Problem Statement

As described in its documentation, Amazon S3 Glacier requires that all uploaded files come with a checksum computed as a Merkle Tree using SHA-256. Specifically, the SHA-256 hash is computed for each 1MiB block of the file. And then, starting from the beginning of the file, the raw hashes of consecutive blocks are paired up and concatenated together, and a new hash is computed from each concatenation. Then these are paired up and concatenated and hashed, and the process continues until there is only one hash left, which is the final checksum. The hexadecimal representation of this checksum is the value that must be included with the AWS API call to upload the object (or complete a multipart upload). Implement this algorithm in your language; you can use the code from the SHA-256 task for the actual hash computations. For better manageability and portability, build the tree using a smaller block size of only 1024 bytes, and demonstrate it on the RosettaCode title image with that block size. The final result should be the hexadecimal digest value a4f902cf9d51fe51eda156a6792e1445dff65edf3a217a1f3334cc9cf1495c2c.

Let's start with the solution:

USING: checksums checksums.sha fry grouping io
io.encodings.binary io.files kernel make math math.parser
namespaces sequences ;

: each-block ( ... size quot: ( ... block -- ... ) -- ... )
    input-stream get spin (each-stream-block) ; inline

: >sha-256 ( seq -- newseq ) sha-256 checksum-bytes ;

: (hash-read) ( path encoding chunk-size -- )
    '[ _ [ >sha-256 , ] each-block ] with-file-reader ;

! Read a file in chunks as a sequence of sha-256 hashes, so as
! not to store a potentially large file in memory all at once.

: hash-read ( path chunk-size -- seq )
    binary swap [ (hash-read) ] { } make ;

: hash-combine ( seq -- newseq )
    2 <groups>
    [ dup length 1 > [ concat >sha-256 ] [ first ] if ] map ;

: merkle-hash ( path chunk-size -- str )
    hash-read [ dup length 1 = ] [ hash-combine ] until first
    bytes>hex-string ;

"title.png" 1024 merkle-hash print