I wrote:
> Looking at what we've got here, it's already a substantial fraction of
> what would be needed to provide a compiler-independent implementation
> of the int128-based aggregate logic in numeric.c. With that in mind,
> I propose that we extract the relevant stuff into a new header file
> that is designed as general-purpose int128 support. Something like the
> attached. I also attach the test program I put together to verify it.
Here's a fleshed-out patch for the original problem based on that.
I found that direct int64-to-int128 coercions were also needed to
handle some of the steps in timestamp.c, so I added those to int128.h.
I think it would be reasonable to back-patch this, although it would
need some adjustments for the back branches since we only recently
got rid of the float-timestamp option. Also I'd not be inclined to
depend on native int128 any further back than it was already in use.
regards, tom lane
diff --git a/src/backend/utils/adt/int128.c b/src/backend/utils/adt/int128.c
index ...8bc0663 .
*** a/src/backend/utils/adt/int128.c
--- b/src/backend/utils/adt/int128.c
***************
*** 0 ****
--- 1,181 ----
+ /*-------------------------------------------------------------------------
+ *
+ * int128.c
+ * Testbed for roll-our-own 128-bit integer arithmetic.
+ *
+ * This file is not meant to be compiled into the backend; rather, it builds
+ * a standalone test program that compares the behavior of an implementation
+ * in int128.h to an (assumed correct) int128 native type.
+ *
+ * Copyright (c) 2017, PostgreSQL Global Development Group
+ *
+ *
+ * IDENTIFICATION
+ * src/backend/utils/adt/int128.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+ #include "postgres.h"
+
+ /*
+ * By default, we test the non-native implementation in int128.h; but
+ * by predefining USE_NATIVE_INT128 to 1, you can test the native
+ * implementation, just to be sure.
+ */
+ #ifndef USE_NATIVE_INT128
+ #define USE_NATIVE_INT128 0
+ #endif
+
+ #include "utils/int128.h"
+
+ /*
+ * We assume the parts of this union are laid out compatibly.
+ */
+ typedef union
+ {
+ int128 i128;
+ INT128 I128;
+ union
+ {
+ #ifdef WORDS_BIGENDIAN
+ int64 hi;
+ uint64 lo;
+ #else
+ uint64 lo;
+ int64 hi;
+ #endif
+ } hl;
+ } test128;
+
+
+ /*
+ * Control version of comparator.
+ */
+ static inline int
+ my_int128_compare(int128 x, int128 y)
+ {
+ if (x < y)
+ return -1;
+ if (x > y)
+ return 1;
+ return 0;
+ }
+
+ /*
+ * Get a random uint64 value.
+ * We don't assume random() is good for more than 16 bits.
+ */
+ static uint64
+ get_random_uint64(void)
+ {
+ uint64 x;
+
+ x = (uint64) (random() & 0xFFFF) << 48;
+ x |= (uint64) (random() & 0xFFFF) << 32;
+ x |= (uint64) (random() & 0xFFFF) << 16;
+ x |= (uint64) (random() & 0xFFFF);
+ return x;
+ }
+
+ /*
+ * Main program.
+ *
+ * You can give it a loop count if you don't like the default 1B iterations.
