From 8659cfeda7afa5cf665e282e927812f0a9d51d03 Mon Sep 17 00:00:00 2001
From: "Steven G. Johnson" <stevenj@alum.mit.edu>
Date: Mon, 21 Sep 2020 18:17:40 -0400
Subject: [PATCH] ispow2(x) for non-Integer x (#37635)

---
 NEWS.md            |  1 +
 base/float.jl      |  2 ++
 base/intfuncs.jl   | 18 ++++++++++++++++--
 base/rational.jl   |  1 +
 test/complex.jl    |  7 +++++++
 test/floatfuncs.jl | 11 +++++++++++
 test/rational.jl   |  7 +++++++
 7 files changed, 45 insertions(+), 2 deletions(-)

diff --git a/NEWS.md b/NEWS.md
index 15229f5c28f58..f507c77a65e65 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -91,6 +91,7 @@ Standard library changes
   by passing a tuple for `dims`, and defaults to reversing all dimensions; there is also a multidimensional
   in-place `reverse!(A; dims)` ([#37367]).
 * The function `isapprox(x,y)` now accepts the `norm` keyword argument also for numeric (i.e., non-array) arguments `x` and `y` ([#35883]).
+* `ispow2(x)` now supports non-`Integer` arguments `x` ([#37635]).
 * `view`, `@view`, and `@views` now work on `AbstractString`s, returning a `SubString` when appropriate ([#35879]).
 * All `AbstractUnitRange{<:Integer}`s now work with `SubString`, `view`, `@view` and `@views` on strings ([#35879]).
 * `sum`, `prod`, `maximum`, and `minimum` now support `init` keyword argument ([#36188], [#35839]).
diff --git a/base/float.jl b/base/float.jl
index 0857d172eaff0..242fddfca8946 100644
--- a/base/float.jl
+++ b/base/float.jl
@@ -711,6 +711,8 @@ function issubnormal(x::T) where {T<:IEEEFloat}
     (y & exponent_mask(T) == 0) & (y & significand_mask(T) != 0)
 end
 
+ispow2(x::AbstractFloat) = !iszero(x) && frexp(x)[1] == 0.5
+
 @eval begin
     typemin(::Type{Float16}) = $(bitcast(Float16, 0xfc00))
     typemax(::Type{Float16}) = $(Inf16)
diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index 198f73191ecb8..de790df019281 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -368,9 +368,9 @@ _prevpow2(x::Unsigned) = one(x) << unsigned((sizeof(x)<<3)-leading_zeros(x)-1)
 _prevpow2(x::Integer) = reinterpret(typeof(x),x < 0 ? -_prevpow2(unsigned(-x)) : _prevpow2(unsigned(x)))
 
 """
-    ispow2(n::Integer) -> Bool
+    ispow2(n::Number) -> Bool
 
-Test whether `n` is a power of two.
+Test whether `n` is an integer power of two.
 
 # Examples
 ```jldoctest
@@ -379,8 +379,22 @@ true
 
 julia> ispow2(5)
 false
+
+julia> ispow2(4.5)
+false
+
+julia> ispow2(0.25)
+true
+
+julia> ispow2(1//8)
+true
 ```
+
+!!! compat "Julia 1.6"
+    Support for non-`Integer` arguments was added in Julia 1.6.
 """
+ispow2(x::Number) = isreal(x) && ispow2(real(x))
+
 ispow2(x::Integer) = x > 0 && count_ones(x) == 1
 
 """
diff --git a/base/rational.jl b/base/rational.jl
index 1f7b0bea79ca4..e92c61c03a7ec 100644
--- a/base/rational.jl
+++ b/base/rational.jl
@@ -262,6 +262,7 @@ typemin(::Type{Rational{T}}) where {T<:Integer} = unsafe_rational(T, zero(T), on
 typemax(::Type{Rational{T}}) where {T<:Integer} = unsafe_rational(T, one(T), zero(T))
 
 isinteger(x::Rational) = x.den == 1
+ispow2(x::Rational) = ispow2(x.num) & ispow2(x.den)
 
 +(x::Rational) = unsafe_rational(+x.num, x.den)
 -(x::Rational) = unsafe_rational(-x.num, x.den)
diff --git a/test/complex.jl b/test/complex.jl
index 07183d7fca354..f02c931ebdda7 100644
--- a/test/complex.jl
+++ b/test/complex.jl
@@ -1187,3 +1187,10 @@ end
 
 # complex with non-concrete eltype
 @test_throws ErrorException complex(Union{Complex{Int}, Nothing}[])
+
+@testset "ispow2" begin
+    @test ispow2(4+0im)
+    @test ispow2(0.25+0im)
+    @test !ispow2(4+5im)
+    @test !ispow2(7+0im)
+end
diff --git a/test/floatfuncs.jl b/test/floatfuncs.jl
index ff105f425ea81..677c07023c85d 100644
--- a/test/floatfuncs.jl
+++ b/test/floatfuncs.jl
@@ -40,6 +40,17 @@ end
     end
 end
 
+@testset "ispow2" begin
+    for T in (Float16,Float32,Float64,BigFloat)
+        for x in (0.25, 1.0, 4.0, exp2(T(exponent(floatmax(T)))), exp2(T(exponent(floatmin(T)))))
+            @test ispow2(T(x))
+        end
+        for x in (1.5, 0.0, 7.0, NaN, Inf)
+            @test !ispow2(T(x))
+        end
+    end
+end
+
 @testset "round" begin
     for elty in (Float32, Float64)
         x = rand(elty)
diff --git a/test/rational.jl b/test/rational.jl
index 81a9ab16c5ff7..76ff20acbf938 100644
--- a/test/rational.jl
+++ b/test/rational.jl
@@ -594,3 +594,10 @@ end
     @test -1//5 * 0x3//0x2 == 0x3//0x2 * -1//5 == -3//10
     @test -2//3 * 0x1 == 0x1 * -2//3 == -2//3
 end
+
+@testset "ispow2" begin
+    @test ispow2(4//1)
+    @test ispow2(1//8)
+    @test !ispow2(3//8)
+    @test !ispow2(0//1)
+end