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Base64-impl

B64-bytes-from-vals

Decode 4 base-64 values into 3 bytes.

Signature
(b64-bytes-from-vals v1 v2 v3 v4) → (mv b1 b2 b3)
Returns: b1 — Type (natp b1).; b2 — Type (natp b2).; b3 — Type (natp b3).

This is just doing the inverse of b64-vals-from-bytes.

Definitions and Theorems

Function: b64-bytes-from-vals$inline

(defun b64-bytes-from-vals$inline (v1 v2 v3 v4)
  (declare (type (unsigned-byte 6) v1 v2 v3 v4))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'b64-bytes-from-vals))
    (declare (ignorable acl2::__function__))
    (b* ((b1 (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (ash (lnfix v1) 2))
                          (the (unsigned-byte 8)
                               (ash (lnfix v2) -4)))))
         (b2 (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (ash (the (unsigned-byte 8)
                                         (logand (lnfix v2) 15))
                                    4))
                          (the (unsigned-byte 8)
                               (ash (lnfix v3) -2)))))
         (b3 (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (ash (the (unsigned-byte 8)
                                         (logand (lnfix v3) 3))
                                    6))
                          (lnfix v4)))))
      (mv b1 b2 b3))))

Theorem: natp-of-b64-bytes-from-vals.b1

(defthm natp-of-b64-bytes-from-vals.b1
  (b* (((mv ?b1 ?b2 ?b3)
        (b64-bytes-from-vals$inline v1 v2 v3 v4)))
    (natp b1))
  :rule-classes :type-prescription)

Theorem: natp-of-b64-bytes-from-vals.b2

(defthm natp-of-b64-bytes-from-vals.b2
  (b* (((mv ?b1 ?b2 ?b3)
        (b64-bytes-from-vals$inline v1 v2 v3 v4)))
    (natp b2))
  :rule-classes :type-prescription)

Theorem: natp-of-b64-bytes-from-vals.b3

(defthm natp-of-b64-bytes-from-vals.b3
  (b* (((mv ?b1 ?b2 ?b3)
        (b64-bytes-from-vals$inline v1 v2 v3 v4)))
    (natp b3))
  :rule-classes :type-prescription)

Theorem: unsigned-byte-p-8-of-b64-decode-4-chars

(defthm unsigned-byte-p-8-of-b64-decode-4-chars
  (implies (and (force (unsigned-byte-p 6 v1))
                (force (unsigned-byte-p 6 v2))
                (force (unsigned-byte-p 6 v3))
                (force (unsigned-byte-p 6 v4)))
           (b* (((mv b1 b2 b3)
                 (b64-bytes-from-vals v1 v2 v3 v4)))
             (and (unsigned-byte-p 8 b1)
                  (unsigned-byte-p 8 b2)
                  (unsigned-byte-p 8 b3)))))

Theorem: b64-bytes-from-vals-of-b64-vals-from-bytes

(defthm b64-bytes-from-vals-of-b64-vals-from-bytes
  (b* (((mv v1 v2 v3 v4)
        (b64-vals-from-bytes b1 b2 b3))
       ((mv x1 x2 x3)
        (b64-bytes-from-vals v1 v2 v3 v4)))
    (implies (and (force (unsigned-byte-p 8 b1))
                  (force (unsigned-byte-p 8 b2))
                  (force (unsigned-byte-p 8 b3)))
             (and (equal x1 b1)
                  (equal x2 b2)
                  (equal x3 b3)))))

Theorem: b64-bytes-from-vals-padding-1

(defthm b64-bytes-from-vals-padding-1
  (b* (((mv v1 v2 v3 ?v4)
        (b64-vals-from-bytes b1 b2 0))
       ((mv x1 x2 ?x3)
        (b64-bytes-from-vals v1 v2 v3 0)))
    (implies (and (force (unsigned-byte-p 8 b1))
                  (force (unsigned-byte-p 8 b2)))
             (and (equal x1 b1) (equal x2 b2)))))

Theorem: b64-bytes-from-vals-padding-2

(defthm b64-bytes-from-vals-padding-2
  (b* (((mv v1 v2 ?v3 ?v4)
        (b64-vals-from-bytes b1 0 0))
       ((mv x1 ?x2 ?x3)
        (b64-bytes-from-vals v1 v2 0 0)))
    (implies (force (unsigned-byte-p 8 b1))
             (equal x1 b1))))