Hi hackers, attached is a proof of concept patch adding a new base type
called "rational" to represent fractions. It includes arithmetic,
simplification, conversion to/from float, finding intermediates with a
stern-brocot tree, custom aggregates, and btree/hash indices.
The primary motivation was as a column type to support user-defined
ordering of rows (with the ability to dynamically rearrange rows). The
postgres wiki has a page [0] about this using pairs of integers to
represent fractions, but it's not particularly elegant.
I wrote about options for implementing user-defined order in an article
[1] and ended up creating a postgres extension, pg_rational [2], to
provide the new type. People have been using the extension, but told me
they wished they could use it on hosted platforms like Amazon RDS which
have a limited set of whitelisted extensions. Thus I'm submitting this
patch to discuss getting the feature in core postgres.
For usage, see the included regression test. To see how it works for the
user-defined order use case see my article. I haven't included docs in
the patch since the interface may change with community feedback.
0: https://wiki.postgresql.org/wiki/User-specified_ordering_with_fractions
1: https://begriffs.com/posts/2018-03-20-user-defined-order.html
2: https://github.com/begriffs/pg_rational
--
Joe Nelson https://begriffs.com
diff --git a/src/backend/utils/adt/Makefile b/src/backend/utils/adt/Makefile
index 13efa9338c..10bdcff5dc 100644
--- a/src/backend/utils/adt/Makefile
+++ b/src/backend/utils/adt/Makefile
@@ -80,6 +80,7 @@ OBJS = \
rangetypes_selfuncs.o \
rangetypes_spgist.o \
rangetypes_typanalyze.o \
+ rational.o \
regexp.o \
regproc.o \
ri_triggers.o \
diff --git a/src/backend/utils/adt/rational.c b/src/backend/utils/adt/rational.c
new file mode 100644
index 0000000000..ab91198da3
--- /dev/null
+++ b/src/backend/utils/adt/rational.c
@@ -0,0 +1,637 @@
+/*-------------------------------------------------------------------------
+ *
+ * rational.c
+ * Rational number data type for the Postgres database system
+ *
+ * Copyright (c) 1998-2020, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ * src/backend/utils/adt/rational.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "postgres.h"
+#include "fmgr.h"
+#include "access/hash.h"
+#include "common/int.h" /* portable overflow detection */
+#include "libpq/pqformat.h" /* send/recv functions */
+#include <limits.h>
+#include <math.h>
+
+PG_MODULE_MAGIC;
+
+typedef struct
+{
+ int32 numer;
+ int32 denom;
+} Rational;
+
+static int32 gcd(int32, int32);
+static bool simplify(Rational *);
+static int32 cmp(Rational *, Rational *);
+static void neg(Rational *);
+static Rational * create(long long, long long);
+static Rational * add(Rational *, Rational *);
+static Rational * mul(Rational *, Rational *);
+static void mediant(Rational *, Rational *, Rational *);
+
+/*
+ ***************** IO ******************
+ */
+
+PG_FUNCTION_INFO_V1(rational_in);
+PG_FUNCTION_INFO_V1(rational_in_float);
+PG_FUNCTION_INFO_V1(rational_out);
+PG_FUNCTION_INFO_V1(rational_out_float);
+PG_FUNCTION_INFO_V1(rational_recv);
+PG_FUNCTION_INFO_V1(rational_create);
+PG_FUNCTION_INFO_V1(rational_in_integer);
+PG_FUNCTION_INFO_V1(rational_send);
+
+Datum
+rational_in(PG_FUNCTION_ARGS)
+{
+ char *s = PG_GETARG_CSTRING(0),
+ *after;
+ long long n,
+ d;
+
+ if (!isdigit(*s) && *s != '-')
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+ errmsg("Missing or invalid numerator")));
+
+ n = strtoll(s, &after, 10);
+
+ if (*after == '\0')
+ {
+ /* if just a number and no slash, interpret as an int */
+ d = 1;
+ }
+ else
+ {
+ /* otherwise look for denominator */
+ if (*after != '/')
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+ errmsg("Expecting '/' after number but found '%c'", *after)));
+ if (*(++after) == '\0')
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+ errmsg("Expecting value after '/' but got '\\0'")));
+
+ d = strtoll(after, &after, 10);
+ if (*after != '\0')
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+ errmsg("Expecting '\\0' but found '%c'", *after)));
+ }
+ PG_RETURN_POINTER(create(n, d));
+}
+
+/*
+ This function taken from John Kennedy's paper, "Algorithm To Convert a
+ Decimal to a Fraction." Translated from Pascal.
+*/
+Datum
+rational_in_float(PG_FUNCTION_ARGS)
+{
+ float8 target = PG_GETARG_FLOAT8(0),
+ z,
+ fnumer,
+ fdenom,
+ error;
+ int32 prev_denom,
+ sign;
+ Rational *result = palloc(sizeof(Rational));
+
+ if (target == (int32) target)
+ {
+ result->numer = (int32) target;
+ result->denom = 1;
+ PG_RETURN_POINTER(result);
+ }
+
+ sign = target < 0.0 ? -1 : 1;
+ target = fabs(target);
+
+ if (!(target <= INT32_MAX))
+ { /* also excludes NaN's */
+ ereport(ERROR,
+ (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+ errmsg("value too large for rational")));
+ }
+ z = target;
+ prev_denom = 0;
+ result->numer = (int32) round(target);
+ result->denom = 1;
+ do
+ {
+ z = 1.0 / (z - floor(z));
+ fdenom = result->denom * floor(z) + prev_denom;
+ fnumer = round(target * fdenom);
+ if (fnumer > INT32_MAX || fdenom > INT32_MAX)
+ break;
+ prev_denom = result->denom;
+ result->numer = (int32) fnumer;
+ result->denom = (int32) fdenom;
+
+ error = fabs(target - ((float8) result->numer / (float8) result->denom));
+ } while (z != floor(z) && error >= 1e-12);
+
+ result->numer *= sign;
+ PG_RETURN_POINTER(result);
+}
+
+Datum
+rational_out(PG_FUNCTION_ARGS)
+{
+ Rational *r = (Rational *) PG_GETARG_POINTER(0);
+
+ PG_RETURN_CSTRING(psprintf("%d/%d", r->numer, r->denom));
+}
+
+Datum
+rational_out_float(PG_FUNCTION_ARGS)
+{
+ Rational *r = (Rational *) PG_GETARG_POINTER(0);
+
+ PG_RETURN_FLOAT8((float8) r->numer / (float8) r->denom);
+}
+
+Datum
+rational_recv(PG_FUNCTION_ARGS)
+{
+ StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
+
+ PG_RETURN_POINTER(create(pq_getmsgint(buf, sizeof(int32)),
+ pq_getmsgint(buf, sizeof(int32))));
+}
+
+Datum
+rational_create(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_POINTER(create(PG_GETARG_INT32(0), PG_GETARG_INT32(1)));
+}
+
+Datum
+rational_in_integer(PG_FUNCTION_ARGS)
+{
+ int32 n = PG_GETARG_INT32(0);
+ Rational *result = palloc(sizeof(Rational));
