Line data Source code
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, 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 :
35 : typedef int128 INT128;
36 :
37 : /*
38 : * Add an unsigned int64 value into an INT128 variable.
39 : */
40 : static inline void
41 : int128_add_uint64(INT128 *i128, uint64 v)
42 : {
43 : *i128 += v;
44 : }
45 :
46 : /*
47 : * Add a signed int64 value into an INT128 variable.
48 : */
49 : static inline void
50 : int128_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 : */
61 : static inline void
62 : int128_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 : */
70 : static inline int
71 : int128_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 : */
83 : static inline INT128
84 : int64_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 : */
93 : static inline int64
94 : int128_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 : */
107 : typedef 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 : */
121 : static inline void
122 15816 : int128_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 15816 : uint64 oldlo = i128->lo;
132 :
133 15816 : i128->lo += v;
134 31541 : if (((int64) v < 0 && (int64) oldlo < 0) ||
135 31345 : (((int64) v < 0 || (int64) oldlo < 0) && (int64) i128->lo >= 0))
136 113 : i128->hi++;
137 15816 : }
138 :
139 : /*
140 : * Add a signed int64 value into an INT128 variable.
141 : */
142 : static inline void
143 : int128_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 : */
176 : static inline void
177 19816 : int128_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 19816 : if (x != 0 && y != 0)
203 : {
204 5272 : int64 x_u32 = INT64_AU32(x);
205 5272 : uint64 x_l32 = INT64_AL32(x);
206 5272 : int64 y_u32 = INT64_AU32(y);
207 5272 : uint64 y_l32 = INT64_AL32(y);
208 : int64 tmp;
209 :
210 : /* the first term */
211 5272 : i128->hi += x_u32 * y_u32;
212 :
213 : /* the second term: sign-extend it only if x is negative */
214 5272 : tmp = x_u32 * y_l32;
215 5272 : if (x < 0)
216 47 : i128->hi += INT64_AU32(tmp);
217 : else
218 5225 : i128->hi += ((uint64) tmp) >> 32;
219 5272 : int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32);
220 :
221 : /* the third term: sign-extend it only if y is negative */
222 5272 : tmp = x_l32 * y_u32;
223 5272 : if (y < 0)
224 0 : i128->hi += INT64_AU32(tmp);
225 : else
226 5272 : i128->hi += ((uint64) tmp) >> 32;
227 5272 : int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32);
228 :
229 : /* the fourth term: always unsigned */
230 5272 : int128_add_uint64(i128, x_l32 * y_l32);
231 : }
232 19816 : }
233 :
234 : /*
235 : * Compare two INT128 values, return -1, 0, or +1.
236 : */
237 : static inline int
238 9897 : int128_compare(INT128 x, INT128 y)
239 : {
240 9897 : if (x.hi < y.hi)
241 500 : return -1;
242 9397 : if (x.hi > y.hi)
243 111 : return 1;
244 9286 : if (x.lo < y.lo)
245 2778 : return -1;
246 6508 : if (x.lo > y.lo)
247 3618 : return 1;
248 2890 : return 0;
249 : }
250 :
251 : /*
252 : * Widen int64 to INT128.
253 : */
254 : static inline INT128
255 19816 : int64_to_int128(int64 v)
256 : {
257 : INT128 val;
258 :
259 19816 : val.lo = (uint64) v;
260 19816 : val.hi = (v < 0) ? -INT64CONST(1) : INT64CONST(0);
261 19816 : 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 : */
268 : static inline int64
269 22 : int128_to_int64(INT128 val)
270 : {
271 22 : return (int64) val.lo;
272 : }
273 :
274 : #endif /* USE_NATIVE_INT128 */
275 :
276 : #endif /* INT128_H */
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