text: /* mpfr_li2 -- Dilogarithm.
  
  Copyright 2007-2016 Free Software Foundation, Inc.
  Contributed by the AriC and Caramba 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"
  
  /* Compute the alternating series
     s = S(z) = \sum_{k=0}^infty B_{2k} (z))^{2k+1} / (2k+1)!
     with 0 < z <= log(2) to the precision of s rounded in the direction
     rnd_mode.
     Return the maximum index of the truncature which is useful
     for determinating the relative error.
  */
  static int
  li2_series (mpfr_t sum, mpfr_srcptr z, mpfr_rnd_t rnd_mode)
  {
    int i, Bm, Bmax;
    mpfr_t s, u, v, w;
    mpfr_prec_t sump, p;
    mpfr_exp_t se, err;
    mpz_t *B;
    MPFR_ZIV_DECL (loop);
  
    /* The series converges for |z| < 2 pi, but in mpfr_li2 the argument is
       reduced so that 0 < z <= log(2). Here is additionnal check that z is
       (nearly) correct */
    MPFR_ASSERTD (MPFR_IS_STRICTPOS (z));
    MPFR_ASSERTD (mpfr_cmp_d (z, 0.6953125) <= 0);
  
    sump = MPFR_PREC (sum);       /* target precision */
    p = sump + MPFR_INT_CEIL_LOG2 (sump) + 4;     /* the working precision */
    mpfr_init2 (s, p);
    mpfr_init2 (u, p);
    mpfr_init2 (v, p);
    mpfr_init2 (w, p);
  
    B = mpfr_bernoulli_internal ((mpz_t *) 0, 0);
    Bm = Bmax = 1;
  
    MPFR_ZIV_INIT (loop, p);
    for (;;)
      {
        mpfr_sqr (u, z, MPFR_RNDU);
        mpfr_set (v, z, MPFR_RNDU);
        mpfr_set (s, z, MPFR_RNDU);
        se = MPFR_GET_EXP (s);
        err = 0;
  
        for (i = 1;; i++)
          {
            if (i >= Bmax)
              B = mpfr_bernoulli_internal (B, Bmax++); /* B_2i*(2i+1)!, exact */
  
            mpfr_mul (v, u, v, MPFR_RNDU);
            mpfr_div_ui (v, v, 2 * i, MPFR_RNDU);
            mpfr_div_ui (v, v, 2 * i, MPFR_RNDU);
            mpfr_div_ui (v, v, 2 * i + 1, MPFR_RNDU);
            mpfr_div_ui (v, v, 2 * i + 1, MPFR_RNDU);
            /* here, v_2i = v_{2i-2} / (2i * (2i+1))^2 */
  
            mpfr_mul_z (w, v, B[i], MPFR_RNDN);
            /* here, w_2i = v_2i * B_2i * (2i+1)! with
               error(w_2i) < 2^(5 * i + 8) ulp(w_2i) (see algorithms.tex) */
  
            mpfr_add (s, s, w, MPFR_RNDN);
  
            err = MAX (err + se, 5 * i + 8 + MPFR_GET_EXP (w))
              - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err);
            se = MPFR_GET_EXP (s);
            if (MPFR_GET_EXP (w) <= se - (mpfr_exp_t) p)
              break;
          }
  
        /* the previous value of err is the rounding error,
           the truncation error is less than EXP(z) - 6 * i - 5
           (see algorithms.tex) */
        err = MAX (err, MPFR_GET_EXP (z) - 6 * i - 5) + 1;
        if (MPFR_CAN_ROUND (s, (mpfr_exp_t) p - err, sump, rnd_mode))
          break;
  
        MPFR_ZIV_NEXT (loop, p);
        mpfr_set_prec (s, p);
        mpfr_set_prec (u, p);
        mpfr_set_prec (v, p);
        mpfr_set_prec (w, p);
      }
    MPFR_ZIV_FREE (loop);
    mpfr_set (sum, s, rnd_mode);
  
