Add a fourthroot function with unicode symbol ∜ (JuliaLang#48899)

* adds fourthroot function

NEWS.md

@@ -27,6 +27,8 @@ Build system changes
 New library functions
 ---------------------
 * `tanpi` is now defined. It computes tan(πx) more accurately than `tan(pi*x)` ([#48575]).
+* `fourthroot(x)` is now defined in `Base.Math` and can be used to compute the fourth root of `x`.
+   It can also be accessed using the unicode character `∜`, which can be typed by `\fourthroot<tab>` ([#48899]).
 
 New library features
 --------------------

base/Base.jl

@@ -342,6 +342,7 @@ include("math.jl")
 using .Math
 const (√)=sqrt
 const (∛)=cbrt
+const (∜)=fourthroot
 
 # now switch to a simple, race-y TLS, relative include for the rest of Base
 delete_method(which(include, (Module, String)))

base/exports.jl

@@ -238,6 +238,7 @@ export
     bitrotate,
     bswap,
     cbrt,
+    fourthroot,
     ceil,
     cis,
     cispi,
@@ -364,6 +365,7 @@ export
     zero,
     √,
     ∛,
+    ∜,
     ≈,
     ≉,
 

base/math.jl

@@ -10,7 +10,7 @@ export sin, cos, sincos, tan, sinh, cosh, tanh, asin, acos, atan,
        acosd, acotd, acscd, asecd, asind, atand,
        rad2deg, deg2rad,
        log, log2, log10, log1p, exponent, exp, exp2, exp10, expm1,
-       cbrt, sqrt, significand,
+       cbrt, sqrt, fourthroot, significand,
        hypot, max, min, minmax, ldexp, frexp,
        clamp, clamp!, modf, ^, mod2pi, rem2pi,
        @evalpoly, evalpoly
@@ -715,6 +715,13 @@ julia> .√(1:4)
 """
 sqrt(x)
 
+"""
+    fourthroot(x)
+
+Return the fourth root of `x` by applying `sqrt` twice successively.
+"""
+fourthroot(x::Number) = sqrt(sqrt(x))
+
 """
     hypot(x, y)
 
@@ -1537,7 +1544,7 @@ include("special/log.jl")
 # Float16 definitions
 
 for func in (:sin,:cos,:tan,:asin,:acos,:atan,:cosh,:tanh,:asinh,:acosh,
-             :atanh,:log,:log2,:log10,:sqrt,:log1p)
+             :atanh,:log,:log2,:log10,:sqrt,:fourthroot,:log1p)
     @eval begin
         $func(a::Float16) = Float16($func(Float32(a)))
         $func(a::ComplexF16) = ComplexF16($func(ComplexF32(a)))
@@ -1573,5 +1580,6 @@ end
 exp2(x::AbstractFloat) = 2^x
 exp10(x::AbstractFloat) = 10^x
 clamp(::Missing, lo, hi) = missing
+fourthroot(::Missing) = missing
 
 end # module

test/math.jl

@@ -180,6 +180,7 @@ end
             @test atan(x,y) ≈ atan(big(x),big(y))
             @test atanh(x) ≈ atanh(big(x))
             @test cbrt(x) ≈ cbrt(big(x))
+            @test fourthroot(x) ≈ fourthroot(big(x))
             @test cos(x) ≈ cos(big(x))
             @test cosh(x) ≈ cosh(big(x))
             @test cospi(x) ≈ cospi(big(x))
@@ -219,6 +220,9 @@ end
             @test isequal(cbrt(T(0)), T(0))
             @test isequal(cbrt(T(1)), T(1))
             @test isequal(cbrt(T(1000000000))^3, T(1000)^3)
+            @test isequal(fourthroot(T(0)), T(0))
+            @test isequal(fourthroot(T(1)), T(1))
+            @test isequal(fourthroot(T(100000000))^4, T(100)^4)
             @test isequal(cos(T(0)), T(1))
             @test cos(T(pi)/2) ≈ T(0) atol=eps(T)
             @test isequal(cos(T(pi)), T(-1))
@@ -271,6 +275,8 @@ end
             @test asin(sin(x)) ≈ x
             @test cbrt(x)^3 ≈ x
             @test cbrt(x^3) ≈ x
+            @test fourthroot(x)^4 ≈ x
+            @test fourthroot(x^4) ≈ x
             @test asinh(sinh(x)) ≈ x
             @test atan(tan(x)) ≈ x
             @test atan(x,y) ≈ atan(x/y)
@@ -1255,6 +1261,22 @@ end
     end
 end
 
+@testset "fourthroot" begin
+    for T in (Float32, Float64)
+        @test fourthroot(zero(T)) === zero(T)
+        @test fourthroot(one(T)) === one(T)
+        @test fourthroot(T(Inf)) === T(Inf)
+        @test isnan_type(T, fourthroot(T(NaN)))
+        for x in (pcnfloat(nextfloat(nextfloat(zero(T))))...,
+                  0.45, 0.6, 0.98,
+                  map(x->x^3, 1.0:1.0:1024.0)...,
+                  prevfloat(T(Inf)))
+            by = fourthroot(big(T(x)))
+            @test fourthroot(T(x)) ≈ by rtol=eps(T)
+        end
+    end
+end
+
 @testset "hypot" begin
     @test hypot(0, 0) == 0.0
     @test hypot(3, 4) == 5.0
@@ -1519,7 +1541,7 @@ end
 end
 
 # test constant-foldability
-for fn in (:sin, :cos, :tan, :log, :log2, :log10, :log1p, :exponent, :sqrt, :cbrt,
+for fn in (:sin, :cos, :tan, :log, :log2, :log10, :log1p, :exponent, :sqrt, :cbrt, :fourthroot,
            :asin, :atan, :acos, :sinh, :cosh, :tanh, :asinh, :acosh, :atanh,
            :exp, :exp2, :exp10, :expm1
            )