是否可以在运行时优化浮点乘以零的运算? [英] Can floating point multiplication by zero be optimised at runtime?

问题描述

我正在编写一种算法来查找nxn矩阵的逆矩阵.让我们以3x3矩阵的具体情况为例.

I am writing an algorithm to find the inverse of an nxn matrix. Let us take the specific case of a 3x3 matrix.

手动反转矩阵时，通常会查找包含一个或多个零的行/列，从而使行列式计算更快，因为它消除了您需要计算的项.

When you invert a matrix by hand, you typically look for rows/columns containing one or more zeros to make the determinant calculation faster as it eliminates terms you need to calculate.

在C/C ++中遵循此逻辑，如果您标识具有一个或多个零的行/列，则最终将得到以下代码:

Following this logic in C/C++, if you identify a row/column with one or more zeros, you will end up with the following code:

float term1 = currentElement * DetOf2x2(...);
//           ^
//           This is equal to 0.
//
// float term2 = ... and so on.

由于编译器无法知道currentElement在编译时为零，因此无法将其优化为float term = 0;之类的东西，因此浮点乘法将在运行时执行.

As the compiler cannot know currentElement will be zero at compile time, it cannot be optimised to something like float term = 0; and thus the floating point multiplication will be carried out at runtime.

我的问题是，这些零值会使浮点乘法运算更快，还是不管currentElement的值如何，乘法运算花费相同的时间?如果无法在运行时优化乘法，则可以删除搜索包含零的行/列的逻辑.

My question is, will these zero values make the floating point multiplication faster, or will the multiplication take the same amount of time regardless of the value of currentElement? If there is no way of optimising the multiplication at runtime, then I can remove the logic that searches for rows/columns containing zeros.

推荐答案

float term1 = currentElement * DetOf2x2(...);

即使currentElement为0，编译器也会调用DetOf2x2(...):这肯定比最终乘法的开销大得多，无论是否为0.造成这种情况的原因有多种:

The compiler will call DetOf2x2(...) even if currentElement is 0: that's sure to be far more costly than the final multiplication, whether by 0 or not. There are multiple reasons for that:

• DetOf2x2(...)可能会有副作用(例如输出到日志文件)，即使currentElement为0，并且
• DetOf2x2(...)可能会返回诸如Not-a-Number/NaN前哨值之类的值，无论如何都应传播到term1(如Nils Pipenbrinck首先指出的那样)

• DetOf2x2(...) may have side effects (like output to a log file) that need to happen even when currentElement is 0, and
• DetOf2x2(...) may return values like the Not-a-Number / NaN sentinel that should propagate to term1 anyway (as noted first by Nils Pipenbrinck)

鉴于DetOf2x2(...)几乎可以肯定，它只能在运行时确定值，而在编译时不能排除后者的可能性.

Given DetOf2x2(...) is almost certainly working on values that can only be determined at run-time, the latter possibility can't be ruled out at compile time.

如果要避免拨打Detof2x2(...)的电话，请尝试:

If you want to avoid the call to Detof2x2(...), try:

float term1 = (currentElement != 0) ? currentElement * DetOf2x2(...) : 0;

这篇关于是否可以在运行时优化浮点乘以零的运算?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！