => Nnn,
907             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
908             Constant_Present    => True,
909             Expression =>
910               Build_Multiply (N,
911                 Build_Conversion (N, QR_Typ, X),
912                 Build_Conversion (N, QR_Typ, Y))),
913
914           Make_Object_Declaration (Loc,
915             Defining_Identifier => Dnn,
916             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
917             Constant_Present    => True,
918             Expression => Build_Conversion (N, QR_Typ, Z)));
919
920         Quo :=
921           Build_Divide (N,
922             New_Occurrence_Of (Nnn, Loc),
923             New_Occurrence_Of (Dnn, Loc));
924
925         Append_To (Code,
926           Make_Object_Declaration (Loc,
927             Defining_Identifier => Qnn,
928             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
929             Constant_Present    => True,
930             Expression          => Quo));
931
932         Append_To (Code,
933           Make_Object_Declaration (Loc,
934             Defining_Identifier => Rnn,
935             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc),
936             Constant_Present    => True,
937             Expression =>
938               Build_Rem (N,
939                 New_Occurrence_Of (Nnn, Loc),
940                 New_Occurrence_Of (Dnn, Loc))));
941
942      --  Case where numerator does not fit in 64 bits, so we have to
943      --  call the runtime routine to compute the quotient and remainder
944
945      else
946         Rnd := Boolean_Literals (Rounded_Result_Set (N));
947
948         Code := New_List (
949           Make_Object_Declaration (Loc,
950             Defining_Identifier => Qnn,
951             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc)),
952
953           Make_Object_Declaration (Loc,
954             Defining_Identifier => Rnn,
955             Object_Definition   => New_Occurrence_Of (QR_Typ, Loc)),
956
957           Make_Procedure_Call_Statement (Loc,
958             Name => New_Occurrence_Of (RTE (RE_Scaled_Divide), Loc),
959             Parameter_Associations => New_List (
960               Build_Conversion (N, QR_Typ, X),
961               Build_Conversion (N, QR_Typ, Y),
962               Build_Conversion (N, QR_Typ, Z),
963               New_Occurrence_Of (Qnn, Loc),
964               New_Occurrence_Of (Rnn, Loc),
965               New_Occurrence_Of (Rnd, Loc))));
966      end if;
967
968      --  Set type of result, for use in caller
969
970      Set_Etype (Qnn, QR_Typ);
971   end Build_Scaled_Divide_Code;
972
973   ---------------------------
974   -- Do_Divide_Fixed_Fixed --
975   ---------------------------
976
977   --  We have:
978
979   --    (Result_Value * Result_Small) =
980   --        (Left_Value * Left_Small) / (Right_Value * Right_Small)
981
982   --    Result_Value = (Left_Value / Right_Value) *
983   --                   (Left_Small / (Right_Small * Result_Small));
984
985   --  we can do the operation in integer arithmetic if this fraction is an
986   --  integer or the reciprocal of an integer, as detailed in (RM G.2.3(21)).
987   --  Otherwise the result is in the close result set and our approach is to
988   --  use floating-point to compute this close result.
989
990   procedure Do_Divide_Fixed_Fixed (N : Node_Id) is
991      Left        : constant Node_Id   := Left_Opnd (N);
992      Right       : constant Node_Id   := Right_Opnd (N);
993      Left_Type   : constant Entity_Id := Etype (Left);
994      Right_Type  : constant Entity_Id := Etype (Right);
995      Result_Type : constant Entity_Id := Etype (N);
996      Right_Small : constant Ureal     := Small_Value (Right_Type);
997      Left_Small  : constant Ureal     := Small_Value (Left_Type);
998
999      Result_Small : Ureal;
1000      Frac         : Ureal;
1001      Frac_Num     : Uint;
1002      Frac_Den     : Uint;
1003      Lit_Int      : Node_Id;
1004
1005   begin
1006      --  Rounding is required if the result is integral
1007
1008      if Is_Integer_Type (Result_Type) then
1009         Set_Rounded_Result (N);
1010      end if;
1011
1012      --  Get result small. If the result is an integer, treat it as though
1013      --  it had a small of 1.0, all other processing is identical.
1014
1015      if Is_Integer_Type (Result_Type) then
1016         Result_Small := Ureal_1;
1017      else
1018         Result_Small := Small_Value (Result_Type);
1019      end if;
1020
1021      --  Get small ratio
1022
1023      Frac     := Left_Small / (Right_Small * Result_Small);
1024      Frac_Num := Norm_Num (Frac);
1025      Frac_Den := Norm_Den (Frac);
1026
1027      --  If the fraction is an integer, then we get the result by multiplying
1028      --  the left operand by the integer, and then dividing by the right
1029      --  operand (the order is important, if we did the divide first, we
1030      --  would lose precision).
1031
1032      if Frac_Den = 1 then
1033         Lit_Int := Integer_Literal (N, Frac_Num); -- always positive
1034
1035         if Present (Lit_Int) then
1036            Set_Result (N, Build_Scaled_Divide (N, Left, Lit_Int, Right));
1037            return;
1038         end if;
1039
1040      --  If the fraction is the reciprocal of an integer, then we get the
1041      --  result by first multiplying the divisor by the integer, and then
1042      --  doing the division with the adjusted divisor.
1043
1044      --  Note: this is much better than doing two divisions: multiplications
1045      --  are much faster than divisions (and certainly faster than rounded
1046      --  divisions), and we don't get inaccuracies from double rounding.
1047
1048      elsif Frac_Num = 1 then
1049         Lit_Int := Integer_Literal (N, Frac_Den); -- always positive
1050
1051         if Present (Lit_Int) then
1052            Set_Result (N, Build_Double_Divide (N, Left, Right, Lit_Int));
1053            return;
1054         end if;
1055      end if;
1056
1057      --  If we fall through, we use floating-point to compute the result
1058
1059      Set_Result (N,
1060        Build_Multiply (N,
1061          Build_Divide (N, Fpt_Value (Left), Fpt_Value (Right)),
1062          Real_Literal (N, Frac)));
1063   end Do_Divide_Fixed_Fixed;
1064
1065   -------------------------------
1066   -- Do_Divide_Fixed_Universal --
1067   -------------------------------
1068
1069   --  We have:
1070
1071   --    (Result_Value * Result_Small) = (Left_Value * Left_Small) / Lit_Value;
1072   --    Result_Value = Left_Value * Left_Small /(Lit_Value * Result_Small);
1073
1074   --  The result is required to be in the perfect result set if the literal
1075   --  can be factored so that the resulting small ratio is an integer or the
1076   --  reciprocal of an integer (RM G.2.3(21-22)). We now give a detailed
1077   --  analysis of these RM requirements:
1078
1079   --  We must factor the literal, finding an integer K:
1080
1081   --     Lit_Value = K * Right_Small
1082   --     Right_Small = Lit_Value / K
1083
1084   --  such that the small ratio:
1085
1086   --              Left_Small
1087   --     ------------------------------
1088   --     (Lit_Value / K) * Result_Small
1089
1090   --            Left_Small
1091   --  =  ------------------------  *  K
1092   --     Lit_Value * Result_Small
1093
1094   --  is an integer or the reciprocal of an integer, and for
1095   --  implementation efficiency we need the smallest such K.
1096
1097   --  First we reduce the left fraction to lowest terms
1098
1099   --    If numerator = 1, then for K = 1, the small ratio is the reciprocal
1100   --    of an integer, and this is clearly the minimum K case, so set K = 1,
1101   --    Right_Small = Lit_Value.
