d2s.c File Reference

#include "postgres.h"
#include "common/shortest_dec.h"
#include "ryu_common.h"
#include "digit_table.h"
#include "d2s_full_table.h"
#include "d2s_intrinsics.h"

Include dependency graph for d2s.c:

Go to the source code of this file.

Data Structures
struct	floating_decimal_64

Macros
#define	DOUBLE_MANTISSA_BITS   52
#define	DOUBLE_EXPONENT_BITS   11
#define	DOUBLE_BIAS   1023
#define	DOUBLE_POW5_INV_BITCOUNT   122
#define	DOUBLE_POW5_BITCOUNT   121

Typedefs
typedef struct floating_decimal_64	floating_decimal_64

Functions
static uint32	pow5Factor (uint64 value)
static bool	multipleOfPowerOf5 (const uint64 value, const uint32 p)
static bool	multipleOfPowerOf2 (const uint64 value, const uint32 p)
static uint64	mulShiftAll (uint64 m, const uint64 *const mul, const int32 j, uint64 *const vp, uint64 *const vm, const uint32 mmShift)
static uint32	decimalLength (const uint64 v)
static floating_decimal_64	d2d (const uint64 ieeeMantissa, const uint32 ieeeExponent)
static int	to_chars_df (const floating_decimal_64 v, const uint32 olength, char *const result)
static int	to_chars (floating_decimal_64 v, const bool sign, char *const result)
static bool	d2d_small_int (const uint64 ieeeMantissa, const uint32 ieeeExponent, floating_decimal_64 *v)
int	double_to_shortest_decimal_bufn (double f, char *result)
int	double_to_shortest_decimal_buf (double f, char *result)
char *	double_to_shortest_decimal (double f)

Macro Definition Documentation

DOUBLE_BIAS

#define DOUBLE_BIAS   1023

Definition at line 67 of file d2s.c.

Referenced by d2d(), and d2d_small_int().

DOUBLE_EXPONENT_BITS

#define DOUBLE_EXPONENT_BITS   11

Definition at line 66 of file d2s.c.

Referenced by double_to_shortest_decimal_bufn().

DOUBLE_MANTISSA_BITS

#define DOUBLE_MANTISSA_BITS   52

Definition at line 65 of file d2s.c.

Referenced by d2d(), d2d_small_int(), and double_to_shortest_decimal_bufn().

DOUBLE_POW5_BITCOUNT

#define DOUBLE_POW5_BITCOUNT   121

Definition at line 70 of file d2s.c.

Referenced by d2d().

DOUBLE_POW5_INV_BITCOUNT

#define DOUBLE_POW5_INV_BITCOUNT   122

Definition at line 69 of file d2s.c.

Referenced by d2d().

Typedef Documentation

floating_decimal_64

typedef struct floating_decimal_64 floating_decimal_64

Function Documentation

d2d()

static floating_decimal_64 d2d ( const uint64  ieeeMantissa, const uint32  ieeeExponent  )

inlinestatic

Definition at line 346 of file d2s.c.

References div10(), div100(), div5(), DOUBLE_BIAS, DOUBLE_MANTISSA_BITS, DOUBLE_POW5_BITCOUNT, DOUBLE_POW5_INV_BITCOUNT, DOUBLE_POW5_INV_SPLIT, DOUBLE_POW5_SPLIT, floating_decimal_64::exponent, fd(), i, log10Pow2(), log10Pow5(), floating_decimal_64::mantissa, mulShiftAll(), multipleOfPowerOf2(), multipleOfPowerOf5(), output(), and pow5bits().

Referenced by double_to_shortest_decimal_bufn().

{
    int32       e2;
    uint64      m2;

    if (ieeeExponent == 0)
    {
        /* We subtract 2 so that the bounds computation has 2 additional bits. */
        e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
        m2 = ieeeMantissa;
    }
    else
    {
        e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
        m2 = (UINT64CONST(1) << DOUBLE_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 uint64 mv = 4 * m2;

    /* Implicit bool -> int conversion. True is 1, false is 0. */
    const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;

    /* We would compute mp and mm like this: */
    /* uint64 mp = 4 * m2 + 2; */
    /* uint64 mm = mv - 1 - mmShift; */

