blocks|key|2251101|text|你最好让它和你能存储的浮点表示一样精确。使用相同类型的更精确的浮点数进行计算不会花费更长的时间。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2251102|准确性通常是以重要数字的数量来衡量的；您需要自己决定您感兴趣的准确数字的数量。如果对pi使用精度较低的值，则该值的不精确性将传播到它所在的其他计算中。|2251103|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|F|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|G|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|H|8|@]|9|@]|A|$]]]|E|$]]

You might as well just make it as accurate as whatever floating-point representation you can store is. It won't take longer to perform calculations using a more accurate floating-point number of the same type.

Accuracy is generally measured as number of significant digits; you'll need to decide for yourself how many digits of accuracy you're interested in. If you use a less accurate value for pi, that value's inaccuracy will propagate to the other calculations it's in.

blocks|key|725706|text|还不完全清楚你在做什么。你是根据角度来查找坐标的吗？在这种情况下，Pi的准确性根本不重要。重要的是查找表的大小，当然，您将以尽可能高的精度预先计算它。进一步的准确性不需要额外的执行时间，而且您正在考虑将数据类型从单个更改为双倍。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|725707|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

It's not fully clear what you are doing. Are you looking up coordinates based on an angle? In this case the accuracy of Pi doesn't matter at all. Important is the size of the lookup table and you will of course precalculate it with the highest possible accuracy. Further accuracy doesn't cost additional execution time besides you are thinking about changing the data type from single to double.

blocks|key|894480|text|如果您预先计算并存储它，您可以使用系统上的数学库尽可能精确地计算它一次。一个很好的选择是：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|894481|double+PI+=+(16.0+*+atan(1/5))+-+(4.0+*+atan(1/239));|code-block|syntax|javascript|894482|这将为PI提供一个相当准确的值，您可以根据需要在启动和重用时进行计算。要获得比容易重用的版本更精确的版本是很困难的。|894483|entityMap^0|0|0|0^^$0|@$1|2|3|4|5|6|7|K|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|L|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|M|8|@]|9|@]|A|$]]|$1|I|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|J|$]]

If you're precalculating it and storing it, you can just use the math library on your system to compute it one time as accurately as possible. A good option is:

<pre><code>double PI = (16.0 * atan(1/5)) - (4.0 * atan(1/239));
</code></pre>

That will give you a fairly accurate value for PI which you can compute at startup and reuse as needed. It's difficult to get a more accurate version than that which is easily reusable.

blocks|key|725753|text|如果你是预先计算的数值，使它尽可能准确的存储，但要获得真正的感觉，在实际需要的准确性，你必须看看你的公式和其他组件的准确性，而不是确保你的准确性，为π匹配的其他组件。数值分析会给你很多线索。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|725754|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

If you are pre-calculating the value make it as accurate as feasible to store but to get the true feel of what accuracy in actually needed you have to look at your formulas and the accuracy of other components and than make sure the accuracy you have for pi matches that for other components. Numerical analysis will give you plaenty of clues.

blocks|key|894492|text|作为一个比较:我认为美国宇航局使用圆周率7小数点的精度，能够停靠到太空。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|894493|首先，我们需要确定你的位置计算需要有多精确，也就是说，你的程序中依赖于π的公式有多精确。我们需要从这里开始，以便知道你需要多精确的π才能达到这个目的。|894494|一旦确定了这一点，你就可以或多或少地使用直接的数值分析来确定你需要多好的π精度。我可以帮你，但我需要职位公式来做:)|894495|编辑:我怀疑你的公式是线性依赖于π的，也就是说，你没有使用某个模糊函数f(x，y，z，pi+)，其中π是平方的或类似的。在这种情况下，公式的精度是π精度的因子，例如k*eps(+pi+)。否则，它基本上是一个因子乘以f对π的导数。不包括所有其他参数的精度f取决于！|894496|干杯！|894497|entityMap^0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|M|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|N|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|O|8|@]|9|@]|A|$]]|$1|H|3|I|5|6|7|P|8|@]|9|@]|A|$]]|$1|J|3|-4|5|6|7|Q|8|@]|9|@]|A|$]]]|K|$]]

As a comparision: I think NASA use pi with 7 decimals accuracy to be able to dock into space.

First of all we need to determine how accurate your position calculations need to be, i.e. how accurate the formulas in your program which depends on pi have to be. We need to start there in order to know how accurate pi you need to achive this.

Once that has been determined, you can probably use more or less straight forward numerical analysis to determine how good accuracy you need for pi. I can help you with that, but I need the position formulas to do that :)

Edit: I suspect that your formulas are linearly dependent on pi, i.e. you aren't using some obscure function f(x,y,z,pi) where pi is squared or similar. In that case the accuracy of your formula is a factor times the pi accuracy, e.g. k*eps(pi). Otherwise it's basically a factor times the derivative of f with respect to pi. Not counting the accuracy of all other parameters f depends on ! 

