int.c

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/*-------------------------------------------------------------------------
 *
 * int.c
 *    Functions for the built-in integer types (except int8).
 *
 * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/utils/adt/int.c
 *
 *-------------------------------------------------------------------------
 */
/*
 * OLD COMMENTS
 *      I/O routines:
 *       int2in, int2out, int2recv, int2send
 *       int4in, int4out, int4recv, int4send
 *       int2vectorin, int2vectorout, int2vectorrecv, int2vectorsend
 *      Boolean operators:
 *       inteq, intne, intlt, intle, intgt, intge
 *      Arithmetic operators:
 *       intpl, intmi, int4mul, intdiv
 *
 *      Arithmetic operators:
 *       intmod
 */
#include "postgres.h"

#include <ctype.h>
#include <limits.h>
#include <math.h>

#include "catalog/pg_type.h"
#include "common/int.h"
#include "funcapi.h"
#include "libpq/pqformat.h"
#include "nodes/nodeFuncs.h"
#include "nodes/supportnodes.h"
#include "optimizer/optimizer.h"
#include "utils/array.h"
#include "utils/builtins.h"

#define Int2VectorSize(n)   (offsetof(int2vector, values) + (n) * sizeof(int16))

typedef struct
{
    int32       current;
    int32       finish;
    int32       step;
} generate_series_fctx;


/*****************************************************************************
 *   USER I/O ROUTINES                                                       *
 *****************************************************************************/

/*
 *      int2in          - converts "num" to short
 */
Datum
int2in(PG_FUNCTION_ARGS)
{
    char       *num = PG_GETARG_CSTRING(0);

    PG_RETURN_INT16(pg_strtoint16(num));
}

/*
 *      int2out         - converts short to "num"
 */
Datum
int2out(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    char       *result = (char *) palloc(7);    /* sign, 5 digits, '\0' */

    pg_itoa(arg1, result);
    PG_RETURN_CSTRING(result);
}

/*
 *      int2recv            - converts external binary format to int2
 */
Datum
int2recv(PG_FUNCTION_ARGS)
{
    StringInfo  buf = (StringInfo) PG_GETARG_POINTER(0);

    PG_RETURN_INT16((int16) pq_getmsgint(buf, sizeof(int16)));
}

/*
 *      int2send            - converts int2 to binary format
 */
Datum
int2send(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    StringInfoData buf;

    pq_begintypsend(&buf);
    pq_sendint16(&buf, arg1);
    PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}

/*
 * construct int2vector given a raw array of int2s
 *
 * If int2s is NULL then caller must fill values[] afterward
 */
int2vector *
buildint2vector(const int16 *int2s, int n)
{
    int2vector *result;

    result = (int2vector *) palloc0(Int2VectorSize(n));

    if (n > 0 && int2s)
        memcpy(result->values, int2s, n * sizeof(int16));

    /*
     * Attach standard array header.  For historical reasons, we set the index
     * lower bound to 0 not 1.
     */
    SET_VARSIZE(result, Int2VectorSize(n));
    result->ndim = 1;
    result->dataoffset = 0;     /* never any nulls */
    result->elemtype = INT2OID;
    result->dim1 = n;
    result->lbound1 = 0;

    return result;
}

/*
 *      int2vectorin            - converts "num num ..." to internal form
 */
Datum
int2vectorin(PG_FUNCTION_ARGS)
{
    char       *intString = PG_GETARG_CSTRING(0);
    int2vector *result;
    int         n;

    result = (int2vector *) palloc0(Int2VectorSize(FUNC_MAX_ARGS));

    for (n = 0; *intString && n < FUNC_MAX_ARGS; n++)
    {
        while (*intString && isspace((unsigned char) *intString))
            intString++;
        if (*intString == '\0')
            break;
        result->values[n] = pg_atoi(intString, sizeof(int16), ' ');
        while (*intString && !isspace((unsigned char) *intString))
            intString++;
    }
    while (*intString && isspace((unsigned char) *intString))
        intString++;
    if (*intString)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("int2vector has too many elements")));

