Re: [問題] 練習題

[GreatShot (我要拿Ph.D.!!!)]

: 另外，如果要算的次方數很大的話
: (應該到五次或是六次就應該呼叫了..)
: 建議呼叫 Math.Pow 會快上很多....
: 裡面用的算法比你自己寫的連乘法好很多..
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  這點跟我認知很不一樣
  我沒看過Math.Pow()的source所以不敢說它演算法好不好
  我只能作實驗來觀察
  source如下

    public partial class Form1 : Form
    {
                [DllImport("kernel32.dll")]
                extern static short QueryPerformanceCounter(ref long x);
                [DllImport("kernel32.dll")]
                extern static short QueryPerformanceFrequency(ref long x);
        public Form1()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            long ctr1 = 0, ctr2 = 0, freq = 0;
            double sum = 0;
            double a = 0;
            Random myrand = new Random();
            if (QueryPerformanceCounter(ref ctr1)!=0)  // Begin timing.
            {
               for (int i=0; i<1000000000; i++)        // Code being timed.
               {
                a = myrand.NextDouble() * 10;      //Generate Random number
               //3 options
                sum = 6 * (a * a * a) + (5 * (a * a)) + (3 * a) - 1;
                //sum = 6*Math.Pow(a,3) + 5*Math.Pow(a,2)+(3*a) - 1;
                //sum = a * (a * (a * (+6) + 5) + 3) - 1;
                }
                QueryPerformanceCounter(ref ctr2);      // Finish timing.
                this.richTextBox1.AppendText("Start Value: " + ctr1 + "\n");
                this.richTextBox1.AppendText("End Value: " + ctr2+"\n");
                QueryPerformanceFrequency(ref freq);
               this.richTextBox1.AppendText("QueryPerformanceCounter minimum
               resolution: 1/" + freq + " seconds."+"\n");
               this.richTextBox1.AppendText("100 Increment time: " +
               (ctr2 - ctr1) * 1.0 / freq + " seconds."+"\n");
            }
            else
            this.richTextBox1.AppendText("High-resolution counter not
            supported."+"\n");
        }
    }

      Result1: sum = 6 * (a * a * a) + (5 * (a * a)) + (3 * a) - 1;
      Start Value: 757143142739
      End Value: 757167788963
      QueryPerformanceCounter minimum resolution: 1/14318180 seconds.
      100 Increment time: 1.72132379953318 seconds.

      Result2: sum = 6*Math.Pow(a,3) + 5*Math.Pow(a,2)+(3*a) - 1;
      Start Value: 758355648048
      End Value: 758755628202
      QueryPerformanceCounter minimum resolution: 1/14318180 seconds.
      100 Increment time: 27.9351254139842 seconds.

      Result3: sum = a * (a * (a * (+6) + 5) + 3) - 1;
      Start Value: 759758768779
      End Value: 759783404913
      QueryPerformanceCounter minimum resolution: 1/14318180 seconds.
      100 Increment time: 1.720619101031 seconds.


      再來換成冪次更高的
      Result1: sum = 
      9 * (a * a * a * a * a * a) + 8 * (a * a * a * a * a) +
      7 * (a * a * a * a) + 6 * (a * a * a) + (5 * (a * a)) + (3 * a) - 1;
      Start Value: 766926901793
      End Value: 766951596182
      QueryPerformanceCounter minimum resolution: 1/14318180 seconds.
      100 Increment time: 1.72468770472225 seconds.

      Result2: sum =
      9 * Math.Pow(a, 6) + 8 * Math.Pow(a, 5) + 7 * Math.Pow(a, 4) + 6 *
      Math.Pow(a, 3) + 5 * Math.Pow(a, 2) + (3 * a) - 1; 
      Start Value: 769278944190
      End Value: 770282636993
      QueryPerformanceCounter minimum resolution: 1/14318180 seconds.
      100 Increment time: 70.0991887935478 seconds.

      Result3: sum =
      a * (a * (a * ( a * (a * (a *  (+9) +8) +7 ) +6) + 5) + 3) - 1;
      Start Value: 774103750407
      End Value: 774128401956
      QueryPerformanceCounter minimum resolution: 1/14318180 seconds.
      100 Increment time: 1.72169570434231 seconds.

     這實驗其實很粗糙
     但是可以看的出有非常明顯的差異
     由此看來
     第一種寫法跟第三種寫法幾乎是沒有差別的
     也許是.net compiler會自己最佳化
     但是第二種(使用Math.Pow())
     很明顯的在執行時間上有段落差
     冪次越大差距就越大
     所以我的認知是要求效率的時候用連乘法會比Math.Pow()來的好

     不過
     也許是我實驗的方式有誤
     有錯的話麻煩請各位賢達指正
     謝謝 :)


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推 yoco315:你是對的.. 我弄錯了 :)
推 GreatShot:因為我吃過虧 所以印象深刻 :)
推 cole945:可能Math.Pow的overhead主要來自於function call?
→ cole945:我在我的電腦上測, Math.Pow(a,x) x在300以內,都是大約固
→ cole945:定在0.22ms左右, 可是a*a*a..卻很雖然連乘數增加@.@a
→ cole945: (我最後一句話的 "雖然" 是要打 "隨著" |||| )
推 GreatShot:我也不知道為何 我執行Math.Pow(a,100)遠比連乘100次慢
→ GreatShot:我用的OS是Vista 64, 不知換個OS跑會不會有不同的結果
推 birdychang:QueryPerformanceCounter跟Environment.TickCount
→ birdychang:有不同嗎？？
→ birdychang:我是都用Environment.TickCount算時間耶～
推 GreatShot:樓上~精確度不同~~
→ GreatShot:精確度 QPC > TickCount > Timer
推 chhuang:我倒是都用 StopWatch 來測試時間...
推 GreatShot:我記得stopwatch就是用QPC來寫的
→ GreatShot:so其實stopwatch應該是最好用的 XD
推 Epimenides:剛試用了stopwatch 好用