    Bm = Bmax;
    while (Bm--)
      mpz_clear (B[Bm]);
    (*__gmp_free_func) (B, Bmax * sizeof (mpz_t));
    mpfr_clears (s, u, v, w, (mpfr_ptr) 0);
  
    /* Let K be the returned value.
       1. As we compute an alternating series, the truncation error has the same
       sign as the next term w_{K+2} which is positive iff K%4 == 0.
       2. Assume that error(z) <= (1+t) z', where z' is the actual value, then
       error(s) <= 2 * (K+1) * t (see algorithms.tex).
     */
    return 2 * i;
  }
  
  /* try asymptotic expansion when x is large and positive:
     Li2(x) = -log(x)^2/2 + Pi^2/3 - 1/x + O(1/x^2).
     More precisely for x >= 2 we have for g(x) = -log(x)^2/2 + Pi^2/3:
     -2 <= x * (Li2(x) - g(x)) <= -1
     thus |Li2(x) - g(x)| <= 2/x.
     Assumes x >= 38, which ensures log(x)^2/2 >= 2*Pi^2/3, and g(x) <= -3.3.
     Return 0 if asymptotic expansion failed (unable to round), otherwise
     returns correct ternary value.
  */
  static int
  mpfr_li2_asympt_pos (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
  {
    mpfr_t g, h;
    mpfr_prec_t w = MPFR_PREC (y) + 20;
    int inex = 0;
  
    MPFR_ASSERTN (mpfr_cmp_ui (x, 38) >= 0);
  
    mpfr_init2 (g, w);
    mpfr_init2 (h, w);
    mpfr_log (g, x, MPFR_RNDN);    /* rel. error <= |(1 + theta) - 1| */
    mpfr_sqr (g, g, MPFR_RNDN);    /* rel. error <= |(1 + theta)^3 - 1| <= 2^(2-w) */
    mpfr_div_2ui (g, g, 1, MPFR_RNDN);     /* rel. error <= 2^(2-w) */
    mpfr_const_pi (h, MPFR_RNDN);  /* error <= 2^(1-w) */
    mpfr_sqr (h, h, MPFR_RNDN);    /* rel. error <= 2^(2-w) */
    mpfr_div_ui (h, h, 3, MPFR_RNDN);      /* rel. error <= |(1 + theta)^4 - 1|
                                             <= 5 * 2^(-w) */
    /* since x is chosen such that log(x)^2/2 >= 2 * (Pi^2/3), we should have
       g >= 2*h, thus |g-h| >= |h|, and the relative error on g is at most
       multiplied by 2 in the difference, and that by h is unchanged. */
    MPFR_ASSERTN (MPFR_EXP (g) > MPFR_EXP (h));
    mpfr_sub (g, h, g, MPFR_RNDN); /* err <= ulp(g)/2 + g*2^(3-w) + g*5*2^(-w)
                                     <= ulp(g) * (1/2 + 8 + 5) < 14 ulp(g).
  
                                     If in addition 2/x <= 2 ulp(g), i.e.,
                                     1/x <= ulp(g), then the total error is
                                     bounded by 16 ulp(g). */
    if ((MPFR_EXP (x) >= (mpfr_exp_t) w - MPFR_EXP (g)) &&
        MPFR_CAN_ROUND (g, w - 4, MPFR_PREC (y), rnd_mode))
      inex = mpfr_set (y, g, rnd_mode);
  
    mpfr_clear (g);
    mpfr_clear (h);
  
    return inex;
  }
  
  /* try asymptotic expansion when x is large and negative:
     Li2(x) = -log(-x)^2/2 - Pi^2/6 - 1/x + O(1/x^2).
     More precisely for x <= -2 we have for g(x) = -log(-x)^2/2 - Pi^2/6:
     |Li2(x) - g(x)| <= 1/|x|.
     Assumes x <= -7, which ensures |log(-x)^2/2| >= Pi^2/6, and g(x) <= -3.5.
     Return 0 if asymptotic expansion failed (unable to round), otherwise
     returns correct ternary value.
  */
  static int
  mpfr_li2_asympt_neg (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
  {
    mpfr_t g, h;
    mpfr_prec_t w = MPFR_PREC (y) + 20;
    int inex = 0;
  
