mpfr 3.1.3

git-svn-id: svn://tug.org/texlive/trunk@37627 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 0 insertions, 426 deletions

diff --git a/Build/source/libs/mpfr/mpfr-3.1.2/src/yn.c b/Build/source/libs/mpfr/mpfr-3.1.2/src/yn.c
deleted file mode 100644
index 24d3e176e20..00000000000
--- a/Build/source/libs/mpfr/mpfr-3.1.2/src/yn.c
+++ /dev/null
@@ -1,426 +0,0 @@
-/* mpfr_y0, mpfr_y1, mpfr_yn -- Bessel functions of 2nd kind, integer order.
-   http://www.opengroup.org/onlinepubs/009695399/functions/y0.html
-
-Copyright 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
-Contributed by the AriC 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"
-
-static int mpfr_yn_asympt (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
-
-int
-mpfr_y0 (mpfr_ptr res, mpfr_srcptr z, mpfr_rnd_t r)
-{
-  return mpfr_yn (res, 0, z, r);
-}
-
-int
-mpfr_y1 (mpfr_ptr res, mpfr_srcptr z, mpfr_rnd_t r)
-{
-  return mpfr_yn (res, 1, z, r);
-}
-
-/* compute in s an approximation of S1 = sum((n-k)!/k!*y^k,k=0..n)
-   return e >= 0 the exponent difference between the maximal value of |s|
-   during the for loop and the final value of |s|.
-*/
-static mpfr_exp_t
-mpfr_yn_s1 (mpfr_ptr s, mpfr_srcptr y, unsigned long n)
-{
-  unsigned long k;
-  mpz_t f;
-  mpfr_exp_t e, emax;
-
-  mpz_init_set_ui (f, 1);
-  /* we compute n!*S1 = sum(a[k]*y^k,k=0..n) where a[k] = n!*(n-k)!/k!,
-     a[0] = (n!)^2, a[1] = n!*(n-1)!, ..., a[n-1] = n, a[n] = 1 */
-  mpfr_set_ui (s, 1, MPFR_RNDN); /* a[n] */
-  emax = MPFR_EXP(s);
-  for (k = n; k-- > 0;)
-    {
-      /* a[k]/a[k+1] = (n-k)!/k!/(n-(k+1))!*(k+1)! = (k+1)*(n-k) */
-      mpfr_mul (s, s, y, MPFR_RNDN);
-      mpz_mul_ui (f, f, n - k);
-      mpz_mul_ui (f, f, k + 1);
-      /* invariant: f = a[k] */
-      mpfr_add_z (s, s, f, MPFR_RNDN);
-      e = MPFR_EXP(s);
-      if (e > emax)
-        emax = e;
-    }
-  /* now we have f = (n!)^2 */
-  mpz_sqrt (f, f);
-  mpfr_div_z (s, s, f, MPFR_RNDN);
-  mpz_clear (f);
-  return emax - MPFR_EXP(s);
-}
-
-/* compute in s an approximation of
-   S3 = c*sum((h(k)+h(n+k))*y^k/k!/(n+k)!,k=0..infinity)
-   where h(k) = 1 + 1/2 + ... + 1/k
-   k=0: h(n)
-   k=1: 1+h(n+1)
-   k=2: 3/2+h(n+2)
-   Returns e such that the error is bounded by 2^e ulp(s).
