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From: Greg Colvin (Gregory.Colvin_at_[hidden])
Date: 2002-08-20 23:45:38

The question of how to support the double word results of
multiplying two words ecently came up on the C++ committee
reflector. The choices seem to be either providing a special
function, or providing typedefs for which idioms like the
following can result in optimal code:

   uword_t x, a;
   ulong_t y = ulong_t(x) * a;

To which we can add:
   uword_t b;
   ulong_t y = ulong_t(x) * a / b;

I should think that most compilers already do a good job,
given suitable choices of uword_t and ulong_t, but I haven't
done any testing to find out.

At 09:49 PM 8/20/2002, you wrote:
>This can be more philisophical question rather than a techical one and if
>it's off topic, please ignore it.
>Many times working on different libraries, particulary on graphic ones I
>felt a lack of a very simple operation. It's not only in C/C++ but in many
>other high-level languages. This is the operation of integer scaling,
>y = x * a / b;
>The problem is with integer overflow. Suppose, we have 32-bit integers on
>32-bit architecture. The semantics of this construction assumes using 32
>bits everywhere, including the intermediate result x*a because any compiler
>must follow the instructions, and so, it *must* use only 32-bit for x*a.
>Afterall, having the overflow may be important for the programmer. On the
>other hand all the 32-bit architectures that I know store the result of
>"mul" in the 64-bit register (or registers). It's also a rule that the "div"
>command accepts 64-bit dividend. It became a standard de facto in the
>hardware. All I need is:
>mov R0, x
>mul b ; 64-bit result is in R0+R1
>div c ; 64-bit R0+R1 / 32-bit c and put into R0.
>But instead of it any compiler will generate:
>mov R0,x
>mul b ; 64-bit result is in R0+R1
>cdq R1,R0 ; lose most significant bits in R1 :-(
>div c
>Again, any compiler *has* to do so because it's told to. OK, I could use all
>64-bit numbers. Great, if it worked as fast as the example above. In fact it
>works about 10 times slower because it uses internal functions like __mul64
>and __div64 (assume, we're talking about 32-bit architecture).
>That's too bad to lose this common possibility of mul-div with 64-bit
>intermediate result.
>But as it was said above the sematics of the expression x * a / b cannot be
>changed, and so, the only way to solve this problem is to include an
>appropriate operation (or function) into the C++ standard. I'm not sure
>about the syntax or name of this operation, maybe
>std::muldiv(x,a,b) or std::scale(x,a,b). I don't expect and don't hope this
>operation to be added into the language, but at least into the standard
>Well, I could use inline assembler (or win32 API MulDiv) but when my
>objective is to create a *compatible* C++ library it's very painful. I want
>this operation (or function) to be a standard one.
>The argument that there true 64-bit architectures are coming is not
>acceptable because as soon as they're available we will want to use 64/128
>bit mul-div operation and so on. This process is endless :-)
>Using floats or doubles is slower and *it_will_always_be_slower* than using
>integers, and besides, there rounding issues arise.
>What if a particular architecture does'n have this possibility? Well, it's
>exactly the same issuse as the int-64 operations on a 32-bit platform. The
>compiler just could use appropriate internal functions. But if the language
>or the standard library could have this operation it could use the benefits
>of the most popular hardware platforms (actually all of those we actually
>Maybe the most advanced compilers can optimize the expression y = (long
>long)x * a / b to the three mentioned above assembler instructions. I
>honestly don't think so because the rule says that all the data of the
>expression are to be converted to the longest and/or most precise type. I
>want to have an integer scaling operation that guarantees the intemediate
>result to be twice longer than its arguments and that would promise the most
>possible optimization for the particular hardware.
>In other words I would propose to include this simple operation into the
>standard. I realize that it can look naive, but at least it would be much
>more useful and practical than, for example, the stupid innovation of
>possibility of initializing static const int members inside the class :-)
>If it's already done in STL or BOOST than sorry. Please just point me out.
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