[gcc] GCC 4.5.0=>4.5.1

gcc/mpfr/const_euler.c

Index: gcc/mpfr/const_euler.c
diff --git a/gcc/mpfr/const_euler.c b/gcc/mpfr/const_euler.c
deleted file mode 100644
index 0eb17e17680ddc063da48b95adeb47f17156b218..0000000000000000000000000000000000000000
--- a/gcc/mpfr/const_euler.c
+++ /dev/null
@@ -1,221 +0,0 @@
-/* mpfr_const_euler -- Euler's constant
-
-Copyright 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
-#include "mpfr-impl.h"
-
-/* Declare the cache */
-MPFR_DECL_INIT_CACHE(__gmpfr_cache_const_euler, mpfr_const_euler_internal);
-
-/* Set User Interface */
-#undef mpfr_const_euler
-int
-mpfr_const_euler (mpfr_ptr x, mp_rnd_t rnd_mode) {
-  return mpfr_cache (x, __gmpfr_cache_const_euler, rnd_mode);
-}
-
-
-static void mpfr_const_euler_S2 (mpfr_ptr, unsigned long);
-static void mpfr_const_euler_R (mpfr_ptr, unsigned long);
-
-int
-mpfr_const_euler_internal (mpfr_t x, mp_rnd_t rnd)
-{
-  mp_prec_t prec = MPFR_PREC(x), m, log2m;
-  mpfr_t y, z;
-  unsigned long n;
-  int inexact;
-  MPFR_ZIV_DECL (loop);
-
-  log2m = MPFR_INT_CEIL_LOG2 (prec);
-  m = prec + 2 * log2m + 23;
-
-  mpfr_init2 (y, m);
-  mpfr_init2 (z, m);
-
-  MPFR_ZIV_INIT (loop, m);
-  for (;;)
-    {
-      mp_exp_t exp_S, err;
-      /* since prec >= 1, we have m >= 24 here, which ensures n >= 9 below */
-      n = 1 + (unsigned long) ((double) m * LOG2 / 2.0);
-      MPFR_ASSERTD (n >= 9);
-      mpfr_const_euler_S2 (y, n); /* error <= 3 ulps */
-      exp_S = MPFR_EXP(y);
-      mpfr_set_ui (z, n, GMP_RNDN);
-      mpfr_log (z, z, GMP_RNDD); /* error <= 1 ulp */
-      mpfr_sub (y, y, z, GMP_RNDN); /* S'(n) - log(n) */
-      /* the error is less than 1/2 + 3*2^(exp_S-EXP(y)) + 2^(EXP(z)-EXP(y))
-         <= 1/2 + 2^(exp_S+2-EXP(y)) + 2^(EXP(z)-EXP(y))
-         <= 1/2 + 2^(1+MAX(exp_S+2,EXP(z))-EXP(y)) */
-      err = 1 + MAX(exp_S + 2, MPFR_EXP(z)) - MPFR_EXP(y);
-      err = (err >= -1) ? err + 1 : 0; /* error <= 2^err ulp(y) */
-      exp_S = MPFR_EXP(y);
-      mpfr_const_euler_R (z, n); /* err <= ulp(1/2) = 2^(-m) */
-      mpfr_sub (y, y, z, GMP_RNDN);
-      /* err <= 1/2 ulp(y) + 2^(-m) + 2^(err + exp_S - EXP(y)) ulp(y).
-         Since the result is between 0.5 and 1, ulp(y) = 2^(-m).
-         So we get 3/2*ulp(y) + 2^(err + exp_S - EXP(y)) ulp(y).
-         3/2 + 2^e <= 2^(e+1) for e>=1, and <= 2^2 otherwise */
-      err = err + exp_S - MPFR_EXP(y);
-      err = (err >= 1) ? err + 1 : 2;
-      if (MPFR_LIKELY (MPFR_CAN_ROUND (y, m - err, prec, rnd)))
-        break;
-      MPFR_ZIV_NEXT (loop, m);
-      mpfr_set_prec (y, m);
-      mpfr_set_prec (z, m);
-    }
-  MPFR_ZIV_FREE (loop);
-
-  inexact = mpfr_set (x, y, rnd);
-
-  mpfr_clear (y);
-  mpfr_clear (z);
-
-  return inexact; /* always inexact */
-}
-
-static void
-mpfr_const_euler_S2_aux (mpz_t P, mpz_t Q, mpz_t T, unsigned long n,
-                         unsigned long a, unsigned long b, int need_P)
-{
-  if (a + 1 == b)
-    {
-      mpz_set_ui (P, n);
-      if (a > 1)
-        mpz_mul_si (P, P, 1 - (long) a);
-      mpz_set (T, P);
-      mpz_set_ui (Q, a);
-      mpz_mul_ui (Q, Q, a);
-    }
-  else
-    {
-      unsigned long c = (a + b) / 2;
-      mpz_t P2, Q2, T2;
-      mpfr_const_euler_S2_aux (P, Q, T, n, a, c, 1);
-      mpz_init (P2);
-      mpz_init (Q2);
-      mpz_init (T2);
-      mpfr_const_euler_S2_aux (P2, Q2, T2, n, c, b, 1);
-      mpz_mul (T, T, Q2);
-      mpz_mul (T2, T2, P);
-      mpz_add (T, T, T2);
-      if (need_P)
-        mpz_mul (P, P, P2);
-      mpz_mul (Q, Q, Q2);
-      mpz_clear (P2);
-      mpz_clear (Q2);
-      mpz_clear (T2);
-      /* divide by 2 if possible */
-      {
-        unsigned long v2;
-        v2 = mpz_scan1 (P, 0);
-        c = mpz_scan1 (Q, 0);
-        if (c < v2)
-          v2 = c;
-        c = mpz_scan1 (T, 0);
-        if (c < v2)
-          v2 = c;
-        if (v2)
-          {
-            mpz_tdiv_q_2exp (P, P, v2);
-            mpz_tdiv_q_2exp (Q, Q, v2);
-            mpz_tdiv_q_2exp (T, T, v2);
-          }
-      }
-    }
-}
-
-/* computes S(n) = sum(n^k*(-1)^(k-1)/k!/k, k=1..ceil(4.319136566 * n))
-   using binary splitting.
