我怎么能解决这个事实，在C ++，sin（M_PI）不是0？ [英] How can I work around the fact that in C++, sin(M_PI) is not 0?

问题描述

在C ++中，

  const double Pi = 3.14159265; 
 cout<< sin（Pi）; // displays：3.58979e-009 
  

它应该显示数字

我理解这是因为Pi是近似的，但是有什么办法我可以有一个值的硬编码到我的程序，将返回0为sin（Pi）？ （一个不同的常量可能？）

如果你想知道我想要做什么：我将极性转换为矩形，虽然有一些printf （）技巧我可以打印它为0.00，它仍然不能一致返回体面的值（在某些情况下，我得到-0.00）

需要正弦和余弦的线是：

  x = r * sin 
 y = r * cos（theta）; 
  

BTW：My Rectangular - > Polar工作正常...它只是Polar - > Rectangular

感谢！

编辑：我正在寻找解决方法，可以打印sin（一些倍数的pi）作为一个好的圆数到控制台（理想情况下没有一千个if语句）

解决方案

每个计算机科学家应该知道的浮点算法（编辑：也链接到评论）是相当硬核的阅读（我不能宣称已经阅读所有的），但它的关键是这是：你永远不会得到完全准确的浮点计算。从文章：

将无限多个实数压缩成有限数量的位需要近似表示。

不要让程序依赖于浮点计算的确切结果 - 始终允许公差范围。 FYI 3.58979e-009约为0.0000000036。这在您选择的任何合理的容差范围内！

In C++,

const double Pi = 3.14159265;
cout << sin(Pi);                          // displays: 3.58979e-009

it SHOULD display the number zero

I understand this is because Pi is being approximated, but is there any way I can have a value of Pi hardcoded into my program that will return 0 for sin(Pi)? (a different constant maybe?)

In case you're wondering what I'm trying to do: I'm converting polar to rectangular, and while there are some printf() tricks I can do to print it as "0.00", it still doesn't consistently return decent values (in some cases I get "-0.00")

The lines that require sin and cosine are:

x = r*sin(theta);
y = r*cos(theta);

BTW: My Rectangular -> Polar is working fine... it's just the Polar -> Rectangular

Thanks!

edit: I'm looking for a workaround so that I can print sin(some multiple of Pi) as a nice round number to the console (ideally without a thousand if-statements)

解决方案

What Every Computer Scientist Should Know About Floating-Point Arithmetic (edit: also got linked in a comment) is pretty hardcore reading (I can't claim to have read all of it), but the crux of it is this: you'll never get perfectly accurate floating point calculations. From the article:

Squeezing infinitely many real numbers into a finite number of bits requires an approximate representation.

Don't let your program depend on exact results from floating point calculations - always allow a tolerance range. FYI 3.58979e-009 is about 0.0000000036. That's well within any reasonable tolerance range you choose!

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