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Date: Mon, 16 Feb 2004 13:19:48 -0600
From: Eric Rudd <rudd AT cyberoptics DOT com>
Subject: Re: Fwd: C99 Functions Under Development and Checkout
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Kbwms AT aol DOT com wrote:

>Can anyone help me here?
>
>One set of functions comes to mind immediately because it is on my "to do 
>list" and is described in C99 paragraph 7.12.13 -- Floating multiply add with 
>subtitle, "The fma functions."  My knowledge of assembler would be extended 
>beyond its limit trying to figure out how to calculate (x*y)+z as one ternary 
>operation.
>
This one is actually pretty difficult to do, if you want to comply with 
the letter of the law.  The description of the function in C99 talks 
about delivering the correctly-rounded result.  On the x87 chip is it 
possible to come pretty close by using the native 64-bit precision, but 
it's not correct rounding in all cases.  gcc actually generates this 
64-bit code by simply writing

double fma(double x, double y, double z) {
   return x*y + z;
}

but it is not guaranteed that the intermediate product will be held in 
the 64-bit x87 register, as it currently seems to be.  Assembler will 
ensure that the intermediate product is held to 64-bit precision, but 
that doesn't even guarantee a correctly-rounded result, as the C99 
standard requires.

If you want assembler, just compile the above fragment with the -S,  
-O2, and -fomit-frame-pointer options and you will get assembler output, 
which, for this particular function, is as good as can be done by hand.

-Eric Rudd