Sync code from obs

1 files changed, 174 insertions, 0 deletions

diff --git a/log.c b/log.c
new file mode 100644
index 0000000..9292198
--- /dev/null
+++ b/log.c
@@ -0,0 +1,174 @@
+/* mpfr_log -- natural logarithm of a floating-point number
+
+Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao 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"
+
+/* The computation of log(x) is done using the formula :
+     if we want p bits of the result,
+
+                       pi
+          log(x) ~ ------------  -   m log 2
+                    2 AG(1,4/s)
+
+     where s = x 2^m > 2^(p/2)
+
+     More precisely, if F(x) = int(1/sqrt(1-(1-x^2)*sin(t)^2), t=0..PI/2),
+     then for s>=1.26 we have log(s) < F(4/s) < log(s)*(1+4/s^2)
+     from which we deduce pi/2/AG(1,4/s)*(1-4/s^2) < log(s) < pi/2/AG(1,4/s)
+     so the relative error 4/s^2 is < 4/2^p i.e. 4 ulps.
+*/
+
+int
+mpfr_log (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode)
+{
+  int inexact;
+  mpfr_prec_t p, q;
+  mpfr_t tmp1, tmp2;
+  mp_limb_t *tmp1p, *tmp2p;
+  MPFR_SAVE_EXPO_DECL (expo);
+  MPFR_ZIV_DECL (loop);
+  MPFR_TMP_DECL(marker);
+
+  MPFR_LOG_FUNC (("a[%#R]=%R rnd=%d", a, a, rnd_mode),
+                 ("r[%#R]=%R inexact=%d", r, r, inexact));
+
+  /* Special cases */
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a)))
+    {
+      /* If a is NaN, the result is NaN */
+      if (MPFR_IS_NAN (a))
+        {
+          MPFR_SET_NAN (r);
+          MPFR_RET_NAN;
+        }
+      /* check for infinity before zero */
+      else if (MPFR_IS_INF (a))
+        {
+          if (MPFR_IS_NEG (a))
+            /* log(-Inf) = NaN */
+            {
+              MPFR_SET_NAN (r);
+              MPFR_RET_NAN;
+            }
+          else /* log(+Inf) = +Inf */
+            {
+              MPFR_SET_INF (r);
+              MPFR_SET_POS (r);
+              MPFR_RET (0);
+            }
+        }
+      else /* a is zero */
+        {
+          MPFR_ASSERTD (MPFR_IS_ZERO (a));
+          MPFR_SET_INF (r);
+          MPFR_SET_NEG (r);
+          MPFR_RET (0); /* log(0) is an exact -infinity */
+        }
+    }
+  /* If a is negative, the result is NaN */
+  else if (MPFR_UNLIKELY (MPFR_IS_NEG (a)))
+    {
+      MPFR_SET_NAN (r);
+      MPFR_RET_NAN;
+    }
+  /* If a is 1, the result is 0 */
+  else if (MPFR_UNLIKELY (MPFR_GET_EXP (a) == 1 && mpfr_cmp_ui (a, 1) == 0))
+    {
+      MPFR_SET_ZERO (r);
+      MPFR_SET_POS (r);
+      MPFR_RET (0); /* only "normal" case where the result is exact */
+    }
+
+  q = MPFR_PREC (r);
+
+  /* use initial precision about q+lg(q)+5 */
+  p = q + 5 + 2 * MPFR_INT_CEIL_LOG2 (q);
+  /* % ~(mpfr_prec_t)GMP_NUMB_BITS  ;
+     m=q; while (m) { p++; m >>= 1; }  */
+  /* if (MPFR_LIKELY(p % GMP_NUMB_BITS != 0))
+      p += GMP_NUMB_BITS - (p%GMP_NUMB_BITS); */
+
+  MPFR_TMP_MARK(marker);
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  MPFR_ZIV_INIT (loop, p);
+  for (;;)
+    {
+      mp_size_t size;
+      long m;
+      mpfr_exp_t cancel;
+
+      /* Calculus of m (depends on p) */
+      m = (p + 1) / 2 - MPFR_GET_EXP (a) + 1;
+
+      /* All the mpfr_t needed have a precision of p */
+      size = (p-1)/GMP_NUMB_BITS+1;
+      MPFR_TMP_INIT (tmp1p, tmp1, p, size);
+      MPFR_TMP_INIT (tmp2p, tmp2, p, size);
+
+      mpfr_mul_2si (tmp2, a, m, MPFR_RNDN);    /* s=a*2^m,        err<=1 ulp  */
+      mpfr_div (tmp1, __gmpfr_four, tmp2, MPFR_RNDN);/* 4/s,      err<=2 ulps */
+      mpfr_agm (tmp2, __gmpfr_one, tmp1, MPFR_RNDN); /* AG(1,4/s),err<=3 ulps */
+      mpfr_mul_2ui (tmp2, tmp2, 1, MPFR_RNDN); /* 2*AG(1,4/s),    err<=3 ulps */
+      mpfr_const_pi (tmp1, MPFR_RNDN);         /* compute pi,     err<=1ulp   */
+      mpfr_div (tmp2, tmp1, tmp2, MPFR_RNDN);  /* pi/2*AG(1,4/s), err<=5ulps  */
+      mpfr_const_log2 (tmp1, MPFR_RNDN);      /* compute log(2),  err<=1ulp   */
+      mpfr_mul_si (tmp1, tmp1, m, MPFR_RNDN); /* compute m*log(2),err<=2ulps  */
+      mpfr_sub (tmp1, tmp2, tmp1, MPFR_RNDN); /* log(a),    err<=7ulps+cancel */
+
+      if (MPFR_LIKELY (MPFR_IS_PURE_FP (tmp1) && MPFR_IS_PURE_FP (tmp2)))
+        {
+          cancel = MPFR_GET_EXP (tmp2) - MPFR_GET_EXP (tmp1);
+          MPFR_LOG_MSG (("canceled bits=%ld\n", (long) cancel));
+          MPFR_LOG_VAR (tmp1);
+          if (MPFR_UNLIKELY (cancel < 0))
+            cancel = 0;
+
+          /* we have 7 ulps of error from the above roundings,
+             4 ulps from the 4/s^2 second order term,
+             plus the canceled bits */
+          if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp1, p-cancel-4, q, rnd_mode)))
+            break;
+
+          /* VL: I think it is better to have an increment that it isn't
+             too low; in particular, the increment must be positive even
+             if cancel = 0 (can this occur?). */
+          p += cancel >= 8 ? cancel : 8;
+        }
+      else
+        {
+          /* TODO: find why this case can occur and what is best to do
+             with it. */
+          p += 32;
+        }
+
+      MPFR_ZIV_NEXT (loop, p);
+    }
+  MPFR_ZIV_FREE (loop);
+  inexact = mpfr_set (r, tmp1, rnd_mode);
+  /* We clean */
+  MPFR_TMP_FREE(marker);
+
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (r, inexact, rnd_mode);
+}