-   We have S(n) = sum(f(k), k=1..N) with N=ceil(4.319136566 * n)
-   and f(k) = n^k*(-1)*(k-1)/k!/k,
-   thus f(k)/f(k-1) = -n*(k-1)/k^2
-*/
-static void
-mpfr_const_euler_S2 (mpfr_t x, unsigned long n)
-{
-  mpz_t P, Q, T;
-  unsigned long N = (unsigned long) (ALPHA * (double) n + 1.0);
-  mpz_init (P);
-  mpz_init (Q);
-  mpz_init (T);
-  mpfr_const_euler_S2_aux (P, Q, T, n, 1, N + 1, 0);
-  mpfr_set_z (x, T, GMP_RNDN);
-  mpfr_div_z (x, x, Q, GMP_RNDN);
-  mpz_clear (P);
-  mpz_clear (Q);
-  mpz_clear (T);
-}
-
-/* computes R(n) = exp(-n)/n * sum(k!/(-n)^k, k=0..n-2)
-   with error at most 4*ulp(x). Assumes n>=2.
-   Since x <= exp(-n)/n <= 1/8, then 4*ulp(x) <= ulp(1).
-*/
-static void
-mpfr_const_euler_R (mpfr_t x, unsigned long n)
-{
-  unsigned long k, m;
-  mpz_t a, s;
-  mpfr_t y;
-
-  MPFR_ASSERTN (n >= 2); /* ensures sum(k!/(-n)^k, k=0..n-2) >= 2/3 */
-
-  /* as we multiply the sum by exp(-n), we need only PREC(x) - n/LOG2 bits */
-  m = MPFR_PREC(x) - (unsigned long) ((double) n / LOG2);
-
-  mpz_init_set_ui (a, 1);
-  mpz_mul_2exp (a, a, m);
-  mpz_init_set (s, a);
-
-  for (k = 1; k <= n; k++)
-    {
-      mpz_mul_ui (a, a, k);
-      mpz_div_ui (a, a, n);
-      /* the error e(k) on a is e(k) <= 1 + k/n*e(k-1) with e(0)=0,
-         i.e. e(k) <= k */
-      if (k % 2)
-        mpz_sub (s, s, a);
-      else
-        mpz_add (s, s, a);
-    }
-  /* the error on s is at most 1+2+...+n = n*(n+1)/2 */
-  mpz_div_ui (s, s, n); /* err <= 1 + (n+1)/2 */
-  MPFR_ASSERTN (MPFR_PREC(x) >= mpz_sizeinbase(s, 2));
-  mpfr_set_z (x, s, GMP_RNDD); /* exact */
-  mpfr_div_2ui (x, x, m, GMP_RNDD);
-  /* now x = 1/n * sum(k!/(-n)^k, k=0..n-2) <= 1/n */
-  /* err(x) <= (n+1)/2^m <= (n+1)*exp(n)/2^PREC(x) */
-
-  mpfr_init2 (y, m);
-  mpfr_set_si (y, -(long)n, GMP_RNDD); /* assumed exact */
-  mpfr_exp (y, y, GMP_RNDD); /* err <= ulp(y) <= exp(-n)*2^(1-m) */
-  mpfr_mul (x, x, y, GMP_RNDD);
-  /* err <= ulp(x) + (n + 1 + 2/n) / 2^prec(x)
-     <= ulp(x) + (n + 1 + 2/n) ulp(x)/x since x*2^(-prec(x)) < ulp(x)
-     <= ulp(x) + (n + 1 + 2/n) 3/(2n) ulp(x) since x >= 2/3*n for n >= 2
-     <= 4 * ulp(x) for n >= 2 */
-  mpfr_clear (y);
-
-  mpz_clear (a);
-  mpz_clear (s);
-}