Notable Software Failure Caused By A Floating Point Error
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Scud struck an American Army barracks and killed 28 soliders. A report of the General Accounting office, GAO/IMTEC-92-26, entitled Patriot Missile Defense: Software Problem Led to System Failure at Dhahran, Saudi Arabia reported on the cause math errors that caused disasters of the failure. It turns out that the cause was an inaccurate calculation of the
The Patriot Missile Failure
time since boot due to computer arithmetic errors. Specifically, the time in tenths of second as measured by the system's internal disasters caused by numerical errors clock was multiplied by 1/10 to produce the time in seconds. This calculation was performed using a 24 bit fixed point register. In particular, the value 1/10, which has a non-terminating binary expansion, was chopped at
Dimensional Analysis Catastrophe
24 bits after the radix point. The small chopping error, when multiplied by the large number giving the time in tenths of a second, lead to a significant error. Indeed, the Patriot battery had been up around 100 hours, and an easy calculation shows that the resulting time error due to the magnified chopping error was about 0.34 seconds. (The number 1/10 equals 1/24+1/25+1/28+1/29+1/212+1/213+.... In other words, the binary expansion of famous unit conversion mistakes 1/10 is 0.0001100110011001100110011001100.... Now the 24 bit register in the Patriot stored instead 0.00011001100110011001100 introducing an error of 0.0000000000000000000000011001100... binary, or about 0.000000095 decimal. Multiplying by the number of tenths of a second in 100 hours gives 0.000000095×100×60×60×10=0.34.) A Scud travels at about 1,676 meters per second, and so travels more than half a kilometer in this time. This was far enough that the incoming Scud was outside the "range gate" that the Patriot tracked. Ironically, the fact that the bad time calculation had been improved in some parts of the code, but not all, contributed to the problem, since it meant that the inaccuracies did not cancel. The following paragraph is excerpted from the GAO report. The range gate's prediction of where the Scud will next appear is a function of the Scud's known velocity and the time of the last radar detection. Velocity is a real number that can be expressed as a whole number and a decimal (e.g., 3750.2563...miles per hour). Time is kept continuously by the system's internal clock in tenths of seconds but is expressed as an integer or whole number (e.g., 32, 33, 34...). The longer the system has been running, the larger the number representing time. To predict where the Scud will next appear, both ti
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Explosion Of The Ariane 5
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Shop Free eBooks A Floating Point Error That Caused A Damage Worth Half A Billion Last updated February 17, 2013 By Abhishek Prakash 1 Comment FacebookTwitterGoogle+1LinkedInPinterestIf you ever did https://itsfoss.com/a-floating-point-error-that-caused-a-damage-worth-half-a-billion/ a little bit of programming, you must be aware of the term: floating point. One of the most neglected and potentially dangerous error one encounters is the floating point error. I bet a programmer must have https://en.wikipedia.org/wiki/Cluster_(spacecraft) seen the floating point error at least once in his/her life. But how much damage a floating point error can do? Ask that to European Space Agency that lost an effort of over a caused by decade and $500 millions, all thanks to a floating point bug. The story of Ariane 5: On 4 June 1996, the maiden flight of the Ariane 5 launcher ended in a failure. Only about 40 seconds after initiation of the flight sequence, at an altitude of about 3700 m, the launcher veered off its flight path, broke up and exploded. The failure of the Ariane 501 was caused by notable software failure the complete loss of guidance and attitude information 37 seconds after start of the main engine ignition sequence (30 seconds after lift-off). This loss of information was due to specification and design errors in the software of the inertial reference system. The internal SRI* software exception was caused during execution of a data conversion from 64-bit floating point to 16-bit signed integer value. The floating point number which was converted had a value greater than what could be represented by a 16-bit signed integer. So, what exactly happened? A 64 bit floating point number relating to the horizontal velocity of the rocket with respect to the platform was converted to a 16 bit signed integer. The number was larger than 32,767, the largest integer storeable in a 16 bit signed integer, and thus the conversion failed. The software ended up triggering a system diagnostic that dumped its debugging data into an area of memory being used by the programs guiding the rocket’s motors. At the same time, control was switched to a backup computer that unfortunately had the same data. This was misinterpreted as necessitating strong corrective action and the rocket’s motors swiveled to the limits of their mountings. Disaster ensued. Suggested Read[How To] Fix "Failed to download repository information" In Ubuntu
ESA Spacecraft properties Launch mass 1,200 kilograms (2,600lb) Start of mission Launch date 12:34:06, June4,1996(1996-06-04T12:34:06) Rocket Ariane 5G Launch site Kourou ELA-3 End of mission Disposal launch failure Destroyed June4,1996(1996-06-04) Orbital parameters Reference system Geocentric Regime Highly elliptical Epoch planned Cluster was a constellation of four European Space Agency spacecraft which were launched on the maiden flight of the Ariane 5 rocket, Flight 501, and subsequently lost when that rocket failed to achieve orbit. The launch, which took place on Tuesday, 4 June 1996, ended in failure due to an error in the software design caused by assertions having been turned off, which in turn caused inadequate protection from integer overflow. This resulted in the rocket veering off its flight path 37 seconds after launch, beginning to disintegrate under high aerodynamic forces, and finally self-destructing by its automated flight termination system. The failure has become known as one of the most infamous and expensive software bugs in history.[1] The failure resulted in a loss of more than US$370 million.[2] Contents 1 Spacecraft 2 Launch failure 3 Aftermath 4 See also 5 References 6 External links Spacecraft[edit] Cluster consisted of four 1,200 kilograms (2,600lb) cylindrical, spin-stabilised spacecraft, powered by 224 watt solar cells. The spacecraft were to have flown in a tetrahedral formation, and were intended to conduct research into the Earth's magnetosphere. The satellites would have been placed into highly elliptical orbits; 17,200 by 120,600 kilometres (10,700 by 74,900mi), inclined at 90 degrees to the equator.[3] Launch failure[edit] Diagram of the Ariane 501 with the four Cluster satellites Fragment fallout zone of failed Ariane 501 launch The Ariane 5 reused the inertial reference platform from the Ariane 4, but the Ariane 5's flight path differed considerably from the previous models. Specifically, the Ariane 5's greater horizontal acceleration caused the computers in both the back-up and primary platforms to crash and emit diagnostic data misinterpreted by the autopilot as spurious position and velocity data. Pre-flight tests had never been performed on the inertial platform under simulated Ariane 5 flight condit