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com/fasterxml/jackson/core/io/schubfach/DoubleToDecimal.java

/*
 * Copyright 2018-2020 Raffaello Giulietti
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

package com.fasterxml.jackson.core.io.schubfach;

import java.io.IOException;

import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog10pow2;
import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog10threeQuartersPow2;
import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog2pow10;
import static com.fasterxml.jackson.core.io.schubfach.MathUtils.g0;
import static com.fasterxml.jackson.core.io.schubfach.MathUtils.g1;
import static com.fasterxml.jackson.core.io.schubfach.MathUtils.multiplyHigh;
import static com.fasterxml.jackson.core.io.schubfach.MathUtils.pow10;
import static java.lang.Double.doubleToRawLongBits;
import static java.lang.Long.numberOfLeadingZeros;

/**
 * This class exposes a method to render a {@code double} as a string.
 *
 * @author Raffaello Giulietti
 */
final public class DoubleToDecimal {
    /*
    For full details about this code see the following references:

    [1] Giulietti, "The Schubfach way to render doubles",
        https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN

    [2] IEEE Computer Society, "IEEE Standard for Floating-Point Arithmetic"

    [3] Bouvier & Zimmermann, "Division-Free Binary-to-Decimal Conversion"

    Divisions are avoided altogether for the benefit of those architectures
    that do not provide specific machine instructions or where they are slow.
    This is discussed in section 10 of [1].
     */

    // Sources with the license are here: https://github.com/c4f7fcce9cb06515/Schubfach/blob/3c92d3c9b1fead540616c918cdfef432bca53dfa/todec/src/math/FloatToDecimal.java

    // The precision in bits.
    static final int P = 53;

    // Exponent width in bits.
    private static final int W = (Double.SIZE - 1) - (P - 1);

    // Minimum value of the exponent: -(2^(W-1)) - P + 3.
    static final int Q_MIN = (-1 << W - 1) - P + 3;

    // Maximum value of the exponent: 2^(W-1) - P.
    static final int Q_MAX = (1 << W - 1) - P;

    // 10^(E_MIN - 1) <= MIN_VALUE < 10^E_MIN
    static final int E_MIN = -323;

    // 10^(E_MAX - 1) <= MAX_VALUE < 10^E_MAX
    static final int E_MAX = 309;

    // Threshold to detect tiny values, as in section 8.1.1 of [1]
    static final long C_TINY = 3;

    // The minimum and maximum k, as in section 8 of [1]
    static final int K_MIN = -324;
    static final int K_MAX = 292;

    // H is as in section 8 of [1].
    static final int H = 17;

    // Minimum value of the significand of a normal value: 2^(P-1).
    private static final long C_MIN = 1L << P - 1;

    // Mask to extract the biased exponent.
    private static final int BQ_MASK = (1 << W) - 1;

    // Mask to extract the fraction bits.
    private static final long T_MASK = (1L << P - 1) - 1;

    // Used in rop().
    private static final long MASK_63 = (1L << 63) - 1;

    // Used for left-to-tight digit extraction.
    private static final int MASK_28 = (1 << 28) - 1;

    private static final int NON_SPECIAL = 0;
    private static final int PLUS_ZERO = 1;
    private static final int MINUS_ZERO = 2;
    private static final int PLUS_INF = 3;
    private static final int MINUS_INF = 4;
    private static final int NAN = 5;

    // For thread-safety, each thread gets its own instance of this class.
    private static final ThreadLocal<DoubleToDecimal> threadLocal =
            ThreadLocal.withInitial(DoubleToDecimal::new);

    /*
    Room for the longer of the forms
        -ddddd.dddddddddddd         H + 2 characters
        -0.00ddddddddddddddddd      H + 5 characters
        -d.ddddddddddddddddE-eee    H + 7 characters
    where there are H digits d
     */
    public final int MAX_CHARS = H + 7;

    // Numerical results are created here...
    private final byte[] bytes = new byte[MAX_CHARS];