    SET_VARSIZE(result, Int2VectorSize(n));
    result->ndim = 1;
    result->dataoffset = 0;     /* never any nulls */
    result->elemtype = INT2OID;
    result->dim1 = n;
    result->lbound1 = 0;

    PG_RETURN_POINTER(result);
}

/*
 *      int2vectorout       - converts internal form to "num num ..."
 */
Datum
int2vectorout(PG_FUNCTION_ARGS)
{
    int2vector *int2Array = (int2vector *) PG_GETARG_POINTER(0);
    int         num,
                nnums = int2Array->dim1;
    char       *rp;
    char       *result;

    /* assumes sign, 5 digits, ' ' */
    rp = result = (char *) palloc(nnums * 7 + 1);
    for (num = 0; num < nnums; num++)
    {
        if (num != 0)
            *rp++ = ' ';
        pg_itoa(int2Array->values[num], rp);
        while (*++rp != '\0')
            ;
    }
    *rp = '\0';
    PG_RETURN_CSTRING(result);
}

/*
 *      int2vectorrecv          - converts external binary format to int2vector
 */
Datum
int2vectorrecv(PG_FUNCTION_ARGS)
{
    LOCAL_FCINFO(locfcinfo, 3);
    StringInfo  buf = (StringInfo) PG_GETARG_POINTER(0);
    int2vector *result;

    /*
     * Normally one would call array_recv() using DirectFunctionCall3, but
     * that does not work since array_recv wants to cache some data using
     * fcinfo->flinfo->fn_extra.  So we need to pass it our own flinfo
     * parameter.
     */
    InitFunctionCallInfoData(*locfcinfo, fcinfo->flinfo, 3,
                             InvalidOid, NULL, NULL);

    locfcinfo->args[0].value = PointerGetDatum(buf);
    locfcinfo->args[0].isnull = false;
    locfcinfo->args[1].value = ObjectIdGetDatum(INT2OID);
    locfcinfo->args[1].isnull = false;
    locfcinfo->args[2].value = Int32GetDatum(-1);
    locfcinfo->args[2].isnull = false;

    result = (int2vector *) DatumGetPointer(array_recv(locfcinfo));

    Assert(!locfcinfo->isnull);

    /* sanity checks: int2vector must be 1-D, 0-based, no nulls */
    if (ARR_NDIM(result) != 1 ||
        ARR_HASNULL(result) ||
        ARR_ELEMTYPE(result) != INT2OID ||
        ARR_LBOUND(result)[0] != 0)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
                 errmsg("invalid int2vector data")));

    /* check length for consistency with int2vectorin() */
    if (ARR_DIMS(result)[0] > FUNC_MAX_ARGS)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("oidvector has too many elements")));

    PG_RETURN_POINTER(result);
}

/*
 *      int2vectorsend          - converts int2vector to binary format
 */
Datum
int2vectorsend(PG_FUNCTION_ARGS)
{
    return array_send(fcinfo);
}


/*****************************************************************************
 *   PUBLIC ROUTINES                                                         *
 *****************************************************************************/

/*
 *      int4in          - converts "num" to int4
 */
Datum
int4in(PG_FUNCTION_ARGS)
{
    char       *num = PG_GETARG_CSTRING(0);

    PG_RETURN_INT32(pg_strtoint32(num));
}

/*
 *      int4out         - converts int4 to "num"
 */
Datum
int4out(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    char       *result = (char *) palloc(12);   /* sign, 10 digits, '\0' */

    pg_ltoa(arg1, result);
    PG_RETURN_CSTRING(result);
}

/*
 *      int4recv            - converts external binary format to int4
 */
Datum
int4recv(PG_FUNCTION_ARGS)
{
    StringInfo  buf = (StringInfo) PG_GETARG_POINTER(0);

    PG_RETURN_INT32((int32) pq_getmsgint(buf, sizeof(int32)));
}

/*
 *      int4send            - converts int4 to binary format
 */
Datum
int4send(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    StringInfoData buf;

    pq_begintypsend(&buf);
    pq_sendint32(&buf, arg1);
    PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*
 *      ===================
 *      CONVERSION ROUTINES
 *      ===================
 */

