Initial data commit

Task/Tonelli-Shanks-algorithm/REXX/tonelli-shanks-algorithm.rexx

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+/* REXX (required by some interpreters) */
+Numeric Digits 1000000
+ttest ='[(10, 13), (56, 101), (1030, 10009), (44402, 100049)]'
+Do While pos('(',ttest)>0
+  Parse Var ttest '(' n ',' p ')' ttest
+  r = tonelli(n, p)
+  Say "n =" n "p =" p
+  Say "          roots :" r (p - r)
+  End
+Exit
+
+legendre: Procedure
+  Parse Arg a, p
+  return pow(a, (p - 1) % 2, p)
+
+tonelli: Procedure
+  Parse Arg n, p
+  q = p - 1
+  s = 0
+  Do while q // 2 == 0
+    q = q % 2
+    s = s+1
+    End
+  if s == 1 Then
+    return pow(n, (p + 1) % 4, p)
+  Do z=2 To p
+    if p - 1 == legendre(z, p) Then
+      Leave
+    End
+  c = pow(z, q, p)
+  r = pow(n, (q + 1) / 2, p)
+  t = pow(n, q, p)
+  m = s
+  t2 = 0
+  Do while (t - 1) // p <> 0
+    t2 = (t * t) // p
+    Do i=1 To m
+      if (t2 - 1) // p == 0 Then
+        Leave
+      t2 = (t2 * t2) // p
+      End
+    y=2**(m - i - 1)
+    b = pow(c, y, p)
+    If b=10008 Then Trace ?R
+    r = (r * b) // p
+    c = (b * b) // p
+    t = (t * c) // p
+    m = i
+    End
+  return r
+pow: Procedure
+  Parse Arg x,y,z
+  If y>0 Then
+    p=x**y
+  Else p=x
+  If z>'' Then
+    p=p//z
+  Return p