+
+ result->numer = n;
+ result->denom = 1;
+
+ PG_RETURN_POINTER(result);
+}
+
+Datum
+rational_send(PG_FUNCTION_ARGS)
+{
+ Rational *r = (Rational *) PG_GETARG_POINTER(0);
+ StringInfoData buf;
+
+ pq_begintypsend(&buf);
+ pq_sendint(&buf, r->numer, sizeof(int32));
+ pq_sendint(&buf, r->denom, sizeof(int32));
+
+ PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ ************* ARITHMETIC **************
+ */
+
+PG_FUNCTION_INFO_V1(rational_simplify);
+PG_FUNCTION_INFO_V1(rational_add);
+PG_FUNCTION_INFO_V1(rational_sub);
+PG_FUNCTION_INFO_V1(rational_mul);
+PG_FUNCTION_INFO_V1(rational_div);
+PG_FUNCTION_INFO_V1(rational_neg);
+
+Datum
+rational_simplify(PG_FUNCTION_ARGS)
+{
+ Rational *in = (Rational *) PG_GETARG_POINTER(0);
+ Rational *out = palloc(sizeof(Rational));
+
+ memcpy(out, in, sizeof(Rational));
+ simplify(out);
+
+ PG_RETURN_POINTER(out);
+}
+
+Datum
+rational_add(PG_FUNCTION_ARGS)
+{
+ Rational x,
+ y;
+
+ memcpy(&x, PG_GETARG_POINTER(0), sizeof(Rational));
+ memcpy(&y, PG_GETARG_POINTER(1), sizeof(Rational));
+
+ PG_RETURN_POINTER(add(&x, &y));
+}
+
+Datum
+rational_sub(PG_FUNCTION_ARGS)
+{
+ Rational x,
+ y;
+
+ memcpy(&x, PG_GETARG_POINTER(0), sizeof(Rational));
+ memcpy(&y, PG_GETARG_POINTER(1), sizeof(Rational));
+
+ neg(&y);
+ PG_RETURN_POINTER(add(&x, &y));
+}
+
+Datum
+rational_mul(PG_FUNCTION_ARGS)
+{
+ Rational x,
+ y;
+
+ memcpy(&x, PG_GETARG_POINTER(0), sizeof(Rational));
+ memcpy(&y, PG_GETARG_POINTER(1), sizeof(Rational));
+
+ PG_RETURN_POINTER(mul(&x, &y));
+}
+
+Datum
+rational_div(PG_FUNCTION_ARGS)
+{
+ Rational x,
+ y;
+ int32 tmp;
+
+ memcpy(&x, PG_GETARG_POINTER(0), sizeof(Rational));
+ memcpy(&y, PG_GETARG_POINTER(1), sizeof(Rational));
+ tmp = y.numer;
+ y.numer = y.denom;
+ y.denom = tmp;
+
+ PG_RETURN_POINTER(mul(&x, &y));
+}
+
+Datum
+rational_neg(PG_FUNCTION_ARGS)
+{
+ Rational *out = palloc(sizeof(Rational));
+
+ memcpy(out, PG_GETARG_POINTER(0), sizeof(Rational));
+ neg(out);
+
+ PG_RETURN_POINTER(out);
+}
+
+/*
+ *************** UTILITY ***************
+ */
+
+PG_FUNCTION_INFO_V1(rational_hash);
+PG_FUNCTION_INFO_V1(rational_intermediate);
+
+Datum
+rational_hash(PG_FUNCTION_ARGS)
+{
+ Rational x;
+
+ memcpy(&x, PG_GETARG_POINTER(0), sizeof(Rational));
+
+ /*
+ * hash_any works at binary level, so we must simplify fraction
+ */
+ simplify(&x);
+
+ return hash_any((const unsigned char *) &x, sizeof(Rational));
+}
+
+Datum
+rational_intermediate(PG_FUNCTION_ARGS)
+{
+ Rational x,
+ y, /* arguments */
+ lo = {0, 1},
+ hi = {1, 0}, /* yes, an internal use of 1/0 */
+ *med = palloc(sizeof(Rational));
+
+ /*
+ * x = coalesce(lo, arg[0]) y = coalesce(hi, arg[1])
+ */
+ memcpy(&x,
+ PG_ARGISNULL(0) ? &lo : (Rational *) PG_GETARG_POINTER(0),
+ sizeof(Rational));
+ memcpy(&y,
+ PG_ARGISNULL(1) ? &hi : (Rational *) PG_GETARG_POINTER(1),
+ sizeof(Rational));
+
+ if (cmp(&x, &lo) < 0 || cmp(&y, &lo) < 0)
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+ errmsg("arguments must be non-negative")));
+
+ if (cmp(&x, &y) >= 0)
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+ errmsg("first argument must be strictly smaller than second")));
+
+ while (true)
+ {
+ mediant(&lo, &hi, med);
+ if (cmp(med, &x) < 1)
+ memcpy(&lo, med, sizeof(Rational));
+ else if (cmp(med, &y) > -1)
+ memcpy(&hi, med, sizeof(Rational));
+ else
+ break;
+ }
+
+ PG_RETURN_POINTER(med);
+}
+
+
+/*
+ ************* COMPARISON **************
+ */
+
+
+PG_FUNCTION_INFO_V1(rational_cmp);
+PG_FUNCTION_INFO_V1(rational_eq);
+PG_FUNCTION_INFO_V1(rational_ne);
+PG_FUNCTION_INFO_V1(rational_lt);
+PG_FUNCTION_INFO_V1(rational_le);
+PG_FUNCTION_INFO_V1(rational_gt);
+PG_FUNCTION_INFO_V1(rational_ge);
+
+PG_FUNCTION_INFO_V1(rational_smaller);
+PG_FUNCTION_INFO_V1(rational_larger);
+
+Datum
+rational_cmp(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_INT32(
+ cmp((Rational *) PG_GETARG_POINTER(0), (Rational *) PG_GETARG_POINTER(1)));
+}
+
+Datum
+rational_eq(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_BOOL(
+ cmp((Rational *) PG_GETARG_POINTER(0), (Rational *) PG_GETARG_POINTER(1)) == 0);
+}
+
+Datum
+rational_ne(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_BOOL(
+ cmp((Rational *) PG_GETARG_POINTER(0), (Rational *) PG_GETARG_POINTER(1)) != 0);
+}
+
+Datum
+rational_lt(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_BOOL(
+ cmp((Rational *) PG_GETARG_POINTER(0), (Rational *) PG_GETARG_POINTER(1)) < 0);
+}
+
+Datum
+rational_le(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_BOOL(
+ cmp((Rational *) PG_GETARG_POINTER(0), (Rational *) PG_GETARG_POINTER(1)) <= 0);
+}
+
+Datum
+rational_gt(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_BOOL(
+ cmp((Rational *) PG_GETARG_POINTER(0), (Rational *) PG_GETARG_POINTER(1)) > 0);
+}
+
+Datum
+rational_ge(PG_FUNCTION_ARGS)
+{
+ PG_RETURN_BOOL(
+ cmp((Rational *) PG_GETARG_POINTER(0), (Rational *) PG_GETARG_POINTER(1)) >= 0);
+}
+
+Datum
+rational_smaller(PG_FUNCTION_ARGS)
+{
+ Rational *a = (Rational *) PG_GETARG_POINTER(0),
+ *b = (Rational *) PG_GETARG_POINTER(1);
+
+ PG_RETURN_POINTER(cmp(a, b) < 0 ? a : b);
+}
+
+Datum
+rational_larger(PG_FUNCTION_ARGS)
+{
+ Rational *a = (Rational *) PG_GETARG_POINTER(0),
+ *b = (Rational *) PG_GETARG_POINTER(1);
+
+ PG_RETURN_POINTER(cmp(a, b) > 0 ? a : b);
+}
+
+
+/*
+ ************** INTERNAL ***************
+ */
+
+int32
+gcd(int32 a, int32 b)
+{
+ int32 temp;
+
+ while (b != 0)
+ {
+ temp = a % b;
+ a = b;
+ b = temp;
+ }
+
+ return a;
+}
+
+bool
+simplify(Rational * r)
+{
+ int32 common = gcd(r->numer, r->denom);
+
+ /*
+ * tricky: avoid overflow from (INT32_MIN / -1)
+ */
+ if (common != -1 || (r->numer != INT32_MIN && r->denom != INT32_MIN))
+ {
+ r->numer /= common;
+ r->denom /= common;
+ }
+
+ /*
+ * prevent negative denominator, but do not negate the smallest value --
+ * that would produce overflow
+ */
+ if (r->denom < 0 && r->numer != INT32_MIN && r->denom != INT32_MIN)
+ {
+ r->numer *= -1;
+ r->denom *= -1;
+ }
+ return (common != 1) && (common != -1);
+}
+
+int32
+cmp(Rational * a, Rational * b)
+{
+ /*
+ * Overflow is not an option, we need a total order so that btree indices
+ * do not die. Hence do the arithmetic in 64 bits.
