# Idiomatic PRNG in Scheme

For reasons that are too dreary to detail, I need to reproduce several pseudo random number generators in different languages. It mostly involves translating ancient C and FORTRAN code. No problems with C, Java, Zig, Julia, etc. But for Lisp-derived languages, I would like to do something more idiomatic.

For example, here is a Scheme interpretation of ACM algorithm 647 for a portable PRNG to generate samples from a uniform distribution.

;; Return a random uniform deviate in the range 0 <= x < 1.0.
(define algo-647-uniform
(let ([seed 12345])
(lambda ()
(let* ([k (floor (/ seed 127773))]
[partial (- (* 16807 (- seed (* k 127773))) (* k 2836))])
(if (< partial 0)
(set! seed (+ partial 2147483647))
(set! seed partial))
(* seed 4.656612875e-10)))))


The above works and I'm satisfied with the implementation (though eager to hear suggestions for improvements).

The implementation below of a function to generate normally distributed PRNGs also works, but looks kind of ugly -- there is so much state to maintain. Is there a better way to do the following?

;; The following is an implementation of the Marsaglia polar
;; method for generating random standard normal deviates. See
;; https://en.wikipedia.org/wiki/Marsaglia_polar_method.

;; Return a random standard normal deviate.
(define gaussian-deviate-marsaglia
(let* ([has-spare #f]
[spare 0.0]
[rsq 0.0] [r1 0.0] [r2 0.0]
[nxt-rsq (lambda ()
(set! r1 (- (* 2.0 (algo-647-uniform)) 1.0))
(set! r2 (- (* 2.0 (algo-647-uniform)) 1.0))
(set! rsq (+ (* r1 r1) (* r2 r2)))
rsq)])
(lambda ()
(if has-spare
(begin
(set! has-spare #f)
spare)
(let loop ([_ (nxt-rsq)])
(if (or (>= rsq 1.0) (= rsq 0.0))
(loop (nxt-rsq))
(let ([fac (sqrt (/ (* -2.0 (log rsq)) rsq))])
(set! spare (* r1 fac))
(set! has-spare #t)
(* r2 fac))))))))


In Chez 9.5.8, the first 10 results should be:

-1.0580380669115383
-0.5790254729247644
0.8434589541668004
-0.6708443571574382
-0.22644041228981196
-0.07818079860601053
-0.7443285279492631
-0.5232388154010481
-0.3300334725931046
0.41341813121639936