1 /* mpf_get_str (digit_ptr, exp, base, n_digits, a) -- Convert the floating 2 point number A to a base BASE number and store N_DIGITS raw digits at 3 DIGIT_PTR, and the base BASE exponent in the word pointed to by EXP. For 4 example, the number 3.1416 would be returned as "31416" in DIGIT_PTR and 5 1 in EXP. 6 7 Copyright 1993, 1994, 1995, 1996, 1997, 2000, 2001, 2002, 2003, 2005, 2006 Free 8 Software Foundation, Inc. 9 10 This file is part of the GNU MP Library. 11 12 The GNU MP Library is free software; you can redistribute it and/or modify 13 it under the terms of the GNU Lesser General Public License as published by 14 the Free Software Foundation; either version 3 of the License, or (at your 15 option) any later version. 16 17 The GNU MP Library is distributed in the hope that it will be useful, but 18 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 19 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 20 License for more details. 21 22 You should have received a copy of the GNU Lesser General Public License 23 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 24 25 #include <stdlib.h> /* for NULL */ 26 #include "gmp.h" 27 #include "gmp-impl.h" 28 #include "longlong.h" /* for count_leading_zeros */ 29 30 /* Could use some more work. 31 32 1. Allocation is excessive. Try to combine areas. Perhaps use result 33 string area for temp limb space? 34 2. We generate up to two limbs of extra digits. This is because we don't 35 check the exact number of bits in the input operand, and from that 36 compute an accurate exponent (variable e in the code). It would be 37 cleaner and probably somewhat faster to change this. 38 */ 39 40 /* Compute base^exp and return the most significant prec limbs in rp[]. 41 Put the count of omitted low limbs in *ign. 42 Return the actual size (which might be less than prec). 43 Allocation of rp[] and the temporary tp[] should be 2*prec+2 limbs. */ 44 static mp_size_t 45 mpn_pow_1_highpart (mp_ptr rp, mp_size_t *ignp, 46 mp_limb_t base, unsigned long exp, 47 mp_size_t prec, mp_ptr tp) 48 { 49 mp_size_t ign; /* counts number of ignored low limbs in r */ 50 mp_size_t off; /* keeps track of offset where value starts */ 51 mp_ptr passed_rp = rp; 52 mp_size_t rn; 53 int cnt; 54 int i; 55 56 if (exp == 0) 57 { 58 rp[0] = 1; 59 *ignp = 0; 60 return 1; 61 } 62 63 rp[0] = base; 64 rn = 1; 65 off = 0; 66 ign = 0; 67 count_leading_zeros (cnt, exp); 68 for (i = GMP_LIMB_BITS - cnt - 2; i >= 0; i--) 69 { 70 mpn_sqr (tp, rp + off, rn); 71 rn = 2 * rn; 72 rn -= tp[rn - 1] == 0; 73 ign <<= 1; 74 75 off = 0; 76 if (rn > prec) 77 { 78 ign += rn - prec; 79 off = rn - prec; 80 rn = prec; 81 } 82 MP_PTR_SWAP (rp, tp); 83 84 if (((exp >> i) & 1) != 0) 85 { 86 mp_limb_t cy; 87 cy = mpn_mul_1 (rp, rp + off, rn, base); 88 rp[rn] = cy; 89 rn += cy != 0; 90 off = 0; 91 } 92 } 93 94 if (rn > prec) 95 { 96 ASSERT (rn == prec + 1); 97 98 ign += rn - prec; 99 rp += rn - prec; 100 rn = prec; 101 } 102 103 /* With somewhat less than 50% probability, we can skip this copy. */ 104 if (passed_rp != rp + off) 105 MPN_COPY_INCR (passed_rp, rp + off, rn); 106 *ignp = ign; 107 return rn; 108 } 109 110 char * 111 mpf_get_str (char *dbuf, mp_exp_t *exp, int base, size_t n_digits, mpf_srcptr u) 112 { 113 mp_exp_t ue; 114 mp_size_t n_limbs_needed; 115 size_t max_digits; 116 mp_ptr up, pp, tp; 117 mp_size_t un, pn, tn; 118 unsigned char *tstr; 119 mp_exp_t exp_in_base; 120 size_t n_digits_computed; 121 mp_size_t i; 122 const char *num_to_text; 123 size_t alloc_size = 0; 124 char *dp; 125 TMP_DECL; 126 127 up = PTR(u); 128 un = ABSIZ(u); 129 ue = EXP(u); 130 131 if (base >= 0) 132 { 133 num_to_text = "0123456789abcdefghijklmnopqrstuvwxyz"; 134 if (base == 0) 135 base = 10; 136 else if (base > 36) 137 { 138 num_to_text = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; 139 if (base > 62) 140 return NULL; 141 } 142 } 143 else 144 { 145 base = -base; 146 num_to_text = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; 147 } 148 149 MPF_SIGNIFICANT_DIGITS (max_digits, base, PREC(u)); 150 if (n_digits == 0 || n_digits > max_digits) 151 n_digits = max_digits; 152 153 if (dbuf == 0) 154 { 155 /* We didn't get a string from the user. Allocate one (and return 156 a pointer to it) with space for `-' and terminating null. */ 157 alloc_size = n_digits + 2; 158 dbuf = (char *) (*__gmp_allocate_func) (n_digits + 2); 159 } 160 161 