+ */
+ int64 cross1 = (int64) a->numer * (int64) b->denom,
+ cross2 = (int64) a->denom * (int64) b->numer;
+
+ return (cross1 > cross2) - (cross1 < cross2);
+}
+
+void
+neg(Rational * r)
+{
+ if (r->numer == INT32_MIN)
+ {
+ simplify(r);
+
+ /*
+ * check again
+ */
+ if (r->numer == INT32_MIN)
+ {
+ /*
+ * denom can't be MIN too or fraction would have previously
+ * simplified to 1/1
+ */
+ r->denom *= -1;
+ return;
+ }
+ }
+ r->numer *= -1;
+}
+
+
+Rational *
+create(long long n, long long d)
+{
+ Rational *result = palloc(sizeof(Rational));
+
+ if (d == 0)
+ ereport(ERROR,
+ (errcode(ERRCODE_DIVISION_BY_ZERO),
+ errmsg("fraction cannot have zero denominator")));
+
+ if (n < INT32_MIN || n > INT32_MAX || d < INT32_MIN || d > INT32_MAX)
+ ereport(ERROR,
+ (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+ errmsg("numerator or denominator outside valid int32 value")));
+
+ /*
+ * prevent negative denominator, but do not negate the smallest value or
+ * else it would overflow
+ */
+ if (d >= 0 || n == INT32_MIN || d == INT32_MIN)
+ {
+ result->numer = (int32) n;
+ result->denom = (int32) d;
+ }
+ else
+ {
+ result->numer = (int32) -n;
+ result->denom = (int32) -d;
+ }
+
+ return result;
+}
+
+Rational *
+add(Rational * x, Rational * y)
+{
+ int32 xnyd,
+ ynxd,
+ numer,
+ denom;
+ bool nxyd_bad,
+ ynxd_bad,
+ numer_bad,
+ denom_bad;
+ Rational *result;
+
+retry_add:
+ nxyd_bad = pg_mul_s32_overflow(x->numer, y->denom, &xnyd);
+ ynxd_bad = pg_mul_s32_overflow(y->numer, x->denom, &ynxd);
+ numer_bad = pg_add_s32_overflow(xnyd, ynxd, &numer);
+ denom_bad = pg_mul_s32_overflow(x->denom, y->denom, &denom);
+
+ if (nxyd_bad || ynxd_bad || numer_bad || denom_bad)
+ {
+ /* overflow in intermediate value */
+ if (!simplify(x) && !simplify(y))
+ {
+ /* neither fraction could reduce, cannot proceed */
+ ereport(ERROR, (
+ errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+ errmsg("intermediate value overflow in rational addition")
+ ));
+ }
+ /* the fraction(s) reduced, good for one more retry */
+ goto retry_add;
+ }
+ result = palloc(sizeof(Rational));
+ result->numer = numer;
+ result->denom = denom;
+ return result;
+}
+
+Rational *
+mul(Rational * x, Rational * y)
+{
+ int32 numer,
+ denom;
+ bool numer_bad,
+ denom_bad;
+ Rational *result;
+
+retry_mul:
+ numer_bad = pg_mul_s32_overflow(x->numer, y->numer, &numer);
+ denom_bad = pg_mul_s32_overflow(x->denom, y->denom, &denom);
+
+ if (numer_bad || denom_bad)
+ {
+ /* overflow in intermediate value */
+ if (!simplify(x) && !simplify(y))
+ {
+ /* neither fraction could reduce, cannot proceed */
+ ereport(ERROR,
+ (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+ errmsg("intermediate value overflow in rational multiplication")));
+ }
+ /* the fraction(s) reduced, good for one more retry */
+ goto retry_mul;
+ }
+ result = palloc(sizeof(Rational));
+ result->numer = numer;
+ result->denom = denom;
+
+ return result;
+}
+
+void
+mediant(Rational * x, Rational * y, Rational * m)
+{
+ /*
+ * Rational_intermediate sends fractions with small numers and denoms, and
+ * slowly builds up. The search will take forever before we ever get close
+ * to arithmetic overflow in this function, so I don't guard it here.
+ */
+ m->numer = x->numer + y->numer;
+ m->denom = x->denom + y->denom;
+}
diff --git a/src/include/catalog/pg_aggregate.dat b/src/include/catalog/pg_aggregate.dat
index ffabe275c0..3954b2d55e 100644
--- a/src/include/catalog/pg_aggregate.dat
+++ b/src/include/catalog/pg_aggregate.dat
@@ -69,6 +69,8 @@
aggcombinefn => 'float4pl', aggtranstype => 'float4' },
{ aggfnoid => 'sum(float8)', aggtransfn => 'float8pl',
aggcombinefn => 'float8pl', aggtranstype => 'float8' },
+{ aggfnoid => 'sum(rational)', aggtransfn => 'rational_add',
+ aggcombinefn => 'rational_add', aggtranstype => 'rational' },
{ aggfnoid => 'sum(money)', aggtransfn => 'cash_pl', aggcombinefn => 'cash_pl',
aggmtransfn => 'cash_pl', aggminvtransfn => 'cash_mi',
aggtranstype => 'money', aggmtranstype => 'money' },
@@ -104,6 +106,9 @@
{ aggfnoid => 'max(float8)', aggtransfn => 'float8larger',
aggcombinefn => 'float8larger', aggsortop => '>(float8,float8)',
aggtranstype => 'float8' },
+{ aggfnoid => 'max(rational)', aggtransfn => 'rational_larger',
+ aggcombinefn => 'rational_larger', aggsortop => '>(rational,rational)',
+ aggtranstype => 'rational' },
{ aggfnoid => 'max(date)', aggtransfn => 'date_larger',
aggcombinefn => 'date_larger', aggsortop => '>(date,date)',
aggtranstype => 'date' },
@@ -169,6 +174,9 @@
{ aggfnoid => 'min(float8)', aggtransfn => 'float8smaller',
aggcombinefn => 'float8smaller', aggsortop => '<(float8,float8)',
aggtranstype => 'float8' },
+{ aggfnoid => 'min(rational)', aggtransfn => 'rational_smaller',
+ aggcombinefn => 'rational_smaller', aggsortop => '<(rational,rational)',
+ aggtranstype => 'rational' },
{ aggfnoid => 'min(date)', aggtransfn => 'date_smaller',
aggcombinefn => 'date_smaller', aggsortop => '<(date,date)',
aggtranstype => 'date' },
diff --git a/src/include/catalog/pg_amop.dat b/src/include/catalog/pg_amop.dat
index 11aaa519c8..1377f05e64 100644
--- a/src/include/catalog/pg_amop.dat
+++ b/src/include/catalog/pg_amop.dat
@@ -281,6 +281,23 @@
amoprighttype => 'float4', amopstrategy => '5', amopopr => '>(float8,float4)',
amopmethod => 'btree' },
+# default operators rational
+{ amopfamily => 'btree/rational_ops', amoplefttype => 'rational',
+ amoprighttype => 'rational', amopstrategy => '1', amopopr => '<(rational,rational)',
+ amopmethod => 'btree' },
+{ amopfamily => 'btree/rational_ops', amoplefttype => 'rational',
+ amoprighttype => 'rational', amopstrategy => '2',
+ amopopr => '<=(rational,rational)', amopmethod => 'btree' },
+{ amopfamily => 'btree/rational_ops', amoplefttype => 'rational',
+ amoprighttype => 'rational', amopstrategy => '3', amopopr => '=(rational,rational)',
+ amopmethod => 'btree' },
+{ amopfamily => 'btree/rational_ops', amoplefttype => 'rational',
+ amoprighttype => 'rational', amopstrategy => '4',
+ amopopr => '>=(rational,rational)', amopmethod => 'btree' },
+{ amopfamily => 'btree/rational_ops', amoplefttype => 'rational',
+ amoprighttype => 'rational', amopstrategy => '5', amopopr => '>(rational,rational)',
+ amopmethod => 'btree' },
+
# btree char_ops
{ amopfamily => 'btree/char_ops', amoplefttype => 'char',
@@ -903,6 +920,11 @@
amoprighttype => 'float4', amopstrategy => '1', amopopr => '=(float8,float4)',
amopmethod => 'hash' },
+# rational_ops
+{ amopfamily => 'hash/rational_ops', amoplefttype => 'rational',
+ amoprighttype => 'rational', amopstrategy => '1', amopopr => '=(rational,rational)',
+ amopmethod => 'hash' },
+
# network_ops
{ amopfamily => 'hash/network_ops', amoplefttype => 'inet',
amoprighttype => 'inet', amopstrategy => '1', amopopr => '=(inet,inet)',
diff --git a/src/include/catalog/pg_amproc.dat b/src/include/catalog/pg_amproc.dat
index c67768fcab..20c977301e 100644
--- a/src/include/catalog/pg_amproc.dat
+++ b/src/include/catalog/pg_amproc.dat
@@ -91,6 +91,11 @@
{ amprocfamily => 'btree/float_ops', amproclefttype => 'float4',
amprocrighttype => 'float8', amprocnum => '3',
amproc => 'in_range(float4,float4,float8,bool,bool)' },
+
+
+{ amprocfamily => 'btree/rational_ops', amproclefttype => 'rational',
+ amprocrighttype => 'rational', amprocnum => '1', amproc => 'rational_cmp' },
+
{ amprocfamily => 'btree/network_ops', amproclefttype => 'inet',
amprocrighttype => 'inet', amprocnum => '1', amproc => 'network_cmp' },
{ amprocfamily => 'btree/network_ops', amproclefttype => 'inet',
@@ -252,6 +257,8 @@
{ amprocfamily => 'hash/float_ops', amproclefttype => 'float4',
amprocrighttype => 'float4', amprocnum => '2',
amproc => 'hashfloat4extended' },
+{ amprocfamily => 'hash/rational_ops', amproclefttype => 'rational',
+ amprocrighttype => 'rational', amprocnum => '1', amproc => 'hashrational' },