Datum
i2toi4(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);

    PG_RETURN_INT32((int32) arg1);
}

Datum
i4toi2(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);

    if (unlikely(arg1 < SHRT_MIN) || unlikely(arg1 > SHRT_MAX))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("smallint out of range")));

    PG_RETURN_INT16((int16) arg1);
}

/* Cast int4 -> bool */
Datum
int4_bool(PG_FUNCTION_ARGS)
{
    if (PG_GETARG_INT32(0) == 0)
        PG_RETURN_BOOL(false);
    else
        PG_RETURN_BOOL(true);
}

/* Cast bool -> int4 */
Datum
bool_int4(PG_FUNCTION_ARGS)
{
    if (PG_GETARG_BOOL(0) == false)
        PG_RETURN_INT32(0);
    else
        PG_RETURN_INT32(1);
}

/*
 *      ============================
 *      COMPARISON OPERATOR ROUTINES
 *      ============================
 */

/*
 *      inteq           - returns 1 iff arg1 == arg2
 *      intne           - returns 1 iff arg1 != arg2
 *      intlt           - returns 1 iff arg1 < arg2
 *      intle           - returns 1 iff arg1 <= arg2
 *      intgt           - returns 1 iff arg1 > arg2
 *      intge           - returns 1 iff arg1 >= arg2
 */

Datum
int4eq(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 == arg2);
}

Datum
int4ne(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 != arg2);
}

Datum
int4lt(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 < arg2);
}

Datum
int4le(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 <= arg2);
}

Datum
int4gt(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 > arg2);
}

Datum
int4ge(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 >= arg2);
}

Datum
int2eq(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 == arg2);
}

Datum
int2ne(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 != arg2);
}

Datum
int2lt(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 < arg2);
}

Datum
int2le(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 <= arg2);
}

Datum
int2gt(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 > arg2);
}

Datum
int2ge(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 >= arg2);
}

Datum
int24eq(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 == arg2);
}

Datum
int24ne(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 != arg2);
}

Datum
int24lt(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 < arg2);
}

Datum
int24le(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 <= arg2);
}

Datum
int24gt(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 > arg2);
}

Datum
int24ge(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(arg1 >= arg2);
}

Datum
int42eq(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 == arg2);
}

Datum
int42ne(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 != arg2);
}

Datum
int42lt(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 < arg2);
}

Datum
int42le(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 <= arg2);
}

Datum
int42gt(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 > arg2);
}

Datum
int42ge(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(arg1 >= arg2);
}


/*----------------------------------------------------------
 *  in_range functions for int4 and int2,
 *  including cross-data-type comparisons.
 *
 *  Note: we provide separate intN_int8 functions for performance
 *  reasons.  This forces also providing intN_int2, else cases with a
 *  smallint offset value would fail to resolve which function to use.
 *  But that's an unlikely situation, so don't duplicate code for it.
 *---------------------------------------------------------*/

Datum
in_range_int4_int4(PG_FUNCTION_ARGS)
{
    int32       val = PG_GETARG_INT32(0);
    int32       base = PG_GETARG_INT32(1);
    int32       offset = PG_GETARG_INT32(2);
    bool        sub = PG_GETARG_BOOL(3);
    bool        less = PG_GETARG_BOOL(4);
    int32       sum;

    if (offset < 0)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
                 errmsg("invalid preceding or following size in window function")));

    if (sub)
        offset = -offset;       /* cannot overflow */

    if (unlikely(pg_add_s32_overflow(base, offset, &sum)))
    {
        /*
         * If sub is false, the true sum is surely more than val, so correct
         * answer is the same as "less".  If sub is true, the true sum is
         * surely less than val, so the answer is "!less".
         */
        PG_RETURN_BOOL(sub ? !less : less);
    }

    if (less)
        PG_RETURN_BOOL(val <= sum);
    else
        PG_RETURN_BOOL(val >= sum);
}