+ */
+ int
+ main(int argc, char **argv)
+ {
+ long count;
+
+ if (argc >= 2)
+ count = strtol(argv[1], NULL, 0);
+ else
+ count = 1000000000;
+
+ while (count-- > 0)
+ {
+ int64 x = get_random_uint64();
+ int64 y = get_random_uint64();
+ int64 z = get_random_uint64();
+ test128 t1;
+ test128 t2;
+
+ /* check unsigned addition */
+ t1.hl.hi = x;
+ t1.hl.lo = y;
+ t2 = t1;
+ t1.i128 += (int128) (uint64) z;
+ int128_add_uint64(&t2.I128, (uint64) z);
+
+ if (t1.hl.hi != t2.hl.hi || t1.hl.lo != t2.hl.lo)
+ {
+ printf("%016lX%016lX + unsigned %lX\n", x, y, z);
+ printf("native = %016lX%016lX\n", t1.hl.hi, t1.hl.lo);
+ printf("result = %016lX%016lX\n", t2.hl.hi, t2.hl.lo);
+ return 1;
+ }
+
+ /* check signed addition */
+ t1.hl.hi = x;
+ t1.hl.lo = y;
+ t2 = t1;
+ t1.i128 += (int128) z;
+ int128_add_int64(&t2.I128, z);
+
+ if (t1.hl.hi != t2.hl.hi || t1.hl.lo != t2.hl.lo)
+ {
+ printf("%016lX%016lX + signed %lX\n", x, y, z);
+ printf("native = %016lX%016lX\n", t1.hl.hi, t1.hl.lo);
+ printf("result = %016lX%016lX\n", t2.hl.hi, t2.hl.lo);
+ return 1;
+ }
+
+ /* check multiplication */
+ t1.i128 = (int128) x *(int128) y;
+
+ t2.hl.hi = t2.hl.lo = 0;
+ int128_add_int64_mul_int64(&t2.I128, x, y);
+
+ if (t1.hl.hi != t2.hl.hi || t1.hl.lo != t2.hl.lo)
+ {
+ printf("%lX * %lX\n", x, y);
+ printf("native = %016lX%016lX\n", t1.hl.hi, t1.hl.lo);
+ printf("result = %016lX%016lX\n", t2.hl.hi, t2.hl.lo);
+ return 1;
+ }
+
+ /* check comparison */
+ t1.hl.hi = x;
+ t1.hl.lo = y;
+ t2.hl.hi = z;
+ t2.hl.lo = get_random_uint64();
+
+ if (my_int128_compare(t1.i128, t2.i128) !=
+ int128_compare(t1.I128, t2.I128))
+ {
+ printf("comparison failure: %d vs %d\n",
+ my_int128_compare(t1.i128, t2.i128),
+ int128_compare(t1.I128, t2.I128));
+ printf("arg1 = %016lX%016lX\n", t1.hl.hi, t1.hl.lo);
+ printf("arg2 = %016lX%016lX\n", t2.hl.hi, t2.hl.lo);
+ return 1;
+ }
+
+ /* check case with identical hi parts; above will hardly ever hit it */
+ t2.hl.hi = x;
+
+ if (my_int128_compare(t1.i128, t2.i128) !=
+ int128_compare(t1.I128, t2.I128))
+ {
+ printf("comparison failure: %d vs %d\n",
+ my_int128_compare(t1.i128, t2.i128),
+ int128_compare(t1.I128, t2.I128));
+ printf("arg1 = %016lX%016lX\n", t1.hl.hi, t1.hl.lo);
+ printf("arg2 = %016lX%016lX\n", t2.hl.hi, t2.hl.lo);
+ return 1;
+ }
+ }
+
+ return 0;
+ }
diff --git a/src/backend/utils/adt/timestamp.c b/src/backend/utils/adt/timestamp.c
index 4be1999..88ecb78 100644
*** a/src/backend/utils/adt/timestamp.c
--- b/src/backend/utils/adt/timestamp.c
***************
*** 33,38 ****
--- 33,40 ----
#include "utils/array.h"
#include "utils/builtins.h"
#include "utils/datetime.h"
+ #include "utils/int128.h"
+
/*
* gcc's -ffast-math switch breaks routines that expect exact results from
*************** timestamptz_cmp_timestamp(PG_FUNCTION_AR
*** 2288,2302 ****
/*
* interval_relop - is interval1 relop interval2
*/
! static inline TimeOffset
interval_cmp_value(const Interval *interval)
{
! TimeOffset span;
! span = interval->time;
! span += interval->month * INT64CONST(30) * USECS_PER_DAY;
! span += interval->day * INT64CONST(24) * USECS_PER_HOUR;
return span;
}
--- 2290,2324 ----
/*
* interval_relop - is interval1 relop interval2
+ *
+ * Interval comparison is based on converting interval values to a linear
+ * representation expressed in the units of the time field (microseconds,
+ * in the case of integer timestamps) with days assumed to be always 24 hours
+ * and months assumed to be always 30 days. To avoid overflow, we need a
+ * wider-than-int64 datatype for the linear representation, so use INT128.
