Elliptic curve arithmetic: Difference between revisions

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 a + b + d = Zero
 a * 12345 = (10.759, 35.387)
+</pre>
+=={{header|PicoLisp}}==
+<lang PicoLisp>(scl 16)
+(load "@lib/math.l")
+(setq *B 7)
+(de from_y (Y)
+   (let
+      (A (* 1.0 (- (* Y Y) *B))
+         B (pow (abs A) (*/ 1.0 1.0 3.0)) )
+      (list
+         (if (gt0 A) B (- B))
+         (* Y 1.0) ) ) )
+(de prn (P)
+   (if (is_zero P)
+      "Zero"
+      (pack
+         (round (car P) 3)
+         " "
+         (round (cadr P) 3) ) ) )
+(de neg (P)
+   (list (car P) (*/ -1.0 (cadr P) 1.0)) )
+(de is_zero (P)
+   (or
+      (=T (car P))
+      (=T (cadr P))
+      (> (length (car P)) 20) ) )
+(de dbl (P)
+   (if (is_zero P)
+      P
+      (let
+         (Y
+            (*/
+.0
+               (*/ 3.0 (car P) (car P) (** 1.0 2))
+               (*/ 2.0 (cadr P) 1.0) )
+            X
+            (-
+               (*/ Y Y 1.0)
+               (*/ 2.0 (car P) 1.0) ) )
+         (list
+            X
+            (-
+               (*/ Y (- (car P) X) 1.0)
+               (cadr P) ) ) ) ) )
+(de add (A B)
+   (cond
+      ((= A B) (dbl A))
+      ((is_zero A) B)
+      ((is_zero B) A)
+      (T
+         (let Z (- (car B) (car A))
+            (if (=0 Z)
+               (list T T)
+               (let
+                  (Y (*/ 1.0 (- (cadr B) (cadr A)) Z)
+                     X
+                     (- (*/ Y Y 1.0) (car A) (car B)) )
+                  (list
+                     X
+                     (-
+                        (*/ Y (- (car A) X) 1.0)
+                        (cadr A) ) ) ) ) ) ) ) )
+(de mul (P N)
+   (let R (list T T)
+      (for (I 1 (>= N I) (* I 2))
+         (when (gt0 (& I N))
+            (setq R (add R P)) )
+         (setq P (dbl P)) )
+      R ) )
+(setq
+   A (from_y 1)
+   B (from_y 2) )
+(prinl "A: " (prn A))
+(prinl "B: " (prn B))
+(setq C (add A B))
+(prinl "C: " (prn C))
+(setq D (neg C))
+(prinl "D: " (prn D))
+(prinl "D + C: " (prn (add C D)))
+(prinl "A + B + D: " (prn (add A (add B D))))
+(prinl "A * 12345: " (prn (mul A 12345)))</lang>
+{{out}}
+<pre>
+A: -1.817 1.000
+B: -1.442 2.000
+C: 10.375 -33.525
+D: 10.375 33.525
+D + C: Zero
+A + B + D: Zero
+A * 12345: 10.759 35.387
 </pre>