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Improve Irrational vs BigFloat comparisons #29196

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Improve Irrational vs BigFloat comparisons #29196

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40 changes: 26 additions & 14 deletions base/irrationals.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -17,7 +17,7 @@ symbol `sym`.
"""
struct Irrational{sym} <: AbstractIrrational end

show(io::IO, x::Irrational{sym}) where {sym} = print(io, "$sym = $(string(float(x))[1:15])...")
show(io::IO, x::Irrational{sym}) where {sym} = print(io, "$sym = $(string(float(x))[1:min(end,15)])...")

promote_rule(::Type{<:AbstractIrrational}, ::Type{Float16}) = Float16
promote_rule(::Type{<:AbstractIrrational}, ::Type{Float32}) = Float32
Expand All @@ -30,24 +30,25 @@ Float16(x::AbstractIrrational) = Float16(Float32(x))
Complex{T}(x::AbstractIrrational) where {T<:Real} = Complex{T}(T(x))

@pure function Rational{T}(x::AbstractIrrational) where T<:Integer
o = precision(BigFloat)
p = 256
while true
setprecision(BigFloat, p)
prec_orig = precision(BigFloat)
for prec in Iterators.countfrom(256, 32)
setprecision(BigFloat, prec)
bx = BigFloat(x)
r = rationalize(T, bx, tol=0)
if abs(BigFloat(r) - bx) > eps(bx)
setprecision(BigFloat, o)
setprecision(BigFloat, prec_orig)
return r
end
p += 32
end
end

(::Type{Rational{BigInt}})(x::AbstractIrrational) = throw(ArgumentError("Cannot convert an AbstractIrrational to a Rational{BigInt}: use rationalize(Rational{BigInt}, x) instead"))

@pure function (t::Type{T})(x::AbstractIrrational, r::RoundingMode) where T<:Union{Float32,Float64}
setprecision(BigFloat, 256) do
T(BigFloat(x), r)
for prec in Iterators.countfrom(256, 32)
bx = BigFloat(x, prec)
u = T(bx, r)
u != bx && return u
end
end

Expand Down Expand Up @@ -76,12 +77,23 @@ end
<(x::Float32, y::AbstractIrrational) = x <= Float32(y,RoundDown)
<(x::AbstractIrrational, y::Float16) = Float32(x,RoundUp) <= y
<(x::Float16, y::AbstractIrrational) = x <= Float32(y,RoundDown)
<(x::AbstractIrrational, y::BigFloat) = setprecision(precision(y)+32) do
big(x) < y
end
<(x::BigFloat, y::AbstractIrrational) = setprecision(precision(x)+32) do
x < big(y)

function cmp(x::BigFloat, y::AbstractIrrational)
if cmp(x, Float64(y, RoundDown)) < 0
return -1
elseif cmp(x, Float64(y, RoundUp)) > 0
return +1
else
for prec in Iterators.countfrom(precision(x), 32)
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This seems dangerous, since if someone defines an "irrational" constant that is actually rational it will never terminate.

How about just something for prec in (precision(x), max(precision(x), precision(BigFloat)) + 32) and return 0 if both of these report equality.

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I'm not sure I agree: that would only occur if (a) you define an irrational as a rational value, and (b) compare it to that same rational. I'm not really sure.

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See #26550 for why some AbstractIrrational subtypes may define rational values.

c = cmp(x, BigFloat(y, prec))
c != 0 && return c
end
end
end
cmp(x::AbstractIrrational, y::BigFloat) = -cmp(y,x)

<(x::AbstractIrrational, y::BigFloat) = !isnan(y) && cmp(y,x) > 0
<(x::BigFloat, y::AbstractIrrational) = !isnan(x) && cmp(x,y) < 0

<=(x::AbstractIrrational, y::AbstractFloat) = x < y
<=(x::AbstractFloat, y::AbstractIrrational) = x < y
Expand Down
10 changes: 10 additions & 0 deletions test/mpfr.jl
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Expand Up @@ -944,3 +944,13 @@ end
@test big(typeof(complex(x, x))) == typeof(big(complex(x, x)))
end
end

Base.@irrational zzz 1.0 1+pi*BigFloat(1e-100)

@testset "Irrational edge cases" begin
@test Float64(zzz, RoundDown) < Float64(zzz, RoundUp)
@test BigFloat(1.0) < zzz
@test !(nextfloat(BigFloat(1.0)) < zzz)
@test !(zzz < BigFloat(1.0))
@test zzz < nextfloat(BigFloat(1.0))
end