move mathematical constants to Base.MathConstants

 - only export pi, π and ℯ from Base
 - remove eu as alias for ℯ

base/exports.jl

@@ -186,10 +186,7 @@ export
     NaN64,
     im,
     π, pi,
-    e, eu,
-    γ, eulergamma,
-    catalan,
-    φ, golden,
+    ℯ,
     I,
 
 # Operators

base/irrationals.jl

@@ -142,91 +142,6 @@ end
 big(x::Irrational) = convert(BigFloat,x)
 big(::Type{<:Irrational}) = BigFloat
 
-## specific irrational mathematical constants
-
-@irrational π        3.14159265358979323846  pi
-@irrational e        2.71828182845904523536  exp(big(1))
-@irrational γ        0.57721566490153286061  euler
-@irrational catalan  0.91596559417721901505  catalan
-@irrational φ        1.61803398874989484820  (1+sqrt(big(5)))/2
-
-# aliases
-"""
-    pi
-    π
-
-The constant pi.
-
-```jldoctest
-julia> pi
-π = 3.1415926535897...
-```
-"""
-π, const pi = π
-
-"""
-    e
-    eu
-
-The constant e.
-
-```jldoctest
-julia> e
-e = 2.7182818284590...
-```
-"""
-e, const eu = e
-
-"""
-    γ
-    eulergamma
-
-Euler's constant.
-
-```jldoctest
-julia> eulergamma
-γ = 0.5772156649015...
-```
-"""
-γ, const eulergamma = γ
-
-"""
-    φ
-    golden
-
-The golden ratio.
-
-```jldoctest
-julia> golden
-φ = 1.6180339887498...
-```
-"""
-φ, const golden = φ
-
-"""
-    catalan
-
-Catalan's constant.
-
-```jldoctest
-julia> catalan
-catalan = 0.9159655941772...
-```
-"""
-catalan
-
-# special behaviors
-
-# use exp for e^x or e.^x, as in
-#    ^(::Irrational{:e}, x::Number) = exp(x)
-# but need to loop over types to prevent ambiguity with generic rules for ^(::Number, x) etc.
-for T in (Irrational, Rational, Integer, Number)
-    ^(::Irrational{:e}, x::T) = exp(x)
-end
-
-log(::Irrational{:e}) = 1 # use 1 to correctly promote expressions like log(x)/log(e)
-log(::Irrational{:e}, x::Number) = log(x)
-
 # align along = for nice Array printing
 function alignment(io::IO, x::Irrational)
     m = match(r"^(.*?)(=.*)$", sprint(0, showcompact, x, env=io))

base/linalg/lapack.jl

@@ -5299,7 +5299,7 @@ for (bdsdc, elty) in
                 u, &ldu, vt, &ldvt,
                 q, iq, work, iwork, info)
             chklapackerror(info[])
-            d, e, u, vt, q, iq
+            d, e_, u, vt, q, iq
         end
     end
 end

base/mathconstants.jl

@@ -0,0 +1,92 @@
+# This file is a part of Julia. License is MIT: https://julialang.org/license
+
+"""
+    Base.MathConstants
+
+Module containing the mathematical constants.
+See [`π`](@ref), [`ℯ`](@ref), [`γ`](@ref), [`φ`](@ref) and [`catalan`](@ref).
+"""
+module MathConstants
+
+export π, pi, ℯ, e, γ, eulergamma, catalan, φ, golden
+
+Base.@irrational π        3.14159265358979323846  pi
+Base.@irrational ℯ        2.71828182845904523536  exp(big(1))
+Base.@irrational γ        0.57721566490153286061  euler
+Base.@irrational φ        1.61803398874989484820  (1+sqrt(big(5)))/2
+Base.@irrational catalan  0.91596559417721901505  catalan
+
+# aliases
+"""
+    π
+    pi
+
+The constant pi.
+
+```jldoctest
+julia> pi
+π = 3.1415926535897...
+```
+"""
+π, const pi = π
+
+"""
+    ℯ
+    e
+
+The constant ℯ.
+
+```jldoctest
+julia> ℯ
+ℯ = 2.7182818284590...
+```
+"""
+ℯ, const e = ℯ
+
+"""
+    γ
+    eulergamma
+
+Euler's constant.
+
+```jldoctest
+julia> eulergamma
+γ = 0.5772156649015...
+```
+"""
+γ, const eulergamma = γ
+
+"""
+    φ
+    golden
+
+The golden ratio.
+
+```jldoctest
+julia> golden
+φ = 1.6180339887498...
+```
+"""
+φ, const golden = φ
+
+"""
+    catalan
+
+Catalan's constant.
+
+```jldoctest
+julia> catalan
+catalan = 0.9159655941772...
+```
+"""
+catalan
+
+# loop over types to prevent ambiguities for ^(::Number, x)
+for T in (Irrational, Rational, Integer, Number)
+    Base.:^(::Irrational{:ℯ}, x::T) = exp(x)
+end
+
+Base.log(::Irrational{:ℯ}) = 1 # use 1 to correctly promote expressions like log(x)/log(ℯ)
+Base.log(::Irrational{:ℯ}, x::Number) = log(x)
+
+end # module

base/sysimg.jl

@@ -323,6 +323,8 @@ include("hashing2.jl")
 
