test: math: test floating-point behavior when mapping zero to zero

The idea for this addition to the test suite originates here, where
stevengj suggested to do this test for `cosc` specifically:

* JuliaLang#59087 (comment)

This PR instead tests all applicable functions I could find.

Author: nsajko

test/math.jl

@@ -590,6 +590,23 @@ end
     @test ismissing(scdm[2])
 end
 
+@testset "behavior at signed zero of monotonic floating-point functions mapping zero to zero" begin
+    @testset "typ: $typ" for typ in (Float32, Float64)
+        @testset "f: $f" for f in (
+            # all strictly increasing
+            identity, deg2rad, rad2deg, cbrt, log1p, expm1, sinh, tanh, asinh, atanh,
+            sin, sind, sinpi, tan, tand, tanpi, asin, asind, atan, atand,
+            Base.Fix1(round, typ), Base.Fix1(trunc, typ), ∘(-, -), ∘(-, cosc),
+        )
+            @testset "s: $s" for s in (-1, 1)
+                z = s * typ(0)
+                z::typ
+                @test z === @inferred f(z)
+            end
+        end
+    end
+end
+
 @testset "Integer and Inf args for sinpi/cospi/tanpi/sinc/cosc" begin
     for (sinpi, cospi) in ((sinpi, cospi), (x->sincospi(x)[1], x->sincospi(x)[2]))
         @test sinpi(1) === 0.0