------------------------------------------------------------------------------ -- -- -- GNAT RUN-TIME COMPONENTS -- -- -- -- S Y S T E M . A R I T H _ 3 2 -- -- -- -- B o d y -- -- -- -- Copyright (C) 2020, Free Software Foundation, Inc. -- -- -- -- GNAT is free software; you can redistribute it and/or modify it under -- -- terms of the GNU General Public License as published by the Free Soft- -- -- ware Foundation; either version 3, or (at your option) any later ver- -- -- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- -- or FITNESS FOR A PARTICULAR PURPOSE. -- -- -- -- As a special exception under Section 7 of GPL version 3, you are granted -- -- additional permissions described in the GCC Runtime Library Exception, -- -- version 3.1, as published by the Free Software Foundation. -- -- -- -- You should have received a copy of the GNU General Public License and -- -- a copy of the GCC Runtime Library Exception along with this program; -- -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see -- -- . -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ with Ada.Unchecked_Conversion; package body System.Arith_32 is pragma Suppress (Overflow_Check); pragma Suppress (Range_Check); subtype Uns32 is Interfaces.Unsigned_32; subtype Uns64 is Interfaces.Unsigned_64; use Interfaces; function To_Int is new Ada.Unchecked_Conversion (Uns32, Int32); ----------------------- -- Local Subprograms -- ----------------------- function "abs" (X : Int32) return Uns32 is (if X = Int32'First then 2**31 else Uns32 (Int32'(abs X))); -- Convert absolute value of X to unsigned. Note that we can't just use -- the expression of the Else since it overflows for X = Int32'First. function Hi (A : Uns64) return Uns32 is (Uns32 (Shift_Right (A, 32))); -- High order half of 64-bit value function To_Neg_Int (A : Uns32) return Int32; -- Convert to negative integer equivalent. If the input is in the range -- 0 .. 2**31, then the corresponding nonpositive signed integer (obtained -- by negating the given value) is returned, otherwise constraint error is -- raised. function To_Pos_Int (A : Uns32) return Int32; -- Convert to positive integer equivalent. If the input is in the range -- 0 .. 2**31 - 1, then the corresponding nonnegative signed integer is -- returned, otherwise constraint error is raised. procedure Raise_Error; pragma No_Return (Raise_Error); -- Raise constraint error with appropriate message ----------------- -- Raise_Error -- ----------------- procedure Raise_Error is begin raise Constraint_Error with "32-bit arithmetic overflow"; end Raise_Error; ------------------- -- Scaled_Divide -- ------------------- procedure Scaled_Divide32 (X, Y, Z : Int32; Q, R : out Int32; Round : Boolean) is Xu : constant Uns32 := abs X; Yu : constant Uns32 := abs Y; Zu : constant Uns32 := abs Z; D : Uns64; -- The dividend Qu : Uns32; Ru : Uns32; -- Unsigned quotient and remainder begin -- First do the 64-bit multiplication D := Uns64 (Xu) * Uns64 (Yu); -- If dividend is too large, raise error if Hi (D) >= Zu then Raise_Error; -- Then do the 64-bit division else Qu := Uns32 (D / Uns64 (Zu)); Ru := Uns32 (D rem Uns64 (Zu)); end if; -- Deal with rounding case if Round and then Ru > (Zu - Uns32'(1)) / Uns32'(2) then -- Protect against wrapping around when rounding, by signaling -- an overflow when the quotient is too large. if Qu = Uns32'Last then Raise_Error; end if; Qu := Qu + Uns32'(1); end if; -- Set final signs (RM 4.5.5(27-30)) -- Case of dividend (X * Y) sign positive if (X >= 0 and then Y >= 0) or else (X < 0 and then Y < 0) then R := To_Pos_Int (Ru); Q := (if Z > 0 then To_Pos_Int (Qu) else To_Neg_Int (Qu)); -- Case of dividend (X * Y) sign negative else R := To_Neg_Int (Ru); Q := (if Z > 0 then To_Neg_Int (Qu) else To_Pos_Int (Qu)); end if; end Scaled_Divide32; ---------------- -- To_Neg_Int -- ---------------- function To_Neg_Int (A : Uns32) return Int32 is R : constant Int32 := (if A = 2**31 then Int32'First else -To_Int (A)); -- Note that we can't just use the expression of the Else, because it -- overflows for A = 2**31. begin if R <= 0 then return R; else Raise_Error; end if; end To_Neg_Int; ---------------- -- To_Pos_Int -- ---------------- function To_Pos_Int (A : Uns32) return Int32 is R : constant Int32 := To_Int (A); begin if R >= 0 then return R; else Raise_Error; end if; end To_Pos_Int; end System.Arith_32;