fix exp(NaN16) and add tests (#42555)

* fix exp(NaN16) and add tests

Author: oscardssmith

base/special/exp.jl

@@ -281,7 +281,7 @@ end
     small_part = expb_kernel(base, r)
     if !(abs(x) <= SUBNORM_EXP(base, T))
         x > MAX_EXP(base, T) && return Inf16
-        N<=Int32(-24) && return zero(Float16)
+        x < MIN_EXP(base, T) && return zero(Float16)
     end
     twopk = reinterpret(T, (N+Int32(127)) << Int32(23))
     return Float16(twopk*small_part)

test/math.jl

@@ -308,47 +308,29 @@ end
     end
 end
 
-@testset "exp function" for T in (Float64, Float32)
-    @testset "$T accuracy" begin
-        X = map(T, vcat(-10:0.0002:10, -80:0.001:80, 2.0^-27, 2.0^-28, 2.0^-14, 2.0^-13))
-        for x in X
-            y, yb = exp(x), exp(big(x))
-            @test abs(y-yb) <= 1.0*eps(T(yb))
-        end
-    end
-    @testset "$T edge cases" begin
-        @test isnan_type(T, exp(T(NaN)))
-        @test exp(T(-Inf)) === T(0.0)
-        @test exp(T(Inf)) === T(Inf)
-        @test exp(T(0.0)) === T(1.0) # exact
-        @test exp(T(5000.0)) === T(Inf)
-        @test exp(T(-5000.0)) === T(0.0)
-    end
-end
-
-@testset "exp10 function" begin
-    @testset "accuracy" begin
-        X = map(Float64, vcat(-10:0.00021:10, -35:0.0023:100, -300:0.001:300))
-        for x in X
-            y, yb = exp10(x), exp10(big(x))
-            @test abs(y-yb) <= 1.2*eps(Float64(yb))
+@testset "exponential functions" for T in (Float64, Float32, Float16)
+    for (func, invfunc) in ((exp2, log2), (exp, log), (exp10, log10))
+        @testset "$T $func accuracy" begin
+            minval, maxval = invfunc(floatmin(T)),prevfloat(invfunc(floatmax(T)))
+            # Test range and extensively test numbers near 0.
+            X = Iterators.flatten((minval:T(.1):maxval,
+                                   minval/100:T(.0021):maxval/100,
+                                   minval/10000:T(.000021):maxval/10000,
+                                   nextfloat(zero(T)) ))
+            for x in X
+                y, yb = func(x), func(widen(x))
+                @test abs(y-yb) <= 1.2*eps(T(yb))
+            end
         end
-        X = map(Float32, vcat(-10:0.00021:10, -35:0.0023:35, -35:0.001:35))
-        for x in X
-            y, yb = exp10(x), exp10(big(x))
-            @test abs(y-yb) <= 1.2*eps(Float32(yb))
+        @testset "$T $func edge cases" begin
+            @test func(T(-Inf)) === T(0.0)
+            @test func(T(Inf)) === T(Inf)
+            @test func(T(NaN)) === T(NaN)
+            @test func(T(0.0)) === T(1.0) # exact
+            @test func(T(5000.0)) === T(Inf)
+            @test func(T(-5000.0)) === T(0.0)
         end
     end
-    @testset "$T edge cases" for T in (Float64, Float32)
-        @test isnan_type(T, exp10(T(NaN)))
-        @test exp10(T(-Inf)) === T(0.0)
-        @test exp10(T(Inf)) === T(Inf)
-        @test exp10(T(0.0)) === T(1.0) # exact
-        @test exp10(T(1.0)) === T(10.0)
-        @test exp10(T(3.0)) === T(1000.0)
-        @test exp10(T(5000.0)) === T(Inf)
-        @test exp10(T(-5000.0)) === T(0.0)
-    end
 end
 
 @testset "test abstractarray trig functions" begin