Has the Decades-Old Floating Point Error Problem Been Solved? (insidehpc.com)

overheardinpdx quotes HPCwire: Wednesday a company called Bounded Floating Point announced a "breakthrough patent in processor design, which allows representation of real numbers accurate to the last digit for the first time in computer history. This bounded floating point system is a game changer for the computing industry, particularly for computationally intensive functions such as weather prediction, GPS, and autonomous vehicles," said the inventor, Alan Jorgensen, PhD. "By using this system, it is possible to guarantee that the display of floating point values is accurate to plus or minus one in the last digit..."

The innovative bounded floating point system computes two limits (or bounds) that contain the represented real number. These bounds are carried through successive calculations. When the calculated result is no longer sufficiently accurate the result is so marked, as are all further calculations made using that value. It is fail-safe and performs in real time.
Jorgensen is described as a cyber bounty hunter and part time instructor at the University of Nevada, Las Vegas teaching computer science to non-computer science students. In November he received US Patent number 9,817,662 -- "Apparatus for calculating and retaining a bound on error during floating point operations and methods thereof." But in a followup, HPCwire reports: After this article was published, a number of readers raised concerns about the originality of Jorgensen's techniques, noting the existence of prior art going back years. Specifically, there is precedent in John Gustafson's work on unums and interval arithmetic both at Sun and in his 2015 book, The End of Error, which was published 19 months before Jorgensen's patent application was filed. We regret the omission of this information from the original article.

Comments

Built-in error bars

[Anonymous Coward]

For those of you too lazy to read the summary, their method is that instead of using one floating point value, they use two and say the real answer is between those two. If the two floats are consistent when rounded to the requested precision, it declares the value correct. If they differ, it gives an accuracy error.

So, for only twice the work and a little ovehead on top, this process can tell you when to switch to a high precision fixed-point model instead of relying on the floating point approximations.

Re:Built-in error bars

[K. S. Kyosuke]

Balls and intervals have been here for quite some time, though. Not sure that this is merely "twice the work", though.

Re:Built-in error bars

[JoshuaZ]

Yeah, I don't see how this isn't just a hardware implementation of interval arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic, which is a topic basic enough that I teach aspects of it as a secondary topic to my Calc I students. It is possible there's something deeper here that we're missing but if so, it doesn't stand out.

Re:Built-in error bars

[Impy the Impiuos Imp]

Every time you multiply two floats you lose a digit of precision. It's a little more complicated but that is the essence.

The butterfly effect was discovered with weather simulations. They saved their initial data and ran it again the next day -- and got a different result, which is impossible.

Turns out they only saved the initial conditions to 5 digits and not the entire float, or what passed for it in the 1970s.

Lo and behold! The downstream numbers, far from returning to the same value, diverged wildly. And no matter how small the difference, it always diverged.

Up until then, scientists had believed small differences would get absorbed away in larger trends. Here was evidence the big trends were completely dependent on initial conditions to the smallest detail.

That's why one stray photon would screw up time travel -- any difference whatsoever would cause the weather to be different in about a month and soon different sperm are meeting different eggs, and the entire next generation is different.

So any time you do more than a trivial number of float multiplies, you are in a whole different world. This is ok if you are looking for statistical averages over many, but miserable if you want to rely on any particular calculation.

back to basics ?

[swell]

In the 1950s, when the public was first becoming aware of computers, computers were considered to be large calculators. They could do math. They could be used by the IRS to compute your taxes or by the military to analyze sensor inputs and guide missiles. Few people could envision a future where computers could manipulate strings, images, sounds and communicate in the many ways that we now enjoy.

But today we have all those unimaginable benefits but one: They can't really do math well. Oh, the irony!