Fletcher’s Checksum
November 22, 2013
We begin with a function to read up to n characters from the current input and return the base-256 number that they represent; this is similar to the undigits function from the Standard Prelude:
(define (readc n)
(if (eof-object? (peek-char)) -1
(let loop ((k n) (v 0))
(if (or (eof-object? (peek-char)) (zero? k)) v
(loop (- k 1) (+ (* v 256) (char->integer (read-char))))))))
Then we write a single function fletcher that reads the current input and returns the checksum defined by its argument; chars is the number of characters to read at each step, base is the base of the checksums, and mod is the modulus, which is one less than the base:
(define (fletcher k) ; k in {16, 32, 64}
(let* ((chars (/ k 16))
(base (expt 2 (/ k 2)))
(mod (- base 1)))
(let loop ((i 0) (c 0) (v (readc chars)))
(if (negative? v)
(+ (* c base) i)
(let* ((i (modulo (+ i v) mod))
(c (modulo (+ c i) mod)))
(loop i c (readc chars)))))))
Here are some examples:
> (with-input-from-string "abcde"
(lambda () (fletcher 16)))
51440
> (with-input-from-string "abcde"
(lambda () (fletcher 32)))
3948201259
> (with-input-from-string "abcde"
(lambda () (fletcher 64)))
14034561336514601929
The program is collected at http://programmingpraxis.codepad.org/ZErlGDad, but you can’t run it because codepad doesn’t provide string ports.
Programming Praxis 
In python.
def readn(fin, n): s = 0 for ti in fin.read(n): s = s * 256 + ord(ti) return s def fletcher(fin, k): if k not in (16, 32, 64): raise ValueError("Valid choices of k are 16, 32 and 64") nbytes = k // 16 mod = 2 ** (8 * nbytes) - 1 s = s2 = 0 t = readn(fin, nbytes) while t: s += t s2 += s t = readn(fin, nbytes) return s % mod + (mod + 1) * (s2 % mod)In guile scheme.
[…] I implemented Fletcher’s checksum as an exercise from Programming Praxis. […]
C# implentation: https://gist.github.com/regularcoder/8254723