1102
1103   --    If numerator > 1, then set K to the denominator of the fraction so
1104   --    that the resulting small ratio is an integer (the numerator value).
1105
1106   procedure Do_Divide_Fixed_Universal (N : Node_Id) is
1107      Left        : constant Node_Id   := Left_Opnd (N);
1108      Right       : constant Node_Id   := Right_Opnd (N);
1109      Left_Type   : constant Entity_Id := Etype (Left);
1110      Result_Type : constant Entity_Id := Etype (N);
1111      Left_Small  : constant Ureal     := Small_Value (Left_Type);
1112      Lit_Value   : constant Ureal     := Realval (Right);
1113
1114      Result_Small : Ureal;
1115      Frac         : Ureal;
1116      Frac_Num     : Uint;
1117      Frac_Den     : Uint;
1118      Lit_K        : Node_Id;
1119      Lit_Int      : Node_Id;
1120
1121   begin
1122      --  Get result small. If the result is an integer, treat it as though
1123      --  it had a small of 1.0, all other processing is identical.
1124
1125      if Is_Integer_Type (Result_Type) then
1126         Result_Small := Ureal_1;
1127      else
1128         Result_Small := Small_Value (Result_Type);
1129      end if;
1130
1131      --  Determine if literal can be rewritten successfully
1132
1133      Frac     := Left_Small / (Lit_Value * Result_Small);
1134      Frac_Num := Norm_Num (Frac);
1135      Frac_Den := Norm_Den (Frac);
1136
1137      --  Case where fraction is the reciprocal of an integer (K = 1, integer
1138      --  = denominator). If this integer is not too large, this is the case
1139      --  where the result can be obtained by dividing by this integer value.
1140
1141      if Frac_Num = 1 then
1142         Lit_Int := Integer_Literal (N, Frac_Den, UR_Is_Negative (Frac));
1143
1144         if Present (Lit_Int) then
1145            Set_Result (N, Build_Divide (N, Left, Lit_Int));
1146            return;
1147         end if;
1148
1149      --  Case where we choose K to make fraction an integer (K = denominator
1150      --  of fraction, integer = numerator of fraction). If both K and the
1151      --  numerator are small enough, this is the case where the result can
1152      --  be obtained by first multiplying by the integer value and then
1153      --  dividing by K (the order is important, if we divided first, we
1154      --  would lose precision).
1155
1156      else
1157         Lit_Int := Integer_Literal (N, Frac_Num, UR_Is_Negative (Frac));
1158         Lit_K   := Integer_Literal (N, Frac_Den, False);
1159
1160         if Present (Lit_Int) and then Present (Lit_K) then
1161            Set_Result (N, Build_Scaled_Divide (N, Left, Lit_Int, Lit_K));
1162            return;
1163         end if;
1164      end if;
1165
1166      --  Fall through if the literal cannot be successfully rewritten, or if
1167      --  the small ratio is out of range of integer arithmetic. In the former
1168      --  case it is fine to use floating-point to get the close result set,
1169      --  and in the latter case, it means that the result is zero or raises
1170      --  constraint error, and we can do that accurately in floating-point.
1171
1172      --  If we end up using floating-point, then we take the right integer
1173      --  to be one, and its small to be the value of the original right real
1174      --  literal. That way, we need only one floating-point multiplication.
1175
1176      Set_Result (N,
1177        Build_Multiply (N, Fpt_Value (Left), Real_Literal (N, Frac)));
1178   end Do_Divide_Fixed_Universal;
1179
1180   -------------------------------
1181   -- Do_Divide_Universal_Fixed --
1182   -------------------------------
1183
1184   --  We have:
1185
1186   --    (Result_Value * Result_Small) =
1187   --          Lit_Value / (Right_Value * Right_Small)
1188   --    Result_Value =
1189   --          (Lit_Value / (Right_Small * Result_Small)) / Right_Value
1190
1191   --  The result is required to be in the perfect result set if the literal
1192   --  can be factored so that the resulting small ratio is an integer or the
1193   --  reciprocal of an integer (RM G.2.3(21-22)). We now give a detailed
1194   --  analysis of these RM requirements:
1195
1196   --  We must factor the literal, finding an integer K:
1197
1198   --     Lit_Value = K * Left_Small
1199   --     Left_Small = Lit_Value / K
1200
1201   --  such that the small ratio:
1202
1203   --           (Lit_Value / K)
1204   --     --------------------------
1205   --     Right_Small * Result_Small
1206
1207   --              Lit_Value             1
1208   --  =  --------------------------  *  -
1209   --     Right_Small * Result_Small     K
1210
1211   --  is an integer or the reciprocal of an integer, and for
1212   --  implementation efficiency we need the smallest such K.
1213
1214   --  First we reduce the left fraction to lowest terms
1215
1216   --    If denominator = 1, then for K = 1, the small ratio is an integer
1217   --    (the numerator) and this is clearly the minimum K case, so set K = 1,
1218   --    and Left_Small = Lit_Value.
1219
1220   --    If denominator > 1, then set K to the numerator of the fraction so
1221   --    that the resulting small ratio is the reciprocal of an integer (the
1222   --    numerator value).
1223
1224   procedure Do_Divide_Universal_Fixed (N : Node_Id) is
1225      Left        : constant Node_Id   := Left_Opnd (N);
1226      Right       : constant Node_Id   := Right_Opnd (N);
1227      Right_Type  : constant Entity_Id := Etype (Right);
1228      Result_Type : constant Entity_Id := Etype (N);
1229      Right_Small : constant Ureal     := Small_Value (Right_Type);
1230      Lit_Value   : constant Ureal     := Realval (Left);
1231
1232      Result_Small : Ureal;
1233      Frac         : Ureal;
1234      Frac_Num     : Uint;
1235      Frac_Den     : Uint;
1236      Lit_K        : Node_Id;
1237      Lit_Int      : Node_Id;
1238
1239   begin
1240      --  Get result small. If the result is an integer, treat it as though
1241      --  it had a small of 1.0, all other processing is identical.
1242
1243      if Is_Integer_Type (Result_Type) then
1244         Result_Small := Ureal_1;
1245      else
1246         Result_Small := Small_Value (Result_Type);
1247      end if;
1248
1249      --  Determine if literal can be rewritten successfully
1250
1251      Frac     := Lit_Value / (Right_Small * Result_Small);
1252      Frac_Num := Norm_Num (Frac);
1253      Frac_Den := Norm_Den (Frac);
1254
1255      --  Case where fraction is an integer (K = 1, integer = numerator). If
1256      --  this integer is not too large, this is the case where the result
1257      --  can be obtained by dividing this integer by the right operand.
1258
1259      if Frac_Den = 1 then
1260         Lit_Int := Integer_Literal (N, Frac_Num, UR_Is_Negative (Frac));
1261
1262         if Present (Lit_Int) then
1263            Set_Result (N, Build_Divide (N, Lit_Int, Right));
1264            return;
1265         end if;
1266
1267      --  Case where we choose K to make the fraction the reciprocal of an
1268      --  integer (K = numerator of fraction, integer = numerator of fraction).
1269      --  If both K and the integer are small enough, this is the case where
1270      --  the result can be obtained by multiplying the right operand by K
1271      --  and then dividing by the integer value. The order of the operations
1272      --  is important (if we divided first, we would lose precision).