-*/
-static mpfr_exp_t
-mpfr_yn_s3 (mpfr_ptr s, mpfr_srcptr y, mpfr_srcptr c, unsigned long n)
-{
-  unsigned long k, zz;
-  mpfr_t t, u;
-  mpz_t p, q; /* p/q will store h(k)+h(n+k) */
-  mpfr_exp_t exps, expU;
-
-  zz = mpfr_get_ui (y, MPFR_RNDU); /* y = z^2/4 */
-  MPFR_ASSERTN (zz < ULONG_MAX - 2);
-  zz += 2; /* z^2 <= 2^zz */
-  mpz_init_set_ui (p, 0);
-  mpz_init_set_ui (q, 1);
-  /* initialize p/q to h(n) */
-  for (k = 1; k <= n; k++)
-    {
-      /* p/q + 1/k = (k*p+q)/(q*k) */
-      mpz_mul_ui (p, p, k);
-      mpz_add (p, p, q);
-      mpz_mul_ui (q, q, k);
-    }
-  mpfr_init2 (t, MPFR_PREC(s));
-  mpfr_init2 (u, MPFR_PREC(s));
-  mpfr_fac_ui (t, n, MPFR_RNDN);
-  mpfr_div (t, c, t, MPFR_RNDN);    /* c/n! */
-  mpfr_mul_z (u, t, p, MPFR_RNDN);
-  mpfr_div_z (s, u, q, MPFR_RNDN);
-  exps = MPFR_EXP (s);
-  expU = exps;
-  for (k = 1; ;k ++)
-    {
-      /* update t */
-      mpfr_mul (t, t, y, MPFR_RNDN);
-      mpfr_div_ui (t, t, k, MPFR_RNDN);
-      mpfr_div_ui (t, t, n + k, MPFR_RNDN);
-      /* update p/q:
-         p/q + 1/k + 1/(n+k) = [p*k*(n+k) + q*(n+k) + q*k]/(q*k*(n+k)) */
-      mpz_mul_ui (p, p, k);
-      mpz_mul_ui (p, p, n + k);
-      mpz_addmul_ui (p, q, n + 2 * k);
-      mpz_mul_ui (q, q, k);
-      mpz_mul_ui (q, q, n + k);
-      mpfr_mul_z (u, t, p, MPFR_RNDN);
-      mpfr_div_z (u, u, q, MPFR_RNDN);
-      exps = MPFR_EXP (u);
-      if (exps > expU)
-        expU = exps;
-      mpfr_add (s, s, u, MPFR_RNDN);
-      exps = MPFR_EXP (s);
-      if (exps > expU)
-        expU = exps;
-      if (MPFR_EXP (u) + (mpfr_exp_t) MPFR_PREC (u) < MPFR_EXP (s) &&
-          zz / (2 * k) < k + n)
-        break;
-    }
-  mpfr_clear (t);
-  mpfr_clear (u);
-  mpz_clear (p);
-  mpz_clear (q);
-  exps = expU - MPFR_EXP (s);
-  /* the error is bounded by (6k^2+33/2k+11) 2^exps ulps
-     <= 8*(k+2)^2 2^exps ulps */
-  return 3 + 2 * MPFR_INT_CEIL_LOG2(k + 2) + exps;
-}
-
-int
-mpfr_yn (mpfr_ptr res, long n, mpfr_srcptr z, mpfr_rnd_t r)
-{
-  int inex;
-  unsigned long absn;
-  MPFR_SAVE_EXPO_DECL (expo);
-
-  MPFR_LOG_FUNC
-    (("n=%ld x[%Pu]=%.*Rg rnd=%d", n, mpfr_get_prec (z), mpfr_log_prec, z, r),
-     ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (res), mpfr_log_prec, res, inex));
-
-  absn = SAFE_ABS (unsigned long, n);
-
-  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (z)))
-    {
-      if (MPFR_IS_NAN (z))
-        {
-          MPFR_SET_NAN (res); /* y(n,NaN) = NaN */
-          MPFR_RET_NAN;
-        }
-      /* y(n,z) tends to zero when z goes to +Inf, oscillating around
-         0. We choose to return +0 in that case. */
-      else if (MPFR_IS_INF (z))
-        {
-          if (MPFR_SIGN(z) > 0)
-            return mpfr_set_ui (res, 0, r);
-          else /* y(n,-Inf) = NaN */
-            {
-              MPFR_SET_NAN (res);
-              MPFR_RET_NAN;
-            }
-        }
-      else /* y(n,z) tends to -Inf for n >= 0 or n even, to +Inf otherwise,
-              when z goes to zero */
-        {
-          MPFR_SET_INF(res);
-          if (n >= 0 || ((unsigned long) n & 1) == 0)
-            MPFR_SET_NEG(res);
-          else
-            MPFR_SET_POS(res);
-          mpfr_set_divby0 ();
-          MPFR_RET(0);
-        }
-    }
-
-  /* for z < 0, y(n,z) is imaginary except when j(n,|z|) = 0, which we
-     assume does not happen for a rational z. */
-  if (MPFR_SIGN(z) < 0)
-    {
-      MPFR_SET_NAN (res);
-      MPFR_RET_NAN;
-    }
-
-  /* now z is not singular, and z > 0 */
-
-  MPFR_SAVE_EXPO_MARK (expo);
-
-  /* Deal with tiny arguments. We have:
-     y0(z) = 2 log(z)/Pi + 2 (euler - log(2))/Pi + O(log(z)*z^2), more
-     precisely for 0 <= z <= 1/2, with g(z) = 2/Pi + 2(euler-log(2))/Pi/log(z),
-                g(z) - 0.41*z^2 < y0(z)/log(z) < g(z)
-     thus since log(z) is negative:
-             g(z)*log(z) < y0(z) < (g(z) - z^2/2)*log(z)
-     and since |g(z)| >= 0.63 for 0 <= z <= 1/2, the relative error on
-     y0(z)/log(z) is bounded by 0.41*z^2/0.63 <= 0.66*z^2.
