“最”和“最不重要”的维度意味着什么？(What does “most” and “least” significant dimension mean?)

“最”和“最不重要”的维度意味着什么？(What does “most” and “least” significant dimension mean?)

我正在读一本关于C ++ AMP的书，并没有真正理解一些术语：

始终选择您的磁贴大小，以便最不重要维度中的线程数至少为16，如果可以，则使用32或甚至64。

我在Eigen文档中看到了类似的术语，所以我怀疑这是很常见的用法。

所以让我假设我有一个2D索引，数组，无论如何：

// construct it: ArrayType my2DArray(rows,columns); // now index it: float element = my2DArray[rowIdx,colIdx];

忘记了ArrayType的类型 ，并更多地考虑术语，这将是该阵列最重要和最不重要的维度？

I am reading a book on C++ AMP and don't really understand some of the terminology:

Always choose your tile size so that the number of threads in the least significant dimension is at least 16, and use 32 or even 64 if you can.

I had seen similar terminology used in the Eigen documentation, so I suspect this is quite common usage.

So let's suppose I have a 2D index, array, whatever:

// construct it: ArrayType my2DArray(rows,columns); // now index it: float element = my2DArray[rowIdx,colIdx];

Forgetting for a moment the type of ArrayType, and thinking more about the terminology, which would be the most and least significant dimension of that array?

最满意答案

当在多个维度上逻辑地分配线程时，通常存在从该N维空间到线性空间的映射。 使线性空间变化最小的维度是最不重要的维度。

作为示例，可以使用表达式（Y * width + X）来确定将2维（X，Y）坐标映射到线性空间。 这里，X是最不重要的维度，Y是最重要的维度。 同样，对于三维（X，Y，Z）空间，表达式可以是（Z *宽度*高度+ Y *宽度+ X）。 在这里，X仍然是最不重要的，但Z是最重要的。 您的布局可能不一定相同，例如您可以选择将线性空间映射到（Z *宽度*高度+ X *高度+ Y），在这种情况下，Y是最不重要的维度。

When allocating threads logically in multiple dimensions, there is generally a mapping from that N-dimensional space to a linear space. The dimension that varies the linear space least is the least significant dimension.

As an example, mapping a 2-dimensional (X,Y) coordinate to linear space might be determined using the expression (Y * width + X). Here, X is the least significant dimension and Y is the most significant dimension. Likewise, for a 3-dimensional (X,Y,Z) space, the expression might be (Z * width * height + Y * width + X). Here, X is still the least significant, but Z is the most significant. Your layout may not necessarily be the same, for example you may choose to map linear space to (Z * width * height + X * height + Y), in which case Y is the least significant dimension.