1273
1274      else
1275         Lit_Int := Integer_Literal (N, Frac_Den, UR_Is_Negative (Frac));
1276         Lit_K   := Integer_Literal (N, Frac_Num, False);
1277
1278         if Present (Lit_Int) and then Present (Lit_K) then
1279            Set_Result (N, Build_Double_Divide (N, Lit_K, Right, Lit_Int));
1280            return;
1281         end if;
1282      end if;
1283
1284      --  Fall through if the literal cannot be successfully rewritten, or if
1285      --  the small ratio is out of range of integer arithmetic. In the former
1286      --  case it is fine to use floating-point to get the close result set,
1287      --  and in the latter case, it means that the result is zero or raises
1288      --  constraint error, and we can do that accurately in floating-point.
1289
1290      --  If we end up using floating-point, then we take the right integer
1291      --  to be one, and its small to be the value of the original right real
1292      --  literal. That way, we need only one floating-point division.
1293
1294      Set_Result (N,
1295        Build_Divide (N, Real_Literal (N, Frac), Fpt_Value (Right)));
1296   end Do_Divide_Universal_Fixed;
1297
1298   -----------------------------
1299   -- Do_Multiply_Fixed_Fixed --
1300   -----------------------------
1301
1302   --  We have:
1303
1304   --    (Result_Value * Result_Small) =
1305   --        (Left_Value * Left_Small) * (Right_Value * Right_Small)
1306
1307   --    Result_Value = (Left_Value * Right_Value) *
1308   --                   (Left_Small * Right_Small) / Result_Small;
1309
1310   --  we can do the operation in integer arithmetic if this fraction is an
1311   --  integer or the reciprocal of an integer, as detailed in (RM G.2.3(21)).
1312   --  Otherwise the result is in the close result set and our approach is to
1313   --  use floating-point to compute this close result.
1314
1315   procedure Do_Multiply_Fixed_Fixed (N : Node_Id) is
1316      Left  : constant Node_Id := Left_Opnd (N);
1317      Right : constant Node_Id := Right_Opnd (N);
1318
1319      Left_Type   : constant Entity_Id := Etype (Left);
1320      Right_Type  : constant Entity_Id := Etype (Right);
1321      Result_Type : constant Entity_Id := Etype (N);
1322      Right_Small : constant Ureal     := Small_Value (Right_Type);
1323      Left_Small  : constant Ureal     := Small_Value (Left_Type);
1324
1325      Result_Small : Ureal;
1326      Frac         : Ureal;
1327      Frac_Num     : Uint;
1328      Frac_Den     : Uint;
1329      Lit_Int      : Node_Id;
1330
1331   begin
1332      --  Get result small. If the result is an integer, treat it as though
1333      --  it had a small of 1.0, all other processing is identical.
1334
1335      if Is_Integer_Type (Result_Type) then
1336         Result_Small := Ureal_1;
1337      else
1338         Result_Small := Small_Value (Result_Type);
1339      end if;
1340
1341      --  Get small ratio
1342
1343      Frac     := (Left_Small * Right_Small) / Result_Small;
1344      Frac_Num := Norm_Num (Frac);
1345      Frac_Den := Norm_Den (Frac);
1346
1347      --  If the fraction is an integer, then we get the result by multiplying
1348      --  the operands, and then multiplying the result by the integer value.
1349
1350      if Frac_Den = 1 then
1351         Lit_Int := Integer_Literal (N, Frac_Num); -- always positive
1352
1353         if Present (Lit_Int) then
1354            Set_Result (N,
1355              Build_Multiply (N, Build_Multiply (N, Left, Right),
1356                Lit_Int));
1357            return;
1358         end if;
1359
1360      --  If the fraction is the reciprocal of an integer, then we get the
1361      --  result by multiplying the operands, and then dividing the result by
1362      --  the integer value. The order of the operations is important, if we
1363      --  divided first, we would lose precision.
1364
1365      elsif Frac_Num = 1 then
1366         Lit_Int := Integer_Literal (N, Frac_Den); -- always positive
1367
1368         if Present (Lit_Int) then
1369            Set_Result (N, Build_Scaled_Divide (N, Left, Right, Lit_Int));
1370            return;
1371         end if;
1372      end if;
1373
1374      --  If we fall through, we use floating-point to compute the result
1375
1376      Set_Result (N,
1377        Build_Multiply (N,
1378          Build_Multiply (N, Fpt_Value (Left), Fpt_Value (Right)),
1379          Real_Literal (N, Frac)));
1380   end Do_Multiply_Fixed_Fixed;
1381
1382   ---------------------------------
1383   -- Do_Multiply_Fixed_Universal --
1384   ---------------------------------
1385
1386   --  We have:
1387
1388   --    (Result_Value * Result_Small) = (Left_Value * Left_Small) * Lit_Value;
1389   --    Result_Value = Left_Value * (Left_Small * Lit_Value) / Result_Small;
1390
1391   --  The result is required to be in the perfect result set if the literal
1392   --  can be factored so that the resulting small ratio is an integer or the
1393   --  reciprocal of an integer (RM G.2.3(21-22)). We now give a detailed
1394   --  analysis of these RM requirements:
1395
1396   --  We must factor the literal, finding an integer K:
1397
1398   --     Lit_Value = K * Right_Small
1399   --     Right_Small = Lit_Value / K
1400
1401   --  such that the small ratio:
1402
1403   --     Left_Small * (Lit_Value / K)
1404   --     ----------------------------
1405   --             Result_Small
1406
1407   --     Left_Small * Lit_Value     1
1408   --  =  ----------------------  *  -
1409   --          Result_Small          K
1410
1411   --  is an integer or the reciprocal of an integer, and for
1412   --  implementation efficiency we need the smallest such K.
1413
1414   --  First we reduce the left fraction to lowest terms
1415
1416   --    If denominator = 1, then for K = 1, the small ratio is an integer, and
1417   --    this is clearly the minimum K case, so set
1418
1419   --      K = 1, Right_Small = Lit_Value
1420
1421   --    If denominator > 1, then set K to the numerator of the fraction, so
1422   --    that the resulting small ratio is the reciprocal of the integer (the
1423   --    denominator value).
1424
1425   procedure Do_Multiply_Fixed_Universal
1426     (N           : Node_Id;
1427      Left, Right : Node_Id)
1428   is
1429      Left_Type   : constant Entity_Id := Etype (Left);
1430      Result_Type : constant Entity_Id := Etype (N);
1431      Left_Small  : constant Ureal     := Small_Value (Left_Type);
1432      Lit_Value   : constant Ureal     := Realval (Right);
1433
1434      Result_Small : Ureal;
1435      Frac         : Ureal;
1436      Frac_Num     : Uint;
1437      Frac_Den     : Uint;
1438      Lit_K        : Node_Id;
1439      Lit_Int      : Node_Id;
1440
1441   begin
1442      --  Get result small. If the result is an integer, treat it as though
1443      --  it had a small of 1.0, all other processing is identical.
1444
1445      if Is_Integer_Type (Result_Type) then
1446         Result_Small := Ureal_1;
1447      else
1448         Result_Small := Small_Value (Result_Type);
1449      end if;
1450
1451      --  Determine if literal can be rewritten successfully
1452
1453      Frac     := (Left_Small * Lit_Value) / Result_Small;
1454      Frac_Num := Norm_Num (Frac);
1455      Frac_Den := Norm_Den (Frac);
1456
1457      --  Case where fraction is an integer (K = 1, integer = numerator). If
1458      --  this integer is not too large, this is the case where the result can
1459      --  be obtained by multiplying by this integer value.
