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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, 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 */
StaticAssertStmt(((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 */
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