Handle Git issue 1137

Author: ckormanyos

include/boost/decimal/detail/cmath/asin.hpp

@@ -1,4 +1,5 @@
-// Copyright 2024 Matt Borland
+// Copyright 2024 - 2025 Matt Borland
+// Copyright 2024 - 2025 Christopher Kormanyos
 // Distributed under the Boost Software License, Version 1.0.
 // https://www.boost.org/LICENSE_1_0.txt
 
@@ -41,20 +42,26 @@ constexpr auto asin_impl(const T x) noexcept
         return x;
     }
 
-    const auto absx {fabs(x)};
-    T result {};
+    const auto absx { fabs(x) };
 
-    if (absx <= std::numeric_limits<T>::epsilon())
+    T result { };
+
+    constexpr T cbrt_eps { cbrt(std::numeric_limits<T>::epsilon()) };
+
+    constexpr T one { 1 };
+
+    if (absx <= cbrt_eps)
     {
-        result = absx;
+        result = absx * (one + (absx / 6) * absx);
     }
-    else if (absx <= T{5, -1})
+    else if (absx <= T { 5, -1 })
     {
         result = asin_series(absx);
     }
-    else if (absx <= T{1, 0})
+    else if (absx <= one)
     {
         constexpr T half_pi {numbers::pi_v<T> / 2};
+
         result = half_pi - 2 * asin_series(sqrt((1 - absx) / 2));
     }
     else

test/test_asin.cpp

@@ -1,4 +1,5 @@
-// Copyright 2024 Matt Borland
+// Copyright 2024 - 2025 Matt Borland
+// Copyright 2024 - 2025 Christopher Kormanyos
 // Distributed under the Boost Software License, Version 1.0.
 // https://www.boost.org/LICENSE_1_0.txt
 
@@ -137,6 +138,40 @@ void print_value(T value, const char* str)
               << "\nExp: " << ptr << "\n" << std::endl;
 }
 
+template<typename T>
+auto test_asin_edge() -> void
+{
+    using nl = std::numeric_limits<T>;
+
+    const T tiny0 { nl::epsilon() * 999 / 1000 };
+    const T tiny1 { nl::epsilon() };
+    const T tiny2 { nl::epsilon() * 1000 / 999 };
+
+    const T asin_tiny0 { asin(tiny0) };
+    const T asin_tiny1 { asin(tiny1) };
+    const T asin_tiny2 { asin(tiny2) };
+
+    // tiny1: 1
+    // tiny2: 1.001001
+    // tiny0: 0.999
+    // tiny1: 1
+    // tiny2: 1.001001001001001
+    // tiny0: 0.999
+    // tiny1: 1
+    // tiny2: 1.001001001001001001001001001001001
+
+    constexpr T ctrl_tiny2
+    {
+          std::numeric_limits<T>::digits10 < 10 ? T("1.001001")
+        : std::numeric_limits<T>::digits10 < 20 ? T("1.001001001001001")
+        :                                         T("1.001001001001001001001001001001001")
+    };
+
+    BOOST_TEST_EQ(asin_tiny0 / nl::epsilon(), T(999, -3));
+    BOOST_TEST_EQ(asin_tiny1 / nl::epsilon(), T(1));
+    BOOST_TEST_EQ(asin_tiny2 / nl::epsilon(), ctrl_tiny2);
+}
+
 int main()
 {
     #ifdef BOOST_DECIMAL_GENERATE_CONSTANT_SIGS
@@ -188,6 +223,10 @@ int main()
     test_asin<decimal32_t>();
     test_asin<decimal64_t>();
 
+    test_asin_edge<decimal32_t>();
+    test_asin_edge<decimal64_t>();
+    test_asin_edge<decimal128_t>();
+
     #if !defined(BOOST_DECIMAL_REDUCE_TEST_DEPTH)
     test_asin<decimal128_t>();
     #endif