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Cover binomial cases for large K (BigInt) #48073

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merged 16 commits into from
Feb 28, 2023
Merged

Cover binomial cases for large K (BigInt) #48073

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ba2a753
Cover binomial cases for large K (BigInt)
originalsouth Jan 2, 2023
386c211
Cover more binomial cases for large K (BigInt)
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175b769
Merge branch 'master' into master
originalsouth Jan 2, 2023
caed084
Fix for BigInt binomial implementation
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15018b6
One less potential allocation for BigInt binomial implementation
originalsouth Jan 3, 2023
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51091de
UInt -> Culong for BigInt binomial functions
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originalsouth Feb 16, 2023
05cb906
Update base/gmp.jl as suggested "will" --> "would"
originalsouth Feb 19, 2023
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10 changes: 9 additions & 1 deletion base/gmp.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -682,8 +682,16 @@ end

factorial(x::BigInt) = isneg(x) ? BigInt(0) : MPZ.fac_ui(x)

function binomial(n::BigInt, k::Integer)
k < 0 && return BigInt(0)
k <= typemax(UInt) && return binomial(n, UInt(k))
n < 0 && return (isodd(k) ? -one(n) : one(n)) * binomial(k - n - 1, k)
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κ = n - k
κ < 0 && return BigInt(0)
κ <= typemax(UInt) && return binomial(n, UInt(κ))
throw(OverflowError("Computation will exceed memory"))
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end
binomial(n::BigInt, k::UInt) = MPZ.bin_ui(n, k)
binomial(n::BigInt, k::Integer) = k < 0 ? BigInt(0) : binomial(n, UInt(k))

==(x::BigInt, y::BigInt) = cmp(x,y) == 0
==(x::BigInt, i::Integer) = cmp(x,i) == 0
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10 changes: 10 additions & 0 deletions test/combinatorics.jl
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Expand Up @@ -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
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