[gcc] GCC 4.5.0=>4.5.1

gcc/mpfr/erfc.c

Index: gcc/mpfr/erfc.c
diff --git a/gcc/mpfr/erfc.c b/gcc/mpfr/erfc.c
deleted file mode 100644
index 9fea237a2f5a7a6d5c530d9f68586f80a0a10a02..0000000000000000000000000000000000000000
--- a/gcc/mpfr/erfc.c
+++ /dev/null
@@ -1,263 +0,0 @@
-/* mpfr_erfc -- The Complementary Error Function of a floating-point number
-
-Copyright 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"
-
-/* erfc(x) = 1 - erf(x) */
-
-/* Put in y an approximation of erfc(x) for large x, using formulae 7.1.23 and
-   7.1.24 from Abramowitz and Stegun.
-   Returns e such that the error is bounded by 2^e ulp(y),
-   or returns 0 in case of underflow.
-*/
-static mp_exp_t
-mpfr_erfc_asympt (mpfr_ptr y, mpfr_srcptr x)
-{
-  mpfr_t t, xx, err;
-  unsigned long k;
-  mp_prec_t prec = MPFR_PREC(y);
-  mp_exp_t exp_err;
-
-  mpfr_init2 (t, prec);
-  mpfr_init2 (xx, prec);
-  mpfr_init2 (err, 31);
-  /* let u = 2^(1-p), and let us represent the error as (1+u)^err
-     with a bound for err */
-  mpfr_mul (xx, x, x, GMP_RNDD); /* err <= 1 */
-  mpfr_ui_div (xx, 1, xx, GMP_RNDU); /* upper bound for 1/(2x^2), err <= 2 */
-  mpfr_div_2ui (xx, xx, 1, GMP_RNDU); /* exact */
-  mpfr_set_ui (t, 1, GMP_RNDN); /* current term, exact */
-  mpfr_set (y, t, GMP_RNDN);    /* current sum  */
-  mpfr_set_ui (err, 0, GMP_RNDN);
-  for (k = 1; ; k++)
-    {
-      mpfr_mul_ui (t, t, 2 * k - 1, GMP_RNDU); /* err <= 4k-3 */
-      mpfr_mul (t, t, xx, GMP_RNDU);           /* err <= 4k */
-      /* for -1 < x < 1, and |nx| < 1, we have |(1+x)^n| <= 1+7/4|nx|.
-         Indeed, for x>=0: log((1+x)^n) = n*log(1+x) <= n*x. Let y=n*x < 1,
-         then exp(y) <= 1+7/4*y.
-         For x<=0, let x=-x, we can prove by induction that (1-x)^n >= 1-n*x.*/
-      mpfr_mul_2si (err, err, MPFR_GET_EXP (y) - MPFR_GET_EXP (t), GMP_RNDU);
-      mpfr_add_ui (err, err, 14 * k, GMP_RNDU); /* 2^(1-p) * t <= 2 ulp(t) */
-      mpfr_div_2si (err, err, MPFR_GET_EXP (y) - MPFR_GET_EXP (t), GMP_RNDU);
-      if (MPFR_GET_EXP (t) + (mp_exp_t) prec <= MPFR_GET_EXP (y))
-        {
-          /* the truncation error is bounded by |t| < ulp(y) */
-          mpfr_add_ui (err, err, 1, GMP_RNDU);
-          break;
-        }
-      if (k & 1)
-        mpfr_sub (y, y, t, GMP_RNDN);
-      else
-        mpfr_add (y, y, t, GMP_RNDN);
-    }
-  /* the error on y is bounded by err*ulp(y) */
-  mpfr_mul (t, x, x, GMP_RNDU); /* rel. err <= 2^(1-p) */
-  mpfr_div_2ui (err, err, 3, GMP_RNDU);  /* err/8 */
-  mpfr_add (err, err, t, GMP_RNDU);      /* err/8 + xx */
-  mpfr_mul_2ui (err, err, 3, GMP_RNDU);  /* err + 8*xx */
-  mpfr_exp (t, t, GMP_RNDU); /* err <= 1/2*ulp(t) + err(x*x)*t
-                                <= 1/2*ulp(t)+2*|x*x|*ulp(t)
-                                <= (2*|x*x|+1/2)*ulp(t) */
-  mpfr_mul (t, t, x, GMP_RNDN); /* err <= 1/2*ulp(t) + (4*|x*x|+1)*ulp(t)
-                                   <= (4*|x*x|+3/2)*ulp(t) */
-  mpfr_const_pi (xx, GMP_RNDZ); /* err <= ulp(Pi) */
-  mpfr_sqrt (xx, xx, GMP_RNDN); /* err <= 1/2*ulp(xx) + ulp(Pi)/2/sqrt(Pi)
-                                   <= 3/2*ulp(xx) */
-  mpfr_mul (t, t, xx, GMP_RNDN); /* err <= (8 |xx| + 13/2) * ulp(t) */
-  mpfr_div (y, y, t, GMP_RNDN); /* the relative error on input y is bounded
-                                   by (1+u)^err with u = 2^(1-p), that on
-                                   t is bounded by (1+u)^(8 |xx| + 13/2),
-                                   thus that on output y is bounded by
-                                   8 |xx| + 7 + err. */
-
-  if (MPFR_IS_ZERO(y))
-    {
-      /* If y is zero, most probably we have underflow. We check it directly
-         using the fact that erfc(x) <= exp(-x^2)/sqrt(Pi)/x for x >= 0.
