1/*-------------------------------------------------------------------------
2 *
3 * int128.h
4 * Roll-our-own 128-bit integer arithmetic.
5 *
6 * We make use of the native int128 type if there is one, otherwise
7 * implement things the hard way based on two int64 halves.
8 *
9 * See src/tools/testint128.c for a simple test harness for this file.
10 *
11 * Copyright (c) 2017-2019, PostgreSQL Global Development Group
12 *
13 * src/include/common/int128.h
14 *
15 *-------------------------------------------------------------------------
16 */
17#ifndef INT128_H
18#define INT128_H
19
20/*
21 * For testing purposes, use of native int128 can be switched on/off by
22 * predefining USE_NATIVE_INT128.
23 */
24#ifndef USE_NATIVE_INT128
25#ifdef HAVE_INT128
26#define USE_NATIVE_INT128 1
27#else
28#define USE_NATIVE_INT128 0
29#endif
30#endif
31
32
33#if USE_NATIVE_INT128
34
35typedef int128 INT128;
36
37/*
38 * Add an unsigned int64 value into an INT128 variable.
39 */
40static inline void
41int128_add_uint64(INT128 *i128, uint64 v)
42{
43 *i128 += v;
44}
45
46/*
47 * Add a signed int64 value into an INT128 variable.
48 */
49static inline void
50int128_add_int64(INT128 *i128, int64 v)
51{
52 *i128 += v;
53}
54
55/*
56 * Add the 128-bit product of two int64 values into an INT128 variable.
57 *
58 * XXX with a stupid compiler, this could actually be less efficient than
59 * the other implementation; maybe we should do it by hand always?
60 */
61static inline void
62int128_add_int64_mul_int64(INT128 *i128, int64 x, int64 y)
63{
64 *i128 += (int128) x * (int128) y;
65}
66
67/*
68 * Compare two INT128 values, return -1, 0, or +1.
69 */
70static inline int
71int128_compare(INT128 x, INT128 y)
72{
73 if (x < y)
74 return -1;
75 if (x > y)
76 return 1;
77 return 0;
78}
79
80/*
81 * Widen int64 to INT128.
82 */
83static inline INT128
84int64_to_int128(int64 v)
85{
86 return (INT128) v;
87}
88
89/*
90 * Convert INT128 to int64 (losing any high-order bits).
91 * This also works fine for casting down to uint64.
92 */
93static inline int64
94int128_to_int64(INT128 val)
95{
96 return (int64) val;
97}
98
99#else /* !USE_NATIVE_INT128 */
100
101/*
102 * We lay out the INT128 structure with the same content and byte ordering
103 * that a native int128 type would (probably) have. This makes no difference
104 * for ordinary use of INT128, but allows union'ing INT128 with int128 for
105 * testing purposes.
106 */
107typedef struct
108{
109#ifdef WORDS_BIGENDIAN
110 int64 hi; /* most significant 64 bits, including sign */
111 uint64 lo; /* least significant 64 bits, without sign */
112#else
113 uint64 lo; /* least significant 64 bits, without sign */
114 int64 hi; /* most significant 64 bits, including sign */
115#endif
116} INT128;
117
118/*
119 * Add an unsigned int64 value into an INT128 variable.
120 */
121static inline void
122int128_add_uint64(INT128 *i128, uint64 v)
123{
124 /*
125 * First add the value to the .lo part, then check to see if a carry needs
126 * to be propagated into the .hi part. A carry is needed if both inputs
127 * have high bits set, or if just one input has high bit set while the new
128 * .lo part doesn't. Remember that .lo part is unsigned; we cast to
129 * signed here just as a cheap way to check the high bit.
130 */
131 uint64 oldlo = i128->lo;
132
133 i128->lo += v;
134 if (((int64) v < 0 && (int64) oldlo < 0) ||
135 (((int64) v < 0 || (int64) oldlo < 0) && (int64) i128->lo >= 0))
136 i128->hi++;
137}
138
139/*
140 * Add a signed int64 value into an INT128 variable.
141 */
142static inline void
143int128_add_int64(INT128 *i128, int64 v)
144{
145 /*
146 * This is much like the above except that the carry logic differs for
147 * negative v. Ordinarily we'd need to subtract 1 from the .hi part
148 * (corresponding to adding the sign-extended bits of v to it); but if
149 * there is a carry out of the .lo part, that cancels and we do nothing.