Datum
in_range_int4_int2(PG_FUNCTION_ARGS)
{
    /* Doesn't seem worth duplicating code for, so just invoke int4_int4 */
    return DirectFunctionCall5(in_range_int4_int4,
                               PG_GETARG_DATUM(0),
                               PG_GETARG_DATUM(1),
                               Int32GetDatum((int32) PG_GETARG_INT16(2)),
                               PG_GETARG_DATUM(3),
                               PG_GETARG_DATUM(4));
}

Datum
in_range_int4_int8(PG_FUNCTION_ARGS)
{
    /* We must do all the math in int64 */
    int64       val = (int64) PG_GETARG_INT32(0);
    int64       base = (int64) PG_GETARG_INT32(1);
    int64       offset = PG_GETARG_INT64(2);
    bool        sub = PG_GETARG_BOOL(3);
    bool        less = PG_GETARG_BOOL(4);
    int64       sum;

    if (offset < 0)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
                 errmsg("invalid preceding or following size in window function")));

    if (sub)
        offset = -offset;       /* cannot overflow */

    if (unlikely(pg_add_s64_overflow(base, offset, &sum)))
    {
        /*
         * If sub is false, the true sum is surely more than val, so correct
         * answer is the same as "less".  If sub is true, the true sum is
         * surely less than val, so the answer is "!less".
         */
        PG_RETURN_BOOL(sub ? !less : less);
    }

    if (less)
        PG_RETURN_BOOL(val <= sum);
    else
        PG_RETURN_BOOL(val >= sum);
}

Datum
in_range_int2_int4(PG_FUNCTION_ARGS)
{
    /* We must do all the math in int32 */
    int32       val = (int32) PG_GETARG_INT16(0);
    int32       base = (int32) PG_GETARG_INT16(1);
    int32       offset = PG_GETARG_INT32(2);
    bool        sub = PG_GETARG_BOOL(3);
    bool        less = PG_GETARG_BOOL(4);
    int32       sum;

    if (offset < 0)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
                 errmsg("invalid preceding or following size in window function")));

    if (sub)
        offset = -offset;       /* cannot overflow */

    if (unlikely(pg_add_s32_overflow(base, offset, &sum)))
    {
        /*
         * If sub is false, the true sum is surely more than val, so correct
         * answer is the same as "less".  If sub is true, the true sum is
         * surely less than val, so the answer is "!less".
         */
        PG_RETURN_BOOL(sub ? !less : less);
    }

    if (less)
        PG_RETURN_BOOL(val <= sum);
    else
        PG_RETURN_BOOL(val >= sum);
}

Datum
in_range_int2_int2(PG_FUNCTION_ARGS)
{
    /* Doesn't seem worth duplicating code for, so just invoke int2_int4 */
    return DirectFunctionCall5(in_range_int2_int4,
                               PG_GETARG_DATUM(0),
                               PG_GETARG_DATUM(1),
                               Int32GetDatum((int32) PG_GETARG_INT16(2)),
                               PG_GETARG_DATUM(3),
                               PG_GETARG_DATUM(4));
}

Datum
in_range_int2_int8(PG_FUNCTION_ARGS)
{
    /* Doesn't seem worth duplicating code for, so just invoke int4_int8 */
    return DirectFunctionCall5(in_range_int4_int8,
                               Int32GetDatum((int32) PG_GETARG_INT16(0)),
                               Int32GetDatum((int32) PG_GETARG_INT16(1)),
                               PG_GETARG_DATUM(2),
                               PG_GETARG_DATUM(3),
                               PG_GETARG_DATUM(4));
}


/*
 *      int[24]pl       - returns arg1 + arg2
 *      int[24]mi       - returns arg1 - arg2
 *      int[24]mul      - returns arg1 * arg2
 *      int[24]div      - returns arg1 / arg2
 */

Datum
int4um(PG_FUNCTION_ARGS)
{
    int32       arg = PG_GETARG_INT32(0);

    if (unlikely(arg == PG_INT32_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(-arg);
}

Datum
int4up(PG_FUNCTION_ARGS)
{
    int32       arg = PG_GETARG_INT32(0);

