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

-- -- | |

-- GNAT COMPILER COMPONENTS -- | |

-- -- | |

-- E X P _ F I X D -- | |

-- -- | |

-- B o d y -- | |

-- -- | |

-- Copyright (C) 1992-2021, Free Software Foundation, Inc. -- | |

-- -- | |

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

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

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

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

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

-- or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License -- | |

-- for more details. You should have received a copy of the GNU General -- | |

-- Public License distributed with GNAT; see file COPYING3. If not, go to -- | |

-- http://www.gnu.org/licenses for a complete copy of the license. -- | |

-- -- | |

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

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

-- -- | |

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

with Atree; use Atree; | |

with Checks; use Checks; | |

with Einfo; use Einfo; | |

with Einfo.Entities; use Einfo.Entities; | |

with Einfo.Utils; use Einfo.Utils; | |

with Exp_Util; use Exp_Util; | |

with Nlists; use Nlists; | |

with Nmake; use Nmake; | |

with Restrict; use Restrict; | |

with Rident; use Rident; | |

with Rtsfind; use Rtsfind; | |

with Sem; use Sem; | |

with Sem_Eval; use Sem_Eval; | |

with Sem_Res; use Sem_Res; | |

with Sem_Util; use Sem_Util; | |

with Sinfo; use Sinfo; | |

with Sinfo.Nodes; use Sinfo.Nodes; | |

with Stand; use Stand; | |

with Tbuild; use Tbuild; | |

with Ttypes; use Ttypes; | |

with Uintp; use Uintp; | |

with Urealp; use Urealp; | |

package body Exp_Fixd is | |

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

-- Local Subprograms -- | |

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

-- General note; in this unit, a number of routines are driven by the | |

-- types (Etype) of their operands. Since we are dealing with unanalyzed | |

-- expressions as they are constructed, the Etypes would not normally be | |

-- set, but the construction routines that we use in this unit do in fact | |

-- set the Etype values correctly. In addition, setting the Etype ensures | |

-- that the analyzer does not try to redetermine the type when the node | |

-- is analyzed (which would be wrong, since in the case where we set the | |

-- Conversion_OK flag, it would think it was still dealing with a normal | |

-- fixed-point operation and mess it up). | |

function Build_Conversion | |

(N : Node_Id; | |

Typ : Entity_Id; | |

Expr : Node_Id; | |

Rchk : Boolean := False; | |

Trunc : Boolean := False) return Node_Id; | |

-- Build an expression that converts the expression Expr to type Typ, | |

-- taking the source location from Sloc (N). If the conversions involve | |

-- fixed-point types, then the Conversion_OK flag will be set so that the | |

-- resulting conversions do not get re-expanded. On return, the resulting | |

-- node has its Etype set. If Rchk is set, then Do_Range_Check is set | |

-- in the resulting conversion node. If Trunc is set, then the | |

-- Float_Truncate flag is set on the conversion, which must be from | |

-- a floating-point type to an integer type. | |

function Build_Divide (N : Node_Id; L, R : Node_Id) return Node_Id; | |

-- Builds an N_Op_Divide node from the given left and right operand | |

-- expressions, using the source location from Sloc (N). The operands are | |

-- either both Universal_Real, in which case Build_Divide differs from | |

-- Make_Op_Divide only in that the Etype of the resulting node is set (to | |

-- Universal_Real), or they can be integer or fixed-point types. In this | |

-- case the types need not be the same, and Build_Divide chooses a type | |

-- long enough to hold both operands (i.e. the size of the longer of the | |

-- two operand types), and both operands are converted to this type. The | |

-- Etype of the result is also set to this value. The Rounded_Result flag | |

-- of the result in this case is set from the Rounded_Result flag of node | |

-- N. On return, the resulting node has its Etype set. | |

function Build_Double_Divide | |

(N : Node_Id; | |

X, Y, Z : Node_Id) return Node_Id; | |

-- Returns a node corresponding to the value X/(Y*Z) using the source | |

-- location from Sloc (N). The division is rounded if the Rounded_Result | |

-- flag of N is set. The integer types of X, Y, Z may be different. On | |

-- return, the resulting node has its Etype set. | |

procedure Build_Double_Divide_Code | |

(N : Node_Id; | |

X, Y, Z : Node_Id; | |

Qnn, Rnn : out Entity_Id; | |

Code : out List_Id); | |

-- Generates a sequence of code for determining the quotient and remainder | |

-- of the division X/(Y*Z), using the source location from Sloc (N). | |

-- Entities of appropriate types are allocated for the quotient and | |

-- remainder and returned in Qnn and Rnn. The result is rounded if the | |

-- Rounded_Result flag of N is set. The Etype fields of Qnn and Rnn are | |

-- appropriately set on return. | |

function Build_Multiply (N : Node_Id; L, R : Node_Id) return Node_Id; | |

-- Builds an N_Op_Multiply node from the given left and right operand | |

-- expressions, using the source location from Sloc (N). The operands are | |

-- either both Universal_Real, in which case Build_Multiply differs from | |

-- Make_Op_Multiply only in that the Etype of the resulting node is set (to | |

-- Universal_Real), or they can be integer or fixed-point types. In this | |

-- case the types need not be the same, and Build_Multiply chooses a type | |

-- long enough to hold the product and both operands are converted to this | |

-- type. The type of the result is also set to this value. On return, the | |

-- resulting node has its Etype set. | |

function Build_Rem (N : Node_Id; L, R : Node_Id) return Node_Id; | |

-- Builds an N_Op_Rem node from the given left and right operand | |

-- expressions, using the source location from Sloc (N). The operands are | |

-- both integer types, which need not be the same. Build_Rem converts the | |

-- operand with the smaller sized type to match the type of the other | |

-- operand and sets this as the result type. The result is never rounded | |

-- (rem operations cannot be rounded in any case). On return, the resulting | |

-- node has its Etype set. | |

function Build_Scaled_Divide | |

(N : Node_Id; | |

X, Y, Z : Node_Id) return Node_Id; | |

-- Returns a node corresponding to the value X*Y/Z using the source | |

-- location from Sloc (N). The division is rounded if the Rounded_Result | |

-- flag of N is set. The integer types of X, Y, Z may be different. On | |

-- return the resulting node has its Etype set. | |

procedure Build_Scaled_Divide_Code | |

(N : Node_Id; | |

X, Y, Z : Node_Id; | |

Qnn, Rnn : out Entity_Id; | |

Code : out List_Id); | |

-- Generates a sequence of code for determining the quotient and remainder | |

-- of the division X*Y/Z, using the source location from Sloc (N). Entities | |

-- of appropriate types are allocated for the quotient and remainder and | |

-- returned in Qnn and Rrr. The integer types for X, Y, Z may be different. | |

-- The division is rounded if the Rounded_Result flag of N is set. The | |

-- Etype fields of Qnn and Rnn are appropriately set on return. | |

procedure Do_Divide_Fixed_Fixed (N : Node_Id); | |

-- Handles expansion of divide for case of two fixed-point operands | |

-- (neither of them universal), with an integer or fixed-point result. | |

-- N is the N_Op_Divide node to be expanded. | |

procedure Do_Divide_Fixed_Universal (N : Node_Id); | |

-- Handles expansion of divide for case of a fixed-point operand divided | |

-- by a universal real operand, with an integer or fixed-point result. N | |

-- is the N_Op_Divide node to be expanded. | |

procedure Do_Divide_Universal_Fixed (N : Node_Id); | |

-- Handles expansion of divide for case of a universal real operand | |

-- divided by a fixed-point operand, with an integer or fixed-point | |

-- result. N is the N_Op_Divide node to be expanded. | |

procedure Do_Multiply_Fixed_Fixed (N : Node_Id); | |

-- Handles expansion of multiply for case of two fixed-point operands | |

-- (neither of them universal), with an integer or fixed-point result. | |

-- N is the N_Op_Multiply node to be expanded. | |

procedure Do_Multiply_Fixed_Universal (N : Node_Id; Left, Right : Node_Id); | |

-- Handles expansion of multiply for case of a fixed-point operand | |

-- multiplied by a universal real operand, with an integer or fixed- | |

-- point result. N is the N_Op_Multiply node to be expanded, and | |

-- Left, Right are the operands (which may have been switched). | |

procedure Expand_Convert_Fixed_Static (N : Node_Id); | |

-- This routine is called where the node N is a conversion of a literal | |

-- or other static expression of a fixed-point type to some other type. | |

-- In such cases, we simply rewrite the operand as a real literal and | |

-- reanalyze. This avoids problems which would otherwise result from | |

-- attempting to build and fold expressions involving constants. | |

function Fpt_Value (N : Node_Id) return Node_Id; | |

-- Given an operand of fixed-point operation, return an expression that | |

-- represents the corresponding Universal_Real value. The expression | |

-- can be of integer type, floating-point type, or fixed-point type. | |

-- The expression returned is neither analyzed nor resolved. The Etype | |

-- of the result is properly set (to Universal_Real). | |

function Get_Size_For_Value (V : Uint) return Pos; | |

-- Given a non-negative universal integer value, return the size of a small | |

-- signed integer type covering -V .. V, or Pos'Max if no such type exists. | |

function Get_Type_For_Size (Siz : Pos; Force : Boolean) return Entity_Id; | |

-- Return the smallest signed integer type containing at least Siz bits. | |

-- If no such type exists, return Empty if Force is False or the largest | |

-- signed integer type if Force is True. | |

function Integer_Literal | |

(N : Node_Id; | |

V : Uint; | |

Negative : Boolean := False) return Node_Id; | |

-- Given a non-negative universal integer value, build a typed integer | |

-- literal node, using the smallest applicable standard integer type. | |

-- If Negative is true, then a negative literal is built. If V exceeds | |

-- 2**(System_Max_Integer_Size - 1) - 1, the largest value allowed for | |

-- perfect result set scaling factors (see RM G.2.3(22)), then Empty is | |

-- returned. The node N provides the Sloc value for the constructed | |

-- literal. The Etype of the resulting literal is correctly set, and it | |

-- is marked as analyzed. | |

function Real_Literal (N : Node_Id; V : Ureal) return Node_Id; | |

-- Build a real literal node from the given value, the Etype of the | |

-- returned node is set to Universal_Real, since all floating-point | |

-- arithmetic operations that we construct use Universal_Real | |

function Rounded_Result_Set (N : Node_Id) return Boolean; | |

-- Returns True if N is a node that contains the Rounded_Result flag | |

-- and if the flag is true or the target type is an integer type. | |

procedure Set_Result | |

(N : Node_Id; | |

Expr : Node_Id; | |

Rchk : Boolean := False; | |

Trunc : Boolean := False); | |

-- N is the node for the current conversion, division or multiplication | |

-- operation, and Expr is an expression representing the result. Expr may | |