{ amprocfamily => 'hash/float_ops', amproclefttype => 'float8',
amprocrighttype => 'float8', amprocnum => '1', amproc => 'hashfloat8' },
{ amprocfamily => 'hash/float_ops', amproclefttype => 'float8',
diff --git a/src/include/catalog/pg_cast.dat b/src/include/catalog/pg_cast.dat
index 6ef8b8a4e7..21b15b0330 100644
--- a/src/include/catalog/pg_cast.dat
+++ b/src/include/catalog/pg_cast.dat
@@ -36,6 +36,14 @@
castcontext => 'i', castmethod => 'f' },
{ castsource => 'int2', casttarget => 'float8', castfunc => 'float8(int2)',
castcontext => 'i', castmethod => 'f' },
+
+{ castsource => 'float8', casttarget => 'rational', castfunc => 'rational_in_float',
+ castcontext => 'i', castmethod => 'f' },
+{ castsource => 'rational', casttarget => 'float8', castfunc => 'rational_out_float',
+ castcontext => 'e', castmethod => 'f' },
+{ castsource => 'int4', casttarget => 'rational', castfunc => 'rational_in_integer',
+ castcontext => 'i', castmethod => 'f' },
+
{ castsource => 'int2', casttarget => 'numeric', castfunc => 'numeric(int2)',
castcontext => 'i', castmethod => 'f' },
{ castsource => 'int4', casttarget => 'int8', castfunc => 'int8(int4)',
diff --git a/src/include/catalog/pg_opclass.dat b/src/include/catalog/pg_opclass.dat
index ab2f50c9eb..c5bae7945d 100644
--- a/src/include/catalog/pg_opclass.dat
+++ b/src/include/catalog/pg_opclass.dat
@@ -47,6 +47,10 @@
opcintype => 'float4' },
{ opcmethod => 'hash', opcname => 'float4_ops', opcfamily => 'hash/float_ops',
opcintype => 'float4' },
+{ opcmethod => 'btree', opcname => 'rational_ops', opcfamily => 'btree/rational_ops',
+ opcintype => 'rational' },
+{ opcmethod => 'hash', opcname => 'rational_ops', opcfamily => 'hash/rational_ops',
+ opcintype => 'rational' },
{ oid => '3123', oid_symbol => 'FLOAT8_BTREE_OPS_OID',
opcmethod => 'btree', opcname => 'float8_ops', opcfamily => 'btree/float_ops',
opcintype => 'float8' },
diff --git a/src/include/catalog/pg_operator.dat b/src/include/catalog/pg_operator.dat
index 7c135da3b1..5219b3bfaf 100644
--- a/src/include/catalog/pg_operator.dat
+++ b/src/include/catalog/pg_operator.dat
@@ -3298,4 +3298,53 @@
oprresult => 'bool', oprcode => 'jsonb_path_match_opr(jsonb,jsonpath)',
oprrest => 'contsel', oprjoin => 'contjoinsel' },
+# Rationals
+
+{ oid => '8565', descr => 'equal',
+ oprname => '=', oprcanmerge => 't', oprcanhash => 't', oprleft => 'rational',
+ oprright => 'rational', oprresult => 'bool', oprcom => '=(rational,rational)',
+ oprnegate => '<>(rational,rational)', oprcode => 'rational_eq', oprrest => 'eqsel',
+ oprjoin => 'eqjoinsel' },
+{ oid => '8566', descr => 'not equal',
+ oprname => '<>', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'bool', oprcom => '<>(rational,rational)',
+ oprnegate => '=(rational,rational)', oprcode => 'rational_ne', oprrest => 'neqsel',
+ oprjoin => 'neqjoinsel' },
+{ oid => '8567', descr => 'less than',
+ oprname => '<', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'bool', oprcom => '>(rational,rational)',
+ oprnegate => '>=(rational,rational)', oprcode => 'rational_lt',
+ oprrest => 'scalarltsel', oprjoin => 'scalarltjoinsel' },
+{ oid => '8568', descr => 'less than or equal',
+ oprname => '<=', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'bool', oprcom => '>=(rational,rational)',
+ oprnegate => '>(rational,rational)', oprcode => 'rational_le',
+ oprrest => 'scalarlesel', oprjoin => 'scalarlejoinsel' },
+{ oid => '8569', descr => 'greater than',
+ oprname => '>', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'bool', oprcom => '<(rational,rational)',
+ oprnegate => '<=(rational,rational)', oprcode => 'rational_gt',
+ oprrest => 'scalargtsel', oprjoin => 'scalargtjoinsel' },
+{ oid => '8570', descr => 'greater than or equal',
+ oprname => '>=', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'bool', oprcom => '<=(rational,rational)',
+ oprnegate => '<(rational,rational)', oprcode => 'rational_ge',
+ oprrest => 'scalargesel', oprjoin => 'scalargejoinsel' },
+
+{ oid => '8571', descr => 'add',
+ oprname => '+', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'rational', oprcom => '+(rational,rational)', oprcode => 'rational_add' },
+{ oid => '8572', descr => 'negate',
+ oprname => '-', oprkind => 'l', oprleft => '0', oprright => 'rational',
+ oprresult => 'rational', oprcode => 'rational_neg' },
+{ oid => '8573', descr => 'subtract',
+ oprname => '-', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'rational', oprcode => 'rational_sub' },
+{ oid => '8574', descr => 'divide',
+ oprname => '/', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'rational', oprcode => 'rational_div' },
+{ oid => '8575', descr => 'multiply',
+ oprname => '*', oprleft => 'rational', oprright => 'rational',
+ oprresult => 'rational', oprcom => '*(rational,rational)',
+ oprcode => 'rational_mul' },
]
diff --git a/src/include/catalog/pg_opfamily.dat b/src/include/catalog/pg_opfamily.dat
index 26227df216..cca4210982 100644
--- a/src/include/catalog/pg_opfamily.dat
+++ b/src/include/catalog/pg_opfamily.dat
@@ -38,6 +38,10 @@
opfmethod => 'btree', opfname => 'float_ops' },
{ oid => '1971',
opfmethod => 'hash', opfname => 'float_ops' },
+{ oid => '8579',
+ opfmethod => 'btree', opfname => 'rational_ops' },
+{ oid => '8580',
+ opfmethod => 'hash', opfname => 'rational_ops' },
{ oid => '1974', oid_symbol => 'NETWORK_BTREE_FAM_OID',
opfmethod => 'btree', opfname => 'network_ops' },
{ oid => '1975',
diff --git a/src/include/catalog/pg_proc.dat b/src/include/catalog/pg_proc.dat
index 226c904c04..469082162a 100644
--- a/src/include/catalog/pg_proc.dat
+++ b/src/include/catalog/pg_proc.dat
@@ -6206,6 +6206,9 @@
{ oid => '2111', descr => 'sum as float8 across all float8 input values',
proname => 'sum', prokind => 'a', proisstrict => 'f', prorettype => 'float8',
proargtypes => 'float8', prosrc => 'aggregate_dummy' },
+{ oid => '8578', descr => 'sum as rational across all rational input values',
+ proname => 'sum', prokind => 'a', proisstrict => 'f', prorettype => 'rational',
+ proargtypes => 'rational', prosrc => 'aggregate_dummy' },
{ oid => '2112', descr => 'sum as money across all money input values',
proname => 'sum', prokind => 'a', proisstrict => 'f', prorettype => 'money',
proargtypes => 'money', prosrc => 'aggregate_dummy' },
@@ -6235,6 +6238,9 @@
{ oid => '2120', descr => 'maximum value of all float8 input values',
proname => 'max', prokind => 'a', proisstrict => 'f', prorettype => 'float8',
proargtypes => 'float8', prosrc => 'aggregate_dummy' },
+{ oid => '8576', descr => 'maximum value of all rational input values',
+ proname => 'max', prokind => 'a', proisstrict => 'f', prorettype => 'rational',
+ proargtypes => 'rational', prosrc => 'aggregate_dummy' },
{ oid => '2122', descr => 'maximum value of all date input values',
proname => 'max', prokind => 'a', proisstrict => 'f', prorettype => 'date',
proargtypes => 'date', prosrc => 'aggregate_dummy' },
@@ -6302,6 +6308,9 @@
{ oid => '2136', descr => 'minimum value of all float8 input values',
proname => 'min', prokind => 'a', proisstrict => 'f', prorettype => 'float8',
proargtypes => 'float8', prosrc => 'aggregate_dummy' },
+{ oid => '8577', descr => 'minimum value of all rational input values',
+ proname => 'min', prokind => 'a', proisstrict => 'f', prorettype => 'rational',
+ proargtypes => 'rational', prosrc => 'aggregate_dummy' },
{ oid => '2138', descr => 'minimum value of all date input values',
proname => 'min', prokind => 'a', proisstrict => 'f', prorettype => 'date',
proargtypes => 'date', prosrc => 'aggregate_dummy' },
@@ -10768,4 +10777,91 @@
proname => 'pg_partition_root', prorettype => 'regclass',
proargtypes => 'regclass', prosrc => 'pg_partition_root' },
+# rational numbers
+{ oid => '8536', descr => 'I/O',
+ proname => 'rational_in', provolatile => 's', prorettype => 'rational',
+ proargtypes => 'cstring', prosrc => 'rational_in' },
