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, 365 insertions, 0 deletions

diff --git a/src/pow_z.c b/src/pow_z.c
new file mode 100644
index 000000000..061d6407c
--- /dev/null
+++ b/src/pow_z.c
@@ -0,0 +1,365 @@
+/* mpfr_pow_z -- power function x^z with z a MPZ
+
+Copyright 2005, 2006, 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"
+
+/* y <- x^|z| with z != 0
+   if cr=1: ensures correct rounding of y
+   if cr=0: does not ensure correct rounding, but avoid spurious overflow
+   or underflow, and uses the precision of y as working precision (warning,
+   y and x might be the same variable). */
+static int
+mpfr_pow_pos_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t rnd, int cr)
+{
+  mpfr_t res;
+  mpfr_prec_t prec, err;
+  int inexact;
+  mpfr_rnd_t rnd1, rnd2;
+  mpz_t absz;
+  mp_size_t size_z;
+  MPFR_ZIV_DECL (loop);
+  MPFR_BLOCK_DECL (flags);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R z=? rnd=%d cr=%d", x, x, rnd, cr),
+                 ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+  MPFR_ASSERTD (mpz_sgn (z) != 0);
+
+  if (MPFR_UNLIKELY (mpz_cmpabs_ui (z, 1) == 0))
+    return mpfr_set (y, x, rnd);
+
+  absz[0] = z[0];
+  SIZ (absz) = ABS(SIZ(absz)); /* Hack to get abs(z) */
+  MPFR_MPZ_SIZEINBASE2 (size_z, z);
+
+  /* round toward 1 (or -1) to avoid spurious overflow or underflow,
+     i.e. if an overflow or underflow occurs, it is a real exception
+     and is not just due to the rounding error. */
+  rnd1 = (MPFR_EXP(x) >= 1) ? MPFR_RNDZ
+    : (MPFR_IS_POS(x) ? MPFR_RNDU : MPFR_RNDD);
+  rnd2 = (MPFR_EXP(x) >= 1) ? MPFR_RNDD : MPFR_RNDU;
+
+  if (cr != 0)
+    prec = MPFR_PREC (y) + 3 + size_z + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y));
+  else
+    prec = MPFR_PREC (y);
+  mpfr_init2 (res, prec);
+
+  MPFR_ZIV_INIT (loop, prec);
+  for (;;)
+    {
+      unsigned int inexmul;  /* will be non-zero if res may be inexact */
+      mp_size_t i = size_z;
+
+      /* now 2^(i-1) <= z < 2^i */
+      /* see below (case z < 0) for the error analysis, which is identical,
+         except if z=n, the maximal relative error is here 2(n-1)2^(-prec)
+         instead of 2(2n-1)2^(-prec) for z<0. */
+      MPFR_ASSERTD (prec > (mpfr_prec_t) i);
+      err = prec - 1 - (mpfr_prec_t) i;
+
+      MPFR_BLOCK (flags,
+                  inexmul = mpfr_mul (res, x, x, rnd2);
+                  MPFR_ASSERTD (i >= 2);
+                  if (mpz_tstbit (absz, i - 2))
+                    inexmul |= mpfr_mul (res, res, x, rnd1);
+                  for (i -= 3; i >= 0 && !MPFR_BLOCK_EXCEP; i--)
+                    {
+                      inexmul |= mpfr_mul (res, res, res, rnd2);
+                      if (mpz_tstbit (absz, i))
+                        inexmul |= mpfr_mul (res, res, x, rnd1);
+                    });
+      if (MPFR_LIKELY (inexmul == 0 || cr == 0
+                       || MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)
+                       || MPFR_CAN_ROUND (res, err, MPFR_PREC (y), rnd)))
+        break;
+      /* Can't decide correct rounding, increase the precision */
+      MPFR_ZIV_NEXT (loop, prec);
+      mpfr_set_prec (res, prec);
+    }
+  MPFR_ZIV_FREE (loop);
+
+  /* Check Overflow */
+  if (MPFR_OVERFLOW (flags))
+    {
+      MPFR_LOG_MSG (("overflow\n", 0));
+      inexact = mpfr_overflow (y, rnd, mpz_odd_p (absz) ?
