source/libs/mpfr/mpfr-3.1.3/src/cbrt.c

   1 /* mpfr_cbrt -- cube root function.
   2
   3 Copyright 2002-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
  22
  23 #define MPFR_NEED_LONGLONG_H
  24 #include "mpfr-impl.h"
  25
  26  /* The computation of y = x^(1/3) is done as follows:
  27
  28     Let x = sign * m * 2^(3*e) where m is an integer
  29
  30     with 2^(3n-3) <= m < 2^(3n) where n = PREC(y)
  31
  32     and m = s^3 + r where 0 <= r and m < (s+1)^3
  33
  34     we want that s has n bits i.e. s >= 2^(n-1), or m >= 2^(3n-3)
  35     i.e. m must have at least 3n-2 bits
  36
  37     then x^(1/3) = s * 2^e if r=0
  38          x^(1/3) = (s+1) * 2^e if round up
  39          x^(1/3) = (s-1) * 2^e if round down
  40          x^(1/3) = s * 2^e if nearest and r < 3/2*s^2+3/4*s+1/8
  41                    (s+1) * 2^e otherwise
  42  */
  43
  44 int
  45 mpfr_cbrt (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
  46 {
  47   mpz_t m;
  48   mpfr_exp_t e, r, sh;
  49   mpfr_prec_t n, size_m, tmp;
  50   int inexact, negative;
  51   MPFR_SAVE_EXPO_DECL (expo);
  52
  53   MPFR_LOG_FUNC (
  54     ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
  55     ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
  56      inexact));
  57
  58   /* special values */
  59   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
  60     {
  61       if (MPFR_IS_NAN (x))
  62         {
  63           MPFR_SET_NAN (y);
  64           MPFR_RET_NAN;
  65         }
  66       else if (MPFR_IS_INF (x))
  67         {
  68           MPFR_SET_INF (y);
  69           MPFR_SET_SAME_SIGN (y, x);
  70           MPFR_RET (0);
  71         }
  72       /* case 0: cbrt(+/- 0) = +/- 0 */
  73       else /* x is necessarily 0 */
  74         {
  75           MPFR_ASSERTD (MPFR_IS_ZERO (x));
  76           MPFR_SET_ZERO (y);
  77           MPFR_SET_SAME_SIGN (y, x);
  78           MPFR_RET (0);
  79         }
  80     }
  81
  82   /* General case */
  83   MPFR_SAVE_EXPO_MARK (expo);
  84   mpz_init (m);
  85
  86   e = mpfr_get_z_2exp (m, x);                /* x = m * 2^e */
  87   if ((negative = MPFR_IS_NEG(x)))
  88     mpz_neg (m, m);
  89   r = e % 3;
  90   if (r < 0)
  91     r += 3;
  92   /* x = (m*2^r) * 2^(e-r) = (m*2^r) * 2^(3*q) */
  93
  94   MPFR_MPZ_SIZEINBASE2 (size_m, m);
  95   n = MPFR_PREC (y) + (rnd_mode == MPFR_RNDN);
  96
  97   /* we want 3*n-2 <= size_m + 3*sh + r <= 3*n
  98      i.e. 3*sh + size_m + r <= 3*n */
  99   sh = (3 * (mpfr_exp_t) n - (mpfr_exp_t) size_m - r) / 3;
 100   sh = 3 * sh + r;
 101   if (sh >= 0)
 102     {
 103       mpz_mul_2exp (m, m, sh);
 104       e = e - sh;
 105     }
 106   else if (r > 0)
 107     {
 108       mpz_mul_2exp (m, m, r);
 109       e = e - r;
 110     }
 111
 112   /* invariant: x = m*2^e, with e divisible by 3 */
 113
 114   /* we reuse the variable m to store the cube root, since it is not needed
 115      any more: we just need to know if the root is exact */
 116   inexact = mpz_root (m, m, 3) == 0;
 117
 118   MPFR_MPZ_SIZEINBASE2 (tmp, m);
 119   sh = tmp - n;
 120   if (sh > 0) /* we have to flush to 0 the last sh bits from m */
 121     {
 122       inexact = inexact || ((mpfr_exp_t) mpz_scan1 (m, 0) < sh);
 123       mpz_fdiv_q_2exp (m, m, sh);
 124       e += 3 * sh;
 125     }
 126
 127   if (inexact)
 128     {
 129       if (negative)
 130         rnd_mode = MPFR_INVERT_RND (rnd_mode);
 131       if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA
 132           || (rnd_mode == MPFR_RNDN && mpz_tstbit (m, 0)))
 133         inexact = 1, mpz_add_ui (m, m, 1);
 134       else
 135         inexact = -1;
 136     }
 137
 138   /* either inexact is not zero, and the conversion is exact, i.e. inexact
 139      is not changed; or inexact=0, and inexact is set only when
 140      rnd_mode=MPFR_RNDN and bit (n+1) from m is 1 */
 141   inexact += mpfr_set_z (y, m, MPFR_RNDN);
 142   MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / 3);
 143
 144   if (negative)
 145     {
 146       MPFR_CHANGE_SIGN (y);
 147       inexact = -inexact;
 148     }
 149
 150   mpz_clear (m);
 151   MPFR_SAVE_EXPO_FREE (expo);
 152   return mpfr_check_range (y, inexact, rnd_mode);
 153 }