在.NET中,GetHashCode方法在整个.NET基类库的许多地方都使用。正确执行它对于在集合中或确定相等时快速查找项目尤为重要。

对于如何为自定义类实现GetHashCode,是否有标准算法或最佳实践,以便不会降低性能?


当前回答

这是一个实现Josh Bloch实现的静态助手类;并且提供了显式重载来“防止”装箱,并且还专门为长原语实现哈希。

您可以传递与equals实现匹配的字符串比较。

因为Hash输出始终是int,所以您可以只链接Hash调用。

using System;
using System.Collections;
using System.Collections.Generic;
using System.Reflection;
using System.Runtime.CompilerServices;


namespace Sc.Util.System
{
    /// <summary>
    /// Static methods that allow easy implementation of hashCode. Example usage:
    /// <code>
    /// public override int GetHashCode()
    ///     => HashCodeHelper.Seed
    ///         .Hash(primitiveField)
    ///         .Hsh(objectField)
    ///         .Hash(iEnumerableField);
    /// </code>
    /// </summary>
    public static class HashCodeHelper
    {
        /// <summary>
        /// An initial value for a hashCode, to which is added contributions from fields.
        /// Using a non-zero value decreases collisions of hashCode values.
        /// </summary>
        public const int Seed = 23;

        private const int oddPrimeNumber = 37;


        /// <summary>
        /// Rotates the seed against a prime number.
        /// </summary>
        /// <param name="aSeed">The hash's first term.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private static int rotateFirstTerm(int aSeed)
        {
            unchecked {
                return HashCodeHelper.oddPrimeNumber * aSeed;
            }
        }


        /// <summary>
        /// Contributes a boolean to the developing HashCode seed.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aBoolean">The value to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, bool aBoolean)
        {
            unchecked {
                return HashCodeHelper.rotateFirstTerm(aSeed)
                        + (aBoolean
                                ? 1
                                : 0);
            }
        }

        /// <summary>
        /// Contributes a char to the developing HashCode seed.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aChar">The value to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, char aChar)
        {
            unchecked {
                return HashCodeHelper.rotateFirstTerm(aSeed)
                        + aChar;
            }
        }

        /// <summary>
        /// Contributes an int to the developing HashCode seed.
        /// Note that byte and short are handled by this method, through implicit conversion.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aInt">The value to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, int aInt)
        {
            unchecked {
                return HashCodeHelper.rotateFirstTerm(aSeed)
                        + aInt;
            }
        }

        /// <summary>
        /// Contributes a long to the developing HashCode seed.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aLong">The value to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, long aLong)
        {
            unchecked {
                return HashCodeHelper.rotateFirstTerm(aSeed)
                        + (int)(aLong ^ (aLong >> 32));
            }
        }

        /// <summary>
        /// Contributes a float to the developing HashCode seed.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aFloat">The value to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, float aFloat)
        {
            unchecked {
                return HashCodeHelper.rotateFirstTerm(aSeed)
                        + Convert.ToInt32(aFloat);
            }
        }

        /// <summary>
        /// Contributes a double to the developing HashCode seed.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aDouble">The value to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, double aDouble)
            => aSeed.Hash(Convert.ToInt64(aDouble));

        /// <summary>
        /// Contributes a string to the developing HashCode seed.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aString">The value to contribute.</param>
        /// <param name="stringComparison">Optional comparison that creates the hash.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(
                this int aSeed,
                string aString,
                StringComparison stringComparison = StringComparison.Ordinal)
        {
            if (aString == null)
                return aSeed.Hash(0);
            switch (stringComparison) {
                case StringComparison.CurrentCulture :
                    return StringComparer.CurrentCulture.GetHashCode(aString);
                case StringComparison.CurrentCultureIgnoreCase :
                    return StringComparer.CurrentCultureIgnoreCase.GetHashCode(aString);
                case StringComparison.InvariantCulture :
                    return StringComparer.InvariantCulture.GetHashCode(aString);
                case StringComparison.InvariantCultureIgnoreCase :
                    return StringComparer.InvariantCultureIgnoreCase.GetHashCode(aString);
                case StringComparison.OrdinalIgnoreCase :
                    return StringComparer.OrdinalIgnoreCase.GetHashCode(aString);
                default :
                    return StringComparer.Ordinal.GetHashCode(aString);
            }
        }