+                               MPFR_SIGN (x) : MPFR_SIGN_POS);
+    }
+  /* Check Underflow */
+  else if (MPFR_UNDERFLOW (flags))
+    {
+      MPFR_LOG_MSG (("underflow\n", 0));
+      if (rnd == MPFR_RNDN)
+        {
+          mpfr_t y2, zz;
+
+          /* We cannot decide now whether the result should be rounded
+             toward zero or +Inf. So, let's use the general case of
+             mpfr_pow, which can do that. But the problem is that the
+             result can be exact! However, it is sufficient to try to
+             round on 2 bits (the precision does not matter in case of
+             underflow, since MPFR does not have subnormals), in which
+             case, the result cannot be exact due to previous filtering
+             of trivial cases. */
+          MPFR_ASSERTD (mpfr_cmp_si_2exp (x, MPFR_SIGN (x),
+                                          MPFR_EXP (x) - 1) != 0);
+          mpfr_init2 (y2, 2);
+          mpfr_init2 (zz, ABS (SIZ (z)) * GMP_NUMB_BITS);
+          inexact = mpfr_set_z (zz, z, MPFR_RNDN);
+          MPFR_ASSERTN (inexact == 0);
+          inexact = mpfr_pow_general (y2, x, zz, rnd, 1,
+                                      (mpfr_save_expo_t *) NULL);
+          mpfr_clear (zz);
+          mpfr_set (y, y2, MPFR_RNDN);
+          mpfr_clear (y2);
+          __gmpfr_flags = MPFR_FLAGS_INEXACT | MPFR_FLAGS_UNDERFLOW;
+        }
+      else
+        {
+          inexact = mpfr_underflow (y, rnd, mpz_odd_p (absz) ?
+                                    MPFR_SIGN (x) : MPFR_SIGN_POS);
+        }
+    }
+  else
+    inexact = mpfr_set (y, res, rnd);
+
+  mpfr_clear (res);
+  return inexact;
+}
+
+/* The computation of y = pow(x,z) is done by
+ *    y = set_ui(1)      if z = 0
+ *    y = pow_ui(x,z)    if z > 0
+ *    y = pow_ui(1/x,-z) if z < 0
+ *
+ * Note: in case z < 0, we could also compute 1/pow_ui(x,-z). However, in
+ * case MAX < 1/MIN, where MAX is the largest positive value, i.e.,
+ * MAX = nextbelow(+Inf), and MIN is the smallest positive value, i.e.,
+ * MIN = nextabove(+0), then x^(-z) might produce an overflow, whereas
+ * x^z is representable.