-     Note: we use both the main term in log(z) and the constant term, because
-     otherwise the relative error would be only in 1/log(|log(z)|).
-  */
-  if (n == 0 && MPFR_EXP(z) < - (mpfr_exp_t) (MPFR_PREC(res) / 2))
-    {
-      mpfr_t l, h, t, logz;
-      mpfr_prec_t prec;
-      int ok, inex2;
-
-      prec = MPFR_PREC(res) + 10;
-      mpfr_init2 (l, prec);
-      mpfr_init2 (h, prec);
-      mpfr_init2 (t, prec);
-      mpfr_init2 (logz, prec);
-      /* first enclose log(z) + euler - log(2) = log(z/2) + euler */
-      mpfr_log (logz, z, MPFR_RNDD);    /* lower bound of log(z) */
-      mpfr_set (h, logz, MPFR_RNDU);    /* exact */
-      mpfr_nextabove (h);              /* upper bound of log(z) */
-      mpfr_const_euler (t, MPFR_RNDD);  /* lower bound of euler */
-      mpfr_add (l, logz, t, MPFR_RNDD); /* lower bound of log(z) + euler */
-      mpfr_nextabove (t);              /* upper bound of euler */
-      mpfr_add (h, h, t, MPFR_RNDU);    /* upper bound of log(z) + euler */
-      mpfr_const_log2 (t, MPFR_RNDU);   /* upper bound of log(2) */
-      mpfr_sub (l, l, t, MPFR_RNDD);    /* lower bound of log(z/2) + euler */
-      mpfr_nextbelow (t);              /* lower bound of log(2) */
-      mpfr_sub (h, h, t, MPFR_RNDU);    /* upper bound of log(z/2) + euler */
-      mpfr_const_pi (t, MPFR_RNDU);     /* upper bound of Pi */
-      mpfr_div (l, l, t, MPFR_RNDD);    /* lower bound of (log(z/2)+euler)/Pi */
-      mpfr_nextbelow (t);              /* lower bound of Pi */
-      mpfr_div (h, h, t, MPFR_RNDD);    /* upper bound of (log(z/2)+euler)/Pi */
-      mpfr_mul_2ui (l, l, 1, MPFR_RNDD); /* lower bound on g(z)*log(z) */
-      mpfr_mul_2ui (h, h, 1, MPFR_RNDU); /* upper bound on g(z)*log(z) */
-      /* we now have l <= g(z)*log(z) <= h, and we need to add -z^2/2*log(z)
-         to h */
-      mpfr_mul (t, z, z, MPFR_RNDU);     /* upper bound on z^2 */
-      /* since logz is negative, a lower bound corresponds to an upper bound
-         for its absolute value */
-      mpfr_neg (t, t, MPFR_RNDD);
-      mpfr_div_2ui (t, t, 1, MPFR_RNDD);
-      mpfr_mul (t, t, logz, MPFR_RNDU); /* upper bound on z^2/2*log(z) */
-      mpfr_add (h, h, t, MPFR_RNDU);
-      inex = mpfr_prec_round (l, MPFR_PREC(res), r);
-      inex2 = mpfr_prec_round (h, MPFR_PREC(res), r);
-      /* we need h=l and inex=inex2 */
-      ok = (inex == inex2) && mpfr_equal_p (l, h);
-      if (ok)
-        mpfr_set (res, h, r); /* exact */
-      mpfr_clear (l);
-      mpfr_clear (h);
-      mpfr_clear (t);
-      mpfr_clear (logz);
-      if (ok)
-        goto end;
-    }
-
-  /* small argument check for y1(z) = -2/Pi/z + O(log(z)):
-     for 0 <= z <= 1, |y1(z) + 2/Pi/z| <= 0.25 */
-  if (n == 1 && MPFR_EXP(z) + 1 < - (mpfr_exp_t) MPFR_PREC(res))
