src/internal/floatscan.c

   1 #include <stdint.h>
   2 #include <stdio.h>
   3 #include <math.h>
   4 #include <float.h>
   5 #include <limits.h>
   6 #include <errno.h>
   7 #include <ctype.h>
   8
   9 #include "shgetc.h"
  10 #include "floatscan.h"
  11
  12 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
  13
  14 #define LD_B1B_DIG 2
  15 #define LD_B1B_MAX 9007199, 254740991
  16 #define KMAX 128
  17
  18 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
  19
  20 #define LD_B1B_DIG 3
  21 #define LD_B1B_MAX 18, 446744073, 709551615
  22 #define KMAX 2048
  23
  24 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
  25
  26 #define LD_B1B_DIG 4
  27 #define LD_B1B_MAX 10384593, 717069655, 257060992, 658440191
  28 #define KMAX 2048
  29
  30 #else
  31 #error Unsupported long double representation
  32 #endif
  33
  34 #define MASK (KMAX-1)
  35
  36 static long long scanexp(FILE *f, int pok)
  37 {
  38         int c;
  39         int x;
  40         long long y;
  41         int neg = 0;
  42
  43         c = shgetc(f);
  44         if (c=='+' || c=='-') {
  45                 neg = (c=='-');
  46                 c = shgetc(f);
  47                 if (c-'0'>=10U && pok) shunget(f);
  48         }
  49         if (c-'0'>=10U) {
  50                 shunget(f);
  51                 return LLONG_MIN;
  52         }
  53         for (x=0; c-'0'<10U && x<INT_MAX/10; c = shgetc(f))
  54                 x = 10*x + c-'0';
  55         for (y=x; c-'0'<10U && y<LLONG_MAX/100; c = shgetc(f))
  56                 y = 10*y + c-'0';
  57         for (; c-'0'<10U; c = shgetc(f));
  58         shunget(f);
  59         return neg ? -y : y;
  60 }
  61
  62
  63 static long double decfloat(FILE *f, int c, int bits, int emin, int sign, int pok)
  64 {
  65         uint32_t x[KMAX];
  66         static const uint32_t th[] = { LD_B1B_MAX };
  67         int i, j, k, a, z;
  68         long long lrp=0, dc=0;
  69         long long e10=0;
  70         int lnz = 0;
  71         int gotdig = 0, gotrad = 0;
  72         int rp;
  73         int e2;
  74         int emax = -emin-bits+3;
  75         int denormal = 0;
  76         long double y;
  77         long double frac=0;
  78         long double bias=0;
  79         static const int p10s[] = { 10, 100, 1000, 10000,
  80                 100000, 1000000, 10000000, 100000000 };
  81
  82         j=0;
  83         k=0;
  84
  85         /* Don't let leading zeros consume buffer space */
  86         for (; c=='0'; c = shgetc(f)) gotdig=1;
  87         if (c=='.') {
  88                 gotrad = 1;
  89                 for (c = shgetc(f); c=='0'; c = shgetc(f)) gotdig=1, lrp--;
  90         }
  91
  92         x[0] = 0;
  93         for (; c-'0'<10U || c=='.'; c = shgetc(f)) {
  94                 if (c == '.') {
  95                         if (gotrad) break;
  96                         gotrad = 1;
  97                         lrp = dc;
  98                 } else if (k < KMAX-3) {
  99                         dc++;
 100                         if (c!='0') lnz = dc;
 101                         if (j) x[k] = x[k]*10 + c-'0';
 102                         else x[k] = c-'0';
 103                         if (++j==9) {
 104                                 k++;
 105                                 j=0;
 106                         }
 107                         gotdig=1;
 108                 } else {
 109                         dc++;
 110                         if (c!='0') {
 111                                 lnz = (KMAX-4)*9;
 112                                 x[KMAX-4] |= 1;
 113                         }
 114                 }
 115         }
 116         if (!gotrad) lrp=dc;
 117
 118         if (gotdig && (c|32)=='e') {
 119                 e10 = scanexp(f, pok);
 120                 if (e10 == LLONG_MIN) {
 121                         if (pok) {
 122                                 shunget(f);
 123                         } else {
 124                                 shlim(f, 0);
 125                                 return 0;
 126                         }
 127                         e10 = 0;
 128                 }
 129                 lrp += e10;
 130         } else if (c>=0) {
 131                 shunget(f);
 132         }
 133         if (!gotdig) {
 134                 errno = EINVAL;
 135                 shlim(f, 0);
 136                 return 0;
 137         }
 138
 139         /* Handle zero specially to avoid nasty special cases later */
 140         if (!x[0]) return sign * 0.0;
 141