+ */
+
+int
+mpfr_pow_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t rnd)
+{
+  int   inexact;
+  mpz_t tmp;
+  MPFR_SAVE_EXPO_DECL (expo);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R z=? rnd=%d", x, x, rnd),
+                 ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+  /* x^0 = 1 for any x, even a NaN */
+  if (MPFR_UNLIKELY (mpz_sgn (z) == 0))
+    return mpfr_set_ui (y, 1, rnd);
+
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+    {
+      if (MPFR_IS_NAN (x))
+        {
+          MPFR_SET_NAN (y);
+          MPFR_RET_NAN;
+        }
+      else if (MPFR_IS_INF (x))
+        {
+          /* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
+          /* Inf ^(-n) = 0, sign = + if x>0 or z even */
+          if (mpz_sgn (z) > 0)
+            MPFR_SET_INF (y);
+          else
+            MPFR_SET_ZERO (y);
+          if (MPFR_UNLIKELY (MPFR_IS_NEG (x) && mpz_odd_p (z)))
+            MPFR_SET_NEG (y);
+          else
+            MPFR_SET_POS (y);
+          MPFR_RET (0);
+        }
+      else /* x is zero */
+        {
+          MPFR_ASSERTD (MPFR_IS_ZERO(x));
+          if (mpz_sgn (z) > 0)
+            /* 0^n = +/-0 for any n */
+            MPFR_SET_ZERO (y);
+          else
+            /* 0^(-n) if +/- INF */
+            MPFR_SET_INF (y);
+          if (MPFR_LIKELY (MPFR_IS_POS (x) || mpz_even_p (z)))
+            MPFR_SET_POS (y);
+          else
+            MPFR_SET_NEG (y);
+          MPFR_RET(0);
+        }
+    }
+
+  /* detect exact powers: x^-n is exact iff x is a power of 2
+     Do it if n > 0 too as this is faster and this filtering is
+     needed in case of underflow. */
+  if (MPFR_UNLIKELY (mpfr_cmp_si_2exp (x, MPFR_SIGN (x),
+                                       MPFR_EXP (x) - 1) == 0))
+    {
+      mpfr_exp_t expx = MPFR_EXP (x); /* warning: x and y may be the same
+                                         variable */
+
+      MPFR_LOG_MSG (("x^n with x power of two\n", 0));
+      mpfr_set_si (y, mpz_odd_p (z) ? MPFR_INT_SIGN(x) : 1, rnd);
+      MPFR_ASSERTD (MPFR_IS_FP (y));
+      mpz_init (tmp);
+      mpz_mul_si (tmp, z, expx - 1);
+      MPFR_ASSERTD (MPFR_GET_EXP (y) == 1);
+      mpz_add_ui (tmp, tmp, 1);
+      inexact = 0;
+      if (MPFR_UNLIKELY (mpz_cmp_si (tmp, __gmpfr_emin) < 0))
+        {
+          MPFR_LOG_MSG (("underflow\n", 0));
+          /* |y| is a power of two, thus |y| <= 2^(emin-2), and in
+             rounding to nearest, the value must be rounded to 0. */
+          if (rnd == MPFR_RNDN)
+            rnd = MPFR_RNDZ;
+          inexact = mpfr_underflow (y, rnd, MPFR_SIGN (y));
+        }
+      else if (MPFR_UNLIKELY (mpz_cmp_si (tmp, __gmpfr_emax) > 0))
+        {
+          MPFR_LOG_MSG (("overflow\n", 0));
+          inexact = mpfr_overflow (y, rnd, MPFR_SIGN (y));
+        }
+      else
+        MPFR_SET_EXP (y, mpz_get_si (tmp));
+      mpz_clear (tmp);
+      MPFR_RET (inexact);
+    }
+
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  if (mpz_sgn (z) > 0)
+    {
+      inexact = mpfr_pow_pos_z (y, x, z, rnd, 1);
+      MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
+    }
+  else
+    {
+      /* Declaration of the intermediary variable */
+      mpfr_t t;
+      mpfr_prec_t Nt;   /* Precision of the intermediary variable */
+      mpfr_rnd_t rnd1;
+      mp_size_t size_z;
+      MPFR_ZIV_DECL (loop);
+
+      MPFR_MPZ_SIZEINBASE2 (size_z, z);
+
+      /* initial working precision */
+      Nt = MPFR_PREC (y);
+      Nt = Nt + size_z + 3 + MPFR_INT_CEIL_LOG2 (Nt);
+      /* ensures Nt >= bits(z)+2 */
+
+      /* initialise of intermediary variable */
+      mpfr_init2 (t, Nt);
+
+      /* We will compute rnd(rnd1(1/x) ^ (-z)), where rnd1 is the rounding
+         toward sign(x), to avoid spurious overflow or underflow. */
+      rnd1 = MPFR_EXP (x) < 1 ? MPFR_RNDZ :
+        (MPFR_SIGN (x) > 0 ? MPFR_RNDU : MPFR_RNDD);
+
+      MPFR_ZIV_INIT (loop, Nt);
+      for (;;)
+        {
+          MPFR_BLOCK_DECL (flags);
+
+          /* compute (1/x)^(-z), -z>0 */
+          /* As emin = -emax, an underflow cannot occur in the division.
