Generating 64-bit values with a 32-bit Mersenne Twister

Question

According to this Boost documentation page, the 64-bit variant of the Mersenne Twister is much slower than its 32-bit counterpart (which makes sense). As I understand, a lot of the features introduced in C++11, including random number generation, are basically Boost in the standard library. This leads me to believe that 32-bit MT performance in standard C++ is also better.

I'm writing a raytracer (for fun, mostly), and speed is one of my primary concerns. Essentially all the numerical values are represented as double precision floats. My question is, since the 32-bit MT is considerably faster, can I use it to generate doubles? What drawbacks (precision loss, performance, etc.) can I expect?

Answer 1

For this I am adding one assumption that you did not mention: I am assuming you are doing one random draw per double. Obviously you can get twice the randomness by doing two draws.

The first question is really "does 32-bits of pseudorandomness have enough randomness for my ray tracer." My guess is yes. Most raytracers are only shooting out a few million rays, so you wont notice that there's only 4 billion bits of pseudorandomness.

Second question is "can I distribute the pseudorandomness across the domain of double values I care about." Again, my guess is yes. If you are shooting rays in a 90 degree field, and there are 4 billion possible results from one pseudorandom draw. For perspective, a sniper looking through a high power scope sees millions of times less angular precision than the average difference between those pseudorandom vectors.

All that being said, profile your code. I'd give a 99.9998% chance that your raytracing code itself takes much longer than the pseudorandom generation unless your scenes all consist of single non-reflective spheres