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_n (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) (n_digits / mp_bases[base].chars_per_bit_exactly)) / GMP_NUMB_BITS; 178 179 if (ue <= n_limbs_needed) 180 { 181 /* We need to multiply number by base^n to get an n_digits integer part. */ 182 mp_size_t n_more_limbs_needed, ign, off; 183 unsigned long e; 184 185 n_more_limbs_needed = n_limbs_needed - ue; 186 e = (unsigned long) n_more_limbs_needed * (GMP_NUMB_BITS * mp_bases[base].chars_per_bit_exactly); 187 188 if (un > n_limbs_needed) 189 { 190 up += un - n_limbs_needed; 191 un = n_limbs_needed; 192 } 193 pp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 194 tp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 195 196 pn = mpn_pow_1_highpart (pp, &ign, (mp_limb_t) base, e, n_limbs_needed, tp); 197 if (un > pn) 198 mpn_mul (tp, up, un, pp, pn); /* FIXME: mpn_mul_highpart */ 199 else 200 mpn_mul (tp, pp, pn, up, un); /* FIXME: mpn_mul_highpart */ 201 tn = un + pn; 202 tn -= tp[tn - 1] == 0; 203 off = un - ue - ign; 204 if (off < 0) 205 { 206 MPN_COPY_DECR (tp - off, tp, tn); 207 MPN_ZERO (tp, -off); 208 tn -= off; 209 off = 0; 210 } 211 n_digits_computed = mpn_get_str (tstr, base, tp + off, tn - off); 212 213 exp_in_base = n_digits_computed - e; 214 } 215 else 216 { 217 /* We need to divide number by base^n to get an n_digits integer part. */ 218 mp_size_t n_less_limbs_needed, ign, off, xn; 219 unsigned long e; 220 mp_ptr dummyp, xp; 221 222 n_less_limbs_needed = ue - n_limbs_needed; 223 e = (unsigned long) n_less_limbs_needed * (GMP_NUMB_BITS * mp_bases[base].chars_per_bit_exactly); 224 225 if (un > n_limbs_needed) 226 { 227 up += un - n_limbs_needed; 228 un = n_limbs_needed; 229 } 230 pp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 231 tp = TMP_ALLOC_LIMBS (2 * n_limbs_needed + 2); 232 233 pn = mpn_pow_1_highpart (pp, &ign, (mp_limb_t) base, e, n_limbs_needed, tp); 234 235 xn = n_limbs_needed + (n_less_limbs_needed-ign); 236 xp = TMP_ALLOC_LIMBS (xn); 237 off = xn - un; 238 MPN_ZERO (xp, off); 239 MPN_COPY (xp + off, up, un); 240 241 dummyp = TMP_ALLOC_LIMBS (pn); 242 mpn_tdiv_qr (tp, dummyp, (mp_size_t) 0, xp, xn, pp, pn); 243 tn = xn - pn + 1; 244 tn -= tp[tn - 1] == 0; 245 n_digits_computed = mpn_get_str (tstr, base, tp, tn); 246 247 exp_in_base = n_digits_computed + e; 248 } 249 250 /* We should normally have computed too many digits. Round the result 251 at the point indicated by n_digits. */ 252 if (n_digits_computed > n_digits) 253 { 254 size_t i; 255 /* Round the result. */ 256 if (tstr[n_digits] * 2 >= base) 257 { 258 n_digits_computed = n_digits; 259 for (i = n_digits - 1;; i--) 260 { 261 unsigned int x; 262 x = ++(tstr[i]); 263 if (x != base) 264 break; 265 n_digits_computed--; 266 if (i == 0) 267 { 268 /* We had something like `bbbbbbb...bd', where 2*d >= base 269 and `b' denotes digit with significance base - 1. 270 This rounds up to `1', increasing the exponent. */ 271 tstr[0] = 1; 272 n_digits_computed = 1; 273 exp_in_base++; 274 break; 275 } 276 } 277 } 278 } 279 280 /* We might have fewer digits than requested as a result of rounding above, 281 (i.e. 0.999999 => 1.0) or because we have a number that simply doesn't 282 need many digits in this base (e.g., 0.125 in base 10). */ 283 if (n_digits > n_digits_computed) 284 n_digits = n_digits_computed; 285 286 /* Remove trailing 0. There can be many zeros. */ 287 while (n_digits != 0 && tstr[n_digits - 1] == 0) 288 n_digits--; 289 290 dp = dbuf + (SIZ(u) < 0); 291 292 /* Translate to ASCII and copy to result string. */ 293 for (i = 0; i < n_digits; i++) 294 dp[i] = num_to_text[tstr[i]]; 295 dp[n_digits] = 0; 296 297 *exp = exp_in_base; 298 299 if (SIZ(u) < 0) 300 { 301 dbuf[0] = '-'; 302 n_digits++; 303 } 304 305 TMP_FREE; 306 307 done: 308 /* If the string was alloced then resize it down to the actual space 309 required. */ 310 if (alloc_size != 0) 311 { 312 __GMP_REALLOCATE_FUNC_MAYBE_TYPE (dbuf, alloc_size, n_digits + 1, char); 313 } 314 315 return dbuf; 316 } 317