-    {
-      mpfr_t y;
-      mpfr_prec_t prec;
-      mpfr_exp_t err1;
-      int ok;
-      MPFR_BLOCK_DECL (flags);
-
-      /* since 2/Pi > 0.5, and |y1(z)| >= |2/Pi/z|, if z <= 2^(-emax-1),
-         then |y1(z)| > 2^emax */
-      prec = MPFR_PREC(res) + 10;
-      mpfr_init2 (y, prec);
-      mpfr_const_pi (y, MPFR_RNDU); /* Pi*(1+u)^2, where here and below u
-                                      represents a quantity <= 1/2^prec */
-      mpfr_mul (y, y, z, MPFR_RNDU); /* Pi*z * (1+u)^4, upper bound */
-      MPFR_BLOCK (flags, mpfr_ui_div (y, 2, y, MPFR_RNDZ));
-      /* 2/Pi/z * (1+u)^6, lower bound, with possible overflow */
-      if (MPFR_OVERFLOW (flags))
-        {
-          mpfr_clear (y);
-          MPFR_SAVE_EXPO_FREE (expo);
-          return mpfr_overflow (res, r, -1);
-        }
-      mpfr_neg (y, y, MPFR_RNDN);
-      /* (1+u)^6 can be written 1+7u [for another value of u], thus the
-         error on 2/Pi/z is less than 7ulp(y). The truncation error is less
-         than 1/4, thus if ulp(y)>=1/4, the total error is less than 8ulp(y),
-         otherwise it is less than 1/4+7/8 <= 2. */
-      if (MPFR_EXP(y) + 2 >= MPFR_PREC(y)) /* ulp(y) >= 1/4 */
-        err1 = 3;
-      else /* ulp(y) <= 1/8 */
-        err1 = (mpfr_exp_t) MPFR_PREC(y) - MPFR_EXP(y) + 1;
-      ok = MPFR_CAN_ROUND (y, prec - err1, MPFR_PREC(res), r);
-      if (ok)
-        inex = mpfr_set (res, y, r);
-      mpfr_clear (y);
-      if (ok)
-        goto end;
-    }
-
-  /* we can use the asymptotic expansion as soon as z > p log(2)/2,
-     but to get some margin we use it for z > p/2 */
-  if (mpfr_cmp_ui (z, MPFR_PREC(res) / 2 + 3) > 0)
-    {
-      inex = mpfr_yn_asympt (res, n, z, r);
-      if (inex != 0)
-        goto end;
-    }
-
-  /* General case */
-  {
-    mpfr_prec_t prec;
-    mpfr_exp_t err1, err2, err3;
-    mpfr_t y, s1, s2, s3;
-    MPFR_ZIV_DECL (loop);
-
-    mpfr_init (y);
-    mpfr_init (s1);
-    mpfr_init (s2);
-    mpfr_init (s3);
-
-    prec = MPFR_PREC(res) + 2 * MPFR_INT_CEIL_LOG2 (MPFR_PREC (res)) + 13;
-    MPFR_ZIV_INIT (loop, prec);
-    for (;;)
-      {
-        mpfr_set_prec (y, prec);
-        mpfr_set_prec (s1, prec);
-        mpfr_set_prec (s2, prec);
-        mpfr_set_prec (s3, prec);
-
-        mpfr_mul (y, z, z, MPFR_RNDN);
-        mpfr_div_2ui (y, y, 2, MPFR_RNDN); /* z^2/4 */
-
-        /* store (z/2)^n temporarily in s2 */
-        mpfr_pow_ui (s2, z, absn, MPFR_RNDN);
-        mpfr_div_2si (s2, s2, absn, MPFR_RNDN);
-
-        /* compute S1 * (z/2)^(-n) */
-        if (n == 0)
-          {
-            mpfr_set_ui (s1, 0, MPFR_RNDN);
-            err1 = 0;
-          }
-        else
-          err1 = mpfr_yn_s1 (s1, y, absn - 1);
-        mpfr_div (s1, s1, s2, MPFR_RNDN); /* (z/2)^(-n) * S1 */
