# How reliable is a floating point operation (how often does it makes mistakes)

While computers are very reliable, they can also do errors because of noise. I would like to have an idea of the rough order of magnitude of error per floating point operation in a computer, in a typical environment (in a typical office, like not deep underground for instance), with a reference to a good paper.

I am not looking for rounding errors but I am looking for errors due to noise in the surrounding environment (parasitic electromagnetic fields could eventually flip bits, hence introduce errors inside of the computer for instance).

[Clarifications]: What we call noise in physics is not related to "audio" noise. It corresponds to a physical (usually random) process that can introduce errors. An example of noise is thermal noise (a hot system is more prone to error than a cold one).

• About 140 decibels of noise can cause permanent damage to your computer. But that's fine, because about 130 decibels can cause permanent damage to you. The magnitude of a floating point operation is about 10^300 for double precision, and 10^4000 for extended precision. Maybe you want to change your question to actually ask what you want to know, Mar 27 at 15:12
• @gnasher729 thanks. I am not sure to see how I could clarify the question. How many floating point operations can I do before one is impacted by an error due to surrounding noise in a typical environment. The motivation for my question is to compare to quantum computing where there is typically 1 error every 1000 operations. Mar 27 at 15:18
• @gnasher729 also: the fact the concept of error correction exists indicates that errors might not be that rare in general (perhaps they are however only used in communication and not computing though: I don't know). Mar 27 at 15:23
• I seem to recall Google published some papers on soft errors and single-event upsets. The problem with these is, they are incredibly rare, so in order to do any meaningful work on it, you kinda have to run millions of computers 24/7. Not many universities or research labs can do that. For example, Google saved a lot of money by raising the temperature in their data centers. They could do this because they had the data to be able to calculate the cost of errors and hardware failures induced by higher temperatures vs. the cost savings on HVAC. Mar 27 at 16:57
• There should also be some interesting data from Hewlett-Packard's Spaceborne Computers (which are standard, non space-rated HPCs installed on the ISS). Mar 27 at 16:59

## 1 Answer

Not an actual answer, but I think you are interested in the soft error rate of modern computers (or perhaps only the single-event upset rate). These rates will likely vary depending on where the computer runs (space/high atmosphere vs underground facilities).

CPU producing companies should probably have some rough figures about these error rates for their components in standard use conditions.