int8.c

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/*-------------------------------------------------------------------------
 *
 * int8.c
 *    Internal 64-bit integer operations
 *
 * Portions Copyright (c) 1996-2021, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *    src/backend/utils/adt/int8.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <ctype.h>
#include <limits.h>
#include <math.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/builtins.h"
#include "utils/int8.h"


typedef struct
{
    int64       current;
    int64       finish;
    int64       step;
} generate_series_fctx;


/***********************************************************************
 **
 **     Routines for 64-bit integers.
 **
 ***********************************************************************/

/*----------------------------------------------------------
 * Formatting and conversion routines.
 *---------------------------------------------------------*/

/*
 * scanint8 --- try to parse a string into an int8.
 *
 * If errorOK is false, ereport a useful error message if the string is bad.
 * If errorOK is true, just return "false" for bad input.
 */
bool
scanint8(const char *str, bool errorOK, int64 *result)
{
    const char *ptr = str;
    int64       tmp = 0;
    bool        neg = false;

    /*
     * Do our own scan, rather than relying on sscanf which might be broken
     * for long long.
     *
     * As INT64_MIN can't be stored as a positive 64 bit integer, accumulate
     * value as a negative number.
     */

    /* skip leading spaces */
    while (*ptr && isspace((unsigned char) *ptr))
        ptr++;

    /* handle sign */
    if (*ptr == '-')
    {
        ptr++;
        neg = true;
    }
    else if (*ptr == '+')
        ptr++;

    /* require at least one digit */
    if (unlikely(!isdigit((unsigned char) *ptr)))
        goto invalid_syntax;

    /* process digits */
    while (*ptr && isdigit((unsigned char) *ptr))
    {
        int8        digit = (*ptr++ - '0');

        if (unlikely(pg_mul_s64_overflow(tmp, 10, &tmp)) ||
            unlikely(pg_sub_s64_overflow(tmp, digit, &tmp)))
            goto out_of_range;
    }

    /* allow trailing whitespace, but not other trailing chars */
    while (*ptr != '\0' && isspace((unsigned char) *ptr))
        ptr++;

    if (unlikely(*ptr != '\0'))
        goto invalid_syntax;

    if (!neg)
    {
        /* could fail if input is most negative number */
        if (unlikely(tmp == PG_INT64_MIN))
            goto out_of_range;
        tmp = -tmp;
    }

    *result = tmp;
    return true;

out_of_range:
    if (!errorOK)
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("value \"%s\" is out of range for type %s",
                        str, "bigint")));
    return false;

invalid_syntax:
    if (!errorOK)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
                 errmsg("invalid input syntax for type %s: \"%s\"",
                        "bigint", str)));
    return false;
}

/* int8in()
 */
Datum
int8in(PG_FUNCTION_ARGS)
{
    char       *str = PG_GETARG_CSTRING(0);
    int64       result;

    (void) scanint8(str, false, &result);
    PG_RETURN_INT64(result);
}


/* int8out()
 */
Datum
int8out(PG_FUNCTION_ARGS)
{
    int64       val = PG_GETARG_INT64(0);
    char        buf[MAXINT8LEN + 1];
    char       *result;
    int         len;

    len = pg_lltoa(val, buf) + 1;

    /*
     * Since the length is already known, we do a manual palloc() and memcpy()
     * to avoid the strlen() call that would otherwise be done in pstrdup().
     */
    result = palloc(len);
    memcpy(result, buf, len);
    PG_RETURN_CSTRING(result);
}

/*
 *      int8recv            - converts external binary format to int8
 */
Datum
int8recv(PG_FUNCTION_ARGS)
{
    StringInfo  buf = (StringInfo) PG_GETARG_POINTER(0);

    PG_RETURN_INT64(pq_getmsgint64(buf));
}

/*
 *      int8send            - converts int8 to binary format
 */
Datum
int8send(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    StringInfoData buf;

    pq_begintypsend(&buf);
    pq_sendint64(&buf, arg1);
    PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*----------------------------------------------------------
 *  Relational operators for int8s, including cross-data-type comparisons.
 *---------------------------------------------------------*/

/* int8relop()
 * Is val1 relop val2?
 */
Datum
int8eq(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 == val2);
}

Datum
int8ne(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 != val2);
}

Datum
int8lt(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 < val2);
}

Datum
int8gt(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 > val2);
}

Datum
int8le(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 <= val2);
}

Datum
int8ge(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 >= val2);
}

/* int84relop()
 * Is 64-bit val1 relop 32-bit val2?
 */
Datum
int84eq(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int32       val2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(val1 == val2);
}