-- be of floating-point or integer type. If the operation result is fixed- | |

-- point, then the value of Expr is in units of small of the result type | |

-- (i.e. small's have already been dealt with). The result of the call is | |

-- to replace N by an appropriate conversion to the result type, dealing | |

-- with rounding for the decimal types case. The node is then analyzed and | |

-- resolved using the result type. If Rchk or Trunc are True, then | |

-- respectively Do_Range_Check and Float_Truncate are set in the | |

-- resulting conversion. | |

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

-- Build_Conversion -- | |

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

function Build_Conversion | |

(N : Node_Id; | |

Typ : Entity_Id; | |

Expr : Node_Id; | |

Rchk : Boolean := False; | |

Trunc : Boolean := False) return Node_Id | |

is | |

Loc : constant Source_Ptr := Sloc (N); | |

Result : Node_Id; | |

Rcheck : Boolean := Rchk; | |

begin | |

-- A special case, if the expression is an integer literal and the | |

-- target type is an integer type, then just retype the integer | |

-- literal to the desired target type. Don't do this if we need | |

-- a range check. | |

if Nkind (Expr) = N_Integer_Literal | |

and then Is_Integer_Type (Typ) | |

and then not Rchk | |

then | |

Result := Expr; | |

-- Cases where we end up with a conversion. Note that we do not use the | |

-- Convert_To abstraction here, since we may be decorating the resulting | |

-- conversion with Rounded_Result and/or Conversion_OK, so we want the | |

-- conversion node present, even if it appears to be redundant. | |

else | |

-- Remove inner conversion if both inner and outer conversions are | |

-- to integer types, since the inner one serves no purpose (except | |

-- perhaps to set rounding, so we preserve the Rounded_Result flag) | |

-- and also preserve the Conversion_OK and Do_Range_Check flags of | |

-- the inner conversion. | |

if Is_Integer_Type (Typ) | |

and then Is_Integer_Type (Etype (Expr)) | |

and then Nkind (Expr) = N_Type_Conversion | |

then | |

Result := | |

Make_Type_Conversion (Loc, | |

Subtype_Mark => New_Occurrence_Of (Typ, Loc), | |

Expression => Expression (Expr)); | |

Set_Rounded_Result (Result, Rounded_Result_Set (Expr)); | |

Set_Conversion_OK (Result, Conversion_OK (Expr)); | |

Rcheck := Rcheck or Do_Range_Check (Expr); | |

-- For all other cases, a simple type conversion will work | |

else | |

Result := | |

Make_Type_Conversion (Loc, | |

Subtype_Mark => New_Occurrence_Of (Typ, Loc), | |

Expression => Expr); | |

Set_Float_Truncate (Result, Trunc); | |

end if; | |

-- Set Conversion_OK if either result or expression type is a | |

-- fixed-point type, since from a semantic point of view, we are | |

-- treating fixed-point values as integers at this stage. | |

if Is_Fixed_Point_Type (Typ) | |

or else Is_Fixed_Point_Type (Etype (Expression (Result))) | |

then | |

Set_Conversion_OK (Result); | |

end if; | |

-- Set Do_Range_Check if either it was requested by the caller, | |

-- or if an eliminated inner conversion had a range check. | |

if Rcheck then | |

Enable_Range_Check (Result); | |

else | |

Set_Do_Range_Check (Result, False); | |

end if; | |

end if; | |

Set_Etype (Result, Typ); | |

return Result; | |

end Build_Conversion; | |

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

-- Build_Divide -- | |

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

function Build_Divide (N : Node_Id; L, R : Node_Id) return Node_Id is | |

Loc : constant Source_Ptr := Sloc (N); | |

Left_Type : constant Entity_Id := Base_Type (Etype (L)); | |

Right_Type : constant Entity_Id := Base_Type (Etype (R)); | |

Left_Size : Int; | |

Right_Size : Int; | |

Result_Type : Entity_Id; | |

Rnode : Node_Id; | |

begin | |

-- Deal with floating-point case first | |

if Is_Floating_Point_Type (Left_Type) then | |

pragma Assert (Left_Type = Universal_Real); | |

pragma Assert (Right_Type = Universal_Real); | |

Rnode := Make_Op_Divide (Loc, L, R); | |

Result_Type := Universal_Real; | |

-- Integer and fixed-point cases | |

else | |

-- An optimization. If the right operand is the literal 1, then we | |

-- can just return the left hand operand. Putting the optimization | |

-- here allows us to omit the check at the call site. | |

if Nkind (R) = N_Integer_Literal and then Intval (R) = 1 then | |

return L; | |

end if; | |

-- Otherwise we need to figure out the correct result type size | |

-- First figure out the effective sizes of the operands. Normally | |

-- the effective size of an operand is the RM_Size of the operand. | |

-- But a special case arises with operands whose size is known at | |

-- compile time. In this case, we can use the actual value of the | |

-- operand to get a size if it would fit in a small signed integer. | |

Left_Size := UI_To_Int (RM_Size (Left_Type)); | |

if Compile_Time_Known_Value (L) then | |

declare | |

Siz : constant Int := | |

Get_Size_For_Value (UI_Abs (Expr_Value (L))); | |

begin | |

if Siz < Left_Size then | |

Left_Size := Siz; | |

end if; | |

end; | |

end if; | |

Right_Size := UI_To_Int (RM_Size (Right_Type)); | |

if Compile_Time_Known_Value (R) then | |

declare | |

Siz : constant Int := | |

Get_Size_For_Value (UI_Abs (Expr_Value (R))); | |

begin | |

if Siz < Right_Size then | |

Right_Size := Siz; | |

end if; | |

end; | |

end if; | |

-- Do the operation using the longer of the two sizes | |

Result_Type := | |

Get_Type_For_Size (Int'Max (Left_Size, Right_Size), Force => True); | |

Rnode := | |

Make_Op_Divide (Loc, | |

Left_Opnd => Build_Conversion (N, Result_Type, L), | |

Right_Opnd => Build_Conversion (N, Result_Type, R)); | |

end if; | |

-- We now have a divide node built with Result_Type set. First | |

-- set Etype of result, as required for all Build_xxx routines | |

Set_Etype (Rnode, Base_Type (Result_Type)); | |

-- The result is rounded if the target of the operation is decimal | |

-- and Rounded_Result is set, or if the target of the operation | |

-- is an integer type, as determined by Rounded_Result_Set. | |

Set_Rounded_Result (Rnode, Rounded_Result_Set (N)); | |

-- One more check. We did the divide operation using the longer of | |

-- the two sizes, which is reasonable. However, in the case where the | |

-- two types have unequal sizes, it is impossible for the result of | |

-- a divide operation to be larger than the dividend, so we can put | |

-- a conversion round the result to keep the evolving operation size | |

-- as small as possible. | |

if not Is_Floating_Point_Type (Left_Type) then | |

Rnode := Build_Conversion (N, Left_Type, Rnode); | |

end if; | |

return Rnode; | |

end Build_Divide; | |

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

-- Build_Double_Divide -- | |

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

function Build_Double_Divide | |

(N : Node_Id; | |

X, Y, Z : Node_Id) return Node_Id | |

is | |

X_Size : constant Nat := UI_To_Int (RM_Size (Etype (X))); | |

Y_Size : constant Nat := UI_To_Int (RM_Size (Etype (Y))); | |

Z_Size : constant Nat := UI_To_Int (RM_Size (Etype (Z))); | |

D_Size : constant Nat := Y_Size + Z_Size; | |

M_Size : constant Nat := Nat'Max (X_Size, Nat'Max (Y_Size, Z_Size)); | |

Expr : Node_Id; | |

begin | |

-- If the denominator fits in Max_Integer_Size bits, we can build the | |

-- operations directly without causing any intermediate overflow. But | |

-- for backward compatibility reasons, we use a 128-bit divide only | |

-- if one of the operands is already larger than 64 bits. | |

if D_Size <= System_Max_Integer_Size | |

and then (D_Size <= 64 or else M_Size > 64) | |

then | |

return Build_Divide (N, X, Build_Multiply (N, Y, Z)); | |

-- Otherwise we use the runtime routine | |

-- [Qnn : Interfaces.Integer_{64|128}; | |

-- Rnn : Interfaces.Integer_{64|128}; | |

-- Double_Divide{64|128} (X, Y, Z, Qnn, Rnn, Round); | |

-- Qnn] | |

else | |

declare | |

Loc : constant Source_Ptr := Sloc (N); | |

Qnn : Entity_Id; | |

Rnn : Entity_Id; | |

Code : List_Id; | |

pragma Warnings (Off, Rnn); | |

begin | |

Build_Double_Divide_Code (N, X, Y, Z, Qnn, Rnn, Code); | |

Insert_Actions (N, Code); | |

Expr := New_Occurrence_Of (Qnn, Loc); | |

-- Set type of result in case used elsewhere (see note at start) | |

Set_Etype (Expr, Etype (Qnn)); | |

-- Set result as analyzed (see note at start on build routines) | |

return Expr; | |

end; | |

end if; | |

end Build_Double_Divide; | |

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

-- Build_Double_Divide_Code -- | |

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

-- If the denominator can be computed in Max_Integer_Size bits, we build | |

-- [Nnn : constant typ := typ (X); | |

-- Dnn : constant typ := typ (Y) * typ (Z) | |

-- Qnn : constant typ := Nnn / Dnn; | |

-- Rnn : constant typ := Nnn rem Dnn; | |

-- If the denominator cannot be computed in Max_Integer_Size bits, we build | |

-- [Qnn : Interfaces.Integer_{64|128}; | |

-- Rnn : Interfaces.Integer_{64|128}; | |

-- Double_Divide{64|128} (X, Y, Z, Qnn, Rnn, Round);] | |

procedure Build_Double_Divide_Code | |

(N : Node_Id; | |

X, Y, Z : Node_Id; | |

Qnn, Rnn : out Entity_Id; | |

Code : out List_Id) | |

is | |

Loc : constant Source_Ptr := Sloc (N); | |

X_Size : constant Nat := UI_To_Int (RM_Size (Etype (X))); | |

Y_Size : constant Nat := UI_To_Int (RM_Size (Etype (Y))); | |

Z_Size : constant Nat := UI_To_Int (RM_Size (Etype (Z))); | |

M_Size : constant Nat := Nat'Max (X_Size, Nat'Max (Y_Size, Z_Size)); | |

QR_Id : RE_Id; | |

QR_Siz : Nat; | |

QR_Typ : Entity_Id; | |

Nnn : Entity_Id; | |

Dnn : Entity_Id; | |

Quo : Node_Id; | |

Rnd : Entity_Id; | |

begin | |

-- Find type that will allow computation of denominator | |

QR_Siz := Nat'Max (X_Size, Y_Size + Z_Size); | |

if QR_Siz <= 16 then | |

QR_Typ := Standard_Integer_16; | |

QR_Id := RE_Null; | |

elsif QR_Siz <= 32 then | |

QR_Typ := Standard_Integer_32; | |

QR_Id := RE_Null; | |

elsif QR_Siz <= 64 then | |

QR_Typ := Standard_Integer_64; | |

QR_Id := RE_Null; | |

-- For backward compatibility reasons, we use a 128-bit divide only | |

-- if one of the operands is already larger than 64 bits. | |

elsif System_Max_Integer_Size < 128 or else M_Size <= 64 then | |

QR_Typ := RTE (RE_Integer_64); | |

QR_Id := RE_Double_Divide64; | |

elsif QR_Siz <= 128 then | |

QR_Typ := Standard_Integer_128; | |

QR_Id := RE_Null; | |

else | |

QR_Typ := RTE (RE_Integer_128); | |

QR_Id := RE_Double_Divide128; | |

end if; | |

-- Define quotient and remainder, and set their Etypes, so | |

-- that they can be picked up by Build_xxx routines. | |

Qnn := Make_Temporary (Loc, 'S'); | |

Rnn := Make_Temporary (Loc, 'R'); | |

Set_Etype (Qnn, QR_Typ); | |

Set_Etype (Rnn, QR_Typ); | |

-- Case where we can compute the denominator in Max_Integer_Size bits | |

if QR_Id = RE_Null then | |

-- Create temporaries for numerator and denominator and set Etypes, | |

-- so that New_Occurrence_Of picks them up for Build_xxx calls. | |

Nnn := Make_Temporary (Loc, 'N'); | |

Dnn := Make_Temporary (Loc, 'D'); | |

Set_Etype (Nnn, QR_Typ); | |

Set_Etype (Dnn, QR_Typ); | |

Code := New_List ( | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Nnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => Build_Conversion (N, QR_Typ, X)), | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Dnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => Build_Multiply (N, Y, Z))); | |

