f2s.c

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/*---------------------------------------------------------------------------
 *
 * Ryu floating-point output for single precision.
 *
 * Portions Copyright (c) 2018-2024, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/common/f2s.c
 *
 * This is a modification of code taken from github.com/ulfjack/ryu under the
 * terms of the Boost license (not the Apache license). The original copyright
 * notice follows:
 *
 * Copyright 2018 Ulf Adams
 *
 * The contents of this file may be used under the terms of the Apache
 * License, Version 2.0.
 *
 *     (See accompanying file LICENSE-Apache or copy at
 *      http://www.apache.org/licenses/LICENSE-2.0)
 *
 * Alternatively, the contents of this file may be used under the terms of the
 * Boost Software License, Version 1.0.
 *
 *     (See accompanying file LICENSE-Boost or copy at
 *      https://www.boost.org/LICENSE_1_0.txt)
 *
 * Unless required by applicable law or agreed to in writing, this software is
 * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.
 *
 *---------------------------------------------------------------------------
 */
 
#ifndef FRONTEND
#include "postgres.h"
#else
#include "postgres_fe.h"
#endif
 
#include "common/shortest_dec.h"
#include "digit_table.h"
#include "ryu_common.h"
 
#define FLOAT_MANTISSA_BITS 23
#define FLOAT_EXPONENT_BITS 8
#define FLOAT_BIAS 127
 
/*
 * This table is generated (by the upstream) by PrintFloatLookupTable,
 * and modified (by us) to add UINT64CONST.
 */
#define FLOAT_POW5_INV_BITCOUNT 59
static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
    UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
    UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
    UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
    UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
    UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
    UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
    UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
    UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
};
#define FLOAT_POW5_BITCOUNT 61
static const uint64 FLOAT_POW5_SPLIT[47] = {
    UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
    UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
    UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
    UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
    UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
    UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
    UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
    UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
    UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
    UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
    UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
    UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
};
 
static inline uint32
pow5Factor(uint32 value)
{
    uint32      count = 0;
 
    for (;;)
    {
        Assert(value != 0);
        const uint32 q = value / 5;
        const uint32 r = value % 5;
 
        if (r != 0)
            break;
 
        value = q;
        ++count;
    }
    return count;
}
 
/*  Returns true if value is divisible by 5^p. */
static inline bool
multipleOfPowerOf5(const uint32 value, const uint32 p)
{
    return pow5Factor(value) >= p;
}
 
/*  Returns true if value is divisible by 2^p. */
static inline bool
multipleOfPowerOf2(const uint32 value, const uint32 p)
{
    /* return __builtin_ctz(value) >= p; */
    return (value & ((1u << p) - 1)) == 0;
}
 
/*
 * It seems to be slightly faster to avoid uint128_t here, although the
 * generated code for uint128_t looks slightly nicer.
 */
static inline uint32
mulShift(const uint32 m, const uint64 factor, const int32 shift)
{
    /*
     * The casts here help MSVC to avoid calls to the __allmul library
     * function.
     */
    const uint32 factorLo = (uint32) (factor);
    const uint32 factorHi = (uint32) (factor >> 32);
    const uint64 bits0 = (uint64) m * factorLo;
    const uint64 bits1 = (uint64) m * factorHi;
 
    Assert(shift > 32);
 
#ifdef RYU_32_BIT_PLATFORM
 
    /*
     * On 32-bit platforms we can avoid a 64-bit shift-right since we only
     * need the upper 32 bits of the result and the shift value is > 32.
     */
    const uint32 bits0Hi = (uint32) (bits0 >> 32);
    uint32      bits1Lo = (uint32) (bits1);
    uint32      bits1Hi = (uint32) (bits1 >> 32);
 
    bits1Lo += bits0Hi;
    bits1Hi += (bits1Lo < bits0Hi);
 
    const int32 s = shift - 32;
 
    return (bits1Hi << (32 - s)) | (bits1Lo >> s);
 