    MPFR_ASSERTN (mpfr_cmp_si (x, -7) <= 0);
  
    mpfr_init2 (g, w);
    mpfr_init2 (h, w);
    mpfr_neg (g, x, MPFR_RNDN);
    mpfr_log (g, g, MPFR_RNDN);    /* rel. error <= |(1 + theta) - 1| */
    mpfr_sqr (g, g, MPFR_RNDN);    /* rel. error <= |(1 + theta)^3 - 1| <= 2^(2-w) */
    mpfr_div_2ui (g, g, 1, MPFR_RNDN);     /* rel. error <= 2^(2-w) */
    mpfr_const_pi (h, MPFR_RNDN);  /* error <= 2^(1-w) */
    mpfr_sqr (h, h, MPFR_RNDN);    /* rel. error <= 2^(2-w) */
    mpfr_div_ui (h, h, 6, MPFR_RNDN);      /* rel. error <= |(1 + theta)^4 - 1|
                                             <= 5 * 2^(-w) */
    MPFR_ASSERTN (MPFR_EXP (g) >= MPFR_EXP (h));
    mpfr_add (g, g, h, MPFR_RNDN); /* err <= ulp(g)/2 + g*2^(2-w) + g*5*2^(-w)
                                     <= ulp(g) * (1/2 + 4 + 5) < 10 ulp(g).
  
                                     If in addition |1/x| <= 4 ulp(g), then the
                                     total error is bounded by 16 ulp(g). */
    if ((MPFR_EXP (x) >= (mpfr_exp_t) (w - 2) - MPFR_EXP (g)) &&
        MPFR_CAN_ROUND (g, w - 4, MPFR_PREC (y), rnd_mode))
      inex = mpfr_neg (y, g, rnd_mode);
  
    mpfr_clear (g);
    mpfr_clear (h);
  
    return inex;
  }
  
  /* Compute the real part of the dilogarithm defined by
     Li2(x) = -\Int_{t=0}^x log(1-t)/t dt */
  int
  mpfr_li2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
  {
    int inexact;
    mpfr_exp_t err;
    mpfr_prec_t yp, m;
    MPFR_ZIV_DECL (loop);
    MPFR_SAVE_EXPO_DECL (expo);
  
    MPFR_LOG_FUNC
      (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
       ("y[%Pu]=%.*Rg inexact=%d",
        mpfr_get_prec (y), mpfr_log_prec, y, inexact));
  
    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))
          {
            MPFR_SET_NEG (y);
            MPFR_SET_INF (y);
            MPFR_RET (0);
          }
        else                      /* x is zero */
          {
            MPFR_ASSERTD (MPFR_IS_ZERO (x));
            MPFR_SET_SAME_SIGN (y, x);
            MPFR_SET_ZERO (y);
            MPFR_RET (0);
          }
      }
  
    /* Li2(x) = x + x^2/4 + x^3/9 + ..., more precisely for 0 < x <= 1/2
       we have |Li2(x) - x| < x^2/2 <= 2^(2EXP(x)-1) and for -1/2 <= x < 0
       we have |Li2(x) - x| < x^2/4 <= 2^(2EXP(x)-2) */
    if (MPFR_IS_POS (x))
      MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -MPFR_GET_EXP (x), 1, 1, rnd_mode,
                                        {});
    else
      MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -MPFR_GET_EXP (x), 2, 0, rnd_mode,
                                        {});
  
