Saturday, September 2, 2017

High performance [mathematical] computing

When talking about supercomputers, there is a temptation to define things in terms of either of the following:
  1. massive simulations 
  2. they mean maths
Here is a phrase used in a recent discussion about high performance computing (hpc) that points to the first definition for my mind ...
The term number-crunching refers to large-scale numerical simulations
Now simulations of spacecraft flight or the effects of adding a dam to a major river really are typical uses of hpc

However, thinking about (2 ... they mean maths), you have many uses of hpc where the Mathematics itself is the outcome.

For people who are learners of hpc, I can see why the 'massive simulations' message is preferred as a way of presenting the utility of hpc

However as a Mathematician I naturally think also of many scenarios where the Mathematics is the outcome.

Not all of those outcomes will be moved onto a powerful workstation in the next decade.

There is also another major use of hpc which is not really [in my opinion] a good fit for the word simulation. Natural language processing at very high speed is one of the prerequisites of AI.

In such a context you are not simulating the process of adding meaning to raw words, you are actually doing it when you task a hpc with such processing.

Tuesday, February 14, 2017

shifting from m1q 898739...000591

Here is a fun loop for you to code up in Pari/GP and examine the output


for(k=9000,10000,n=m1q+2+3*k;n6=n%6;prim=0;if(0==n6,prim=isprime(n/6));print("k=",k," gives ",prim,"=isprime(n/6)");if(prim>0,break))

Sample output for loop starting k=9000

k=9000 gives 0=isprime(n/6)
k=9001 gives 0=isprime(n/6)
k=9250 gives 0=isprime(n/6)
k=9251 gives 1=isprime(n/6)

Here is a slightly improved loop:

for(k=9000,10000,n=m1q+2+3*k;n6=n%6;prim=0;if(0==n6,print("k=",k," 0==n/6");prim=isprime(n/6));print(" gives ",prim,"=isprime(n/6)");if(prim>0,break))

 gives 0=isprime(n/6)
 gives 0=isprime(n/6)
k=9251 0==n/6
 gives 1=isprime(n/6)

m1q is prime and has the following construction: