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随机数（二）

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Numerical Recipes, The Art of Scientific Computing, Third Edition , Chapter 7 Random Numbers :

随机数（二）

Ran 程序

随机数（二）

typedef unsigned int Uint;             // 32-bit unsinged integer typedef unsigned long long int Ullong; // 64-bit unsinged integer typedef double Doub;                   // 64-bit floating point

注意，由于 Ullong 和 Doub 都是 64-bit 的，所以把 Ullong 转换为 Doub 时有可能丧失精度。即，上述程序中的 int64() 的不同的值有可能对应 doub() 的相同的值。

1.0 / (1.0 + ULLONG_MAX) == 1.0 / ULLONG_MAX == 5.42101086242752E-20 0.0 <= doub() <= 1.0  // 注意: doub() 有可能等于 1.0

NrRandom 类

使用上述 Ran 程序中的算法，可以得到以下 C# 程序：

namespace Skyiv {   using System;    public sealed class NrRandom : Random   {     ulong v1, v8, v16, v32, u, v = 4101842887655102017, w = 1;     int c1 = 0, c8 = 0, c16 = 0, c32 = 0;      protected override double Sample() {       return 1 / (1.0 + uint.MaxValue) * NextUInt32(); }     public override double NextDouble() { return Sample(); }     public override int Next() { return Next(int.MaxValue); }     public NrRandom() : this((ulong)DateTime.Now.Ticks) { }      public NrRandom(ulong seed)     {       u = v ^ seed; NextUInt64();       v = u;        NextUInt64();       w = v;        NextUInt64();     }      public ulong NextUInt64()     {       u = u * 2862933555777941757 + 7046029254386353087;       v ^= v >> 17; v ^= v << 31; v ^= v >> 8;       w = 4294957665U * (w & 0xffffffff) + (w >> 32);       ulong x = u ^ (u << 21); x ^= x >> 35; x ^= x << 4;       return (x + v) ^ w;     }      public override int Next(int max)     {       if (max < 0) throw new ArgumentOutOfRangeException(nameof(max));       return (int)(Sample() * max);     }      public override int Next(int min, int max)     {       if (min > max) throw new ArgumentOutOfRangeException(nameof(min));       return (int)(min + (long)(Sample() * (max - (long)min)));     }      public override void NextBytes(byte [] buffer)     {       if (buffer == null) throw new ArgumentNullException(nameof(buffer));       for (int i = 0; i < buffer.Length; i++) buffer[i] = NextByte();     }      public uint NextUInt32()     {       if (c32-- != 0) return (uint)(v32 >>= 32);       c32 = 1; return (uint)(v32 = NextUInt64());     }      public ushort NextUInt16()     {       if (c16-- != 0) return (ushort)(v16 >>= 16);       c16 = 3; return (ushort)(v16 = NextUInt64());     }      public byte NextByte()     {       if (c8-- != 0) return (byte)(v8 >>= 8);       c8 = 7; return (byte)(v8 = NextUInt64());     }      public bool NextBoolean()     {       if (c1-- != 0) return ((v1 >>= 1) & 1) != 0;       c1 = 63; return ((v1 = NextUInt64()) & 1) != 0;     }   } }

简要说明：