Jackson Core Source Code

Jackson is "the Java JSON library" or "the best JSON parser for Java". Or simply as "JSON for Java".

Jackson Core Source Code files are provided in the source packge (jackson-core-2.14.0-sources.jar). You can download it at Jackson Maven Website.

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com/fasterxml/jackson/core/io/doubleparser/FastFloatMath.java

/**
 * References:
 * <dl>
 *     <dt>This class has been derived from "FastDoubleParser".</dt>
 *     <dd>Copyright (c) Werner Randelshofer. Apache 2.0 License.
 *         <a href="https://github.com/wrandelshofer/FastDoubleParser">github.com</a>.</dd>
 * </dl>
 */

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

import static com.fasterxml.jackson.core.io.doubleparser.FastDoubleMath.DOUBLE_MIN_EXPONENT_POWER_OF_TEN;
import static com.fasterxml.jackson.core.io.doubleparser.FastDoubleMath.MANTISSA_128;
import static com.fasterxml.jackson.core.io.doubleparser.FastDoubleMath.MANTISSA_64;
import static com.fasterxml.jackson.core.io.doubleparser.FastDoubleMath.fullMultiplication;

/**
 * This class complements {@link FastDoubleMath} with methods for
 * converting {@code FloatingPointLiteral} productions to floats.
 * <p>
 * See {@link com.fasterxml.jackson.core.io.doubleparser} for a description of
 * {@code FloatingPointLiteral}.
 */
class FastFloatMath {
    /**
     * Bias used in the exponent of a float.
     */
    private static final int FLOAT_EXPONENT_BIAS = 127;
    /**
     * The number of bits in the significand, including the implicit bit.
     */
    private static final int FLOAT_SIGNIFICAND_WIDTH = 24;
    private final static int FLOAT_MIN_EXPONENT_POWER_OF_TEN = -45;
    private final static int FLOAT_MAX_EXPONENT_POWER_OF_TEN = 38;
    private final static int FLOAT_MIN_EXPONENT_POWER_OF_TWO = Float.MIN_EXPONENT;
    private final static int FLOAT_MAX_EXPONENT_POWER_OF_TWO = Float.MAX_EXPONENT;
    /**
     * Precomputed powers of ten from 10^0 to 10^10. These
     * can be represented exactly using the float type.
     */
    private static final float[] FLOAT_POWER_OF_TEN = {
            1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f, 1e6f, 1e7f, 1e8f, 1e9f, 1e10f};

    /**
     * Don't let anyone instantiate this class.
     */
    private FastFloatMath() {

    }

    static float decFloatLiteralToFloat(boolean isNegative, long significand, int exponent,
                                        boolean isSignificandTruncated,
                                        int exponentOfTruncatedSignificand) {
        if (significand == 0) {
            return isNegative ? -0.0f : 0.0f;
        }

        final float result;
        if (isSignificandTruncated) {

            // We have too many digits. We may have to round up.
            // To know whether rounding up is needed, we may have to examine up to 768 digits.

            // There are cases, in which rounding has no effect.
            if (FLOAT_MIN_EXPONENT_POWER_OF_TEN <= exponentOfTruncatedSignificand
                    && exponentOfTruncatedSignificand <= FLOAT_MAX_EXPONENT_POWER_OF_TEN) {
                float withoutRounding = tryDecToFloatWithFastAlgorithm(isNegative, significand, exponentOfTruncatedSignificand);
                float roundedUp = tryDecToFloatWithFastAlgorithm(isNegative, significand + 1, exponentOfTruncatedSignificand);
                if (!Float.isNaN(withoutRounding) && roundedUp == withoutRounding) {
                    return withoutRounding;
                }
            }

            // We have to take a slow path.
            //return Double.parseDouble(str.toString());
            result = Float.NaN;


        } else if (FLOAT_MIN_EXPONENT_POWER_OF_TEN <= exponent && exponent <= FLOAT_MAX_EXPONENT_POWER_OF_TEN) {
            result = tryDecToFloatWithFastAlgorithm(isNegative, significand, exponent);
        } else {
            result = Float.NaN;
        }
        return result;
    }

    static float hexFloatLiteralToFloat(boolean isNegative, long significand, int exponent,
                                        boolean isSignificandTruncated,
                                        int exponentOfTruncatedSignificand) {
        if (significand == 0) {
            return isNegative ? -0.0f : 0.0f;
        }
        final float result;
        if (isSignificandTruncated) {

            // We have too many digits. We may have to round up.
            // To know whether rounding up is needed, we may have to examine up to 768 digits.