    MPFR_SAVE_EXPO_MARK (expo);
    yp = MPFR_PREC (y);
    m = yp + MPFR_INT_CEIL_LOG2 (yp) + 13;
  
    if (MPFR_LIKELY ((mpfr_cmp_ui (x, 0) > 0) && (mpfr_cmp_d (x, 0.5) <= 0)))
      /* 0 < x <= 1/2: Li2(x) = S(-log(1-x))-log^2(1-x)/4 */
      {
        mpfr_t s, u;
        mpfr_exp_t expo_l;
        int k;
  
        mpfr_init2 (u, m);
        mpfr_init2 (s, m);
  
        MPFR_ZIV_INIT (loop, m);
        for (;;)
          {
            mpfr_ui_sub (u, 1, x, MPFR_RNDN);
            mpfr_log (u, u, MPFR_RNDU);
            if (MPFR_IS_ZERO(u))
              goto next_m;
            mpfr_neg (u, u, MPFR_RNDN);    /* u = -log(1-x) */
            expo_l = MPFR_GET_EXP (u);
            k = li2_series (s, u, MPFR_RNDU);
            err = 1 + MPFR_INT_CEIL_LOG2 (k + 1);
  
            mpfr_sqr (u, u, MPFR_RNDU);
            mpfr_div_2ui (u, u, 2, MPFR_RNDU);     /* u = log^2(1-x) / 4 */
            mpfr_sub (s, s, u, MPFR_RNDN);
  
            /* error(s) <= (0.5 + 2^(d-EXP(s))
               + 2^(3 + MAX(1, - expo_l) - EXP(s))) ulp(s) */
            err = MAX (err, MAX (1, - expo_l) - 1) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err);
            if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode))
              break;
  
          next_m:
            MPFR_ZIV_NEXT (loop, m);
            mpfr_set_prec (u, m);
            mpfr_set_prec (s, m);
          }
        MPFR_ZIV_FREE (loop);
        inexact = mpfr_set (y, s, rnd_mode);
  
        mpfr_clear (u);
        mpfr_clear (s);
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_check_range (y, inexact, rnd_mode);
      }
    else if (!mpfr_cmp_ui (x, 1))
      /* Li2(1)= pi^2 / 6 */
      {
        mpfr_t u;
        mpfr_init2 (u, m);
  
        MPFR_ZIV_INIT (loop, m);
        for (;;)
          {
            mpfr_const_pi (u, MPFR_RNDU);
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_ui (u, u, 6, MPFR_RNDN);
  
            err = m - 4;          /* error(u) <= 19/2 ulp(u) */
            if (MPFR_CAN_ROUND (u, err, yp, rnd_mode))
              break;
  
            MPFR_ZIV_NEXT (loop, m);
            mpfr_set_prec (u, m);
          }
        MPFR_ZIV_FREE (loop);
        inexact = mpfr_set (y, u, rnd_mode);
  
        mpfr_clear (u);
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_check_range (y, inexact, rnd_mode);
      }
    else if (mpfr_cmp_ui (x, 2) >= 0)
      /* x >= 2: Li2(x) = -S(-log(1-1/x))-log^2(x)/2+log^2(1-1/x)/4+pi^2/3 */
      {
        int k;
        mpfr_exp_t expo_l;
        mpfr_t s, u, xx;
  
        if (mpfr_cmp_ui (x, 38) >= 0)
          {
            inexact = mpfr_li2_asympt_pos (y, x, rnd_mode);
            if (inexact != 0)
              goto end_of_case_gt2;
          }
  
        mpfr_init2 (u, m);
        mpfr_init2 (s, m);
        mpfr_init2 (xx, m);
  
        MPFR_ZIV_INIT (loop, m);
        for (;;)
          {
            mpfr_ui_div (xx, 1, x, MPFR_RNDN);
            mpfr_neg (xx, xx, MPFR_RNDN);
            mpfr_log1p (u, xx, MPFR_RNDD);
            mpfr_neg (u, u, MPFR_RNDU);    /* u = -log(1-1/x) */
            expo_l = MPFR_GET_EXP (u);
            k = li2_series (s, u, MPFR_RNDN);
            mpfr_neg (s, s, MPFR_RNDN);
            err = MPFR_INT_CEIL_LOG2 (k + 1) + 1; /* error(s) <= 2^err ulp(s) */
  
