什么是计算正弦和余弦在一起最快的方法是什么？ [英] What is the fastest way to compute sin and cos together?

问题描述

我想同时计算正弦和共同的正弦值在一起（例如，创建一个旋转矩阵）。当然，我可以分别计算它们一个接一个像 A = COS（X）; B = SIN（X）; ，但我不知道是否有需要这两个数值时更快的方法

编辑： 总结的答案迄今：

• 的弗拉德的说，有ASM的命令 FSINCOS （作为单独调用 FSIN 在几乎相同的时间）计算两者

• 如的志的注意到，这种优化有时已经完成由编译器（当采用优化的标志）。

• 的 CAF 的指出，其功能正余弦和 sincosf 可能是有效的，可直接通过只包括文件math.h

• 的 tanascius 的使用查表的方法进行了讨论争议。 （不过在我的电脑，并在基准情况下它的运行速度比正余弦 3倍速度更快，几乎相同的精度为32位浮点。）

• 的乔尔·古德温的链接到有着非常快逼近技术与一个相当有趣的方法良好的ACCURAY（对我来说，这是更快然后查表）

解决方案

现代的Intel / AMD处理器有指令 FSINCOS 可同时计算正弦和余弦函数。如果你需要强大的优化，也许你应该使用它。

下面是一个小例子：<一href="http://home.broadpark.no/~alein/fsincos.html">http://home.broadpark.no/~alein/fsincos.html

下面是另一个例子（对于MSVC）：<一href="http://www.$c$cguru.com/forum/showthread.php?t=328669">http://www.$c$cguru.com/forum/showthread.php?t=328669

下面是另一个例子（与海湾合作委员会）： http://www.allegro.cc/forums/thread/588470

希望他们中的一个帮助。 （我没有使用这个指令我自己，对不起。）

，因为它们是在处理器层面的支持，我希望他们会比查表的方式要快得多。

编辑：
维基百科表明， FSINCOS 溶液中加入387处理器，这样你就可以很难找到一个处理器，该处理器不支持它。

编辑：
Intel的文档指出 FSINCOS 只是约5慢于 FDIV 倍（即，浮点除法）。

编辑：
请注意，并非所有的现代编译器优化的正弦和余弦的计算成一个呼叫 FSINCOS 。特别是，我的VS 2008并没有这样做的。

编辑：
第一个例子链接是死的，但还是一个版本在Wayback机器。

I would like to compute both the sine and co-sine of a value together (for example to create a rotation matrix). Of course I could compute them separately one after another like a = cos(x); b = sin(x);, but I wonder if there is a faster way when needing both values.

Edit: To summarize the answers so far:

• Vlad said, that there is the asm command FSINCOS computing both of them (in almost the same time as a call to FSIN alone)

• Like Chi noticed, this optimization is sometimes already done by the compiler (when using optimization flags).

• caf pointed out, that functions sincos and sincosf are probably available and can be called directly by just including math.h

• tanascius approach of using a look-up table is discussed controversial. (However on my computer and in a benchmark scenario it runs 3x faster than sincos with almost the same accuracy for 32-bit floating points.)

• Joel Goodwin linked to an interesting approach of an extremly fast approximation technique with quite good accuray (for me, this is even faster then the table look-up)

解决方案

Modern Intel/AMD processors have instruction FSINCOS for calculating sine and cosine functions simultaneously. If you need strong optimization, perhaps you should use it.

Here is a small example: http://home.broadpark.no/~alein/fsincos.html

Here is another example (for MSVC): http://www.codeguru.com/forum/showthread.php?t=328669

Here is yet another example (with gcc): http://www.allegro.cc/forums/thread/588470

Hope one of them helps. (I didn't use this instruction myself, sorry.)

As they are supported on processor level, I expect them to be way much faster than table lookups.

Edit:
Wikipedia suggests that FSINCOS was added at 387 processors, so you can hardly find a processor which doesn't support it.

Edit:
Intel's documentation states that FSINCOS is just about 5 times slower than FDIV (i.e., floating point division).

Edit:
Please note that not all modern compilers optimize calculation of sine and cosine into a call to FSINCOS. In particular, my VS 2008 didn't do it that way.

Edit:
The first example link is dead, but there is still a version at the Wayback Machine.

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