Source reorganization. In short:

  * Added directories and moved related files into them:
      - src for the MPFR source files (to build the library).
      - doc for documentation files (except INSTALL, README...).
      - tools for various tools (scripts) and mbench.
      - tune for tuneup-related source files.
      - other for other source files (not distributed in tarballs).
    Existing directories:
      - tests for the source files of the test suite (make check).
      - examples for examples.
      - m4 for m4 files.
  * Renamed configure.in to configure.ac.
  * Added/updated Makefile.am files where needed.
  * Updated acinclude.m4 and configure.ac (AC_CONFIG_FILES line).
  * Updated the documentation (INSTALL, README, doc/README.dev and
    doc/mpfr.texi).
  * Updated NEWS and TODO.
  * Updated the scripts now in tools.

The following script was used:

#!/usr/bin/env zsh
svn mkdir doc other src tools tune
svn mv ${${(M)$(sed -n '/libmpfr_la_SOURCES/,/[^\]$/p' \
         Makefile.am):#*.[ch]}:#get_patches.c} mparam_h.in \
       round_raw_generic.c jyn_asympt.c src
svn mv mbench check_inits_clears coverage get_patches.sh mpfrlint \
  nightly-test update-patchv update-version tools
svn mv bidimensional_sample.c speed.c tuneup.c tune
svn mv *.{c,h} other
svn mv FAQ.html README.dev algorithm* faq.xsl fdl.texi mpfr.texi \
  update-faq doc
svn mv configure.in configure.ac
svn cp Makefile.am src/Makefile.am
svn rm replace_all
[Modifying some files, see above]
svn add doc/Makefile.am
svn add tune/Makefile.am

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@7087 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 243 insertions, 0 deletions