150 */
151 uint64 oldlo = i128->lo;
152
153 i128->lo += v;
154 if (v >= 0)
155 {
156 if ((int64) oldlo < 0 && (int64) i128->lo >= 0)
157 i128->hi++;
158 }
159 else
160 {
161 if (!((int64) oldlo < 0 || (int64) i128->lo >= 0))
162 i128->hi--;
163 }
164}
165
166/*
167 * INT64_AU32 extracts the most significant 32 bits of int64 as int64, while
168 * INT64_AL32 extracts the least significant 32 bits as uint64.
169 */
170#define INT64_AU32(i64) ((i64) >> 32)
171#define INT64_AL32(i64) ((i64) & UINT64CONST(0xFFFFFFFF))
172
173/*
174 * Add the 128-bit product of two int64 values into an INT128 variable.
175 */
176static inline void
177int128_add_int64_mul_int64(INT128 *i128, int64 x, int64 y)
178{
179 /* INT64_AU32 must use arithmetic right shift */
180 StaticAssertStmt(((int64) -1 >> 1) == (int64) -1,
181 "arithmetic right shift is needed");
182
183 /*----------
184 * Form the 128-bit product x * y using 64-bit arithmetic.
185 * Considering each 64-bit input as having 32-bit high and low parts,
186 * we can compute
187 *
188 * x * y = ((x.hi << 32) + x.lo) * (((y.hi << 32) + y.lo)
189 * = (x.hi * y.hi) << 64 +
190 * (x.hi * y.lo) << 32 +
191 * (x.lo * y.hi) << 32 +
192 * x.lo * y.lo
193 *
194 * Each individual product is of 32-bit terms so it won't overflow when
195 * computed in 64-bit arithmetic. Then we just have to shift it to the
196 * correct position while adding into the 128-bit result. We must also
197 * keep in mind that the "lo" parts must be treated as unsigned.
198 *----------
199 */
200
201 /* No need to work hard if product must be zero */
202 if (x != 0 && y != 0)
203 {
204 int64 x_u32 = INT64_AU32(x);
205 uint64 x_l32 = INT64_AL32(x);
206 int64 y_u32 = INT64_AU32(y);
207 uint64 y_l32 = INT64_AL32(y);
208 int64 tmp;
209
210 /* the first term */
211 i128->hi += x_u32 * y_u32;
212
213 /* the second term: sign-extend it only if x is negative */
214 tmp = x_u32 * y_l32;
215 if (x < 0)
216 i128->hi += INT64_AU32(tmp);
217 else
218 i128->hi += ((uint64) tmp) >> 32;
219 int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32);
220
221 /* the third term: sign-extend it only if y is negative */
222 tmp = x_l32 * y_u32;
223 if (y < 0)
224 i128->hi += INT64_AU32(tmp);
225 else
226 i128->hi += ((uint64) tmp) >> 32;
227 int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32);
228
229 /* the fourth term: always unsigned */
230 int128_add_uint64(i128, x_l32 * y_l32);
231 }
232}
233
234/*
235 * Compare two INT128 values, return -1, 0, or +1.
236 */
237static inline int
238int128_compare(INT128 x, INT128 y)
239{
240 if (x.hi < y.hi)
241 return -1;
242 if (x.hi > y.hi)
243 return 1;
244 if (x.lo < y.lo)
245 return -1;
246 if (x.lo > y.lo)
247 return 1;
248 return 0;
249}
250
251/*
252 * Widen int64 to INT128.
253 */
254static inline INT128
255int64_to_int128(int64 v)
256{
257 INT128 val;
258
259 val.lo = (uint64) v;
260 val.hi = (v < 0) ? -INT64CONST(1) : INT64CONST(0);
261 return val;
262}
263
264/*
265 * Convert INT128 to int64 (losing any high-order bits).
266 * This also works fine for casting down to uint64.
267 */
268static inline int64
269int128_to_int64(INT128 val)
270{
271 return (int64) val.lo;
272}
273
274#endif /* USE_NATIVE_INT128 */
275
276#endif /* INT128_H */
277