Make false a strong zero against 1//0 (#57409)

Make false a strong zero against rationals and add tests.

Also adds tests for `*(::Bool, ::Float64)` because I didn't find tests
for that anywhere.

Implements #57068

Author: LilithHafner

base/rational.jl

@@ -415,6 +415,12 @@ function *(y::Integer, x::Rational)
     yn, xd = divgcd(promote(y, x.den)...)
     unsafe_rational(checked_mul(yn, x.num), xd)
 end
+# make `false` a "strong zero": false*1//0 == 0//1 #57409
+# This is here instead of in bool.jl with the AbstractFloat method for bootstrapping
+function *(x::Bool, y::T)::promote_type(Bool,T) where T<:Rational
+    return ifelse(x, y, copysign(zero(y), y))
+end
+*(y::Rational, x::Bool) = x * y
 /(x::Rational, y::Union{Rational, Integer, Complex{<:Union{Integer,Rational}}}) = x//y
 /(x::Union{Integer, Complex{<:Union{Integer,Rational}}}, y::Rational) = x//y
 inv(x::Rational{T}) where {T} = checked_den(x.den, x.num)

test/numbers.jl

@@ -2192,11 +2192,36 @@ for T = (UInt8,Int8,UInt16,Int16,UInt32,Int32,UInt64,Int64,UInt128,Int128)
     end
 end
 
-@testset "Irrational/Bool multiplication" begin
+@testset "Bool multiplication" begin
     @test false*pi === 0.0
     @test pi*false === 0.0
     @test true*pi === Float64(pi)
     @test pi*true === Float64(pi)
+
+    @test false*Inf === 0.0
+    @test Inf*false === 0.0
+    @test true*Inf === Inf
+    @test Inf*true === Inf
+
+    @test false*NaN === 0.0
+    @test NaN*false === 0.0
+    @test true*NaN === NaN
+    @test NaN*true === NaN
+
+    @test false*-Inf === -0.0
+    @test -Inf*false === -0.0
+    @test true*-Inf === -Inf
+    @test -Inf*true === -Inf
+
+    @test false*1//0 === 0//1
+    @test 1//0*false === 0//1
+    @test true*1//0 === 1//0
+    @test 1//0*true === 1//0
+
+    @test false*-1//0 === 0//1
+    @test -1//0*false === 0//1
+    @test true*-1//0 === -1//0
+    @test -1//0*true === -1//0
 end
 # issue #5492
 @test -0.0 + false === -0.0