+             And if an overflow occurs, then this means that x^z overflows
+             too (since we have rounded toward 1 or -1). */
+          MPFR_BLOCK (flags, mpfr_ui_div (t, 1, x, rnd1));
+          MPFR_ASSERTD (! MPFR_UNDERFLOW (flags));
+          /* t = (1/x)*(1+theta) where |theta| <= 2^(-Nt) */
+          if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
+            goto overflow;
+          MPFR_BLOCK (flags, mpfr_pow_pos_z (t, t, z, rnd, 0));
+          /* Now if z=-n, t = x^z*(1+theta)^(2n-1) where |theta| <= 2^(-Nt),
+             with theta maybe different from above. If (2n-1)*2^(-Nt) <= 1/2,
+             which is satisfied as soon as Nt >= bits(z)+2, then we can use
+             Lemma \ref{lemma_graillat} from algorithms.tex, which yields
+             t = x^z*(1+theta) with |theta| <= 2(2n-1)*2^(-Nt), thus the
+             error is bounded by 2(2n-1) ulps <= 2^(bits(z)+2) ulps. */
+          if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
+            {
+            overflow:
+              MPFR_ZIV_FREE (loop);
+              mpfr_clear (t);
+              MPFR_SAVE_EXPO_FREE (expo);
+              MPFR_LOG_MSG (("overflow\n", 0));
+              return mpfr_overflow (y, rnd,
+                                    mpz_odd_p (z) ? MPFR_SIGN (x) :
+                                    MPFR_SIGN_POS);
+            }
+          if (MPFR_UNLIKELY (MPFR_UNDERFLOW (flags)))
+            {
+              MPFR_ZIV_FREE (loop);
+              mpfr_clear (t);
+              MPFR_LOG_MSG (("underflow\n", 0));
+              if (rnd == MPFR_RNDN)
+                {
+                  mpfr_t y2, zz;
+
+                  /* We cannot decide now whether the result should be
+                     rounded toward zero or away from zero. So, like
+                     in mpfr_pow_pos_z, let's use the general case of
+                     mpfr_pow in precision 2. */
+                  MPFR_ASSERTD (mpfr_cmp_si_2exp (x, MPFR_SIGN (x),
+                                                  MPFR_EXP (x) - 1) != 0);
+                  mpfr_init2 (y2, 2);
+                  mpfr_init2 (zz, ABS (SIZ (z)) * GMP_NUMB_BITS);
+                  inexact = mpfr_set_z (zz, z, MPFR_RNDN);
+                  MPFR_ASSERTN (inexact == 0);
+                  inexact = mpfr_pow_general (y2, x, zz, rnd, 1,
+                                              (mpfr_save_expo_t *) NULL);
+                  mpfr_clear (zz);
+                  mpfr_set (y, y2, MPFR_RNDN);
+                  mpfr_clear (y2);
+                  MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_UNDERFLOW);
+                  goto end;
+                }
+              else
+                {
+                  MPFR_SAVE_EXPO_FREE (expo);
+                  return mpfr_underflow (y, rnd, mpz_odd_p (z) ?
+                                         MPFR_SIGN (x) : MPFR_SIGN_POS);
+                }
+            }
+          if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - size_z - 2, MPFR_PREC (y),
+                                           rnd)))
+            break;
+          /* actualisation of the precision */
+          MPFR_ZIV_NEXT (loop, Nt);
+          mpfr_set_prec (t, Nt);
+        }
+      MPFR_ZIV_FREE (loop);
+
+      inexact = mpfr_set (y, t, rnd);
+      mpfr_clear (t);
+    }
+
+ end:
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd);
+}