1460
1461      if Frac_Den = 1 then
1462         Lit_Int := Integer_Literal (N, Frac_Num, UR_Is_Negative (Frac));
1463
1464         if Present (Lit_Int) then
1465            Set_Result (N, Build_Multiply (N, Left, Lit_Int));
1466            return;
1467         end if;
1468
1469      --  Case where we choose K to make fraction the reciprocal of an integer
1470      --  (K = numerator of fraction, integer = denominator of fraction). If
1471      --  both K and the denominator are small enough, this is the case where
1472      --  the result can be obtained by first multiplying by K, and then
1473      --  dividing by the integer value.
1474
1475      else
1476         Lit_Int := Integer_Literal (N, Frac_Den, UR_Is_Negative (Frac));
1477         Lit_K   := Integer_Literal (N, Frac_Num);
1478
1479         if Present (Lit_Int) and then Present (Lit_K) then
1480            Set_Result (N, Build_Scaled_Divide (N, Left, Lit_K, Lit_Int));
1481            return;
1482         end if;
1483      end if;
1484
1485      --  Fall through if the literal cannot be successfully rewritten, or if
1486      --  the small ratio is out of range of integer arithmetic. In the former
1487      --  case it is fine to use floating-point to get the close result set,
1488      --  and in the latter case, it means that the result is zero or raises
1489      --  constraint error, and we can do that accurately in floating-point.
1490
1491      --  If we end up using floating-point, then we take the right integer
1492      --  to be one, and its small to be the value of the original right real
1493      --  literal. That way, we need only one floating-point multiplication.
1494
1495      Set_Result (N,
1496        Build_Multiply (N, Fpt_Value (Left), Real_Literal (N, Frac)));
1497   end Do_Multiply_Fixed_Universal;
1498
1499   ---------------------------------
1500   -- Expand_Convert_Fixed_Static --
1501   ---------------------------------
1502
1503   procedure Expand_Convert_Fixed_Static (N : Node_Id) is
1504   begin
1505      Rewrite (N,
1506        Convert_To (Etype (N),
1507          Make_Real_Literal (Sloc (N), Expr_Value_R (Expression (N)))));
1508      Analyze_And_Resolve (N);
1509   end Expand_Convert_Fixed_Static;
1510
1511   -----------------------------------
1512   -- Expand_Convert_Fixed_To_Fixed --
1513   -----------------------------------
1514
1515   --  We have:
1516
1517   --    Result_Value * Result_Small = Source_Value * Source_Small
1518   --    Result_Value = Source_Value * (Source_Small / Result_Small)
1519
1520   --  If the small ratio (Source_Small / Result_Small) is a sufficiently small
1521   --  integer, then the perfect result set is obtained by a single integer
1522   --  multiplication.
1523
1524   --  If the small ratio is the reciprocal of a sufficiently small integer,
1525   --  then the perfect result set is obtained by a single integer division.
1526
1527   --  In other cases, we obtain the close result set by calculating the
1528   --  result in floating-point.
1529
1530   procedure Expand_Convert_Fixed_To_Fixed (N : Node_Id) is
1531      Rng_Check   : constant Boolean   := Do_Range_Check (N);
1532      Expr        : constant Node_Id   := Expression (N);
1533      Result_Type : constant Entity_Id := Etype (N);
1534      Source_Type : constant Entity_Id := Etype (Expr);
1535      Small_Ratio : Ureal;
1536      Ratio_Num   : Uint;
1537      Ratio_Den   : Uint;
1538      Lit         : Node_Id;
1539
1540   begin
1541      if Is_OK_Static_Expression (Expr) then
1542         Expand_Convert_Fixed_Static (N);
1543         return;
1544      end if;
1545
1546      Small_Ratio := Small_Value (Source_Type) / Small_Value (Result_Type);
1547      Ratio_Num   := Norm_Num (Small_Ratio);
1548      Ratio_Den   := Norm_Den (Small_Ratio);
1549
1550      if Ratio_Den = 1 then
1551         if Ratio_Num = 1 then
1552            Set_Result (N, Expr);
1553            return;
1554
1555         else
1556            Lit := Integer_Literal (N, Ratio_Num);
1557
1558            if Present (Lit) then
1559               Set_Result (N, Build_Multiply (N, Expr, Lit));
1560               return;
1561            end if;
1562         end if;
1563
1564      elsif Ratio_Num = 1 then
1565         Lit := Integer_Literal (N, Ratio_Den);
1566
1567         if Present (Lit) then
1568            Set_Result (N, Build_Divide (N, Expr, Lit), Rng_Check);
1569            return;
1570         end if;
1571      end if;
1572
1573      --  Fall through to use floating-point for the close result set case
1574      --  either as a result of the small ratio not being an integer or the
1575      --  reciprocal of an integer, or if the integer is out of range.
1576
1577      Set_Result (N,
1578        Build_Multiply (N,
1579          Fpt_Value (Expr),
1580          Real_Literal (N, Small_Ratio)),
1581        Rng_Check);
1582   end Expand_Convert_Fixed_To_Fixed;
1583
1584   -----------------------------------
1585   -- Expand_Convert_Fixed_To_Float --
1586   -----------------------------------
1587
1588   --  If the small of the fixed type is 1.0, then we simply convert the
1589   --  integer value directly to the target floating-point type, otherwise
1590   --  we first have to multiply by the small, in Universal_Real, and then
1591   --  convert the result to the target floating-point type.
1592
1593   procedure Expand_Convert_Fixed_To_Float (N : Node_Id) is
1594      Rng_Check   : constant Boolean    := Do_Range_Check (N);
1595      Expr        : constant Node_Id    := Expression (N);
1596      Source_Type : constant Entity_Id  := Etype (Expr);
1597      Small       : constant Ureal      := Small_Value (Source_Type);
1598
1599   begin
1600      if Is_OK_Static_Expression (Expr) then
1601         Expand_Convert_Fixed_Static (N);
1602         return;
1603      end if;
1604
1605      if Small = Ureal_1 then
1606         Set_Result (N, Expr);
1607
1608      else
1609         Set_Result (N,
1610           Build_Multiply (N,
1611             Fpt_Value (Expr),
1612             Real_Literal (N, Small)),
1613           Rng_Check);
1614      end if;
1615   end Expand_Convert_Fixed_To_Float;
1616
1617   -------------------------------------
1618   -- Expand_Convert_Fixed_To_Integer --
1619   -------------------------------------
1620
1621   --  We have:
1622
1623   --    Result_Value = Source_Value * Source_Small
1624
1625   --  If the small value is a sufficiently small integer, then the perfect
1626   --  result set is obtained by a single integer multiplication.
1627
1628   --  If the small value is the reciprocal of a sufficiently small integer,
1629   --  then the perfect result set is obtained by a single integer division.
1630
1631   --  In other cases, we obtain the close result set by calculating the
1632   --  result in floating-point.
1633
1634   procedure Expand_Convert_Fixed_To_Integer (N : Node_Id) is
1635      Rng_Check   : constant Boolean   := Do_Range_Check (N);
1636      Expr        : constant Node_Id   := Expression (N);
1637      Source_Type : constant Entity_Id := Etype (Expr);
1638      Small       : constant Ureal     := Small_Value (Source_Type);
1639      Small_Num   : constant Uint      := Norm_Num (Small);
1640      Small_Den   : constant Uint      := Norm_Den (Small);
1641      Lit         : Node_Id;
1642
1643   begin
1644      if Is_OK_Static_Expression (Expr) then
1645         Expand_Convert_Fixed_Static (N);
1646         return;
1647      end if;
1648
1649      if Small_Den = 1 then
1650         Lit := Integer_Literal (N, Small_Num);
1651
1652         if Present (Lit) then
1653            Set_Result (N, Build_Multiply (N, Expr, Lit), Rng_Check);
1654            return;
1655         end if;
1656
1657      elsif Small_Num = 1 then
1658         Lit := Integer_Literal (N, Small_Den);
1659
1660         if Present (Lit) then
1661            Set_Result (N, Build_Divide (N, Expr, Lit), Rng_Check);
1662            return;
1663         end if;
1664      end if;
1665
1666      --  Fall through to use floating-point for the close result set case
1667      --  either as a result of the small value not being an integer or the
1668      --  reciprocal of an integer, or if the integer is out of range.
