1/* mpfr_get_ld, mpfr_get_ld_2exp -- convert a multiple precision floating-point 2 number to a machine long double 3 4Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. 5Contributed by the AriC and Caramel projects, INRIA. 6 7This file is part of the GNU MPFR Library. 8 9The GNU MPFR Library is free software; you can redistribute it and/or modify 10it under the terms of the GNU Lesser General Public License as published by 11the Free Software Foundation; either version 3 of the License, or (at your 12option) any later version. 13 14The GNU MPFR Library is distributed in the hope that it will be useful, but 15WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 16or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 17License for more details. 18 19You should have received a copy of the GNU Lesser General Public License 20along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 21http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2251 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 23 24#include <float.h> 25 26#include "mpfr-impl.h" 27 28#ifndef HAVE_LDOUBLE_IEEE_EXT_LITTLE 29 30long double 31mpfr_get_ld (mpfr_srcptr x, mpfr_rnd_t rnd_mode) 32{ 33 34 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 35 return (long double) mpfr_get_d (x, rnd_mode); 36 else /* now x is a normal non-zero number */ 37 { 38 long double r; /* result */ 39 long double m; 40 double s; /* part of result */ 41 mpfr_exp_t sh; /* exponent shift, so that x/2^sh is in the double range */ 42 mpfr_t y, z; 43 int sign; 44 45 /* first round x to the target long double precision, so that 46 all subsequent operations are exact (this avoids double rounding 47 problems) */ 48 mpfr_init2 (y, MPFR_LDBL_MANT_DIG); 49 mpfr_init2 (z, MPFR_LDBL_MANT_DIG); 50 /* Note about the precision of z: even though IEEE_DBL_MANT_DIG is 51 sufficient, z has been set to the same precision as y so that 52 the mpfr_sub below calls mpfr_sub1sp, which is faster than the 53 generic subtraction, even in this particular case (from tests 54 done by Patrick Pelissier on a 64-bit Core2 Duo against r7285). 55 But here there is an important cancellation in the subtraction. 56 TODO: get more information about what has been tested. */ 57 58 mpfr_set (y, x, rnd_mode); 59 sh = MPFR_GET_EXP (y); 60 sign = MPFR_SIGN (y); 61 MPFR_SET_EXP (y, 0); 62 MPFR_SET_POS (y); 63 64 r = 0.0; 65 do { 66 s = mpfr_get_d (y, MPFR_RNDN); /* high part of y */ 67 r += (long double) s; 68 mpfr_set_d (z, s, MPFR_RNDN); /* exact */ 69 mpfr_sub (y, y, z, MPFR_RNDN); /* exact */ 70 } while (!MPFR_IS_ZERO (y)); 71 72 mpfr_clear (z); 73 mpfr_clear (y); 74 75 /* we now have to multiply back by 2^sh */ 76 MPFR_ASSERTD (r > 0); 77 if (sh != 0) 78 { 79 /* An overflow may occurs (example: 0.5*2^1024) */ 80 while (r < 1.0) 81 { 82 r += r; 83 sh--; 84 } 85 86 if (sh > 0) 87 m = 2.0; 88 else 89 { 90 m = 0.5; 91 sh = -sh; 92 } 93 94 for (;;) 95 { 96 if (sh % 2) 