Investigate small-arg logic as in issue

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

@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED T bessel_jn(int n, T x, const Policy& pol)
             current = value;
         }
     }
-    else if((x < 1) || (n > x * x / 4) || (x < 5))
+    else if((x < 5) || (n > x * x / 4))
     {
        return factor * bessel_j_small_z_series(T(n), x, pol);
     }

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

@@ -327,7 +327,10 @@ namespace boost { namespace math {
          // x is positive until reflection
          W = T(2) / (x * pi<T>());               // Wronskian
          T Yv_scale = 1;
-         if(((kind & need_y) == 0) && ((x < 1) || (v > x * x / 4) || (x < 5)))
+
+         const bool kind_does_not_need_y { ((kind & need_y) == 0) };
+
+         if(kind_does_not_need_y && ((x < 5) || (v > x * x / 4)))
          {
             //
             // This series will actually converge rapidly for all small

test/test_bessel_j.cpp

@@ -345,7 +345,3 @@ BOOST_AUTO_TEST_CASE( test_main )
       "to pass.</note>" << std::endl;
 #endif
 }
-
-
-
-

test/test_bessel_j.hpp

@@ -128,6 +128,82 @@ void do_test_sph_bessel_j(const T& data, const char* type_name, const char* test
 #endif
 }
 