    PG_RETURN_INT32(arg);
}

Datum
int4pl(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    if (unlikely(pg_add_s32_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int4mi(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    if (unlikely(pg_sub_s32_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int4mul(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    if (unlikely(pg_mul_s32_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int4div(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    if (arg2 == 0)
    {
        ereport(ERROR,
                (errcode(ERRCODE_DIVISION_BY_ZERO),
                 errmsg("division by zero")));
        /* ensure compiler realizes we mustn't reach the division (gcc bug) */
        PG_RETURN_NULL();
    }

    /*
     * INT_MIN / -1 is problematic, since the result can't be represented on a
     * two's-complement machine.  Some machines produce INT_MIN, some produce
     * zero, some throw an exception.  We can dodge the problem by recognizing
     * that division by -1 is the same as negation.
     */
    if (arg2 == -1)
    {
        if (unlikely(arg1 == PG_INT32_MIN))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("integer out of range")));
        result = -arg1;
        PG_RETURN_INT32(result);
    }

    /* No overflow is possible */

    result = arg1 / arg2;

    PG_RETURN_INT32(result);
}

Datum
int4inc(PG_FUNCTION_ARGS)
{
    int32       arg = PG_GETARG_INT32(0);
    int32       result;

    if (unlikely(pg_add_s32_overflow(arg, 1, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));

    PG_RETURN_INT32(result);
}

Datum
int2um(PG_FUNCTION_ARGS)
{
    int16       arg = PG_GETARG_INT16(0);

    if (unlikely(arg == PG_INT16_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("smallint out of range")));
    PG_RETURN_INT16(-arg);
}

Datum
int2up(PG_FUNCTION_ARGS)
{
    int16       arg = PG_GETARG_INT16(0);

    PG_RETURN_INT16(arg);
}

Datum
int2pl(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int16       result;

    if (unlikely(pg_add_s16_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("smallint out of range")));
    PG_RETURN_INT16(result);
}

Datum
int2mi(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int16       result;

    if (unlikely(pg_sub_s16_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("smallint out of range")));
    PG_RETURN_INT16(result);
}

Datum
int2mul(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int16       result;

    if (unlikely(pg_mul_s16_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("smallint out of range")));

    PG_RETURN_INT16(result);
}

Datum
int2div(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int16       result;

    if (arg2 == 0)
    {
        ereport(ERROR,
                (errcode(ERRCODE_DIVISION_BY_ZERO),
                 errmsg("division by zero")));
        /* ensure compiler realizes we mustn't reach the division (gcc bug) */
        PG_RETURN_NULL();
    }

    /*
     * SHRT_MIN / -1 is problematic, since the result can't be represented on
     * a two's-complement machine.  Some machines produce SHRT_MIN, some
     * produce zero, some throw an exception.  We can dodge the problem by
     * recognizing that division by -1 is the same as negation.
     */
    if (arg2 == -1)
    {
        if (unlikely(arg1 == PG_INT16_MIN))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("smallint out of range")));
        result = -arg1;
        PG_RETURN_INT16(result);
    }

    /* No overflow is possible */

    result = arg1 / arg2;

    PG_RETURN_INT16(result);
}

Datum
int24pl(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    if (unlikely(pg_add_s32_overflow((int32) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int24mi(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    if (unlikely(pg_sub_s32_overflow((int32) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int24mul(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    if (unlikely(pg_mul_s32_overflow((int32) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int24div(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    if (unlikely(arg2 == 0))
    {
        ereport(ERROR,
                (errcode(ERRCODE_DIVISION_BY_ZERO),
                 errmsg("division by zero")));
        /* ensure compiler realizes we mustn't reach the division (gcc bug) */
        PG_RETURN_NULL();
    }

    /* No overflow is possible */
    PG_RETURN_INT32((int32) arg1 / arg2);
}

Datum
int42pl(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int32       result;

    if (unlikely(pg_add_s32_overflow(arg1, (int32) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int42mi(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int32       result;

    if (unlikely(pg_sub_s32_overflow(arg1, (int32) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int42mul(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int32       result;

    if (unlikely(pg_mul_s32_overflow(arg1, (int32) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    PG_RETURN_INT32(result);
}