    /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
    uint64      vr,
                vp,
                vm;
    int32       e10;
    bool        vmIsTrailingZeros = false;
    bool        vrIsTrailingZeros = false;

    if (e2 >= 0)
    {
        /*
         * I tried special-casing q == 0, but there was no effect on
         * performance.
         *
         * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
         */
        const uint32 q = log10Pow2(e2) - (e2 > 3);
        const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
        const int32 i = -e2 + q + k;

        e10 = q;

        vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);

        if (q <= 21)
        {
            /*
             * This should use q <= 22, but I think 21 is also safe. Smaller
             * values may still be safe, but it's more difficult to reason
             * about them.
             *
             * Only one of mp, mv, and mm can be a multiple of 5, if any.
             */
            const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));

            if (mvMod5 == 0)
            {
                vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
            }
            else if (acceptBounds)
            {
                /*----
                 * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
                 * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
                 * <=> true && pow5Factor(mm) >= q, since e2 >= q.
                 *----
                 */
                vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
            }
            else
            {
                /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
                vp -= multipleOfPowerOf5(mv + 2, q);
            }
        }
    }
    else
    {
        /*
         * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
         */
        const uint32 q = log10Pow5(-e2) - (-e2 > 1);
        const int32 i = -e2 - q;
        const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
        const int32 j = q - k;

        e10 = q + e2;

        vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);

        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 < 63)
        {
            /* TODO(ulfjack):Use a tighter bound here. */
            /*
             * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
             */
            /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
            /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
            /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */

            /*
             * We also need to make sure that the left shift does not
             * overflow.
             */
            vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
        }
    }

    /*
     * Step 4: Find the shortest decimal representation in the interval of
     * legal representations.
     */
    uint32      removed = 0;
    uint8       lastRemovedDigit = 0;
    uint64      output;

    /* On average, we remove ~2 digits. */
    if (vmIsTrailingZeros || vrIsTrailingZeros)
    {
        /* General case, which happens rarely (~0.7%). */
        for (;;)
        {
            const uint64 vpDiv10 = div10(vp);
            const uint64 vmDiv10 = div10(vm);

            if (vpDiv10 <= vmDiv10)
                break;

            const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
            const uint64 vrDiv10 = div10(vr);
            const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);

            vmIsTrailingZeros &= vmMod10 == 0;
            vrIsTrailingZeros &= lastRemovedDigit == 0;
            lastRemovedDigit = (uint8) vrMod10;
            vr = vrDiv10;
            vp = vpDiv10;
            vm = vmDiv10;
            ++removed;
        }

        if (vmIsTrailingZeros)
        {
            for (;;)
            {
                const uint64 vmDiv10 = div10(vm);
                const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);

                if (vmMod10 != 0)
                    break;

                const uint64 vpDiv10 = div10(vp);
                const uint64 vrDiv10 = div10(vr);
                const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);

                vrIsTrailingZeros &= lastRemovedDigit == 0;
                lastRemovedDigit = (uint8) vrMod10;
                vr = vrDiv10;
                vp = vpDiv10;
                vm = vmDiv10;
                ++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 (~99.3%). Percentages below are
         * relative to this.
         */
        bool        roundUp = false;
        const uint64 vpDiv100 = div100(vp);
        const uint64 vmDiv100 = div100(vm);

        if (vpDiv100 > vmDiv100)
        {
            /* Optimization:remove two digits at a time(~86.2 %). */
            const uint64 vrDiv100 = div100(vr);
            const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);

            roundUp = vrMod100 >= 50;
            vr = vrDiv100;
            vp = vpDiv100;
            vm = vmDiv100;
            removed += 2;
        }

        /*----
         * Loop iterations below (approximately), without optimization
         * above:
         *
         * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
         * 6+: 0.02%
         *
         * Loop iterations below (approximately), with optimization
         * above:
         *
         * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
         *----
         */
        for (;;)
        {
            const uint64 vpDiv10 = div10(vp);
            const uint64 vmDiv10 = div10(vm);

            if (vpDiv10 <= vmDiv10)
                break;

            const uint64 vrDiv10 = div10(vr);
            const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);

            roundUp = vrMod10 >= 5;
            vr = vrDiv10;
            vp = vpDiv10;
            vm = vmDiv10;
            ++removed;
        }

        /*
         * We need to take vr + 1 if vr is outside bounds or we need to round
         * up.
         */
        output = vr + (vr == vm || roundUp);
    }

    const int32 exp = e10 + removed;

    floating_decimal_64 fd;

    fd.exponent = exp;
    fd.mantissa = output;
    return fd;
}

d2d_small_int()

static bool d2d_small_int ( const uint64  ieeeMantissa, const uint32  ieeeExponent, floating_decimal_64 *  v  )

inlinestatic

Definition at line 962 of file d2s.c.

