Feeds

Floating point numbers - what else can be done?

Avoiding errors

  • alert
  • submit to reddit

Build a business case: developing custom apps

Column In a recent article here in The Register we saw some of the problems that result when floating point numbers are misused or chosen inappropriately.

Many people wrote in to say they had seen first hand some of the voodoo techniques we decried, so clearly we're in the midst of a numerical calculation crisis and, if we don't do something, there's going to be satellites falling from the skies around us - in itself undesirable, but so much more so when the satellite in question is the one the TV channels depend on.

In this article we're going to look at other ways of handling real numbers, including some upcoming extensions to the C and C++ languages that could well see floats become much less used.

To recap briefly, last time we looked at the approximation error in floating point numbers that results because floats and doubles represent real numbers as a fraction over 2n. As we humans have 10 fingers, and we reserve the right to lay the foundations of our number system on such anatomical considerations, the values we deal with in software will often be some fraction over 10n, for example .37 is 37 over 102. Because there is no way to express this number in a base-2 floating point format, there was a small approximation error and we saw that this small approximation error turned into a big error when we tried to round and convert back to a base-10 real number.

This time round we're going to see what the methods are for avoiding this type of error. The comments made about the first article suggested many approaches, so we're going to weigh up the pros and cons of each. The main contenders are fixed point numbers, rational numbers, and base-10 floating point numbers.

The idea behind scaled integers is to fix a precision at the outset and use it consistently for all the operations involving a particular type of value. Take working with dollars and cents as an example. Instead of using a floating point to represent the value '$1.37' we would use an integral number to hold the value '137' and remember that the value has an implicit a scaling factor of 10-2.

The advantage of this approach is its simplicity; we can use native data types and the integral operations built into our hardware so the storage is efficient and the calculations are fast.

However, the problem with this approach is its inflexibility. The least significant place is chosen early in a project and it's difficult to change afterwards. If calculations result in numbers more precise than the representation then the extra precision is lost by truncation. Such errors accumulate and while steps can be taken to reduce them they are inhibited by encapsulation across function and class boundaries. Because flexibility and extensibility are important in software architecture, this is probably a sufficiently severe shortcoming to render this attractively simple solution unusable in many cases.

Gartner critical capabilities for enterprise endpoint backup

Next page: Rational numbers

More from The Register

next story
Why has the web gone to hell? Market chaos and HUMAN NATURE
Tim Berners-Lee isn't happy, but we should be
Microsoft boots 1,500 dodgy apps from the Windows Store
DEVELOPERS! DEVELOPERS! DEVELOPERS! Naughty, misleading developers!
'Stop dissing Google or quit': OK, I quit, says Code Club co-founder
And now a message from our sponsors: 'STFU or else'
Apple promises to lift Curse of the Drained iPhone 5 Battery
Have you tried turning it off and...? Never mind, here's a replacement
Linux turns 23 and Linus Torvalds celebrates as only he can
No, not with swearing, but by controlling the release cycle
Scratched PC-dispatch patch patched, hatched in batch rematch
Windows security update fixed after triggering blue screens (and screams) of death
This is how I set about making a fortune with my own startup
Would you leave your well-paid job to chase your dream?
prev story

Whitepapers

Top 10 endpoint backup mistakes
Avoid the ten endpoint backup mistakes to ensure that your critical corporate data is protected and end user productivity is improved.
Implementing global e-invoicing with guaranteed legal certainty
Explaining the role local tax compliance plays in successful supply chain management and e-business and how leading global brands are addressing this.
Backing up distributed data
Eliminating the redundant use of bandwidth and storage capacity and application consolidation in the modern data center.
The essential guide to IT transformation
ServiceNow discusses three IT transformations that can help CIOs automate IT services to transform IT and the enterprise
Next gen security for virtualised datacentres
Legacy security solutions are inefficient due to the architectural differences between physical and virtual environments.