schemeracketnumerical

How to find the minimum positive number that added to 1.0 gives something larger?

While translating some Fortran to Scheme/Racket I have come across the function:

; EPSILON(X)      The  least  positive  number  that added
;                 to 1 returns a number that is greater than 1

How do I find the number in Scheme?

Solution 
  • #lang racket/base

;; http://en.wikipedia.org/wiki/Machine_epsilon
;; approximates the machine epsilon

(require racket/flonum)

(define (compute-machine-epsilon)
  (let loop ([n 1.0])
    (define next-n (fl/ n 2.0))
    (if (fl= 1.0 (fl+ 1.0 next-n))
        n
        (loop next-n))))