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Elliptic curve arithmetic: Difference between revisions
Added Julia language
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(Added Julia language) |
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Line 705:
a + b + d = Zero
a * 12345 = (10.759,35.387)</pre>
=={{header|Julia}}==
{{works with|Julia|0.6}}
<lang julia>struct Point{T<:AbstractFloat}
x::T
y::T
end
Point{T}() where T<:AbstractFloat = Point{T}(Inf, Inf)
Point() = Point{Float64}()
Base.show(io::IO, p::Point{T}) where T = iszero(p) ? print(io, "Zero{$T}") : @printf(io, "{%s}(%.3f, %.3f)", T, p.x, p.y)
Base.copy(p::Point) = Point(p.x, p.y)
Base.iszero(p::Point{T}) where T = p.x in (-Inf, Inf)
Base.:-(p::Point) = Point(p.x, -p.y)
function dbl(p::Point{T}) where T
iszero(p) && return p
L = 3p.x ^ 2 / 2p.y
x = L ^ 2 - 2p.x
y = L * (p.x - x) - p.y
return Point{T}(x, y)
end
Base.:(==)(a::Point{T}, C::Point{T}) where T = a.x == C.x && a.y == C.y
function Base.:+(p::Point{T}, q::Point{T}) where T
p == q && return dbl(p)
iszero(p) && return q
iszero(q) && return p
L = (q.y - p.y) / (q.x - p.x)
x = L ^ 2 - p.x - q.x
y = L * (p.x - x) - p.y
return Point{T}(x, y)
end
function Base.:*(p::Point, n::Integer)
r = Point()
i = 1
while i ≤ n
if i & n != 0 r += p end
p = dbl(p)
i <<= 1
end
return r
end
Base.:*(n::Integer, p::Point) = p * n
const C = 7
function Point(y::AbstractFloat)
n = y ^ 2 - C
x = n ≥ 0 ? n ^ (1 / 3) : -((-n) ^ (1 / 3))
return Point{typeof(y)}(x, y)
end
a = Point(1.0)
b = Point(2.0)
@show a b
@show c = a + b
@show d = -c
@show c + d
@show a + b + d
@show 12345a</lang>
{{out}}
<pre>a = {Float64}(-1.817, 1.000)
b = {Float64}(-1.442, 2.000)
c = a + b = {Float64}(10.375, -33.525)
d = -c = {Float64}(10.375, 33.525)
c + d = Zero{Float64}
a + b + d = Zero{Float64}
12345a = {Float64}(10.759, 35.387)</pre>
=={{header|Kotlin}}==
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