I started with Ryan's code from `~r` and tried to emulate some special
cases I see the C code (and didn't worry about negative numbers) and
ended up with something 4-5x slower than the C code version. :(  Code
follows.

Robby

#lang racket
(define (number->string* N)
  (cond [(zero? N)
         (string #\0)]
        [else
         (let* ([short-size 10]
                [str (make-string short-size)])
           (let loop ([N N] [digits null] [i short-size])
             (cond
               [(zero? N)
                (if (<= i 0)
                    (if (null? digits)
                        str
                        (string-append (apply string digits) str))
                    (substring str i short-size))]
               [else
                (define-values (q r) (quotient/remainder N 10))
                (define d (integer->char (+ r (char->integer #\0))))
                (cond
                  [(<= i 0)
                   (loop q (cons d digits) i)]
                  [else
                   (string-set! str (- i 1) d)
                   (loop q '() (- i 1))])])))]))

(module+ test
  (require rackunit)
  (check-equal? (number->string* 1234567890987654321)
                (number->string 1234567890987654321))
  (for ([x (in-range 1000)])
    (check-equal? (number->string* x )
                  (number->string x))))

(define iterations 1000000)
(define number-to-convert 123)

(collect-garbage)
(time
 (for ([x (in-range iterations)])
   (number->string 100)))

(collect-garbage)
(time
 (for ([x (in-range iterations)])
   (number->string* number-to-convert)))

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