 # irrational mathematical constants
 include("irrationals.jl")
+include("mathconstants.jl")
+using .MathConstants: ℯ, π, pi
 
 # random number generation
 include("random/dSFMT.jl")

test/bigfloat.jl

@@ -7,7 +7,7 @@ for T in [Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt
     @test big(2.0)^T(3) == 8
 end
 
-for x in (2f0, pi, 7.8, big(e))
+for x in (2f0, pi, 7.8, big(ℯ))
     @test big(typeof(x)) == typeof(big(x))
     @test big(typeof(complex(x, x))) == typeof(big(complex(x, x)))
 end

test/complex.jl

@@ -901,7 +901,7 @@ end
     @test round.([1:5;] + 0.5im) == [1.0:5.0;]
 
     @test float(Complex(1, 2)) == Complex(1.0, 2.0)
-    @test round(float(Complex(π, e)),3) == Complex(3.142, 2.718)
+    @test round(float(Complex(π, ℯ)),3) == Complex(3.142, 2.718)
 end
 
 @testset "Complex32 arithmetic, PR #10003" begin
@@ -947,7 +947,7 @@ end
 @test big(1)/(10+10im) ≈ (5-5im)/big(100) ≈ big"0.05" - big"0.05"*im
 
 @testset "Complex Irrationals, issue #21204" begin
-    for x in (pi, e, catalan) # No need to test all of them
+    for x in (pi, ℯ, Base.MathConstants.catalan) # No need to test all of them
         z = Complex(x, x)
         @test typeof(z) == Complex{typeof(x)}
         @test exp(z) ≈ exp(x) * cis(x)

test/core.jl

@@ -942,7 +942,7 @@ end
 
 @test unsafe_pointer_to_objref(ccall(:jl_call1, Ptr{Void}, (Any,Any),
                                      x -> x+1, 314158)) == 314159
-@test unsafe_pointer_to_objref(pointer_from_objref(e+pi)) == e+pi
+@test unsafe_pointer_to_objref(pointer_from_objref(ℯ+pi)) == ℯ+pi
 
 let
     local a, aa

test/floatfuncs.jl

@@ -68,7 +68,7 @@ for elty in (Float32,Float64)
 end
 
 @testset "Types" begin
-    for x in (Int16(0), 1, 2f0, pi, 3//4, big(5//6), 7.8, big(9), big(e))
+    for x in (Int16(0), 1, 2f0, pi, 3//4, big(5//6), 7.8, big(9), big(ℯ))
         @test float(typeof(x)) == typeof(float(x))
         @test float(typeof(complex(x, x))) == typeof(float(complex(x, x)))
     end

test/math.jl

@@ -23,16 +23,16 @@
 end
 
 @testset "constants" begin
-    @test pi != e
-    @test e != 1//2
-    @test 1//2 <= e
-    @test e <= 15//3
-    @test big(1//2) < e
-    @test e < big(20//6)
-    @test e^pi == exp(pi)
-    @test e^2 == exp(2)
-    @test e^2.4 == exp(2.4)
-    @test e^(2//3) == exp(2//3)
+    @test pi != ℯ
+    @test ℯ != 1//2
+    @test 1//2 <= ℯ
+    @test ℯ <= 15//3
+    @test big(1//2) < ℯ
+    @test ℯ < big(20//6)
+    @test ℯ^pi == exp(pi)
+    @test ℯ^2 == exp(2)
+    @test ℯ^2.4 == exp(2.4)
+    @test ℯ^(2//3) == exp(2//3)
 
