added Bessel functions of first kind: j0, j1, jn

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@4385 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 140 insertions, 0 deletions

diff --git a/jn.c b/jn.c
new file mode 100644
index 000000000..7dab618f4
--- /dev/null
+++ b/jn.c
@@ -0,0 +1,140 @@
+/* mpfr_j0, mpfr_j1, mpfr_jn -- Bessel functions of 1st kind and integer order.
+   http://www.opengroup.org/onlinepubs/009695399/functions/j0.html
+
+Copyright 2007 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+
+This file is part of the MPFR Library.
+
+The MPFR Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version.
+
+The MPFR Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the MPFR Library; see the file COPYING.LIB.  If not, write to
+the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA 02110-1301, USA. */
+
+#define MPFR_NEED_LONGLONG_H
+#include "mpfr-impl.h"
+
+/* Relations: j(-n,z) = (-1)^n j(n,z) */
+
+int
+mpfr_j0 (mpfr_ptr res, mpfr_srcptr z, mp_rnd_t r)
+{
+  return mpfr_jn (res, z, 0, r);
+}
+
+int
+mpfr_j1 (mpfr_ptr res, mpfr_srcptr z, mp_rnd_t r)
+{
+  return mpfr_jn (res, z, 1, r);
+}
+
+int
+mpfr_jn (mpfr_ptr res, mpfr_srcptr z, int n, mp_rnd_t r)
+{
+  int inex, absn;
+  mp_prec_t prec, err;
+  mp_exp_t exps, expT;
+  mpfr_t y, s, t;
+  unsigned long k, zz;
+  MPFR_ZIV_DECL (loop);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R n=%d rnd=%d", z, z, n, r),
+                 ("y[%#R]=%R inexact=%d", res, res, inex));
+
+  absn = (n >= 0) ? n : -n;
+
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (z)))
+    {
+      if (MPFR_IS_NAN (z))
+        {
+          MPFR_SET_NAN (res);
+          MPFR_RET_NAN;
+        }
+      /* j(n,z) tends to zero when z goes to +Inf or -Inf, oscillating around
+         0. We choose to return +0 in that case. */
+      else if (MPFR_IS_INF (z)) /* FIXME: according to j(-n,z) = (-1)^n j(n,z)
+                                   we might want to give a sign depending on
+                                   z and n */
+        return mpfr_set_ui (res, 0, r);
+      else /* z=0: j(0,0)=1, j(n odd,+/-0) = +/-0 if n > 0, -/+0 if n < 0,
+              j(n even,+/-0) = +0 */
+        {
+          if (n == 0)
+            return mpfr_set_ui (res, 1, r);
+          else if (absn & 1) /* n odd */
+            return (n > 0) ? mpfr_set (res, z, r) : mpfr_neg (res, z, r);
+          else /* n even */
+            return mpfr_set_ui (res, 0, r);
+        }
+    }
+  
+  prec = MPFR_PREC (res) + MPFR_INT_CEIL_LOG2 (MPFR_PREC (res)) + 3;
+
+  mpfr_init2 (y, prec);
+  mpfr_init2 (s, prec);
+  mpfr_init2 (t, prec);
+
+  MPFR_ZIV_INIT (loop, prec);
+  for (;;)
+    {
+      mpfr_pow_ui (t, z, absn, GMP_RNDN);
+      mpfr_mul (y, z, z, GMP_RNDN);
+      zz = mpfr_get_ui (y, GMP_RNDU);
+      MPFR_ASSERTN (zz < ULONG_MAX);
+      mpfr_div_2ui (y, y, 2, GMP_RNDN);
+      mpfr_fac_ui (s, absn, GMP_RNDN);
+      mpfr_div (t, t, s, GMP_RNDN);
+      if (absn > 0)
+        mpfr_div_2ui (t, t, absn, GMP_RNDN);
+      mpfr_set (s, t, GMP_RNDN);
+      exps = MPFR_EXP (s);
+      expT = exps;
+      for (k = 1; ; k++)
+        {
+          mpfr_mul (t, t, y, GMP_RNDN);
+          mpfr_neg (t, t, GMP_RNDN);
+          if (k + absn <= ULONG_MAX / k)
+            mpfr_div_ui (t, t, k * (k + absn), GMP_RNDN);
+          else
+            {
+              mpfr_div_ui (t, t, k, GMP_RNDN);
+              mpfr_div_ui (t, t, absn, GMP_RNDN);
+            }
+          exps = MPFR_EXP (t);
+          if (exps > expT)
+            expT = exps;
+          mpfr_add (s, s, t, GMP_RNDN);
+          exps = MPFR_EXP (s);
+          if (exps > expT)
+            expT = exps;
+          if (MPFR_EXP (t) + (mp_exp_t) prec <= MPFR_EXP (s) &&
+              zz / (2 * k) < k + n)
+            break;
+        }
+      /* the error is bounded by (4k^2+21/2k+7) ulp(s)*2^(expT-exps)
+         <= (k+2)^2 ulp(s)*2^(2+expT-exps) */
+      err = 2 * MPFR_INT_CEIL_LOG2(k + 2) + 2 + expT - MPFR_EXP (s);
+      if (MPFR_LIKELY (MPFR_CAN_ROUND (s, prec - err, MPFR_PREC(res), r)))
+          break;
+      MPFR_ZIV_NEXT (loop, prec);
+    }
+  MPFR_ZIV_FREE (loop);
+
+  inex = (n >= 0) ? mpfr_set (res, s, r) : mpfr_neg (res, s, r);
+
+  mpfr_clear (y);
+  mpfr_clear (s);
+  mpfr_clear (t);
+
+  return inex;
+}