Why Computers Suck At Math

antdude writes "This TechRadar article explains why computers suck at math, and how simple calculations can be a matter of life and death, like in the case of a Patriot defense system failing to take down a Scud missile attack: 'The calculation of where to look for confirmation of an incoming missile requires knowledge of the system time, which is stored as the number of 0.1-second ticks since the system was started up. Unfortunately, 0.1 seconds cannot be expressed accurately as a binary number, so when it's shoehorned into a 24-bit register — as used in the Patriot system — it's out by a tiny amount. But all these tiny amounts add up. At the time of the missile attack, the system had been running for about 100 hours, or 3,600,000 ticks to be more specific. Multiplying this count by the tiny error led to a total error of 0.3433 seconds, during which time the Scud missile would cover 687m. The radar looked in the wrong place to receive a confirmation and saw no target. Accordingly no missile was launched to intercept the incoming Scud — and 28 people paid with their lives.'"

Comments

Poor QA

[slifox]

It's pretty pathetic and negligent that software that controls explosive missles was not tested for over 100 hours of operation. That's a standard Quality Assurance procedure for even the simplest low-budget hardware...

It's also pretty pathetic that the system designers implemented a broken design and did not foresee this problem. High-resolution timekeeping has been accomplished pretty successfully already...

I wonder how much time and money was spent in research and development for this thing
It doesn't seem like we're getting a quality product for the likely huge sum that was paid for it...

Re:Poor QA

[Anonymous Coward]

What Every Computer Scientist Should Know About Floating-Point Arithmetic

Re:Poor QA

[Anonymous Coward]

This particular story took place in 1991, and most of the code for Patriot was written in the 70s - needless to say, software QA was a little more lax back then. The fix for this problem was out a couple days after the incident.

Re:Poor QA

[Anonymous Coward]

Hindsight is almost 20/20. Except that the original purpose of the Patriot was to shoot down much slower aircraft, flying parallel to the earth, not ballistic missles. This new use for Patriot was essentially experimental and had had been rushed to war - and in war you run into alot of unexpexcted circumstances. For example, conventional doctrine in the 1980's required Patriots to move constantly on the battlefield to avoid air attack. The clock would then reset when repositioned. No one expected a Patriot in air defense mode to stay stationary for 10 hours let alone 100. But in a missle defense role they did. There is a good GAO report on this.

Re:Poor QA

[OeLeWaPpErKe]

Mod parent up ! This idiotic article blames computers for programmers using numerical approximation algorithms illadvisedly.

which is stored as the number of 0.1-second ticks since the system was started up. Unfortunately, 0.1 seconds cannot be expressed accurately as a binary number, so when it's shoehorned into a 24-bit register — as used in the Patriot system — it's out by a tiny amount. But all these tiny amounts add up. At the time of the missile attack, the system had been running for about 100 hours, or 3,600,000 ticks to be more specific. Multiplying this count by the tiny error led to a total error of 0.3433 seconds, during which time the Scud missile would cover 687m. The radar looked in the wrong place to receive a confirmation and saw no target. Accordingly no missile was launched to intercept the incoming Scud — and 28 people paid with their lives.'"

So in a system that should have clocks synchronized to less than a microsecond nobody bothered to run "ntpdate" even once in hundred days ? And surely the military has better clock synch than a stupid home pc ? This is stupidity, also known as "human error", causing those deaths. It's a case of "the correct answer to the wrong question".

What is always brought up as a "computer problem" is the crash in Paris of a jet due to infighting between the human pilot and the autopilot. Of course, there the ultimate mistake was the pilot's : he had forgotten to turn off the autopilot to land. It was set for cruising altitude (3km), and the pilot was trying to land. This resulted in ever more desperate attempts by the autopilot to get the plane to gain height, which eventually resulted in a total loss of lift for the plane, which naturally resulted in the plane hitting the ground nose-down and a big fireball. The computer did exactly as instructed, it's just that the pilot's (unintentionally given) instructions were stupid, and the fact that it took the pilot over 3 minutes to realize just how stupid he had been.

Re:Poor QA

[OeLeWaPpErKe]

The Iron dome system works perfectly. It's just not capable of protecting any kind of large area. It can, however, make a military base invulnerable to rocket fire, and they're working on making the system mobile, to protect tanks. The only real problem left for doing this is the power requirements.

For ships, another such system exists, and protected the ships perfectly well from those same rockets fired by hizbullah. It's "protection range" ? In the largest deployment about 200 square meters.

There is also the problem that a downed missile presents. What is a "downed missile" ? Well it's a large collection of very-high speed pieces of metal that have been heated up by a large explosion that's about to crash into the ground. So far so good.