+{ oid => '8537', descr => 'I/O',
+ proname => 'rational_in_float', provolatile => 's', prorettype => 'rational',
+ proargtypes => 'float8', prosrc => 'rational_in_float' },
+{ oid => '8535', descr => 'I/O',
+ proname => 'rational_in_integer', provolatile => 's', prorettype => 'rational',
+ proargtypes => 'int4', prosrc => 'rational_in_integer' },
+{ oid => '8538', descr => 'I/O',
+ proname => 'rational_out', provolatile => 's', prorettype => 'cstring',
+ proargtypes => 'rational', prosrc => 'rational_out' },
+{ oid => '8539', descr => 'I/O',
+ proname => 'rational_out_float', provolatile => 's', prorettype => 'float8',
+ proargtypes => 'rational', prosrc => 'rational_out_float' },
+{ oid => '8540', descr => 'I/O',
+ proname => 'rational_recv', prorettype => 'rational', proargtypes => 'internal',
+ prosrc => 'rational_recv' },
+{ oid => '8541', descr => 'I/O',
+ proname => 'rational_send', prorettype => 'bytea', proargtypes => 'rational',
+ prosrc => 'rational_send' },
+
+{ oid => '8542', descr => 'Construction',
+ proname => 'rational', prorettype => 'rational',
+ proargtypes => 'int4 int4', prosrc => 'rational_create' },
+{ oid => '8543', descr => 'Construction',
+ proname => 'rational', prorettype => 'rational',
+ proargtypes => 'int4', prosrc => 'rational_in_integer' },
+
+{ oid => '8547', descr => 'Arithmetic',
+ proname => 'rational_add', prorettype => 'rational',
+ proargtypes => 'rational rational', prosrc => 'rational_add' },
+{ oid => '8548', descr => 'Arithmetic',
+ proname => 'rational_sub', prorettype => 'rational',
+ proargtypes => 'rational rational', prosrc => 'rational_sub' },
+{ oid => '8549', descr => 'Arithmetic',
+ proname => 'rational_mul', prorettype => 'rational',
+ proargtypes => 'rational rational', prosrc => 'rational_mul' },
+{ oid => '8550', descr => 'Arithmetic',
+ proname => 'rational_div', prorettype => 'rational',
+ proargtypes => 'rational rational', prosrc => 'rational_div' },
+{ oid => '8551', descr => 'Arithmetic',
+ proname => 'rational_neg', prorettype => 'rational',
+ proargtypes => 'rational', prosrc => 'rational_neg' },
+{ oid => '8552', descr => 'Manipulation',
+ proname => 'rational_simplify', prorettype => 'rational',
+ proargtypes => 'rational', prosrc => 'rational_simplify' },
+{ oid => '8553', descr => 'Manipulation',
+ proname => 'rational_intermediate', prorettype => 'rational',
+ proargtypes => 'rational rational', proisstrict => 'f',
+ prosrc => 'rational_intermediate' },
+
+{ oid => '8554', descr => 'Comparison',
+ proname => 'rational_eq', prorettype => 'bool',
+ proargtypes => 'rational rational', prosrc => 'rational_eq' },
+{ oid => '8555', descr => 'Comparison',
+ proname => 'rational_ne', prorettype => 'bool',
+ proargtypes => 'rational rational', prosrc => 'rational_ne' },
+{ oid => '8556', descr => 'Comparison',
+ proname => 'rational_lt', prorettype => 'bool',
+ proargtypes => 'rational rational', prosrc => 'rational_lt' },
+{ oid => '8557', descr => 'Comparison',
+ proname => 'rational_le', prorettype => 'bool',
+ proargtypes => 'rational rational', prosrc => 'rational_le' },
+{ oid => '8558', descr => 'Comparison',
+ proname => 'rational_gt', prorettype => 'bool',
+ proargtypes => 'rational rational', prosrc => 'rational_gt' },
+{ oid => '8559', descr => 'Comparison',
+ proname => 'rational_ge', prorettype => 'bool',
+ proargtypes => 'rational rational', prosrc => 'rational_ge' },
+{ oid => '8560', descr => 'Comparison',
+ proname => 'rational_cmp', prorettype => 'int4',
+ proargtypes => 'rational rational', prosrc => 'rational_cmp' },
+{ oid => '8561', descr => 'smaller of two',
+ proname => 'rational_smaller', prorettype => 'rational',
+ proargtypes => 'rational rational', prosrc => 'rational_smaller' },
+{ oid => '8562', descr => 'larger of two',
+ proname => 'rational_larger', prorettype => 'rational',
+ proargtypes => 'rational rational', prosrc => 'rational_larger' },
+
+{ oid => '8563', descr => 'hash',
+ proname => 'hashrational', prorettype => 'int4',
+ proargtypes => 'rational', prosrc => 'rational_hash' },
+
]
diff --git a/src/include/catalog/pg_type.dat b/src/include/catalog/pg_type.dat
index fe2c4eabb4..9fcf969d10 100644
--- a/src/include/catalog/pg_type.dat
+++ b/src/include/catalog/pg_type.dat
@@ -595,4 +595,10 @@
typcategory => 'P', typinput => 'anyrange_in', typoutput => 'anyrange_out',
typreceive => '-', typsend => '-', typalign => 'd', typstorage => 'x' },
+{ oid => '8564', array_type_oid => '8601',
+ descr => 'rational numbers (fractions) with int4 numerator and denominator',
+ typname => 'rational', typlen => '8', typbyval => 'f', typtype => 'b',
+ typcategory => 'N', typinput => 'rational_in', typoutput => 'rational_out',
+ typreceive => 'rational_recv', typsend => 'rational_send',
+ typalign => 'd' },
]
diff --git a/src/test/regress/expected/opr_sanity.out b/src/test/regress/expected/opr_sanity.out
index c19740e5db..c441ced3ed 100644
--- a/src/test/regress/expected/opr_sanity.out
+++ b/src/test/regress/expected/opr_sanity.out
@@ -168,9 +168,10 @@ WHERE p1.oid < p2.oid AND
p1.proretset != p2.proretset OR
p1.provolatile != p2.provolatile OR
p1.pronargs != p2.pronargs);
- oid | proname | oid | proname
------+---------+-----+---------
-(0 rows)
+ oid | proname | oid | proname
+------+---------------------+------+----------
+ 8535 | rational_in_integer | 8543 | rational
+(1 row)
-- Look for uses of different type OIDs in the argument/result type fields
-- for different aliases of the same built-in function.
@@ -1301,9 +1302,20 @@ SELECT * FROM funcdescs
WHERE prodesc IS DISTINCT FROM expecteddesc
AND oprdesc NOT LIKE 'deprecated%'
AND prodesc IS DISTINCT FROM oprdesc;
- p_oid | proname | o_oid | prodesc | expecteddesc | oprdesc
--------+---------+-------+---------+--------------+---------
-(0 rows)
+ p_oid | proname | o_oid | prodesc | expecteddesc | oprdesc
+-------+--------------+-------+------------+-------------------------------+-----------------------
+ 8554 | rational_eq | 8565 | Comparison | implementation of = operator | equal
+ 8555 | rational_ne | 8566 | Comparison | implementation of <> operator | not equal
+ 8556 | rational_lt | 8567 | Comparison | implementation of < operator | less than
+ 8557 | rational_le | 8568 | Comparison | implementation of <= operator | less than or equal
+ 8558 | rational_gt | 8569 | Comparison | implementation of > operator | greater than
+ 8559 | rational_ge | 8570 | Comparison | implementation of >= operator | greater than or equal
+ 8547 | rational_add | 8571 | Arithmetic | implementation of + operator | add
+ 8551 | rational_neg | 8572 | Arithmetic | implementation of - operator | negate
+ 8548 | rational_sub | 8573 | Arithmetic | implementation of - operator | subtract
+ 8550 | rational_div | 8574 | Arithmetic | implementation of / operator | divide
+ 8549 | rational_mul | 8575 | Arithmetic | implementation of * operator | multiply
+(11 rows)
-- Show all the operator-implementation functions that have their own
-- comments. This should happen only in cases where the function and
@@ -1336,7 +1348,18 @@ ORDER BY 1;
3940 | jsonb_extract_path_text | get value from jsonb as text with path elements
3951 | json_extract_path | get value from json with path elements
3953 | json_extract_path_text | get value from json as text with path elements
-(9 rows)
+ 8547 | rational_add | Arithmetic
+ 8548 | rational_sub | Arithmetic
+ 8549 | rational_mul | Arithmetic
+ 8550 | rational_div | Arithmetic
+ 8551 | rational_neg | Arithmetic
+ 8554 | rational_eq | Comparison
+ 8555 | rational_ne | Comparison
+ 8556 | rational_lt | Comparison
+ 8557 | rational_le | Comparison
+ 8558 | rational_gt | Comparison
+ 8559 | rational_ge | Comparison
+(20 rows)
-- Operators that are commutator pairs should have identical volatility
-- and leakproofness markings on their implementation functions.