Datum
int42div(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int32       result;

    if (unlikely(arg2 == 0))
    {
        ereport(ERROR,
                (errcode(ERRCODE_DIVISION_BY_ZERO),
                 errmsg("division by zero")));
        /* ensure compiler realizes we mustn't reach the division (gcc bug) */
        PG_RETURN_NULL();
    }

    /*
     * INT_MIN / -1 is problematic, since the result can't be represented on a
     * two's-complement machine.  Some machines produce INT_MIN, some produce
     * zero, some throw an exception.  We can dodge the problem by recognizing
     * that division by -1 is the same as negation.
     */
    if (arg2 == -1)
    {
        if (unlikely(arg1 == PG_INT32_MIN))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("integer out of range")));
        result = -arg1;
        PG_RETURN_INT32(result);
    }

    /* No overflow is possible */

    result = arg1 / arg2;

    PG_RETURN_INT32(result);
}

Datum
int4mod(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    if (unlikely(arg2 == 0))
    {
        ereport(ERROR,
                (errcode(ERRCODE_DIVISION_BY_ZERO),
                 errmsg("division by zero")));
        /* ensure compiler realizes we mustn't reach the division (gcc bug) */
        PG_RETURN_NULL();
    }

    /*
     * Some machines throw a floating-point exception for INT_MIN % -1, which
     * is a bit silly since the correct answer is perfectly well-defined,
     * namely zero.
     */
    if (arg2 == -1)
        PG_RETURN_INT32(0);

    /* No overflow is possible */

    PG_RETURN_INT32(arg1 % arg2);
}

Datum
int2mod(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    if (unlikely(arg2 == 0))
    {
        ereport(ERROR,
                (errcode(ERRCODE_DIVISION_BY_ZERO),
                 errmsg("division by zero")));
        /* ensure compiler realizes we mustn't reach the division (gcc bug) */
        PG_RETURN_NULL();
    }

    /*
     * Some machines throw a floating-point exception for INT_MIN % -1, which
     * is a bit silly since the correct answer is perfectly well-defined,
     * namely zero.  (It's not clear this ever happens when dealing with
     * int16, but we might as well have the test for safety.)
     */
    if (arg2 == -1)
        PG_RETURN_INT16(0);

    /* No overflow is possible */

    PG_RETURN_INT16(arg1 % arg2);
}


/* int[24]abs()
 * Absolute value
 */
Datum
int4abs(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       result;

    if (unlikely(arg1 == PG_INT32_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));
    result = (arg1 < 0) ? -arg1 : arg1;
    PG_RETURN_INT32(result);
}

Datum
int2abs(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       result;

    if (unlikely(arg1 == PG_INT16_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("smallint out of range")));
    result = (arg1 < 0) ? -arg1 : arg1;
    PG_RETURN_INT16(result);
}

/*
 * Greatest Common Divisor
 *
 * Returns the largest positive integer that exactly divides both inputs.
 * Special cases:
 *   - gcd(x, 0) = gcd(0, x) = abs(x)
 *          because 0 is divisible by anything
 *   - gcd(0, 0) = 0
 *          complies with the previous definition and is a common convention
 *
 * Special care must be taken if either input is INT_MIN --- gcd(0, INT_MIN),
 * gcd(INT_MIN, 0) and gcd(INT_MIN, INT_MIN) are all equal to abs(INT_MIN),
 * which cannot be represented as a 32-bit signed integer.
 */
static int32
int4gcd_internal(int32 arg1, int32 arg2)
{
    int32       swap;
    int32       a1,
                a2;

    /*
     * Put the greater absolute value in arg1.
     *
     * This would happen automatically in the loop below, but avoids an
     * expensive modulo operation, and simplifies the special-case handling
     * for INT_MIN below.
     *
     * We do this in negative space in order to handle INT_MIN.
     */
    a1 = (arg1 < 0) ? arg1 : -arg1;
    a2 = (arg2 < 0) ? arg2 : -arg2;
    if (a1 > a2)
    {
        swap = arg1;
        arg1 = arg2;
        arg2 = swap;
    }

