From 18cb92bcde025abe9d39ad10cc1e442908289dc9 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Sun, 24 Oct 2021 19:10:36 +0100
Subject: [PATCH 1/3] Update limits used in erf/erfc approximations. Fixes
 https://github.com/boostorg/math/issues/710.

---
 include/boost/math/special_functions/erf.hpp |  4 +-
 test/Jamfile.v2                              |  1 +
 test/erf_limits_test.cpp                     | 73 ++++++++++++++++++++
 3 files changed, 76 insertions(+), 2 deletions(-)
 create mode 100644 test/erf_limits_test.cpp

diff --git a/include/boost/math/special_functions/erf.hpp b/include/boost/math/special_functions/erf.hpp
index 1f1071fc4d..69c6bd22d0 100644
--- a/include/boost/math/special_functions/erf.hpp
+++ b/include/boost/math/special_functions/erf.hpp
@@ -260,7 +260,7 @@ T erf_imp(T z, bool invert, const Policy& pol, const std::integral_constant<int,
          result = z * (Y + tools::evaluate_polynomial(P, zz) / tools::evaluate_polynomial(Q, zz));
       }
    }
-   else if(invert ? (z < 28) : (z < 5.8f))
+   else if(invert ? (z < 28) : (z < 5.93f))
    {
       //
       // We'll be calculating erfc:
@@ -483,7 +483,7 @@ T erf_imp(T z, bool invert, const Policy& pol, const std::integral_constant<int,
          result = z * (Y + tools::evaluate_polynomial(P, T(z * z)) / tools::evaluate_polynomial(Q, T(z * z)));
       }
    }
-   else if(invert ? (z < 110) : (z < 6.4f))
+   else if(invert ? (z < 110) : (z < 6.6f))
    {
       //
       // We'll be calculating erfc:
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index dc6682abaf..cfca783981 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -194,6 +194,7 @@ test-suite special_fun :
    [ run test_jacobi_zeta.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
    [ run test_heuman_lambda.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
    [ run test_erf.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
+   [ run erf_limits_test.cpp ]
    [ run test_expint.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
    [ run test_factorials.cpp pch ../../test/build//boost_unit_test_framework  ]
    [ run test_gamma.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
diff --git a/test/erf_limits_test.cpp b/test/erf_limits_test.cpp
new file mode 100644
index 0000000000..a7adda5c7c
--- /dev/null
+++ b/test/erf_limits_test.cpp
@@ -0,0 +1,73 @@
+//  (C) Copyright John Maddock 2021.
+//  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)
+
+//
+// This test verifies that the limits we use in the numerical approximations to erf/erc
+// are indeed correct.  The values tested must of course match the values used in erf.hpp.
+// See https://github.com/boostorg/math/issues/710
+//
+
+#define BOOST_TEST_MODULE erf_limits
+
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/test/included/unit_test.hpp>
+
+#include <cfloat>
+
+BOOST_AUTO_TEST_CASE(limits_53_digits)
+{
+   double arg = 5.93f;
+
+   double t = (double)boost::math::erf(boost::multiprecision::cpp_bin_float_50(arg));
+   BOOST_CHECK_EQUAL(t, 1.0);
+
+   arg = 5.9;
+   BOOST_CHECK_LT(boost::math::erf(arg), 1.0);
+
+   arg = 28;
+   t = (double)boost::math::erfc(boost::multiprecision::cpp_bin_float_50(arg));
+   BOOST_CHECK_EQUAL(t, 0.0);
+
+   arg = 27.2;
+
+   BOOST_CHECK_GT(boost::math::erfc(arg), 0.0);
+}
+
+BOOST_AUTO_TEST_CASE(limits_64_digits)
+{
+   float arg = 6.6f;
+
+   boost::multiprecision::cpp_bin_float_double_extended t = (boost::multiprecision::cpp_bin_float_double_extended)boost::math::erf(boost::multiprecision::cpp_bin_float_50(arg));
+   BOOST_CHECK_EQUAL(t, 1.0);
+
+#if (LDBL_MANT_DIG == 64) && !defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
+   arg = 6.5;
+   BOOST_CHECK_LT(boost::math::erf(static_cast<long double>(arg)), 1.0L);
+#endif
+   arg = 110;
+   t = (boost::multiprecision::cpp_bin_float_double_extended)boost::math::erfc(boost::multiprecision::cpp_bin_float_50(arg));
+   BOOST_CHECK_EQUAL(t, 0.0);
+
+#if (LDBL_MANT_DIG == 64) && !defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
+   arg = 106.5;
+   BOOST_CHECK_GT(boost::math::erfc(static_cast<long double>(arg)), 0.0L);
+#endif
+}
+
+BOOST_AUTO_TEST_CASE(limits_113_digits)
+{
+   //
+   // This limit is not actually used in the code, logged here for future reference...
+   //
+   float arg = 8.8f;
+
+   boost::multiprecision::cpp_bin_float_quad t = (boost::multiprecision::cpp_bin_float_quad)boost::math::erf(boost::multiprecision::cpp_bin_float_50(arg));
+   BOOST_CHECK_EQUAL(t, 1.0);
+
+   arg = 110;
+   t = (boost::multiprecision::cpp_bin_float_quad)boost::math::erfc(boost::multiprecision::cpp_bin_float_50(arg));
+   BOOST_CHECK_EQUAL(t, 0.0);
+}

From d8078c71a34214de536433d3edaedb7684760e26 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Mon, 1 Nov 2021 18:32:07 +0000
Subject: [PATCH 2/3] Fix copyright declaration.

---
 test/erf_limits_test.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/erf_limits_test.cpp b/test/erf_limits_test.cpp
index a7adda5c7c..3fc599fd8a 100644
--- a/test/erf_limits_test.cpp
+++ b/test/erf_limits_test.cpp
@@ -1,4 +1,4 @@
-//  (C) Copyright John Maddock 2021.
+//  Copyright John Maddock 2021.
 //  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)

From 08ff95dd148d3daf7a8f7855c5156460cf3ea07c Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Mon, 1 Nov 2021 19:24:31 +0000
Subject: [PATCH 3/3] Convert file to ASCII.

---
 test/erf_limits_test.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/erf_limits_test.cpp b/test/erf_limits_test.cpp
index 3fc599fd8a..cf05bbd7a9 100644
--- a/test/erf_limits_test.cpp
+++ b/test/erf_limits_test.cpp
@@ -1,4 +1,4 @@
-//  Copyright John Maddock 2021.
+//  (C) Copyright John Maddock 2021.
 //  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)