 142         /* Optimize small integers (w/no exponent) and over/under-flow */
 143         if (lrp==dc && dc<10 && (bits>30 || x[0]>>bits==0))
 144                 return sign * (long double)x[0];
 145         if (lrp > -emin/2) {
 146                 errno = ERANGE;
 147                 return sign * LDBL_MAX * LDBL_MAX;
 148         }
 149         if (lrp < emin-2*LDBL_MANT_DIG) {
 150                 errno = ERANGE;
 151                 return sign * LDBL_MIN * LDBL_MIN;
 152         }
 153
 154         /* Align incomplete final B1B digit */
 155         if (j) {
 156                 for (; j<9; j++) x[k]*=10;
 157                 k++;
 158                 j=0;
 159         }
 160
 161         a = 0;
 162         z = k;
 163         e2 = 0;
 164         rp = lrp;
 165
 166         /* Optimize small to mid-size integers (even in exp. notation) */
 167         if (lnz<9 && lnz<=rp && rp < 18) {
 168                 if (rp == 9) return sign * (long double)x[0];
 169                 if (rp < 9) return sign * (long double)x[0] / p10s[8-rp];
 170                 int bitlim = bits-3*(int)(rp-9);
 171                 if (bitlim>30 || x[0]>>bitlim==0)
 172                         return sign * (long double)x[0] * p10s[rp-10];
 173         }
 174
 175         /* Drop trailing zeros */
 176         for (; !x[z-1]; z--);
 177
 178         /* Align radix point to B1B digit boundary */
 179         if (rp % 9) {
 180                 int rpm9 = rp>=0 ? rp%9 : rp%9+9;
 181                 int p10 = p10s[8-rpm9];
 182                 uint32_t carry = 0;
 183                 for (k=a; k!=z; k++) {
 184                         uint32_t tmp = x[k] % p10;
 185                         x[k] = x[k]/p10 + carry;
 186                         carry = 1000000000/p10 * tmp;
 187                         if (k==a && !x[k]) {
 188                                 a = (a+1 & MASK);
 189                                 rp -= 9;
 190                         }
 191                 }
 192                 if (carry) x[z++] = carry;
 193                 rp += 9-rpm9;
 194         }
 195
 196         /* Upscale until desired number of bits are left of radix point */
 197         while (rp < 9*LD_B1B_DIG || (rp == 9*LD_B1B_DIG && x[a]<th[0])) {
 198                 uint32_t carry = 0;
 199                 e2 -= 29;
 200                 for (k=(z-1 & MASK); ; k=(k-1 & MASK)) {
 201                         uint64_t tmp = ((uint64_t)x[k] << 29) + carry;
 202                         if (tmp > 1000000000) {
 203                                 carry = tmp / 1000000000;
 204                                 x[k] = tmp % 1000000000;
 205                         } else {
 206                                 carry = 0;
 207                                 x[k] = tmp;
 208                         }
 209                         if (k==(z-1 & MASK) && k!=a && !x[k]) z = k;
 210                         if (k==a) break;
 211                 }
 212                 if (carry) {
 213                         rp += 9;
 214                         a = (a-1 & MASK);
 215                         if (a == z) {
 216                                 z = (z-1 & MASK);
 217                                 x[z-1 & MASK] |= x[z];
 218                         }
 219                         x[a] = carry;
 220                 }
 221         }
 222
 223         /* Downscale until exactly number of bits are left of radix point */
 224         for (;;) {
 225                 uint32_t carry = 0;
 226                 int sh = 1;
 227                 for (i=0; i<LD_B1B_DIG; i++) {
 228                         k = (a+i & MASK);
 229                         if (k == z || x[k] < th[i]) {
 230                                 i=LD_B1B_DIG;
 231                                 break;
 232                         }
 233                         if (x[a+i & MASK] > th[i]) break;
 234                 }
 235                 if (i==LD_B1B_DIG && rp==9*LD_B1B_DIG) break;
 236                 /* FIXME: find a way to compute optimal sh */
 237                 if (rp > 9+9*LD_B1B_DIG) sh = 9;
 238                 e2 += sh;
 239                 for (k=a; k!=z; k=(k+1 & MASK)) {
 240                         uint32_t tmp = x[k] & (1<<sh)-1;
 241                         x[k] = (x[k]>>sh) + carry;
 242                         carry = (1000000000>>sh) * tmp;
 243                         if (k==a && !x[k]) {
 244                                 a = (a+1 & MASK);
 245                                 i--;
 246                                 rp -= 9;
 247                         }