            // There are cases, in which rounding has no effect.
            if (FLOAT_MIN_EXPONENT_POWER_OF_TWO <= exponentOfTruncatedSignificand && exponentOfTruncatedSignificand <= FLOAT_MAX_EXPONENT_POWER_OF_TWO) {
                float withoutRounding = tryHexToFloatWithFastAlgorithm(isNegative, significand, exponentOfTruncatedSignificand);
                float roundedUp = tryHexToFloatWithFastAlgorithm(isNegative, significand + 1, exponentOfTruncatedSignificand);
                if (!Double.isNaN(withoutRounding) && roundedUp == withoutRounding) {
                    return withoutRounding;
                }
            }

            // We have to take a slow path.
            result = Float.NaN;

        } else if (FLOAT_MIN_EXPONENT_POWER_OF_TWO <= exponent && exponent <= FLOAT_MAX_EXPONENT_POWER_OF_TWO) {
            result = tryHexToFloatWithFastAlgorithm(isNegative, significand, exponent);
        } else {
            result = Float.NaN;
        }
        return result;
    }

    /**
     * Attempts to compute {@literal digits * 10^(power)} exactly;
     * and if "negative" is true, negate the result.
     * <p>
     * This function will only work in some cases, when it does not work it
     * returns null. This should work *most of the time* (like 99% of the time).
     * We assume that power is in the
     * [{@value FastDoubleMath#DOUBLE_MIN_EXPONENT_POWER_OF_TEN},
     * {@value FastDoubleMath#DOUBLE_MAX_EXPONENT_POWER_OF_TEN}]
     * interval: the caller is responsible for this check.
     *
     * @param isNegative whether the number is negative
     * @param digits     uint64 the digits of the number
     * @param power      int32 the exponent of the number
     * @return the computed double on success, {@link Double#NaN} on failure
     */
    static float tryDecToFloatWithFastAlgorithm(boolean isNegative, long digits, int power) {

        // we start with a fast path
        if (-10 <= power && power <= 10 && Long.compareUnsigned(digits, (1L << FLOAT_SIGNIFICAND_WIDTH) - 1L) <= 0) {
            // convert the integer into a float. This is lossless since
            // 0 <= i <= 2^24 - 1.
            float d = (float) digits;
            //
            // The general idea is as follows.
            // If 0 <= s < 2^24 and if 10^0 <= p <= 10^10 then
            // 1) Both s and p can be represented exactly as 32-bit floating-point values
            // 2) Because s and p can be represented exactly as floating-point values,
            // then s * p and s / p will produce correctly rounded values.
            //
            if (power < 0) {
                d = d / FLOAT_POWER_OF_TEN[-power];
            } else {
                d = d * FLOAT_POWER_OF_TEN[power];
            }
            return (isNegative) ? -d : d;
        }


        // The fast path has now failed, so we are falling back on the slower path.

        // We are going to need to do some 64-bit arithmetic to get a more precise product.
        // We use a table lookup approach.
        // It is safe because
        // power >= DOUBLE_MIN_EXPONENT_POWER_OF_TEN
        // and power <= DOUBLE_MAX_EXPONENT_POWER_OF_TEN
        // We recover the mantissa of the power, it has a leading 1. It is always
        // rounded down.
        long factorMantissa = MANTISSA_64[power - DOUBLE_MIN_EXPONENT_POWER_OF_TEN];


        // The exponent is 127 + 64 + power
        //     + floor(log(5**power)/log(2)).
        // The 127 is the exponent bias.
        // The 64 comes from the fact that we use a 64-bit word.
        //
        // Computing floor(log(5**power)/log(2)) could be
        // slow. Instead ,we use a fast function.
        //
        // For power in (-400,350), we have that
        // (((152170 + 65536) * power ) >> 16);
        // is equal to
        //  floor(log(5**power)/log(2)) + power when power >= 0
        // and it is equal to
        //  ceil(log(5**-power)/log(2)) + power when power < 0
        //
        //
        // The 65536 is (1<<16) and corresponds to
        // (65536 * power) >> 16 ---> power
        //
        // ((152170 * power ) >> 16) is equal to
        // floor(log(5**power)/log(2))
        //
        // Note that this is not magic: 152170/(1<<16) is
        // approximately equal to log(5)/log(2).
        // The 1<<16 value is a power of two; we could use a
        // larger power of 2 if we wanted to.
        //
        long exponent = (((152170L + 65536L) * power) >> 16) + FLOAT_EXPONENT_BIAS + 64;
        // We want the most significant bit of digits to be 1. Shift if needed.
        int lz = Long.numberOfLeadingZeros(digits);
        digits <<= lz;
        // We want the most significant 64 bits of the product. We know
        // this will be non-zero because the most significant bit of i is
        // 1.
        FastDoubleMath.UInt128 product = fullMultiplication(digits, factorMantissa);
        long lower = product.low;
        long upper = product.high;
        // We know that upper has at most one leading zero because
        // both i and factor_mantissa have a leading one. This means
        // that the result is at least as large as ((1<<63)*(1<<63))/(1<<64).