Quo := | |

Build_Divide (N, | |

New_Occurrence_Of (Nnn, Loc), | |

New_Occurrence_Of (Dnn, Loc)); | |

Set_Rounded_Result (Quo, Rounded_Result_Set (N)); | |

Append_To (Code, | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Qnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => Quo)); | |

Append_To (Code, | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Rnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => | |

Build_Rem (N, | |

New_Occurrence_Of (Nnn, Loc), | |

New_Occurrence_Of (Dnn, Loc)))); | |

-- Case where denominator does not fit in Max_Integer_Size bits, we have | |

-- to call the runtime routine to compute the quotient and remainder. | |

else | |

Rnd := Boolean_Literals (Rounded_Result_Set (N)); | |

Code := New_List ( | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Qnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc)), | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Rnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc)), | |

Make_Procedure_Call_Statement (Loc, | |

Name => New_Occurrence_Of (RTE (QR_Id), Loc), | |

Parameter_Associations => New_List ( | |

Build_Conversion (N, QR_Typ, X), | |

Build_Conversion (N, QR_Typ, Y), | |

Build_Conversion (N, QR_Typ, Z), | |

New_Occurrence_Of (Qnn, Loc), | |

New_Occurrence_Of (Rnn, Loc), | |

New_Occurrence_Of (Rnd, Loc)))); | |

end if; | |

end Build_Double_Divide_Code; | |

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

-- Build_Multiply -- | |

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

function Build_Multiply (N : Node_Id; L, R : Node_Id) return Node_Id is | |

Loc : constant Source_Ptr := Sloc (N); | |

Left_Type : constant Entity_Id := Etype (L); | |

Right_Type : constant Entity_Id := Etype (R); | |

Left_Size : Int; | |

Right_Size : Int; | |

Result_Type : Entity_Id; | |

Rnode : Node_Id; | |

begin | |

-- Deal with floating-point case first | |

if Is_Floating_Point_Type (Left_Type) then | |

pragma Assert (Left_Type = Universal_Real); | |

pragma Assert (Right_Type = Universal_Real); | |

Result_Type := Universal_Real; | |

Rnode := Make_Op_Multiply (Loc, L, R); | |

-- Integer and fixed-point cases | |

else | |

-- An optimization. If the right operand is the literal 1, then we | |

-- can just return the left hand operand. Putting the optimization | |

-- here allows us to omit the check at the call site. Similarly, if | |

-- the left operand is the integer 1 we can return the right operand. | |

if Nkind (R) = N_Integer_Literal and then Intval (R) = 1 then | |

return L; | |

elsif Nkind (L) = N_Integer_Literal and then Intval (L) = 1 then | |

return R; | |

end if; | |

-- Otherwise we need to figure out the correct result type size | |

-- First figure out the effective sizes of the operands. Normally | |

-- the effective size of an operand is the RM_Size of the operand. | |

-- But a special case arises with operands whose size is known at | |

-- compile time. In this case, we can use the actual value of the | |

-- operand to get a size if it would fit in a small signed integer. | |

Left_Size := UI_To_Int (RM_Size (Left_Type)); | |

if Compile_Time_Known_Value (L) then | |

declare | |

Siz : constant Int := | |

Get_Size_For_Value (UI_Abs (Expr_Value (L))); | |

begin | |

if Siz < Left_Size then | |

Left_Size := Siz; | |

end if; | |

end; | |

end if; | |

Right_Size := UI_To_Int (RM_Size (Right_Type)); | |

if Compile_Time_Known_Value (R) then | |

declare | |

Siz : constant Int := | |

Get_Size_For_Value (UI_Abs (Expr_Value (R))); | |

begin | |

if Siz < Right_Size then | |

Right_Size := Siz; | |

end if; | |

end; | |

end if; | |

-- Now the result size must be at least the sum of the two sizes, | |

-- to accommodate all possible results. | |

Result_Type := | |

Get_Type_For_Size (Left_Size + Right_Size, Force => True); | |

Rnode := | |

Make_Op_Multiply (Loc, | |

Left_Opnd => Build_Conversion (N, Result_Type, L), | |

Right_Opnd => Build_Conversion (N, Result_Type, R)); | |

end if; | |

-- We now have a multiply node built with Result_Type set. First | |

-- set Etype of result, as required for all Build_xxx routines | |

Set_Etype (Rnode, Base_Type (Result_Type)); | |

return Rnode; | |

end Build_Multiply; | |

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

-- Build_Rem -- | |

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

function Build_Rem (N : Node_Id; L, R : Node_Id) return Node_Id is | |

Loc : constant Source_Ptr := Sloc (N); | |

Left_Type : constant Entity_Id := Etype (L); | |

Right_Type : constant Entity_Id := Etype (R); | |

Result_Type : Entity_Id; | |

Rnode : Node_Id; | |

begin | |

if Left_Type = Right_Type then | |

Result_Type := Left_Type; | |

Rnode := | |

Make_Op_Rem (Loc, | |

Left_Opnd => L, | |

Right_Opnd => R); | |

-- If left size is larger, we do the remainder operation using the | |

-- size of the left type (i.e. the larger of the two integer types). | |

elsif Esize (Left_Type) >= Esize (Right_Type) then | |

Result_Type := Left_Type; | |

Rnode := | |

Make_Op_Rem (Loc, | |

Left_Opnd => L, | |

Right_Opnd => Build_Conversion (N, Left_Type, R)); | |

-- Similarly, if the right size is larger, we do the remainder | |

-- operation using the right type. | |

else | |

Result_Type := Right_Type; | |

Rnode := | |

Make_Op_Rem (Loc, | |

Left_Opnd => Build_Conversion (N, Right_Type, L), | |

Right_Opnd => R); | |

end if; | |

-- We now have an N_Op_Rem node built with Result_Type set. First | |

-- set Etype of result, as required for all Build_xxx routines | |

Set_Etype (Rnode, Base_Type (Result_Type)); | |

-- One more check. We did the rem operation using the larger of the | |

-- two types, which is reasonable. However, in the case where the | |

-- two types have unequal sizes, it is impossible for the result of | |

-- a remainder operation to be larger than the smaller of the two | |

-- types, so we can put a conversion round the result to keep the | |

-- evolving operation size as small as possible. | |

if Esize (Left_Type) >= Esize (Right_Type) then | |

Rnode := Build_Conversion (N, Right_Type, Rnode); | |

elsif Esize (Right_Type) >= Esize (Left_Type) then | |

Rnode := Build_Conversion (N, Left_Type, Rnode); | |

end if; | |

return Rnode; | |

end Build_Rem; | |

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

-- Build_Scaled_Divide -- | |

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

function Build_Scaled_Divide | |

(N : Node_Id; | |

X, Y, Z : Node_Id) return Node_Id | |

is | |

X_Size : constant Nat := UI_To_Int (RM_Size (Etype (X))); | |

Y_Size : constant Nat := UI_To_Int (RM_Size (Etype (Y))); | |

Z_Size : constant Nat := UI_To_Int (RM_Size (Etype (Z))); | |

N_Size : constant Nat := X_Size + Y_Size; | |

M_Size : constant Nat := Nat'Max (X_Size, Nat'Max (Y_Size, Z_Size)); | |

Expr : Node_Id; | |

begin | |

-- If the numerator fits in Max_Integer_Size bits, we can build the | |

-- operations directly without causing any intermediate overflow. But | |

-- for backward compatibility reasons, we use a 128-bit divide only | |

-- if one of the operands is already larger than 64 bits. | |

if N_Size <= System_Max_Integer_Size | |

and then (N_Size <= 64 or else M_Size > 64) | |

then | |

return Build_Divide (N, Build_Multiply (N, X, Y), Z); | |

-- Otherwise we use the runtime routine | |

-- [Qnn : Integer_{64|128}, | |

-- Rnn : Integer_{64|128}; | |

-- Scaled_Divide{64|128} (X, Y, Z, Qnn, Rnn, Round); | |

-- Qnn] | |

else | |

declare | |

Loc : constant Source_Ptr := Sloc (N); | |

Qnn : Entity_Id; | |

Rnn : Entity_Id; | |

Code : List_Id; | |

pragma Warnings (Off, Rnn); | |

begin | |

Build_Scaled_Divide_Code (N, X, Y, Z, Qnn, Rnn, Code); | |

Insert_Actions (N, Code); | |

Expr := New_Occurrence_Of (Qnn, Loc); | |

-- Set type of result in case used elsewhere (see note at start) | |

Set_Etype (Expr, Etype (Qnn)); | |

return Expr; | |

end; | |

end if; | |

end Build_Scaled_Divide; | |

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

-- Build_Scaled_Divide_Code -- | |

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

-- If the numerator can be computed in Max_Integer_Size bits, we build | |

-- [Nnn : constant typ := typ (X) * typ (Y); | |

-- Dnn : constant typ := typ (Z) | |

-- Qnn : constant typ := Nnn / Dnn; | |

-- Rnn : constant typ := Nnn rem Dnn; | |

-- If the numerator cannot be computed in Max_Integer_Size bits, we build | |

-- [Qnn : Interfaces.Integer_{64|128}; | |

-- Rnn : Interfaces.Integer_{64|128}; | |

-- Scaled_Divide_{64|128} (X, Y, Z, Qnn, Rnn, Round);] | |

procedure Build_Scaled_Divide_Code | |

(N : Node_Id; | |

X, Y, Z : Node_Id; | |

Qnn, Rnn : out Entity_Id; | |

Code : out List_Id) | |

is | |

Loc : constant Source_Ptr := Sloc (N); | |

X_Size : constant Nat := UI_To_Int (RM_Size (Etype (X))); | |

Y_Size : constant Nat := UI_To_Int (RM_Size (Etype (Y))); | |

Z_Size : constant Nat := UI_To_Int (RM_Size (Etype (Z))); | |

M_Size : constant Nat := Nat'Max (X_Size, Nat'Max (Y_Size, Z_Size)); | |

QR_Id : RE_Id; | |

QR_Siz : Nat; | |

QR_Typ : Entity_Id; | |

Nnn : Entity_Id; | |

Dnn : Entity_Id; | |

Quo : Node_Id; | |

Rnd : Entity_Id; | |

begin | |

-- Find type that will allow computation of numerator | |

QR_Siz := Nat'Max (X_Size + Y_Size, Z_Size); | |

if QR_Siz <= 16 then | |

QR_Typ := Standard_Integer_16; | |

QR_Id := RE_Null; | |

elsif QR_Siz <= 32 then | |

QR_Typ := Standard_Integer_32; | |

QR_Id := RE_Null; | |

elsif QR_Siz <= 64 then | |

QR_Typ := Standard_Integer_64; | |

QR_Id := RE_Null; | |

-- For backward compatibility reasons, we use a 128-bit divide only | |

-- if one of the operands is already larger than 64 bits. | |

elsif System_Max_Integer_Size < 128 or else M_Size <= 64 then | |

QR_Typ := RTE (RE_Integer_64); | |

QR_Id := RE_Scaled_Divide64; | |

elsif QR_Siz <= 128 then | |

QR_Typ := Standard_Integer_128; | |

QR_Id := RE_Null; | |

else | |

QR_Typ := RTE (RE_Integer_128); | |

QR_Id := RE_Scaled_Divide128; | |

end if; | |

-- Define quotient and remainder, and set their Etypes, so | |

-- that they can be picked up by Build_xxx routines. | |

Qnn := Make_Temporary (Loc, 'S'); | |

Rnn := Make_Temporary (Loc, 'R'); | |

Set_Etype (Qnn, QR_Typ); | |

Set_Etype (Rnn, QR_Typ); | |

-- Case where we can compute the numerator in Max_Integer_Size bits | |

if QR_Id = RE_Null then | |

Nnn := Make_Temporary (Loc, 'N'); | |

Dnn := Make_Temporary (Loc, 'D'); | |

-- Set Etypes, so that they can be picked up by New_Occurrence_Of | |

Set_Etype (Nnn, QR_Typ); | |

Set_Etype (Dnn, QR_Typ); | |