     @test Float16(3.0) < pi
     @test pi < Float16(4.0)
@@ -171,19 +171,19 @@ end
             @test isequal(cos(T(0)), T(1))
             @test cos(T(pi)/2) ≈ T(0) atol=eps(T)
             @test isequal(cos(T(pi)), T(-1))
-            @test exp(T(1)) ≈ T(e) atol=10*eps(T)
+            @test exp(T(1)) ≈ T(ℯ) atol=10*eps(T)
             @test isequal(exp10(T(1)), T(10))
             @test isequal(exp2(T(1)), T(2))
             @test isequal(expm1(T(0)), T(0))
-            @test expm1(T(1)) ≈ T(e)-1 atol=10*eps(T)
+            @test expm1(T(1)) ≈ T(ℯ)-1 atol=10*eps(T)
             @test isequal(hypot(T(3),T(4)), T(5))
             @test isequal(log(T(1)), T(0))
-            @test isequal(log(e,T(1)), T(0))
-            @test log(T(e)) ≈ T(1) atol=eps(T)
+            @test isequal(log(ℯ,T(1)), T(0))
+            @test log(T(ℯ)) ≈ T(1) atol=eps(T)
             @test isequal(log10(T(1)), T(0))
             @test isequal(log10(T(10)), T(1))
             @test isequal(log1p(T(0)), T(0))
-            @test log1p(T(e)-1) ≈ T(1) atol=eps(T)
+            @test log1p(T(ℯ)-1) ≈ T(1) atol=eps(T)
             @test isequal(log2(T(1)), T(0))
             @test isequal(log2(T(2)), T(1))
             @test isequal(sin(T(0)), T(0))
@@ -402,7 +402,7 @@ end
 end
 
 @testset "Irrational args to sinpi/cospi/sinc/cosc" begin
-    for x in (pi, e, golden)
+    for x in (pi, ℯ, Base.MathConstants.golden)
         @test sinpi(x) ≈ Float64(sinpi(big(x)))
         @test cospi(x) ≈ Float64(cospi(big(x)))
         @test sinc(x)  ≈ Float64(sinc(big(x)))
@@ -662,8 +662,8 @@ end
 @testset "test fallback definitions" begin
     @test exp10(5) ≈ exp10(5.0)
     @test exp10(50//10) ≈ exp10(5.0)
-    @test log10(exp10(e)) ≈ e
-    @test log(e) === 1
+    @test log10(exp10(ℯ)) ≈ ℯ
+    @test log(ℯ) === 1
     @test exp2(Float16(2.0)) ≈ exp2(2.0)
     @test exp2(Float16(1.0)) === Float16(exp2(1.0))
     @test exp10(Float16(1.0)) === Float16(exp10(1.0))

test/numbers.jl

@@ -1,5 +1,6 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
+using Base.MathConstants
 const ≣ = isequal # convenient for comparing NaNs
 
 # basic booleans
@@ -2491,7 +2492,7 @@ z2 = read(zbuf, Complex128)
 @test bswap(z2) ===  3.5 - 4.5im
 
 #isreal(x::Real) = true
-for x in [1.23, 7, e, 4//5] #[FP, Int, Irrational, Rat]
+for x in [1.23, 7, ℯ, 4//5] #[FP, Int, Irrational, Rat]
     @test isreal(x) == true
 end
 
@@ -2526,7 +2527,7 @@ let number_types = Set()
 end
 
 #getindex(x::Number) = x
-for x in [1.23, 7, e, 4//5] #[FP, Int, Irrational, Rat]
+for x in [1.23, 7, ℯ, 4//5] #[FP, Int, Irrational, Rat]
     @test getindex(x) == x
     @test getindex(x, 1, 1) == x
 end
@@ -2537,7 +2538,7 @@ end
 #getindex(x::Array,-1) throws BoundsError
 #getindex(x::Array,0 throws BoundsError
 #getindex(x::Array,length(x::Array)+1) throws BoundsError
-for x in [1.23, 7, e, 4//5] #[FP, Int, Irrational, Rat]
+for x in [1.23, 7, ℯ, 4//5] #[FP, Int, Irrational, Rat]
     @test_throws BoundsError getindex(x,-1)
     @test_throws BoundsError getindex(x,0)
     @test_throws BoundsError getindex(x,2)
@@ -2549,8 +2550,8 @@ end
 
 # copysign(x::Real, y::Real) = ifelse(signbit(x)!=signbit(y), -x, x)
 # flipsign(x::Real, y::Real) = ifelse(signbit(y), -x, x)
-for x in [1.23, 7, e, 4//5]
-    for y in [1.23, 7, e, 4//5]
+for x in [1.23, 7, ℯ, 4//5]
+    for y in [1.23, 7, ℯ, 4//5]
         @test copysign(x, y) == x
         @test copysign(x, -y) == -x
         @test copysign(-x, y) == x
@@ -2570,7 +2571,7 @@ end
 #in(x::Number, y::Number) = x == y
 @test in(3,3) == true #Int
 @test in(2.0,2.0) == true #FP
-@test in(e,e) == true #Const
+@test in(ℯ,ℯ) == true #Const
 @test in(4//5,4//5) == true #Rat
 @test in(1+2im, 1+2im) == true #Imag
 @test in(3, 3.0) == true #mixed
@@ -2952,7 +2953,7 @@ end
     end
     @test !iszero(nextfloat(BigFloat(0)))
     @test !isone(nextfloat(BigFloat(1)))
-    for x in (π, e, γ, catalan, φ)
+    for x in (π, ℯ, γ, catalan, φ)
         @test !iszero(x)
         @test !isone(x)
     end