add kronecker function (useful for lots of number theory stuff)

Project.toml

@@ -1,6 +1,6 @@
 name = "IntegerMathUtils"
 uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
-version = "0.1.1"
+version = "0.1.2"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

src/IntegerMathUtils.jl

@@ -1,5 +1,5 @@
 module IntegerMathUtils
-export iroot, ispower, rootrem, find_exponent, is_probably_prime
+export iroot, ispower, rootrem, find_exponent, is_probably_prime, kronecker
 
 iroot(x::Integer, n::Integer) = iroot(x, Cint(n))
 
@@ -10,7 +10,7 @@ function iroot(x::BigInt, n::Cint)
     n <= 0 && throw(DomainError(n, "Exponent must be > 0"))
     x <= 0 && iseven(x) && throw(DomainError(n, "This is a math no-no"))
     ans = BigInt()
-    ccall((:__gmpz_root, :libgmp), Cint, (Ref{BigInt}, Ref{BigInt}, Cint), ans, x, n)
+    @ccall :libgmp.__gmpz_root(ans::Ref{BigInt}, x::Ref{BigInt}, n::Cint)::Cint
     ans
 end
 
@@ -22,15 +22,15 @@ function rootrem(x::T, n::Integer) where {T<:Integer}
     x <= 0 && iseven(x) && throw(DomainError(n, "This is a math no-no"))
     root = BigInt()
     rem  = BigInt()
-    ccall((:__gmpz_rootrem, :libgmp), Nothing,(Ref{BigInt}, Ref{BigInt}, Ref{BigInt}, Int), root, rem, x, n)
+    @ccall :libgmp.__gmpz_rootrem(root::Ref{BigInt}, rem::Ref{BigInt}, x::Ref{BigInt}, n::Int)::Nothing
     return (root, T(rem))
 end
 
 # TODO: Add more efficient implimentation for smaller types
 ispower(x::Integer) = ispower(big(x))
 
 function ispower(x::BigInt)
-    return 0 != ccall((:__gmpz_perfect_power_p, :libgmp), Cint, (Ref{BigInt},), x)
+    return 0 != @ccall :libgmp.__gmpz_perfect_power_p(x::Ref{BigInt})::Cint
 end
 
 # TODO: Add more efficient implimentation for smaller types
@@ -43,7 +43,55 @@ function find_exponent(x::Integer)
 end
 
 function is_probably_prime(x::Integer; reps=25)
-    return ccall((:__gmpz_probab_prime_p, :libgmp), Cint, (Ref{BigInt}, Cint), x, reps) != 0
+    if !(x isa BigInt)
+        x = BigInt(x)
+    end
+    return 0 != @ccall :libgmp.__gmpz_probab_prime_p(x::Ref{BigInt}, reps::Cint)::Cint
+end
+
+function kronecker(a::BigInt, b::Clong)
+    return @ccall :libgmp.__gmpz_kronecker_si(a::Ref{BigInt}, b::Clong)::Cint
+end
+function kronecker(a::Clong, b::BigInt)
+    return @ccall :libgmp.__gmpz_si_kronecker(a::Clong, b::Ref{BigInt})::Cint
+end
+function kronecker(a, n)
+    @assert n != -n || n == 0
+    @assert a != -a || a == 0
+    t = 1
+    if iszero(n)
+        return Int(abs(a) == 1)
+    end
+    if n < 0
+        n = abs(n)
+        if a < 0
+            t = -t
+        end
+    end
+    trail = trailing_zeros(n)
+    if trail > 0
+        n >>= trail
+        if iseven(a)
+            return 0
+        elseif isodd(trail) && a&7 in (3,5)
+            t = -t
+        end
+    end
+    a = mod(a, n)
+    while a != 0
+        while iseven(a)
+            a = a >> 1
+            if n&7 in (3, 5)
+                t = -t
+            end
+        end
+        a, n = n, a
+        if a&3 == n&3 == 3
+            t = -t
+        end
+        a = mod(a, n)
+    end
+    return n == 1 ? t : 0
 end
 
 end