Add tests for elliptic curves

src/Math/ec.jl

@@ -1,4 +1,4 @@
-module EllipticCurves
+@reexport module EllipticCurves
 
 # http://jeremykun.com/2014/02/08/introducing-elliptic-curves/
 # http://jeremykun.com/2014/02/24/elliptic-curves-as-python-objects/

src/Math/math.jl

@@ -38,6 +38,7 @@ macro activate_matlab(); Expr(:using, :MATLAB); end
 
 include("gmp.jl")
 include("mpfr.jl")
+include("ec.jl")
 include("Series/series.jl")
 include("NumberTheory/numbertheory.jl")
 include("Combinatorics/combinatorics.jl")

test/Math/ec.jl

@@ -0,0 +1,96 @@
+module EllipticCurves
+
+using Base.Test
+using Brainstorm.Math
+
+function test_wnf_QQ()
+    c = curve(big(-2//1), big(4//1))
+    p = point(c, 3, 5)
+    q = point(c, -2, 0)
+
+    @test p-q == point(c, 0, -2)
+    @test p+p+p+p+p == point(c, 2312883//1142761, -3507297955//1221611509)
+    @test 5p == point(c, 2312883//1142761, -3507297955//1221611509)
+    @test q-3p == point(c, 240, 3718)
+    @test -20p == point(c,
+        872171688955240345797378940145384578112856996417727644408306502486841054959621893457430066791656001//520783120481946829397143140761792686044102902921369189488390484560995418035368116532220330470490000,
+        -27483290931268103431471546265260141280423344817266158619907625209686954671299076160289194864753864983185162878307166869927581148168092234359162702751//11884621345605454720092065232176302286055268099954516777276277410691669963302621761108166472206145876157873100626715793555129780028801183525093000000)
+end
+
+function test_wnf_ZZp()
+    R = ResidueRing(ZZ, 5)
+
+    c = curve(R(1), R(1))
+    p = point(c, R(2), R(1))
+
+    @test 2p == point(c, R(2), R(4))
+    @test 3p == point(c)
+end
+
+function test_wnf_polyZZp()
+    R = ResidueRing(ZZ, 5)
+    S, s = PolynomialRing(R, "s")
+    T, t = FiniteField(3 + s^2, "t")
+
+    c = curve(T(1), T(1))
+    p = point(c, 2 + t, 2t)
+
+    @test  -p == point(c, 2 +  t,     3t)
+    @test p+p == point(c, 3 +  t, 2 + 0t)
+    @test  4p == point(c, 3 + 2t, 4 + 4t)
+    @test  9p == point(c)
+end
+
+function test_gwnf_QQ()
+    c = curve(0, 0, 0, big(-2//1), big(4//1))
+    p = point(c, 3, 5)
+    q = point(c, -2, 0)
+
+    @test p-q == point(c, 0, -2)
+    @test p+p+p+p+p == point(c, 2312883//1142761, -3507297955//1221611509)
+    @test 5p == point(c, 2312883//1142761, -3507297955//1221611509)
+    @test q-3p == point(c, 240, 3718)
+    @test -20p == point(c,
+        872171688955240345797378940145384578112856996417727644408306502486841054959621893457430066791656001//520783120481946829397143140761792686044102902921369189488390484560995418035368116532220330470490000,
+        -27483290931268103431471546265260141280423344817266158619907625209686954671299076160289194864753864983185162878307166869927581148168092234359162702751//11884621345605454720092065232176302286055268099954516777276277410691669963302621761108166472206145876157873100626715793555129780028801183525093000000)
+end
+
+function test_gwnf_ZZp()
+    R = ResidueRing(ZZ, 5)
+
+    c = curve(R(0), R(0), R(0), R(1), R(1))
+    p = point(c, R(2), R(1))
+
+    @test 2p == point(c, R(2), R(4))
+    @test 3p == point(c)
+end
+
+function test_gwnf_polyZZp()
+    R = ResidueRing(ZZ, 5)
+    S, s = PolynomialRing(R, "s")
+    T, t = FiniteField(3 + s^2, "t")
+
+    c = curve(T(0), T(0), T(0), T(1), T(1))
+    p = point(c, 2 + t, 2t)
+
+    @test  -p == point(c, 2 +  t,     3t)
+    @test p+p == point(c, 3 +  t, 2 + 0t)
+    @test  4p == point(c, 3 + 2t, 4 + 4t)
+    @test  9p == point(c)
+end
+
+function test_all()
+    print(rpad("Math.EllipticCurves...", 50, ' '))
+
+    test_wnf_QQ()
+    test_wnf_ZZp()
+    test_wnf_polyZZp()
+
+    test_gwnf_QQ()
+    test_gwnf_ZZp()
+    test_gwnf_polyZZp()
+
+    println("PASS")
+end
+
+end

test/Math/math.jl

@@ -18,6 +18,7 @@ function test_math_setbits()
     @test setbits(big(0), [1000]) == big(2)^1000
 end
 
+include("ec.jl")
 include("Series/series.jl")
 include("NumberTheory/numbertheory.jl")
 include("Combinatorics/combinatorics.jl")
@@ -30,6 +31,8 @@ function test_all()
 
     println("PASS")
 
+    println("")
+    EllipticCurves.test_all()
     println("")
     Series.test_all()
     println("")