normally distributed random number generator?

That's essentially the Box-Mueller method.

http://mathworld.wolfram.com/Box-MullerTransformat...

If you have two independent standard normal random variables x and y as the components of a vector, then the magnitude r = sqrt(x^2 + y^2) will be Rayleigh distributed. f(r) = r e^(-r^2/2), and cumulative distribution F(r) = 1 - e^(-r^2/2).

The phase will be uniformly distributed on [0, 2pi].

There's a theorem that says if you want to generate a random variable with an arbitrary distribution, then you generate a uniform random number U on [0, 1], then take X = F^(-1)(U) where F is the cumulative distribution for the distribution you want. That's why you use NORMINV. Well, if F(r) = 1 - e^(-r^2/2), let's invert that.

U = 1 - e^(-r^2/2)

1 - U = e^(-r^2/2)

ln(1 - U) = -r^2/2

r^2 = -2ln(1 - U)

r = sqrt(-2 ln(1 - U)). And they've just noted that 1 - U is also a uniform random number on [0, 1], so you can just do r = sqrt(-2 ln(U)). So this makes r a Rayleigh-distributed random number.

2*pi()*rand() is a uniform random number on [0, 2pi]. So this is taking the vector with Rayleigh distributed magnitude and uniformly distributed phase. This vector has x and y coordinates which are independent normal random variables. The sine gives you the y coordinate.

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