    /* Special care needs to be taken with INT_MIN.  See comments above. */
    if (arg1 == PG_INT32_MIN)
    {
        if (arg2 == 0 || arg2 == PG_INT32_MIN)
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("integer out of range")));

        /*
         * Some machines throw a floating-point exception for INT_MIN % -1,
         * which is a bit silly since the correct answer is perfectly
         * well-defined, namely zero.  Guard against this and just return the
         * result, gcd(INT_MIN, -1) = 1.
         */
        if (arg2 == -1)
            return 1;
    }

    /* Use the Euclidean algorithm to find the GCD */
    while (arg2 != 0)
    {
        swap = arg2;
        arg2 = arg1 % arg2;
        arg1 = swap;
    }

    /*
     * Make sure the result is positive. (We know we don't have INT_MIN
     * anymore).
     */
    if (arg1 < 0)
        arg1 = -arg1;

    return arg1;
}

Datum
int4gcd(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       result;

    result = int4gcd_internal(arg1, arg2);

    PG_RETURN_INT32(result);
}

/*
 * Least Common Multiple
 */
Datum
int4lcm(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int32       gcd;
    int32       result;

    /*
     * Handle lcm(x, 0) = lcm(0, x) = 0 as a special case.  This prevents a
     * division-by-zero error below when x is zero, and an overflow error from
     * the GCD computation when x = INT_MIN.
     */
    if (arg1 == 0 || arg2 == 0)
        PG_RETURN_INT32(0);

    /* lcm(x, y) = abs(x / gcd(x, y) * y) */
    gcd = int4gcd_internal(arg1, arg2);
    arg1 = arg1 / gcd;

    if (unlikely(pg_mul_s32_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));

    /* If the result is INT_MIN, it cannot be represented. */
    if (unlikely(result == PG_INT32_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));

    if (result < 0)
        result = -result;

    PG_RETURN_INT32(result);
}

Datum
int2larger(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_INT16((arg1 > arg2) ? arg1 : arg2);
}

Datum
int2smaller(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_INT16((arg1 < arg2) ? arg1 : arg2);
}

Datum
int4larger(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT32((arg1 > arg2) ? arg1 : arg2);
}

Datum
int4smaller(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT32((arg1 < arg2) ? arg1 : arg2);
}

/*
 * Bit-pushing operators
 *
 *      int[24]and      - returns arg1 & arg2
 *      int[24]or       - returns arg1 | arg2
 *      int[24]xor      - returns arg1 # arg2
 *      int[24]not      - returns ~arg1
 *      int[24]shl      - returns arg1 << arg2
 *      int[24]shr      - returns arg1 >> arg2
 */

Datum
int4and(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT32(arg1 & arg2);
}

Datum
int4or(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT32(arg1 | arg2);
}

Datum
int4xor(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT32(arg1 ^ arg2);
}

Datum
int4shl(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT32(arg1 << arg2);
}

Datum
int4shr(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT32(arg1 >> arg2);
}

Datum
int4not(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);

    PG_RETURN_INT32(~arg1);
}

Datum
int2and(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_INT16(arg1 & arg2);
}

Datum
int2or(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_INT16(arg1 | arg2);
}

Datum
int2xor(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int16       arg2 = PG_GETARG_INT16(1);

    PG_RETURN_INT16(arg1 ^ arg2);
}

Datum
int2not(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);

    PG_RETURN_INT16(~arg1);
}


Datum
int2shl(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT16(arg1 << arg2);
}

Datum
int2shr(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT16(arg1 >> arg2);
}

/*
 * non-persistent numeric series generator
 */
Datum
generate_series_int4(PG_FUNCTION_ARGS)
{
    return generate_series_step_int4(fcinfo);
}

Datum
generate_series_step_int4(PG_FUNCTION_ARGS)
{
    FuncCallContext *funcctx;
    generate_series_fctx *fctx;
    int32       result;
    MemoryContext oldcontext;

    /* stuff done only on the first call of the function */
    if (SRF_IS_FIRSTCALL())
    {
        int32       start = PG_GETARG_INT32(0);
        int32       finish = PG_GETARG_INT32(1);
        int32       step = 1;