Datum
int84ne(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int32       val2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(val1 != val2);
}

Datum
int84lt(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int32       val2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(val1 < val2);
}

Datum
int84gt(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int32       val2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(val1 > val2);
}

Datum
int84le(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int32       val2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(val1 <= val2);
}

Datum
int84ge(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int32       val2 = PG_GETARG_INT32(1);

    PG_RETURN_BOOL(val1 >= val2);
}

/* int48relop()
 * Is 32-bit val1 relop 64-bit val2?
 */
Datum
int48eq(PG_FUNCTION_ARGS)
{
    int32       val1 = PG_GETARG_INT32(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 == val2);
}

Datum
int48ne(PG_FUNCTION_ARGS)
{
    int32       val1 = PG_GETARG_INT32(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 != val2);
}

Datum
int48lt(PG_FUNCTION_ARGS)
{
    int32       val1 = PG_GETARG_INT32(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 < val2);
}

Datum
int48gt(PG_FUNCTION_ARGS)
{
    int32       val1 = PG_GETARG_INT32(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 > val2);
}

Datum
int48le(PG_FUNCTION_ARGS)
{
    int32       val1 = PG_GETARG_INT32(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 <= val2);
}

Datum
int48ge(PG_FUNCTION_ARGS)
{
    int32       val1 = PG_GETARG_INT32(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 >= val2);
}

/* int82relop()
 * Is 64-bit val1 relop 16-bit val2?
 */
Datum
int82eq(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int16       val2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(val1 == val2);
}

Datum
int82ne(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int16       val2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(val1 != val2);
}

Datum
int82lt(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int16       val2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(val1 < val2);
}

Datum
int82gt(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int16       val2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(val1 > val2);
}

Datum
int82le(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int16       val2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(val1 <= val2);
}

Datum
int82ge(PG_FUNCTION_ARGS)
{
    int64       val1 = PG_GETARG_INT64(0);
    int16       val2 = PG_GETARG_INT16(1);

    PG_RETURN_BOOL(val1 >= val2);
}

/* int28relop()
 * Is 16-bit val1 relop 64-bit val2?
 */
Datum
int28eq(PG_FUNCTION_ARGS)
{
    int16       val1 = PG_GETARG_INT16(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 == val2);
}

Datum
int28ne(PG_FUNCTION_ARGS)
{
    int16       val1 = PG_GETARG_INT16(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 != val2);
}

Datum
int28lt(PG_FUNCTION_ARGS)
{
    int16       val1 = PG_GETARG_INT16(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 < val2);
}

Datum
int28gt(PG_FUNCTION_ARGS)
{
    int16       val1 = PG_GETARG_INT16(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 > val2);
}

Datum
int28le(PG_FUNCTION_ARGS)
{
    int16       val1 = PG_GETARG_INT16(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 <= val2);
}

Datum
int28ge(PG_FUNCTION_ARGS)
{
    int16       val1 = PG_GETARG_INT16(0);
    int64       val2 = PG_GETARG_INT64(1);

    PG_RETURN_BOOL(val1 >= val2);
}

/*
 * in_range support function for int8.
 *
 * Note: we needn't supply int8_int4 or int8_int2 variants, as implicit
 * coercion of the offset value takes care of those scenarios just as well.
 */
Datum
in_range_int8_int8(PG_FUNCTION_ARGS)
{
    int64       val = PG_GETARG_INT64(0);
    int64       base = PG_GETARG_INT64(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);
}


/*----------------------------------------------------------
 *  Arithmetic operators on 64-bit integers.
 *---------------------------------------------------------*/

Datum
int8um(PG_FUNCTION_ARGS)
{
    int64       arg = PG_GETARG_INT64(0);
    int64       result;

    if (unlikely(arg == PG_INT64_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    result = -arg;
    PG_RETURN_INT64(result);
}

Datum
int8up(PG_FUNCTION_ARGS)
{
    int64       arg = PG_GETARG_INT64(0);

    PG_RETURN_INT64(arg);
}

Datum
int8pl(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_add_s64_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int8mi(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_sub_s64_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int8mul(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_mul_s64_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int8div(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       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();
    }

    /*
     * INT64_MIN / -1 is problematic, since the result can't be represented on
     * a two's-complement machine.  Some machines produce INT64_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_INT64_MIN))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));
        result = -arg1;
        PG_RETURN_INT64(result);
    }

    /* No overflow is possible */

    result = arg1 / arg2;