Code := New_List ( | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Nnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => Build_Multiply (N, X, Y)), | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Dnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => Build_Conversion (N, QR_Typ, Z))); | |

Quo := | |

Build_Divide (N, | |

New_Occurrence_Of (Nnn, Loc), | |

New_Occurrence_Of (Dnn, Loc)); | |

Append_To (Code, | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Qnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => Quo)); | |

Append_To (Code, | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Rnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc), | |

Constant_Present => True, | |

Expression => | |

Build_Rem (N, | |

New_Occurrence_Of (Nnn, Loc), | |

New_Occurrence_Of (Dnn, Loc)))); | |

-- Case where numerator does not fit in Max_Integer_Size bits, we have | |

-- to call the runtime routine to compute the quotient and remainder. | |

else | |

Rnd := Boolean_Literals (Rounded_Result_Set (N)); | |

Code := New_List ( | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Qnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc)), | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Rnn, | |

Object_Definition => New_Occurrence_Of (QR_Typ, Loc)), | |

Make_Procedure_Call_Statement (Loc, | |

Name => New_Occurrence_Of (RTE (QR_Id), Loc), | |

Parameter_Associations => New_List ( | |

Build_Conversion (N, QR_Typ, X), | |

Build_Conversion (N, QR_Typ, Y), | |

Build_Conversion (N, QR_Typ, Z), | |

New_Occurrence_Of (Qnn, Loc), | |

New_Occurrence_Of (Rnn, Loc), | |

New_Occurrence_Of (Rnd, Loc)))); | |

end if; | |

-- Set type of result, for use in caller | |

Set_Etype (Qnn, QR_Typ); | |

end Build_Scaled_Divide_Code; | |

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

-- Do_Divide_Fixed_Fixed -- | |

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

-- We have: | |

-- (Result_Value * Result_Small) = | |

-- (Left_Value * Left_Small) / (Right_Value * Right_Small) | |

-- Result_Value = (Left_Value / Right_Value) * | |

-- (Left_Small / (Right_Small * Result_Small)); | |

-- we can do the operation in integer arithmetic if this fraction is an | |

-- integer or the reciprocal of an integer, as detailed in (RM G.2.3(21)). | |

-- Otherwise the result is in the close result set and our approach is to | |

-- use floating-point to compute this close result. | |

procedure Do_Divide_Fixed_Fixed (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

Left_Type : constant Entity_Id := Etype (Left); | |

Right_Type : constant Entity_Id := Etype (Right); | |

Result_Type : constant Entity_Id := Etype (N); | |

Right_Small : constant Ureal := Small_Value (Right_Type); | |

Left_Small : constant Ureal := Small_Value (Left_Type); | |

Result_Small : Ureal; | |

Frac : Ureal; | |

Frac_Num : Uint; | |

Frac_Den : Uint; | |

Lit_Int : Node_Id; | |

begin | |

-- Rounding is required if the result is integral | |

if Is_Integer_Type (Result_Type) then | |

Set_Rounded_Result (N); | |

end if; | |

-- Get result small. If the result is an integer, treat it as though | |

-- it had a small of 1.0, all other processing is identical. | |

if Is_Integer_Type (Result_Type) then | |

Result_Small := Ureal_1; | |

else | |

Result_Small := Small_Value (Result_Type); | |

end if; | |

-- Get small ratio | |

Frac := Left_Small / (Right_Small * Result_Small); | |

Frac_Num := Norm_Num (Frac); | |

Frac_Den := Norm_Den (Frac); | |

-- If the fraction is an integer, then we get the result by multiplying | |

-- the left operand by the integer, and then dividing by the right | |

-- operand (the order is important, if we did the divide first, we | |

-- would lose precision). | |

if Frac_Den = 1 then | |

Lit_Int := Integer_Literal (N, Frac_Num); -- always positive | |

if Present (Lit_Int) then | |

Set_Result (N, Build_Scaled_Divide (N, Left, Lit_Int, Right)); | |

return; | |

end if; | |

-- If the fraction is the reciprocal of an integer, then we get the | |

-- result by first multiplying the divisor by the integer, and then | |

-- doing the division with the adjusted divisor. | |

-- Note: this is much better than doing two divisions: multiplications | |

-- are much faster than divisions (and certainly faster than rounded | |

-- divisions), and we don't get inaccuracies from double rounding. | |

elsif Frac_Num = 1 then | |

Lit_Int := Integer_Literal (N, Frac_Den); -- always positive | |

if Present (Lit_Int) then | |

Set_Result (N, Build_Double_Divide (N, Left, Right, Lit_Int)); | |

return; | |

end if; | |

end if; | |

-- If we fall through, we use floating-point to compute the result | |

Set_Result (N, | |

Build_Multiply (N, | |

Build_Divide (N, Fpt_Value (Left), Fpt_Value (Right)), | |

Real_Literal (N, Frac))); | |

end Do_Divide_Fixed_Fixed; | |

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

-- Do_Divide_Fixed_Universal -- | |

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

-- We have: | |

-- (Result_Value * Result_Small) = (Left_Value * Left_Small) / Lit_Value; | |

-- Result_Value = Left_Value * Left_Small /(Lit_Value * Result_Small); | |

-- The result is required to be in the perfect result set if the literal | |

-- can be factored so that the resulting small ratio is an integer or the | |

-- reciprocal of an integer (RM G.2.3(21-22)). We now give a detailed | |

-- analysis of these RM requirements: | |

-- We must factor the literal, finding an integer K: | |

-- Lit_Value = K * Right_Small | |

-- Right_Small = Lit_Value / K | |

-- such that the small ratio: | |

-- Left_Small | |

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

-- (Lit_Value / K) * Result_Small | |

-- Left_Small | |

-- = ------------------------ * K | |

-- Lit_Value * Result_Small | |

-- is an integer or the reciprocal of an integer, and for | |

-- implementation efficiency we need the smallest such K. | |

-- First we reduce the left fraction to lowest terms | |

-- If numerator = 1, then for K = 1, the small ratio is the reciprocal | |

-- of an integer, and this is clearly the minimum K case, so set K = 1, | |

-- Right_Small = Lit_Value. | |

-- If numerator > 1, then set K to the denominator of the fraction so | |

-- that the resulting small ratio is an integer (the numerator value). | |

procedure Do_Divide_Fixed_Universal (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

Left_Type : constant Entity_Id := Etype (Left); | |

Result_Type : constant Entity_Id := Etype (N); | |

Left_Small : constant Ureal := Small_Value (Left_Type); | |

Lit_Value : constant Ureal := Realval (Right); | |

Result_Small : Ureal; | |

Frac : Ureal; | |

Frac_Num : Uint; | |

Frac_Den : Uint; | |

Lit_K : Node_Id; | |

Lit_Int : Node_Id; | |

begin | |

-- Get result small. If the result is an integer, treat it as though | |

-- it had a small of 1.0, all other processing is identical. | |

if Is_Integer_Type (Result_Type) then | |

Result_Small := Ureal_1; | |

else | |

Result_Small := Small_Value (Result_Type); | |

end if; | |

-- Determine if literal can be rewritten successfully | |

Frac := Left_Small / (Lit_Value * Result_Small); | |

Frac_Num := Norm_Num (Frac); | |

Frac_Den := Norm_Den (Frac); | |

-- Case where fraction is the reciprocal of an integer (K = 1, integer | |

-- = denominator). If this integer is not too large, this is the case | |

-- where the result can be obtained by dividing by this integer value. | |

if Frac_Num = 1 then | |

Lit_Int := Integer_Literal (N, Frac_Den, UR_Is_Negative (Frac)); | |

if Present (Lit_Int) then | |

Set_Result (N, Build_Divide (N, Left, Lit_Int)); | |

return; | |

end if; | |

-- Case where we choose K to make fraction an integer (K = denominator | |

-- of fraction, integer = numerator of fraction). If both K and the | |

-- numerator are small enough, this is the case where the result can | |

-- be obtained by first multiplying by the integer value and then | |

-- dividing by K (the order is important, if we divided first, we | |

-- would lose precision). | |

else | |

Lit_Int := Integer_Literal (N, Frac_Num, UR_Is_Negative (Frac)); | |

Lit_K := Integer_Literal (N, Frac_Den, False); | |

if Present (Lit_Int) and then Present (Lit_K) then | |

Set_Result (N, Build_Scaled_Divide (N, Left, Lit_Int, Lit_K)); | |

return; | |

end if; | |

end if; | |

-- Fall through if the literal cannot be successfully rewritten, or if | |

-- the small ratio is out of range of integer arithmetic. In the former | |

-- case it is fine to use floating-point to get the close result set, | |

-- and in the latter case, it means that the result is zero or raises | |

-- constraint error, and we can do that accurately in floating-point. | |

-- If we end up using floating-point, then we take the right integer | |

-- to be one, and its small to be the value of the original right real | |

-- literal. That way, we need only one floating-point multiplication. | |

Set_Result (N, | |

Build_Multiply (N, Fpt_Value (Left), Real_Literal (N, Frac))); | |

end Do_Divide_Fixed_Universal; | |

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

-- Do_Divide_Universal_Fixed -- | |

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

-- We have: | |

-- (Result_Value * Result_Small) = | |

-- Lit_Value / (Right_Value * Right_Small) | |

-- Result_Value = | |

-- (Lit_Value / (Right_Small * Result_Small)) / Right_Value | |

-- The result is required to be in the perfect result set if the literal | |

-- can be factored so that the resulting small ratio is an integer or the | |

-- reciprocal of an integer (RM G.2.3(21-22)). We now give a detailed | |

-- analysis of these RM requirements: | |

-- We must factor the literal, finding an integer K: | |

-- Lit_Value = K * Left_Small | |

-- Left_Small = Lit_Value / K | |

-- such that the small ratio: | |

-- (Lit_Value / K) | |

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

-- Right_Small * Result_Small | |

-- Lit_Value 1 | |

-- = -------------------------- * - | |

-- Right_Small * Result_Small K | |

-- is an integer or the reciprocal of an integer, and for | |

-- implementation efficiency we need the smallest such K. | |

-- First we reduce the left fraction to lowest terms | |

-- If denominator = 1, then for K = 1, the small ratio is an integer | |

-- (the numerator) and this is clearly the minimum K case, so set K = 1, | |

-- and Left_Small = Lit_Value. | |

-- If denominator > 1, then set K to the numerator of the fraction so | |

-- that the resulting small ratio is the reciprocal of an integer (the | |

-- numerator value). | |

procedure Do_Divide_Universal_Fixed (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