1669
1670      Set_Result (N,
1671        Build_Multiply (N,
1672          Fpt_Value (Expr),
1673          Real_Literal (N, Small)),
1674        Rng_Check);
1675   end Expand_Convert_Fixed_To_Integer;
1676
1677   -----------------------------------
1678   -- Expand_Convert_Float_To_Fixed --
1679   -----------------------------------
1680
1681   --  We have
1682
1683   --    Result_Value * Result_Small = Operand_Value
1684
1685   --  so compute:
1686
1687   --    Result_Value = Operand_Value * (1.0 / Result_Small)
1688
1689   --  We do the small scaling in floating-point, and we do a multiplication
1690   --  rather than a division, since it is accurate enough for the perfect
1691   --  result cases, and faster.
1692
1693   procedure Expand_Convert_Float_To_Fixed (N : Node_Id) is
1694      Rng_Check   : constant Boolean   := Do_Range_Check (N);
1695      Expr        : constant Node_Id   := Expression (N);
1696      Result_Type : constant Entity_Id := Etype (N);
1697      Small       : constant Ureal     := Small_Value (Result_Type);
1698
1699   begin
1700      --  Optimize small = 1, where we can avoid the multiply completely
1701
1702      if Small = Ureal_1 then
1703         Set_Result (N, Expr, Rng_Check, Trunc => True);
1704
1705      --  Normal case where multiply is required
1706      --  Rounding is truncating for decimal fixed point types only,
1707      --  see RM 4.6(29).
1708
1709      else
1710         Set_Result (N,
1711           Build_Multiply (N,
1712             Fpt_Value (Expr),
1713             Real_Literal (N, Ureal_1 / Small)),
1714           Rng_Check, Trunc => Is_Decimal_Fixed_Point_Type (Result_Type));
1715      end if;
1716   end Expand_Convert_Float_To_Fixed;
1717
1718   -------------------------------------
1719   -- Expand_Convert_Integer_To_Fixed --
1720   -------------------------------------
1721
1722   --  We have
1723
1724   --    Result_Value * Result_Small = Operand_Value
1725   --    Result_Value = Operand_Value / Result_Small
1726
1727   --  If the small value is a sufficiently small integer, then the perfect
1728   --  result set is obtained by a single integer division.
1729
1730   --  If the small value is the reciprocal of a sufficiently small integer,
1731   --  the perfect result set is obtained by a single integer multiplication.
1732
1733   --  In other cases, we obtain the close result set by calculating the
1734   --  result in floating-point using a multiplication by the reciprocal
1735   --  of the Result_Small.
1736
1737   procedure Expand_Convert_Integer_To_Fixed (N : Node_Id) is
1738      Rng_Check   : constant Boolean   := Do_Range_Check (N);
1739      Expr        : constant Node_Id   := Expression (N);
1740      Result_Type : constant Entity_Id := Etype (N);
1741      Small       : constant Ureal     := Small_Value (Result_Type);
1742      Small_Num   : constant Uint      := Norm_Num (Small);
1743      Small_Den   : constant Uint      := Norm_Den (Small);
1744      Lit         : Node_Id;
1745
1746   begin
1747      if Small_Den = 1 then
1748         Lit := Integer_Literal (N, Small_Num);
1749
1750         if Present (Lit) then
1751            Set_Result (N, Build_Divide (N, Expr, Lit), Rng_Check);
1752            return;
1753         end if;
1754
1755      elsif Small_Num = 1 then
1756         Lit := Integer_Literal (N, Small_Den);
1757
1758         if Present (Lit) then
1759            Set_Result (N, Build_Multiply (N, Expr, Lit), Rng_Check);
1760            return;
1761         end if;
1762      end if;
1763
1764      --  Fall through to use floating-point for the close result set case
1765      --  either as a result of the small value not being an integer or the
1766      --  reciprocal of an integer, or if the integer is out of range.
1767
1768      Set_Result (N,
1769        Build_Multiply (N,
1770          Fpt_Value (Expr),
1771          Real_Literal (N, Ureal_1 / Small)),
1772        Rng_Check);
1773   end Expand_Convert_Integer_To_Fixed;
1774
1775   --------------------------------
1776   -- Expand_Decimal_Divide_Call --
1777   --------------------------------
1778
1779   --  We have four operands
1780
1781   --    Dividend
1782   --    Divisor
1783   --    Quotient
1784   --    Remainder
1785
1786   --  All of which are decimal types, and which thus have associated
1787   --  decimal scales.
1788
1789   --  Computing the quotient is a similar problem to that faced by the
1790   --  normal fixed-point division, except that it is simpler, because
1791   --  we always have compatible smalls.
1792
1793   --    Quotient = (Dividend / Divisor) * 10**q
1794
1795   --      where 10 ** q = Dividend'Small / (Divisor'Small * Quotient'Small)
1796   --      so q = Divisor'Scale + Quotient'Scale - Dividend'Scale
1797
1798   --    For q >= 0, we compute
1799
1800   --      Numerator   := Dividend * 10 ** q
1801   --      Denominator := Divisor
1802   --      Quotient    := Numerator / Denominator
1803
1804   --    For q < 0, we compute
1805
1806   --      Numerator   := Dividend
1807   --      Denominator := Divisor * 10 ** q
1808   --      Quotient    := Numerator / Denominator
1809
1810   --  Both these divisions are done in truncated mode, and the remainder
1811   --  from these divisions is used to compute the result Remainder. This
1812   --  remainder has the effective scale of the numerator of the division,
1813
1814   --    For q >= 0, the remainder scale is Dividend'Scale + q
1815   --    For q <  0, the remainder scale is Dividend'Scale
1816
1817   --  The result Remainder is then computed by a normal truncating decimal
1818   --  conversion from this scale to the scale of the remainder, i.e. by a
1819   --  division or multiplication by the appropriate power of 10.
1820
1821   procedure Expand_Decimal_Divide_Call (N : Node_Id) is
1822      Loc : constant Source_Ptr := Sloc (N);
1823
1824      Dividend  : Node_Id := First_Actual (N);
1825      Divisor   : Node_Id := Next_Actual (Dividend);
1826      Quotient  : Node_Id := Next_Actual (Divisor);
1827      Remainder : Node_Id := Next_Actual (Quotient);
1828
1829      Dividend_Type   : constant Entity_Id := Etype (Dividend);
1830      Divisor_Type    : constant Entity_Id := Etype (Divisor);
1831      Quotient_Type   : constant Entity_Id := Etype (Quotient);
1832      Remainder_Type  : constant Entity_Id := Etype (Remainder);
1833
1834      Dividend_Scale  : constant Uint := Scale_Value (Dividend_Type);
1835      Divisor_Scale   : constant Uint := Scale_Value (Divisor_Type);
1836      Quotient_Scale  : constant Uint := Scale_Value (Quotient_Type);
1837      Remainder_Scale : constant Uint := Scale_Value (Remainder_Type);
1838
1839      Q                  : Uint;
1840      Numerator_Scale    : Uint;
1841      Stmts              : List_Id;
1842      Qnn                : Entity_Id;
1843      Rnn                : Entity_Id;
1844      Computed_Remainder : Node_Id;
1845      Adjusted_Remainder : Node_Id;
1846      Scale_Adjust       : Uint;
1847
1848   begin
1849      --  Relocate the operands, since they are now list elements, and we
1850      --  need to reference them separately as operands in the expanded code.
