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Arithmetics: Implement Base.inv (#104)
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‎src/Decimals.jl

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@@ -27,6 +27,7 @@ include("conversion.jl")
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include("decimal.jl")
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include("arithmetic/elementary.jl")
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include("arithmetic/exceptions.jl")
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include("arithmetic/inv.jl")
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include("arithmetic/sqrt.jl")
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include("equals.jl")
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include("round.jl")

‎src/arithmetic/inv.jl

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function Base.inv(x::Decimal)
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if iszero(x)
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throw(DivisionByZeroError())
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elseif isone(x)
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return x
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end
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prec = precision(Decimal)
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# inv(x) = inv(c) * inv(10^q)
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# = inv(c) * 10^-q
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# = inv(c) * 10^t * 10^(-q - t)
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# = 10^t / c * 10^(-q - t)
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#
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# We pick `t` such that
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#
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# 10^t ÷ c
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#
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# has at least `prec + 1` digits (an extra digit for dealing with
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# rounding).
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t = prec + ndigits(x.c) + 1
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c, rem = divrem(BigTen^t, x.c)
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q = -x.q - t
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# When the result is non-exact, and the last coefficient digit is 5, we
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# need to increment the coefficient for correct rounding
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if rem > 0 && isdivisible(c, 5)
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c += 1
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end
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c, m = cancelfactor(c, Val(10))
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q = q + m
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return fix(Decimal(x.s, c, q))
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end

‎test/arithmetic/test_inv.jl

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using Decimals
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using Test
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@testset "inv" begin
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# Taken from dectests for division
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1") == dec"1")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"2") == dec"0.5")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"3") == dec"0.333333333")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"2") == dec"0.5")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"4") == dec"0.25")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"8") == dec"0.125")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"16") == dec"0.0625")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"32") == dec"0.03125")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"64") == dec"0.015625")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"-2") == dec"-0.5")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"-4") == dec"-0.25")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"-8") == dec"-0.125")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"-16") == dec"-0.0625")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"-32") == dec"-0.03125")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"-64") == dec"-0.015625")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1e-8") == dec"1e+8")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1e-9") == dec"1e+9")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1e-10") == dec"1e+10")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1e-11") == dec"1e+11")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1e-12") == dec"1e+12")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1") == dec"1")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"2") == dec"0.5")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"3") == dec"0.333333333")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"4") == dec"0.25")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"5") == dec"0.2")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"6") == dec"0.166666667")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"7") == dec"0.142857143")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"8") == dec"0.125")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"9") == dec"0.111111111")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"10") == dec"0.1")
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@with_context (Emax = 384, Emin = -383, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1") == dec"1")
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@with_context (Emax = 999999999, Emin = -999999999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1e999999999") == dec"1e-999999999")
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@with_context (Emax = 999999999, Emin = -999999999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"0.9e999999999") == dec"1.11111111e-999999999")
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@with_context (Emax = 999999999, Emin = -999999999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"0.99e999999999") == dec"1.01010101e-999999999")
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@with_context (Emax = 999999999, Emin = -999999999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"0.999999999e999999999") == dec"1.00000000e-999999999")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"12345678000") == dec"8.10000066e-11")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567800") == dec"8.10000066e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567890") == dec"8.10000007e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567891") == dec"8.10000007e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"12345678901") == dec"8.10000007e-11")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567896") == dec"8.10000003e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567897") == dec"8.10000003e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567898") == dec"8.10000002e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567899") == dec"8.10000001e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567900") == dec"8.10000001e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567901") == dec"8.10000000e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567902") == dec"8.09999999e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567896.000000000000") == dec"8.10000003e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567896.000000000001") == dec"8.10000003e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567896.000000000000000000000000000000000000000009") == dec"8.10000003e-10")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567897.900010000000000000000000000000000000000009") == dec"8.10000002e-10")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"12345678000") == dec"8.10000066420005e-11")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567800") == dec"8.10000066420005e-10")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567890") == dec"8.10000007371000e-10")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567891") == dec"8.10000006714900e-10")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"12345678901") == dec"8.10000007305390e-11")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1234567896") == dec"8.10000003434400e-10")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1.0e+33") == dec"1e-33")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"10e+33") == dec"1e-34")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"1.0e-33") == dec"1e+33")
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@with_context (Emax = 999, Emin = -999, precision = 15, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"10e-33") == dec"1e+32")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"9.9") == dec"0.101010101")
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@with_context (Emax = 999, Emin = -999, precision = 8, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"9.9") == dec"0.10101010")
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@with_context (Emax = 999, Emin = -999, precision = 7, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"9.9") == dec"0.1010101")
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@with_context (Emax = 999, Emin = -999, precision = 6, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"9.9") == dec"0.101010")
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@with_context (Emax = 999, Emin = -999, precision = 9, rounding = RoundingMode{:NearestTiesAway}()) @test(inv(dec"2") == dec"0.5")
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@with_context (Emax = 384, Emin = -383, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"0"))
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@with_context (Emax = 384, Emin = -383, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"-0"))
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@with_context (Emax = 384, Emin = -383, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"0.0"))
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@with_context (Emax = 384, Emin = -383, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"-0.0"))
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@with_context (Emax = 999999999, Emin = -999999999, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"0"))
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@with_context (Emax = 999999999, Emin = -999999999, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"0.0"))
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@with_context (Emax = 999999999, Emin = -999999999, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"-0"))
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@with_context (Emax = 999999999, Emin = -999999999, precision = 16, rounding = RoundingMode{:NearestTiesAway}()) @test_throws(DivisionByZeroError, inv(dec"-0.0"))
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end
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‎test/runtests.jl

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@@ -14,6 +14,7 @@ include("test_round.jl")
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include("test_show.jl")
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include("arithmetic/test_sqrt.jl")
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include("arithmetic/test_inv.jl")
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@testset "DecTests" begin
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include("dectests/test_abs.jl")

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