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

   1 /* mpfr_hypot -- Euclidean distance
   2
   3 Copyright 2001-2015 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 hypot of x and y is done by  *
  27  *    hypot(x,y)= sqrt(x^2+y^2) = z                */
  28
  29 int
  30 mpfr_hypot (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd_mode)
  31 {
  32   int inexact, exact;
  33   mpfr_t t, te, ti; /* auxiliary variables */
  34   mpfr_prec_t N, Nz; /* size variables */
  35   mpfr_prec_t Nt;   /* precision of the intermediary variable */
  36   mpfr_prec_t threshold;
  37   mpfr_exp_t Ex, sh;
  38   mpfr_uexp_t diff_exp;
  39
  40   MPFR_SAVE_EXPO_DECL (expo);
  41   MPFR_ZIV_DECL (loop);
  42   MPFR_BLOCK_DECL (flags);
  43
  44   MPFR_LOG_FUNC
  45     (("x[%Pu]=%.*Rg y[%Pu]=%.*Rg rnd=%d",
  46       mpfr_get_prec (x), mpfr_log_prec, x,
  47       mpfr_get_prec (y), mpfr_log_prec, y, rnd_mode),
  48      ("z[%Pu]=%.*Rg inexact=%d",
  49       mpfr_get_prec (z), mpfr_log_prec, z, inexact));
  50
  51   /* particular cases */
  52   if (MPFR_ARE_SINGULAR (x, y))
  53     {
  54       if (MPFR_IS_INF (x) || MPFR_IS_INF (y))
  55         {
  56           /* Return +inf, even when the other number is NaN. */
  57           MPFR_SET_INF (z);
  58           MPFR_SET_POS (z);
  59           MPFR_RET (0);
  60         }
  61       else if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y))
  62         {
  63           MPFR_SET_NAN (z);
  64           MPFR_RET_NAN;
  65         }
  66       else if (MPFR_IS_ZERO (x))
  67         return mpfr_abs (z, y, rnd_mode);
  68       else /* y is necessarily 0 */
  69         return mpfr_abs (z, x, rnd_mode);
  70     }
  71
  72   if (mpfr_cmpabs (x, y) < 0)
  73     {
  74       mpfr_srcptr u;
  75       u = x;
  76       x = y;
  77       y = u;
  78     }
  79
  80   /* now |x| >= |y| */
  81
  82   Ex = MPFR_GET_EXP (x);
  83   diff_exp = (mpfr_uexp_t) Ex - MPFR_GET_EXP (y);
  84
  85   N = MPFR_PREC (x);   /* Precision of input variable */
  86   Nz = MPFR_PREC (z);   /* Precision of output variable */
  87   threshold = (MAX (N, Nz) + (rnd_mode == MPFR_RNDN ? 1 : 0)) << 1;
  88   if (rnd_mode == MPFR_RNDA)
  89     rnd_mode = MPFR_RNDU; /* since the result is positive, RNDA = RNDU */
  90
  91   /* Is |x| a suitable approximation to the precision Nz ?
  92      (see algorithms.tex for explanations) */
  93   if (diff_exp > threshold)
  94     /* result is |x| or |x|+ulp(|x|,Nz) */
  95     {
  96       if (MPFR_UNLIKELY (rnd_mode == MPFR_RNDU))
  97         {
  98           /* If z > abs(x), then it was already rounded up; otherwise
  99              z = abs(x), and we need to add one ulp due to y. */
 100           if (mpfr_abs (z, x, rnd_mode) == 0)
 101             mpfr_nexttoinf (z);
 102           MPFR_RET (1);
 103         }
 104       else /* MPFR_RNDZ, MPFR_RNDD, MPFR_RNDN */
 105         {
 106           if (MPFR_LIKELY (Nz >= N))
 107             {
 108               mpfr_abs (z, x, rnd_mode);  /* exact */
 109               MPFR_RET (-1);
 110             }
 111           else
 112             {
 113               MPFR_SET_EXP (z, Ex);
 114               MPFR_SET_SIGN (z, 1);
 115               MPFR_RNDRAW_GEN (inexact, z, MPFR_MANT (x), N, rnd_mode, 1,
 116                                goto addoneulp,
 117                                if (MPFR_UNLIKELY (++ MPFR_EXP (z) >
 118                                                   __gmpfr_emax))
 119                                  return mpfr_overflow (z, rnd_mode, 1);
 120                                );
 121
 122               if (MPFR_UNLIKELY (inexact == 0))
 123                 inexact = -1;
 124               MPFR_RET (inexact);
 125             }
 126         }
 127     }
 128
 129   /* General case */
 130
 131   N = MAX (MPFR_PREC (x), MPFR_PREC (y));
 132
 133   /* working precision */
 134   Nt = Nz + MPFR_INT_CEIL_LOG2 (Nz) + 4;
 135
 136   mpfr_init2 (t, Nt);
 137   mpfr_init2 (te, Nt);
 138   mpfr_init2 (ti, Nt);
 139
 140   MPFR_SAVE_EXPO_MARK (expo);
 141
 142   /* Scale x and y to avoid overflow/underflow in x^2 and overflow in y^2
 143      (as |x| >= |y|). The scaling of y can underflow only when the target
 144      precision is huge, otherwise the case would already have been handled
 145      by the diff_exp > threshold code. */
 146   sh = mpfr_get_emax () / 2 - Ex - 1;
 147
 148   MPFR_ZIV_INIT (loop, Nt);
 149   for (;;)
 150     {
 151       mpfr_prec_t err;
 152
 153       exact = mpfr_mul_2si (te, x, sh, MPFR_RNDZ);
 154       exact |= mpfr_mul_2si (ti, y, sh, MPFR_RNDZ);
 155       exact |= mpfr_sqr (te, te, MPFR_RNDZ);
 156       /* Use fma in order to avoid underflow when diff_exp<=MPFR_EMAX_MAX-2 */
 157       exact |= mpfr_fma (t, ti, ti, te, MPFR_RNDZ);
 158       exact |= mpfr_sqrt (t, t, MPFR_RNDZ);
 159
 160       err = Nt < N ? 4 : 2;
 161       if (MPFR_LIKELY (exact == 0
 162                        || MPFR_CAN_ROUND (t, Nt-err, Nz, rnd_mode)))
 163         break;
 164
 165       MPFR_ZIV_NEXT (loop, Nt);
 166       mpfr_set_prec (t, Nt);
 167       mpfr_set_prec (te, Nt);
 168       mpfr_set_prec (ti, Nt);
 169     }
 170   MPFR_ZIV_FREE (loop);
 171
 172   MPFR_BLOCK (flags, inexact = mpfr_div_2si (z, t, sh, rnd_mode));
 173   MPFR_ASSERTD (exact == 0 || inexact != 0);
 174
 175   mpfr_clear (t);
 176   mpfr_clear (ti);
 177   mpfr_clear (te);
 178
 179   /*
 180     exact  inexact
 181     0         0         result is exact, ternary flag is 0
 182     0       non zero    t is exact, ternary flag given by inexact
 183     1         0         impossible (see above)
 184     1       non zero    ternary flag given by inexact
 185   */
 186
 187   MPFR_SAVE_EXPO_FREE (expo);
 188
 189   if (MPFR_OVERFLOW (flags))
 190     mpfr_set_overflow ();
 191   /* hypot(x,y) >= |x|, thus underflow is not possible. */
 192
 193   return mpfr_check_range (z, inexact, rnd_mode);
 194 }