    PG_RETURN_INT64(result);
}

/* int8abs()
 * Absolute value
 */
Datum
int8abs(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       result;

    if (unlikely(arg1 == PG_INT64_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    result = (arg1 < 0) ? -arg1 : arg1;
    PG_RETURN_INT64(result);
}

/* int8mod()
 * Modulo operation.
 */
Datum
int8mod(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(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 INT64_MIN % -1,
     * which is a bit silly since the correct answer is perfectly
     * well-defined, namely zero.
     */
    if (arg2 == -1)
        PG_RETURN_INT64(0);

    /* No overflow is possible */

    PG_RETURN_INT64(arg1 % arg2);
}

/*
 * 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 INT64_MIN ---
 * gcd(0, INT64_MIN), gcd(INT64_MIN, 0) and gcd(INT64_MIN, INT64_MIN) are
 * all equal to abs(INT64_MIN), which cannot be represented as a 64-bit signed
 * integer.
 */
static int64
int8gcd_internal(int64 arg1, int64 arg2)
{
    int64       swap;
    int64       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 INT64_MIN below.
     *
     * We do this in negative space in order to handle INT64_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 INT64_MIN.  See comments above. */
    if (arg1 == PG_INT64_MIN)
    {
        if (arg2 == 0 || arg2 == PG_INT64_MIN)
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));

        /*
         * Some machines throw a floating-point exception for INT64_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(INT64_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 INT64_MIN
     * anymore).
     */
    if (arg1 < 0)
        arg1 = -arg1;

    return arg1;
}

Datum
int8gcd(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    result = int8gcd_internal(arg1, arg2);

    PG_RETURN_INT64(result);
}

/*
 * Least Common Multiple
 */
Datum
int8lcm(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       gcd;
    int64       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 = INT64_MIN.
     */
    if (arg1 == 0 || arg2 == 0)
        PG_RETURN_INT64(0);

    /* lcm(x, y) = abs(x / gcd(x, y) * y) */
    gcd = int8gcd_internal(arg1, arg2);
    arg1 = arg1 / gcd;

    if (unlikely(pg_mul_s64_overflow(arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));

    /* If the result is INT64_MIN, it cannot be represented. */
    if (unlikely(result == PG_INT64_MIN))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));

    if (result < 0)
        result = -result;

    PG_RETURN_INT64(result);
}

Datum
int8inc(PG_FUNCTION_ARGS)
{
    /*
     * When int8 is pass-by-reference, we provide this special case to avoid
     * palloc overhead for COUNT(): when called as an aggregate, we know that
     * the argument is modifiable local storage, so just update it in-place.
     * (If int8 is pass-by-value, then of course this is useless as well as
     * incorrect, so just ifdef it out.)
     */
#ifndef USE_FLOAT8_BYVAL        /* controls int8 too */
    if (AggCheckCallContext(fcinfo, NULL))
    {
        int64      *arg = (int64 *) PG_GETARG_POINTER(0);

        if (unlikely(pg_add_s64_overflow(*arg, 1, arg)))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));

        PG_RETURN_POINTER(arg);
    }
    else
#endif
    {
        /* Not called as an aggregate, so just do it the dumb way */
        int64       arg = PG_GETARG_INT64(0);
        int64       result;

        if (unlikely(pg_add_s64_overflow(arg, 1, &result)))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));

        PG_RETURN_INT64(result);
    }
}

Datum
int8dec(PG_FUNCTION_ARGS)
{
    /*
     * When int8 is pass-by-reference, we provide this special case to avoid
     * palloc overhead for COUNT(): when called as an aggregate, we know that
     * the argument is modifiable local storage, so just update it in-place.
     * (If int8 is pass-by-value, then of course this is useless as well as
     * incorrect, so just ifdef it out.)
     */
#ifndef USE_FLOAT8_BYVAL        /* controls int8 too */
    if (AggCheckCallContext(fcinfo, NULL))
    {
        int64      *arg = (int64 *) PG_GETARG_POINTER(0);

        if (unlikely(pg_sub_s64_overflow(*arg, 1, arg)))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));
        PG_RETURN_POINTER(arg);
    }
    else
#endif
    {
        /* Not called as an aggregate, so just do it the dumb way */
        int64       arg = PG_GETARG_INT64(0);
        int64       result;

        if (unlikely(pg_sub_s64_overflow(arg, 1, &result)))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));