97 r = r * m; 98 sh >>= 1; 99 if (sh == 0) 100 break; 101 m = m * m; 102 } 103 } 104 if (sign < 0) 105 r = -r; 106 return r; 107 } 108} 109 110#else 111 112long double 113mpfr_get_ld (mpfr_srcptr x, mpfr_rnd_t rnd_mode) 114{ 115 mpfr_long_double_t ld; 116 mpfr_t tmp; 117 int inex; 118 MPFR_SAVE_EXPO_DECL (expo); 119 120 MPFR_SAVE_EXPO_MARK (expo); 121 122 mpfr_init2 (tmp, MPFR_LDBL_MANT_DIG); 123 inex = mpfr_set (tmp, x, rnd_mode); 124 125 mpfr_set_emin (-16382-63); 126 mpfr_set_emax (16384); 127 mpfr_subnormalize (tmp, mpfr_check_range (tmp, inex, rnd_mode), rnd_mode); 128 mpfr_prec_round (tmp, 64, MPFR_RNDZ); /* exact */ 129 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (tmp))) 130 ld.ld = (long double) mpfr_get_d (tmp, rnd_mode); 131 else 132 { 133 mp_limb_t *tmpmant; 134 mpfr_exp_t e, denorm; 135 136 tmpmant = MPFR_MANT (tmp); 137 e = MPFR_GET_EXP (tmp); 138 /* the smallest normal number is 2^(-16382), which is 0.5*2^(-16381) 139 in MPFR, thus any exponent <= -16382 corresponds to a subnormal 140 number */ 141 denorm = MPFR_UNLIKELY (e <= -16382) ? - e - 16382 + 1 : 0; 142#if GMP_NUMB_BITS >= 64 143 ld.s.manl = (tmpmant[0] >> denorm); 144 ld.s.manh = (tmpmant[0] >> denorm) >> 32; 145#elif GMP_NUMB_BITS == 32 146 if (MPFR_LIKELY (denorm == 0)) 147 { 148 ld.s.manl = tmpmant[0]; 149 ld.s.manh = tmpmant[1]; 150 } 151 else if (denorm < 32) 152 { 153 ld.s.manl = (tmpmant[0] >> denorm) | (tmpmant[1] << (32 - denorm)); 154 ld.s.manh = tmpmant[1] >> denorm; 155 } 156 else /* 32 <= denorm <= 64 */ 157 { 158 ld.s.manl = tmpmant[1] >> (denorm - 32); 159 ld.s.manh = 0; 160 } 161#else 162# error "GMP_NUMB_BITS must be 32 or >= 64" 163 /* Other values have never been supported anyway. */ 164#endif 165 if (MPFR_LIKELY (denorm == 0)) 166 { 167 ld.s.exph = (e + 0x3FFE) >> 8; 168 ld.s.expl = (e + 0x3FFE); 169 } 170 else 171 ld.s.exph = ld.s.expl = 0; 172 ld.s.sign = MPFR_IS_NEG (x); 173 } 174 175 mpfr_clear (tmp); 176 MPFR_SAVE_EXPO_FREE (expo); 177 return ld.ld; 178} 179 180#endif 181 182/* contributed by Damien Stehle */ 183long double 184mpfr_get_ld_2exp (long *expptr, mpfr_srcptr src, mpfr_rnd_t rnd_mode) 185{ 186 long double ret; 187 mpfr_exp_t exp; 188 mpfr_t tmp; 189 190 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src))) 191 return (long double) mpfr_get_d_2exp (expptr, src, rnd_mode); 192 193 tmp[0] = *src; /* Hack copy mpfr_t */ 194 MPFR_SET_EXP (tmp, 0); 195 ret = mpfr_get_ld (tmp, rnd_mode); 196 197 if (MPFR_IS_PURE_FP(src)) 198 { 199 exp = MPFR_GET_EXP (src); 200 201 /* rounding can give 1.0, adjust back to 0.5 <= abs(ret) < 1.0 */ 202 if (ret == 1.0) 203 { 204 ret = 0.5; 205 exp ++; 206 } 207 else if (ret == -1.0) 208 { 209 ret = -0.5; 210 exp ++; 211 } 212 213 MPFR_ASSERTN ((ret >= 0.5 && ret < 1.0) 214 || (ret <= -0.5 && ret > -1.0)); 215 MPFR_ASSERTN (exp >= LONG_MIN && exp <= LONG_MAX); 216 } 217 else 218 exp = 0; 219 220 *expptr = exp; 221 return ret; 222} 223