    // ... and copied here in appendTo()
    private final char[] chars = new char[MAX_CHARS];

    // Index into bytes of rightmost valid character.
    private int index;

    private DoubleToDecimal() {
    }

    /**
     * Returns a string rendering of the {@code double} argument.
     *
     * <p>The characters of the result are all drawn from the ASCII set.
     * <ul>
     * <li> Any NaN, whether quiet or signaling, is rendered as
     * {@code "NaN"}, regardless of the sign bit.
     * <li> The infinities +&infin; and -&infin; are rendered as
     * {@code "Infinity"} and {@code "-Infinity"}, respectively.
     * <li> The positive and negative zeroes are rendered as
     * {@code "0.0"} and {@code "-0.0"}, respectively.
     * <li> A finite negative {@code v} is rendered as the sign
     * '{@code -}' followed by the rendering of the magnitude -{@code v}.
     * <li> A finite positive {@code v} is rendered in two stages:
     * <ul>
     * <li> <em>Selection of a decimal</em>: A well-defined
     * decimal <i>d</i><sub><code>v</code></sub> is selected
     * to represent {@code v}.
     * <li> <em>Formatting as a string</em>: The decimal
     * <i>d</i><sub><code>v</code></sub> is formatted as a string,
     * either in plain or in computerized scientific notation,
     * depending on its value.
     * </ul>
     * </ul>
     *
     * <p>A <em>decimal</em> is a number of the form
     * <i>d</i>&times;10<sup><i>i</i></sup>
     * for some (unique) integers <i>d</i> &gt; 0 and <i>i</i> such that
     * <i>d</i> is not a multiple of 10.
     * These integers are the <em>significand</em> and
     * the <em>exponent</em>, respectively, of the decimal.
     * The <em>length</em> of the decimal is the (unique)
     * integer <i>n</i> meeting
     * 10<sup><i>n</i>-1</sup> &le; <i>d</i> &lt; 10<sup><i>n</i></sup>.
     *
     * <p>The decimal <i>d</i><sub><code>v</code></sub>
     * for a finite positive {@code v} is defined as follows:
     * <ul>
     * <li>Let <i>R</i> be the set of all decimals that round to {@code v}
     * according to the usual round-to-closest rule of
     * IEEE 754 floating-point arithmetic.
     * <li>Let <i>m</i> be the minimal length over all decimals in <i>R</i>.
     * <li>When <i>m</i> &ge; 2, let <i>T</i> be the set of all decimals
     * in <i>R</i> with length <i>m</i>.
     * Otherwise, let <i>T</i> be the set of all decimals
     * in <i>R</i> with length 1 or 2.
     * <li>Define <i>d</i><sub><code>v</code></sub> as
     * the decimal in <i>T</i> that is closest to {@code v}.
     * Or if there are two such decimals in <i>T</i>,
     * select the one with the even significand (there is exactly one).
     * </ul>
     *
     * <p>The (uniquely) selected decimal <i>d</i><sub><code>v</code></sub>
     * is then formatted.
     *
     * <p>Let <i>d</i>, <i>i</i> and <i>n</i> be the significand, exponent and
     * length of <i>d</i><sub><code>v</code></sub>, respectively.
     * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
     * <i>d</i><sub>1</sub>&hellip;<i>d</i><sub><i>n</i></sub>
     * be the usual decimal expansion of the significand.
     * Note that <i>d</i><sub>1</sub> &ne; 0 &ne; <i>d</i><sub><i>n</i></sub>.
     * <ul>
     * <li>Case -3 &le; <i>e</i> &lt; 0:
     * <i>d</i><sub><code>v</code></sub> is formatted as
     * <code>0.0</code>&hellip;<code>0</code><!--
     * --><i>d</i><sub>1</sub>&hellip;<i>d</i><sub><i>n</i></sub>,
     * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
     * the decimal point and <i>d</i><sub>1</sub>.
     * For example, 123 &times; 10<sup>-4</sup> is formatted as
     * {@code 0.0123}.
     * <li>Case 0 &le; <i>e</i> &lt; 7:
     * <ul>
     * <li>Subcase <i>i</i> &ge; 0:
     * <i>d</i><sub><code>v</code></sub> is formatted as
     * <i>d</i><sub>1</sub>&hellip;<i>d</i><sub><i>n</i></sub><!--
     * --><code>0</code>&hellip;<code>0.0</code>,
     * where there are exactly <i>i</i> zeroes
     * between <i>d</i><sub><i>n</i></sub> and the decimal point.
     * For example, 123 &times; 10<sup>2</sup> is formatted as
     * {@code 12300.0}.
     * <li>Subcase <i>i</i> &lt; 0:
     * <i>d</i><sub><code>v</code></sub> is formatted as
     * <i>d</i><sub>1</sub>&hellip;<!--
     * --><i>d</i><sub><i>n</i>+<i>i</i></sub>.<!--
     * --><i>d</i><sub><i>n</i>+<i>i</i>+1</sub>&hellip;<!--
     * --><i>d</i><sub><i>n</i></sub>.
     * There are exactly -<i>i</i> digits to the right of
     * the decimal point.
     * For example, 123 &times; 10<sup>-1</sup> is formatted as
     * {@code 12.3}.
     * </ul>
     * <li>Case <i>e</i> &lt; -3 or <i>e</i> &ge; 7:
     * computerized scientific notation is used to format
     * <i>d</i><sub><code>v</code></sub>.
     * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
     * <ul>
     * <li>Subcase <i>n</i> = 1:
     * <i>d</i><sub><code>v</code></sub> is formatted as
     * <i>d</i><sub>1</sub><code>.0E</code><i>e</i>.
     * For example, 1 &times; 10<sup>23</sup> is formatted as
     * {@code 1.0E23}.
     * <li>Subcase <i>n</i> &gt; 1:
     * <i>d</i><sub><code>v</code></sub> is formatted as
     * <i>d</i><sub>1</sub><code>.</code><i>d</i><sub>2</sub><!--
     * -->&hellip;<i>d</i><sub><i>n</i></sub><code>E</code><i>e</i>.
     * For example, 123 &times; 10<sup>-21</sup> is formatted as
     * {@code 1.23E-19}.
     * </ul>
     * </ul>
     *
     * @param v the {@code double} to be rendered.
     * @return a string rendering of the argument.
     */
    public static String toString(double v) {
        return threadLocalInstance().toDecimalString(v);
    }

