summaryrefslogtreecommitdiff
path: root/exp.c
blob: 471a5f6bdaa1eaab54376e39d32ed320d0291166 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
/* mpfr_exp -- exponential of a floating-point number

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao 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 2.1 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.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

#include "mpfr-impl.h"

/* #define DEBUG */

int
mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mp_exp_t expx;
  mp_prec_t precy;
  int inexact;
  MPFR_SAVE_EXPO_DECL (expo);

  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
                 ("y[%#R]=%R inexact=%d", y, 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))
        {
          if (MPFR_IS_POS(x))
            MPFR_SET_INF(y);
          else
            MPFR_SET_ZERO(y);
          MPFR_SET_POS(y);
          MPFR_RET(0);
        }
      else
        {
          MPFR_ASSERTD(MPFR_IS_ZERO(x));
          return mpfr_set_ui (y, 1, rnd_mode);
        }
    }

  /* First, let's detect most overflow and underflow cases. */
  {
    mpfr_t e, bound;

    /* We must extended the exponent range and save the flags now. */
    MPFR_SAVE_EXPO_MARK (expo);

    mpfr_init2 (e, sizeof (mp_exp_t) * CHAR_BIT);
    mpfr_init2 (bound, 32);

    inexact = mpfr_set_exp_t (e, expo.saved_emax, GMP_RNDN);
    MPFR_ASSERTD (inexact == 0);
    mpfr_const_log2 (bound, expo.saved_emax < 0 ? GMP_RNDD : GMP_RNDU);
    mpfr_mul (bound, bound, e, GMP_RNDU);
    if (MPFR_UNLIKELY (mpfr_cmp (x, bound) >= 0))
      {
        /* x > log(2^emax), thus exp(x) > 2^emax */
        mpfr_clears (e, bound, (mpfr_ptr) 0);
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_overflow (y, rnd_mode, 1);
      }

    inexact = mpfr_set_exp_t (e, expo.saved_emin, GMP_RNDN);
    MPFR_ASSERTD (inexact == 0);
    inexact = mpfr_sub_ui (e, e, 2, GMP_RNDN);
    MPFR_ASSERTD (inexact == 0);
    mpfr_const_log2 (bound, expo.saved_emin < 0 ? GMP_RNDU : GMP_RNDD);
    mpfr_mul (bound, bound, e, GMP_RNDD);
    if (MPFR_UNLIKELY (mpfr_cmp (x, bound) <= 0))
      {
        /* x < log(2^(emin - 2)), thus exp(x) < 2^(emin - 2) */
        mpfr_clears (e, bound, (mpfr_ptr) 0);
        MPFR_SAVE_EXPO_FREE (expo);
        return mpfr_underflow (y, rnd_mode == GMP_RNDN ? GMP_RNDZ : rnd_mode,
                               1);
      }

    /* Other overflow/underflow cases must be detected
       by the generic routines. */
    mpfr_clears (e, bound, (mpfr_ptr) 0);
    MPFR_SAVE_EXPO_FREE (expo);
  }

  MPFR_CLEAR_FLAGS (y);

  expx  = MPFR_GET_EXP (x);
  precy = MPFR_PREC (y);

  /* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
  if (MPFR_UNLIKELY (expx < 0 && (mpfr_uexp_t) (-expx) > precy))
    {
      mp_exp_t emin = __gmpfr_emin;
      mp_exp_t emax = __gmpfr_emax;
      int signx = MPFR_SIGN (x);

      MPFR_SET_POS (y);
      if (MPFR_IS_NEG_SIGN (signx) && (rnd_mode == GMP_RNDD ||
                                       rnd_mode == GMP_RNDZ))
        {
          __gmpfr_emin = 0;
          __gmpfr_emax = 0;
          mpfr_setmax (y, 0);  /* y = 1 - epsilon */
          inexact = -1;
        }
      else
        {
          __gmpfr_emin = 1;
          __gmpfr_emax = 1;
          mpfr_setmin (y, 1);  /* y = 1 */
          if (MPFR_IS_POS_SIGN (signx) && rnd_mode == GMP_RNDU)
            {
              mp_size_t yn;
              int sh;

              yn = 1 + (MPFR_PREC(y) - 1) / BITS_PER_MP_LIMB;
              sh = (mp_prec_t) yn * BITS_PER_MP_LIMB - MPFR_PREC(y);
              MPFR_MANT(y)[0] += MPFR_LIMB_ONE << sh;
              inexact = 1;
            }
          else
            inexact = -MPFR_FROM_SIGN_TO_INT(signx);
        }

      __gmpfr_emin = emin;
      __gmpfr_emax = emax;
    }
  else  /* General case */
    {
      if (MPFR_UNLIKELY (precy > MPFR_EXP_THRESHOLD))
        /* mpfr_exp_3 saves the exponent range and flags itself, otherwise
           the flag changes in mpfr_exp_3 are lost */
        inexact = mpfr_exp_3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
      else
        {
          MPFR_SAVE_EXPO_MARK (expo);
          inexact = mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
          MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
          MPFR_SAVE_EXPO_FREE (expo);
        }
    }

  return mpfr_check_range (y, inexact, rnd_mode);
}