GY-63_MS5611/libraries/infiniteAverage

infinteAverage

Arduino Library to calculate an average of many samples

Description

This library is an experimental library that cascades a float and a uint32_t type. It was created from an idea when an overflow was encountered in my Statistic Class due too many samples.

Problem

As an 32 bit float has ~7 decimals precision, after 10 million additions the sum becomes 7 orders of magnitude larger than individual samples. From that moment the addition will not increase the sum correctly or even not at all.

Taking the average is taking the sum and divide that by the count of the numbers. Only if the count is fixed one could divide the samples first and then sum them. This library supports the first scenario.

Idea

To cope with the overflow problem, this lib uses an float combined with an uint32_t.

The float is used for the decimal part and the uint32_t for the whole part. In theory this should give about 15 significant digits for the average in a 9.6 format. but this precision is only internal to do some math. WHen the average() is calculated the value returned is "just" a float.

(since 0.1.2) If the library detects that there are 2 billion++ (0x8000000) added or if the whole part of the sum reaches that number, all internal counters are divided by 2. That does not affect the minimum and maximum and the average only slightly.

An experiment

Conclusion (for now)

The library allows two things

1. take the average of many many samples where normally a summing float would "overflow"
2. take the average of numbers that differ in order of magnitude

Future

This library also has its limits which needs to be investigated.

Ultimately one could upgrade the idea to a combination of a 8 byte double and a uint64_t to get around 28 significant digits => 18.10 format

• investigate "adaptive" scaling, now there is a virtual border at 1, but that could be at value (and might be user definable) This would allow to adjust to known order of size of the numbers. (e.g. if numbers are all in the billions the uint32_t would overflow fast)
• investigate other math with this datatype, starting with + - / *
• printable interface?
• play if time permits.

Notes

Note the practical meaning of the average of millions or billions of numbers is a discussion worth taking. Normally the outliers are the most interesting.

Note the library is not tested extensively, so use (with care) at your own risk.

Interface

• IAVG() constructor, resets the internal counters to 0
• void reset() resets the internal counters to 0
• void add(float value) adds value to the internal float uint32_t pair.
• float decimals() returns the internal float = decimals part.
• uint32_t whole() returns the internal whole part.
• uint32_t count() returns the number of values added.
• float average() returns the average in float format, or NAN if count == 0
• float minimum() returns the minimum in float format, or NAN if count == 0
• float maximum() returns the maximum in float format, or NAN if count == 0

Operation

See examples