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 7Copyright 1993-1997, 2000-2003, 2005, 2006, 2011, 2015, 2017 Free 8Software Foundation, Inc. 9 10This file is part of the GNU MP Library. 11 12The GNU MP Library is free software; you can redistribute it and/or modify 13it under the terms of either: 14 15 * the GNU Lesser General Public License as published by the Free 16 Software Foundation; either version 3 of the License, or (at your 17 option) any later version. 18 19or 20 21 * the GNU General Public License as published by the Free Software 22 Foundation; either version 2 of the License, or (at your option) any 23 later version. 24 25or both in parallel, as here. 26 27The GNU MP Library is distributed in the hope that it will be useful, but 28WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 29or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 30for more details. 31 32You should have received copies of the GNU General Public License and the 33GNU Lesser General Public License along with the GNU MP Library. If not, 34see https://www.gnu.org/licenses/. */ 35 36#include <stdlib.h> /* for NULL */ 37#include "gmp-impl.h" 38#include "longlong.h" /* for count_leading_zeros */ 39 40/* Could use some more work. 41 42 1. Allocation is excessive. Try to combine areas. Perhaps use result 43 string area for temp limb space? 44 2. We generate up to two limbs of extra digits. This is because we don't 45 check the exact number of bits in the input operand, and from that 46 compute an accurate exponent (variable e in the code). It would be 47 cleaner and probably somewhat faster to change this. 48*/ 49 50/* Compute base^exp and return the most significant prec limbs in rp[]. 51 Put the count of omitted low limbs in *ign. 52 Return the actual size (which might be less than prec). 53 Allocation of rp[] and the temporary tp[] should be 2*prec+2 limbs. */ 54static mp_size_t 55mpn_pow_1_highpart (mp_ptr rp, mp_size_t *ignp, 56 mp_limb_t base, unsigned long exp, 57 mp_size_t prec, mp_ptr tp) 58{ 59 mp_size_t ign; /* counts number of ignored low limbs in r */ 60 mp_size_t off; /* keeps track of offset where value starts */ 61 mp_ptr passed_rp = rp; 62 mp_size_t rn; 63 int cnt; 64 int i; 65 66 if (exp == 0) 67 { 68 rp[0] = 1; 69 *ignp = 0; 70 return 1; 71 } 72 73 rp[0] = base; 74 rn = 1; 75 off = 0; 76 ign = 0; 77 count_leading_zeros (cnt, exp); 78 for (i = GMP_LIMB_BITS - cnt - 2; i >= 0; i--) 79 { 80 mpn_sqr (tp, rp + off, rn); 81 rn = 2 * rn; 82 rn -= tp[rn - 1] == 0; 83 ign <<= 1; 84 85 off = 0; 86 if (rn > prec) 87 { 88 ign += rn - prec; 89 off = rn - prec; 90 rn = prec; 91 } 92 MP_PTR_SWAP (rp, tp); 93 94 if (((exp >> i) & 1) != 0) 95 { 96 mp_limb_t cy; 97 cy = mpn_mul_1 (rp, rp + off, rn, base); 98 rp[rn] = cy; 99 rn += cy != 0; 100 off = 0; 101 } 102 } 103 104 if (rn > prec) 105 { 106 ASSERT (rn == prec + 1); 107 108 ign += rn - prec; 109 rp += rn - prec; 110 rn = prec; 111 } 112 113 /* With somewhat less than 50% probability, we can skip this copy. */ 114 if (passed_rp != rp + off) 115 MPN_COPY_INCR (passed_rp, rp + off, rn); 116 *ignp = ign; 117 return rn; 118} 119 120char * 121mpf_get_str (char *dbuf, mp_exp_t *exp, int base, size_t n_digits, mpf_srcptr u) 122{ 123 mp_exp_t ue; 124 mp_size_t n_limbs_needed; 125 size_t max_digits; 126 mp_ptr up, pp, tp; 127 mp_size_t un, pn, tn; 128 unsigned char *tstr; 129 mp_exp_t exp_in_base; 130 size_t n_digits_computed; 131 mp_size_t i; 132 const char *num_to_text; 133 size_t alloc_size = 0; 134 char *dp; 135 TMP_DECL; 136 137 up = PTR(u); 138 un = ABSIZ(u); 139 ue = EXP(u); 140 141 num_to_text = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; 142 if (base > 1) 143 { 144 if (base <= 36) 145 num_to_text = "0123456789abcdefghijklmnopqrstuvwxyz"; 146 else if (UNLIKELY (base > 62)) 147 return NULL; 148 } 149 else if (base > -2) 150 { 151 base = 10; 152 } 153 else 154 { 155 base = -base; 156 if (UNLIKELY (base > 36)) 157 return NULL; 158 } 159 160 MPF_SIGNIFICANT_DIGITS (max_digits, base, PREC(u)); 161 if (n_digits == 0 || n_digits > max_digits) 162 n_digits = max_digits; 163 164 if (dbuf == 0) 165 { 166 /* We didn't get a string from the user. Allocate one (and return 