        /// <summary>
        /// Contributes a possibly-null array to the developing HashCode seed.
        /// Each element may be a primitive, a reference, or a possibly-null array.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aArray">CAN be null.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, IEnumerable aArray)
        {
            if (aArray == null)
                return aSeed.Hash(0);
            int countPlusOne = 1; // So it differs from null
            foreach (object item in aArray) {
                ++countPlusOne;
                if (item is IEnumerable arrayItem) {
                    if (!object.ReferenceEquals(aArray, arrayItem))
                        aSeed = aSeed.Hash(arrayItem); // recursive call!
                } else
                    aSeed = aSeed.Hash(item);
            }
            return aSeed.Hash(countPlusOne);
        }

        /// <summary>
        /// Contributes a possibly-null array to the developing HashCode seed.
        /// You must provide the hash function for each element.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aArray">CAN be null.</param>
        /// <param name="hashElement">Required: yields the hash for each element
        /// in <paramref name="aArray"/>.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash<T>(this int aSeed, IEnumerable<T> aArray, Func<T, int> hashElement)
        {
            if (aArray == null)
                return aSeed.Hash(0);
            int countPlusOne = 1; // So it differs from null
            foreach (T item in aArray) {
                ++countPlusOne;
                aSeed = aSeed.Hash(hashElement(item));
            }
            return aSeed.Hash(countPlusOne);
        }

        /// <summary>
        /// Contributes a possibly-null object to the developing HashCode seed.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="aObject">CAN be null.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int Hash(this int aSeed, object aObject)
        {
            switch (aObject) {
                case null :
                    return aSeed.Hash(0);
                case bool b :
                    return aSeed.Hash(b);
                case char c :
                    return aSeed.Hash(c);
                case int i :
                    return aSeed.Hash(i);
                case long l :
                    return aSeed.Hash(l);
                case float f :
                    return aSeed.Hash(f);
                case double d :
                    return aSeed.Hash(d);
                case string s :
                    return aSeed.Hash(s);
                case IEnumerable iEnumerable :
                    return aSeed.Hash(iEnumerable);
            }
            return aSeed.Hash(aObject.GetHashCode());
        }


        /// <summary>
        /// This utility method uses reflection to iterate all specified properties that are readable
        /// on the given object, excluding any property names given in the params arguments, and
        /// generates a hashcode.
        /// </summary>
        /// <param name="aSeed">The developing hash code, or the seed: if you have no seed, use
        /// the <see cref="Seed"/>.</param>
        /// <param name="aObject">CAN be null.</param>
        /// <param name="propertySelector"><see cref="BindingFlags"/> to select the properties to hash.</param>
        /// <param name="ignorePropertyNames">Optional.</param>
        /// <returns>A hash from the properties contributed to <c>aSeed</c>.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int HashAllProperties(
                this int aSeed,
                object aObject,
                BindingFlags propertySelector
                        = BindingFlags.Instance
                        | BindingFlags.Public
                        | BindingFlags.GetProperty,
                params string[] ignorePropertyNames)
        {
            if (aObject == null)
                return aSeed.Hash(0);
            if ((ignorePropertyNames != null)
                    && (ignorePropertyNames.Length != 0)) {
                foreach (PropertyInfo propertyInfo in aObject.GetType()
                        .GetProperties(propertySelector)) {
                    if (!propertyInfo.CanRead
                            || (Array.IndexOf(ignorePropertyNames, propertyInfo.Name) >= 0))
                        continue;
                    aSeed = aSeed.Hash(propertyInfo.GetValue(aObject));
                }
            } else {
                foreach (PropertyInfo propertyInfo in aObject.GetType()
                        .GetProperties(propertySelector)) {
                    if (propertyInfo.CanRead)
                        aSeed = aSeed.Hash(propertyInfo.GetValue(aObject));
                }
            }
            return aSeed;
        }