diff --git a/src/jn.c b/src/jn.c
new file mode 100644
index 000000000..3db992e4c
--- /dev/null
+++ b/src/jn.c
@@ -0,0 +1,243 @@
+/* mpfr_j0, mpfr_j1, mpfr_jn -- Bessel functions of 1st kind, integer order.
+   http://www.opengroup.org/onlinepubs/009695399/functions/j0.html
+
+Copyright 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
+Contributed by the Arenaire and Caramel projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU 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 3 of the License, or (at your
+option) any later version.
+
+The GNU 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 GNU MPFR Library; see the file COPYING.LESSER.  If not, see
+http://www.gnu.org/licenses/ or 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)
+              j(n,-z) = (-1)^n j(n,z)
+*/
+
+static int mpfr_jn_asympt (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
+
+int
+mpfr_j0 (mpfr_ptr res, mpfr_srcptr z, mpfr_rnd_t r)
+{
+  return mpfr_jn (res, 0, z, r);
+}
+
+int
+mpfr_j1 (mpfr_ptr res, mpfr_srcptr z, mpfr_rnd_t r)
+{
+  return mpfr_jn (res, 1, z, r);
+}
+
+/* Estimate k0 such that z^2/4 = k0 * (k0 + n)
+   i.e., (sqrt(n^2+z^2)-n)/2 = n/2 * (sqrt(1+(z/n)^2) - 1).
+   Return min(2*k0/log(2), ULONG_MAX).
+*/
+static unsigned long
+mpfr_jn_k0 (long n, mpfr_srcptr z)
+{
+  mpfr_t t, u;
+  unsigned long k0;
+
+  mpfr_init2 (t, 32);
+  mpfr_init2 (u, 32);
+  mpfr_div_si (t, z, n, MPFR_RNDN);
+  mpfr_sqr (t, t, MPFR_RNDN);
+  mpfr_add_ui (t, t, 1, MPFR_RNDN);
+  mpfr_sqrt (t, t, MPFR_RNDN);
+  mpfr_sub_ui (t, t, 1, MPFR_RNDN);
+  mpfr_mul_si (t, t, n, MPFR_RNDN);
+  /* the following is a 32-bit approximation to nearest of log(2) */
+  mpfr_set_str_binary (u, "0.10110001011100100001011111111");
+  mpfr_div (t, t, u, MPFR_RNDN);
+  if (mpfr_fits_ulong_p (t, MPFR_RNDN))
+    k0 = mpfr_get_ui (t, MPFR_RNDN);
+  else
+    k0 = ULONG_MAX;
+  mpfr_clear (t);
+  mpfr_clear (u);
+  return k0;
+}
+
+int
+mpfr_jn (mpfr_ptr res, long n, mpfr_srcptr z, mpfr_rnd_t r)
+{
+  int inex;
+  unsigned long absn;
+  mpfr_prec_t prec, pbound, err;
+  mpfr_exp_t exps, expT;
+  mpfr_t y, s, t, absz;
+  unsigned long k, zz, k0;
+  MPFR_ZIV_DECL (loop);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R n=%d rnd=%d", z, z, n, r),
+                 ("y[%#R]=%R", res, res));
+
+  absn = SAFE_ABS (unsigned long, 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);
+        }
+    }
+
+  /* check for tiny input for j0: j0(z) = 1 - z^2/4 + ..., more precisely
+     |j0(z) - 1| <= z^2/4 for -1 <= z <= 1. */
+  if (n == 0)
+    MPFR_FAST_COMPUTE_IF_SMALL_INPUT (res, __gmpfr_one, -2 * MPFR_GET_EXP (z),
+                                      2, 0, r, return _inexact);
+
+  /* idem for j1: j1(z) = z/2 - z^3/16 + ..., more precisely
+     |j1(z) - z/2| <= |z^3|/16 for -1 <= z <= 1, with the sign of j1(z) - z/2
+     being the opposite of that of z. */
+  if (n == 1)
+    /* we first compute 2j1(z) = z - z^3/8 + ..., then divide by 2 using
+       the "extra" argument of MPFR_FAST_COMPUTE_IF_SMALL_INPUT. */
+    MPFR_FAST_COMPUTE_IF_SMALL_INPUT (res, z, -2 * MPFR_GET_EXP (z), 3,
+                                      0, r, mpfr_div_2ui (res, res, 1, r));
+
+  /* we can use the asymptotic expansion as soon as |z| > p log(2)/2,
+     but to get some margin we use it for |z| > p/2 */
+  pbound = MPFR_PREC (res) / 2 + 3;
+  MPFR_ASSERTN (pbound <= ULONG_MAX);
+  MPFR_ALIAS (absz, z, 1, MPFR_EXP (z));
+  if (mpfr_cmp_ui (absz, pbound) > 0)
+    {
+      inex = mpfr_jn_asympt (res, n, z, r);
+      if (inex != 0)
+        return inex;
+    }
+
+  mpfr_init2 (y, 32);
+
+  /* check underflow case: |j(n,z)| <= 1/sqrt(2 Pi n) (ze/2n)^n
+     (see algorithms.tex) */
+  if (absn > 0)
+    {
+      /* the following is an upper 32-bit approximation of exp(1)/2 */
+      mpfr_set_str_binary (y, "1.0101101111110000101010001011001");
+      if (MPFR_SIGN(z) > 0)
+        mpfr_mul (y, y, z, MPFR_RNDU);
+      else
+        {
+          mpfr_mul (y, y, z, MPFR_RNDD);
+          mpfr_neg (y, y, MPFR_RNDU);
+        }
+      mpfr_div_ui (y, y, absn, MPFR_RNDU);
+      /* now y is an upper approximation of |ze/2n|: y < 2^EXP(y),
+         thus |j(n,z)| < 1/2*y^n < 2^(n*EXP(y)-1).
+         If n*EXP(y) < __gmpfr_emin then we have an underflow.
+         Warning: absn is an unsigned long. */
+      if ((MPFR_EXP(y) < 0 && absn > (unsigned long) (-__gmpfr_emin))
+          || (absn <= (unsigned long) (-MPFR_EMIN_MIN) &&
+              MPFR_EXP(y) < __gmpfr_emin / (mpfr_exp_t) absn))
+        {
+          mpfr_clear (y);
+          return mpfr_underflow (res, (r == MPFR_RNDN) ? MPFR_RNDZ : r,
+                         (n % 2) ? ((n > 0) ? MPFR_SIGN(z) : -MPFR_SIGN(z))
+                                 : MPFR_SIGN_POS);
+        }
+    }
+
+  mpfr_init (s);
+  mpfr_init (t);
+
+  /* the logarithm of the ratio between the largest term in the series
+     and the first one is roughly bounded by k0, which we add to the
+     working precision to take into account this cancellation */
+  k0 = mpfr_jn_k0 (absn, z);
+  prec = MPFR_PREC (res) + k0 + 2 * MPFR_INT_CEIL_LOG2 (MPFR_PREC (res)) + 3;
+
+  MPFR_ZIV_INIT (loop, prec);
+  for (;;)
+    {
+      mpfr_set_prec (y, prec);
+      mpfr_set_prec (s, prec);
+      mpfr_set_prec (t, prec);
+      mpfr_pow_ui (t, z, absn, MPFR_RNDN); /* z^|n| */
+      mpfr_mul (y, z, z, MPFR_RNDN);       /* z^2 */
+      zz = mpfr_get_ui (y, MPFR_RNDU);
+      MPFR_ASSERTN (zz < ULONG_MAX);
+      mpfr_div_2ui (y, y, 2, MPFR_RNDN);   /* z^2/4 */
+      mpfr_fac_ui (s, absn, MPFR_RNDN);    /* |n|! */
+      mpfr_div (t, t, s, MPFR_RNDN);
+      if (absn > 0)
+        mpfr_div_2ui (t, t, absn, MPFR_RNDN);
+      mpfr_set (s, t, MPFR_RNDN);
+      exps = MPFR_EXP (s);
+      expT = exps;
+      for (k = 1; ; k++)
+        {
+          mpfr_mul (t, t, y, MPFR_RNDN);
+          mpfr_neg (t, t, MPFR_RNDN);
+          if (k + absn <= ULONG_MAX / k)
+            mpfr_div_ui (t, t, k * (k + absn), MPFR_RNDN);
+          else
+            {
+              mpfr_div_ui (t, t, k, MPFR_RNDN);
+              mpfr_div_ui (t, t, k + absn, MPFR_RNDN);
+            }
+          exps = MPFR_EXP (t);
+          if (exps > expT)
+            expT = exps;
+          mpfr_add (s, s, t, MPFR_RNDN);
+          exps = MPFR_EXP (s);
+          if (exps > expT)
+            expT = exps;
+          if (MPFR_EXP (t) + (mpfr_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) || ((n & 1) == 0)) ? mpfr_set (res, s, r)
+                                      : mpfr_neg (res, s, r);
+
+  mpfr_clear (y);
+  mpfr_clear (s);
+  mpfr_clear (t);
+
+  return inex;
+}
+
+#define MPFR_JN
+#include "jyn_asympt.c"