## Double vs Single Precision, Matlab in 2019

### Mark Brandon (view profile)

on 17 Feb 2019
Latest activity Answered by Mark Brandon

on 17 Feb 2019

### John D'Errico (view profile)

Matlab defaults to double precision, but single precision is sufficient for many computational problems. In addition, single precision uses half the memory, and is generally twice as fast.
To convert from double to single precision is easy, in that all that is needed is to define the starting variables as single, and then all subsequent variables will default to the variable in each calculation with the lowest precision.
The best approach to define type single is:
X = zeros(10,10, 'single');
The construction: X = single(zeros(10,10)); is four times slower!!
Note that there is no difference between these two constructions for type double given that double precision is the default.
PROBLEMS
I ran into two problems that dimmed my enthusiasm for single precision.
1) Some Matlab functions will only work with double precision. The interpolation functions are the main examples that I have come across. (It would be great to have some documentation, either informal or formal, listing those Matlab functions that have type limitations. I have yet to find this information on the web.) To use the interpolation functions, you have to convert the input arguments to double, and then convert the output arguments back to single, which is cumbersome, and perhaps troublesome as well, as noted below.
2) A second problem is that the transition back and forth between single and double can cause errors in the limits for the interpolation. I ran across an error where the interpolation started to return nans after conversion to single precision. This problem would not have occured if the interpolation functions were able to work with single precision. That said, it might be possible to set the extrapolation option to "nearest" in order to navigate around the small round-off errors associated with the transition between single and double precision. Of course, this option could only be trusted when the algorithm was known to be fully functional.
For now, I have decided to stick with double precision.
I found very little discussion of this issue on the web. Surely there are others out there with experiences and recommendations about single precision.
Best,
Mark

### John D'Errico (view profile)

on 17 Feb 2019
Edited by John D'Errico

### John D'Errico (view profile)

on 17 Feb 2019

This topic is worth discussing.
X = zeros(10,10, 'single');
The construction: X = single(zeros(10,10)); is four times slower!!
Of course it is! Why would you not expect that? The former just fills the assigned memory locations with the same zero element. The latter fills it with double precision zeros, then needs to move the entire array to a new location, converting each element to a single on the fly.
"In addition, single precision uses half the memory, and is generally twice as fast."
Had you stated that it is SOMETIMES twice as fast, you would be correct. Newer releases have improved in this respect, although users wth older releases may find that single is no faster than double computations.
The problem is that single precision can be dangerous. You may not always know when you are near the edge of a numerical cliff. Using doubles keeps you much farther away from that edge. Yes, good numerical analysis, good numerical methods is a good thing. But if you use singles just to save some CPU time and some memory, then you are forgetting a major thing - CPU time is cheap, as is memory. So if you are using singles just to be frugal, then you are making a mistake. Use single precision when you absolutely need to do so, and only when you have the numerical skills to know that you can safely afford the lower precision.
Effectively, if you use single precision for no valid reason than pure frugality, then you are pre-optimizing your code, often a bad thing.
"Matlab defaults to double precision, but single precision is sufficient for many..."
A better way to say that is:
Matlab defaults to double precision, but you can sometimes survive the use of single precision. As the precision gets smaller, the risks grow greater.

Mark Brandon

### Mark Brandon (view profile)

on 17 Feb 2019
John,
Thanks for your comments. Yes, memory and speed are cheap now, but that is often matched by an interest in larger problems.
My motivation is to keep a very large parallel computation within the time and memory bounds of the computer cluster I am using. The scale of the problem has caused me to move from 24 hours with 20 workers, to 48 hours with 20 to 28 workers. So, I was looking for some way to get back to a faster and smaller computation.
Over the last 15 years, I have experimented with single precision twice. Yes, you are right: in the dark old days, there was no difference in speed between single and double precision. But my experiments, and others, indicates about a factor two difference in speed with the modern version of Matlab. So that extra speed might be useful in some cases. The computation I am doing does not require double precision, so I decided see if single precision would work. Compared to the past, almost all Matlab functions support multiple types, except for the interpolation functions. My problem was mostly with the scatteredIntepolation algorithm.
So, I am back to using double precision....
Best,
Mark
Walter Roberson

### Walter Roberson (view profile)

on 17 Feb 2019
Several Intel chips are compared in http://nicolas.limare.net/pro/notes/2014/12/12_arit_speed/ .
The pattern is fairly consistent: single precision addition is notably faster than double precision addition, but single precision multiplication is slower than double precision multiplication, or at most barely faster (older chips.)
Note, though, that this is for CPUs. The relative performances of single and double precision on NVIDIA GPU is considerably more complicated. Single precision on GPU can be 3 times, 8 times, 24 times, or 32 times faster than double precision, depending on the NVIDIA GPU model.

### Walter Roberson (view profile)

on 17 Feb 2019

>> x = linspace(single(0),single(pi),20);
>> y = single(rand(1,20));
>> z = interp1(x, y, linspace(single(0),single(1),20))
z =
1×20 single row vector
Columns 1 through 9
0.7323988 0.5099056 0.2874124 0.06491931 0.2007067 0.3955918 0.5904768 0.6504743 0.6571828
Columns 10 through 18
0.6638914 0.6852249 0.7173581 0.7494914 0.7815178 0.8134047 0.8452916 0.8761108 0.9043419
Columns 19 through 20
0.9325731 0.9475382
That looks like it supports single to me.
x— Sample points
vector
Data Types: single| double| duration| datetime
That looks like it supports single to me.

### Mark Brandon (view profile)

on 17 Feb 2019

Walter,
Yes, you are right... interp1 is supported for a range of types. I should have been more precise, stating only that some of the interpolation schemes are not supported. My experience is with scatteredInterpolant, which can be used by itself and is also invoked internally in some other interpolation functions.
I had thought, mistakenly, that Matlab was now fully converted to single and double types, but that hunch was wrong. In addition, I started to realize that I would have to look up every function that I am using to see if the single type is supported. There is no list of functions that are doubles only.
I should note that Matlab is my favorite computational tool, and I have been using it in my research for 15 years now. I found this particular issue of the "singles game" to be rather poorly documented. Many people have suggested that the single precision is a useful method for getting a smaller and faster computation. I agree with John D'Errico that there are dangers involved in using single precision. Nonetheless, I am looking to get suggestions from people who have used this approach for large computations. What are the problems and does the outcome justify the work involved in the transition?
Best,
Mark
p.s. Thanks to you and John for your comments. The two of you are among my favorites at MATLAB Answers!
https://www.mathworks.com/help/matlab/ref/scatteredinterpolant.html
Input Arguments
x, y, z Sample points
vector
Sample points, specified as vectors of the same size as v. The sample points should be unique. However, if the sample points contain duplicates, scatteredInterpolant displays a warning and merges the duplicates into a single point.
Data Types: double
P Sample points array
matrix
Sample points array, specified as an m-by-n matrix, where m is the number of points and n is the dimension of the space where the points reside. Each row of P contains the (x, y) or (x, y, z) coordinates of a sample point. The sample points should be unique. However, if the sample points contain duplicates, scatteredInterpolant displays a warning and merges the duplicates into a single point.
Data Types: double
v Sample values
vector
Sample values, specified as a vector that defines the function values at the sample points, v = F(x,y,z).
Data Types: double