        /// <summary>
        /// NOTICE: this method is provided to contribute a <see cref="KeyValuePair{TKey,TValue}"/> to
        /// the developing HashCode seed; by hashing the key and the value independently. HOWEVER,
        /// this method has a different name since it will not be automatically invoked by
        /// <see cref="Hash(int,object)"/>, <see cref="Hash(int,IEnumerable)"/>,
        /// or <see cref="HashAllProperties"/> --- you MUST NOT mix this method with those unless
        /// you are sure that no KeyValuePair instances will be passed to those methods; or otherwise
        /// the generated hash code will not be consistent. This method itself ALSO will not invoke
        /// this method on the Key or Value here if that itself is a KeyValuePair.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="keyValuePair">The value to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int HashKeyAndValue<TKey, TValue>(this int aSeed, KeyValuePair<TKey, TValue> keyValuePair)
            => aSeed.Hash(keyValuePair.Key)
                    .Hash(keyValuePair.Value);

        /// <summary>
        /// NOTICE: this method is provided to contribute a collection of <see cref="KeyValuePair{TKey,TValue}"/>
        /// to the developing HashCode seed; by hashing the key and the value independently. HOWEVER,
        /// this method has a different name since it will not be automatically invoked by
        /// <see cref="Hash(int,object)"/>, <see cref="Hash(int,IEnumerable)"/>,
        /// or <see cref="HashAllProperties"/> --- you MUST NOT mix this method with those unless
        /// you are sure that no KeyValuePair instances will be passed to those methods; or otherwise
        /// the generated hash code will not be consistent. This method itself ALSO will not invoke
        /// this method on a Key or Value here if that itself is a KeyValuePair or an Enumerable of
        /// KeyValuePair.
        /// </summary>
        /// <param name="aSeed">The developing HashCode value or seed.</param>
        /// <param name="keyValuePairs">The values to contribute.</param>
        /// <returns>The new hash code.</returns>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static int HashKeysAndValues<TKey, TValue>(
                this int aSeed,
                IEnumerable<KeyValuePair<TKey, TValue>> keyValuePairs)
        {
            if (keyValuePairs == null)
                return aSeed.Hash(null);
            foreach (KeyValuePair<TKey, TValue> keyValuePair in keyValuePairs) {
                aSeed = aSeed.HashKeyAndValue(keyValuePair);
            }
            return aSeed;
        }
    }
}

其他回答

与夜编码器的解决方案非常相似,只是如果你想提高素数更容易。

PS:这是你嘴里吐出一点东西的时候之一,因为你知道这可以用9个默认值重构成一个方法,但它会更慢,所以你闭上眼睛,试着忘掉它。

/// <summary>
/// Try not to look at the source code. It works. Just rely on it.
/// </summary>
public static class HashHelper
{
    private const int PrimeOne = 17;
    private const int PrimeTwo = 23;