    /**
     * Appends the rendering of the {@code v} to {@code app}.
     *
     * <p>The outcome is the same as if {@code v} were first
     * {@link #toString(double) rendered} and the resulting string were then
     * {@link Appendable#append(CharSequence) appended} to {@code app}.
     *
     * @param v the {@code double} whose rendering is appended.
     * @param app the {@link Appendable} to append to.
     * @throws IOException If an I/O error occurs
     */
    public static Appendable appendTo(double v, Appendable app)
            throws IOException {
        return threadLocalInstance().appendDecimalTo(v, app);
    }

    private static DoubleToDecimal threadLocalInstance() {
        return threadLocal.get();
    }

    private String toDecimalString(double v) {
        switch (toDecimal(v)) {
            case NON_SPECIAL: return charsToString();
            case PLUS_ZERO: return "0.0";
            case MINUS_ZERO: return "-0.0";
            case PLUS_INF: return "Infinity";
            case MINUS_INF: return "-Infinity";
            default: return "NaN";
        }
    }

    private Appendable appendDecimalTo(double v, Appendable app)
            throws IOException {
        switch (toDecimal(v)) {
            case NON_SPECIAL:
                for (int i = 0; i <= index; ++i) {
                    chars[i] = (char) bytes[i];
                }
                if (app instanceof StringBuilder) {
                    return ((StringBuilder) app).append(chars, 0, index + 1);
                }
                if (app instanceof StringBuffer) {
                    return ((StringBuffer) app).append(chars, 0, index + 1);
                }
                for (int i = 0; i <= index; ++i) {
                    app.append(chars[i]);
                }
                return app;
            case PLUS_ZERO: return app.append("0.0");
            case MINUS_ZERO: return app.append("-0.0");
            case PLUS_INF: return app.append("Infinity");
            case MINUS_INF: return app.append("-Infinity");
            default: return app.append("NaN");
        }
    }

