Typographically inclined people can debate for hours the importance of font selection in the presentation of a message; a proper font(1) sets the right type of message.(2) With programs, data type is used to specify range and resolution of the data as well as determining the total memory and speed of your program.
I is for integer, at least in FORTRAN
In modern programing languages there are three primary data formats; integer, fixed point(3) and floating point. The range of integer data types is determined by the size of the data, e.g. 8, 16, 32 or 64 bit data types and the signed / unsigned nature.(4)
Floating point data represents information as a combination of a sign bit, an exponent component and a fractional component. This gives floating point data a greater range and resolution; however this can lead to issues when performing operations on data of significantly different orders of magnitude. For an overview of floating point data I would recommend this Wikipedia entry.(5)
What is the “point”?
Memory usage is easy to understand,(6) using all 32 bit integers in your program will use twice the memory of 16 bit integers; the same idea applies to floating point data types. The trade-off then comes with accuracy and speed. Integer based arithmetic is computationally faster then floating point; likewise, 64 bit floating point takes longer then 32 bit. The objective should be to use the smallest data type that fully represents your data after completion of the operation.
Tips and tricks!
- Overflow, underflow and precision loss can be detected through the use of simulation or tools such as Polyspace
- Disable range checking and overflow options for generated code to create more efficient implementations
Footnotes
- Here in this blog I lack the control of what font you see in your browser or in your email; for all I know you are using Wingdings (🕈︎♓︎■︎♑︎♎︎♓︎■︎♑︎⬧︎).
- And of course typesetting is part of the act of printing, the precursor to publishing electronically.
- Fixed-point could be considered a special case of integer data type, we will look at it in a future blog post.
- E.g. an 8-bit unsigned integer would have a range of 0 to 2^8 (256), while a signed 16-bit integer would have a range of (2^15 – 1) to 2^15 (-32767 to 32768). In every case they have a resolution of 1.
- There is a conceptual overlap between fixed point data floating point operations work; this link provides a general overview of fixed-point data.
- There is a caveat here; all hardware has a “smallest data type.” If you specify a data type smaller then the smallest data type you do not see any memory savings.