if (un == 0) 162 { 163 *exp = 0; 164 *dbuf = 0; 165 n_digits = 0; 166 goto done; 167 } 168 169 TMP_MARK; 170 171 /* Allocate temporary digit space. We can't put digits directly in the user 172 area, since we generate more digits than requested. (We allocate 173 2 * GMP_LIMB_BITS extra bytes because of the digit block nature of the 174 conversion.) */ 175 tstr = (unsigned char *) TMP_ALLOC (n_digits + 2 * GMP_LIMB_BITS + 3); 176 177 n_limbs_needed = 2 + (mp_size_t) 178 (n_digits / (GMP_NUMB_BITS * mp_bases[base].chars_per_bit_exactly)); 179 180 if (ue <= n_limbs_needed) 181 { 182 /* We need to multiply number by base^n to get an n_digits integer part. */ 183 mp_size_t n_more_limbs_needed, ign, off; 184 unsigned long e; 185 186 n_more_limbs_needed = n_limbs_needed - ue; 187 e = (unsigned long) n_more_limbs_needed * (GMP_NUMB_BITS * mp_bases[base].chars_per_bit_exactly); 188 189 if (un > n_limbs_needed) 190 { 191 up += un - n_limbs_needed; 192 un = n_limbs_needed; 193 } 194 pp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 195 tp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 196 197 pn = mpn_pow_1_highpart (pp, &ign, (mp_limb_t) base, e, n_limbs_needed, tp); 198 if (un > pn) 199 mpn_mul (tp, up, un, pp, pn); /* FIXME: mpn_mul_highpart */ 200 else 201 mpn_mul (tp, pp, pn, up, un); /* FIXME: mpn_mul_highpart */ 202 tn = un + pn; 203 tn -= tp[tn - 1] == 0; 204 off = un - ue - ign; 205 if (off < 0) 206 { 207 MPN_COPY_DECR (tp - off, tp, tn); 208 MPN_ZERO (tp, -off); 209 tn -= off; 210 off = 0; 211 } 212 n_digits_computed = mpn_get_str (tstr, base, tp + off, tn - off); 213 214 exp_in_base = n_digits_computed - e; 215 } 216 else 217 { 218 /* We need to divide number by base^n to get an n_digits integer part. */ 219 mp_size_t n_less_limbs_needed, ign, off, xn; 220 unsigned long e; 221 mp_ptr dummyp, xp; 222 223 n_less_limbs_needed = ue - n_limbs_needed; 224 e = (unsigned long) n_less_limbs_needed * (GMP_NUMB_BITS * mp_bases[base].chars_per_bit_exactly); 225 226 if (un > n_limbs_needed) 227 { 228 up += un - n_limbs_needed; 229 un = n_limbs_needed; 230 } 231 pp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 232 tp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 233 234 pn = mpn_pow_1_highpart (pp, &ign, (mp_limb_t) base, e, n_limbs_needed, tp); 235 236 xn = n_limbs_needed + (n_less_limbs_needed-ign); 237 xp = TMP_ALLOC_LIMBS (xn); 238 off = xn - un; 239 MPN_ZERO (xp, off); 240 MPN_COPY (xp + off, up, un); 241 242 dummyp = TMP_ALLOC_LIMBS (pn); 243 mpn_tdiv_qr (tp, dummyp, (mp_size_t) 0, xp, xn, pp, pn); 244 tn = xn - pn + 1; 245 tn -= tp[tn - 1] == 0; 246 n_digits_computed = mpn_get_str (tstr, base, tp, tn); 247 248 exp_in_base = n_digits_computed + e; 249 } 250 251 /* We should normally have computed too many digits. Round the result 252 at the point indicated by n_digits. */ 253 if (n_digits_computed > n_digits) 254 { 255 size_t i; 256 /* Round the result. */ 257 if (tstr[n_digits] * 2 >= base) 258 { 259 n_digits_computed = n_digits; 260 for (i = n_digits - 1;; i--) 261 { 262 unsigned int x; 263 x = ++(tstr[i]); 264 if (x != base) 265 break; 266 n_digits_computed--; 267 if (i == 0) 268 { 269 /* We had something like `bbbbbbb...bd', where 2*d >= base 270 and `b' denotes digit with significance base - 1. 271 This rounds up to `1', increasing the exponent. */ 272 tstr[0] = 1; 273 n_digits_computed = 1; 274 exp_in_base++; 275 break; 276 } 277 } 278 } 279 } 280 281 /* We might have fewer digits than requested as a result of rounding above, 282 (i.e. 0.999999 => 1.0) or because we have a number that simply doesn't 283 need many digits in this base (e.g., 0.125 in base 10). */ 284 if (n_digits > n_digits_computed) 285 n_digits = n_digits_computed; 286 287 /* Remove trailing 0. There can be many zeros. */ 288 while (n_digits != 0 && tstr[n_digits - 1] == 0) 289 n_digits--; 290 291 dp = dbuf + (SIZ(u) < 0); 292 293 /* Translate to ASCII and copy to result string. */ 294 for (i = 0; i < n_digits; i++) 295 dp[i] = num_to_text[tstr[i]]; 296 dp[n_digits] = 0; 297 298 *exp = exp_in_base; 299 300 if (SIZ(u) < 0) 301 { 302 dbuf[0] = '-'; 303 n_digits++; 304 } 305 306 TMP_FREE; 307 308 done: 309 /* If the string was alloced then resize it down to the actual space 310 required. */ 311 if (alloc_size != 0) 312 { 313 __GMP_REALLOCATE_FUNC_MAYBE_TYPE (dbuf, alloc_size, n_digits + 1, char); 314 } 315 316 return dbuf; 317 } 318