1851
1852      Dividend  := Relocate_Node (Dividend);
1853      Divisor   := Relocate_Node (Divisor);
1854      Quotient  := Relocate_Node (Quotient);
1855      Remainder := Relocate_Node (Remainder);
1856
1857      --  Now compute Q, the adjustment scale
1858
1859      Q := Divisor_Scale + Quotient_Scale - Dividend_Scale;
1860
1861      --  If Q is non-negative then we need a scaled divide
1862
1863      if Q >= 0 then
1864         Build_Scaled_Divide_Code
1865           (N,
1866            Dividend,
1867            Integer_Literal (N, Uint_10 ** Q),
1868            Divisor,
1869            Qnn, Rnn, Stmts);
1870
1871         Numerator_Scale := Dividend_Scale + Q;
1872
1873      --  If Q is negative, then we need a double divide
1874
1875      else
1876         Build_Double_Divide_Code
1877           (N,
1878            Dividend,
1879            Divisor,
1880            Integer_Literal (N, Uint_10 ** (-Q)),
1881            Qnn, Rnn, Stmts);
1882
1883         Numerator_Scale := Dividend_Scale;
1884      end if;
1885
1886      --  Add statement to set quotient value
1887
1888      --    Quotient := quotient-type!(Qnn);
1889
1890      Append_To (Stmts,
1891        Make_Assignment_Statement (Loc,
1892          Name => Quotient,
1893          Expression =>
1894            Unchecked_Convert_To (Quotient_Type,
1895              Build_Conversion (N, Quotient_Type,
1896                New_Occurrence_Of (Qnn, Loc)))));
1897
1898      --  Now we need to deal with computing and setting the remainder. The
1899      --  scale of the remainder is in Numerator_Scale, and the desired
1900      --  scale is the scale of the given Remainder argument. There are
1901      --  three cases:
1902
1903      --    Numerator_Scale > Remainder_Scale
1904
1905      --      in this case, there are extra digits in the computed remainder
1906      --      which must be eliminated by an extra division:
1907
1908      --        computed-remainder := Numerator rem Denominator
1909      --        scale_adjust = Numerator_Scale - Remainder_Scale
1910      --        adjusted-remainder := computed-remainder / 10 ** scale_adjust
1911
1912      --    Numerator_Scale = Remainder_Scale
1913
1914      --      in this case, the we have the remainder we need
1915
1916      --        computed-remainder := Numerator rem Denominator
1917      --        adjusted-remainder := computed-remainder
1918
1919      --    Numerator_Scale < Remainder_Scale
1920
1921      --      in this case, we have insufficient digits in the computed
1922      --      remainder, which must be eliminated by an extra multiply
1923
1924      --        computed-remainder := Numerator rem Denominator
1925      --        scale_adjust = Remainder_Scale - Numerator_Scale
1926      --        adjusted-remainder := computed-remainder * 10 ** scale_adjust
1927
1928      --  Finally we assign the adjusted-remainder to the result Remainder
1929      --  with conversions to get the proper fixed-point type representation.
1930
1931      Computed_Remainder := New_Occurrence_Of (Rnn, Loc);
1932
1933      if Numerator_Scale > Remainder_Scale then
1934         Scale_Adjust := Numerator_Scale - Remainder_Scale;
1935         Adjusted_Remainder :=
1936           Build_Divide
1937             (N, Computed_Remainder, Integer_Literal (N, 10 ** Scale_Adjust));
1938
1939      elsif Numerator_Scale = Remainder_Scale then
1940         Adjusted_Remainder := Computed_Remainder;
1941
1942      else -- Numerator_Scale < Remainder_Scale
1943         Scale_Adjust := Remainder_Scale - Numerator_Scale;
1944         Adjusted_Remainder :=
1945           Build_Multiply
1946             (N, Computed_Remainder, Integer_Literal (N, 10 ** Scale_Adjust));
1947      end if;
1948
1949      --  Assignment of remainder result
1950
1951      Append_To (Stmts,
1952        Make_Assignment_Statement (Loc,
1953          Name => Remainder,
1954          Expression =>
1955            Unchecked_Convert_To (Remainder_Type, Adjusted_Remainder)));
1956
1957      --  Final step is to rewrite the call with a block containing the
1958      --  above sequence of constructed statements for the divide operation.
1959
1960      Rewrite (N,
1961        Make_Block_Statement (Loc,
1962          Handled_Statement_Sequence =>
1963            Make_Handled_Sequence_Of_Statements (Loc,
1964              Statements => Stmts)));
1965
1966      Analyze (N);
1967   end Expand_Decimal_Divide_Call;
1968
1969   -----------------------------------------------
1970   -- Expand_Divide_Fixed_By_Fixed_Giving_Fixed --
1971   -----------------------------------------------
1972
1973   procedure Expand_Divide_Fixed_By_Fixed_Giving_Fixed (N : Node_Id) is
1974      Left  : constant Node_Id := Left_Opnd (N);
1975      Right : constant Node_Id := Right_Opnd (N);
1976
1977   begin
1978      --  Suppress expansion of a fixed-by-fixed division if the
1979      --  operation is supported directly by the target.
1980
1981      if Target_Has_Fixed_Ops (Etype (Left), Etype (Right), Etype (N)) then
1982         return;
1983      end if;
1984
1985      if Etype (Left) = Universal_Real then
1986         Do_Divide_Universal_Fixed (N);
1987
1988      elsif Etype (Right) = Universal_Real then
1989         Do_Divide_Fixed_Universal (N);
1990
1991      else
1992         Do_Divide_Fixed_Fixed (N);
1993      end if;
1994   end Expand_Divide_Fixed_By_Fixed_Giving_Fixed;
1995
1996   -----------------------------------------------
1997   -- Expand_Divide_Fixed_By_Fixed_Giving_Float --
1998   -----------------------------------------------
1999
2000   --  The division is done in Universal_Real, and the result is multiplied
2001   --  by the small ratio, which is Small (Right) / Small (Left). Special
2002   --  treatment is required for universal operands, which represent their
2003   --  own value and do not require conversion.
2004
2005   procedure Expand_Divide_Fixed_By_Fixed_Giving_Float (N : Node_Id) is
2006      Left  : constant Node_Id := Left_Opnd (N);
2007      Right : constant Node_Id := Right_Opnd (N);
2008
2009      Left_Type  : constant Entity_Id := Etype (Left);
2010      Right_Type : constant Entity_Id := Etype (Right);
2011
2012   begin
2013      --  Case of left operand is universal real, the result we want is:
2014
2015      --    Left_Value / (Right_Value * Right_Small)
2016
2017      --  so we compute this as:
2018
2019      --    (Left_Value / Right_Small) / Right_Value
2020
2021      if Left_Type = Universal_Real then
2022         Set_Result (N,
2023           Build_Divide (N,
2024             Real_Literal (N, Realval (Left) / Small_Value (Right_Type)),
2025             Fpt_Value (Right)));
2026
2027      --  Case of right operand is universal real, the result we want is
2028
2029      --    (Left_Value * Left_Small) / Right_Value
2030
2031      --  so we compute this as:
2032
2033      --    Left_Value * (Left_Small / Right_Value)
2034
2035      --  Note we invert to a multiplication since usually floating-point
2036      --  multiplication is much faster than floating-point division.
