1/* mpfr_exp -- exponential of a floating-point number 2 3Copyright 1999-2023 Free Software Foundation, Inc. 4Contributed by the AriC and Caramba projects, INRIA. 5 6This file is part of the GNU MPFR Library. 7 8The GNU MPFR Library is free software; you can redistribute it and/or modify 9it under the terms of the GNU Lesser General Public License as published by 10the Free Software Foundation; either version 3 of the License, or (at your 11option) any later version. 12 13The GNU MPFR Library is distributed in the hope that it will be useful, but 14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16License for more details. 17 18You should have received a copy of the GNU Lesser General Public License 19along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2151 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. */ 28static MPFR_THREAD_ATTR mpfr_exp_t previous_emin; 29static MPFR_THREAD_ATTR mp_limb_t bound_emin_limb[(32 - 1) / GMP_NUMB_BITS + 1]; 30static MPFR_THREAD_ATTR mpfr_t bound_emin; 31static MPFR_THREAD_ATTR mpfr_exp_t previous_emax; 32static MPFR_THREAD_ATTR mp_limb_t bound_emax_limb[(32 - 1) / GMP_NUMB_BITS + 1]; 33static MPFR_THREAD_ATTR mpfr_t bound_emax; 34 35int 36mpfr_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} 188