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_2ui (u, u, 2, MPFR_RNDN);     /* u= log^2(1-1/x)/4 */
            mpfr_add (s, s, u, MPFR_RNDN);
            err =
              MAX (err,
                   3 + MAX (1, -expo_l) + MPFR_GET_EXP (u)) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err);      /* error(s) <= 2^err ulp(s) */
            err += MPFR_GET_EXP (s);
  
            mpfr_log (u, x, MPFR_RNDU);
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_2ui (u, u, 1, MPFR_RNDN);     /* u = log^2(x)/2 */
            mpfr_sub (s, s, u, MPFR_RNDN);
            err = MAX (err, 3 + MPFR_GET_EXP (u)) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err);      /* error(s) <= 2^err ulp(s) */
            err += MPFR_GET_EXP (s);
  
            mpfr_const_pi (u, MPFR_RNDU);
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_ui (u, u, 3, MPFR_RNDN);      /* u = pi^2/3 */
            mpfr_add (s, s, u, MPFR_RNDN);
            err = MAX (err, 2) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err);      /* error(s) <= 2^err ulp(s) */
            if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode))
              break;
  
            MPFR_ZIV_NEXT (loop, m);
            mpfr_set_prec (u, m);
            mpfr_set_prec (s, m);
            mpfr_set_prec (xx, m);
          }
        MPFR_ZIV_FREE (loop);
        inexact = mpfr_set (y, s, rnd_mode);
        mpfr_clears (s, u, xx, (mpfr_ptr) 0);
  
      end_of_case_gt2:
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_check_range (y, inexact, rnd_mode);
      }
    else if (mpfr_cmp_ui (x, 1) > 0)
      /* 2 > x > 1: Li2(x) = S(log(x))+log^2(x)/4-log(x)log(x-1)+pi^2/6 */
      {
        int k;
        mpfr_exp_t e1, e2;
        mpfr_t s, u, v, xx;
        mpfr_init2 (s, m);
        mpfr_init2 (u, m);
        mpfr_init2 (v, m);
        mpfr_init2 (xx, m);
  
        MPFR_ZIV_INIT (loop, m);
        for (;;)
          {
            mpfr_log (v, x, MPFR_RNDU);
            k = li2_series (s, v, MPFR_RNDN);
            e1 = MPFR_GET_EXP (s);
  
            mpfr_sqr (u, v, MPFR_RNDN);
            mpfr_div_2ui (u, u, 2, MPFR_RNDN);     /* u = log^2(x)/4 */
            mpfr_add (s, s, u, MPFR_RNDN);
  
            mpfr_sub_ui (xx, x, 1, MPFR_RNDN);
            mpfr_log (u, xx, MPFR_RNDU);
            e2 = MPFR_GET_EXP (u);
            mpfr_mul (u, v, u, MPFR_RNDN); /* u = log(x) * log(x-1) */
            mpfr_sub (s, s, u, MPFR_RNDN);
  
            mpfr_const_pi (u, MPFR_RNDU);
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_ui (u, u, 6, MPFR_RNDN);      /* u = pi^2/6 */
            mpfr_add (s, s, u, MPFR_RNDN);
            /* error(s) <= (31 + (k+1) * 2^(1-e1) + 2^(1-e2)) ulp(s)
               see algorithms.tex */
            err = MAX (MPFR_INT_CEIL_LOG2 (k + 1) + 1 - e1, 1 - e2);
            err = 2 + MAX (5, err);
            if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode))
              break;
  