167 a pointer to it) with space for `-' and terminating null. */ 168 alloc_size = n_digits + 2; 169 dbuf = __GMP_ALLOCATE_FUNC_TYPE (n_digits + 2, char); 170 } 171 172 if (un == 0) 173 { 174 *exp = 0; 175 *dbuf = 0; 176 n_digits = 0; 177 goto done; 178 } 179 180 TMP_MARK; 181 182 /* Allocate temporary digit space. We can't put digits directly in the user 183 area, since we generate more digits than requested. (We allocate 184 2 * GMP_LIMB_BITS extra bytes because of the digit block nature of the 185 conversion.) */ 186 tstr = (unsigned char *) TMP_ALLOC (n_digits + 2 * GMP_LIMB_BITS + 3); 187 188 LIMBS_PER_DIGIT_IN_BASE (n_limbs_needed, n_digits, base); 189 190 if (un > n_limbs_needed) 191 { 192 up += un - n_limbs_needed; 193 un = n_limbs_needed; 194 } 195 196 TMP_ALLOC_LIMBS_2 (pp, 2 * n_limbs_needed + 4, 197 tp, 2 * n_limbs_needed + 4); 198 199 if (ue <= n_limbs_needed) 200 { 201 /* We need to multiply number by base^n to get an n_digits integer part. */ 202 mp_size_t n_more_limbs_needed, ign, off; 203 unsigned long e; 204 205 n_more_limbs_needed = n_limbs_needed - ue; 206 DIGITS_IN_BASE_PER_LIMB (e, n_more_limbs_needed, base); 207 208 pn = mpn_pow_1_highpart (pp, &ign, (mp_limb_t) base, e, n_limbs_needed + 1, tp); 209 if (un > pn) 210 mpn_mul (tp, up, un, pp, pn); /* FIXME: mpn_mul_highpart */ 211 else 212 mpn_mul (tp, pp, pn, up, un); /* FIXME: mpn_mul_highpart */ 213 tn = un + pn; 214 tn -= tp[tn - 1] == 0; 215 off = un - ue - ign; 216 if (off < 0) 217 { 218 MPN_COPY_DECR (tp - off, tp, tn); 219 MPN_ZERO (tp, -off); 220 tn -= off; 221 off = 0; 222 } 223 n_digits_computed = mpn_get_str (tstr, base, tp + off, tn - off); 224 225 exp_in_base = n_digits_computed - e; 226 } 227 else 228 { 229 /* We need to divide number by base^n to get an n_digits integer part. */ 230 mp_size_t n_less_limbs_needed, ign, off, xn; 231 unsigned long e; 232 mp_ptr dummyp, xp; 233 234 n_less_limbs_needed = ue - n_limbs_needed; 235 DIGITS_IN_BASE_PER_LIMB (e, n_less_limbs_needed, base); 236 237 pn = mpn_pow_1_highpart (pp, &ign, (mp_limb_t) base, e, n_limbs_needed + 1, tp); 238 239 xn = n_limbs_needed + (n_less_limbs_needed-ign); 240 xp = TMP_ALLOC_LIMBS (xn); 241 off = xn - un; 242 MPN_ZERO (xp, off); 243 MPN_COPY (xp + off, up, un); 244 245 dummyp = TMP_ALLOC_LIMBS (pn); 246 mpn_tdiv_qr (tp, dummyp, (mp_size_t) 0, xp, xn, pp, pn); 247 tn = xn - pn + 1; 248 tn -= tp[tn - 1] == 0; 249 n_digits_computed = mpn_get_str (tstr, base, tp, tn); 250 251 exp_in_base = n_digits_computed + e; 252 } 253 254 /* We should normally have computed too many digits. Round the result 255 at the point indicated by n_digits. */ 256 if (n_digits_computed > n_digits) 257 { 258 size_t i; 259 /* Round the result. */ 260 if (tstr[n_digits] * 2 >= base) 261 { 262 n_digits_computed = n_digits; 263 for (i = n_digits - 1;; i--) 264 { 265 unsigned int x; 266 x = ++(tstr[i]); 267 if (x != base) 268 break; 269 n_digits_computed--; 270 if (i == 0) 271 { 272 /* We had something like `bbbbbbb...bd', where 2*d >= base 273 and `b' denotes digit with significance base - 1. 274 This rounds up to `1', increasing the exponent. */ 275 tstr[0] = 1; 276 n_digits_computed = 1; 277 exp_in_base++; 278 break; 279 } 280 } 281 } 282 } 283 284 /* We might have fewer digits than requested as a result of rounding above, 285 (i.e. 0.999999 => 1.0) or because we have a number that simply doesn't 286 need many digits in this base (e.g., 0.125 in base 10). */ 287 if (n_digits > n_digits_computed) 288 n_digits = n_digits_computed; 289 290 /* Remove trailing 0. There can be many zeros. */ 291 while (n_digits != 0 && tstr[n_digits - 1] == 0) 292 n_digits--; 293 294 dp = dbuf + (SIZ(u) < 0); 295 296 /* Translate to ASCII and copy to result string. */ 297 for (i = 0; i < n_digits; i++) 298 dp[i] = num_to_text[tstr[i]]; 299 dp[n_digits] = 0; 300 301 *exp = exp_in_base; 302 303 if (SIZ(u) < 0) 304 { 305 dbuf[0] = '-'; 306 n_digits++; 307 } 308 309 TMP_FREE; 310 311 done: 312 /* If the string was alloced then resize it down to the actual space 313 required. */ 314 if (alloc_size != 0) 315 { 316 __GMP_REALLOCATE_FUNC_MAYBE_TYPE (dbuf, alloc_size, n_digits + 1, char); 317 } 318 319 return dbuf; 320} 321