    /*
    Returns
        PLUS_ZERO       iff v is 0.0
        MINUS_ZERO      iff v is -0.0
        PLUS_INF        iff v is POSITIVE_INFINITY
        MINUS_INF       iff v is NEGATIVE_INFINITY
        NAN             iff v is NaN
     */
    private int toDecimal(double v) {
        /*
        For full details see references [2] and [1].

        For finite v != 0, determine integers c and q such that
            |v| = c 2^q    and
            Q_MIN <= q <= Q_MAX    and
                either    2^(P-1) <= c < 2^P                 (normal)
                or        0 < c < 2^(P-1)  and  q = Q_MIN    (subnormal)
         */
        long bits = doubleToRawLongBits(v);
        long t = bits & T_MASK;
        int bq = (int) (bits >>> P - 1) & BQ_MASK;
        if (bq < BQ_MASK) {
            index = -1;
            if (bits < 0) {
                append('-');
            }
            if (bq != 0) {
                // normal value. Here mq = -q
                int mq = -Q_MIN + 1 - bq;
                long c = C_MIN | t;
                // The fast path discussed in section 8.2 of [1].
                if (0 < mq & mq < P) {
                    long f = c >> mq;
                    if (f << mq == c) {
                        return toChars(f, 0);
                    }
                }
                return toDecimal(-mq, c, 0);
            }
            if (t != 0) {
                // subnormal value
                return t < C_TINY
                        ? toDecimal(Q_MIN, 10 * t, -1)
                        : toDecimal(Q_MIN, t, 0);
            }
            return bits == 0 ? PLUS_ZERO : MINUS_ZERO;
        }
        if (t != 0) {
            return NAN;
        }
        return bits > 0 ? PLUS_INF : MINUS_INF;
    }

    private int toDecimal(int q, long c, int dk) {
        /*
        The skeleton corresponds to figure 4 of [1].
        The efficient computations are those summarized in figure 7.

        Here's a correspondence between Java names and names in [1],
        expressed as approximate LaTeX source code and informally.
        Other names are identical.
        cb:     \bar{c}     "c-bar"
        cbr:    \bar{c}_r   "c-bar-r"
        cbl:    \bar{c}_l   "c-bar-l"

        vb:     \bar{v}     "v-bar"
        vbr:    \bar{v}_r   "v-bar-r"
        vbl:    \bar{v}_l   "v-bar-l"

        rop:    r_o'        "r-o-prime"
         */
        int out = (int) c & 0x1;
        long cb = c << 2;
        long cbr = cb + 2;
        long cbl;
        int k;
        /*
        flog10pow2(e) = floor(log_10(2^e))
        flog10threeQuartersPow2(e) = floor(log_10(3/4 2^e))
        flog2pow10(e) = floor(log_2(10^e))
         */
        if (c != C_MIN | q == Q_MIN) {
            // regular spacing
            cbl = cb - 2;
            k = flog10pow2(q);
        } else {
            // irregular spacing
            cbl = cb - 1;
            k = flog10threeQuartersPow2(q);
        }
        int h = q + flog2pow10(-k) + 2;