References DOUBLE_BIAS, DOUBLE_MANTISSA_BITS, floating_decimal_64::exponent, and floating_decimal_64::mantissa.

Referenced by double_to_shortest_decimal_bufn().

{
    const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;

    /*
     * Avoid using multiple "return false;" here since it tends to provoke the
     * compiler into inlining multiple copies of d2d, which is undesirable.
     */

    if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
    {
        /*----
         * Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52:
         *   1 <= f = m2 / 2^-e2 < 2^53.
         *
         * 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 < -DOUBLE_MANTISSA_BITS which we already
         * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53)
         */
        const uint64 mask = (UINT64CONST(1) << -e2) - 1;
        const uint64 fraction = ieeeMantissa & mask;

        if (fraction == 0)
        {
            /*----
             * f is an integer in the range [1, 2^53).
             * Note: mantissa might contain trailing (decimal) 0's.
             * Note: since 2^53 < 10^16, there is no need to adjust
             * decimalLength().
             */
            const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;

            v->mantissa = m2 >> -e2;
            v->exponent = 0;
            return true;
        }
    }

    return false;
}

decimalLength()

static uint32 decimalLength ( const uint64  v )

inlinestatic

Definition at line 264 of file d2s.c.

References Assert.

Referenced by to_chars().

{
    /* This is slightly faster than a loop. */
    /* The average output length is 16.38 digits, so we check high-to-low. */
    /* Function precondition: v is not an 18, 19, or 20-digit number. */
    /* (17 digits are sufficient for round-tripping.) */
    Assert(v < 100000000000000000L);
    if (v >= 10000000000000000L)
    {
        return 17;
    }
    if (v >= 1000000000000000L)
    {
        return 16;
    }
    if (v >= 100000000000000L)
    {
        return 15;
    }
    if (v >= 10000000000000L)
    {
        return 14;
    }
    if (v >= 1000000000000L)
    {
        return 13;
    }
    if (v >= 100000000000L)
    {
        return 12;
    }
    if (v >= 10000000000L)
    {
        return 11;
    }
    if (v >= 1000000000L)
    {
        return 10;
    }
    if (v >= 100000000L)
    {
        return 9;
    }
    if (v >= 10000000L)
    {
        return 8;
    }
    if (v >= 1000000L)
    {
        return 7;
    }
    if (v >= 100000L)
    {
        return 6;
    }
    if (v >= 10000L)
    {
        return 5;
    }
    if (v >= 1000L)
    {
        return 4;
    }
    if (v >= 100L)
    {
        return 3;
    }
    if (v >= 10L)
    {
        return 2;
    }
    return 1;
}

double_to_shortest_decimal()

char* double_to_shortest_decimal

(

double

f

)

Definition at line 1070 of file d2s.c.

References DOUBLE_SHORTEST_DECIMAL_LEN, double_to_shortest_decimal_buf(), and palloc().

{
    char       *const result = (char *) palloc(DOUBLE_SHORTEST_DECIMAL_LEN);

    double_to_shortest_decimal_buf(f, result);
    return result;
}

double_to_shortest_decimal_buf()

int double_to_shortest_decimal_buf	(	double	f,
		char *	result
	)

Definition at line 1053 of file d2s.c.

References Assert, DOUBLE_SHORTEST_DECIMAL_LEN, and double_to_shortest_decimal_bufn().

Referenced by double_to_shortest_decimal(), and float8out_internal().

{
    const int   index = double_to_shortest_decimal_bufn(f, result);

    /* Terminate the string. */
    Assert(index < DOUBLE_SHORTEST_DECIMAL_LEN);
    result[index] = '\0';
    return index;
}

double_to_shortest_decimal_bufn()

int double_to_shortest_decimal_bufn	(	double	f,
		char *	result
	)

Definition at line 1015 of file d2s.c.