-        /* See algorithms.tex: the relative error on s1 is bounded by
-           (3n+3)*2^(e+1-prec). */
-        err1 = MPFR_INT_CEIL_LOG2 (3 * absn + 3) + err1 + 1;
-        /* rel_err(s1) <= 2^(err1-prec), thus err(s1) <= 2^err1 ulps */
-
-        /* compute (z/2)^n * S3 */
-        mpfr_neg (y, y, MPFR_RNDN); /* -z^2/4 */
-        err3 = mpfr_yn_s3 (s3, y, s2, absn); /* (z/2)^n * S3 */
-        /* the error on s3 is bounded by 2^err3 ulps */
-
-        /* add s1+s3 */
-        err1 += MPFR_EXP(s1);
-        mpfr_add (s1, s1, s3, MPFR_RNDN);
-        /* the error is bounded by 1/2 + 2^err1*2^(- EXP(s1))
-           + 2^err3*2^(EXP(s3) - EXP(s1)) */
-        err3 += MPFR_EXP(s3);
-        err1 = (err3 > err1) ? err3 + 1 : err1 + 1;
-        err1 -= MPFR_EXP(s1);
-        err1 = (err1 >= 0) ? err1 + 1 : 1;
-        /* now the error on s1 is bounded by 2^err1*ulp(s1) */
-
-        /* compute S2 */
-        mpfr_div_2ui (s2, z, 1, MPFR_RNDN); /* z/2 */
-        mpfr_log (s2, s2, MPFR_RNDN); /* log(z/2) */
-        mpfr_const_euler (s3, MPFR_RNDN);
-        err2 = MPFR_EXP(s2) > MPFR_EXP(s3) ? MPFR_EXP(s2) : MPFR_EXP(s3);
-        mpfr_add (s2, s2, s3, MPFR_RNDN); /* log(z/2) + gamma */
-        err2 -= MPFR_EXP(s2);
-        mpfr_mul_2ui (s2, s2, 1, MPFR_RNDN); /* 2*(log(z/2) + gamma) */
-        mpfr_jn (s3, absn, z, MPFR_RNDN); /* Jn(z) */
-        mpfr_mul (s2, s2, s3, MPFR_RNDN); /* 2*(log(z/2) + gamma)*Jn(z) */
-        err2 += 4; /* the error on s2 is bounded by 2^err2 ulps, see
-                      algorithms.tex */
-
-        /* add all three sums */
-        err1 += MPFR_EXP(s1); /* the error on s1 is bounded by 2^err1 */
-        err2 += MPFR_EXP(s2); /* the error on s2 is bounded by 2^err2 */
-        mpfr_sub (s2, s2, s1, MPFR_RNDN); /* s2 - (s1+s3) */
-        err2 = (err1 > err2) ? err1 + 1 : err2 + 1;
-        err2 -= MPFR_EXP(s2);
-        err2 = (err2 >= 0) ? err2 + 1 : 1;
-        /* now the error on s2 is bounded by 2^err2*ulp(s2) */
-        mpfr_const_pi (y, MPFR_RNDN); /* error bounded by 1 ulp */
-        mpfr_div (s2, s2, y, MPFR_RNDN); /* error bounded by
-                                           2^(err2+1)*ulp(s2) */
-        err2 ++;
-
-        if (MPFR_LIKELY (MPFR_CAN_ROUND (s2, prec - err2, MPFR_PREC(res), r)))
-          break;
-        MPFR_ZIV_NEXT (loop, prec);
-      }
-    MPFR_ZIV_FREE (loop);
-
-    /* Assume two's complement for the test n & 1 */
-    inex = mpfr_set4 (res, s2, r, n >= 0 || (n & 1) == 0 ?
-                      MPFR_SIGN (s2) : - MPFR_SIGN (s2));
-
-    mpfr_clear (y);
-    mpfr_clear (s1);
-    mpfr_clear (s2);
-    mpfr_clear (s3);
-  }
-
- end:
-  MPFR_SAVE_EXPO_FREE (expo);
-  return mpfr_check_range (res, inex, r);
-}
-
-#define MPFR_YN
-#include "jyn_asympt.c"