        // As long as the first 39 bits of "upper" are not "1", then we
        // know that we have an exact computed value for the leading
        // 25 bits because any imprecision would play out as a +1, in
        // the worst case.
        // Having 25 bits is necessary because
        // we need 24 bits for the mantissa, but we have to have one rounding bit, and
        // we can waste a bit if the most significant bit of the product is zero.
        // We expect this next branch to be rarely taken (say 1% of the time).
        // When (upper &0x3FFFFFFFFF) == 0x3FFFFFFFFF, it can be common for
        // lower + i < lower to be true (proba. much higher than 1%).
        if ((upper & 0x3_FFFFF_FFFFL) == 0x3_FFFFF_FFFFL && Long.compareUnsigned(lower + digits, lower) < 0) {
            long factor_mantissa_low =
                    MANTISSA_128[power - DOUBLE_MIN_EXPONENT_POWER_OF_TEN];
            // next, we compute the 64-bit x 128-bit multiplication, getting a 192-bit
            // result (three 64-bit values)
            product = fullMultiplication(digits, factor_mantissa_low);
            long product_low = product.low;
            long product_middle2 = product.high;
            long product_middle1 = lower;
            long product_high = upper;
            long product_middle = product_middle1 + product_middle2;
            if (Long.compareUnsigned(product_middle, product_middle1) < 0) {
                product_high++; // overflow carry
            }


            // we want to check whether mantissa *i + i would affect our result
            // This does happen, e.g. with 7.3177701707893310e+15 ????
            if (((product_middle + 1 == 0) && ((product_high & 0x7_FFFFF_FFFFL) == 0x7_FFFFF_FFFFL) &&
                    (product_low + Long.compareUnsigned(digits, product_low) < 0))) { // let us be prudent and bail out.
                return Float.NaN;
            }
            upper = product_high;
            //lower = product_middle;
        }

        // The final mantissa should be 24 bits with a leading 1.
        // We shift it so that it occupies 25 bits with a leading 1.
        long upperbit = upper >>> 63;
        long mantissa = upper >>> (upperbit + 38);
        lz += (int) (1 ^ upperbit);
        // Here we have mantissa < (1<<25).
        //assert mantissa < (1<<25);

        // We have to round to even. The "to even" part
        // is only a problem when we are right in between two floating-point values
        // which we guard against.
        // If we have lots of trailing zeros, we may fall right between two
        // floating-point values.
        if (((upper & 0x3_FFFFF_FFFFL) == 0x3_FFFFF_FFFFL)
                || ((upper & 0x3_FFFFF_FFFFL) == 0) && (mantissa & 3) == 1) {
            // if mantissa & 1 == 1 we might need to round up.
            //
            // Scenarios:
            // 1. We are not in the middle. Then we should round up.
            //
            // 2. We are right in the middle. Whether we round up depends
            // on the last significant bit: if it is "one" then we round
            // up (round to even) otherwise, we do not.
            //
            // So if the last significant bit is 1, we can safely round up.
            // Hence, we only need to bail out if (mantissa & 3) == 1.
            // Otherwise, we may need more accuracy or analysis to determine whether
            // we are exactly between two floating-point numbers.
            // It can be triggered with 1e23. ??
            // Note: because the factor_mantissa and factor_mantissa_low are
            // almost always rounded down (except for small positive powers),
            // almost always should round up.
            return Float.NaN;
        }

        mantissa += 1;
        mantissa >>>= 1;

        // Here we have mantissa < (1<<24), unless there was an overflow
        if (mantissa >= (1L << FLOAT_SIGNIFICAND_WIDTH)) {
            // This will happen when parsing values such as 7.2057594037927933e+16 ??
            mantissa = (1L << (FLOAT_SIGNIFICAND_WIDTH - 1));
            lz--; // undo previous addition
        }

        mantissa &= ~(1L << (FLOAT_SIGNIFICAND_WIDTH - 1));


        long real_exponent = exponent - lz;
        // we have to check that real_exponent is in range, otherwise we bail out
        if ((real_exponent < 1) || (real_exponent > FLOAT_MAX_EXPONENT_POWER_OF_TWO + FLOAT_EXPONENT_BIAS)) {
            return Float.NaN;
        }

        int bits = (int) (mantissa | real_exponent << (FLOAT_SIGNIFICAND_WIDTH - 1)
                | (isNegative ? 1L << 31 : 0));
        return Float.intBitsToFloat(bits);
    }

    static float tryHexToFloatWithFastAlgorithm(boolean isNegative, long digits, int power) {
        if (digits == 0 || power < Float.MIN_EXPONENT - 54) {
            return isNegative ? -0.0f : 0.0f;
        }
        if (power > Float.MAX_EXPONENT) {
            return isNegative ? Float.NEGATIVE_INFINITY : Float.POSITIVE_INFINITY;
        }

        // we start with a fast path
        // We try to mimic the fast described by Clinger WD for decimal
        // float number literals. How to read floating point numbers accurately.
        // ACM SIGPLAN Notices. 1990
        if (Long.compareUnsigned(digits, 0x1fffffffffffffL) <= 0) {
            // convert the integer into a double. This is lossless since
            // 0 <= i <= 2^53 - 1.
            float d = (float) digits;
            //
            // The general idea is as follows.
            // If 0 <= s < 2^53  then
            // 1) Both s and p can be represented exactly as 64-bit floating-point
            // values (binary64).
            // 2) Because s and p can be represented exactly as floating-point values,
            // then s * p will produce correctly rounded values.
            //
            d = d * Math.scalb(1f, power);
            if (isNegative) {
                d = -d;
            }
            return d;
        }

        // The fast path has failed
        return Float.NaN;
    }


}

com/fasterxml/jackson/core/io/doubleparser/FastFloatMath.java

 

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