Increasing the size of the state of a PRNG always improves a lot the quality of the generated sequence of numbers.
While multiplicative congruential PRNGs with a 32-bit state are poor, those with an 128-bit state, like yours, may be quite good.
However, for any application that needs pseudo-random numbers, you must have a good understanding of its requirements, in order to be able to choose the right PRNG.
For example, when the random numbers are used to choose the coordinates of random points in a multi-dimensional space, simple congruential PRNGs are guaranteed to show some correlations between the coordinates that should have been independent, though for a PRNG with an 128-bit state, unless it uses a poorly chosen multiplicative constant, the correlations will appear only for rather long sequences.
There is another kind of PRNG, which has exactly the same speed as yours, but which produces much better pseudo random sequences, the MLFG (Multiplicative Lagged Fibonacci Generator, 1984). Unlike yours, it is a non-linear generator, which is the reason for the good quality. While the speed is the same, it uses a larger state.
The choice of a PRNG can be important in 2 cases, for embedded microcontrollers, like in the parent article, and for applications which have to generate a huge amount of random numbers, e.g. billions of numbers per second.
Otherwise, there is a simpler choice, just use AES in counter mode as the PRNG.
Even when cryptographic strength is not needed, it does not hurt. The AES speed on all modern CPUs is not much lower than that of the fastest PRNGs, and only very few applications need faster PRNGs than AES. Moreover, a PRNG in counter mode has many advantages over the PRNGs based on a recurrence formula. It is possible to access quickly any arbitrary point in the random sequence. It is possible to split the random sequence in any number of subsequences, which can be computed in parallel and which are guaranteed to be uncorrelated, which is important in many multi-threaded programs.
While multiplicative congruential PRNGs with a 32-bit state are poor, those with an 128-bit state, like yours, may be quite good.
However, for any application that needs pseudo-random numbers, you must have a good understanding of its requirements, in order to be able to choose the right PRNG.
For example, when the random numbers are used to choose the coordinates of random points in a multi-dimensional space, simple congruential PRNGs are guaranteed to show some correlations between the coordinates that should have been independent, though for a PRNG with an 128-bit state, unless it uses a poorly chosen multiplicative constant, the correlations will appear only for rather long sequences.
There is another kind of PRNG, which has exactly the same speed as yours, but which produces much better pseudo random sequences, the MLFG (Multiplicative Lagged Fibonacci Generator, 1984). Unlike yours, it is a non-linear generator, which is the reason for the good quality. While the speed is the same, it uses a larger state.
The choice of a PRNG can be important in 2 cases, for embedded microcontrollers, like in the parent article, and for applications which have to generate a huge amount of random numbers, e.g. billions of numbers per second.
Otherwise, there is a simpler choice, just use AES in counter mode as the PRNG.
Even when cryptographic strength is not needed, it does not hurt. The AES speed on all modern CPUs is not much lower than that of the fastest PRNGs, and only very few applications need faster PRNGs than AES. Moreover, a PRNG in counter mode has many advantages over the PRNGs based on a recurrence formula. It is possible to access quickly any arbitrary point in the random sequence. It is possible to split the random sequence in any number of subsequences, which can be computed in parallel and which are guaranteed to be uncorrelated, which is important in many multi-threaded programs.