我正在开发一种游戏,把如此众多的数学功能用于物理学和制造。 ,在Quke3中使用的“Fast inverse sqrt”,其背景是美丽的。
你们是否知道任何比通常更快、准确损失的其他算法?
这些算法在文献中称为“近似算法”。 http://www.amazon.com/s?search-alias=stripbooks&field-isbn=3540653678“rel=“nofollow noreferer”>Approximation Algorithms by Vijay V. Vazirani 。
sinx ~ x 的情况是一个特例,略为笼统: 查阅
另一种(一些残酷的)技术是随机地将你的一些职能集中起来,然后对你进行直线的倒退。 这样,你就能够很好地描述你的职能,而且:
任何连续职能(包括最常见的数学业务)都可能与多功能的交际相当。 这与普通数学功能通常符合的相对简单特性(如补充法)和桌旁观一起,为建立快速近似算法的标准技术(以及像系统数学图书馆所使用的高准确性方法的基础)提供了依据。
但是,泰勒系列通常是一个不好的选择;Chebyshev或微型聚合物在大多数计算用途方面有更好的错误特征。 小型聚合物的标准技术是使用Remes Algorithm,该软件以多种商业数学软件实施,或者如果你知道你会做些什么,你可以开展日常工作。
对于记录,应当避免在现代处理器上出现“最深层的根基”,因为使用浮点对等地估算指令(rsqrts/>/>>>上载SSE、vrsqrte上的“近地天体N”,vrsqrtefp<>。 即便是目前英特尔处理器的(非近似)硬件根基也相当快。
小型X:in(x) ~= x 是常用于物理学的一种
Niko有一些很好的建议,我补充说,老的时装表。
I ve多次在高效实时精度方面成功地利用了循环功能(sin/cos/tan)一览表。 泥土的这种方式更为困难,但如果你的投入范围受到限制(如 screen板),那么它就难以为速度打上标语,而且你可以确切地调整空间/精密贸易。 你们也可以利用寻找共同的范围,然后就少有的情况而言,框架附带作用。
Paul
从Doom源代码来看,大约距离2个D点之间,无需使用泥土或三元测量功能:
fixed_t P_AproxDistance(fixed_t dx, fixed_t dy )
{
dx = abs(dx);
dy = abs(dy);
if (dx < dy)
return dx+dy-(dx>>1);
else
return dx+dy-(dy>>1);
}
注:x >> 1与x / 2相同,但较快的是,良好的现代汇编者现在自动这样做,但后来又如此大。
任何令人兴奋的倾向通常都是如此。 进行模拟的10次速度将加快,但结果比模拟的1 000次少。
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