1 /* mpfr_exp -- exponential of a floating-point number
2
3 Copyright 1999-2023 Free Software Foundation, Inc.
4 Contributed by the AriC and Caramba 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 https://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 #include "mpfr-impl.h"
24
25 /* Cache for emin and emax bounds.
26 Contrary to other caches, it uses a fixed size for the mantissa,
27 so there is no dynamic allocation, and no need to free them. */
28 static MPFR_THREAD_ATTR mpfr_exp_t previous_emin;
29 static MPFR_THREAD_ATTR mp_limb_t bound_emin_limb[(32 - 1) / GMP_NUMB_BITS + 1];
30 static MPFR_THREAD_ATTR mpfr_t bound_emin;
31 static MPFR_THREAD_ATTR mpfr_exp_t previous_emax;
32 static MPFR_THREAD_ATTR mp_limb_t bound_emax_limb[(32 - 1) / GMP_NUMB_BITS + 1];
33 static MPFR_THREAD_ATTR mpfr_t bound_emax;
34
35 int
36 mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
37 {
38 mpfr_exp_t expx;
39 mpfr_prec_t precy;
40 int inexact;
41 MPFR_SAVE_EXPO_DECL (expo);
42
43 MPFR_LOG_FUNC
44 (("x[%Pd]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
45 ("y[%Pd]=%.*Rg inexact=%d",
46 mpfr_get_prec (y), mpfr_log_prec, y, inexact));
47
48 if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) ))
49 {
50 if (MPFR_IS_NAN(x))
51 {
52 MPFR_SET_NAN(y);
53 MPFR_RET_NAN;
54 }
55 else if (MPFR_IS_INF(x))
56 {
57 if (MPFR_IS_POS(x))
58 MPFR_SET_INF(y);
59 else
60 MPFR_SET_ZERO(y);
61 MPFR_SET_POS(y);
62 MPFR_RET(0);
63 }
64 else
65 {
66 MPFR_ASSERTD(MPFR_IS_ZERO(x));
67 return mpfr_set_ui (y, 1, rnd_mode);
68 }
69 }
70
71 /* First, let's detect most overflow and underflow cases. */
72 /* emax bound is cached. Check if the value in cache is ok */
73 if (MPFR_UNLIKELY (mpfr_get_emax() != previous_emax))
74 {
75 /* Recompute the emax bound */
76 mp_limb_t e_limb[MPFR_EXP_LIMB_SIZE];
77 mpfr_t e;
78
79 /* We extend the exponent range and save the flags. */
80 MPFR_SAVE_EXPO_MARK (expo);
81
82 MPFR_TMP_INIT1(e_limb, e, sizeof (mpfr_exp_t) * CHAR_BIT);
83 MPFR_TMP_INIT1(bound_emax_limb, bound_emax, 32);
84
85 inexact = mpfr_set_exp_t (e, expo.saved_emax, MPFR_RNDN);
86 MPFR_ASSERTD (inexact == 0);
87 mpfr_mul (bound_emax, expo.saved_emax < 0 ?
88 __gmpfr_const_log2_RNDD : __gmpfr_const_log2_RNDU,
89 e, MPFR_RNDU);
90 previous_emax = expo.saved_emax;
91 MPFR_SAVE_EXPO_FREE (expo);
92 }
93
94 /* mpfr_cmp works even in reduced emin,emax range */
95 if (MPFR_UNLIKELY (mpfr_cmp (x, bound_emax) >= 0))
96 {
97 /* x > log(2^emax), thus exp(x) > 2^emax */
98 return mpfr_overflow (y, rnd_mode, 1);
99 }
100
101 /* emin bound is cached. Check if the value in cache is ok */
102 if (MPFR_UNLIKELY (mpfr_get_emin() != previous_emin))
103 {
104 mp_limb_t e_limb[MPFR_EXP_LIMB_SIZE];
105 mpfr_t e;
106
107 /* We extend the exponent range and save the flags. */
108 MPFR_SAVE_EXPO_MARK (expo);
109
110 /* avoid using a full limb since arithmetic might be slower */
111 MPFR_TMP_INIT1(e_limb, e, sizeof (mpfr_exp_t) * CHAR_BIT - 1);
112 MPFR_TMP_INIT1(bound_emin_limb, bound_emin, 32);
113
114 inexact = mpfr_set_exp_t (e, expo.saved_emin, MPFR_RNDN);
115 MPFR_ASSERTD (inexact == 0);
116 inexact = mpfr_sub_ui (e, e, 2, MPFR_RNDN);
117 MPFR_ASSERTD (inexact == 0);
118 mpfr_const_log2 (bound_emin, expo.saved_emin < 0 ? MPFR_RNDU : MPFR_RNDD);
119 mpfr_mul (bound_emin, bound_emin, e, MPFR_RNDD);
120 previous_emin = expo.saved_emin;
121 MPFR_SAVE_EXPO_FREE (expo);
122 }
123
124 if (MPFR_UNLIKELY (mpfr_cmp (x, bound_emin) <= 0))
125 {
126 /* x < log(2^(emin - 2)), thus exp(x) < 2^(emin - 2) */
127 return mpfr_underflow (y, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
128 1);
129 }
130
131 expx = MPFR_GET_EXP (x);
132 precy = MPFR_PREC (y);
133
134 /* if x < 2^(-precy), then exp(x) gives 1 +/- 1 ulp(1) */
135 if (MPFR_UNLIKELY (expx < 0 && (mpfr_uexp_t) (-expx) > precy))
136 {
137 mpfr_exp_t emin = __gmpfr_emin;
138 mpfr_exp_t emax = __gmpfr_emax;
139 int signx = MPFR_SIGN (x);
140
141 /* Make sure that the exponent range is large enough:
142 * [0,2] is sufficient in all precisions.
143 */
144 __gmpfr_emin = 0;
145 __gmpfr_emax = 2;
146
147 MPFR_SET_POS (y);
148 if (MPFR_IS_NEG_SIGN (signx) && (rnd_mode == MPFR_RNDD ||
149 rnd_mode == MPFR_RNDZ))
150 {
151 mpfr_setmax (y, 0); /* y = 1 - epsilon */
152 inexact = -1;
153 }
154 else
155 {
156 mpfr_setmin (y, 1); /* y = 1 */
157 if (MPFR_IS_POS_SIGN (signx) && (rnd_mode == MPFR_RNDU ||
158 rnd_mode == MPFR_RNDA))
159 {
160 /* Warning: should work for precision 1 bit too! */
161 mpfr_nextabove (y);
162 inexact = 1;
163 }
164 else
165 inexact = -MPFR_FROM_SIGN_TO_INT(signx);
166 }
167
168 __gmpfr_emin = emin;
169 __gmpfr_emax = emax;
170 }
171 else /* General case */
172 {
173 if (MPFR_UNLIKELY (precy >= MPFR_EXP_THRESHOLD))
174 /* mpfr_exp_3 saves the exponent range and flags itself, otherwise
175 the flag changes in mpfr_exp_3 are lost */
176 inexact = mpfr_exp_3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
177 else
178 {
179 MPFR_SAVE_EXPO_MARK (expo);
180 inexact = mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
181 MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
182 MPFR_SAVE_EXPO_FREE (expo);
183 }
184 }
185
186 return mpfr_check_range (y, inexact, rnd_mode);
187 }