-         We compute an upper approximation of exp(-x^2)/sqrt(Pi)/x.
-      */
-      mpfr_mul (t, x, x, GMP_RNDD); /* t <= x^2 */
-      mpfr_neg (t, t, GMP_RNDU);    /* -x^2 <= t */
-      mpfr_exp (t, t, GMP_RNDU);    /* exp(-x^2) <= t */
-      mpfr_const_pi (xx, GMP_RNDD); /* xx <= sqrt(Pi), cached */
-      mpfr_mul (xx, xx, x, GMP_RNDD); /* xx <= sqrt(Pi)*x */
-      mpfr_div (y, t, xx, GMP_RNDN); /* if y is zero, this means that the upper
-                                        approximation of exp(-x^2)/sqrt(Pi)/x
-                                        is nearer from 0 than from 2^(-emin-1),
-                                        thus we have underflow. */
-      exp_err = 0;
-    }
-  else
-    {
-      mpfr_add_ui (err, err, 7, GMP_RNDU);
-      exp_err = MPFR_GET_EXP (err);
-    }
-
-  mpfr_clear (t);
-  mpfr_clear (xx);
-  mpfr_clear (err);
-  return exp_err;
-}
-
-int
-mpfr_erfc (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd)
-{
-  int inex;
-  mpfr_t tmp;
-  mp_exp_t te, err;
-  mp_prec_t prec;
-  MPFR_SAVE_EXPO_DECL (expo);
-  MPFR_ZIV_DECL (loop);
-
-  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd),
-                 ("y[%#R]=%R inexact=%d", y, y, inex));
-
-  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
-    {
-      if (MPFR_IS_NAN (x))
-        {
-          MPFR_SET_NAN (y);
-          MPFR_RET_NAN;
-        }
-      /* erfc(+inf) = 0+, erfc(-inf) = 2 erfc (0) = 1 */
-      else if (MPFR_IS_INF (x))
-        return mpfr_set_ui (y, MPFR_IS_POS (x) ? 0 : 2, rnd);
-      else
-        return mpfr_set_ui (y, 1, rnd);
-    }
-
-  if (MPFR_SIGN (x) > 0)
-    {
-      /* for x >= 27282, erfc(x) < 2^(-2^30-1) */
-      if (mpfr_cmp_ui (x, 27282) >= 0)
-        return mpfr_underflow (y, (rnd == GMP_RNDN) ? GMP_RNDZ : rnd, 1);
-    }
-
-  if (MPFR_SIGN (x) < 0)
-    {
-      mp_exp_t e = MPFR_EXP(x);
-      /* For x < 0 going to -infinity, erfc(x) tends to 2 by below.
-         More precisely, we have 2 + 1/sqrt(Pi)/x/exp(x^2) < erfc(x) < 2.
-         Thus log2 |2 - erfc(x)| <= -log2|x| - x^2 / log(2).
-         If |2 - erfc(x)| < 2^(-PREC(y)) then the result is either 2 or
-         nextbelow(2).
-         For x <= -27282, -log2|x| - x^2 / log(2) <= -2^30.