*/
!
! static inline INT128
interval_cmp_value(const Interval *interval)
{
! INT128 span;
! int64 dayfraction;
! int64 days;
! /*
! * Separate time field into days and dayfraction, then add the month and
! * day fields to the days part. We cannot overflow int64 days here.
! */
! dayfraction = interval->time % USECS_PER_DAY;
! days = interval->time / USECS_PER_DAY;
! days += interval->month * INT64CONST(30);
! days += interval->day;
!
! /* Widen dayfraction to 128 bits */
! span = int64_to_int128(dayfraction);
!
! /* Scale up days to microseconds, forming a 128-bit product */
! int128_add_int64_mul_int64(&span, days, USECS_PER_DAY);
return span;
}
*************** interval_cmp_value(const Interval *inter
*** 2304,2313 ****
static int
interval_cmp_internal(Interval *interval1, Interval *interval2)
{
! TimeOffset span1 = interval_cmp_value(interval1);
! TimeOffset span2 = interval_cmp_value(interval2);
! return ((span1 < span2) ? -1 : (span1 > span2) ? 1 : 0);
}
Datum
--- 2326,2335 ----
static int
interval_cmp_internal(Interval *interval1, Interval *interval2)
{
! INT128 span1 = interval_cmp_value(interval1);
! INT128 span2 = interval_cmp_value(interval2);
! return int128_compare(span1, span2);
}
Datum
*************** Datum
*** 2384,2392 ****
interval_hash(PG_FUNCTION_ARGS)
{
Interval *interval = PG_GETARG_INTERVAL_P(0);
! TimeOffset span = interval_cmp_value(interval);
! return DirectFunctionCall1(hashint8, Int64GetDatumFast(span));
}
/* overlaps_timestamp() --- implements the SQL OVERLAPS operator.
--- 2406,2423 ----
interval_hash(PG_FUNCTION_ARGS)
{
Interval *interval = PG_GETARG_INTERVAL_P(0);
! INT128 span = interval_cmp_value(interval);
! int64 span64;
! /*
! * Use only the least significant 64 bits for hashing. The upper 64 bits
! * seldom add any useful information, and besides we must do it like this
! * for compatibility with hashes calculated before use of INT128 was
! * introduced.
! */
! span64 = int128_to_int64(span);
!
! return DirectFunctionCall1(hashint8, Int64GetDatumFast(span64));
}
/* overlaps_timestamp() --- implements the SQL OVERLAPS operator.
diff --git a/src/include/utils/int128.h b/src/include/utils/int128.h
index ...876610b .
*** a/src/include/utils/int128.h
--- b/src/include/utils/int128.h
***************
*** 0 ****
--- 1,274 ----
+ /*-------------------------------------------------------------------------
+ *
+ * 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.