        /* see if we were given an explicit step size */
        if (PG_NARGS() == 3)
            step = PG_GETARG_INT32(2);
        if (step == 0)
            ereport(ERROR,
                    (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                     errmsg("step size cannot equal zero")));

        /* create a function context for cross-call persistence */
        funcctx = SRF_FIRSTCALL_INIT();

        /*
         * switch to memory context appropriate for multiple function calls
         */
        oldcontext = MemoryContextSwitchTo(funcctx->multi_call_memory_ctx);

        /* allocate memory for user context */
        fctx = (generate_series_fctx *) palloc(sizeof(generate_series_fctx));

        /*
         * Use fctx to keep state from call to call. Seed current with the
         * original start value
         */
        fctx->current = start;
        fctx->finish = finish;
        fctx->step = step;

        funcctx->user_fctx = fctx;
        MemoryContextSwitchTo(oldcontext);
    }

    /* stuff done on every call of the function */
    funcctx = SRF_PERCALL_SETUP();

    /*
     * get the saved state and use current as the result for this iteration
     */
    fctx = funcctx->user_fctx;
    result = fctx->current;

    if ((fctx->step > 0 && fctx->current <= fctx->finish) ||
        (fctx->step < 0 && fctx->current >= fctx->finish))
    {
        /*
         * Increment current in preparation for next iteration. If next-value
         * computation overflows, this is the final result.
         */
        if (pg_add_s32_overflow(fctx->current, fctx->step, &fctx->current))
            fctx->step = 0;

        /* do when there is more left to send */
        SRF_RETURN_NEXT(funcctx, Int32GetDatum(result));
    }
    else
        /* do when there is no more left */
        SRF_RETURN_DONE(funcctx);
}

/*
 * Planner support function for generate_series(int4, int4 [, int4])
 */
Datum
generate_series_int4_support(PG_FUNCTION_ARGS)
{
    Node       *rawreq = (Node *) PG_GETARG_POINTER(0);
    Node       *ret = NULL;

    if (IsA(rawreq, SupportRequestRows))
    {
        /* Try to estimate the number of rows returned */
        SupportRequestRows *req = (SupportRequestRows *) rawreq;

        if (is_funcclause(req->node))   /* be paranoid */
        {
            List       *args = ((FuncExpr *) req->node)->args;
            Node       *arg1,
                       *arg2,
                       *arg3;

            /* We can use estimated argument values here */
            arg1 = estimate_expression_value(req->root, linitial(args));
            arg2 = estimate_expression_value(req->root, lsecond(args));
            if (list_length(args) >= 3)
                arg3 = estimate_expression_value(req->root, lthird(args));
            else
                arg3 = NULL;

            /*
             * If any argument is constant NULL, we can safely assume that
             * zero rows are returned.  Otherwise, if they're all non-NULL
             * constants, we can calculate the number of rows that will be
             * returned.  Use double arithmetic to avoid overflow hazards.
             */
            if ((IsA(arg1, Const) &&
                 ((Const *) arg1)->constisnull) ||
                (IsA(arg2, Const) &&
                 ((Const *) arg2)->constisnull) ||
                (arg3 != NULL && IsA(arg3, Const) &&
                 ((Const *) arg3)->constisnull))
            {
                req->rows = 0;
                ret = (Node *) req;
            }
            else if (IsA(arg1, Const) &&
                     IsA(arg2, Const) &&
                     (arg3 == NULL || IsA(arg3, Const)))
            {
                double      start,
                            finish,
                            step;

                start = DatumGetInt32(((Const *) arg1)->constvalue);
                finish = DatumGetInt32(((Const *) arg2)->constvalue);
                step = arg3 ? DatumGetInt32(((Const *) arg3)->constvalue) : 1;

                /* This equation works for either sign of step */
                if (step != 0)
                {
                    req->rows = floor((finish - start + step) / step);
                    ret = (Node *) req;
                }
            }
        }
    }

    PG_RETURN_POINTER(ret);
}