        // g1 and g0 are as in section 9.9.3 of [1], so g = g1 2^63 + g0
        long g1 = g1(k);
        long g0 = g0(k);

        long vb = rop(g1, g0, cb << h);
        long vbl = rop(g1, g0, cbl << h);
        long vbr = rop(g1, g0, cbr << h);

        long s = vb >> 2;
        if (s >= 100) {
            /*
            For n = 17, m = 1 the table in section 10 of [1] shows
                s' = floor(s / 10) = floor(s 115_292_150_460_684_698 / 2^60)
                   = floor(s 115_292_150_460_684_698 2^4 / 2^64)

            sp10 = 10 s'
            tp10 = 10 t'
            upin    iff    u' = sp10 10^k in Rv
            wpin    iff    w' = tp10 10^k in Rv
            See section 9.4 of [1].
             */
            long sp10 = 10 * multiplyHigh(s, 115_292_150_460_684_698L << 4);
            long tp10 = sp10 + 10;
            boolean upin = vbl + out <= sp10 << 2;
            boolean wpin = (tp10 << 2) + out <= vbr;
            if (upin != wpin) {
                return toChars(upin ? sp10 : tp10, k);
            }
        }

        /*
        10 <= s < 100    or    s >= 100  and  u', w' not in Rv
        uin    iff    u = s 10^k in Rv
        win    iff    w = t 10^k in Rv
        See section 9.4 of [1].
         */
        long t = s + 1;
        boolean uin = vbl + out <= s << 2;
        boolean win = (t << 2) + out <= vbr;
        if (uin != win) {
            // Exactly one of u or w lies in Rv.
            return toChars(uin ? s : t, k + dk);
        }
        /*
        Both u and w lie in Rv: determine the one closest to v.
        See section 9.4 of [1].
         */
        long cmp = vb - (s + t << 1);
        return toChars(cmp < 0 || cmp == 0 && (s & 0x1) == 0 ? s : t, k + dk);
    }

    /*
    Computes rop(cp g 2^(-127)), where g = g1 2^63 + g0
    See section 9.10 and figure 5 of [1].
     */
    private static long rop(long g1, long g0, long cp) {
        long x1 = multiplyHigh(g0, cp);
        long y0 = g1 * cp;
        long y1 = multiplyHigh(g1, cp);
        long z = (y0 >>> 1) + x1;
        long vbp = y1 + (z >>> 63);
        return vbp | (z & MASK_63) + MASK_63 >>> 63;
    }

    /*
    Formats the decimal f 10^e.
     */
    private int toChars(long f, int e) {
        /*
        For details not discussed here see section 10 of [1].

        Determine len such that
            10^(len-1) <= f < 10^len
         */
        int len = flog10pow2(Long.SIZE - numberOfLeadingZeros(f));
        if (f >= pow10(len)) {
            len += 1;
        }

        /*
        Let fp and ep be the original f and e, respectively.
        Transform f and e to ensure
            10^(H-1) <= f < 10^H
            fp 10^ep = f 10^(e-H) = 0.f 10^e
         */
        f *= pow10(H - len);
        e += len;

        /*
        The toChars?() methods perform left-to-right digits extraction
        using ints, provided that the arguments are limited to 8 digits.
        Therefore, split the H = 17 digits of f into:
            h = the most significant digit of f
            m = the next 8 most significant digits of f
            l = the last 8, least significant digits of f

        For n = 17, m = 8 the table in section 10 of [1] shows
            floor(f / 10^8) = floor(193_428_131_138_340_668 f / 2^84) =
            floor(floor(193_428_131_138_340_668 f / 2^64) / 2^20)
        and for n = 9, m = 8
            floor(hm / 10^8) = floor(1_441_151_881 hm / 2^57)
         */
        long hm = multiplyHigh(f, 193_428_131_138_340_668L) >>> 20;
        int l = (int) (f - 100_000_000L * hm);
        int h = (int) (hm * 1_441_151_881L >>> 57);
        int m = (int) (hm - 100_000_000 * h);

        if (0 < e && e <= 7) {
            return toChars1(h, m, l, e);
        }
        if (-3 < e && e <= 0) {
            return toChars2(h, m, l, e);
        }
        return toChars3(h, m, l, e);
    }

