Add adder Test(s)

[DavePearce]

Here is my code:

(defcolumns
  (X3 :i16@prove) (X2 :i16@prove) (X1 :i16@prove) (X0 :i16@prove)
  (Y3 :i16@prove) (Y2 :i16@prove) (Y1 :i16@prove) (Y0 :i16@prove)
  (C3 :i1@prove)  (C2 :i1@prove)  (C1 :i1@prove)  (C0 :i1@prove)
  (Z3 :i16)       (Z2 :i16)       (Z1 :i16)       (Z0 :i16))

(defconst OVERFLOW 65536)

(defpurefun (ADDER cin arg1 arg2 out cout)
  (eq! (+ out (* cout OVERFLOW)) (+ arg1 arg2 cin)))

(defconstraint X_Y_Z ()
  (begin
   (ADDER 0 X0 Y0 Z0 C0)
   (ADDER C0 X1 Y1 Z1 C1)
   (ADDER C1 X2 Y2 Z2 C2)
   (ADDER C2 X3 Y3 Z3 C3)))

And an example trace:

{ "<prelude>": {
    "X3": [0], "X2": [0], "X1": [0], "X0": [33000],
    "Y3": [0], "Y2": [0], "Y1": [0], "Y0": [33001],
    "C3": [0], "C2": [0], "C1": [0], "C0": [1],        
    "Z3": [0], "Z2": [0], "Z1": [1], "Z0": [465]
}}

What we could do is actually enumerate all input / output values and check it really works. We could repeat this for other operators related to field agnosticity.

[DavePearce]

(defcolumns
  (X3 :i16@prove) (X2 :i16@prove) (X1 :i16@prove) (X0 :i16@prove)
  (RES :binary@prove)
)

(defpurefun ((IS-ZERO :binary@loob :force) w3 w2 w1 w0) (+ w3 w2 w1 w0))

(defconstraint c1 ()
  (if (IS-ZERO X3 X2 X1 X0)
      (vanishes! RES) (eq! RES 1)))

And an example trace:

{ "<prelude>": {
    "X3": [0], "X2": [0], "X1": [0], "X0": [0],
    "RES": [0]
}}

[DavePearce]

Another example (bit shift):

(module m1)

(defcolumns
  X Y
  ;; X bits
  (x1 :binary@prove)
  (x2 :binary@prove)
  (x3 :binary@prove)
  (x4 :binary@prove)
  ;; Y bits
  (y1 :binary@prove)
  (y2 :binary@prove)
  (y3 :binary@prove)
  (y4 :binary@prove))

;; Combine bits into a nibble
(defpurefun (bits a1 a2 a3 a4)
  (+ (* 1 a1)
     (* 2 a2)
     (* 4 a3)
     (* 8 a4)))

;; For X
(defconstraint X_bits () (eq! X (bits x1 x2 x3 x4)))
;; For Y
(defconstraint Y_bits () (eq! Y (bits y1 y2 y3 y4)))
;; Relating X and Y
(defconstraint X_Y_bits ()
  (begin
   (eq!  0 y1)   
   (eq! x1 y2)
   (eq! x2 y3)
   (eq! x3 y4)))

Which accepts this trace:

{ "m1": {
    "X": [0,1,14],
    "Y": [0,2,12],
    
    "x1": [0,1,0],
    "x2": [0,0,1],
    "x3": [0,0,1],
    "x4": [0,0,1],
    
    "y1": [0,0,0],
    "y2": [0,1,0],
    "y3": [0,0,1],
    "y4": [0,0,1]
   }
}