#else                           /* RYU_32_BIT_PLATFORM */
 
    const uint64 sum = (bits0 >> 32) + bits1;
    const uint64 shiftedSum = sum >> (shift - 32);
 
    Assert(shiftedSum <= PG_UINT32_MAX);
    return (uint32) shiftedSum;
 
#endif                          /* RYU_32_BIT_PLATFORM */
}
 
static inline uint32
mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
{
    return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
}
 
static inline uint32
mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
{
    return mulShift(m, FLOAT_POW5_SPLIT[i], j);
}
 
static inline uint32
decimalLength(const uint32 v)
{
    /* Function precondition: v is not a 10-digit number. */
    /* (9 digits are sufficient for round-tripping.) */
    Assert(v < 1000000000);
    if (v >= 100000000)
    {
        return 9;
    }
    if (v >= 10000000)
    {
        return 8;
    }
    if (v >= 1000000)
    {
        return 7;
    }
    if (v >= 100000)
    {
        return 6;
    }
    if (v >= 10000)
    {
        return 5;
    }
    if (v >= 1000)
    {
        return 4;
    }
    if (v >= 100)
    {
        return 3;
    }
    if (v >= 10)
    {
        return 2;
    }
    return 1;
}
 
/*  A floating decimal representing m * 10^e. */
typedef struct floating_decimal_32
{
    uint32      mantissa;
    int32       exponent;
} floating_decimal_32;
 
static inline floating_decimal_32
f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
{
    int32       e2;
    uint32      m2;
 
    if (ieeeExponent == 0)
    {
        /* We subtract 2 so that the bounds computation has 2 additional bits. */
        e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
        m2 = ieeeMantissa;
    }
    else
    {
        e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
        m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
    }
 
#if STRICTLY_SHORTEST
    const bool  even = (m2 & 1) == 0;
    const bool  acceptBounds = even;
#else
    const bool  acceptBounds = false;
#endif
 
    /* Step 2: Determine the interval of legal decimal representations. */
    const uint32 mv = 4 * m2;
    const uint32 mp = 4 * m2 + 2;
 
    /* Implicit bool -> int conversion. True is 1, false is 0. */
    const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
    const uint32 mm = 4 * m2 - 1 - mmShift;
 
    /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
    uint32      vr,
                vp,
                vm;
    int32       e10;
    bool        vmIsTrailingZeros = false;
    bool        vrIsTrailingZeros = false;
    uint8       lastRemovedDigit = 0;
 
    if (e2 >= 0)
    {
        const uint32 q = log10Pow2(e2);
 
        e10 = q;
 
        const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
        const int32 i = -e2 + q + k;
 
        vr = mulPow5InvDivPow2(mv, q, i);
        vp = mulPow5InvDivPow2(mp, q, i);
        vm = mulPow5InvDivPow2(mm, q, i);
 
        if (q != 0 && (vp - 1) / 10 <= vm / 10)
        {
            /*
             * We need to know one removed digit even if we are not going to
             * loop below. We could use q = X - 1 above, except that would
             * require 33 bits for the result, and we've found that 32-bit
             * arithmetic is faster even on 64-bit machines.
             */
            const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
 
            lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
        }
        if (q <= 9)
        {
            /*
             * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
             * seems to be safe as well.
             *
             * Only one of mp, mv, and mm can be a multiple of 5, if any.
             */
            if (mv % 5 == 0)
            {
                vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
            }
            else if (acceptBounds)
            {
                vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
            }
            else
            {
                vp -= multipleOfPowerOf5(mp, q);
            }
        }
    }
    else
    {
        const uint32 q = log10Pow5(-e2);
 
        e10 = q + e2;
 
        const int32 i = -e2 - q;
        const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
        int32       j = q - k;
 
        vr = mulPow5divPow2(mv, i, j);
        vp = mulPow5divPow2(mp, i, j);
        vm = mulPow5divPow2(mm, i, j);
 