+template<class T>
+auto test_issue1292_n() -> void
+{
+  using local_ctrl_array_type = std::array<T, std::size_t { UINT8_C(43) }>;
+
+  // Table[N[BesselJ[3, n/10], 40], {n, 9, 51, 1}]
+  const local_ctrl_array_type ctrl_data =
+  {{
+    SC_(0.01443402847586617545767791623904539755731), SC_(0.01956335398266840591890532162175150825451), SC_(0.02569452861246328174726417617756888741432), SC_(0.03287433692499494270867882730165246683837),
+    SC_(0.04113582571991693187673486447516908751463), SC_(0.05049771328895129623567992727476043273558), SC_(0.06096395114113963064394955997646387979571), SC_(0.07252344333261900300034928368068248675877),
+    SC_(0.08514992694801526415321095754253909148633), SC_(0.09880201565861918291536618746528733463749), SC_(0.1134234066389601112649841240858617923591), SC_(0.1289432494744020510987933329692398352700),
+    SC_(0.1452766740542063665759023355570418120750), SC_(0.1623254728332874543121706910035271736854), SC_(0.1799789312775334540800304157279732327839), SC_(0.1981147987975668248498434552081155790183),
+    SC_(0.2166003910391135247666890035159637217168), SC_(0.2352938130489638091015220916013129483423), SC_(0.2540452915872273499615464996563039918262), SC_(0.2726986037216204380267188592437356599939),
+    SC_(0.2910925878291867784836313080855848616815), SC_(0.3090627222552516436182601949468331494291), SC_(0.3264427561473409695937042738575781129080), SC_(0.3430663764006682009386373318558777864023),
+    SC_(0.3587688942275418259451574456258027163924), SC_(0.3733889346000900583527754127339797472980), SC_(0.3867701117168813668578718121131100327218), SC_(0.3987626737105880326848194417650226836608),
+    SC_(0.4092251000454309977422936498249743734653), SC_(0.4180256354477855744864458808409348352597), SC_(0.4250437447674560017637404058105525727991), SC_(0.4301714738756219403581834788533355563393),
+    SC_(0.4333147025616927046073022200802734463060), SC_(0.4343942763872007823091130214493427347554), SC_(0.4333470055809823422144251313032973397899), SC_(0.4301265203055088083605755042771532591535),
+    SC_(0.4247039729774556002468140098011553543390), SC_(0.4170685797734672711167804755454067582755), SC_(0.4072279949807128989552790124633945783765), SC_(0.3952085134465309348696666123753181072022),
+    SC_(0.3810550980268886849843356923521907577982), SC_(0.3648312306136669944635769493587219791343), SC_(0.3466185870197064968846647990300282094299)
+  }};
+
+  const T tolerance { 128 * std::numeric_limits<T>::epsilon() };
+
+  int n_val { 9 };
+
+  for(const T& ctrl: ctrl_data)
+  {
+    const T x_val { static_cast<T>(static_cast<T>(n_val) / 10) };
+
+    const T jn_val { boost::math::cyl_bessel_j(3, x_val) };
+
+    ++n_val;
+
+    BOOST_CHECK_CLOSE_FRACTION(jn_val, ctrl, tolerance);
+  }
+}
+
+template<class T>
+auto test_issue1292_vu() -> void
+{
+  using local_ctrl_array_type = std::array<T, std::size_t { UINT8_C(43) }>;
+
+  // Table[N[BesselJ[31 / 10, n/10], 40], {n, 9, 51, 1}]
+  const local_ctrl_array_type ctrl_data =
+  {{
+    SC_(0.01175139795214295170487105485346781171863), SC_(0.01610092560641321584451701371378836908343), SC_(0.02135659148701787280713314897691402425560), SC_(0.02757316602094671775387912184375438913864),
+    SC_(0.03479372470942323424236519547108889796879), SC_(0.04304884612770317349181083608393216357649), SC_(0.05235595486839477302545989170267853515412), SC_(0.06271881444009116864560457340917173135492),
+    SC_(0.07412717428914531462554459978389560408816), SC_(0.08655657401374878955779092959288219537482), SC_(0.09996830657138141192006478769855556316995), SC_(0.1143095409011066041623799431143340837007),
+    SC_(0.1295136029333754366226206053365805922136), SC_(0.1455004124749064242445094865982308151833), SC_(0.1621770719619318324763655518038365467780), SC_(0.1794386015949089605595848208470049166853),
+    SC_(0.1971688139222575484595939469080319406355), SC_(0.2152413195483352761119610246805962611319), SC_(0.2335206543185642795903443565627832597552), SC_(0.2518635170977563283446184976264924077045),
+    SC_(0.2701201061202457234361463802484836927464), SC_(0.2881355408650536940851830262098172944660), SC_(0.3057513555072237123913927136839853900197), SC_(0.3228070492275195774383850177821175151772),
+    SC_(0.3391416780352496831991017115498371039332), SC_(0.3545954722799571667706920253581728149226), SC_(0.3690114637024459111815176585531943143085), SC_(0.3822371057078773326211699424651752096338),
+    SC_(0.3941258705356621024731438508712990073773), SC_(0.4045388071531719615179931506197074798366), SC_(0.4133460440118967760814988295083688541739), SC_(0.4204282212729730452147271372029342292548),
+    SC_(0.4256778377298582292448895379334671298297), SC_(0.4290004984236535775073755577697874033289), SC_(0.4303160498540635572666996674883665298558), SC_(0.4295595907277138677145484170304736319185),
+    SC_(0.4266823473457215250850626209433240464185), SC_(0.4216524040030023831246842156638018726147), SC_(0.4144552801406973126588418824207056743782), SC_(0.4050943474472003316564108983454900189419),
+    SC_(0.3935910816286283019261303507307813773886), SC_(0.3799851451515116989978414766085547417497), SC_(0.3643342988837623802358278078893847672838)
+  }};
+
+  const T tolerance { 128 * std::numeric_limits<T>::epsilon() };
+
+  const T vu_val { static_cast<T>(static_cast<T>(31) / 10) };
+
+  int n_val { 9 };
+
+  for(const T& ctrl : ctrl_data)
+  {
+    const T x_val { static_cast<T>(static_cast<T>(n_val) / 10) };
+
+    const T jn_val { boost::math::cyl_bessel_j(vu_val, x_val) };
+
+    ++n_val;
+
+    BOOST_CHECK_CLOSE_FRACTION(jn_val, ctrl, tolerance);
+  }
+}
+
 template <class T>
 void test_bessel(T, const char* name)
 {
@@ -261,6 +337,10 @@ void test_bessel(T, const char* name)
     //
     // Some special cases:
     //
+
+    test_issue1292_n<double>();
+    test_issue1292_vu<double>();
+
     BOOST_CHECK_EQUAL(boost::math::sph_bessel(0, T(0)), T(1));
     BOOST_CHECK_EQUAL(boost::math::sph_bessel(1, T(0)), T(0));
     BOOST_CHECK_EQUAL(boost::math::sph_bessel(100000, T(0)), T(0));