1
2/**********************************************
3 * This module implements integral arithmetic primitives that check
4 * for out-of-range results.
5 * This is a translation to C++ of D's core.checkedint
6 *
7 * Integral arithmetic operators operate on fixed width types.
8 * Results that are not representable in those fixed widths are silently
9 * truncated to fit.
10 * This module offers integral arithmetic primitives that produce the
11 * same results, but set an 'overflow' flag when such truncation occurs.
12 * The setting is sticky, meaning that numerous operations can be cascaded
13 * and then the flag need only be checked at the end.
14 * Whether the operation is signed or unsigned is indicated by an 's' or 'u'
15 * suffix, respectively. While this could be achieved without such suffixes by
16 * using overloading on the signedness of the types, the suffix makes it clear
17 * which is happening without needing to examine the types.
18 *
19 * While the generic versions of these functions are computationally expensive
20 * relative to the cost of the operation itself, compiler implementations are free
21 * to recognize them and generate equivalent and faster code.
22 *
23 * References: $(LINK2 http://blog.regehr.org/archives/1139, Fast Integer Overflow Checks)
24 * Copyright: Copyright (C) 2014-2019 by The D Language Foundation, All Rights Reserved
25 * License:   $(LINK2 http://www.boost.org/LICENSE_1_0.txt, Boost License 1.0)
26 * Authors:   Walter Bright
27 * Source:    https://github.com/D-Programming-Language/dmd/blob/master/src/root/checkedint.c
28 */
29
30#include "dsystem.h"
31#include "checkedint.h"
32
33
34/*******************************
35 * Add two signed integers, checking for overflow.
36 *
37 * The overflow is sticky, meaning a sequence of operations can
38 * be done and overflow need only be checked at the end.
39 * Params:
40 *      x = left operand
41 *      y = right operand
42 *      overflow = set if an overflow occurs, is not affected otherwise
43 * Returns:
44 *      the sum
45 */
46
47int adds(int x, int y, bool& overflow)
48{
49    int64_t r = (int64_t)x + (int64_t)y;
50    if (r < INT32_MIN || r > INT32_MAX)
51        overflow = true;
52    return (int)r;
53}
54
55/// ditto
56int64_t adds(int64_t x, int64_t y, bool& overflow)
57{
58    int64_t r = (uint64_t)x + (uint64_t)y;
59    if ((x <  0 && y <  0 && r >= 0) ||
60        (x >= 0 && y >= 0 && r <  0))
61        overflow = true;
62    return r;
63}
64
65/*******************************
66 * Add two unsigned integers, checking for overflow (aka carry).
67 *
68 * The overflow is sticky, meaning a sequence of operations can
69 * be done and overflow need only be checked at the end.
70 * Params:
71 *      x = left operand
72 *      y = right operand
73 *      overflow = set if an overflow occurs, is not affected otherwise
74 * Returns:
75 *      the sum
76 */
77
78unsigned addu(unsigned x, unsigned y, bool& overflow)
79{
80    unsigned r = x + y;
81    if (r < x || r < y)
82        overflow = true;
83    return r;
84}
85
86/// ditto
87uint64_t addu(uint64_t x, uint64_t y, bool& overflow)
88{
89    uint64_t r = x + y;
90    if (r < x || r < y)
91        overflow = true;
92    return r;
93}
94
95/*******************************
96 * Subtract two signed integers, checking for overflow.
97 *
98 * The overflow is sticky, meaning a sequence of operations can
99 * be done and overflow need only be checked at the end.
100 * Params:
101 *      x = left operand
102 *      y = right operand
103 *      overflow = set if an overflow occurs, is not affected otherwise
104 * Returns:
105 *      the sum
106 */
107
108int subs(int x, int y, bool& overflow)
109{
110    int64_t r = (int64_t)x - (int64_t)y;
111    if (r < INT32_MIN || r > INT32_MAX)
112        overflow = true;
113    return (int)r;
114}
115
116/// ditto
117int64_t subs(int64_t x, int64_t y, bool& overflow)
118{
119    int64_t r = (uint64_t)x - (uint64_t)y;
120    if ((x <  0 && y >= 0 && r >= 0) ||
121        (x >= 0 && y <  0 && (r <  0 || y == INT64_MIN)))
122        overflow = true;
123    return r;
124}
125
126/*******************************
127 * Subtract two unsigned integers, checking for overflow (aka borrow).
128 *
129 * The overflow is sticky, meaning a sequence of operations can
130 * be done and overflow need only be checked at the end.
131 * Params:
132 *      x = left operand
133 *      y = right operand
134 *      overflow = set if an overflow occurs, is not affected otherwise
135 * Returns:
136 *      the sum
137 */
138
139unsigned subu(unsigned x, unsigned y, bool& overflow)
140{
141    if (x < y)
142        overflow = true;
143    return x - y;
144}
145
146/// ditto
147uint64_t subu(uint64_t x, uint64_t y, bool& overflow)
148{
149    if (x < y)
150        overflow = true;
151    return x - y;
152}
153
154/***********************************************
155 * Negate an integer.
156 *
157 * Params:
158 *      x = operand
159 *      overflow = set if x cannot be negated, is not affected otherwise
160 * Returns:
161 *      the negation of x
162 */
163
164int negs(int x, bool& overflow)
165{
166    if (x == (int)INT32_MIN)
167        overflow = true;
168    return -x;
169}
170
171/// ditto
172int64_t negs(int64_t x, bool& overflow)
173{
174    if (x == INT64_MIN)
175        overflow = true;
176    return -x;
177}
178
179/*******************************
180 * Multiply two signed integers, checking for overflow.
181 *
182 * The overflow is sticky, meaning a sequence of operations can
183 * be done and overflow need only be checked at the end.
184 * Params:
185 *      x = left operand
186 *      y = right operand
187 *      overflow = set if an overflow occurs, is not affected otherwise
188 * Returns:
189 *      the sum
190 */
191
192int muls(int x, int y, bool& overflow)
193{
194    int64_t r = (int64_t)x * (int64_t)y;
195    if (r < INT32_MIN || r > INT32_MAX)
196        overflow = true;
197    return (int)r;
198}
199
200/// ditto
201int64_t muls(int64_t x, int64_t y, bool& overflow)
202{
203    int64_t r = (uint64_t)x * (uint64_t)y;
204    int64_t not0or1 = ~(int64_t)1;
205    if ((x & not0or1) && ((r == y) ? r : (r / x) != y))
206        overflow = true;
207    return r;
208}
209
210/*******************************
211 * Multiply two unsigned integers, checking for overflow (aka carry).
212 *
213 * The overflow is sticky, meaning a sequence of operations can
214 * be done and overflow need only be checked at the end.
215 * Params:
216 *      x = left operand
217 *      y = right operand
218 *      overflow = set if an overflow occurs, is not affected otherwise
219 * Returns:
220 *      the sum
221 */
222
223unsigned mulu(unsigned x, unsigned y, bool& overflow)
224{
225    uint64_t r = (uint64_t)x * (uint64_t)y;
226    if (r > UINT32_MAX)
227        overflow = true;
228    return (unsigned)r;
229}
230
231/// ditto
232uint64_t mulu(uint64_t x, uint64_t y, bool& overflow)
233{
234    uint64_t r = x * y;
235    if (x && (r / x) != y)
236        overflow = true;
237    return r;
238}
239