Distribution of floating-point operations in scientific computing
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I am looking for data about the distribution of floating-point operations - what percentage are additions/subtractions, what percentage are multiplications, etc. My Google-fu isn't working today, so I would appreciate any pointers.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
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I'd need crack to want to read it!
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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42 The time unit is arbitrary.
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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I'd need crack to want to read it!
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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I am looking for data about the distribution of floating-point operations - what percentage are additions/subtractions, what percentage are multiplications, etc. My Google-fu isn't working today, so I would appreciate any pointers.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
Are you looking for exact values (measured values) or statistics? For statistical purposes it is 25% each :-)
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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I am looking for data about the distribution of floating-point operations - what percentage are additions/subtractions, what percentage are multiplications, etc. My Google-fu isn't working today, so I would appreciate any pointers.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
This can't be answered since FMA (Multiply–accumulate operation - Wikipedia[^]) has been introduced because it would require to know the distribution of zero FMA arguments.
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I remember reading that someone had performed such an analysis, but I can't find any pointers to it. The idea was that additions/subtractions are more common than multiplications, which in turn are much more common than divisions/square root. This implies that optimizing the less common operations is likely to give a lower return than optimizing the more common operations. As I said, my Google-fu is non-functional today. :(
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
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Are you looking for exact values (measured values) or statistics? For statistical purposes it is 25% each :-)
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Kornfeld Eliyahu Peter wrote:
For statistical purposes it is 25% each :)
Actually, it isn't. A review of floating-point programs that I have written shows that addition/subtraction is more common than multiplication, and these are much more common than division/square root. I am writing various floating-point libraries, and would like this information so I can know where to spend my optimization time.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
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I am looking for data about the distribution of floating-point operations - what percentage are additions/subtractions, what percentage are multiplications, etc. My Google-fu isn't working today, so I would appreciate any pointers.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
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Looks to me that every body is wrong. There are clearly more zeros than ones. Each byte is packed with leading zeros. The ones are big-time losers. QED. :laugh:
Wrong thread?
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Wrong thread?
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I am looking for data about the distribution of floating-point operations - what percentage are additions/subtractions, what percentage are multiplications, etc. My Google-fu isn't working today, so I would appreciate any pointers.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
What for ?
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What for ?
I'm writing a floating-point package in C++ that provides: 1. A full implementation of the binary part of the IEEE-754-2008 Standard for Floating-Point Arithmetic (single-, double- and quad-precision) 2. Implementation of higher-precision formats, compatible with the Standard (up to binary1024). I have a basic implementation written using the "standard" algorithms, and would like some idea of where to invest time on improvements. Obviously, spending a lot of time on an operation that is rarely executed is not the best use of my time... :)
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
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Woops! Yes, it should be the thread below. :-O You will understand my difficulty when you see my next thread. :laugh:
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I'm writing a floating-point package in C++ that provides: 1. A full implementation of the binary part of the IEEE-754-2008 Standard for Floating-Point Arithmetic (single-, double- and quad-precision) 2. Implementation of higher-precision formats, compatible with the Standard (up to binary1024). I have a basic implementation written using the "standard" algorithms, and would like some idea of where to invest time on improvements. Obviously, spending a lot of time on an operation that is rarely executed is not the best use of my time... :)
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
Daniel Pfeffer wrote:
I'm writing a floating-point package in C++
That was not clear from your original question. So I will dig in here: I would not think about that. All basic operations will be used often (more or less) and should be therefore optimised as far as possible. Because division is the slowest operation it might be the first candidate even used probably less than the other operations. When a calculation uses divisions, a better implementation would probably reduce the overall calculation time by a greater factor than without division optimsation but with addition and multiplication optimisation.
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Daniel Pfeffer wrote:
I'm writing a floating-point package in C++
That was not clear from your original question. So I will dig in here: I would not think about that. All basic operations will be used often (more or less) and should be therefore optimised as far as possible. Because division is the slowest operation it might be the first candidate even used probably less than the other operations. When a calculation uses divisions, a better implementation would probably reduce the overall calculation time by a greater factor than without division optimsation but with addition and multiplication optimisation.
OK, that makes sense. Thanks.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
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OK, that makes sense. Thanks.
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
You are welcome. It is an interesting and challenging topic. Did you plan to publish it as an article?
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You are welcome. It is an interesting and challenging topic. Did you plan to publish it as an article?
Eventually - yes. The code works for the few problems that I've thrown at it, but that's not good enough (see the Pentium bug...). My biggest problem is finding an appropriate test suite; most of them cost an arm and a leg, and I can't justify spending that sort of money on a hobby. :(
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
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Eventually - yes. The code works for the few problems that I've thrown at it, but that's not good enough (see the Pentium bug...). My biggest problem is finding an appropriate test suite; most of them cost an arm and a leg, and I can't justify spending that sort of money on a hobby. :(
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack. --Winston Churchill
The distribution of operations depends on the problem set. However, you might be able to take some general guidelines from the evolution of computers themselves. Addition/subtraction came first, with floating point units being added later. If you look at those floating point units, you'll probably see that later ones implemented more operators. On the other hand, if you look at GPUs, they've always had floating point hardware -- those problem sets were never tractable in real time until floating point hardware existed. As for testing, the best way I found was to look at the architecture of the hardware, and design a test that tested it. For example, the old VAX FPUs used a nibble lookup table for multiplication, so I concluded that I needed to test every pattern in that lookup table to know if the hardware was OK. That did not reliably happen by simply pounding a lot of math-happy code at the FPU -- it required a specially created dataset that could be proven to be exercising each entry in the lookup table. If your hardware doesn't use a nibble lookup table, that test would likely be useless since it might not achieve full coverage.
We can program with only 1's, but if all you've got are zeros, you've got nothing.
