[gcc] GCC 4.5.0=>4.5.1

gcc/mpfr/exp3.c

Index: gcc/mpfr/exp3.c
diff --git a/gcc/mpfr/exp3.c b/gcc/mpfr/exp3.c
deleted file mode 100644
index 845f78ce4db2d412e78d4668ef0aa1408c6b3556..0000000000000000000000000000000000000000
--- a/gcc/mpfr/exp3.c
+++ /dev/null
@@ -1,333 +0,0 @@
-/* mpfr_exp -- exponential of a floating-point number
-
-Copyright 1999, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 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 2.1 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.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 /* for MPFR_MPZ_SIZEINBASE2 */
-#include "mpfr-impl.h"
-
-/* y <- exp(p/2^r) within 1 ulp, using 2^m terms from the series
-   Assume |p/2^r| < 1.
-   We use the following binary splitting formula:
-   P(a,b) = p if a+1=b, P(a,c)*P(c,b) otherwise
-   Q(a,b) = a*2^r if a+1=b [except Q(0,1)=1], Q(a,c)*Q(c,b) otherwise
-   T(a,b) = P(a,b) if a+1=b, Q(c,b)*T(a,c)+P(a,c)*T(c,b) otherwise
-   Then exp(p/2^r) ~ T(0,i)/Q(0,i) for i so that (p/2^r)^i/i! is small enough.
-
-   Since P(a,b) = p^(b-a), and we consider only values of b-a of the form 2^j,
-   we don't need to compute P(), we only precompute p^(2^j) in the ptoj[] array
-   below.
-
-   Since Q(a,b) is divisible by 2^(r*(b-a-1)), we don't compute the power of
-   two part.
-*/
-static void
-mpfr_exp_rational (mpfr_ptr y, mpz_ptr p, long r, int m,
-                   mpz_t *Q, mp_prec_t *mult)
-{
-  unsigned long n, i, j;
-  mpz_t *S, *ptoj;
-  mp_prec_t *log2_nb_terms;
-  mp_exp_t diff, expo;
-  mp_prec_t precy = MPFR_PREC(y), prec_i_have, prec_ptoj;
-  int k, l;
-
-  MPFR_ASSERTN ((size_t) m < sizeof (long) * CHAR_BIT - 1);
-
-  S    = Q + (m+1);
-  ptoj = Q + 2*(m+1);                     /* ptoj[i] = mantissa^(2^i) */
-  log2_nb_terms = mult + (m+1);
-
-  /* Normalize p */
-  MPFR_ASSERTD (mpz_cmp_ui (p, 0) != 0);
-  n = mpz_scan1 (p, 0); /* number of trailing zeros in p */
-  mpz_tdiv_q_2exp (p, p, n);
-  r -= n; /* since |p/2^r| < 1 and p >= 1, r >= 1 */
-
-  /* Set initial var */
-  mpz_set (ptoj[0], p);
-  for (k = 1; k < m; k++)
-    mpz_mul (ptoj[k], ptoj[k-1], ptoj[k-1]); /* ptoj[k] = p^(2^k) */
-  mpz_set_ui (Q[0], 1);
-  mpz_set_ui (S[0], 1);
-  k = 0;
-  mult[0] = 0; /* the multiplier P[k]/Q[k] for the remaining terms
-                  satisfies P[k]/Q[k] <= 2^(-mult[k]) */
-  log2_nb_terms[0] = 0; /* log2(#terms) [exact in 1st loop where 2^k] */
-  prec_i_have = 0;
-
-  /* Main Loop */
-  n = 1UL << m;
-  for (i = 1; (prec_i_have < precy) && (i < n); i++)
-    {
-      /* invariant: Q[0]*Q[1]*...*Q[k] equals i! */
-      k++;
-      log2_nb_terms[k] = 0; /* 1 term */
-      mpz_set_ui (Q[k], i + 1);
-      mpz_set_ui (S[k], i + 1);
-      j = i + 1; /* we have computed j = i+1 terms so far */
-      l = 0;
-      while ((j & 1) == 0) /* combine and reduce */
-        {
-          /* invariant: S[k] corresponds to 2^l consecutive terms */
-          mpz_mul (S[k], S[k], ptoj[l]);
-          mpz_mul (S[k-1], S[k-1], Q[k]);
-          /* Q[k] corresponds to 2^l consecutive terms too.