    public static int GetHashCode<T1, T2, T3, T4, T5, T6, T7, T8, T9, T10>(T1 arg1, T2 arg2, T3 arg3, T4 arg4, T5 arg5, T6 arg6, T7 arg7, T8 arg8, T9 arg9, T10 arg10)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();
            hash = hash * PrimeTwo + arg4.GetHashCode();
            hash = hash * PrimeTwo + arg5.GetHashCode();
            hash = hash * PrimeTwo + arg6.GetHashCode();
            hash = hash * PrimeTwo + arg7.GetHashCode();
            hash = hash * PrimeTwo + arg8.GetHashCode();
            hash = hash * PrimeTwo + arg9.GetHashCode();
            hash = hash * PrimeTwo + arg10.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2, T3, T4, T5, T6, T7, T8, T9>(T1 arg1, T2 arg2, T3 arg3, T4 arg4, T5 arg5, T6 arg6, T7 arg7, T8 arg8, T9 arg9)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();
            hash = hash * PrimeTwo + arg4.GetHashCode();
            hash = hash * PrimeTwo + arg5.GetHashCode();
            hash = hash * PrimeTwo + arg6.GetHashCode();
            hash = hash * PrimeTwo + arg7.GetHashCode();
            hash = hash * PrimeTwo + arg8.GetHashCode();
            hash = hash * PrimeTwo + arg9.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2, T3, T4, T5, T6, T7, T8>(T1 arg1, T2 arg2, T3 arg3, T4 arg4, T5 arg5, T6 arg6, T7 arg7, T8 arg8)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();
            hash = hash * PrimeTwo + arg4.GetHashCode();
            hash = hash * PrimeTwo + arg5.GetHashCode();
            hash = hash * PrimeTwo + arg6.GetHashCode();
            hash = hash * PrimeTwo + arg7.GetHashCode();
            hash = hash * PrimeTwo + arg8.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2, T3, T4, T5, T6, T7>(T1 arg1, T2 arg2, T3 arg3, T4 arg4, T5 arg5, T6 arg6, T7 arg7)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();
            hash = hash * PrimeTwo + arg4.GetHashCode();
            hash = hash * PrimeTwo + arg5.GetHashCode();
            hash = hash * PrimeTwo + arg6.GetHashCode();
            hash = hash * PrimeTwo + arg7.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2, T3, T4, T5, T6>(T1 arg1, T2 arg2, T3 arg3, T4 arg4, T5 arg5, T6 arg6)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();
            hash = hash * PrimeTwo + arg4.GetHashCode();
            hash = hash * PrimeTwo + arg5.GetHashCode();
            hash = hash * PrimeTwo + arg6.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2, T3, T4, T5>(T1 arg1, T2 arg2, T3 arg3, T4 arg4, T5 arg5)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();
            hash = hash * PrimeTwo + arg4.GetHashCode();
            hash = hash * PrimeTwo + arg5.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2, T3, T4>(T1 arg1, T2 arg2, T3 arg3, T4 arg4)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();
            hash = hash * PrimeTwo + arg4.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2, T3>(T1 arg1, T2 arg2, T3 arg3)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();
            hash = hash * PrimeTwo + arg3.GetHashCode();

            return hash;
        }
    }

    public static int GetHashCode<T1, T2>(T1 arg1, T2 arg2)
    {
        unchecked
        {
            int hash = PrimeOne;
            hash = hash * PrimeTwo + arg1.GetHashCode();
            hash = hash * PrimeTwo + arg2.GetHashCode();

            return hash;
        }
    }
}

我在使用上面选择的实现时遇到了浮点和小数的问题。

此测试失败(浮点数;哈希值相同,即使我将2个值切换为负值):

        var obj1 = new { A = 100m, B = 100m, C = 100m, D = 100m};
        var obj2 = new { A = 100m, B = 100m, C = -100m, D = -100m};
        var hash1 = ComputeHash(obj1.A, obj1.B, obj1.C, obj1.D);
        var hash2 = ComputeHash(obj2.A, obj2.B, obj2.C, obj2.D);
        Assert.IsFalse(hash1 == hash2, string.Format("Hashcode values should be different   hash1:{0}  hash2:{1}",hash1,hash2));

但是这个测试通过了(int):

        var obj1 = new { A = 100m, B = 100m, C = 100, D = 100};
        var obj2 = new { A = 100m, B = 100m, C = -100, D = -100};
        var hash1 = ComputeHash(obj1.A, obj1.B, obj1.C, obj1.D);
        var hash2 = ComputeHash(obj2.A, obj2.B, obj2.C, obj2.D);
        Assert.IsFalse(hash1 == hash2, string.Format("Hashcode values should be different   hash1:{0}  hash2:{1}",hash1,hash2));

我改变了我的实现,不再对原始类型使用GetHashCode,它似乎工作得更好

    private static int InternalComputeHash(params object[] obj)
    {
        unchecked
        {
            var result = (int)SEED_VALUE_PRIME;
            for (uint i = 0; i < obj.Length; i++)
            {
                var currval = result;
                var nextval = DetermineNextValue(obj[i]);
                result = (result * MULTIPLIER_VALUE_PRIME) + nextval;