        if (q != 0 && (vp - 1) / 10 <= vm / 10)
        {
            j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
            lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
        }
        if (q <= 1)
        {
            /*
             * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
             * trailing 0 bits.
             */
            /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
            vrIsTrailingZeros = true;
            if (acceptBounds)
            {
                /*
                 * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
                 * mmShift == 1.
                 */
                vmIsTrailingZeros = mmShift == 1;
            }
            else
            {
                /*
                 * mp = mv + 2, so it always has at least one trailing 0 bit.
                 */
                --vp;
            }
        }
        else if (q < 31)
        {
            /* TODO(ulfjack):Use a tighter bound here. */
            vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
        }
    }
 
    /*
     * Step 4: Find the shortest decimal representation in the interval of
     * legal representations.
     */
    uint32      removed = 0;
    uint32      output;
 
    if (vmIsTrailingZeros || vrIsTrailingZeros)
    {
        /* General case, which happens rarely (~4.0%). */
        while (vp / 10 > vm / 10)
        {
            vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
            vrIsTrailingZeros &= lastRemovedDigit == 0;
            lastRemovedDigit = (uint8) (vr % 10);
            vr /= 10;
            vp /= 10;
            vm /= 10;
            ++removed;
        }
        if (vmIsTrailingZeros)
        {
            while (vm % 10 == 0)
            {
                vrIsTrailingZeros &= lastRemovedDigit == 0;
                lastRemovedDigit = (uint8) (vr % 10);
                vr /= 10;
                vp /= 10;
                vm /= 10;
                ++removed;
            }
        }
 
        if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
        {
            /* Round even if the exact number is .....50..0. */
            lastRemovedDigit = 4;
        }
 
        /*
         * We need to take vr + 1 if vr is outside bounds or we need to round
         * up.
         */
        output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
    }
    else
    {
        /*
         * Specialized for the common case (~96.0%). Percentages below are
         * relative to this.
         *
         * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
         * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
         */
        while (vp / 10 > vm / 10)
        {
            lastRemovedDigit = (uint8) (vr % 10);
            vr /= 10;
            vp /= 10;
            vm /= 10;
            ++removed;
        }
 
        /*
         * We need to take vr + 1 if vr is outside bounds or we need to round
         * up.
         */
        output = vr + (vr == vm || lastRemovedDigit >= 5);
    }
 
    const int32 exp = e10 + removed;
 
    floating_decimal_32 fd;
 
    fd.exponent = exp;
    fd.mantissa = output;
    return fd;
}
 
static inline int
to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
{
    /* Step 5: Print the decimal representation. */
    int         index = 0;
 
    uint32      output = v.mantissa;
    int32       exp = v.exponent;
 
    /*----
     * On entry, mantissa * 10^exp is the result to be output.
     * Caller has already done the - sign if needed.
     *
     * We want to insert the point somewhere depending on the output length
     * and exponent, which might mean adding zeros:
     *
     *            exp  | format
     *            1+   |  ddddddddd000000
     *            0    |  ddddddddd
     *  -1 .. -len+1   |  dddddddd.d to d.ddddddddd
     *  -len ...       |  0.ddddddddd to 0.000dddddd
     */
    uint32      i = 0;
    int32       nexp = exp + olength;
 
    if (nexp <= 0)
    {
        /* -nexp is number of 0s to add after '.' */
        Assert(nexp >= -3);
        /* 0.000ddddd */
        index = 2 - nexp;
        /* copy 8 bytes rather than 5 to let compiler optimize */
        memcpy(result, "0.000000", 8);
    }
    else if (exp < 0)
    {
        /*
         * dddd.dddd; leave space at the start and move the '.' in after
         */
        index = 1;
    }
    else
    {
        /*
         * We can save some code later by pre-filling with zeros. We know that
         * there can be no more than 6 output digits in this form, otherwise
         * we would not choose fixed-point output. memset 8 rather than 6
         * bytes to let the compiler optimize it.
         */
        Assert(exp < 6 && exp + olength <= 6);
        memset(result, '0', 8);
    }
 