diff --git a/src/test/regress/expected/rational.out b/src/test/regress/expected/rational.out
new file mode 100644
index 0000000000..7aa9a3e49b
--- /dev/null
+++ b/src/test/regress/expected/rational.out
@@ -0,0 +1,690 @@
+--
+-- Rational numbers
+-- I/O
+-- can parse a simple fraction
+select '1/3'::rational;
+ rational
+----------
+ 1/3
+(1 row)
+
+-- can parse negatives
+select '-1/3'::rational;
+ rational
+----------
+ -1/3
+(1 row)
+
+select '1/-3'::rational;
+ rational
+----------
+ -1/3
+(1 row)
+
+-- SEND works
+select rational_send('1/3');
+ rational_send
+--------------------
+ \x0000000100000003
+(1 row)
+
+-- constructor proc
+select rational(1,2) = '1/2'::rational;
+ ?column?
+----------
+ t
+(1 row)
+
+-- casting
+-- int
+select 42 = '42/1'::rational;
+ ?column?
+----------
+ t
+(1 row)
+
+-- from float
+select 0.263157894737::float::rational;
+ rational
+----------
+ 5/19
+(1 row)
+
+select 3.141592625359::float::rational;
+ rational
+-----------------
+ 4712235/1499951
+(1 row)
+
+select 0.606557377049::float::rational;
+ rational
+----------
+ 37/61
+(1 row)
+
+select -0.5::float::rational;
+ ?column?
+----------
+ -1/2
+(1 row)
+
+select 1.000001::float::rational;
+ rational
+-----------------
+ 1000001/1000000
+(1 row)
+
+select 1.0000001::float::rational;
+ rational
+------------------
+ 10000000/9999999
+(1 row)
+
+select 1.00000001::float::rational;
+ rational
+---------------------
+ 100000001/100000000
+(1 row)
+
+select 1.000000001::float::rational;
+ rational
+---------------------
+ 999999918/999999917
+(1 row)
+
+select 1.0000000001::float::rational;
+ rational
+----------
+ 1/1
+(1 row)
+
+select 2147483647::float::rational;
+ rational
+--------------
+ 2147483647/1
+(1 row)
+
+select 2147483647.1::float::rational;
+ERROR: value too large for rational
+select 'NAN'::float::rational;
+ERROR: value too large for rational
+-- to float
+select '1/2'::rational::float;
+ float8
+--------
+ 0.5
+(1 row)
+
+set extra_float_digits = 0; -- default changed in PG12
+select '1/3'::rational::float;
+ float8
+-------------------
+ 0.333333333333333
+(1 row)
+
+reset extra_float_digits;
+select '-1/2'::rational::float;
+ float8
+--------
+ -0.5
+(1 row)
+
+-- too big
+select '2147483648/2147483647'::rational;
+ERROR: numerator or denominator outside valid int32 value
+LINE 1: select '2147483648/2147483647'::rational;
+ ^
+-- no spaces
+select '1 /3'::rational;
+ERROR: Expecting '/' after number but found ' '
+LINE 1: select '1 /3'::rational;
+ ^
+-- no zero denominator
+select '1/0'::rational;
+ERROR: fraction cannot have zero denominator
+LINE 1: select '1/0'::rational;
+ ^
+-- quoted number treated as int
+select '1'::rational;
+ rational
+----------
+ 1/1
+(1 row)
+
+select '-1'::rational;
+ rational
+----------
+ -1/1
+(1 row)
+
+-- no garbage
+select ''::rational;
+ERROR: Missing or invalid numerator
+LINE 1: select ''::rational;
+ ^
+select '/'::rational;
+ERROR: Missing or invalid numerator
+LINE 1: select '/'::rational;
+ ^
+select '2/'::rational;
+ERROR: Expecting value after '/' but got '\0'
+LINE 1: select '2/'::rational;
+ ^
+select '/2'::rational;
+ERROR: Missing or invalid numerator
+LINE 1: select '/2'::rational;
+ ^
+select 'sdfkjsdfj34984538'::rational;
+ERROR: Missing or invalid numerator
+LINE 1: select 'sdfkjsdfj34984538'::rational;
+ ^
+-- simplification
+-- double negative becomes positive
+select rational_simplify('-1/-3');
+ rational_simplify
+-------------------
+ 1/3
+(1 row)
+
+-- works with negative value
+select rational_simplify('-3/12');
+ rational_simplify
+-------------------
+ -1/4
+(1 row)
+
+-- dodge the INT32_MIN/-1 mistake
+select rational_simplify('-2147483648/2147483647');
+ rational_simplify
+------------------------
+ -2147483648/2147483647
+(1 row)
+
+-- don't move negative if it would overflow
+select rational_simplify('1/-2147483648');
+ rational_simplify
+-------------------
+ 1/-2147483648
+(1 row)
+
+-- biggest value reduces
+select rational_simplify('2147483647/2147483647');
+ rational_simplify
+-------------------
+ 1/1
+(1 row)
+
+-- smallest value reduces
+select rational_simplify('-2147483648/-2147483648');
+ rational_simplify
+-------------------
+ 1/1
+(1 row)
+
+-- idempotent on simplified expression
+select rational_simplify('1/1');
+ rational_simplify
+-------------------
+ 1/1
+(1 row)
+
+-- addition
+-- additive identity
+select '0/1'::rational + '1/2';
+ ?column?
+----------
+ 1/2
+(1 row)
+
+-- additive inverse
+select '1/2'::rational + '-1/2';
+ ?column?
+----------
+ 0/4
+(1 row)
+
+-- just regular
+select '1/2'::rational + '1/2';
+ ?column?
+----------
+ 4/4
+(1 row)
+
+-- forcing intermediate simplification
+select '2147483647/2147483647'::rational + '1/1';
+ ?column?
+----------
+ 2/1
+(1 row)
+
+-- overflow (sqrt(max)+1)/1 + 1/sqrt(max)
+select '46342/1'::rational + '1/46341';
+ERROR: intermediate value overflow in rational addition
+-- multiplication
+-- multiplicative identity
+select '1/1'::rational * '1/2';
+ ?column?
+----------
+ 1/2
+(1 row)
+
+-- multiplicative inverse
+select '2/1'::rational * '1/2';
+ ?column?
+----------
+ 2/2
+(1 row)
+
+-- just regular
+select '5/8'::rational * '3/5';
+ ?column?
+----------
+ 15/40
+(1 row)
+
+-- forcing intermediate simplification
+select '2147483647/2147483647'::rational * '2/2';
+ ?column?
+----------
+ 2/2
+(1 row)
+
+-- overflow
+select '46342/46341'::rational * '46341/46342';
+ERROR: intermediate value overflow in rational multiplication
+-- division
+select 1::rational / 3;
+ ?column?
+----------
+ 1/3
+(1 row)
+
+select '2/3'::rational / '2/3';
+ ?column?
+----------
+ 6/6
+(1 row)
+
+-- negation
+-- flips sign of numerator
+select -('1/2'::rational);
+ ?column?
+----------
+ -1/2
+(1 row)
+
+-- flips back
+select -('-1/2'::rational);
+ ?column?
+----------
+ 1/2
+(1 row)
+
+-- overflow not possible
+select -('-2147483648/1'::rational);
+ ?column?
+----------------
+ -2147483648/-1
+(1 row)
+
+select -('1/-2147483648'::rational);
+ ?column?
+----------------
+ -1/-2147483648
+(1 row)
+
+select -('-2147483648/-2147483648'::rational);
+ ?column?
+----------
+ -1/1
+(1 row)
+
+-- subtraction
+-- just regular
+select '1/2'::rational - '1/2';
+ ?column?
