1 /* mpfr_nextabove, mpfr_nextbelow, mpfr_nexttoward -- next representable 2 floating-point number 3 4 Copyright 1999, 2001-2018 Free Software Foundation, Inc. 5 Contributed by the AriC and Caramba projects, INRIA. 6 7 This file is part of the GNU MPFR Library. 8 9 The GNU MPFR Library is free software; you can redistribute it and/or modify 10 it under the terms of the GNU Lesser General Public License as published by 11 the Free Software Foundation; either version 3 of the License, or (at your 12 option) any later version. 13 14 The GNU MPFR Library is distributed in the hope that it will be useful, but 15 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 16 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 17 License for more details. 18 19 You should have received a copy of the GNU Lesser General Public License 20 along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 21 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 22 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 23 24 /* Note concerning the exceptions: In case of NaN result, the NaN flag is 25 * set as usual. No underflow or overflow is generated (this contradicts 26 * the obsolete IEEE 754-1985 standard for Nextafter, but conforms to the 27 * current standard IEEE 754-2008 for nextUp and nextDown). 28 */ 29 30 #include "mpfr-impl.h" 31 32 void 33 mpfr_nexttozero (mpfr_ptr x) 34 { 35 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 36 { 37 if (MPFR_IS_INF (x)) 38 { 39 mpfr_setmax (x, __gmpfr_emax); 40 } 41 else 42 { 43 MPFR_ASSERTN (MPFR_IS_ZERO (x)); 44 MPFR_CHANGE_SIGN(x); 45 mpfr_setmin (x, __gmpfr_emin); 46 } 47 } 48 else 49 { 50 mp_size_t xn; 51 int sh; 52 mp_limb_t *xp; 53 54 xn = MPFR_LIMB_SIZE (x); 55 MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC(x)); 56 xp = MPFR_MANT(x); 57 mpn_sub_1 (xp, xp, xn, MPFR_LIMB_ONE << sh); 58 if (MPFR_UNLIKELY (MPFR_LIMB_MSB (xp[xn-1]) == 0)) 59 { /* was an exact power of two: not normalized any more, 60 thus do not use MPFR_GET_EXP. */ 61 mpfr_exp_t exp = MPFR_EXP (x); 62 if (MPFR_UNLIKELY (exp == __gmpfr_emin)) 63 MPFR_SET_ZERO(x); 64 else 65 { 66 MPFR_SET_EXP (x, exp - 1); 67 /* The following is valid whether xn = 1 or xn > 1. */ 68 xp[xn-1] |= MPFR_LIMB_HIGHBIT; 69 } 70 } 71 } 72 } 73 74 void 75 mpfr_nexttoinf (mpfr_ptr x) 76 { 77 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 78 { 79 if (MPFR_IS_ZERO (x)) 80 mpfr_setmin (x, __gmpfr_emin); 81 } 82 else 83 { 84 mp_size_t xn; 85 int sh; 86 mp_limb_t *xp; 87 88 xn = MPFR_LIMB_SIZE (x); 89 MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC(x)); 90 xp = MPFR_MANT(x); 91 if (MPFR_UNLIKELY (mpn_add_1 (xp, xp, xn, MPFR_LIMB_ONE << sh))) 92 /* got 1.0000... */ 93 { 94 mpfr_exp_t exp = MPFR_EXP (x); 95 if (MPFR_UNLIKELY (exp == __gmpfr_emax)) 96 MPFR_SET_INF (x); 97 else 98 { 99 MPFR_SET_EXP (x, exp + 1); 100 xp[xn-1] = MPFR_LIMB_HIGHBIT; 101 } 102 } 103 } 104 } 105 106 void 107 mpfr_nextabove (mpfr_ptr x) 108 { 109 if (MPFR_UNLIKELY(MPFR_IS_NAN(x))) 110 { 111 __gmpfr_flags |= MPFR_FLAGS_NAN; 112 return; 113 } 114 if (MPFR_IS_NEG(x)) 115 mpfr_nexttozero (x); 116 else 117 mpfr_nexttoinf (x); 118 } 119 120 void 121 mpfr_nextbelow (mpfr_ptr x) 122 { 123 if (MPFR_UNLIKELY(MPFR_IS_NAN(x))) 124 { 125 __gmpfr_flags |= MPFR_FLAGS_NAN; 126 return; 127 } 128 129 if (MPFR_IS_NEG(x)) 130 mpfr_nexttoinf (x); 131 else 132 mpfr_nexttozero (x); 133 } 134 135 void 136 mpfr_nexttoward (mpfr_ptr x, mpfr_srcptr y) 137 { 138 int s; 139 140 if (MPFR_UNLIKELY(MPFR_IS_NAN(x))) 141 { 142 __gmpfr_flags |= MPFR_FLAGS_NAN; 143 return; 144 } 145 else if (MPFR_UNLIKELY(MPFR_IS_NAN(x) || MPFR_IS_NAN(y))) 146 { 147 MPFR_SET_NAN(x); 148 __gmpfr_flags |= MPFR_FLAGS_NAN; 149 return; 150 } 151 152 s = mpfr_cmp (x, y); 153 if (s == 0) 154 return; 155 else if (s < 0) 156 mpfr_nextabove (x); 157 else 158 mpfr_nextbelow (x); 159 } 160