-             Since it does not contains the factor 2^(r*2^l),
-             when going from l to l+1 we need to multiply
-             by 2^(r*2^(l+1))/2^(r*2^l) = 2^(r*2^l) */
-          mpz_mul_2exp (S[k-1], S[k-1], r << l);
-          mpz_add (S[k-1], S[k-1], S[k]);
-          mpz_mul (Q[k-1], Q[k-1], Q[k]);
-          log2_nb_terms[k-1] ++; /* number of terms in S[k-1]
-                                    is a power of 2 by construction */
-          MPFR_MPZ_SIZEINBASE2 (prec_i_have, Q[k]);
-          MPFR_MPZ_SIZEINBASE2 (prec_ptoj, ptoj[l]);
-          mult[k-1] += prec_i_have + (r << l) - prec_ptoj - 1;
-          prec_i_have = mult[k] = mult[k-1];
-          /* since mult[k] >= mult[k-1] + nbits(Q[k]),
-             we have Q[0]*...*Q[k] <= 2^mult[k] = 2^prec_i_have */
-          l ++;
-          j >>= 1;
-          k --;
-        }
-    }
-
-  /* accumulate all products in S[0] and Q[0]. Warning: contrary to above,
-     here we do not have log2_nb_terms[k-1] = log2_nb_terms[k]+1. */
-  l = 0; /* number of accumulated terms in the right part S[k]/Q[k] */
-  while (k > 0)
-    {
-      j = log2_nb_terms[k-1];
-      mpz_mul (S[k], S[k], ptoj[j]);
-      mpz_mul (S[k-1], S[k-1], Q[k]);
-      l += 1 << log2_nb_terms[k];
-      mpz_mul_2exp (S[k-1], S[k-1], r * l);
-      mpz_add (S[k-1], S[k-1], S[k]);
-      mpz_mul (Q[k-1], Q[k-1], Q[k]);
-      k--;
-    }
-
-  /* Q[0] now equals i! */
-  MPFR_MPZ_SIZEINBASE2 (prec_i_have, S[0]);
-  diff = (mp_exp_t) prec_i_have - 2 * (mp_exp_t) precy;
-  expo = diff;
-  if (diff >= 0)
-    mpz_div_2exp (S[0], S[0], diff);
-  else
-    mpz_mul_2exp (S[0], S[0], -diff);
-
-  MPFR_MPZ_SIZEINBASE2 (prec_i_have, Q[0]);
-  diff = (mp_exp_t) prec_i_have - (mp_prec_t) precy;
-  expo -= diff;
-  if (diff > 0)
-    mpz_div_2exp (Q[0], Q[0], diff);
-  else
-    mpz_mul_2exp (Q[0], Q[0], -diff);
-
-  mpz_tdiv_q (S[0], S[0], Q[0]);
-  mpfr_set_z (y, S[0], GMP_RNDD);
-  MPFR_SET_EXP (y, MPFR_GET_EXP (y) + expo - r * (i - 1) );
-}
-
-#define shift (BITS_PER_MP_LIMB/2)
-
-int
-mpfr_exp_3 (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
-{
-  mpfr_t t, x_copy, tmp;
-  mpz_t uk;
-  mp_exp_t ttt, shift_x;
-  unsigned long twopoweri;
-  mpz_t *P;
-  mp_prec_t *mult;
-  int i, k, loop;
-  int prec_x;
-  mp_prec_t realprec, Prec;
-  int iter;
-  int inexact = 0;
-  MPFR_SAVE_EXPO_DECL (expo);
-  MPFR_ZIV_DECL (ziv_loop);
-
-  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
-                 ("y[%#R]=%R inexact=%d", y, y, inexact));
-
-  MPFR_SAVE_EXPO_MARK (expo);
-
-  /* decompose x */
-  /* we first write x = 1.xxxxxxxxxxxxx
-     ----- k bits -- */
-  prec_x = MPFR_INT_CEIL_LOG2 (MPFR_PREC (x)) - MPFR_LOG2_BITS_PER_MP_LIMB;
-  if (prec_x < 0)
-    prec_x = 0;
-
-  ttt = MPFR_GET_EXP (x);
-  mpfr_init2 (x_copy, MPFR_PREC(x));
-  mpfr_set (x_copy, x, GMP_RNDD);
-
-  /* we shift to get a number less than 1 */
-  if (ttt > 0)
-    {
-      shift_x = ttt;
-      mpfr_div_2ui (x_copy, x, ttt, GMP_RNDN);
-      ttt = MPFR_GET_EXP (x_copy);
-    }
-  else
-    shift_x = 0;
-  MPFR_ASSERTD (ttt <= 0);
-
-  /* Init prec and vars */
-  realprec = MPFR_PREC (y) + MPFR_INT_CEIL_LOG2 (prec_x + MPFR_PREC (y));
-  Prec = realprec + shift + 2 + shift_x;
-  mpfr_init2 (t, Prec);
-  mpfr_init2 (tmp, Prec);
-  mpz_init (uk);
-
-  /* Main loop */
-  MPFR_ZIV_INIT (ziv_loop, realprec);
-  for (;;)
-    {
-      int scaled = 0;
-      MPFR_BLOCK_DECL (flags);
-
-      k = MPFR_INT_CEIL_LOG2 (Prec) - MPFR_LOG2_BITS_PER_MP_LIMB;
-
-      /* now we have to extract */
-      twopoweri = BITS_PER_MP_LIMB;
-
-      /* Allocate tables */
-      P    = (mpz_t*) (*__gmp_allocate_func) (3*(k+2)*sizeof(mpz_t));
-      for (i = 0; i < 3*(k+2); i++)
-        mpz_init (P[i]);
-      mult = (mp_prec_t*) (*__gmp_allocate_func) (2*(k+2)*sizeof(mp_prec_t));
-
-      /* Particular case for i==0 */
-      mpfr_extract (uk, x_copy, 0);
-      MPFR_ASSERTD (mpz_cmp_ui (uk, 0) != 0);
-      mpfr_exp_rational (tmp, uk, shift + twopoweri - ttt, k + 1, P, mult);
