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PHP实现投镖求PI法，最笨但最有意思

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Jun 23, 2016 pm 01:23 PM

#### 原理见下图：被称为利用投飞镖的方法求PI![circle pi](http://static.oschina.net/uploads/img/201408/30103044_VJtv.jpg)#### 以下总结选自其他网友：1. Figure2是Figure1的右上角的部分。 2. 向Figure2中投掷飞镖若干次（一个很大的数目），并且每次都仍在不同的点上。 3. 如果投掷的次数非常多，Figure2将被刺得“千疮百孔”。 4. 这时，“投掷在圆里的次数”除以“总投掷次数”，再乘以4，就是PI的值！（具体的推导过程参见原文） 在这个算法中，很重要的一点是：如何做到“随机地向Figure2投掷”，就是说如何做到Figure2上的每个点被投中的概率相等。 有人总结了一下，这个实际上叫做蒙特卡洛算法，我们取一个单位的正方形（1 x 1） 里面做一个内切圆（单位圆），则 单位正方形面积 ：内切单位圆面积 = 单位正方形内的飞镖数 : 内切单位圆内的飞镖数 ，通过计算飞镖个数就可以把单位圆面积算出来， 通过面积，在把圆周率计算出来。 注意 ，精度和你投掷的飞镖次数成正比。#### 我的PHP源码实现：PHP自带的mt_rand随机函数偏差较大，换成Halton sequence的方法，测试结果见后面~~~.php<?php$count = 0;// 忍受不了运算时间，可以把$num 改小// $num 越大，越接近真值$num = 100000;for ($i = 0; $i < $num; $i++) {    // list($x, $y) = array(mt_rand(0, 10000), mt_rand(0, 10000));    // $x /= 10000; $y /= 10000;    $x = halton($i, 3);    $y = halton($i, 7);    if (($x*$x + $y*$y) < 1) {        $count++;    }}$pi = 4.0 * $count / $num;echo $pi."\n";// 参考Halton sequence// https://en.wikipedia.org/wiki/Halton_sequencefunction halton($index, $base) {    $result = 0;    $f = 1;    $i = $index;    while ($i > 0) {        $f /= $base;        $result += $f * ($i % $base);        $i = floor($i / $base);    }    return $result;}~~~源码中halton传入参数是经过几次调整后的，更精确一些，测试PI = 3.14156mt_rand误差较大，3次结果如下：	mt_rand-1 => 3.142904	mt_rand-2 => 3.143196	mt_rand-3 => 3.139312

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