            MPFR_ZIV_NEXT (loop, m);
            mpfr_set_prec (s, m);
            mpfr_set_prec (u, m);
            mpfr_set_prec (v, m);
            mpfr_set_prec (xx, m);
          }
        MPFR_ZIV_FREE (loop);
        inexact = mpfr_set (y, s, rnd_mode);
  
        mpfr_clears (s, u, v, xx, (mpfr_ptr) 0);
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_check_range (y, inexact, rnd_mode);
      }
    else if (mpfr_cmp_ui_2exp (x, 1, -1) > 0) /*  1/2 < x < 1 */
      /* 1 > x > 1/2: Li2(x) = -S(-log(x))+log^2(x)/4-log(x)log(1-x)+pi^2/6 */
      {
        int k;
        mpfr_t s, u, v, xx;
        mpfr_init2 (s, m);
        mpfr_init2 (u, m);
        mpfr_init2 (v, m);
        mpfr_init2 (xx, m);
  
  
        MPFR_ZIV_INIT (loop, m);
        for (;;)
          {
            mpfr_log (u, x, MPFR_RNDD);
            mpfr_neg (u, u, MPFR_RNDN);
            k = li2_series (s, u, MPFR_RNDN);
            mpfr_neg (s, s, MPFR_RNDN);
            err = 1 + MPFR_INT_CEIL_LOG2 (k + 1) - MPFR_GET_EXP (s);
  
            mpfr_ui_sub (xx, 1, x, MPFR_RNDN);
            mpfr_log (v, xx, MPFR_RNDU);
            mpfr_mul (v, v, u, MPFR_RNDN); /* v = - log(x) * log(1-x) */
            mpfr_add (s, s, v, MPFR_RNDN);
            err = MAX (err, 1 - MPFR_GET_EXP (v));
            err = 2 + MAX (3, err) - MPFR_GET_EXP (s);
  
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_2ui (u, u, 2, MPFR_RNDN);     /* u = log^2(x)/4 */
            mpfr_add (s, s, u, MPFR_RNDN);
            err = MAX (err, 2 + MPFR_GET_EXP (u)) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err) + MPFR_GET_EXP (s);
  
            mpfr_const_pi (u, MPFR_RNDU);
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_ui (u, u, 6, MPFR_RNDN);      /* u = pi^2/6 */
            mpfr_add (s, s, u, MPFR_RNDN);
            err = MAX (err, 3) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err);
  
            if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode))
              break;
  
            MPFR_ZIV_NEXT (loop, m);
            mpfr_set_prec (s, m);
            mpfr_set_prec (u, m);
            mpfr_set_prec (v, m);
            mpfr_set_prec (xx, m);
          }
        MPFR_ZIV_FREE (loop);
        inexact = mpfr_set (y, s, rnd_mode);
  
        mpfr_clears (s, u, v, xx, (mpfr_ptr) 0);
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_check_range (y, inexact, rnd_mode);
      }
    else if (mpfr_cmp_si (x, -1) >= 0)
      /* 0 > x >= -1: Li2(x) = -S(log(1-x))-log^2(1-x)/4 */
      {
        int k;
        mpfr_exp_t expo_l;
        mpfr_t s, u, xx;
        mpfr_init2 (s, m);
        mpfr_init2 (u, m);
        mpfr_init2 (xx, m);
  
        MPFR_ZIV_INIT (loop, m);
        for (;;)
          {
            mpfr_neg (xx, x, MPFR_RNDN);
            mpfr_log1p (u, xx, MPFR_RNDN);
            k = li2_series (s, u, MPFR_RNDN);
            mpfr_neg (s, s, MPFR_RNDN);
            expo_l = MPFR_GET_EXP (u);
            err = 1 + MPFR_INT_CEIL_LOG2 (k + 1) - MPFR_GET_EXP (s);
  
            mpfr_sqr (u, u, MPFR_RNDN);
            mpfr_div_2ui (u, u, 2, MPFR_RNDN);     /* u = log^2(1-x)/4 */
            mpfr_sub (s, s, u, MPFR_RNDN);
            err = MAX (err, - expo_l);
            err = 2 + MAX (err, 3);
            if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode))
              break;
  