    while (output >= 10000)
    {
        const uint32 c = output - 10000 * (output / 10000);
        const uint32 c0 = (c % 100) << 1;
        const uint32 c1 = (c / 100) << 1;
 
        output /= 10000;
 
        memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
        memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
        i += 4;
    }
    if (output >= 100)
    {
        const uint32 c = (output % 100) << 1;
 
        output /= 100;
        memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
        i += 2;
    }
    if (output >= 10)
    {
        const uint32 c = output << 1;
 
        memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
    }
    else
    {
        result[index] = (char) ('0' + output);
    }
 
    if (index == 1)
    {
        /*
         * nexp is 1..6 here, representing the number of digits before the
         * point. A value of 7+ is not possible because we switch to
         * scientific notation when the display exponent reaches 6.
         */
        Assert(nexp < 7);
        /* gcc only seems to want to optimize memmove for small 2^n */
        if (nexp & 4)
        {
            memmove(result + index - 1, result + index, 4);
            index += 4;
        }
        if (nexp & 2)
        {
            memmove(result + index - 1, result + index, 2);
            index += 2;
        }
        if (nexp & 1)
        {
            result[index - 1] = result[index];
        }
        result[nexp] = '.';
        index = olength + 1;
    }
    else if (exp >= 0)
    {
        /* we supplied the trailing zeros earlier, now just set the length. */
        index = olength + exp;
    }
    else
    {
        index = olength + (2 - nexp);
    }
 
    return index;
}
 
static inline int
to_chars(const floating_decimal_32 v, const bool sign, char *const result)
{
    /* Step 5: Print the decimal representation. */
    int         index = 0;
 
    uint32      output = v.mantissa;
    uint32      olength = decimalLength(output);
    int32       exp = v.exponent + olength - 1;
 
    if (sign)
        result[index++] = '-';
 
    /*
     * The thresholds for fixed-point output are chosen to match printf
     * defaults. Beware that both the code of to_chars_f and the value of
     * FLOAT_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
     */
    if (exp >= -4 && exp < 6)
        return to_chars_f(v, olength, result + index) + sign;
 
    /*
     * If v.exponent is exactly 0, we might have reached here via the small
     * integer fast path, in which case v.mantissa might contain trailing
     * (decimal) zeros. For scientific notation we need to move these zeros
     * into the exponent. (For fixed point this doesn't matter, which is why
     * we do this here rather than above.)
     *
     * Since we already calculated the display exponent (exp) above based on
     * the old decimal length, that value does not change here. Instead, we
     * just reduce the display length for each digit removed.
     *
     * If we didn't get here via the fast path, the raw exponent will not
     * usually be 0, and there will be no trailing zeros, so we pay no more
     * than one div10/multiply extra cost. We claw back half of that by
     * checking for divisibility by 2 before dividing by 10.
     */
    if (v.exponent == 0)
    {
        while ((output & 1) == 0)
        {
            const uint32 q = output / 10;
            const uint32 r = output - 10 * q;
 
            if (r != 0)
                break;
            output = q;
            --olength;
        }
    }
 
    /*----
     * Print the decimal digits.
     * The following code is equivalent to:
     *
     * for (uint32 i = 0; i < olength - 1; ++i) {
     *   const uint32 c = output % 10; output /= 10;
     *   result[index + olength - i] = (char) ('0' + c);
     * }
     * result[index] = '0' + output % 10;
     */
    uint32      i = 0;
 
    while (output >= 10000)
    {
        const uint32 c = output - 10000 * (output / 10000);
        const uint32 c0 = (c % 100) << 1;
        const uint32 c1 = (c / 100) << 1;
 
        output /= 10000;
 
        memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
        memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
        i += 4;
    }
    if (output >= 100)
    {
        const uint32 c = (output % 100) << 1;
 
        output /= 100;
        memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
        i += 2;
    }
    if (output >= 10)
    {
        const uint32 c = output << 1;
 