Right_Type : constant Entity_Id := Etype (Right); | |

Result_Type : constant Entity_Id := Etype (N); | |

Right_Small : constant Ureal := Small_Value (Right_Type); | |

Lit_Value : constant Ureal := Realval (Left); | |

Result_Small : Ureal; | |

Frac : Ureal; | |

Frac_Num : Uint; | |

Frac_Den : Uint; | |

Lit_K : Node_Id; | |

Lit_Int : Node_Id; | |

begin | |

-- Get result small. If the result is an integer, treat it as though | |

-- it had a small of 1.0, all other processing is identical. | |

if Is_Integer_Type (Result_Type) then | |

Result_Small := Ureal_1; | |

else | |

Result_Small := Small_Value (Result_Type); | |

end if; | |

-- Determine if literal can be rewritten successfully | |

Frac := Lit_Value / (Right_Small * Result_Small); | |

Frac_Num := Norm_Num (Frac); | |

Frac_Den := Norm_Den (Frac); | |

-- Case where fraction is an integer (K = 1, integer = numerator). If | |

-- this integer is not too large, this is the case where the result | |

-- can be obtained by dividing this integer by the right operand. | |

if Frac_Den = 1 then | |

Lit_Int := Integer_Literal (N, Frac_Num, UR_Is_Negative (Frac)); | |

if Present (Lit_Int) then | |

Set_Result (N, Build_Divide (N, Lit_Int, Right)); | |

return; | |

end if; | |

-- Case where we choose K to make the fraction the reciprocal of an | |

-- integer (K = numerator of fraction, integer = numerator of fraction). | |

-- If both K and the integer are small enough, this is the case where | |

-- the result can be obtained by multiplying the right operand by K | |

-- and then dividing by the integer value. The order of the operations | |

-- is important (if we divided first, we would lose precision). | |

else | |

Lit_Int := Integer_Literal (N, Frac_Den, UR_Is_Negative (Frac)); | |

Lit_K := Integer_Literal (N, Frac_Num, False); | |

if Present (Lit_Int) and then Present (Lit_K) then | |

Set_Result (N, Build_Double_Divide (N, Lit_K, Right, Lit_Int)); | |

return; | |

end if; | |

end if; | |

-- Fall through if the literal cannot be successfully rewritten, or if | |

-- the small ratio is out of range of integer arithmetic. In the former | |

-- case it is fine to use floating-point to get the close result set, | |

-- and in the latter case, it means that the result is zero or raises | |

-- constraint error, and we can do that accurately in floating-point. | |

-- If we end up using floating-point, then we take the right integer | |

-- to be one, and its small to be the value of the original right real | |

-- literal. That way, we need only one floating-point division. | |

Set_Result (N, | |

Build_Divide (N, Real_Literal (N, Frac), Fpt_Value (Right))); | |

end Do_Divide_Universal_Fixed; | |

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

-- Do_Multiply_Fixed_Fixed -- | |

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

-- We have: | |

-- (Result_Value * Result_Small) = | |

-- (Left_Value * Left_Small) * (Right_Value * Right_Small) | |

-- Result_Value = (Left_Value * Right_Value) * | |

-- (Left_Small * Right_Small) / Result_Small; | |

-- we can do the operation in integer arithmetic if this fraction is an | |

-- integer or the reciprocal of an integer, as detailed in (RM G.2.3(21)). | |

-- Otherwise the result is in the close result set and our approach is to | |

-- use floating-point to compute this close result. | |

procedure Do_Multiply_Fixed_Fixed (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