        PG_RETURN_INT64(result);
    }
}


/*
 * These functions are exactly like int8inc/int8dec but are used for
 * aggregates that count only non-null values.  Since the functions are
 * declared strict, the null checks happen before we ever get here, and all we
 * need do is increment the state value.  We could actually make these pg_proc
 * entries point right at int8inc/int8dec, but then the opr_sanity regression
 * test would complain about mismatched entries for a built-in function.
 */

Datum
int8inc_any(PG_FUNCTION_ARGS)
{
    return int8inc(fcinfo);
}

Datum
int8inc_float8_float8(PG_FUNCTION_ARGS)
{
    return int8inc(fcinfo);
}

Datum
int8dec_any(PG_FUNCTION_ARGS)
{
    return int8dec(fcinfo);
}


Datum
int8larger(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    result = ((arg1 > arg2) ? arg1 : arg2);

    PG_RETURN_INT64(result);
}

Datum
int8smaller(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    result = ((arg1 < arg2) ? arg1 : arg2);

    PG_RETURN_INT64(result);
}

Datum
int84pl(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int64       result;

    if (unlikely(pg_add_s64_overflow(arg1, (int64) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int84mi(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int64       result;

    if (unlikely(pg_sub_s64_overflow(arg1, (int64) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int84mul(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int64       result;

    if (unlikely(pg_mul_s64_overflow(arg1, (int64) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int84div(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int32       arg2 = PG_GETARG_INT32(1);
    int64       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();
    }

    /*
     * INT64_MIN / -1 is problematic, since the result can't be represented on
     * a two's-complement machine.  Some machines produce INT64_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_INT64_MIN))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));
        result = -arg1;
        PG_RETURN_INT64(result);
    }

    /* No overflow is possible */

    result = arg1 / arg2;

    PG_RETURN_INT64(result);
}

Datum
int48pl(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_add_s64_overflow((int64) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int48mi(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_sub_s64_overflow((int64) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int48mul(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_mul_s64_overflow((int64) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int48div(PG_FUNCTION_ARGS)
{
    int32       arg1 = PG_GETARG_INT32(0);
    int64       arg2 = PG_GETARG_INT64(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_INT64((int64) arg1 / arg2);
}

Datum
int82pl(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int64       result;

    if (unlikely(pg_add_s64_overflow(arg1, (int64) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int82mi(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int64       result;

    if (unlikely(pg_sub_s64_overflow(arg1, (int64) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int82mul(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int64       result;

    if (unlikely(pg_mul_s64_overflow(arg1, (int64) arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int82div(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int16       arg2 = PG_GETARG_INT16(1);
    int64       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();
    }

    /*
     * INT64_MIN / -1 is problematic, since the result can't be represented on
     * a two's-complement machine.  Some machines produce INT64_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_INT64_MIN))
            ereport(ERROR,
                    (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                     errmsg("bigint out of range")));
        result = -arg1;
        PG_RETURN_INT64(result);
    }

    /* No overflow is possible */

    result = arg1 / arg2;

    PG_RETURN_INT64(result);
}

Datum
int28pl(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_add_s64_overflow((int64) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int28mi(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_sub_s64_overflow((int64) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int28mul(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int64       arg2 = PG_GETARG_INT64(1);
    int64       result;

    if (unlikely(pg_mul_s64_overflow((int64) arg1, arg2, &result)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));
    PG_RETURN_INT64(result);
}

Datum
int28div(PG_FUNCTION_ARGS)
{
    int16       arg1 = PG_GETARG_INT16(0);
    int64       arg2 = PG_GETARG_INT64(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_INT64((int64) arg1 / arg2);
}

/* Binary arithmetics
 *
 *      int8and     - returns arg1 & arg2
 *      int8or      - returns arg1 | arg2
 *      int8xor     - returns arg1 # arg2
 *      int8not     - returns ~arg1
 *      int8shl     - returns arg1 << arg2
 *      int8shr     - returns arg1 >> arg2
 */

Datum
int8and(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);

    PG_RETURN_INT64(arg1 & arg2);
}

Datum
int8or(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);

    PG_RETURN_INT64(arg1 | arg2);
}

Datum
int8xor(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int64       arg2 = PG_GETARG_INT64(1);

    PG_RETURN_INT64(arg1 ^ arg2);
}

Datum
int8not(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);

    PG_RETURN_INT64(~arg1);
}

Datum
int8shl(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT64(arg1 << arg2);
}

Datum
int8shr(PG_FUNCTION_ARGS)
{
    int64       arg1 = PG_GETARG_INT64(0);
    int32       arg2 = PG_GETARG_INT32(1);