2037
2038      elsif Right_Type = Universal_Real then
2039         Set_Result (N,
2040           Build_Multiply (N,
2041             Fpt_Value (Left),
2042             Real_Literal (N, Small_Value (Left_Type) / Realval (Right))));
2043
2044      --  Both operands are fixed, so the value we want is
2045
2046      --    (Left_Value * Left_Small) / (Right_Value * Right_Small)
2047
2048      --  which we compute as:
2049
2050      --    (Left_Value / Right_Value) * (Left_Small / Right_Small)
2051
2052      else
2053         Set_Result (N,
2054           Build_Multiply (N,
2055             Build_Divide (N, Fpt_Value (Left), Fpt_Value (Right)),
2056             Real_Literal (N,
2057               Small_Value (Left_Type) / Small_Value (Right_Type))));
2058      end if;
2059   end Expand_Divide_Fixed_By_Fixed_Giving_Float;
2060
2061   -------------------------------------------------
2062   -- Expand_Divide_Fixed_By_Fixed_Giving_Integer --
2063   -------------------------------------------------
2064
2065   procedure Expand_Divide_Fixed_By_Fixed_Giving_Integer (N : Node_Id) is
2066      Left  : constant Node_Id := Left_Opnd (N);
2067      Right : constant Node_Id := Right_Opnd (N);
2068   begin
2069      if Etype (Left) = Universal_Real then
2070         Do_Divide_Universal_Fixed (N);
2071      elsif Etype (Right) = Universal_Real then
2072         Do_Divide_Fixed_Universal (N);
2073      else
2074         Do_Divide_Fixed_Fixed (N);
2075      end if;
2076   end Expand_Divide_Fixed_By_Fixed_Giving_Integer;
2077
2078   -------------------------------------------------
2079   -- Expand_Divide_Fixed_By_Integer_Giving_Fixed --
2080   -------------------------------------------------
2081
2082   --  Since the operand and result fixed-point type is the same, this is
2083   --  a straight divide by the right operand, the small can be ignored.
2084
2085   procedure Expand_Divide_Fixed_By_Integer_Giving_Fixed (N : Node_Id) is
2086      Left  : constant Node_Id := Left_Opnd (N);
2087      Right : constant Node_Id := Right_Opnd (N);
2088   begin
2089      Set_Result (N, Build_Divide (N, Left, Right));
2090   end Expand_Divide_Fixed_By_Integer_Giving_Fixed;
2091
2092   -------------------------------------------------
2093   -- Expand_Multiply_Fixed_By_Fixed_Giving_Fixed --
2094   -------------------------------------------------
2095
2096   procedure Expand_Multiply_Fixed_By_Fixed_Giving_Fixed (N : Node_Id) is
2097      Left  : constant Node_Id := Left_Opnd (N);
2098      Right : constant Node_Id := Right_Opnd (N);
2099
2100      procedure Rewrite_Non_Static_Universal (Opnd : Node_Id);
2101      --  The operand may be a non-static universal value, such an
2102      --  exponentiation with a non-static exponent. In that case, treat
2103      --  as a fixed * fixed multiplication, and convert the argument to
2104      --  the target fixed type.
2105
2106      ----------------------------------
2107      -- Rewrite_Non_Static_Universal --
2108      ----------------------------------
2109
2110      procedure Rewrite_Non_Static_Universal (Opnd : Node_Id) is
2111         Loc : constant Source_Ptr := Sloc (N);
2112      begin
2113         Rewrite (Opnd,
2114           Make_Type_Conversion (Loc,
2115             Subtype_Mark => New_Occurrence_Of (Etype (N), Loc),
2116             Expression   => Expression (Opnd)));
2117         Analyze_And_Resolve (Opnd, Etype (N));
2118      end Rewrite_Non_Static_Universal;
2119
2120   --  Start of processing for Expand_Multiply_Fixed_By_Fixed_Giving_Fixed
2121
2122   begin
2123      --  Suppress expansion of a fixed-by-fixed multiplication if the
2124      --  operation is supported directly by the target.
2125
2126      if Target_Has_Fixed_Ops (Etype (Left), Etype (Right), Etype (N)) then
2127         return;
2128      end if;
2129
2130      if Etype (Left) = Universal_Real then
2131         if Nkind (Left) = N_Real_Literal then
2132            Do_Multiply_Fixed_Universal (N, Left => Right, Right => Left);
2133
2134         elsif Nkind (Left) = N_Type_Conversion then
2135            Rewrite_Non_Static_Universal (Left);
2136            Do_Multiply_Fixed_Fixed (N);
2137         end if;
2138
2139      elsif Etype (Right) = Universal_Real then
2140         if Nkind (Right) = N_Real_Literal then
2141            Do_Multiply_Fixed_Universal (N, Left, Right);
2142
2143         elsif Nkind (Right) = N_Type_Conversion then
2144            Rewrite_Non_Static_Universal (Right);
2145            Do_Multiply_Fixed_Fixed (N);
2146         end if;
2147
2148      else
2149         Do_Multiply_Fixed_Fixed (N);
2150      end if;
2151   end Expand_Multiply_Fixed_By_Fixed_Giving_Fixed;
2152
2153   -------------------------------------------------
2154   -- Expand_Multiply_Fixed_By_Fixed_Giving_Float --
2155   -------------------------------------------------
2156
2157   --  The multiply is done in Universal_Real, and the result is multiplied
2158   --  by the adjustment for the smalls which is Small (Right) * Small (Left).
2159   --  Special treatment is required for universal operands.
2160
2161   procedure Expand_Multiply_Fixed_By_Fixed_Giving_Float (N : Node_Id) is
2162      Left  : constant Node_Id := Left_Opnd (N);
2163      Right : constant Node_Id := Right_Opnd (N);
2164
2165      Left_Type  : constant Entity_Id := Etype (Left);
2166      Right_Type : constant Entity_Id := Etype (Right);
2167
2168   begin
2169      --  Case of left operand is universal real, the result we want is
2170
2171      --    Left_Value * (Right_Value * Right_Small)
2172
2173      --  so we compute this as:
2174
2175      --    (Left_Value * Right_Small) * Right_Value;
2176
2177      if Left_Type = Universal_Real then
2178         Set_Result (N,
2179           Build_Multiply (N,
2180             Real_Literal (N, Realval (Left) * Small_Value (Right_Type)),
2181             Fpt_Value (Right)));
2182
2183      --  Case of right operand is universal real, the result we want is
2184
2185      --    (Left_Value * Left_Small) * Right_Value
2186
2187      --  so we compute this as:
2188
2189      --    Left_Value * (Left_Small * Right_Value)
2190
2191      elsif Right_Type = Universal_Real then
2192         Set_Result (N,
2193           Build_Multiply (N,
2194             Fpt_Value (Left),
2195             Real_Literal (N, Small_Value (Left_Type) * Realval (Right))));
2196
2197      --  Both operands are fixed, so the value we want is
2198
2199      --    (Left_Value * Left_Small) * (Right_Value * Right_Small)
2200
2201      --  which we compute as:
2202
2203      --    (Left_Value * Right_Value) * (Right_Small * Left_Small)
2204
2205      else
2206         Set_Result (N,
2207           Build_Multiply (N,
2208             Build_Multiply (N, Fpt_Value (Left), Fpt_Value (Right)),
2209             Real_Literal (N,
2210               Small_Value (Right_Type) * Small_Value (Left_Type))));
2211      end if;
2212   end Expand_Multiply_Fixed_By_Fixed_Giving_Float;
2213
2214   ---------------------------------------------------
2215   -- Expand_Multiply_Fixed_By_Fixed_Giving_Integer --
2216   ---------------------------------------------------
2217
2218   procedure Expand_Multiply_Fixed_By_Fixed_Giving_Integer (N : Node_Id) is
2219      Loc   : constant Source_Ptr := Sloc (N);
2220      Left  : constant Node_Id    := Left_Opnd (N);
2221      Right : constant Node_Id    := Right_Opnd (N);
2222
2223   begin
2224      if Etype (Left) = Universal_Real then
2225         Do_Multiply_Fixed_Universal (N, Left => Right, Right => Left);
2226
2227      elsif Etype (Right) = Universal_Real then
2228         Do_Multiply_Fixed_Universal (N, Left, Right);
2229
2230      --  If both types are equal and we need to avoid floating point
2231      --  instructions, it's worth introducing a temporary with the
2232      --  common type, because it may be evaluated more simply without
2233      --  the need for run-time use of floating point.