References copy_special_str(), d2d(), d2d_small_int(), DOUBLE_EXPONENT_BITS, DOUBLE_MANTISSA_BITS, double_to_bits(), and to_chars().

Referenced by double_to_shortest_decimal_buf().

{
    /*
     * Step 1: Decode the floating-point number, and unify normalized and
     * subnormal cases.
     */
    const uint64 bits = double_to_bits(f);

    /* Decode bits into sign, mantissa, and exponent. */
    const bool  ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
    const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
    const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));

    /* Case distinction; exit early for the easy cases. */
    if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
    {
        return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0));
    }

    floating_decimal_64 v;
    const bool  isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);

    if (!isSmallInt)
    {
        v = d2d(ieeeMantissa, ieeeExponent);
    }

    return to_chars(v, ieeeSign, result);
}

mulShiftAll()

static uint64 mulShiftAll ( uint64  m, const uint64 *const  mul, const int32  j, uint64 *const  vp, uint64 *const  vm, const uint32  mmShift  )

inlinestatic

Definition at line 220 of file d2s.c.

References shiftright128(), and umul128().

Referenced by d2d(), and multipleOfPowerOf2().

{
    m <<= 1;                    /* m is maximum 55 bits */

    uint64      tmp;
    const uint64 lo = umul128(m, mul[0], &tmp);
    uint64      hi;
    const uint64 mid = tmp + umul128(m, mul[1], &hi);

    hi += mid < tmp;            /* overflow into hi */

    const uint64 lo2 = lo + mul[0];
    const uint64 mid2 = mid + mul[1] + (lo2 < lo);
    const uint64 hi2 = hi + (mid2 < mid);

    *vp = shiftright128(mid2, hi2, j - 64 - 1);

    if (mmShift == 1)
    {
        const uint64 lo3 = lo - mul[0];
        const uint64 mid3 = mid - mul[1] - (lo3 > lo);
        const uint64 hi3 = hi - (mid3 > mid);

        *vm = shiftright128(mid3, hi3, j - 64 - 1);
    }
    else
    {
        const uint64 lo3 = lo + lo;
        const uint64 mid3 = mid + mid + (lo3 < lo);
        const uint64 hi3 = hi + hi + (mid3 < mid);
        const uint64 lo4 = lo3 - mul[0];
        const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
        const uint64 hi4 = hi3 - (mid4 > mid3);

        *vm = shiftright128(mid4, hi4, j - 64);
    }

    return shiftright128(mid, hi, j - 64 - 1);
}

multipleOfPowerOf2()

static bool multipleOfPowerOf2 ( const uint64  value, const uint32  p  )

inlinestatic

Definition at line 106 of file d2s.c.

References mulShift(), mulShiftAll(), shiftright128(), and umul128().

Referenced by d2d().

{
    /* return __builtin_ctzll(value) >= p; */
    return (value & ((UINT64CONST(1) << p) - 1)) == 0;
}

multipleOfPowerOf5()

static bool multipleOfPowerOf5 ( const uint64  value, const uint32  p  )

inlinestatic

Definition at line 95 of file d2s.c.

References pow5Factor().

Referenced by d2d().

{
    /*
     * I tried a case distinction on p, but there was no performance
     * difference.
     */
    return pow5Factor(value) >= p;
}

pow5Factor()

static uint32 pow5Factor ( uint64  value )

inlinestatic

Definition at line 74 of file d2s.c.

References Assert, and div5().

Referenced by multipleOfPowerOf5().

{
    uint32      count = 0;

    for (;;)
    {
        Assert(value != 0);
        const uint64 q = div5(value);
        const uint32 r = (uint32) (value - 5 * q);

        if (r != 0)
            break;

        value = q;
        ++count;
    }
    return count;
}

to_chars()

static int to_chars ( floating_decimal_64  v, const bool  sign, char *const  result  )

inlinestatic

Definition at line 787 of file d2s.c.

References decimalLength(), DIGIT_TABLE, div10(), div1e8(), floating_decimal_64::exponent, i, floating_decimal_64::mantissa, output(), sign, and to_chars_df().

Referenced by double_to_shortest_decimal_bufn().