    private int toChars1(int h, int m, int l, int e) {
        /*
        0 < e <= 7: plain format without leading zeroes.
        Left-to-right digits extraction:
        algorithm 1 in [3], with b = 10, k = 8, n = 28.
         */
        appendDigit(h);
        int y = y(m);
        int t;
        int i = 1;
        for (; i < e; ++i) {
            t = 10 * y;
            appendDigit(t >>> 28);
            y = t & MASK_28;
        }
        append('.');
        for (; i <= 8; ++i) {
            t = 10 * y;
            appendDigit(t >>> 28);
            y = t & MASK_28;
        }
        lowDigits(l);
        return NON_SPECIAL;
    }

    private int toChars2(int h, int m, int l, int e) {
        // -3 < e <= 0: plain format with leading zeroes.
        appendDigit(0);
        append('.');
        for (; e < 0; ++e) {
            appendDigit(0);
        }
        appendDigit(h);
        append8Digits(m);
        lowDigits(l);
        return NON_SPECIAL;
    }

    private int toChars3(int h, int m, int l, int e) {
        // -3 >= e | e > 7: computerized scientific notation
        appendDigit(h);
        append('.');
        append8Digits(m);
        lowDigits(l);
        exponent(e - 1);
        return NON_SPECIAL;
    }

    private void lowDigits(int l) {
        if (l != 0) {
            append8Digits(l);
        }
        removeTrailingZeroes();
    }

    private void append8Digits(int m) {
        /*
        Left-to-right digits extraction:
        algorithm 1 in [3], with b = 10, k = 8, n = 28.
         */
        int y = y(m);
        for (int i = 0; i < 8; ++i) {
            int t = 10 * y;
            appendDigit(t >>> 28);
            y = t & MASK_28;
        }
    }

    private void removeTrailingZeroes() {
        while (bytes[index] == '0') {
            --index;
        }
        // ... but do not remove the one directly to the right of '.'
        if (bytes[index] == '.') {
            ++index;
        }
    }

    private int y(int a) {
        /*
        Algorithm 1 in [3] needs computation of
            floor((a + 1) 2^n / b^k) - 1
        with a < 10^8, b = 10, k = 8, n = 28.
        Noting that
            (a + 1) 2^n <= 10^8 2^28 < 10^17
        For n = 17, m = 8 the table in section 10 of [1] leads to:
         */
        return (int) (multiplyHigh(
                (long) (a + 1) << 28,
                193_428_131_138_340_668L) >>> 20) - 1;
    }

    private void exponent(int e) {
        append('E');
        if (e < 0) {
            append('-');
            e = -e;
        }
        if (e < 10) {
            appendDigit(e);
            return;
        }
        int d;
        if (e >= 100) {
            /*
            For n = 3, m = 2 the table in section 10 of [1] shows
                floor(e / 100) = floor(1_311 e / 2^17)
             */
            d = e * 1_311 >>> 17;
            appendDigit(d);
            e -= 100 * d;
        }
        /*
        For n = 2, m = 1 the table in section 10 of [1] shows
            floor(e / 10) = floor(103 e / 2^10)
         */
        d = e * 103 >>> 10;
        appendDigit(d);
        appendDigit(e - 10 * d);
    }

    private void append(int c) {
        bytes[++index] = (byte) c;
    }

    private void appendDigit(int d) {
        bytes[++index] = (byte) ('0' + d);
    }

    // Using the deprecated constructor enhances performance.
    @SuppressWarnings("deprecation")
    private String charsToString() {
        return new String(bytes, 0, 0, index + 1);
    }

}

com/fasterxml/jackson/core/io/schubfach/DoubleToDecimal.java

 

Or download all of them as a single archive file:

File name: jackson-core-2.14.0-sources.jar
File size: 497693 bytes
Release date: 2022-11-05
Download 

 

Download and Install Jackson Binary Package

What Is Jackson

Downloading and Reviewing jackson-*.jar

⇑⇑ Jackson - Java JSON library

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