using Requires for Statistics

Because Statistics is no longer part of the Julia sysimage, the package loading
time of FixedPointNumbers is then donimated by Statistics. This commit uses
Requires to conditionally add the needed method without making more one-line
package. This, of course, adds some additional overhead but I do believe it's
currently the best tradeoff until we have first-class support on conditional
package loading.

Author: johnnychen94

Project.toml

@@ -4,9 +4,11 @@ version = "0.8.4"
 
 [deps]
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
+Requires = "1"
 julia = "1"
 
 [extras]

src/FixedPointNumbers.jl

@@ -9,7 +9,7 @@ import Base: ==, <, <=, -, +, *, /, ~, isapprox,
              signed, unsigned, copysign, flipsign, signbit,
              length
 
-import Statistics   # for _mean_promote
+using Requires
 import Random: Random, AbstractRNG, SamplerType, rand!
 
 import Base.Checked: checked_neg, checked_abs, checked_add, checked_sub, checked_mul,
@@ -557,10 +557,6 @@ Base.mul_prod(x::FixedPoint, y::FixedPoint) = Treduce(x) * Treduce(y)
 Base.reduce_empty(::typeof(Base.mul_prod), ::Type{F}) where {F<:FixedPoint} = one(Treduce)
 Base.reduce_first(::typeof(Base.mul_prod), x::FixedPoint)  = Treduce(x)
 
-if isdefined(Statistics, :_mean_promote)
-    Statistics._mean_promote(x::Real, y::FixedPoint) = Treduce(y)
-end
-
 """
     sd, ad = scaledual(s::Number, a)
 
@@ -629,4 +625,20 @@ if VERSION >= v"1.1" # work around https://github.com/JuliaLang/julia/issues/341
     _precompile_()
 end
 
+@static if VERSION >= v"1.9.0-DEV.873"
+    function __init__()
+        # Statistics and SparseArrays are moved out from sysimage
+        # https://github.com/JuliaLang/julia/pull/44247#issuecomment-1172847231
+        @require Statistics="10745b16-79ce-11e8-11f9-7d13ad32a3b2" begin
+            Statistics._mean_promote(x::Real, y::FixedPoint) = Treduce(y)
+        end
+    end
+else
+    import Statistics
+    if isdefined(Statistics, :_mean_promote)
+        # https://github.com/JuliaMath/FixedPointNumbers.jl/pull/183
+        Statistics._mean_promote(x::Real, y::FixedPoint) = Treduce(y)
+    end
+end
+
 end # module