Handle issue 1255 and update docs

README.md

@@ -3,11 +3,12 @@ Boost Math Library
 
 >ANNOUNCEMENT: This library requires a compliant C++14 compiler.
 
+
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+| Codecov          | [![codecov](https://codecov.io/gh/boostorg/math/branch/master/graph/badge.svg)](https://codecov.io/gh/boostorg/math/branch/master)                                   | [![codecov](https://codecov.io/gh/boostorg/math/branch/develop/graph/badge.svg)](https://codecov.io/gh/boostorg/math/branch/develop) |
 
 
 The Math library provides numerous advanced mathematical functions
@@ -26,11 +27,11 @@ Utility functions for dealing with floating point arithmetic, includes functions
 
 ### Specific Width Floating Point Types
 
-A set of typedefs similar to those provided by `<cstdint>` but for floating point types.
+A set of `typedef`s similar to those provided by C++20's `<stdfloat>` but in `namespace boost`.
 
 ### Mathematical Constants
 
-A wide range of constants ranging from various multiples of π, fractions, Euler's constant, etc.
+A wide range of constants ranging from fractions to various multiples of $\pi$, Euler's constant, etc.
 
 These are of course usable from template code, or as non-templates with a simplified interface if that is more appropriate.
 
@@ -100,12 +101,12 @@ The full documentation is available on [boost.org](http://www.boost.org/doc/libs
 
 ### Standalone Mode
 
-Defining BOOST_MATH_STANDALONE allows Boost.Math to be used without any Boost dependencies.
+Defining `BOOST_MATH_STANDALONE` allows Boost.Math to be used without any Boost dependencies.
 Some functionality is reduced in this mode. A static_assert message will alert you
 if a particular feature has been disabled by standalone mode. Standalone mode is not designed to 
 be used with the rest of boost, and may result in compiler errors.
 
-## Supported Compilers ##
+## Supported Compilers
 
 The following compilers are tested with the CI system, and are known to work.
 Currently a compiler that is fully compliant with C++14 is required to use Boost.Math.
@@ -114,7 +115,7 @@ Currently a compiler that is fully compliant with C++14 is required to use Boost
 * clang++ 5 or later
 * Visual Studio 2015 (14.0) or later
 
-## Support, bugs and feature requests ##
+## Support, bugs and feature requests
 
 Bugs and feature requests can be reported through the [GitHub issue tracker](https://github.com/boostorg/math/issues)
 (see [open issues](https://github.com/boostorg/math/issues) and
@@ -125,7 +126,7 @@ You can submit your changes through a [pull request](https://github.com/boostorg
 There is no mailing-list specific to Boost Math, although you can use the general-purpose Boost [mailing-list](http://lists.boost.org/mailman/listinfo.cgi/boost-users) using the tag [math].
 
 
-## Development ##
+## Development
 
 Clone the whole boost project, which includes the individual Boost projects as submodules ([see boost+git doc](https://github.com/boostorg/boost/wiki/Getting-Started)):
 
@@ -135,7 +136,8 @@ Clone the whole boost project, which includes the individual Boost projects as s
 
 The Boost Math Library is located in `libs/math/`.
 
-### Running tests ###
+### Running tests
+
 First, make sure you are in `libs/math/test`.
 You can either run all the tests listed in `Jamfile.v2` or run a single test:
 
@@ -144,7 +146,8 @@ You can either run all the tests listed in `Jamfile.v2` or run a single test:
     test$ # A more advanced syntax, demoing various options for building the tests:
     test$ ../../../b2 -a -j2 -q --reconfigure toolset=clang cxxflags="--std=c++14 -fsanitize=address -fsanitize=undefined" linkflags="-fsanitize=undefined -fsanitize=address"
 
-### Continuous Integration ###
+### Continuous Integration
+
 The default action for a PR or commit to a PR is for CI to run the full complement of tests. The following can be appended to the end of a commit message to modify behavior:
 
     * [ci skip] to skip all tests
@@ -153,7 +156,8 @@ The default action for a PR or commit to a PR is for CI to run the full compleme
     * [windows] to test MSVC-14.0, MSVC-14.2, MSVC-14.3, CYGWIN, and mingw on the latest version of Windows.
     * [standalone] to run standalone mode compile tests
      
-### Building documentation ###
+
+### Building documentation
 
 Full instructions can be found [here](https://svn.boost.org/trac10/wiki/BoostDocs/GettingStarted), but to reiterate slightly:
 

include/boost/math/special_functions/detail/bessel_yn.hpp

@@ -59,7 +59,7 @@ BOOST_MATH_GPU_ENABLED T bessel_yn(int n, T x, const Policy& pol)
        value = bessel_yn_small_z(n, x, &scale, pol);
        if (tools::max_value<T>() * fabs(scale) < fabs(value))
           return boost::math::sign(scale) * boost::math::sign(value) * policies::raise_overflow_error<T>(function, nullptr, pol);
-       value /= scale;
+       value = (factor * value) / scale;
     }
     else if(asymptotic_bessel_large_x_limit(n, x))
     {

test/Jamfile.v2

@@ -194,6 +194,7 @@ test-suite special_fun :
    [ run git_issue_1139.cpp ]
    [ run git_issue_1175.cpp ]
    [ run git_issue_1194.cpp ]
+   [ run git_issue_1255.cpp ]
    [ run special_functions_test.cpp /boost/test//boost_unit_test_framework  ]
    [ run test_airy.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework  ]
    [ run test_bessel_j.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework  ]

test/git_issue_1255.cpp

@@ -0,0 +1,30 @@
+//  (C) Copyright Christopher Kormanyos 2025.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/core/lightweight_test.hpp>
+#include <boost/math/special_functions/bessel.hpp>
+
+#include <cmath>
+#include <limits>
+
+auto main() -> int
+{
+  using float_type = float;
+
+  const float_type x { 0x1.03ebbp-128F };
+
+  const float_type ctrl { 0x1.41085ep+127F };
+
+  const float_type result = ::boost::math::cyl_neumann(-1, x);
+
+  const float_type tol = std::numeric_limits<float_type>::epsilon() * 16;
+
+  using std::fabs;
+
+  BOOST_TEST(result > 0);
+  BOOST_TEST(fabs(1 - (result / ctrl)) < tol);
+
+  return boost::report_errors();
+}