AK/Math: Make lgamma_r's sign computation more sound

This still doesn't always produce the correct result for negative values
of x, but at least this fixes the reasoning.

AK/Math/Gamma.h

@@ -56,12 +56,21 @@ constexpr T lgamma(T x)
     return Detail::stirling_approximation(x);
 }
 
+// The lgamma_r variant uses an out parameter to return a sign value.
+// lgamma can be written as lgamma(x) = log(|Γ(x)|), the out parameter
+// corresponds to the sign of Γ(x).
 template<FloatingPoint T>
 constexpr T lgamma_r(T x, int* sign)
 {
-    auto result = lgamma(x);
-    *sign = signbit(result) ? -1 : 1;
-    return result;
+    if (x > 0) {
+        // ∀ x ∈ ℝ, x > 0 ⇒ Γ(x) > 0
+        *sign = 1;
+    } else {
+        // FIXME: Correctly compute sign's value.
+        *sign = -1;
+    }
+
+    return lgamma(x);
 }
 
 }

Tests/LibC/TestMath.cpp

@@ -346,7 +346,7 @@ TEST_CASE(gamma)
     EXPECT(isnan(lgamma(NAN)));
     EXPECT(isinf(lgamma(INFINITY)));
     EXPECT(isinf(lgamma(-INFINITY)));
-    EXPECT_EQ(signgam, 1);
+    EXPECT_EQ(signgam, -1); // This is not specified by POSIX.
     lgamma(-2.5);
     EXPECT_EQ(signgam, -1);
 }