text: /* mpfr_pow_ui-- compute the power of a floating-point
                                    by a machine integer
  
  Copyright 1999-2016 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"
  
  /* sets y to x^n, and return 0 if exact, non-zero otherwise */
  int
  mpfr_pow_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int n, mpfr_rnd_t rnd)
  {
    unsigned long m;
    mpfr_t res;
    mpfr_prec_t prec, err;
    int inexact;
    mpfr_rnd_t rnd1;
    MPFR_SAVE_EXPO_DECL (expo);
    MPFR_ZIV_DECL (loop);
    MPFR_BLOCK_DECL (flags);
  
    MPFR_LOG_FUNC
      (("x[%Pu]=%.*Rg n=%lu rnd=%d",
        mpfr_get_prec (x), mpfr_log_prec, x, n, rnd),
       ("y[%Pu]=%.*Rg inexact=%d",
        mpfr_get_prec (y), mpfr_log_prec, y, inexact));
  
    /* x^0 = 1 for any x, even a NaN */
    if (MPFR_UNLIKELY (n == 0))
      return mpfr_set_ui (y, 1, rnd);
  
    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))
          {
            /* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
            if (MPFR_IS_NEG (x) && (n & 1) == 1)
              MPFR_SET_NEG (y);
            else
              MPFR_SET_POS (y);
            MPFR_SET_INF (y);
            MPFR_RET (0);
          }
        else /* x is zero */
          {
            MPFR_ASSERTD (MPFR_IS_ZERO (x));
            /* 0^n = 0 for any n */
            MPFR_SET_ZERO (y);
            if (MPFR_IS_POS (x) || (n & 1) == 0)
              MPFR_SET_POS (y);
            else
              MPFR_SET_NEG (y);
            MPFR_RET (0);
          }
      }
    else if (MPFR_UNLIKELY (n <= 2))
      {
        if (n < 2)
          /* x^1 = x */
          return mpfr_set (y, x, rnd);
        else
          /* x^2 = sqr(x) */
          return mpfr_sqr (y, x, rnd);
      }
  
    /* Augment exponent range */
    MPFR_SAVE_EXPO_MARK (expo);
  
    /* setup initial precision */
    prec = MPFR_PREC (y) + 3 + GMP_NUMB_BITS
      + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y));
    mpfr_init2 (res, prec);
  
    rnd1 = MPFR_IS_POS (x) ? MPFR_RNDU : MPFR_RNDD; /* away */
  
    MPFR_ZIV_INIT (loop, prec);
    for (;;)
      {
        int i;
  
        for (m = n, i = 0; m; i++, m >>= 1)
          ;
        /* now 2^(i-1) <= n < 2^i */
        MPFR_ASSERTD (prec > (mpfr_prec_t) i);
        err = prec - 1 - (mpfr_prec_t) i;
        /* First step: compute square from x */
        MPFR_BLOCK (flags,
                    inexact = mpfr_mul (res, x, x, MPFR_RNDU);
                    MPFR_ASSERTD (i >= 2);
                    if (n & (1UL << (i-2)))
                      inexact |= mpfr_mul (res, res, x, rnd1);
                    for (i -= 3; i >= 0 && !MPFR_BLOCK_EXCEP; i--)
                      {
                        inexact |= mpfr_mul (res, res, res, MPFR_RNDU);
                        if (n & (1UL << i))
                          inexact |= mpfr_mul (res, res, x, rnd1);
                      });
        /* let r(n) be the number of roundings: we have r(2)=1, r(3)=2,
           and r(2n)=2r(n)+1, r(2n+1)=2r(n)+2, thus r(n)=n-1.
           Using Higham's method, to each rounding corresponds a factor
           (1-theta) with 0 <= theta <= 2^(1-p), thus at the end the
           absolute error is bounded by (n-1)*2^(1-p)*res <= 2*(n-1)*ulp(res)
           since 2^(-p)*x <= ulp(x). Since n < 2^i, this gives a maximal
           error of 2^(1+i)*ulp(res).
        */
        if (MPFR_LIKELY (inexact == 0
                         || MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)
                         || MPFR_CAN_ROUND (res, err, MPFR_PREC (y), rnd)))
          break;
        /* Actualisation of the precision */
        MPFR_ZIV_NEXT (loop, prec);
        mpfr_set_prec (res, prec);
      }
    MPFR_ZIV_FREE (loop);
  
    if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)))
      {
        mpz_t z;
  
        /* Internal overflow or underflow. However the approximation error has
         * not been taken into account. So, let's solve this problem by using
         * mpfr_pow_z, which can handle it. This case could be improved in the
         * future, without having to use mpfr_pow_z.
         */
        MPFR_LOG_MSG (("Internal overflow or underflow,"
                       " let's use mpfr_pow_z.\n", 0));
        mpfr_clear (res);
        MPFR_SAVE_EXPO_FREE (expo);
        mpz_init (z);
        mpz_set_ui (z, n);
        inexact = mpfr_pow_z (y, x, z, rnd);
        mpz_clear (z);
        return inexact;
      }
  
    inexact = mpfr_set (y, res, rnd);
    mpfr_clear (res);
  
    MPFR_SAVE_EXPO_FREE (expo);
    return mpfr_check_range (y, inexact, rnd);
  }
  