random_sorted, a Python code which generates vectors of random values which are already sorted.

Since the computation of the spacing between the values requires some additional arithmetic, it is not immediately obvious when this procedure will be faster than simply generating a vector of random values and then sorting it.

Because the code can generate a sorted random vector of values between 0 and 1, it is possible to generate sorted data samples from any distribution for which the inverse Cumulative Density Function (CDF) is known. For instance, to generate sorted normal data, simply generate sorted uniform data, and then apply the inverse of the normal CDF, as in the example code listed below.


The computer code and data files described and made available on this web page are distributed under the MIT license


random_sorted is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

normal, a Python code which computes a sequence of pseudorandom normally distributed values.

randlc, a Python code which generates a sequence of pseudorandom numbers, used by the NAS Benchmark programs.

rnglib, a Python code which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

toms515, a Python code which can select subsets of size K from a set of size N. This is a version of ACM TOMS Algorithm 515, by Bill Buckles, Matthew Lybanon.

uniform, a Python code which computes a sequence of uniformly distributed pseudorandom values.

van_der_corput, a Python code which computes elements of a 1D van der Corput Quasi Monte Carlo (QMC) sequence using a simple interface.


  1. Jon Bentley, James Saxe,
    Generating sorted lists of random numbers,
    ACM Transactions on Mathematical Software,
    Volume 6, Number 3, September 1980, pages 359-364.

Source Code:

Last revised on 01 February 2020.