Cheers !

blocks|key|2251211|text|这取决于您的计算中有多少有效位数。给出公式|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|2251212|C=+pi+*d|2251213|如果你想知道一个直径一英里的圆周有多少英寸，你需要六位数的圆周率来保持你想要的精度，因为一英里有63,360英寸，而圆周有199,051英寸。因为答案中有六个有效数字，所以我需要六位圆周率来计算到所需的精度。|2251214|3.14+*63+360=+198950.4|2251215|3.142+*63+360=+199077.12|2251216|3.1416+*63+360=+199051.776|2251217|3.14159+*63+360=+199051.1424|2251218|正如你所看到的，在这个例子中，我得到了正确的答案，只有5位数的pi，但情况并不总是这样。为了确保足够的精度，您至少需要和重要数字一样多的pi数字。|2251219|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Significant_figures^0|C|4|0|0|0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|Z|8|@]|9|@$A|10|B|11|1|12]]|C|$]]|$1|D|3|E|5|6|7|13|8|@]|9|@]|C|$]]|$1|F|3|G|5|6|7|14|8|@]|9|@]|C|$]]|$1|H|3|I|5|6|7|15|8|@]|9|@]|C|$]]|$1|J|3|K|5|6|7|16|8|@]|9|@]|C|$]]|$1|L|3|M|5|6|7|17|8|@]|9|@]|C|$]]|$1|N|3|O|5|6|7|18|8|@]|9|@]|C|$]]|$1|P|3|Q|5|6|7|19|8|@]|9|@]|C|$]]|$1|R|3|-4|5|6|7|1A|8|@]|9|@]|C|$]]]|S|$T|$5|U|V|W|C|$X|Y]]]]

It depends on how many <a href="http://en.wikipedia.org/wiki/Significant_figures" rel="nofollow noreferrer">significant digits</a> you have in your calculation. Given the formula

C = pi * d

if you want to know how many inches in the circumference of a circle one mile in diameter, you'd need six digits of pi to keep the accuracy you want, since there are 63,360 inches in a mile, and there would be 199,051 inches in the circumference. Since there are six significant digits in the answer, I need six digits of pi to calculate it to the needed accuracy.

3.14 * 63,360 = 198950.4

3.142 * 63,360 = 199077.12

3.1416 * 63,360 = 199051.776

3.14159 * 63,360 = 199051.1424

As you can see, I got the right answer in this case with only 5 digits of pi, but that's not always going to be the case. You need at least as many digits of pi as you have significant digits to ensure you have enough precision.

blocks|key|894522|text|圣经上说Pi的值是3+(链接)。因此，当然，您应该只使用:)|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|894523|entityMap|0|LINK|mutability|MUTABLE|url|http://www.purplemath.com/modules/bibleval.htm^0|C|2|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

Bible says value of Pi is 3 (<a href="http://www.purplemath.com/modules/bibleval.htm" rel="nofollow noreferrer">link</a>). So of course you should just use that
:)

blocks|key|2251237|text|π的新公式|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2251238|Pi=2.m.sin(90/m)

Pi=3.m.sin(60/m)

Pi=4.m.sin(45/m)

Pi=5.m.sin(36/m)|code-block|syntax|javascript|2251239|在无PI计算器XP、XM、…的值中，有数百万。。推荐m=1.0E%2B10000000以成功安装netframework2.0+2.0所需的计算器|2251240|http://harry-j-smith-memorial.com/index.html|offset|length|2251241|entityMap|0|LINK|mutability|MUTABLE|url^0|0|0|0|0|18|0|0^^$0|@$1|2|3|4|5|6|7|T|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|U|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|V|8|@]|9|@]|A|$]]|$1|I|3|J|5|6|7|W|8|@]|9|@$K|X|L|Y|1|Z]]|A|$]]|$1|M|3|-4|5|6|7|10|8|@]|9|@]|A|$]]]|N|$O|$5|P|Q|R|A|$S|J]]]]

new formula for pi

<pre><code>Pi=2.m.sin(90/m)

Pi=3.m.sin(60/m)

Pi=4.m.sin(45/m)

Pi=5.m.sin(36/m)
</code></pre>

For millions across the value of PI free calculator XP,XM,….. recommend m=1.0E+10000000 to the success of the calculator you need to install netframework2.0

<a href="http://harry-j-smith-memorial.com/index.html" rel="nofollow">http://harry-j-smith-memorial.com/index.html</a>

Optimizing a game we're developing, we're running into the phase where every CPU cycle won counts. We using radians for position calculations of objects circling around other objects and I want to cut the needless accuracy in my lookup tables. For that, we make heavy use of a predefined Pi. How accurate should this Pi be?

So, my question is:

<ul>
<li>How accurate is accurate enough?</li>
<li>Or even better, how to determine the needed accuracy?</li>
</ul>

How to determine the accuracy of Pi (π)

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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优化我们正在开发的游戏，我们将进入每一个CPU周期都获胜的阶段。我们使用弧度来计算围绕其他物体旋转的物体的位置，我想在查找表中减少不必要的准确性。为此，我们大量使用了预先定义的Pi。这个Pi应该有多精确？所以，我的问题是：有多精确？或者更好的是，如何确定所需的精度？

问如何确定Pi (π)的精度
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