        /*
         * We can't use memcpy here: the decimal dot goes between these two
         * digits.
         */
        result[index + olength - i] = DIGIT_TABLE[c + 1];
        result[index] = DIGIT_TABLE[c];
    }
    else
    {
        result[index] = (char) ('0' + output);
    }
 
    /* Print decimal point if needed. */
    if (olength > 1)
    {
        result[index + 1] = '.';
        index += olength + 1;
    }
    else
    {
        ++index;
    }
 
    /* Print the exponent. */
    result[index++] = 'e';
    if (exp < 0)
    {
        result[index++] = '-';
        exp = -exp;
    }
    else
        result[index++] = '+';
 
    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
    index += 2;
 
    return index;
}
 
static inline bool
f2d_small_int(const uint32 ieeeMantissa,
              const uint32 ieeeExponent,
              floating_decimal_32 *v)
{
    const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS;
 
    /*
     * Avoid using multiple "return false;" here since it tends to provoke the
     * compiler into inlining multiple copies of f2d, which is undesirable.
     */
 
    if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0)
    {
        /*----
         * Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23:
         *   1 <= f = m2 / 2^-e2 < 2^24.
         *
         * Test if the lower -e2 bits of the significand are 0, i.e. whether
         * the fraction is 0. We can use ieeeMantissa here, since the implied
         * 1 bit can never be tested by this; the implied 1 can only be part
         * of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already
         * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24)
         */
        const uint32 mask = (1U << -e2) - 1;
        const uint32 fraction = ieeeMantissa & mask;
 
        if (fraction == 0)
        {
            /*----
             * f is an integer in the range [1, 2^24).
             * Note: mantissa might contain trailing (decimal) 0's.
             * Note: since 2^24 < 10^9, there is no need to adjust
             * decimalLength().
             */
            const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
 
            v->mantissa = m2 >> -e2;
            v->exponent = 0;
            return true;
        }
    }
 
    return false;
}
 
/*
 * Store the shortest decimal representation of the given float as an
 * UNTERMINATED string in the caller's supplied buffer (which must be at least
 * FLOAT_SHORTEST_DECIMAL_LEN-1 bytes long).
 *
 * Returns the number of bytes stored.
 */
int
float_to_shortest_decimal_bufn(float f, char *result)
{
    /*
     * Step 1: Decode the floating-point number, and unify normalized and
     * subnormal cases.
     */
    const uint32 bits = float_to_bits(f);
 
    /* Decode bits into sign, mantissa, and exponent. */
    const bool  ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
    const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
    const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
 
    /* Case distinction; exit early for the easy cases. */
    if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
    {
        return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0));
    }
 
    floating_decimal_32 v;
    const bool  isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v);
 
    if (!isSmallInt)
    {
        v = f2d(ieeeMantissa, ieeeExponent);
    }
 
    return to_chars(v, ieeeSign, result);
}
 
/*
 * Store the shortest decimal representation of the given float as a
 * null-terminated string in the caller's supplied buffer (which must be at
 * least FLOAT_SHORTEST_DECIMAL_LEN bytes long).
 *
 * Returns the string length.
 */
int
float_to_shortest_decimal_buf(float f, char *result)
{
    const int   index = float_to_shortest_decimal_bufn(f, result);
 
    /* Terminate the string. */
    Assert(index < FLOAT_SHORTEST_DECIMAL_LEN);
    result[index] = '\0';
    return index;
}
 
/*
 * Return the shortest decimal representation as a null-terminated palloc'd
 * string (outside the backend, uses malloc() instead).
 *
 * Caller is responsible for freeing the result.
 */
char *
float_to_shortest_decimal(float f)
{
    char       *const result = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN);
 
    float_to_shortest_decimal_buf(f, result);
    return result;
}