So what is "the ground" in the case of a hizbullah or hamas missile launch ? Well it's the center of the city that's controlled by the terrorists. It's their human shields. Markets, schools, you name it. So a successfull missile intercept is reported in the press as "Israel fires a rocket into a palestinian kindergarten". That is, by the way, the literal truth, even if the rather important detail of a rocket's presence above said kindergarten is left out. In the deployed missile intercept installations "the ground" is chosen to be something else, like the ocean surface.

Missile intercept systems are no solution for terrorism. Most unfortunately, the only solution for those rocket attacks is preventing they're fired in the first place. Which obviously requires either palestinians police their own terrorists, or someone does it for them (that's called "occupation").

These systems work, they are deployed successfully in the field. They're no silver bullets, and any bullet that's fired, whether a missile or a missile-intercept-missile, will eventually hit the ground at rather high speeds. Which makes their use above urban environments result in civilian casualties.

Re:Poor QA

[Hal_Porter]

There is a good GAO report on this.

This one?

http://www.fas.org/spp/starwars/gao/im92026.htm

Wow. People complain about the US government. Still look at the transparency. The GAO wrote a very readable report for the House Of Representatives and now we can all read it on the web. It's not unreasonable to think that the US's vast military superiority over everyone else on the planet is at least in part due to this sort of thing. I don't think any other government would do this - mistakes in the military would just get covered up as state secrets and anyone who tried to talk about them would get locked up or worse.

Re:Poor QA

[Jeremi]

The computer did exactly as instructed, it's just that the pilot's (unintentionally given) instructions were stupid, and the fact that it took the pilot over 3 minutes to realize just how stupid he had been.

Sounds like a user interface problem to me. Given the potential consequences of that particular user error, the fact that the autopilot was still engaged should have been made more obvious to the pilot. (e.g. when the plane computer sees that a struggle is going on between the autopilot and the manual controls, it should prompt a loud, un-maskable synthesized voice shouting "THE AUTOPILOT IS ENGAGED, YOU IDIOT!")

Curse of binary floating point

[Carewolf]

Use decimal floating point or simple swich to fixed point. Fixed point not used as often as it should, and many developers don't know how difficult ordinary floiting point really is.

Re:Curse of binary floating point

[Carewolf]

Fixed point never rounds when operating in the range and precision for which it is designed. In this case they needed a precision of .1, using INT/10 would be 100% accurate and never give them any rounding errors for this use case.

So, in other words: You are wrong, and should probably considering using fixed point more.

Fixed point numbers?

[Big_Mamma]

Use fixed point numbers? You know, in financial apps, you never store things as floating points, use cents or 1/1000th dollars instead!

Computers don't suck at math, those programmers do. You can get any precision mathematics on even 8 bit processors, most of the time compilers will figure out everything for you just fine. If you really have to use 24 bits counters with 0.1s precision, you *know* that your timer will wrap around every 466 hours, just issue a warning to reboot every 10 days or auto reboot when it overflows.

Stupid article, too

[hellfire]

Translation: computers are only as smart as the people programming them... and there's plenty of stupid people out there.

We knew this. This is no great revelation. So why is this news?

What?!

[jointm1k]

of 0.1-second ticks since the system was started up. Unfortunately, 0.1 seconds cannot be expressed accurately as a binary number, so when it's shoehorned into a 24-bit register

All they had to do is use integers, where a value of 1 represents 0.1 s.

Re:"User error"?

[betterunixthanunix]

So they designed a system that accumulated rounding errors over time, and their solution was to ask the system's users to reboot the system every so often? Somehow, that does not add to my sympathy for these programmers...

don't blame the computer for bad programming

[frovingslosh]

It is absurd to blame the computer (or worse, all computers) for what is bad programming. Computers can store a 1/10 of a second perfectly accurately, as long as it is stored in a variable that counts tenths of seconds rather than seconds. It can easily be stored as an integer that way, avoiding any floating point rounding errors.

There certainly are cases of bad math in computers, particularly Intel computers. But this isn't such an example. This is just a lazy and stupid programmer who didn't understand what he was really doing who should take the blame for the failure that killed people, not the computer.

Re:retrospective technological excuses

[david duncan scott]

Regardless, what isn't possible is is to design a system that can accurately track and shoot down missiles in flight. As the Patriot defence system so patently demonstrated.

You're right. Just as the failure of Samuel Langley's aircraft demonstrated that man would never fly, the failure of an anti-aircraft missile to destroy only half of the ballistic missiles (targets moving at what, twice the speed of the targets it was designed to destroy?) demonstrates that ABM's will never work.

Paid with their lives

[sochdot]

I'd just like to point out here that the 28 people were not killed by the failure of the intercept system. They were killed by the nice folks who launched the missile in the first place.