1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
|
------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- S Y S T E M . A R I T H _ 3 2 --
-- --
-- B o d y --
-- --
-- Copyright (C) 2020-2021, Free Software Foundation, Inc. --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
-- terms of the GNU General Public License as published by the Free Soft- --
-- ware Foundation; either version 3, or (at your option) any later ver- --
-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE. --
-- --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception, --
-- version 3.1, as published by the Free Software Foundation. --
-- --
-- You should have received a copy of the GNU General Public License and --
-- a copy of the GCC Runtime Library Exception along with this program; --
-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
-- <http://www.gnu.org/licenses/>. --
-- --
-- GNAT was originally developed by the GNAT team at New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
with Ada.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;
|