    PG_RETURN_INT64(arg1 >> arg2);
}

/*----------------------------------------------------------
 *  Conversion operators.
 *---------------------------------------------------------*/

Datum
int48(PG_FUNCTION_ARGS)
{
    int32       arg = PG_GETARG_INT32(0);

    PG_RETURN_INT64((int64) arg);
}

Datum
int84(PG_FUNCTION_ARGS)
{
    int64       arg = PG_GETARG_INT64(0);

    if (unlikely(arg < PG_INT32_MIN) || unlikely(arg > PG_INT32_MAX))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("integer out of range")));

    PG_RETURN_INT32((int32) arg);
}

Datum
int28(PG_FUNCTION_ARGS)
{
    int16       arg = PG_GETARG_INT16(0);

    PG_RETURN_INT64((int64) arg);
}

Datum
int82(PG_FUNCTION_ARGS)
{
    int64       arg = PG_GETARG_INT64(0);

    if (unlikely(arg < PG_INT16_MIN) || unlikely(arg > PG_INT16_MAX))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("smallint out of range")));

    PG_RETURN_INT16((int16) arg);
}

Datum
i8tod(PG_FUNCTION_ARGS)
{
    int64       arg = PG_GETARG_INT64(0);
    float8      result;

    result = arg;

    PG_RETURN_FLOAT8(result);
}

/* dtoi8()
 * Convert float8 to 8-byte integer.
 */
Datum
dtoi8(PG_FUNCTION_ARGS)
{
    float8      num = PG_GETARG_FLOAT8(0);

    /*
     * Get rid of any fractional part in the input.  This is so we don't fail
     * on just-out-of-range values that would round into range.  Note
     * assumption that rint() will pass through a NaN or Inf unchanged.
     */
    num = rint(num);

    /* Range check */
    if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT64(num)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));

    PG_RETURN_INT64((int64) num);
}

Datum
i8tof(PG_FUNCTION_ARGS)
{
    int64       arg = PG_GETARG_INT64(0);
    float4      result;

    result = arg;

    PG_RETURN_FLOAT4(result);
}

/* ftoi8()
 * Convert float4 to 8-byte integer.
 */
Datum
ftoi8(PG_FUNCTION_ARGS)
{
    float4      num = PG_GETARG_FLOAT4(0);

    /*
     * Get rid of any fractional part in the input.  This is so we don't fail
     * on just-out-of-range values that would round into range.  Note
     * assumption that rint() will pass through a NaN or Inf unchanged.
     */
    num = rint(num);

    /* Range check */
    if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT64(num)))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("bigint out of range")));

    PG_RETURN_INT64((int64) num);
}

Datum
i8tooid(PG_FUNCTION_ARGS)
{
    int64       arg = PG_GETARG_INT64(0);

    if (unlikely(arg < 0) || unlikely(arg > PG_UINT32_MAX))
        ereport(ERROR,
                (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
                 errmsg("OID out of range")));

    PG_RETURN_OID((Oid) arg);
}

Datum
oidtoi8(PG_FUNCTION_ARGS)
{
    Oid         arg = PG_GETARG_OID(0);

    PG_RETURN_INT64((int64) arg);
}

/*
 * non-persistent numeric series generator
 */
Datum
generate_series_int8(PG_FUNCTION_ARGS)
{
    return generate_series_step_int8(fcinfo);
}

Datum
generate_series_step_int8(PG_FUNCTION_ARGS)
{
    FuncCallContext *funcctx;
    generate_series_fctx *fctx;
    int64       result;
    MemoryContext oldcontext;

    /* stuff done only on the first call of the function */
    if (SRF_IS_FIRSTCALL())
    {
        int64       start = PG_GETARG_INT64(0);
        int64       finish = PG_GETARG_INT64(1);
        int64       step = 1;

        /* see if we were given an explicit step size */
        if (PG_NARGS() == 3)
            step = PG_GETARG_INT64(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_s64_overflow(fctx->current, fctx->step, &fctx->current))
            fctx->step = 0;

        /* do when there is more left to send */
        SRF_RETURN_NEXT(funcctx, Int64GetDatum(result));
    }
    else
        /* do when there is no more left */
        SRF_RETURN_DONE(funcctx);
}

/*
 * Planner support function for generate_series(int8, int8 [, int8])
 */
Datum
generate_series_int8_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 = DatumGetInt64(((Const *) arg1)->constvalue);
                finish = DatumGetInt64(((Const *) arg2)->constvalue);
                step = arg3 ? DatumGetInt64(((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);
}