Left_Type : constant Entity_Id := Etype (Left); | |

Right_Type : constant Entity_Id := Etype (Right); | |

Result_Type : constant Entity_Id := Etype (N); | |

Right_Small : constant Ureal := Small_Value (Right_Type); | |

Left_Small : constant Ureal := Small_Value (Left_Type); | |

Result_Small : Ureal; | |

Frac : Ureal; | |

Frac_Num : Uint; | |

Frac_Den : Uint; | |

Lit_Int : Node_Id; | |

begin | |

-- Get result small. If the result is an integer, treat it as though | |

-- it had a small of 1.0, all other processing is identical. | |

if Is_Integer_Type (Result_Type) then | |

Result_Small := Ureal_1; | |

else | |

Result_Small := Small_Value (Result_Type); | |

end if; | |

-- Get small ratio | |

Frac := (Left_Small * Right_Small) / Result_Small; | |

Frac_Num := Norm_Num (Frac); | |

Frac_Den := Norm_Den (Frac); | |

-- If the fraction is an integer, then we get the result by multiplying | |

-- the operands, and then multiplying the result by the integer value. | |

if Frac_Den = 1 then | |

Lit_Int := Integer_Literal (N, Frac_Num); -- always positive | |

if Present (Lit_Int) then | |

Set_Result (N, | |

Build_Multiply (N, Build_Multiply (N, Left, Right), Lit_Int)); | |

return; | |

end if; | |

-- If the fraction is the reciprocal of an integer, then we get the | |

-- result by multiplying the operands, and then dividing the result by | |

-- the integer value. The order of the operations is important, if we | |

-- divided first, we would lose precision. | |

elsif Frac_Num = 1 then | |

Lit_Int := Integer_Literal (N, Frac_Den); -- always positive | |

if Present (Lit_Int) then | |

Set_Result (N, Build_Scaled_Divide (N, Left, Right, Lit_Int)); | |

return; | |

end if; | |

end if; | |

-- If we fall through, we use floating-point to compute the result | |

Set_Result (N, | |

Build_Multiply (N, | |

Build_Multiply (N, Fpt_Value (Left), Fpt_Value (Right)), | |

Real_Literal (N, Frac))); | |

end Do_Multiply_Fixed_Fixed; | |

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

-- Do_Multiply_Fixed_Universal -- | |

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

-- We have: | |

-- (Result_Value * Result_Small) = (Left_Value * Left_Small) * Lit_Value; | |

-- Result_Value = Left_Value * (Left_Small * Lit_Value) / Result_Small; | |

-- The result is required to be in the perfect result set if the literal | |

-- can be factored so that the resulting small ratio is an integer or the | |

-- reciprocal of an integer (RM G.2.3(21-22)). We now give a detailed | |

-- analysis of these RM requirements: | |

-- We must factor the literal, finding an integer K: | |

-- Lit_Value = K * Right_Small | |

-- Right_Small = Lit_Value / K | |

-- such that the small ratio: | |

-- Left_Small * (Lit_Value / K) | |

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

-- Result_Small | |

-- Left_Small * Lit_Value 1 | |

-- = ---------------------- * - | |

-- Result_Small K | |

-- is an integer or the reciprocal of an integer, and for | |

-- implementation efficiency we need the smallest such K. | |

-- First we reduce the left fraction to lowest terms | |

-- If denominator = 1, then for K = 1, the small ratio is an integer, and | |

-- this is clearly the minimum K case, so set | |

-- K = 1, Right_Small = Lit_Value | |

-- If denominator > 1, then set K to the numerator of the fraction, so | |

-- that the resulting small ratio is the reciprocal of the integer (the | |

-- denominator value). | |

procedure Do_Multiply_Fixed_Universal | |

(N : Node_Id; | |

Left, Right : Node_Id) | |

is | |

Left_Type : constant Entity_Id := Etype (Left); | |

Result_Type : constant Entity_Id := Etype (N); | |

Left_Small : constant Ureal := Small_Value (Left_Type); | |

Lit_Value : constant Ureal := Realval (Right); | |

Result_Small : Ureal; | |

Frac : Ureal; | |

Frac_Num : Uint; | |

Frac_Den : Uint; | |

Lit_K : Node_Id; | |

Lit_Int : Node_Id; | |

begin | |

-- Get result small. If the result is an integer, treat it as though | |

-- it had a small of 1.0, all other processing is identical. | |

if Is_Integer_Type (Result_Type) then | |

Result_Small := Ureal_1; | |

else | |

Result_Small := Small_Value (Result_Type); | |

end if; | |

-- Determine if literal can be rewritten successfully | |

Frac := (Left_Small * Lit_Value) / Result_Small; | |

Frac_Num := Norm_Num (Frac); | |

Frac_Den := Norm_Den (Frac); | |

-- Case where fraction is an integer (K = 1, integer = numerator). If | |

-- this integer is not too large, this is the case where the result can | |

-- be obtained by multiplying by this integer value. | |

if Frac_Den = 1 then | |

Lit_Int := Integer_Literal (N, Frac_Num, UR_Is_Negative (Frac)); | |

if Present (Lit_Int) then | |

Set_Result (N, Build_Multiply (N, Left, Lit_Int)); | |

return; | |

end if; | |

-- Case where we choose K to make fraction the reciprocal of an integer | |

-- (K = numerator of fraction, integer = denominator of fraction). If | |

-- both K and the denominator are small enough, this is the case where | |

-- the result can be obtained by first multiplying by K, and then | |

-- dividing by the integer value. | |

else | |

Lit_Int := Integer_Literal (N, Frac_Den, UR_Is_Negative (Frac)); | |

Lit_K := Integer_Literal (N, Frac_Num, False); | |

if Present (Lit_Int) and then Present (Lit_K) then | |

Set_Result (N, Build_Scaled_Divide (N, Left, Lit_K, Lit_Int)); | |

return; | |

end if; | |

end if; | |

-- Fall through if the literal cannot be successfully rewritten, or if | |

-- the small ratio is out of range of integer arithmetic. In the former | |

-- case it is fine to use floating-point to get the close result set, | |

-- and in the latter case, it means that the result is zero or raises | |

-- constraint error, and we can do that accurately in floating-point. | |

-- If we end up using floating-point, then we take the right integer | |

-- to be one, and its small to be the value of the original right real | |

-- literal. That way, we need only one floating-point multiplication. | |

Set_Result (N, | |

Build_Multiply (N, Fpt_Value (Left), Real_Literal (N, Frac))); | |

end Do_Multiply_Fixed_Universal; | |

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

-- Expand_Convert_Fixed_Static -- | |

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

procedure Expand_Convert_Fixed_Static (N : Node_Id) is | |

begin | |

Rewrite (N, | |

Convert_To (Etype (N), | |

Make_Real_Literal (Sloc (N), Expr_Value_R (Expression (N))))); | |

Analyze_And_Resolve (N); | |

end Expand_Convert_Fixed_Static; | |

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

-- Expand_Convert_Fixed_To_Fixed -- | |

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

-- We have: | |

-- Result_Value * Result_Small = Source_Value * Source_Small | |

-- Result_Value = Source_Value * (Source_Small / Result_Small) | |

-- If the small ratio (Source_Small / Result_Small) is a sufficiently small | |

-- integer, then the perfect result set is obtained by a single integer | |

-- multiplication. | |

-- If the small ratio is the reciprocal of a sufficiently small integer, | |

-- then the perfect result set is obtained by a single integer division. | |

-- If the numerator and denominator of the small ratio are sufficiently | |

-- small integers, then the perfect result set is obtained by a scaled | |

-- divide operation. | |

-- In other cases, we obtain the close result set by calculating the | |

-- result in floating-point. | |

procedure Expand_Convert_Fixed_To_Fixed (N : Node_Id) is | |

Rng_Check : constant Boolean := Do_Range_Check (N); | |

Expr : constant Node_Id := Expression (N); | |

Result_Type : constant Entity_Id := Etype (N); | |

Source_Type : constant Entity_Id := Etype (Expr); | |

Small_Ratio : Ureal; | |

Ratio_Num : Uint; | |

Ratio_Den : Uint; | |

Lit_Num : Node_Id; | |

Lit_Den : Node_Id; | |

begin | |

if Is_OK_Static_Expression (Expr) then | |

Expand_Convert_Fixed_Static (N); | |

return; | |

end if; | |

Small_Ratio := Small_Value (Source_Type) / Small_Value (Result_Type); | |

Ratio_Num := Norm_Num (Small_Ratio); | |

Ratio_Den := Norm_Den (Small_Ratio); | |

if Ratio_Den = 1 then | |

if Ratio_Num = 1 then | |

Set_Result (N, Expr); | |

return; | |

else | |

Lit_Num := Integer_Literal (N, Ratio_Num); | |

if Present (Lit_Num) then | |

Set_Result (N, Build_Multiply (N, Expr, Lit_Num)); | |

return; | |

end if; | |

end if; | |

elsif Ratio_Num = 1 then | |

Lit_Den := Integer_Literal (N, Ratio_Den); | |

if Present (Lit_Den) then | |

Set_Result (N, Build_Divide (N, Expr, Lit_Den), Rng_Check); | |

return; | |

end if; | |

else | |

Lit_Num := Integer_Literal (N, Ratio_Num); | |

Lit_Den := Integer_Literal (N, Ratio_Den); | |

if Present (Lit_Num) and then Present (Lit_Den) then | |

Set_Result | |

(N, Build_Scaled_Divide (N, Expr, Lit_Num, Lit_Den), Rng_Check); | |

return; | |

end if; | |

end if; | |

-- Fall through to use floating-point for the close result set case, | |

-- as a result of the numerator or denominator of the small ratio not | |

-- being a sufficiently small integer. | |

Set_Result (N, | |

Build_Multiply (N, | |

Fpt_Value (Expr), | |

Real_Literal (N, Small_Ratio)), | |

Rng_Check); | |

end Expand_Convert_Fixed_To_Fixed; | |

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

-- Expand_Convert_Fixed_To_Float -- | |

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

-- If the small of the fixed type is 1.0, then we simply convert the | |

-- integer value directly to the target floating-point type, otherwise | |

-- we first have to multiply by the small, in Universal_Real, and then | |

-- convert the result to the target floating-point type. | |

procedure Expand_Convert_Fixed_To_Float (N : Node_Id) is | |

Rng_Check : constant Boolean := Do_Range_Check (N); | |

Expr : constant Node_Id := Expression (N); | |

Source_Type : constant Entity_Id := Etype (Expr); | |

Small : constant Ureal := Small_Value (Source_Type); | |

begin | |

if Is_OK_Static_Expression (Expr) then | |

Expand_Convert_Fixed_Static (N); | |

return; | |

end if; | |

if Small = Ureal_1 then | |

Set_Result (N, Expr); | |

else | |

Set_Result (N, | |

Build_Multiply (N, | |

Fpt_Value (Expr), | |

Real_Literal (N, Small)), | |

Rng_Check); | |

end if; | |

end Expand_Convert_Fixed_To_Float; | |

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

-- Expand_Convert_Fixed_To_Integer -- | |

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

-- We have: | |

-- Result_Value = Source_Value * Source_Small | |

-- If the small value is a sufficiently small integer, then the perfect | |

-- result set is obtained by a single integer multiplication. | |

-- If the small value is the reciprocal of a sufficiently small integer, | |

-- then the perfect result set is obtained by a single integer division. | |

-- If the numerator and denominator of the small value are sufficiently | |

-- small integers, then the perfect result set is obtained by a scaled | |

-- divide operation. | |

-- In other cases, we obtain the close result set by calculating the | |

-- result in floating-point. | |

procedure Expand_Convert_Fixed_To_Integer (N : Node_Id) is | |

Rng_Check : constant Boolean := Do_Range_Check (N); | |

Expr : constant Node_Id := Expression (N); | |

Source_Type : constant Entity_Id := Etype (Expr); | |

Small : constant Ureal := Small_Value (Source_Type); | |

Small_Num : constant Uint := Norm_Num (Small); | |

Small_Den : constant Uint := Norm_Den (Small); | |

Lit_Num : Node_Id; | |

Lit_Den : Node_Id; | |

begin | |

if Is_OK_Static_Expression (Expr) then | |

Expand_Convert_Fixed_Static (N); | |

return; | |

end if; | |

if Small_Den = 1 then | |

Lit_Num := Integer_Literal (N, Small_Num); | |

if Present (Lit_Num) then | |

Set_Result (N, Build_Multiply (N, Expr, Lit_Num), Rng_Check); | |

return; | |

end if; | |

elsif Small_Num = 1 then | |

Lit_Den := Integer_Literal (N, Small_Den); | |

if Present (Lit_Den) then | |

Set_Result (N, Build_Divide (N, Expr, Lit_Den), Rng_Check); | |

return; | |

end if; | |

else | |

Lit_Num := Integer_Literal (N, Small_Num); | |

Lit_Den := Integer_Literal (N, Small_Den); | |

if Present (Lit_Num) and then Present (Lit_Den) then | |

Set_Result | |

(N, Build_Scaled_Divide (N, Expr, Lit_Num, Lit_Den), Rng_Check); | |

return; | |

end if; | |

end if; | |

-- Fall through to use floating-point for the close result set case, | |

-- as a result of the numerator or denominator of the small value not | |

-- being a sufficiently small integer. | |

Set_Result (N, | |

Build_Multiply (N, | |

Fpt_Value (Expr), | |

Real_Literal (N, Small)), | |

Rng_Check); | |

end Expand_Convert_Fixed_To_Integer; | |

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

-- Expand_Convert_Float_To_Fixed -- | |

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

-- We have | |

-- Result_Value * Result_Small = Operand_Value | |

-- so compute: | |

-- Result_Value = Operand_Value * (1.0 / Result_Small) | |

-- We do the small scaling in floating-point, and we do a multiplication | |

-- rather than a division, since it is accurate enough for the perfect | |

-- result cases, and faster. | |

procedure Expand_Convert_Float_To_Fixed (N : Node_Id) is | |

Expr : constant Node_Id := Expression (N); | |

Result_Type : constant Entity_Id := Etype (N); | |

Rng_Check : constant Boolean := Do_Range_Check (N); | |

Small : constant Ureal := Small_Value (Result_Type); | |

begin | |

-- Optimize small = 1, where we can avoid the multiply completely | |

if Small = Ureal_1 then | |

Set_Result (N, Expr, Rng_Check, Trunc => True); | |

-- Normal case where multiply is required. Rounding is truncating | |