-      */
-      if ((MPFR_PREC(y) <= 7 && e >= 2) ||  /* x <= -2 */
-          (MPFR_PREC(y) <= 25 && e >= 3) || /* x <= -4 */
-          (MPFR_PREC(y) <= 120 && mpfr_cmp_si (x, -9) <= 0) ||
-          mpfr_cmp_si (x, -27282) <= 0)
-        {
-        near_two:
-          mpfr_set_ui (y, 2, GMP_RNDN);
-          mpfr_set_inexflag ();
-          if (rnd == GMP_RNDZ || rnd == GMP_RNDD)
-            {
-              mpfr_nextbelow (y);
-              return -1;
-            }
-          else
-            return 1;
-        }
-      else if (e >= 3) /* more accurate test */
-        {
-          mpfr_t t, u;
-          int near_2;
-          mpfr_init2 (t, 32);
-          mpfr_init2 (u, 32);
-          /* the following is 1/log(2) rounded to zero on 32 bits */
-          mpfr_set_str_binary (t, "1.0111000101010100011101100101001");
-          mpfr_sqr (u, x, GMP_RNDZ);
-          mpfr_mul (t, t, u, GMP_RNDZ); /* t <= x^2/log(2) */
-          mpfr_neg (u, x, GMP_RNDZ); /* 0 <= u <= |x| */
-          mpfr_log2 (u, u, GMP_RNDZ); /* u <= log2(|x|) */
-          mpfr_add (t, t, u, GMP_RNDZ); /* t <= log2|x| + x^2 / log(2) */
-          near_2 = mpfr_cmp_ui (t, MPFR_PREC(y)) >= 0;
-          mpfr_clear (t);
-          mpfr_clear (u);
-          if (near_2)
-            goto near_two;
-        }
-    }
-
-  /* Init stuff */
-  MPFR_SAVE_EXPO_MARK (expo);
-
-  /* erfc(x) ~ 1, with error < 2^(EXP(x)+1) */
-  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, - MPFR_GET_EXP (x) - 1,
-                                    0, MPFR_SIGN(x) < 0,
-                                    rnd, inex = _inexact; goto end);
-
-  prec = MPFR_PREC (y) + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y)) + 3;
-  if (MPFR_GET_EXP (x) > 0)
-    prec += 2 * MPFR_GET_EXP(x);
-
-  mpfr_init2 (tmp, prec);
-
-  MPFR_ZIV_INIT (loop, prec);            /* Initialize the ZivLoop controler */
-  for (;;)                               /* Infinite loop */
-    {
-      /* use asymptotic formula only whenever x^2 >= p*log(2),
-         otherwise it will not converge */
-      if (MPFR_SIGN (x) > 0 &&
-          2 * MPFR_GET_EXP (x) - 2 >= MPFR_INT_CEIL_LOG2 (prec))
-        /* we have x^2 >= p in that case */
-        {
-          err = mpfr_erfc_asympt (tmp, x);
-          if (err == 0) /* underflow case */
-            {
-              mpfr_clear (tmp);
-              MPFR_SAVE_EXPO_FREE (expo);
-              return mpfr_underflow (y, (rnd == GMP_RNDN) ? GMP_RNDZ : rnd, 1);
-            }
-        }
-      else
-        {
-          mpfr_erf (tmp, x, GMP_RNDN);
-          MPFR_ASSERTD (!MPFR_IS_SINGULAR (tmp)); /* FIXME: 0 only for x=0 ? */
-          te = MPFR_GET_EXP (tmp);
-          mpfr_ui_sub (tmp, 1, tmp, GMP_RNDN);
-          /* See error analysis in algorithms.tex for details */
-          if (MPFR_IS_ZERO (tmp))
-            {
-              prec *= 2;
-              err = prec; /* ensures MPFR_CAN_ROUND fails */
-            }
-          else
-            err = MAX (te - MPFR_GET_EXP (tmp), 0) + 1;
-        }
-      if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - err, MPFR_PREC (y), rnd)))
-        break;
-      MPFR_ZIV_NEXT (loop, prec);        /* Increase used precision */
-      mpfr_set_prec (tmp, prec);
-    }
-  MPFR_ZIV_FREE (loop);                  /* Free the ZivLoop Controler */
-
-  inex = mpfr_set (y, tmp, rnd);    /* Set y to the computed value */
-  mpfr_clear (tmp);
-
- end:
-  MPFR_SAVE_EXPO_FREE (expo);
-  return mpfr_check_range (y, inex, rnd);
-}