-      for (loop = 0; loop < shift; loop++)
-        mpfr_sqr (tmp, tmp, GMP_RNDD);
-      twopoweri *= 2;
-
-      /* General case */
-      iter = (k <= prec_x) ? k : prec_x;
-      for (i = 1; i <= iter; i++)
-        {
-          mpfr_extract (uk, x_copy, i);
-          if (MPFR_LIKELY (mpz_cmp_ui (uk, 0) != 0))
-            {
-              mpfr_exp_rational (t, uk, twopoweri - ttt, k  - i + 1, P, mult);
-              mpfr_mul (tmp, tmp, t, GMP_RNDD);
-            }
-          MPFR_ASSERTN (twopoweri <= LONG_MAX/2);
-          twopoweri *=2;
-        }
-
-      /* Clear tables */
-      for (i = 0; i < 3*(k+2); i++)
-        mpz_clear (P[i]);
-      (*__gmp_free_func) (P, 3*(k+2)*sizeof(mpz_t));
-      (*__gmp_free_func) (mult, 2*(k+2)*sizeof(mp_prec_t));
-
-      if (shift_x > 0)
-        {
-          MPFR_BLOCK (flags, {
-              for (loop = 0; loop < shift_x - 1; loop++)
-                mpfr_sqr (tmp, tmp, GMP_RNDD);
-              mpfr_sqr (t, tmp, GMP_RNDD);
-            } );
-
-          if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
-            {
-              /* tmp <= exact result, so that it is a real overflow. */
-              inexact = mpfr_overflow (y, rnd_mode, 1);
-              MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
-              break;
-            }
-
-          if (MPFR_UNLIKELY (MPFR_UNDERFLOW (flags)))
-            {
-              /* This may be a spurious underflow. So, let's scale
-                 the result. */
-              mpfr_mul_2ui (tmp, tmp, 1, GMP_RNDD);  /* no overflow, exact */
-              mpfr_sqr (t, tmp, GMP_RNDD);
-              if (MPFR_IS_ZERO (t))
-                {
-                  /* approximate result < 2^(emin - 3), thus
-                     exact result < 2^(emin - 2). */
-                  inexact = mpfr_underflow (y, (rnd_mode == GMP_RNDN) ?
-                                            GMP_RNDZ : rnd_mode, 1);
-                  MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_UNDERFLOW);
-                  break;
-                }
-              scaled = 1;
-            }
-        }
-
-      if (mpfr_can_round (shift_x > 0 ? t : tmp, realprec, GMP_RNDD, GMP_RNDZ,
-                          MPFR_PREC(y) + (rnd_mode == GMP_RNDN)))
-        {
-          inexact = mpfr_set (y, shift_x > 0 ? t : tmp, rnd_mode);
-          if (MPFR_UNLIKELY (scaled && MPFR_IS_PURE_FP (y)))
-            {
-              int inex2;
-              mp_exp_t ey;
-
-              /* The result has been scaled and needs to be corrected. */
-              ey = MPFR_GET_EXP (y);
-              inex2 = mpfr_mul_2si (y, y, -2, rnd_mode);
-              if (inex2)  /* underflow */
-                {
-                  if (rnd_mode == GMP_RNDN && inexact < 0 &&
-                      MPFR_IS_ZERO (y) && ey == __gmpfr_emin + 1)
-                    {
-                      /* Double rounding case: in GMP_RNDN, the scaled
-                         result has been rounded downward to 2^emin.
-                         As the exact result is > 2^(emin - 2), correct
-                         rounding must be done upward. */
-                      /* TODO: make sure in coverage tests that this line
-                         is reached. */
-                      inexact = mpfr_underflow (y, GMP_RNDU, 1);
-                    }
-                  else
-                    {
-                      /* No double rounding. */
-                      inexact = inex2;
-                    }
-                  MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_UNDERFLOW);
-                }
-            }
-          break;
-        }
-
-      MPFR_ZIV_NEXT (ziv_loop, realprec);
-      Prec = realprec + shift + 2 + shift_x;
-      mpfr_set_prec (t, Prec);
-      mpfr_set_prec (tmp, Prec);
-    }
-  MPFR_ZIV_FREE (ziv_loop);
-
-  mpz_clear (uk);
-  mpfr_clear (tmp);
-  mpfr_clear (t);
-  mpfr_clear (x_copy);
-  MPFR_SAVE_EXPO_FREE (expo);
-  return inexact;
-}