-- for decimal fixed point types only, see RM 4.6(29), except if the | |

-- conversion comes from an attribute reference 'Round (RM 3.5.10 (14)): | |

-- The attribute is implemented by means of a conversion that must | |

-- round. | |

else | |

Set_Result | |

(N => N, | |

Expr => | |

Build_Multiply | |

(N => N, | |

L => Fpt_Value (Expr), | |

R => Real_Literal (N, Ureal_1 / Small)), | |

Rchk => Rng_Check, | |

Trunc => Is_Decimal_Fixed_Point_Type (Result_Type) | |

and not Rounded_Result (N)); | |

end if; | |

end Expand_Convert_Float_To_Fixed; | |

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

-- Expand_Convert_Integer_To_Fixed -- | |

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

-- We have | |

-- Result_Value * Result_Small = Operand_Value | |

-- Result_Value = Operand_Value / Result_Small | |

-- If the small value is a sufficiently small integer, then the perfect | |

-- result set is obtained by a single integer division. | |

-- If the small value is the reciprocal of a sufficiently small integer, | |

-- the perfect result set is obtained by a single integer multiplication. | |

-- If the numerator and denominator of the small value are sufficiently | |

-- small integers, then the perfect result set is obtained by a scaled | |

-- divide operation. | |

-- In other cases, we obtain the close result set by calculating the | |

-- result in floating-point using a multiplication by the reciprocal | |

-- of the Result_Small. | |

procedure Expand_Convert_Integer_To_Fixed (N : Node_Id) is | |

Rng_Check : constant Boolean := Do_Range_Check (N); | |

Expr : constant Node_Id := Expression (N); | |

Result_Type : constant Entity_Id := Etype (N); | |

Small : constant Ureal := Small_Value (Result_Type); | |

Small_Num : constant Uint := Norm_Num (Small); | |

Small_Den : constant Uint := Norm_Den (Small); | |

Lit_Num : Node_Id; | |

Lit_Den : Node_Id; | |

begin | |

if Small_Den = 1 then | |

Lit_Num := Integer_Literal (N, Small_Num); | |

if Present (Lit_Num) then | |

Set_Result (N, Build_Divide (N, Expr, Lit_Num), Rng_Check); | |

return; | |

end if; | |

elsif Small_Num = 1 then | |

Lit_Den := Integer_Literal (N, Small_Den); | |

if Present (Lit_Den) then | |

Set_Result (N, Build_Multiply (N, Expr, Lit_Den), Rng_Check); | |

return; | |

end if; | |

else | |

Lit_Num := Integer_Literal (N, Small_Num); | |

Lit_Den := Integer_Literal (N, Small_Den); | |

if Present (Lit_Num) and then Present (Lit_Den) then | |

Set_Result | |

(N, Build_Scaled_Divide (N, Expr, Lit_Den, Lit_Num), Rng_Check); | |

return; | |

end if; | |

end if; | |

-- Fall through to use floating-point for the close result set case, | |

-- as a result of the numerator or denominator of the small value not | |

-- being a sufficiently small integer. | |

Set_Result (N, | |

Build_Multiply (N, | |

Fpt_Value (Expr), | |

Real_Literal (N, Ureal_1 / Small)), | |

Rng_Check); | |

end Expand_Convert_Integer_To_Fixed; | |

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

-- Expand_Decimal_Divide_Call -- | |

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

-- We have four operands | |

-- Dividend | |

-- Divisor | |

-- Quotient | |

-- Remainder | |

-- All of which are decimal types, and which thus have associated | |

-- decimal scales. | |

-- Computing the quotient is a similar problem to that faced by the | |

-- normal fixed-point division, except that it is simpler, because | |

-- we always have compatible smalls. | |

-- Quotient = (Dividend / Divisor) * 10**q | |

-- where 10 ** q = Dividend'Small / (Divisor'Small * Quotient'Small) | |

-- so q = Divisor'Scale + Quotient'Scale - Dividend'Scale | |

-- For q >= 0, we compute | |

-- Numerator := Dividend * 10 ** q | |

-- Denominator := Divisor | |

-- Quotient := Numerator / Denominator | |

-- For q < 0, we compute | |

-- Numerator := Dividend | |

-- Denominator := Divisor * 10 ** q | |

-- Quotient := Numerator / Denominator | |

-- Both these divisions are done in truncated mode, and the remainder | |

-- from these divisions is used to compute the result Remainder. This | |

-- remainder has the effective scale of the numerator of the division, | |

-- For q >= 0, the remainder scale is Dividend'Scale + q | |

-- For q < 0, the remainder scale is Dividend'Scale | |

-- The result Remainder is then computed by a normal truncating decimal | |

-- conversion from this scale to the scale of the remainder, i.e. by a | |

-- division or multiplication by the appropriate power of 10. | |

procedure Expand_Decimal_Divide_Call (N : Node_Id) is | |

Loc : constant Source_Ptr := Sloc (N); | |

Dividend : Node_Id := First_Actual (N); | |

Divisor : Node_Id := Next_Actual (Dividend); | |

Quotient : Node_Id := Next_Actual (Divisor); | |

Remainder : Node_Id := Next_Actual (Quotient); | |

Dividend_Type : constant Entity_Id := Etype (Dividend); | |

Divisor_Type : constant Entity_Id := Etype (Divisor); | |

Quotient_Type : constant Entity_Id := Etype (Quotient); | |

Remainder_Type : constant Entity_Id := Etype (Remainder); | |

Dividend_Scale : constant Uint := Scale_Value (Dividend_Type); | |

Divisor_Scale : constant Uint := Scale_Value (Divisor_Type); | |

Quotient_Scale : constant Uint := Scale_Value (Quotient_Type); | |

Remainder_Scale : constant Uint := Scale_Value (Remainder_Type); | |

Q : Uint; | |

Numerator_Scale : Uint; | |

Stmts : List_Id; | |

Qnn : Entity_Id; | |

Rnn : Entity_Id; | |

Computed_Remainder : Node_Id; | |

Adjusted_Remainder : Node_Id; | |

Scale_Adjust : Uint; | |

begin | |

-- Relocate the operands, since they are now list elements, and we | |

-- need to reference them separately as operands in the expanded code. | |

Dividend := Relocate_Node (Dividend); | |

Divisor := Relocate_Node (Divisor); | |

Quotient := Relocate_Node (Quotient); | |

Remainder := Relocate_Node (Remainder); | |

-- Now compute Q, the adjustment scale | |

Q := Divisor_Scale + Quotient_Scale - Dividend_Scale; | |

-- If Q is non-negative then we need a scaled divide | |

if Q >= 0 then | |

Build_Scaled_Divide_Code | |

(N, | |

Dividend, | |

Integer_Literal (N, Uint_10 ** Q), | |

Divisor, | |

Qnn, Rnn, Stmts); | |

Numerator_Scale := Dividend_Scale + Q; | |

-- If Q is negative, then we need a double divide | |

else | |

Build_Double_Divide_Code | |

(N, | |

Dividend, | |

Divisor, | |

Integer_Literal (N, Uint_10 ** (-Q)), | |

Qnn, Rnn, Stmts); | |

Numerator_Scale := Dividend_Scale; | |

end if; | |

-- Add statement to set quotient value | |

-- Quotient := quotient-type!(Qnn); | |

Append_To (Stmts, | |

Make_Assignment_Statement (Loc, | |

Name => Quotient, | |

Expression => | |

Unchecked_Convert_To (Quotient_Type, | |

Build_Conversion (N, Quotient_Type, | |

New_Occurrence_Of (Qnn, Loc))))); | |

-- Now we need to deal with computing and setting the remainder. The | |

-- scale of the remainder is in Numerator_Scale, and the desired | |

-- scale is the scale of the given Remainder argument. There are | |

-- three cases: | |

-- Numerator_Scale > Remainder_Scale | |

-- in this case, there are extra digits in the computed remainder | |

-- which must be eliminated by an extra division: | |

-- computed-remainder := Numerator rem Denominator | |

-- scale_adjust = Numerator_Scale - Remainder_Scale | |

-- adjusted-remainder := computed-remainder / 10 ** scale_adjust | |

-- Numerator_Scale = Remainder_Scale | |

-- in this case, the we have the remainder we need | |

-- computed-remainder := Numerator rem Denominator | |

-- adjusted-remainder := computed-remainder | |

-- Numerator_Scale < Remainder_Scale | |

-- in this case, we have insufficient digits in the computed | |

-- remainder, which must be eliminated by an extra multiply | |

-- computed-remainder := Numerator rem Denominator | |

-- scale_adjust = Remainder_Scale - Numerator_Scale | |

-- adjusted-remainder := computed-remainder * 10 ** scale_adjust | |

-- Finally we assign the adjusted-remainder to the result Remainder | |

-- with conversions to get the proper fixed-point type representation. | |

Computed_Remainder := New_Occurrence_Of (Rnn, Loc); | |

if Numerator_Scale > Remainder_Scale then | |

Scale_Adjust := Numerator_Scale - Remainder_Scale; | |

Adjusted_Remainder := | |

Build_Divide | |

(N, Computed_Remainder, Integer_Literal (N, 10 ** Scale_Adjust)); | |

elsif Numerator_Scale = Remainder_Scale then | |

Adjusted_Remainder := Computed_Remainder; | |

else -- Numerator_Scale < Remainder_Scale | |

Scale_Adjust := Remainder_Scale - Numerator_Scale; | |

Adjusted_Remainder := | |

Build_Multiply | |

(N, Computed_Remainder, Integer_Literal (N, 10 ** Scale_Adjust)); | |

end if; | |

-- Assignment of remainder result | |

Append_To (Stmts, | |

Make_Assignment_Statement (Loc, | |

Name => Remainder, | |

Expression => | |

Unchecked_Convert_To (Remainder_Type, Adjusted_Remainder))); | |

-- Final step is to rewrite the call with a block containing the | |

-- above sequence of constructed statements for the divide operation. | |

Rewrite (N, | |

Make_Block_Statement (Loc, | |

Handled_Statement_Sequence => | |

Make_Handled_Sequence_Of_Statements (Loc, | |

Statements => Stmts))); | |

Analyze (N); | |

end Expand_Decimal_Divide_Call; | |

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

-- Expand_Divide_Fixed_By_Fixed_Giving_Fixed -- | |

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

procedure Expand_Divide_Fixed_By_Fixed_Giving_Fixed (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

begin | |

if Etype (Left) = Universal_Real then | |

Do_Divide_Universal_Fixed (N); | |

elsif Etype (Right) = Universal_Real then | |

Do_Divide_Fixed_Universal (N); | |

else | |

Do_Divide_Fixed_Fixed (N); | |

-- A focused optimization: if after constant folding the | |

-- expression is of the form: T ((Exp * D) / D), where D is | |

-- a static constant, return T (Exp). This form will show up | |

-- when D is the denominator of the static expression for the | |

-- 'small of fixed-point types involved. This transformation | |

-- removes a division that may be expensive on some targets. | |

if Nkind (N) = N_Type_Conversion | |

and then Nkind (Expression (N)) = N_Op_Divide | |

then | |

declare | |

Num : constant Node_Id := Left_Opnd (Expression (N)); | |

Den : constant Node_Id := Right_Opnd (Expression (N)); | |

begin | |

if Nkind (Den) = N_Integer_Literal | |

and then Nkind (Num) = N_Op_Multiply | |

and then Nkind (Right_Opnd (Num)) = N_Integer_Literal | |

and then Intval (Den) = Intval (Right_Opnd (Num)) | |

then | |

Rewrite (Expression (N), Left_Opnd (Num)); | |

end if; | |

end; | |

end if; | |

end if; | |

end Expand_Divide_Fixed_By_Fixed_Giving_Fixed; | |

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

-- Expand_Divide_Fixed_By_Fixed_Giving_Float -- | |

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

-- The division is done in Universal_Real, and the result is multiplied | |

-- by the small ratio, which is Small (Right) / Small (Left). Special | |

-- treatment is required for universal operands, which represent their | |

-- own value and do not require conversion. | |

procedure Expand_Divide_Fixed_By_Fixed_Giving_Float (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

Left_Type : constant Entity_Id := Etype (Left); | |

Right_Type : constant Entity_Id := Etype (Right); | |

begin | |

-- Case of left operand is universal real, the result we want is: | |

-- Left_Value / (Right_Value * Right_Small) | |

-- so we compute this as: | |

-- (Left_Value / Right_Small) / Right_Value | |

if Left_Type = Universal_Real then | |

Set_Result (N, | |

Build_Divide (N, | |

Real_Literal (N, Realval (Left) / Small_Value (Right_Type)), | |

Fpt_Value (Right))); | |

-- Case of right operand is universal real, the result we want is | |

-- (Left_Value * Left_Small) / Right_Value | |

-- so we compute this as: | |

-- Left_Value * (Left_Small / Right_Value) | |

-- Note we invert to a multiplication since usually floating-point | |

-- multiplication is much faster than floating-point division. | |

elsif Right_Type = Universal_Real then | |

Set_Result (N, | |

Build_Multiply (N, | |

Fpt_Value (Left), | |

Real_Literal (N, Small_Value (Left_Type) / Realval (Right)))); | |

-- Both operands are fixed, so the value we want is | |

-- (Left_Value * Left_Small) / (Right_Value * Right_Small) | |

-- which we compute as: | |

-- (Left_Value / Right_Value) * (Left_Small / Right_Small) | |

else | |

Set_Result (N, | |

Build_Multiply (N, | |

Build_Divide (N, Fpt_Value (Left), Fpt_Value (Right)), | |

Real_Literal (N, | |

Small_Value (Left_Type) / Small_Value (Right_Type)))); | |

end if; | |

end Expand_Divide_Fixed_By_Fixed_Giving_Float; | |

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

-- Expand_Divide_Fixed_By_Fixed_Giving_Integer -- | |

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

procedure Expand_Divide_Fixed_By_Fixed_Giving_Integer (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

begin | |

if Etype (Left) = Universal_Real then | |

Do_Divide_Universal_Fixed (N); | |

elsif Etype (Right) = Universal_Real then | |

Do_Divide_Fixed_Universal (N); | |

else | |

Do_Divide_Fixed_Fixed (N); | |

end if; | |

end Expand_Divide_Fixed_By_Fixed_Giving_Integer; | |

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

-- Expand_Divide_Fixed_By_Integer_Giving_Fixed -- | |

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

-- Since the operand and result fixed-point type is the same, this is | |

-- a straight divide by the right operand, the small can be ignored. | |

procedure Expand_Divide_Fixed_By_Integer_Giving_Fixed (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