 248                 }
 249                 if (carry) {
 250                         if ((z+1 & MASK) != a) {
 251                                 x[z] = carry;
 252                                 z = (z+1 & MASK);
 253                         } else x[z-1 & MASK] |= 1;
 254                 }
 255         }
 256
 257         /* Assemble desired bits into floating point variable */
 258         for (y=i=0; i<LD_B1B_DIG; i++) {
 259                 if ((a+i & MASK)==z) x[(z=(z+1 & MASK))-1] = 0;
 260                 y = 1000000000.0L * y + x[a+i & MASK];
 261         }
 262
 263         y *= sign;
 264
 265         /* Limit precision for denormal results */
 266         if (bits > LDBL_MANT_DIG+e2-emin) {
 267                 bits = LDBL_MANT_DIG+e2-emin;
 268                 if (bits<0) bits=0;
 269                 denormal = 1;
 270         }
 271
 272         /* Calculate bias term to force rounding, move out lower bits */
 273         if (bits < LDBL_MANT_DIG) {
 274                 bias = copysignl(scalbn(1, 2*LDBL_MANT_DIG-bits-1), y);
 275                 frac = fmodl(y, scalbn(1, LDBL_MANT_DIG-bits));
 276                 y -= frac;
 277                 y += bias;
 278         }
 279
 280         /* Process tail of decimal input so it can affect rounding */
 281         if ((a+i & MASK) != z) {
 282                 uint32_t t = x[a+i & MASK];
 283                 if (t < 500000000 && (t || (a+i+1 & MASK) != z))
 284                         frac += 0.25*sign;
 285                 else if (t > 500000000)
 286                         frac += 0.75*sign;
 287                 else if (t == 500000000) {
 288                         if ((a+i+1 & MASK) == z)
 289                                 frac += 0.5*sign;
 290                         else
 291                                 frac += 0.75*sign;
 292                 }
 293                 if (LDBL_MANT_DIG-bits >= 2 && !fmodl(frac, 1))
 294                         frac++;
 295         }
 296
 297         y += frac;
 298         y -= bias;
 299
 300         if ((e2+LDBL_MANT_DIG & INT_MAX) > emax-5) {
 301                 if (fabsl(y) >= 2/LDBL_EPSILON) {
 302                         if (denormal && bits==LDBL_MANT_DIG+e2-emin)
 303                                 denormal = 0;
 304                         y *= 0.5;
 305                         e2++;
 306                 }
 307                 if (e2+LDBL_MANT_DIG>emax || (denormal && frac))
 308                         errno = ERANGE;
 309         }
 310
 311         return scalbnl(y, e2);
 312 }
 313
 314 static long double hexfloat(FILE *f, int bits, int emin, int sign, int pok)
 315 {
 316         uint32_t x = 0;
 317         long double y = 0;
 318         long double scale = 1;
 319         long double bias = 0;
 320         int gottail = 0, gotrad = 0, gotdig = 0;
 321         long long rp = 0;
 322         long long dc = 0;
 323         long long e2 = 0;
 324         int d;
 325         int c;
 326
 327         c = shgetc(f);
 328
 329         /* Skip leading zeros */
 330         for (; c=='0'; c = shgetc(f)) gotdig = 1;
 331
 332         if (c=='.') {
 333                 gotrad = 1;
 334                 c = shgetc(f);
 335                 /* Count zeros after the radix point before significand */
 336                 for (rp=0; c=='0'; c = shgetc(f), rp--) gotdig = 1;
 337         }
 338
 339         for (; c-'0'<10U || (c|32)-'a'<6U || c=='.'; c = shgetc(f)) {
 340                 if (c=='.') {
 341                         if (gotrad) break;
 342                         rp = dc;
 343                         gotrad = 1;
 344                 } else {
 345                         gotdig = 1;
 346                         if (c > '9') d = (c|32)+10-'a';
 347                         else d = c-'0';
 348                         if (dc<8) {
 349                                 x = x*16 + d;
 350                         } else if (dc < LDBL_MANT_DIG/4+1) {
 351                                 y += d*(scale/=16);
 352                         } else if (d && !gottail) {
 353                                 y += 0.5*scale;
 354                                 gottail = 1;
 355                         }
 356                         dc++;
 357                 }
 358         }
 359         if (!gotdig) {
 360                 shunget(f);
 361                 if (pok) {
 362                         shunget(f);
 363                         if (gotrad) shunget(f);
 364                 } else {
 365                         shlim(f, 0);
 366                 }