            }
            return result;
        }
    }



    private static int DetermineNextValue(object value)
    {
        unchecked
        {

                int hashCode;
                if (value is short
                    || value is int
                    || value is byte
                    || value is sbyte
                    || value is uint
                    || value is ushort
                    || value is ulong
                    || value is long
                    || value is float
                    || value is double
                    || value is decimal)
                {
                    return Convert.ToInt32(value);
                }
                else
                {
                    return value != null ? value.GetHashCode() : 0;
                }
        }
    }

我想把我的最新发现添加到我经常提到的这个主题中。

我当前的visual studio/项目设置提供了将元组自动重构为结构的功能。这将生成如下GetHashCode函数:

        public override int GetHashCode()
        {
            int hashCode = -2088324004;
            hashCode = hashCode * -1521134295 + AuftragGesperrt.GetHashCode();
            hashCode = hashCode * -1521134295 + Auftrag_gesperrt_von.GetHashCode();
            hashCode = hashCode * -1521134295 + Auftrag_gesperrt_am.GetHashCode();
            return hashCode;
        }

编辑:为了澄清AuftragGesperrt、Auftrag _gesperrt_von和Auftrag-gesperrt _am是财产。如果微软的开发人员使用这个功能,这可能是一个不错的解决方案。

可以尝试采用C++Boost库的方法。类似于:

class HashUtil
{
  public static int HashCombine(int seed, int other)
  {
    unchecked
    {
      return other + 0x9e3779b9 + (seed << 6) + (seed >> 2);
    }
  }
}

然后:

class MyClass
{
  private string _field1;
  private int _field2;
  private AnotherClass _field3;
  private YetAnotherClass _field4;

  public override int GetHashCode()
  {
    int result = HashUtil.HashCombine(_field1.GetHashCode(), _field2);
    result = HashUtil.HashCombine(result, _field3.GetHashCode());
    return HashUtil.HashCombine(result, _field4.GetHashCode());
  }
}

如果我们的财产不超过8处(希望如此),这里还有另一种选择。

ValueTuple是一个结构,似乎有一个可靠的GetHashCode实现。

这意味着我们可以简单地这样做:

// Yay, no allocations and no custom implementations!
public override int GetHashCode() => (this.PropA, this.PropB).GetHashCode();

让我们来看看.NETCore当前对ValueTuple的GetHashCode的实现。

这来自ValueTuple:

    internal static int CombineHashCodes(int h1, int h2)
    {
        return HashHelpers.Combine(HashHelpers.Combine(HashHelpers.RandomSeed, h1), h2);
    }

    internal static int CombineHashCodes(int h1, int h2, int h3)
    {
        return HashHelpers.Combine(CombineHashCodes(h1, h2), h3);
    }

这来自HashHelper:

    public static readonly int RandomSeed = Guid.NewGuid().GetHashCode();

    public static int Combine(int h1, int h2)
    {
        unchecked
        {
            // RyuJIT optimizes this to use the ROL instruction
            // Related GitHub pull request: dotnet/coreclr#1830
            uint rol5 = ((uint)h1 << 5) | ((uint)h1 >> 27);
            return ((int)rol5 + h1) ^ h2;
        }
    }

英语:

向左旋转(循环移位)h1 5个位置。将结果和h1相加。将结果与h2进行异或运算。首先对{static random seed,h1}执行上述操作。对于每个其他项目,对上一个结果和下一个项目(例如h2)执行操作。

如果能更多地了解这个ROL-5散列代码算法的财产,那就太好了。

遗憾的是,为我们自己的GetHashCode延迟ValueTuple可能不像我们希望的那样快。相关讨论中的这条评论说明了直接调用HashHelpers.Combine更具性能。另一方面,这是内部的,所以我们必须复制代码,牺牲了我们在这里获得的大部分。此外,我们将负责记住首先与随机种子结合。我不知道如果我们跳过这一步会有什么后果。