Embedded Systems Design - June 2008 - (Page 16)

programmer’s toolbox store size or shape information anywhere in the executable software. Look at the two arrays with any debugger, and you’ll see the exact same block of nine consecutive doubles. What’s more, we’ve all read the introductory C textbooks where we were told that any reference to an array is equivalent to a pointer to its ﬁrst element. Thus: a b ptr_a = &a[0]; double b[3][3] = {1, 2, 3, 4, 5, 6, 7, 8, 9}; I tend to use this kind of construct a lot, but strictly speaking, it’s not good practice. I’ve declared the array to be doubly dimensioned, but used a singly dimensioned initializer. That it works at all is yet another indication of the on-again, off-again equivalence of singly and doubly dimensioned arrays. To be rigorously correct, I should have written: double b[3][3] = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; and: ptr_b = &b[0][0]; should all give the same result: a simple pointer to a double. Indeed, all through my code for class matrix, you’ll see references like p[i], where p is declared double*. It’s a common practice and a fundamental part of the C idiom. Despite all this obvious stuff, try passing a reference to the array b, and you’ll ﬁnd that some pointers are more equal than others. The declaration: Matrix B(b, 3, 3); doesn’t work. How can this be? If no size data are stored anywhere, the arrays a and b look identical in memory (and are perhaps in the same memory locations), and both references are passed as simple pointers, why then does the statement work differently for the two arrays? The answer is simple enough: the compiler knows all. Although it doesn’t ﬁnd the need to store extra information anywhere, it knows that the two arrays are fundamentally different, syntactically. It won’t let you treat them the same. To do so would be like equating two objects of different types. What we’d really like to do is to deﬁne the constructor as: Matrix::Matrix(double a[ ][ ], size_t nr, size_t nc) To those who e-mailed me that the storage arrangement used by the compiler—row-major or column-major—shouldn’t matter to the programmer, I can’t resist pointing out that, in this declaration, it danged well does matter. The three inner brackets in that initializer refer to rows, not columns, and we had better not forget it. What should we make of all this? Mostly, it’s that trying to do useful matrix math in C/C++ is not fun. The C constructs, including esoterics like: *b++ = *a++; but this doesn’t work. The compiler has no way to tell the constructor the number of rows in a. Hence my earlier rant concerning C’s lack of support for conformant arrays. Of course, I can still use the converting constructor with a doubly dimensioned C array. I only have to make sure it’s passed a pointer to its first element. The statement: Matrix B(&b[0][0], 3, 3); work great for singly dimensioned arrays, but not so great for multiply dimensioned ones. I’ve found it best to tell the compiler that all the arrays are singly dimensioned, and keep the truth to myself, hiding the details down inside functions or objects. That’s why I wrote the class Matrix and its ancestors in the ﬁrst place. One word of caution concerning the converting constructor: there is not (nor can there be) any range checking on the size parameters. If you create a matrix from an array, you’re expected to provide size parameters that don’t violate the range of the input array. If you break this rule, you won’t break the compiler or anything, but you will get garbage elements towards the end of the matrix. Finally, I should mention that, because I’m so enamored with 3-vectors and 3x3 matrices, I sought to have the dimensions of this constructor default to 3x3, independently of the class variables. This would have let me write things like: Matrix A(a); works just ﬁne, albeit a little inscrutable. Before we leave the topic, take one last look at the declaration: without having to pass any size parameters. This, however, turned out to be a Terrible Idea. Because the call looks just like a call to the copy constructor, my compiler tried to typecast the array to an object of class Matrix. I guess I could have overcome this obstacle with use of the verbatim keyword, but what if I had? Then I would have been able to write two declarations: 16 JUNE 2008 | embedded systems design | www.embedded.com http://www.embedded.com

Table of Contents Feed for the Digital Edition of Embedded Systems Design - June 2008

Embedded Systems Design - June 2008 Contents #Include Party Bit Programmer's Toolbox Cover Feature: Virtual Hardware Platforms for Embedded Software Validation Allocating Memory in MATLAB-to-C Code MDD and IDEs: Making the Twain Meet in Embedded Systems Design Avoid a Thrashing Guest Editor Advertising Index Break Points Marketplace

Embedded Systems Design - June 2008

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