Improve factorial(n, k) performance for BigInt (#149)

* Improve `factorial(n, k)` performance for `BigInt`

Use in-place operations from `Base.GMP.MPZ` to reduce allocations.

* Add tests for `factorial(::BigInt, ::BigInt)`

* Avoid mutating first input of `factorial(::BigInt, ::BigInt)`

Co-authored-by: Chengyu Han <[email protected]>

---------

Co-authored-by: Chengyu Han <[email protected]>

Author: FedericoStra

src/factorials.jl

@@ -28,6 +28,18 @@ function Base.factorial(n::T, k::T) where T<:Integer
     end
     return f
 end
+function Base.factorial(n::BigInt, k::BigInt)
+    if k < 0 || n < 0 || k > n
+        throw(DomainError((n, k), "n and k must be nonnegative with k ≤ n"))
+    end
+    f = BigInt(1)
+    n = deepcopy(n)  # avoid mutating input
+    while n > k
+        Base.GMP.MPZ.mul!(f, n)
+        Base.GMP.MPZ.sub_ui!(n, 1)
+    end
+    return f
+end
 Base.factorial(n::Integer, k::Integer) = factorial(promote(n, k)...)
 
 

test/factorials.jl

@@ -3,6 +3,9 @@
     @test_throws DomainError factorial(3, 7)
     @test_throws DomainError factorial(-3, -7)
     @test_throws DomainError factorial(-7, -3)
+    @test_throws DomainError factorial(big"3", big"7")
+    @test_throws DomainError factorial(big"-3", big"7")
+    @test_throws DomainError factorial(big"3", big"-7")
     #JuliaLang/julia#9943
     @test factorial(big(100), (80)) == 1303995018204712451095685346159820800000
     #JuliaLang/julia#9950