+----------
+ 0/4
+(1 row)
+
+-- can go negative
+select '1/2'::rational - '1/1';
+ ?column?
+----------
+ -1/2
+(1 row)
+
+-- forcing intermediate simplification
+select '2147483647/2147483647'::rational - '100/100';
+ ?column?
+----------
+ 0/100
+(1 row)
+
+-- overflow (sqrt(max)+1)/1 - 1/sqrt(max)
+select '46342/1'::rational - '1/46341';
+ERROR: intermediate value overflow in rational addition
+-- comparison
+-- equal in every way
+select '1/1'::rational = '1/1';
+ ?column?
+----------
+ t
+(1 row)
+
+-- same equivalence class
+select '20/40'::rational = '22/44';
+ ?column?
+----------
+ t
+(1 row)
+
+-- negatives work too
+select '-20/40'::rational = '-22/44';
+ ?column?
+----------
+ t
+(1 row)
+
+-- overflow not possible
+select '46342/46341'::rational = '46342/46341';
+ ?column?
+----------
+ t
+(1 row)
+
+-- high precision
+select '1/2147483647'::rational = '1/2147483646';
+ ?column?
+----------
+ f
+(1 row)
+
+select '1/3'::rational * 3 = 1;
+ ?column?
+----------
+ t
+(1 row)
+
+select 1.0/3.0 = 1.0;
+ ?column?
+----------
+ f
+(1 row)
+
+-- not everything is equal
+select '2/3'::rational = '8/5';
+ ?column?
+----------
+ f
+(1 row)
+
+-- negates equality
+select '1/1'::rational <> '1/1';
+ ?column?
+----------
+ f
+(1 row)
+
+-- overflow not possible
+select '46342/46341'::rational <> '46342/46341';
+ ?column?
+----------
+ f
+(1 row)
+
+-- not equal
+select '2/3'::rational <> '8/5';
+ ?column?
+----------
+ t
+(1 row)
+
+-- lt anti-reflexive
+select '1/2'::rational < '1/2';
+ ?column?
+----------
+ f
+(1 row)
+
+-- gt anti-reflexive
+select '1/2'::rational > '1/2';
+ ?column?
+----------
+ f
+(1 row)
+
+-- overflow not possible
+select '1/2147483647'::rational < '2/2147483647';
+ ?column?
+----------
+ t
+(1 row)
+
+-- lte
+select r
+ from unnest(ARRAY[
+ '303700050/303700050',
+ '-2/1',
+ '0/9999999',
+ '-11/17',
+ '100/1',
+ '3/4',
+ '-1/2',
+ '-1/1',
+ '5/8',
+ '6/9',
+ '5/8'
+ ]::rational[]) as r
+order by r asc;
+ r
+---------------------
+ -2/1
+ -1/1
+ -11/17
+ -1/2
+ 0/9999999
+ 5/8
+ 5/8
+ 6/9
+ 3/4
+ 303700050/303700050
+ 100/1
+(11 rows)
+
+-- gte
+select r
+ from unnest(ARRAY[
+ '303700050/303700050',
+ '-2/1',
+ '0/9999999',
+ '-11/17',
+ '100/1',
+ '3/4',
+ '-1/2',
+ '-1/1',
+ '5/8',
+ '6/9',
+ '5/8'
+ ]::rational[]) as r
+order by r desc;
+ r
+---------------------
+ 100/1
+ 303700050/303700050
+ 3/4
+ 6/9
+ 5/8
+ 5/8
+ 0/9999999
+ -1/2
+ -11/17
+ -1/1
+ -2/1
+(11 rows)
+
+-- btree
+create table rs (
+ r rational
+);
+create index rs_r_btree on rs using btree(r);
+insert into rs values ('0/7'), ('1/7'), ('2/7'), ('3/7'),
+ ('4/7'), ('5/7'), ('6/7');
+set enable_seqscan=false;
+explain select * from rs where r > '1/7' and r <= '10/14';
+ QUERY PLAN
+--------------------------------------------------------------------------
+ Bitmap Heap Scan on rs (cost=4.27..14.97 rows=11 width=8)
+ Recheck Cond: ((r > '1/7'::rational) AND (r <= '10/14'::rational))
+ -> Bitmap Index Scan on rs_r_btree (cost=0.00..4.27 rows=11 width=0)
+ Index Cond: ((r > '1/7'::rational) AND (r <= '10/14'::rational))
+(4 rows)
+
+select * from rs where r > '1/7' and r <= '10/14';
+ r
+-----
+ 2/7
+ 3/7
+ 4/7
+ 5/7
+(4 rows)
+
+set enable_seqscan=true;
+drop table rs cascade;
+-- hash
+create table rs (
+ r rational
+);
+create index rs_r_hash on rs using hash(r);
+insert into rs values ('0/7'), ('1/7');
+set enable_seqscan=false;
+explain select * from rs where r = '0/1';
+ QUERY PLAN
+-------------------------------------------------------------------------
+ Bitmap Heap Scan on rs (cost=4.09..14.76 rows=11 width=8)
+ Recheck Cond: (r = '0/1'::rational)
+ -> Bitmap Index Scan on rs_r_hash (cost=0.00..4.08 rows=11 width=0)
+ Index Cond: (r = '0/1'::rational)
+(4 rows)
+
+select * from rs where r = '0/1';
+ r
+-----
+ 0/7
+(1 row)
+
+select * from rs where r = '2/7';
+ r
+---
+(0 rows)
+
+set enable_seqscan=true;
+drop table rs cascade;
+-- aggregates
+select min(r)
+ from unnest(ARRAY[
+ '100/1',
+ NULL,
+ '-11/17',
+ '-1/1'
+ ]::rational[]) as r;
+ min
+------
+ -1/1
+(1 row)
+
+select max(r)
+ from unnest(ARRAY[
+ '100/1',
+ NULL,
+ '-11/17',
+ '-1/1'
+ ]::rational[]) as r;
+ max
+-------
+ 100/1
+(1 row)
+
+select max(r)
+ from unnest(ARRAY[
+ NULL, NULL, NULL
+ ]::rational[]) as r;
+ max
+-----
+
+(1 row)
+
+select rational_simplify(sum(r))
+ from unnest(ARRAY[
+ '1/1', '1/2', NULL,
+ '-3/2', '1/16'
+ ]::rational[]) as r;
+ rational_simplify
+-------------------
+ 1/16
+(1 row)
+
+select sum(r)
+ from unnest(ARRAY[
+ NULL, NULL, NULL
+ ]::rational[]) as r;
+ sum
+-----
+
+(1 row)
+
+-- stern-brocot intermediates
+-- intermediates start at 1 -- between 0 and Infinity
+select rational_intermediate(NULL, NULL);
+ rational_intermediate
+-----------------------
+ 1/1
+(1 row)
+
+-- random example
+select rational_intermediate('15/16', 1);
+ rational_intermediate
+-----------------------
+ 16/17
+(1 row)
+
+select rational_intermediate('15/16', 1)
+ between '15/16'::rational and 1;
+ ?column?
+----------
+ t
+(1 row)
+
+select rational_intermediate('44320/39365', '77200/12184');
+ rational_intermediate
+-----------------------
+ 2/1
+(1 row)
+
+select rational_intermediate('44320/39365', '77200/12184')
+ between '44320/39365'::rational and '77200/12184';
+ ?column?