 367                 return sign * 0.0;
 368         }
 369         if (!gotrad) rp = dc;
 370         while (dc<8) x *= 16, dc++;
 371         if ((c|32)=='p') {
 372                 e2 = scanexp(f, pok);
 373                 if (e2 == LLONG_MIN) {
 374                         if (pok) {
 375                                 shunget(f);
 376                         } else {
 377                                 shlim(f, 0);
 378                                 return 0;
 379                         }
 380                         e2 = 0;
 381                 }
 382         } else {
 383                 shunget(f);
 384         }
 385         e2 += 4*rp - 32;
 386
 387         if (!x) return sign * 0.0;
 388         if (e2 > -emin) {
 389                 errno = ERANGE;
 390                 return sign * LDBL_MAX * LDBL_MAX;
 391         }
 392         if (e2 < emin-2*LDBL_MANT_DIG) {
 393                 errno = ERANGE;
 394                 return sign * LDBL_MIN * LDBL_MIN;
 395         }
 396
 397         while (x < 0x80000000) {
 398                 if (y>=0.5) {
 399                         x += x + 1;
 400                         y += y - 1;
 401                 } else {
 402                         x += x;
 403                         y += y;
 404                 }
 405                 e2--;
 406         }
 407
 408         if (bits > 32+e2-emin) {
 409                 bits = 32+e2-emin;
 410                 if (bits<0) bits=0;
 411         }
 412
 413         if (bits < LDBL_MANT_DIG)
 414                 bias = copysignl(scalbn(1, 32+LDBL_MANT_DIG-bits-1), sign);
 415
 416         if (bits<32 && y && !(x&1)) x++, y=0;
 417
 418         y = bias + sign*(long double)x + sign*y;
 419         y -= bias;
 420
 421         if (!y) errno = ERANGE;
 422
 423         return scalbnl(y, e2);
 424 }
 425
 426 long double __floatscan(FILE *f, int prec, int pok)
 427 {
 428         int sign = 1;
 429         size_t i;
 430         int bits;
 431         int emin;
 432         int c;
 433
 434         switch (prec) {
 435         case 0:
 436                 bits = FLT_MANT_DIG;
 437                 emin = FLT_MIN_EXP-bits;
 438                 break;
 439         case 1:
 440                 bits = DBL_MANT_DIG;
 441                 emin = DBL_MIN_EXP-bits;
 442                 break;
 443         case 2:
 444                 bits = LDBL_MANT_DIG;
 445                 emin = LDBL_MIN_EXP-bits;
 446                 break;
 447         default:
 448                 return 0;
 449         }
 450
 451         while (isspace((c=shgetc(f))));
 452
 453         if (c=='+' || c=='-') {
 454                 sign -= 2*(c=='-');
 455                 c = shgetc(f);
 456         }
 457
 458         for (i=0; i<8 && (c|32)=="infinity"[i]; i++)
 459                 if (i<7) c = shgetc(f);
 460         if (i==3 || i==8 || (i>3 && pok)) {
 461                 if (i!=8) {
 462                         shunget(f);
 463                         if (pok) for (; i>3; i--) shunget(f);
 464                 }
 465                 return sign * INFINITY;
 466         }
 467         if (!i) for (i=0; i<3 && (c|32)=="nan"[i]; i++)
 468                 if (i<2) c = shgetc(f);
 469         if (i==3) {
 470                 if (shgetc(f) != '(') {
 471                         shunget(f);
 472                         return NAN;
 473                 }
 474                 for (i=1; ; i++) {
 475                         c = shgetc(f);
 476                         if (c-'0'<10U || c-'A'<26U || c-'a'<26U || c=='_')
 477                                 continue;
 478                         if (c==')') return NAN;
 479                         shunget(f);
 480                         if (!pok) {
 481                                 errno = EINVAL;
 482                                 shlim(f, 0);
 483                                 return 0;
 484                         }
 485                         while (i--) shunget(f);
 486                         return NAN;
 487                 }
 488                 return NAN;
 489         }
 490
 491         if (i) {
 492                 shunget(f);
 493                 errno = EINVAL;
 494                 shlim(f, 0);
 495                 return 0;
 496         }
 497
 498         if (c=='0') {
 499                 c = shgetc(f);
 500                 if ((c|32) == 'x')
 501                         return hexfloat(f, bits, emin, sign, pok);
 502                 shunget(f);
 503                 c = '0';
 504         }
 505
 506         return decfloat(f, c, bits, emin, sign, pok);
 507 }