            MPFR_ZIV_NEXT (loop, m);
            mpfr_set_prec (s, m);
            mpfr_set_prec (u, m);
            mpfr_set_prec (xx, m);
          }
        MPFR_ZIV_FREE (loop);
        inexact = mpfr_set (y, s, rnd_mode);
  
        mpfr_clears (s, u, xx, (mpfr_ptr) 0);
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_check_range (y, inexact, rnd_mode);
      }
    else
      /* x < -1: Li2(x)
         = S(log(1-1/x))-log^2(-x)/4-log(1-x)log(-x)/2+log^2(1-x)/4-pi^2/6 */
      {
        int k;
        mpfr_t s, u, v, w, xx;
  
        if (mpfr_cmp_si (x, -7) <= 0)
          {
            inexact = mpfr_li2_asympt_neg (y, x, rnd_mode);
            if (inexact != 0)
              goto end_of_case_ltm1;
          }
  
        mpfr_init2 (s, m);
        mpfr_init2 (u, m);
        mpfr_init2 (v, m);
        mpfr_init2 (w, m);
        mpfr_init2 (xx, m);
  
        MPFR_ZIV_INIT (loop, m);
        for (;;)
          {
            mpfr_ui_div (xx, 1, x, MPFR_RNDN);
            mpfr_neg (xx, xx, MPFR_RNDN);
            mpfr_log1p (u, xx, MPFR_RNDN);
            k = li2_series (s, u, MPFR_RNDN);
  
            mpfr_ui_sub (xx, 1, x, MPFR_RNDN);
            mpfr_log (u, xx, MPFR_RNDU);
            mpfr_neg (xx, x, MPFR_RNDN);
            mpfr_log (v, xx, MPFR_RNDU);
            mpfr_mul (w, v, u, MPFR_RNDN);
            mpfr_div_2ui (w, w, 1, MPFR_RNDN);  /* w = log(-x) * log(1-x) / 2 */
            mpfr_sub (s, s, w, MPFR_RNDN);
            err = 1 + MAX (3, MPFR_INT_CEIL_LOG2 (k+1) + 1  - MPFR_GET_EXP (s))
              + MPFR_GET_EXP (s);
  
            mpfr_sqr (w, v, MPFR_RNDN);
            mpfr_div_2ui (w, w, 2, MPFR_RNDN);  /* w = log^2(-x) / 4 */
            mpfr_sub (s, s, w, MPFR_RNDN);
            err = MAX (err, 3 + MPFR_GET_EXP(w)) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err) + MPFR_GET_EXP (s);
  
            mpfr_sqr (w, u, MPFR_RNDN);
            mpfr_div_2ui (w, w, 2, MPFR_RNDN);     /* w = log^2(1-x) / 4 */
            mpfr_add (s, s, w, MPFR_RNDN);
            err = MAX (err, 3 + MPFR_GET_EXP (w)) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err) + MPFR_GET_EXP (s);
  
            mpfr_const_pi (w, MPFR_RNDU);
            mpfr_sqr (w, w, MPFR_RNDN);
            mpfr_div_ui (w, w, 6, MPFR_RNDN);      /* w = pi^2 / 6 */
            mpfr_sub (s, s, w, MPFR_RNDN);
            err = MAX (err, 3) - MPFR_GET_EXP (s);
            err = 2 + MAX (-1, err) + MPFR_GET_EXP (s);
  
            if (MPFR_CAN_ROUND (s, (mpfr_exp_t) m - err, yp, rnd_mode))
              break;
  
            MPFR_ZIV_NEXT (loop, m);
            mpfr_set_prec (s, m);
            mpfr_set_prec (u, m);
            mpfr_set_prec (v, m);
            mpfr_set_prec (w, m);
            mpfr_set_prec (xx, m);
          }
        MPFR_ZIV_FREE (loop);
        inexact = mpfr_set (y, s, rnd_mode);
        mpfr_clears (s, u, v, w, xx, (mpfr_ptr) 0);
  
      end_of_case_ltm1:
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_check_range (y, inexact, rnd_mode);
      }
  
    MPFR_RET_NEVER_GO_HERE ();
  }
  