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Walter Bright

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Vector Operations

August 10, 2008

Vector operations are when an operation is applied to each element of an array, and each operation is independent of the other elements of the array. For example, taking an array and multiplying each element by a constant, is typically expressed as a loop:

    for (int i = 0; i < array.length; i++)
         a[i] *= 4;

A more complex vector might be to add and scale:

    for (int i = 0; i < array.length; i++)
          a[i] = b[i] + c[i] * scale;

Since these are such common operations, in order to speed them up many computers added support for vector operations, so that multiple operations can be done in parallel (such as AMD and Intel's SIMD instructions). The trouble was that the loops specify the operations sequentially, one at a time.

This led to the development of auto-vectorizing compilers, which would recognize such loops, transform them internally into a higher level construct, then compile that construct down into vector machine code. Puzzlingly, the languages themselves rarely took the next logical step and provided a syntax to directly express a vector operation.

The irony is that the programmer must specify the vector operation in a low level manner, which the compiler transforms into a high level construct, which is then translated back down into low level code. It's like writing assembler code which the compiler transforms into C code and then compiles the C code. Why not write the C code directly?

The D programming language has done just that, providing a syntax to specify vector operations directly (without loops). The previous two examples would look like:

    a[ ] *= 4;

and:

    a[ ] = b[ ] + c[ ] * scale;

Here the [ ] notation means "the elements of the array", signaling a vector operation. An optional check is inserted to ensure that the arrays are all the same length, and a[] does not overlap b[ ] or c[ ].

The compiler has many ways it can implement this. The Digital Mars D compiler does it by converting it to a function call, one function for each combination of arguments and types. The most common cases of such functions get a hand-coded assembler implementation, the rest get a custom function generated by the compiler. This method was chosen for its easy adaptability to different architectures, as it doesn't require altering the code generator. There's certainly plenty of room for competing D implementations to aggressively pursue better optimization for these.

The advantages of vector operation syntax for the programmer are:

  • It succinctly and intuitively expresses the intent, which usually means faster programming and less buggy programs.
  • Auto vectorizing compilers are complex and tricky to build, and so most compilers aren't. With vector operations expressible in the language, the hard part is done already.
  • Even for relatively unsophisticated compilers, programmers can expect them to take advantage of any vector abilities of the target computer.
  • There becomes less need to buy expensive third party libraries just to speed up vector operations.
  • It encourages healthy competition among compiler vendors for doing a better job of compiling the vector operations, all to the benefit of the programmer.

At one point I investigated having vector operations be part of a user supplied library, but as Eric Niebler correctly pointed out to me, since arrays are a built-in first class type for D, then array operations must be as well.


Note: the gnu C compiler has, as a compiler extension, a syntax for vector operations. But I'm not aware of any momentum behind adding it to the future C or C++ language standards.

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