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/*------------------------------------------------------------------------- * * int128.h * Roll-our-own 128-bit integer arithmetic. * * We make use of the native int128 type if there is one, otherwise * implement things the hard way based on two int64 halves. * * See src/tools/testint128.c for a simple test harness for this file. * * Copyright (c) 2017-2025, PostgreSQL Global Development Group * * src/include/common/int128.h * *------------------------------------------------------------------------- */ #ifndef INT128_H #define INT128_H /* * For testing purposes, use of native int128 can be switched on/off by * predefining USE_NATIVE_INT128. */ #ifndef USE_NATIVE_INT128 #ifdef HAVE_INT128 #define USE_NATIVE_INT128 1 #else #define USE_NATIVE_INT128 0 #endif #endif #if USE_NATIVE_INT128 typedef int128 INT128; /* * Add an unsigned int64 value into an INT128 variable. */ static inline void int128_add_uint64(INT128 *i128, uint64 v) { *i128 += v; } /* * Add a signed int64 value into an INT128 variable. */ static inline void int128_add_int64(INT128 *i128, int64 v) { *i128 += v; } /* * Add the 128-bit product of two int64 values into an INT128 variable. * * XXX with a stupid compiler, this could actually be less efficient than * the other implementation; maybe we should do it by hand always? */ static inline void int128_add_int64_mul_int64(INT128 *i128, int64 x, int64 y) { *i128 += (int128) x * (int128) y; } /* * Compare two INT128 values, return -1, 0, or +1. */ static inline int int128_compare(INT128 x, INT128 y) { if (x < y) return -1; if (x > y) return 1; return 0; } /* * Widen int64 to INT128. */ static inline INT128 int64_to_int128(int64 v) { return (INT128) v; } /* * Convert INT128 to int64 (losing any high-order bits). * This also works fine for casting down to uint64. */ static inline int64 int128_to_int64(INT128 val) { return (int64) val; } #else /* !USE_NATIVE_INT128 */ /* * We lay out the INT128 structure with the same content and byte ordering * that a native int128 type would (probably) have. This makes no difference * for ordinary use of INT128, but allows union'ing INT128 with int128 for * testing purposes. */ typedef struct { #ifdef WORDS_BIGENDIAN int64 hi; /* most significant 64 bits, including sign */ uint64 lo; /* least significant 64 bits, without sign */ #else uint64 lo; /* least significant 64 bits, without sign */ int64 hi; /* most significant 64 bits, including sign */ #endif } INT128; /* * Add an unsigned int64 value into an INT128 variable. */ static inline void int128_add_uint64(INT128 *i128, uint64 v) { /* * First add the value to the .lo part, then check to see if a carry needs * to be propagated into the .hi part. A carry is needed if both inputs * have high bits set, or if just one input has high bit set while the new * .lo part doesn't. Remember that .lo part is unsigned; we cast to * signed here just as a cheap way to check the high bit. */ uint64 oldlo = i128->lo; i128->lo += v; if (((int64) v < 0 && (int64) oldlo < 0) || (((int64) v < 0 || (int64) oldlo < 0) && (int64) i128->lo >= 0)) i128->hi++; } /* * Add a signed int64 value into an INT128 variable. */ static inline void int128_add_int64(INT128 *i128, int64 v) { /* * This is much like the above except that the carry logic differs for * negative v. Ordinarily we'd need to subtract 1 from the .hi part * (corresponding to adding the sign-extended bits of v to it); but if * there is a carry out of the .lo part, that cancels and we do nothing. */ uint64 oldlo = i128->lo; i128->lo += v; if (v >= 0) { if ((int64) oldlo < 0 && (int64) i128->lo >= 0) i128->hi++; } else { if (!((int64) oldlo < 0 || (int64) i128->lo >= 0)) i128->hi--; } } /* * INT64_AU32 extracts the most significant 32 bits of int64 as int64, while * INT64_AL32 extracts the least significant 32 bits as uint64. */ #define INT64_AU32(i64) ((i64) >> 32) #define INT64_AL32(i64) ((i64) & UINT64CONST(0xFFFFFFFF)) /* * Add the 128-bit product of two int64 values into an INT128 variable. */ static inline void int128_add_int64_mul_int64(INT128 *i128, int64 x, int64 y) { /* INT64_AU32 must use arithmetic right shift */ StaticAssertDecl(((int64) -1 >> 1) == (int64) -1, "arithmetic right shift is needed"); /*---------- * Form the 128-bit product x * y using 64-bit arithmetic. * Considering each 64-bit input as having 32-bit high and low parts, * we can compute * * x * y = ((x.hi << 32) + x.lo) * (((y.hi << 32) + y.lo) * = (x.hi * y.hi) << 64 + * (x.hi * y.lo) << 32 + * (x.lo * y.hi) << 32 + * x.lo * y.lo * * Each individual product is of 32-bit terms so it won't overflow when * computed in 64-bit arithmetic. Then we just have to shift it to the * correct position while adding into the 128-bit result. We must also * keep in mind that the "lo" parts must be treated as unsigned. *---------- */ /* No need to work hard if product must be zero */ if (x != 0 && y != 0) { int64 x_u32 = INT64_AU32(x); uint64 x_l32 = INT64_AL32(x); int64 y_u32 = INT64_AU32(y); uint64 y_l32 = INT64_AL32(y); int64 tmp; /* the first term */ i128->hi += x_u32 * y_u32; /* the second term: sign-extend it only if x is negative */ tmp = x_u32 * y_l32; if (x < 0) i128->hi += INT64_AU32(tmp); else i128->hi += ((uint64) tmp) >> 32; int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32); /* the third term: sign-extend it only if y is negative */ tmp = x_l32 * y_u32; if (y < 0) i128->hi += INT64_AU32(tmp); else i128->hi += ((uint64) tmp) >> 32; int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32); /* the fourth term: always unsigned */ int128_add_uint64(i128, x_l32 * y_l32); } } /* * Compare two INT128 values, return -1, 0, or +1. */ static inline int int128_compare(INT128 x, INT128 y) { if (x.hi < y.hi) return -1; if (x.hi > y.hi) return 1; if (x.lo < y.lo) return -1; if (x.lo > y.lo) return 1; return 0; } /* * Widen int64 to INT128. */ static inline INT128 int64_to_int128(int64 v) { INT128 val; val.lo = (uint64) v; val.hi = (v < 0) ? -INT64CONST(1) : INT64CONST(0); return val; } /* * Convert INT128 to int64 (losing any high-order bits). * This also works fine for casting down to uint64. */ static inline int64 int128_to_int64(INT128 val) { return (int64) val.lo; } #endif /* USE_NATIVE_INT128 */ #endif /* INT128_H */