+ *
+ * Copyright (c) 2017, PostgreSQL Global Development Group
+ *
+ * src/include/utils/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 */
diff --git a/src/test/regress/expected/interval.out b/src/test/regress/expected/interval.out
index 946c97a..d4e6a00 100644
*** a/src/test/regress/expected/interval.out
--- b/src/test/regress/expected/interval.out
*************** SELECT '' AS fortyfive, r1.*, r2.*
*** 207,212 ****
--- 207,248 ----
| 34 years | 6 years
(45 rows)
+ -- intervals out of 64bit linear value in microseconds
+ CREATE TABLE INTERVAL_TBL_OF (f1 interval);
+ INSERT INTO INTERVAL_TBL_OF (f1) VALUES ('2147483647 days 2147483647 months');
+ INSERT INTO INTERVAL_TBL_OF (f1) VALUES ('1 year');
+ INSERT INTO INTERVAL_TBL_OF (f1) VALUES ('-2147483648 days -2147483648 months');
+ SELECT '' AS "64bits", r1.*, r2.*
+ FROM INTERVAL_TBL_OF r1, INTERVAL_TBL_OF r2
+ WHERE r1.f1 > r2.f1
+ ORDER BY r1.f1, r2.f1;
+ 64bits | f1 | f1
+ --------+----------------------------------------+-------------------------------------------
+ | 1 year | -178956970 years -8 mons -2147483648 days
+ | 178956970 years 7 mons 2147483647 days | -178956970 years -8 mons -2147483648 days
+ | 178956970 years 7 mons 2147483647 days | 1 year
+ (3 rows)
+
+ CREATE INDEX ON INTERVAL_TBL_OF USING btree (f1);
+ SET enable_seqscan to false;
+ EXPLAIN SELECT '' AS "64bits_2", f1
+ FROM INTERVAL_TBL_OF r1 ORDER BY f1;
+ QUERY PLAN
+ --------------------------------------------------------------------------------------------------------
+ Index Only Scan using interval_tbl_of_f1_idx on interval_tbl_of r1 (cost=0.13..12.18 rows=3 width=48)
+ (1 row)
+
+ SELECT '' AS "64bits_2", f1
+ FROM INTERVAL_TBL_OF r1 ORDER BY f1;
+ 64bits_2 | f1
+ ----------+-------------------------------------------
+ | -178956970 years -8 mons -2147483648 days
+ | 1 year
+ | 178956970 years 7 mons 2147483647 days
+ (3 rows)
+
+ SET enable_seqscan to default;
+ DROP TABLE INTERVAL_TBL_OF;
-- Test multiplication and division with intervals.
-- Floating point arithmetic rounding errors can lead to unexpected results,
-- though the code attempts to do the right thing and round up to days and
diff --git a/src/test/regress/sql/interval.sql b/src/test/regress/sql/interval.sql
index cff9ada..aa21673 100644
*** a/src/test/regress/sql/interval.sql
--- b/src/test/regress/sql/interval.sql
*************** SELECT '' AS fortyfive, r1.*, r2.*
*** 59,64 ****
--- 59,81 ----
WHERE r1.f1 > r2.f1
ORDER BY r1.f1, r2.f1;
+ -- intervals out of 64bit linear value in microseconds
+ CREATE TABLE INTERVAL_TBL_OF (f1 interval);
+ INSERT INTO INTERVAL_TBL_OF (f1) VALUES ('2147483647 days 2147483647 months');
+ INSERT INTO INTERVAL_TBL_OF (f1) VALUES ('1 year');
+ INSERT INTO INTERVAL_TBL_OF (f1) VALUES ('-2147483648 days -2147483648 months');
+ SELECT '' AS "64bits", r1.*, r2.*
+ FROM INTERVAL_TBL_OF r1, INTERVAL_TBL_OF r2
+ WHERE r1.f1 > r2.f1
+ ORDER BY r1.f1, r2.f1;
+ CREATE INDEX ON INTERVAL_TBL_OF USING btree (f1);
+ SET enable_seqscan to false;
+ EXPLAIN SELECT '' AS "64bits_2", f1
+ FROM INTERVAL_TBL_OF r1 ORDER BY f1;
+ SELECT '' AS "64bits_2", f1
+ FROM INTERVAL_TBL_OF r1 ORDER BY f1;
+ SET enable_seqscan to default;
+ DROP TABLE INTERVAL_TBL_OF;
-- Test multiplication and division with intervals.
-- Floating point arithmetic rounding errors can lead to unexpected results,
--
Sent via pgsql-general mailing list (pgsql-general@xxxxxxxxxxxxxx)
To make changes to your subscription:
http://www.postgresql.org/mailpref/pgsql-general