begin | |

Set_Result (N, Build_Divide (N, Left, Right)); | |

end Expand_Divide_Fixed_By_Integer_Giving_Fixed; | |

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

-- Expand_Multiply_Fixed_By_Fixed_Giving_Fixed -- | |

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

procedure Expand_Multiply_Fixed_By_Fixed_Giving_Fixed (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

procedure Rewrite_Non_Static_Universal (Opnd : Node_Id); | |

-- The operand may be a non-static universal value, such an | |

-- exponentiation with a non-static exponent. In that case, treat | |

-- as a fixed * fixed multiplication, and convert the argument to | |

-- the target fixed type. | |

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

-- Rewrite_Non_Static_Universal -- | |

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

procedure Rewrite_Non_Static_Universal (Opnd : Node_Id) is | |

Loc : constant Source_Ptr := Sloc (N); | |

begin | |

Rewrite (Opnd, | |

Make_Type_Conversion (Loc, | |

Subtype_Mark => New_Occurrence_Of (Etype (N), Loc), | |

Expression => Expression (Opnd))); | |

Analyze_And_Resolve (Opnd, Etype (N)); | |

end Rewrite_Non_Static_Universal; | |

-- Start of processing for Expand_Multiply_Fixed_By_Fixed_Giving_Fixed | |

begin | |

if Etype (Left) = Universal_Real then | |

if Nkind (Left) = N_Real_Literal then | |

Do_Multiply_Fixed_Universal (N, Left => Right, Right => Left); | |

elsif Nkind (Left) = N_Type_Conversion then | |

Rewrite_Non_Static_Universal (Left); | |

Do_Multiply_Fixed_Fixed (N); | |

end if; | |

elsif Etype (Right) = Universal_Real then | |

if Nkind (Right) = N_Real_Literal then | |

Do_Multiply_Fixed_Universal (N, Left, Right); | |

elsif Nkind (Right) = N_Type_Conversion then | |

Rewrite_Non_Static_Universal (Right); | |

Do_Multiply_Fixed_Fixed (N); | |

end if; | |

else | |

Do_Multiply_Fixed_Fixed (N); | |

end if; | |

end Expand_Multiply_Fixed_By_Fixed_Giving_Fixed; | |

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

-- Expand_Multiply_Fixed_By_Fixed_Giving_Float -- | |

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

-- The multiply is done in Universal_Real, and the result is multiplied | |

-- by the adjustment for the smalls which is Small (Right) * Small (Left). | |

-- Special treatment is required for universal operands. | |

procedure Expand_Multiply_Fixed_By_Fixed_Giving_Float (N : Node_Id) is | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

Left_Type : constant Entity_Id := Etype (Left); | |

Right_Type : constant Entity_Id := Etype (Right); | |

begin | |

-- Case of left operand is universal real, the result we want is | |

-- Left_Value * (Right_Value * Right_Small) | |

-- so we compute this as: | |

-- (Left_Value * Right_Small) * Right_Value; | |

if Left_Type = Universal_Real then | |

Set_Result (N, | |

Build_Multiply (N, | |

Real_Literal (N, Realval (Left) * Small_Value (Right_Type)), | |

Fpt_Value (Right))); | |

-- Case of right operand is universal real, the result we want is | |

-- (Left_Value * Left_Small) * Right_Value | |

-- so we compute this as: | |

-- Left_Value * (Left_Small * Right_Value) | |

elsif Right_Type = Universal_Real then | |

Set_Result (N, | |

Build_Multiply (N, | |

Fpt_Value (Left), | |

Real_Literal (N, Small_Value (Left_Type) * Realval (Right)))); | |

-- Both operands are fixed, so the value we want is | |

-- (Left_Value * Left_Small) * (Right_Value * Right_Small) | |

-- which we compute as: | |

-- (Left_Value * Right_Value) * (Right_Small * Left_Small) | |

else | |

Set_Result (N, | |

Build_Multiply (N, | |

Build_Multiply (N, Fpt_Value (Left), Fpt_Value (Right)), | |

Real_Literal (N, | |

Small_Value (Right_Type) * Small_Value (Left_Type)))); | |

end if; | |

end Expand_Multiply_Fixed_By_Fixed_Giving_Float; | |

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

-- Expand_Multiply_Fixed_By_Fixed_Giving_Integer -- | |

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

procedure Expand_Multiply_Fixed_By_Fixed_Giving_Integer (N : Node_Id) is | |

Loc : constant Source_Ptr := Sloc (N); | |

Left : constant Node_Id := Left_Opnd (N); | |

Right : constant Node_Id := Right_Opnd (N); | |

begin | |

if Etype (Left) = Universal_Real then | |

Do_Multiply_Fixed_Universal (N, Left => Right, Right => Left); | |

elsif Etype (Right) = Universal_Real then | |

Do_Multiply_Fixed_Universal (N, Left, Right); | |

-- If both types are equal and we need to avoid floating point | |

-- instructions, it's worth introducing a temporary with the | |

-- common type, because it may be evaluated more simply without | |

-- the need for run-time use of floating point. | |

elsif Etype (Right) = Etype (Left) | |

and then Restriction_Active (No_Floating_Point) | |

then | |

declare | |

Temp : constant Entity_Id := Make_Temporary (Loc, 'F'); | |

Mult : constant Node_Id := Make_Op_Multiply (Loc, Left, Right); | |

Decl : constant Node_Id := | |

Make_Object_Declaration (Loc, | |

Defining_Identifier => Temp, | |

Object_Definition => New_Occurrence_Of (Etype (Right), Loc), | |

Expression => Mult); | |

begin | |

Insert_Action (N, Decl); | |

Rewrite (N, | |

OK_Convert_To (Etype (N), New_Occurrence_Of (Temp, Loc))); | |

Analyze_And_Resolve (N, Standard_Integer); | |

end; | |

else | |

Do_Multiply_Fixed_Fixed (N); | |

end if; | |

end Expand_Multiply_Fixed_By_Fixed_Giving_Integer; | |

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

-- Expand_Multiply_Fixed_By_Integer_Giving_Fixed -- | |

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

-- Since the operand and result fixed-point type is the same, this is | |

-- a straight multiply by the right operand, the small can be ignored. | |

procedure Expand_Multiply_Fixed_By_Integer_Giving_Fixed (N : Node_Id) is | |

begin | |

Set_Result (N, | |

Build_Multiply (N, Left_Opnd (N), Right_Opnd (N))); | |

end Expand_Multiply_Fixed_By_Integer_Giving_Fixed; | |

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

-- Expand_Multiply_Integer_By_Fixed_Giving_Fixed -- | |

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

-- Since the operand and result fixed-point type is the same, this is | |

-- a straight multiply by the right operand, the small can be ignored. | |

procedure Expand_Multiply_Integer_By_Fixed_Giving_Fixed (N : Node_Id) is | |

begin | |

Set_Result (N, | |

Build_Multiply (N, Left_Opnd (N), Right_Opnd (N))); | |

end Expand_Multiply_Integer_By_Fixed_Giving_Fixed; | |

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

-- Fpt_Value -- | |

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

function Fpt_Value (N : Node_Id) return Node_Id is | |

begin | |

return Build_Conversion (N, Universal_Real, N); | |

end Fpt_Value; | |

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

-- Get_Size_For_Value -- | |

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

function Get_Size_For_Value (V : Uint) return Pos is | |

begin | |

pragma Assert (V >= Uint_0); | |

if V < Uint_2 ** 7 then | |

return 8; | |

elsif V < Uint_2 ** 15 then | |

return 16; | |

elsif V < Uint_2 ** 31 then | |

return 32; | |

elsif V < Uint_2 ** 63 then | |

return 64; | |

elsif V < Uint_2 ** 127 then | |

return 128; | |

else | |

return Pos'Last; | |

end if; | |

end Get_Size_For_Value; | |

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

-- Get_Type_For_Size -- | |

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

function Get_Type_For_Size (Siz : Pos; Force : Boolean) return Entity_Id is | |

begin | |

if Siz <= 8 then | |

return Standard_Integer_8; | |

elsif Siz <= 16 then | |

return Standard_Integer_16; | |

elsif Siz <= 32 then | |

return Standard_Integer_32; | |

elsif Siz <= 64 | |

or else (Force and then System_Max_Integer_Size < 128) | |

then | |

return Standard_Integer_64; | |

elsif (Siz <= 128 and then System_Max_Integer_Size = 128) | |

or else Force | |

then | |

return Standard_Integer_128; | |

else | |

return Empty; | |

end if; | |

end Get_Type_For_Size; | |

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

-- Integer_Literal -- | |

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

function Integer_Literal | |

(N : Node_Id; | |

V : Uint; | |

Negative : Boolean := False) return Node_Id | |

is | |

T : Entity_Id; | |

L : Node_Id; | |

begin | |

T := Get_Type_For_Size (Get_Size_For_Value (V), Force => False); | |

if No (T) then | |

return Empty; | |

end if; | |

if Negative then | |

L := Make_Integer_Literal (Sloc (N), UI_Negate (V)); | |

else | |

L := Make_Integer_Literal (Sloc (N), V); | |

end if; | |

-- Set type of result in case used elsewhere (see note at start) | |

Set_Etype (L, T); | |

Set_Is_Static_Expression (L); | |

-- We really need to set Analyzed here because we may be creating a | |

-- very strange beast, namely an integer literal typed as fixed-point | |

-- and the analyzer won't like that. | |

Set_Analyzed (L); | |

return L; | |

end Integer_Literal; | |

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

-- Real_Literal -- | |

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

function Real_Literal (N : Node_Id; V : Ureal) return Node_Id is | |

L : Node_Id; | |

begin | |

L := Make_Real_Literal (Sloc (N), V); | |

-- Set type of result in case used elsewhere (see note at start) | |

Set_Etype (L, Universal_Real); | |

return L; | |

end Real_Literal; | |

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

-- Rounded_Result_Set -- | |

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

function Rounded_Result_Set (N : Node_Id) return Boolean is | |

K : constant Node_Kind := Nkind (N); | |

begin | |

if (K = N_Type_Conversion or else | |

K = N_Op_Divide or else | |

K = N_Op_Multiply) | |

and then | |

(Rounded_Result (N) or else Is_Integer_Type (Etype (N))) | |

then | |

return True; | |

else | |

return False; | |

end if; | |

end Rounded_Result_Set; | |

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

-- Set_Result -- | |

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

procedure Set_Result | |

(N : Node_Id; | |

Expr : Node_Id; | |

Rchk : Boolean := False; | |

Trunc : Boolean := False) | |

is | |

Cnode : Node_Id; | |

Expr_Type : constant Entity_Id := Etype (Expr); | |

Result_Type : constant Entity_Id := Etype (N); | |

begin | |

-- No conversion required if types match and no range check or truncate | |

if Result_Type = Expr_Type and then not (Rchk or Trunc) then | |

Cnode := Expr; | |

-- Else perform required conversion | |

else | |

Cnode := Build_Conversion (N, Result_Type, Expr, Rchk, Trunc); | |

end if; | |

Rewrite (N, Cnode); | |

Analyze_And_Resolve (N, Result_Type); | |

end Set_Result; | |

end Exp_Fixd; |