Fibonacci in finite fields, in racket

fibint.scm

#!/usr/bin/env racket
#lang racket

(define (addmod a b p)
  (if  (> (- p b) a)
      (+ a b)
      (- (+ a b) p)
  )
)

(define (submod a b p)
  (if (>= a b)
      (- a b)
      (+ (- p b) a)
  )
)

(define (mulmod a b p)
  (mulmod_rec a b p 0)
)

(define (mulmod_rec a b p r)
  (if (> b 0)
      (mulmod_rec (addmod a a p)
              (arithmetic-shift b -1)
              p
              (if (= 1 (bitwise-and b 1)) (addmod a r p) r)
      )
      r
  )
)

(define (powmod a e p)
  (powmod_rec a e p 1)
)

(define (powmod_rec a e p r)
  (if (> e 0)
      (powmod_rec (mulmod a a p)
              (arithmetic-shift e -1)
              p
              (if (= 1 (bitwise-and e 1)) (mulmod r a p) r)
      )
      r
  )
)

(define (fib n)
  (define (q)     12200160415121876909)
  (define (v)     833731445503647576)
  (define (v_inv) 2606778372125104897)
  (mulmod (submod (powmod (+ 1 (v)) n (q))
                  (powmod (- (+ (q) 1) (v)) n (q))
                  (q)
          )
          (mulmod (v_inv)
                  (powmod 2 (- (q) 1 n) (q))
                  (q)
          )
          (q)
  )
)

(define (fib-iter n count result)
  (display "Computing fib for ")(display count)(display ": ")(display result)(newline)
  (when (< count n)
      (fib-iter n
                (+ count 1)
                (fib count)
      )
   )
)

(define (multifib n)
  (fib-iter n 1 0)
)

(multifib 93)