{
    /* Step 5: Print the decimal representation. */
    int         index = 0;

    uint64      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_df and the value of
     * DOUBLE_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
     */
    if (exp >= -4 && exp < 15)
        return to_chars_df(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 uint64 q = div10(output);
            const uint32 r = (uint32) (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;

    /*
     * We prefer 32-bit operations, even on 64-bit platforms. We have at most
     * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
     * uint32, we cut off 8 digits, so the rest will fit into uint32.
     */
    if ((output >> 32) != 0)
    {
        /* Expensive 64-bit division. */
        const uint64 q = div1e8(output);
        uint32      output2 = (uint32) (output - 100000000 * q);

        output = q;

        const uint32 c = output2 % 10000;

        output2 /= 10000;

        const uint32 d = output2 % 10000;
        const uint32 c0 = (c % 100) << 1;
        const uint32 c1 = (c / 100) << 1;
        const uint32 d0 = (d % 100) << 1;
        const uint32 d1 = (d / 100) << 1;

        memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
        memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
        memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
        memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
        i += 8;
    }

    uint32      output2 = (uint32) output;

    while (output2 >= 10000)
    {
        const uint32 c = output2 - 10000 * (output2 / 10000);

        output2 /= 10000;

        const uint32 c0 = (c % 100) << 1;
        const uint32 c1 = (c / 100) << 1;

        memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
        memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
        i += 4;
    }
    if (output2 >= 100)
    {
        const uint32 c = (output2 % 100) << 1;

        output2 /= 100;
        memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
        i += 2;
    }
    if (output2 >= 10)
    {
        const uint32 c = output2 << 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' + output2);
    }

    /* 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++] = '+';

    if (exp >= 100)
    {
        const int32 c = exp % 10;

        memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
        result[index + 2] = (char) ('0' + c);
        index += 3;
    }
    else
    {
        memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
        index += 2;
    }

    return index;
}

to_chars_df()

static int to_chars_df ( const floating_decimal_64  v, const uint32  olength, char *const  result  )

inlinestatic

Definition at line 631 of file d2s.c.

References Assert, DIGIT_TABLE, div1e8(), floating_decimal_64::exponent, i, floating_decimal_64::mantissa, and output().

Referenced by to_chars().

{
    /* Step 5: Print the decimal representation. */
    int         index = 0;

    uint64      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;
        /* won't need more than this many 0s */
        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 16 output digits in this form, otherwise
         * we would not choose fixed-point output.
         */
        Assert(exp < 16 && exp + olength <= 16);
        memset(result, '0', 16);
    }

    /*
     * We prefer 32-bit operations, even on 64-bit platforms. We have at most
     * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
     * uint32, we cut off 8 digits, so the rest will fit into uint32.
     */
    if ((output >> 32) != 0)
    {
        /* Expensive 64-bit division. */
        const uint64 q = div1e8(output);
        uint32      output2 = (uint32) (output - 100000000 * q);
        const uint32 c = output2 % 10000;

        output = q;
        output2 /= 10000;

        const uint32 d = output2 % 10000;
        const uint32 c0 = (c % 100) << 1;
        const uint32 c1 = (c / 100) << 1;
        const uint32 d0 = (d % 100) << 1;
        const uint32 d1 = (d / 100) << 1;

        memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
        memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
        memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
        memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
        i += 8;
    }

    uint32      output2 = (uint32) output;

    while (output2 >= 10000)
    {
        const uint32 c = output2 - 10000 * (output2 / 10000);
        const uint32 c0 = (c % 100) << 1;
        const uint32 c1 = (c / 100) << 1;

        output2 /= 10000;
        memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
        memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
        i += 4;
    }
    if (output2 >= 100)
    {
        const uint32 c = (output2 % 100) << 1;

        output2 /= 100;
        memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
        i += 2;
    }
    if (output2 >= 10)
    {
        const uint32 c = output2 << 1;

        memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
    }
    else
    {
        result[index] = (char) ('0' + output2);
    }

    if (index == 1)
    {
        /*
         * nexp is 1..15 here, representing the number of digits before the
         * point. A value of 16 is not possible because we switch to
         * scientific notation when the display exponent reaches 15.
         */
        Assert(nexp < 16);
        /* gcc only seems to want to optimize memmove for small 2^n */
        if (nexp & 8)
        {
            memmove(result + index - 1, result + index, 8);
            index += 8;
        }
        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;
}