2234
2235      elsif Etype (Right) = Etype (Left)
2236        and then Restriction_Active (No_Floating_Point)
2237      then
2238         declare
2239            Temp : constant Entity_Id := Make_Temporary (Loc, 'F');
2240            Mult : constant Node_Id   := Make_Op_Multiply (Loc, Left, Right);
2241            Decl : constant Node_Id   :=
2242              Make_Object_Declaration (Loc,
2243                Defining_Identifier => Temp,
2244                Object_Definition   => New_Occurrence_Of (Etype (Right), Loc),
2245                Expression          => Mult);
2246
2247         begin
2248            Insert_Action (N, Decl);
2249            Rewrite (N,
2250              OK_Convert_To (Etype (N), New_Occurrence_Of (Temp, Loc)));
2251            Analyze_And_Resolve (N, Standard_Integer);
2252         end;
2253
2254      else
2255         Do_Multiply_Fixed_Fixed (N);
2256      end if;
2257   end Expand_Multiply_Fixed_By_Fixed_Giving_Integer;
2258
2259   ---------------------------------------------------
2260   -- Expand_Multiply_Fixed_By_Integer_Giving_Fixed --
2261   ---------------------------------------------------
2262
2263   --  Since the operand and result fixed-point type is the same, this is
2264   --  a straight multiply by the right operand, the small can be ignored.
2265
2266   procedure Expand_Multiply_Fixed_By_Integer_Giving_Fixed (N : Node_Id) is
2267   begin
2268      Set_Result (N,
2269        Build_Multiply (N, Left_Opnd (N), Right_Opnd (N)));
2270   end Expand_Multiply_Fixed_By_Integer_Giving_Fixed;
2271
2272   ---------------------------------------------------
2273   -- Expand_Multiply_Integer_By_Fixed_Giving_Fixed --
2274   ---------------------------------------------------
2275
2276   --  Since the operand and result fixed-point type is the same, this is
2277   --  a straight multiply by the right operand, the small can be ignored.
2278
2279   procedure Expand_Multiply_Integer_By_Fixed_Giving_Fixed (N : Node_Id) is
2280   begin
2281      Set_Result (N,
2282        Build_Multiply (N, Left_Opnd (N), Right_Opnd (N)));
2283   end Expand_Multiply_Integer_By_Fixed_Giving_Fixed;
2284
2285   ---------------
2286   -- Fpt_Value --
2287   ---------------
2288
2289   function Fpt_Value (N : Node_Id) return Node_Id is
2290      Typ   : constant Entity_Id  := Etype (N);
2291
2292   begin
2293      if Is_Integer_Type (Typ)
2294        or else Is_Floating_Point_Type (Typ)
2295      then
2296         return Build_Conversion (N, Universal_Real, N);
2297
2298      --  Fixed-point case, must get integer value first
2299
2300      else
2301         return Build_Conversion (N, Universal_Real, N);
2302      end if;
2303   end Fpt_Value;
2304
2305   ---------------------
2306   -- Integer_Literal --
2307   ---------------------
2308
2309   function Integer_Literal
2310     (N        : Node_Id;
2311      V        : Uint;
2312      Negative : Boolean := False) return Node_Id
2313   is
2314      T : Entity_Id;
2315      L : Node_Id;
2316
2317   begin
2318      if V < Uint_2 ** 7 then
2319         T := Standard_Integer_8;
2320
2321      elsif V < Uint_2 ** 15 then
2322         T := Standard_Integer_16;
2323
2324      elsif V < Uint_2 ** 31 then
2325         T := Standard_Integer_32;
2326
2327      elsif V < Uint_2 ** 63 then
2328         T := Standard_Integer_64;
2329
2330      else
2331         return Empty;
2332      end if;
2333
2334      if Negative then
2335         L := Make_Integer_Literal (Sloc (N), UI_Negate (V));
2336      else
2337         L := Make_Integer_Literal (Sloc (N), V);
2338      end if;
2339
2340      --  Set type of result in case used elsewhere (see note at start)
2341
2342      Set_Etype (L, T);
2343      Set_Is_Static_Expression (L);
2344
2345      --  We really need to set Analyzed here because we may be creating a
2346      --  very strange beast, namely an integer literal typed as fixed-point
2347      --  and the analyzer won't like that. Probably we should allow the
2348      --  Treat_Fixed_As_Integer flag to appear on integer literal nodes
2349      --  and teach the analyzer how to handle them ???
2350
2351      Set_Analyzed (L);
2352      return L;
2353   end Integer_Literal;
2354
2355   ------------------
2356   -- Real_Literal --
2357   ------------------
2358
2359   function Real_Literal (N : Node_Id; V : Ureal) return Node_Id is
2360      L : Node_Id;
2361
2362   begin
2363      L := Make_Real_Literal (Sloc (N), V);
2364
2365      --  Set type of result in case used elsewhere (see note at start)
2366
2367      Set_Etype (L, Universal_Real);
2368      return L;
2369   end Real_Literal;
2370
2371   ------------------------
2372   -- Rounded_Result_Set --
2373   ------------------------
2374
2375   function Rounded_Result_Set (N : Node_Id) return Boolean is
2376      K : constant Node_Kind := Nkind (N);
2377   begin
2378      if (K = N_Type_Conversion or else
2379          K = N_Op_Divide       or else
2380          K = N_Op_Multiply)
2381        and then
2382          (Rounded_Result (N) or else Is_Integer_Type (Etype (N)))
2383      then
2384         return True;
2385      else
2386         return False;
2387      end if;
2388   end Rounded_Result_Set;
2389
2390   ----------------
2391   -- Set_Result --
2392   ----------------
2393
2394   procedure Set_Result
2395     (N     : Node_Id;
2396      Expr  : Node_Id;
2397      Rchk  : Boolean := False;
2398      Trunc : Boolean := False)
2399   is
2400      Cnode : Node_Id;
2401
2402      Expr_Type   : constant Entity_Id := Etype (Expr);
2403      Result_Type : constant Entity_Id := Etype (N);
2404
2405   begin
2406      --  No conversion required if types match and no range check or truncate
2407
2408      if Result_Type = Expr_Type and then not (Rchk or Trunc) then
2409         Cnode := Expr;
2410
2411      --  Else perform required conversion
2412
2413      else
2414         Cnode := Build_Conversion (N, Result_Type, Expr, Rchk, Trunc);
2415      end if;
2416
2417      Rewrite (N, Cnode);
2418      Analyze_And_Resolve (N, Result_Type);
2419   end Set_Result;
2420
2421end Exp_Fixd;
2422