Initial data commit

Task/Tonelli-Shanks-algorithm/Julia/tonelli-shanks-algorithm-1.julia

@@ -0,0 +1,42 @@
+module TonelliShanks
+
+legendre(a, p) = powermod(a, (p - 1) ÷ 2, p)
+
+function solve(n::T, p::T) where T <: Union{Int, Int128, BigInt}
+    legendre(n, p) != 1 && throw(ArgumentError("$n not a square (mod $p)"))
+    local q::T = p - one(p)
+    local s::T = 0
+    while iszero(q % 2)
+        q ÷= 2
+        s += one(s)
+    end
+    if s == one(s)
+        r = powermod(n, (p + 1) >> 2, p)
+        return r, p - r
+    end
+    local z::T
+    for z in 2:(p - 1)
+        p - 1 == legendre(z, p) && break
+    end
+    local c::T = powermod(z, q, p)
+    local r::T = powermod(n, (q + 1) >> 1, p)
+    local t::T = powermod(n, q, p)
+    local m::T = s
+    local t2::T = zero(p)
+    while !iszero((t - 1) % p)
+        t2 = (t * t) % p
+        local i::T
+        for i in Base.OneTo(m)
+            iszero((t2 - 1) % p) && break
+            t2 = (t2 * t2) % p
+        end
+        b = powermod(c, 1 << (m - i - 1), p)
+        r = (r * b) % p
+        c = (b * b) % p
+        t = (t * c) % p
+        m = i
+    end
+    return r, p - r
+end
+
+end  # module TonelliShanks

Task/Tonelli-Shanks-algorithm/Julia/tonelli-shanks-algorithm-2.julia

@@ -0,0 +1,7 @@
+@show TonelliShanks.solve(10, 13)
+@show TonelliShanks.solve(56, 101)
+@show TonelliShanks.solve(1030, 10009)
+@show TonelliShanks.solve(44402, 100049)
+@show TonelliShanks.solve(665820697, 1000000009)
+@show TonelliShanks.solve(881398088036, 1000000000039)
+@show TonelliShanks.solve(41660815127637347468140745042827704103445750172002, big"10" ^ 50 + 577)