Cover binomial cases for large K (BigInt) (#48073)

* Cover binomial cases for large K (BigInt)

Co-authored-by: Sebastian Stock <42280794+sostock@users.noreply.github.com>

base/gmp.jl

@@ -707,8 +707,16 @@ end
 
 factorial(x::BigInt) = isneg(x) ? BigInt(0) : MPZ.fac_ui(x)
 
-binomial(n::BigInt, k::UInt) = MPZ.bin_ui(n, k)
-binomial(n::BigInt, k::Integer) = k < 0 ? BigInt(0) : binomial(n, UInt(k))
+function binomial(n::BigInt, k::Integer)
+    k < 0 && return BigInt(0)
+    k <= typemax(Culong) && return binomial(n, Culong(k))
+    n < 0 && return isodd(k) ? -binomial(k - n - 1, k) : binomial(k - n - 1, k)
+    κ = n - k
+    κ < 0 && return BigInt(0)
+    κ <= typemax(Culong) && return binomial(n, Culong(κ))
+    throw(OverflowError("Computation would exceed memory"))
+end
+binomial(n::BigInt, k::Culong) = MPZ.bin_ui(n, k)
 
 ==(x::BigInt, y::BigInt) = cmp(x,y) == 0
 ==(x::BigInt, i::Integer) = cmp(x,i) == 0

test/combinatorics.jl

@@ -16,6 +16,16 @@ using Random: randcycle
     @test binomial(Int64(67), Int64(29)) == binomial(BigInt(67), BigInt(29)) == 7886597962249166160
     @test binomial(Int128(131), Int128(62)) == binomial(BigInt(131), BigInt(62)) == 157311720980559117816198361912717812000
     @test_throws OverflowError binomial(Int64(67), Int64(30))
+
+    #Issue 48072
+    ∐ = parse(BigInt, "1" * "0"^13 * "666" * "0"^13 * "1")
+    @test binomial(∐, ∐ - 1) == ∐
+    @test binomial(∐, ∐ - 2) == 500000000000066600000000002218280000000000033300000000000000
+    @test binomial(∐, ∐ - 3) == binomial(∐, 3)
+    @test binomial(-big(2), ∐ - 3) == 1000000000000066599999999999999
+    @test_throws OverflowError binomial(big(2)^65, big(2)^64)
+    @test_throws OverflowError binomial(-big(2)^65, big(2)^64)
+    @test binomial(∐, 2 * ∐) == BigInt(0)
 end
 
 @testset "permutations" begin