Delta encoding

Apr 22, 2026 - 14:10
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Delta encoding

Numeric: ~

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The delta of numeric values is straightforwardly defined by subtraction, as shown in the example above. Due to the property of arithmetic operations, the numeric delta is ''symmetric'': if the latter value {{var|b}} is known, it is possible to apply the delta {{nowrap|{{var|a}} - {{var|b}}}} in reverse to obtain the previous value {{var|a}}.
The delta of numeric values is straightforwardly defined by subtraction, as shown in the example above. Due to the property of arithmetic operations, the numeric delta is ''symmetric'': if the latter value {{var|b}} is known, it is possible to apply the delta {{nowrap|{{var|a}} - {{var|b}}}} in reverse to obtain the previous value {{var|a}}.


It is also possible to produce a numeric "delta of deltas". This can be useful if the underlying data is generated by a process resembling f(x) = ax + b, as second-order delta would flatten the data to a string of zeros. Timestamps often correspond to this kind of function. Even higher-order deltas may be useful for real-life data: for example, the measured distance ([[pseudorange]]) to a navigation satellite over time is best compressed using a third-order delta, a "delta of deltas of deltas".{{cite journal|last1=Hatanaka|first1=Yuki|title=A Compression Format and Tools for GNSS Observation Data| journal = Bulletin of the [[Geographical Survey Institute]] | volume = 55 | pages = 21–30| year = 2008|url=https://www.gsi.go.jp/common/000045517.pdf|accessdate=2020-09-25}}
It is also possible to produce a numeric "delta of deltas". This can be useful if the underlying data is generated by a process resembling f(x) = ax + b, as second-order delta would flatten the data to a string of zeros. [[Timestamp]]s often behave this way. Even higher-order deltas may be useful for real-life data: for example, the measured distance ([[pseudorange]]) to a navigation satellite over time is best compressed using a third-order delta, a "delta of deltas of deltas".{{cite journal|last1=Hatanaka|first1=Yuki|title=A Compression Format and Tools for GNSS Observation Data| journal = Bulletin of the [[Geographical Survey Institute]] | volume = 55 | pages = 21–30| year = 2008|url=https://www.gsi.go.jp/common/000045517.pdf|accessdate=2020-09-25}}


In addition to subtraction, the [[bitwise]] [[exclusive or]] (XOR) also produces a symmetric delta. [[Time series database]]s often use the XOR operation as a delta between floating-point numbers.{{cite web |title=Time-series compression algorithms, explained |url=https://www.tigerdata.com/blog/time-series-compression-algorithms-explained |website=Tiger Data Blog |language=en |date=22 April 2020}}
In addition to subtraction, the [[bitwise]] [[exclusive or]] (XOR) also produces a symmetric delta. [[Time series database]]s often use the XOR operation as a delta between floating-point numbers.{{cite web |title=Time-series compression algorithms, explained |url=https://www.tigerdata.com/blog/time-series-compression-algorithms-explained |website=Tiger Data Blog |language=en |date=22 April 2020}}
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