+----------
+ t
+(1 row)
+
+-- unbounded upper limit produces least greater integer
+select rational_intermediate('1/3', NULL);
+ rational_intermediate
+-----------------------
+ 1/1
+(1 row)
+
+select rational_intermediate('3/2', NULL);
+ rational_intermediate
+-----------------------
+ 2/1
+(1 row)
+
+-- though not the other direction
+select rational_intermediate(NULL, '15/16');
+ rational_intermediate
+-----------------------
+ 1/2
+(1 row)
+
diff --git a/src/test/regress/parallel_schedule b/src/test/regress/parallel_schedule
index d2b17dd3ea..50b4eb1220 100644
--- a/src/test/regress/parallel_schedule
+++ b/src/test/regress/parallel_schedule
@@ -13,7 +13,7 @@ test: tablespace
# ----------
# The first group of parallel tests
# ----------
-test: boolean char name varchar text int2 int4 int8 oid float4 float8 bit numeric txid uuid enum money rangetypes
pg_lsnregproc
+test: boolean char name varchar text int2 int4 int8 oid float4 float8 rational bit numeric txid uuid enum money
rangetypespg_lsn
# ----------
# The second group of parallel tests
@@ -27,7 +27,7 @@ test: strings numerology point lseg line box path polygon circle date time timet
# geometry depends on point, lseg, box, path, polygon and circle
# horology depends on interval, timetz, timestamp, timestamptz
# ----------
-test: geometry horology regex oidjoins type_sanity opr_sanity misc_sanity comments expressions
+test: geometry horology regex regproc oidjoins type_sanity opr_sanity misc_sanity comments expressions
# ----------
# These four each depend on the previous one
diff --git a/src/test/regress/serial_schedule b/src/test/regress/serial_schedule
index acba391332..9a32246d58 100644
--- a/src/test/regress/serial_schedule
+++ b/src/test/regress/serial_schedule
@@ -12,6 +12,7 @@ test: int8
test: oid
test: float4
test: float8
+test: rational
test: bit
test: numeric
test: txid
diff --git a/src/test/regress/sql/rational.sql b/src/test/regress/sql/rational.sql
new file mode 100644
index 0000000000..48462ad8d3
--- /dev/null
+++ b/src/test/regress/sql/rational.sql
@@ -0,0 +1,272 @@
+--
+-- Rational numbers
+
+-- I/O
+
+-- can parse a simple fraction
+select '1/3'::rational;
+-- can parse negatives
+select '-1/3'::rational;
+select '1/-3'::rational;
+-- SEND works
+select rational_send('1/3');
+
+-- constructor proc
+select rational(1,2) = '1/2'::rational;
+
+-- casting
+
+-- int
+select 42 = '42/1'::rational;
+
+-- from float
+select 0.263157894737::float::rational;
+select 3.141592625359::float::rational;
+select 0.606557377049::float::rational;
+select -0.5::float::rational;
+select 1.000001::float::rational;
+select 1.0000001::float::rational;
+select 1.00000001::float::rational;
+select 1.000000001::float::rational;
+select 1.0000000001::float::rational;
+select 2147483647::float::rational;
+select 2147483647.1::float::rational;
+select 'NAN'::float::rational;
+
+-- to float
+select '1/2'::rational::float;
+set extra_float_digits = 0; -- default changed in PG12
+select '1/3'::rational::float;
+reset extra_float_digits;
+select '-1/2'::rational::float;
+
+-- too big
+select '2147483648/2147483647'::rational;
+-- no spaces
+select '1 /3'::rational;
+-- no zero denominator
+select '1/0'::rational;
+-- quoted number treated as int
+select '1'::rational;
+select '-1'::rational;
+-- no garbage
+select ''::rational;
+select '/'::rational;
+select '2/'::rational;
+select '/2'::rational;
+select 'sdfkjsdfj34984538'::rational;
+
+-- simplification
+
+-- double negative becomes positive
+select rational_simplify('-1/-3');
+-- works with negative value
+select rational_simplify('-3/12');
+-- dodge the INT32_MIN/-1 mistake
+select rational_simplify('-2147483648/2147483647');
+-- don't move negative if it would overflow
+select rational_simplify('1/-2147483648');
+-- biggest value reduces
+select rational_simplify('2147483647/2147483647');
+-- smallest value reduces
+select rational_simplify('-2147483648/-2147483648');
+-- idempotent on simplified expression
+select rational_simplify('1/1');
+
+-- addition
+
+-- additive identity
+select '0/1'::rational + '1/2';
+-- additive inverse
+select '1/2'::rational + '-1/2';
+-- just regular
+select '1/2'::rational + '1/2';
+-- forcing intermediate simplification
+select '2147483647/2147483647'::rational + '1/1';
+-- overflow (sqrt(max)+1)/1 + 1/sqrt(max)
+select '46342/1'::rational + '1/46341';
+
+-- multiplication
+
+-- multiplicative identity
+select '1/1'::rational * '1/2';
+-- multiplicative inverse
+select '2/1'::rational * '1/2';
+-- just regular
+select '5/8'::rational * '3/5';
+-- forcing intermediate simplification
+select '2147483647/2147483647'::rational * '2/2';
+-- overflow
+select '46342/46341'::rational * '46341/46342';
+
+-- division
+
+select 1::rational / 3;
+select '2/3'::rational / '2/3';
+
+-- negation
+
+-- flips sign of numerator
+select -('1/2'::rational);
+-- flips back
+select -('-1/2'::rational);
+-- overflow not possible
+select -('-2147483648/1'::rational);
+select -('1/-2147483648'::rational);
+select -('-2147483648/-2147483648'::rational);
+
+-- subtraction
+
+-- just regular
+select '1/2'::rational - '1/2';
+-- can go negative
+select '1/2'::rational - '1/1';
+-- forcing intermediate simplification
+select '2147483647/2147483647'::rational - '100/100';
+-- overflow (sqrt(max)+1)/1 - 1/sqrt(max)
+select '46342/1'::rational - '1/46341';
+
+-- comparison
+
+-- equal in every way
+select '1/1'::rational = '1/1';
+-- same equivalence class
+select '20/40'::rational = '22/44';
+-- negatives work too
+select '-20/40'::rational = '-22/44';
+-- overflow not possible
+select '46342/46341'::rational = '46342/46341';
+-- high precision
+select '1/2147483647'::rational = '1/2147483646';
+select '1/3'::rational * 3 = 1;
+select 1.0/3.0 = 1.0;
+-- not everything is equal
+select '2/3'::rational = '8/5';
+
+-- negates equality
+select '1/1'::rational <> '1/1';
+-- overflow not possible
+select '46342/46341'::rational <> '46342/46341';
+-- not equal
+select '2/3'::rational <> '8/5';
+
+-- lt anti-reflexive
+select '1/2'::rational < '1/2';
+-- gt anti-reflexive
+select '1/2'::rational > '1/2';
+-- overflow not possible
+select '1/2147483647'::rational < '2/2147483647';
+
+-- lte
+select r
+ from unnest(ARRAY[
+ '303700050/303700050',
+ '-2/1',
+ '0/9999999',
+ '-11/17',
+ '100/1',
+ '3/4',
+ '-1/2',
+ '-1/1',
+ '5/8',
+ '6/9',
+ '5/8'
+ ]::rational[]) as r
+order by r asc;
+-- gte
+select r
+ from unnest(ARRAY[
+ '303700050/303700050',
+ '-2/1',
+ '0/9999999',
+ '-11/17',
+ '100/1',
+ '3/4',
+ '-1/2',
+ '-1/1',
+ '5/8',
+ '6/9',
+ '5/8'
+ ]::rational[]) as r
+order by r desc;
+
+-- btree
+create table rs (
+ r rational
+);
+create index rs_r_btree on rs using btree(r);
+insert into rs values ('0/7'), ('1/7'), ('2/7'), ('3/7'),
+ ('4/7'), ('5/7'), ('6/7');
+set enable_seqscan=false;
+
+explain select * from rs where r > '1/7' and r <= '10/14';
+select * from rs where r > '1/7' and r <= '10/14';
+
+set enable_seqscan=true;
+drop table rs cascade;
+
+-- hash
+create table rs (
+ r rational
+);
+create index rs_r_hash on rs using hash(r);
+insert into rs values ('0/7'), ('1/7');
+set enable_seqscan=false;
+
+explain select * from rs where r = '0/1';
+select * from rs where r = '0/1';
+select * from rs where r = '2/7';
+
+set enable_seqscan=true;
+drop table rs cascade;
+
+-- aggregates
+
+select min(r)
+ from unnest(ARRAY[
+ '100/1',
+ NULL,
+ '-11/17',
+ '-1/1'
+ ]::rational[]) as r;
+
+select max(r)
+ from unnest(ARRAY[
+ '100/1',
+ NULL,
+ '-11/17',
+ '-1/1'
+ ]::rational[]) as r;
+
+select max(r)
+ from unnest(ARRAY[
+ NULL, NULL, NULL
+ ]::rational[]) as r;
+
+select rational_simplify(sum(r))
+ from unnest(ARRAY[
+ '1/1', '1/2', NULL,
+ '-3/2', '1/16'
+ ]::rational[]) as r;
+
+select sum(r)
+ from unnest(ARRAY[
+ NULL, NULL, NULL
+ ]::rational[]) as r;
+
+-- stern-brocot intermediates
+
+-- intermediates start at 1 -- between 0 and Infinity
+select rational_intermediate(NULL, NULL);
+-- random example
+select rational_intermediate('15/16', 1);
+select rational_intermediate('15/16', 1)
+ between '15/16'::rational and 1;
+select rational_intermediate('44320/39365', '77200/12184');
+select rational_intermediate('44320/39365', '77200/12184')
+ between '44320/39365'::rational and '77200/12184';
+-- unbounded upper limit produces least greater integer
+select rational_intermediate('1/3', NULL);
+select rational_intermediate('3/2', NULL);
+-- though not the other direction
+select rational_intermediate(NULL, '15/16');
