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 #define CONCAT2(x,y) x ## y
  37 #define CONCAT(x,y) CONCAT2(x,y)
  38
  39 static long long scanexp(FILE *f, int pok)
  40 {
  41         int c;
  42         int x;
  43         long long y;
  44         int neg = 0;
  45
  46         c = shgetc(f);
  47         if (c=='+' || c=='-') {
  48                 neg = (c=='-');
  49                 c = shgetc(f);
  50                 if (c-'0'>=10U && pok) shunget(f);
  51         }
  52         if (c-'0'>=10U) {
  53                 shunget(f);
  54                 return LLONG_MIN;
  55         }
  56         for (x=0; c-'0'<10U && x<INT_MAX/10; c = shgetc(f))
  57                 x = 10*x + c-'0';
  58         for (y=x; c-'0'<10U && y<LLONG_MAX/100; c = shgetc(f))
  59                 y = 10*y + c-'0';
  60         for (; c-'0'<10U; c = shgetc(f));
  61         shunget(f);
  62         return neg ? -y : y;
  63 }
  64
  65
  66 static long double decfloat(FILE *f, int c, int bits, int emin, int sign, int pok)
  67 {
  68         uint32_t x[KMAX];
  69         static const uint32_t th[] = { LD_B1B_MAX };
  70         int i, j, k, a, z;
  71         long long lrp=0, dc=0;
  72         long long e10=0;
  73         int lnz = 0;
  74         int gotdig = 0, gotrad = 0;
  75         int rp;
  76         int e2;
  77         int emax = -emin-bits+3;
  78         int denormal = 0;
  79         long double y;
  80         long double frac=0;
  81         long double bias=0;
  82         static const int p10s[] = { 10, 100, 1000, 10000,
  83                 100000, 1000000, 10000000, 100000000 };
  84
  85         j=0;
  86         k=0;
  87
  88         /* Don't let leading zeros consume buffer space */
  89         for (; c=='0'; c = shgetc(f)) gotdig=1;
  90         if (c=='.') {
  91                 gotrad = 1;
  92                 for (c = shgetc(f); c=='0'; c = shgetc(f)) gotdig=1, lrp--;
  93         }
  94
  95         x[0] = 0;
  96         for (; c-'0'<10U || c=='.'; c = shgetc(f)) {
  97                 if (c == '.') {
  98                         if (gotrad) break;
  99                         gotrad = 1;
 100                         lrp = dc;
 101                 } else if (k < KMAX-3) {
 102                         dc++;
 103                         if (c!='0') lnz = dc;
 104                         if (j) x[k] = x[k]*10 + c-'0';
 105                         else x[k] = c-'0';
 106                         if (++j==9) {
 107                                 k++;
 108                                 j=0;
 109                         }
 110                         gotdig=1;
 111                 } else {
 112                         dc++;
 113                         if (c!='0') {
 114                                 lnz = (KMAX-4)*9;
 115                                 x[KMAX-4] |= 1;
 116                         }
 117                 }
 118         }
 119         if (!gotrad) lrp=dc;
 120
 121         if (gotdig && (c|32)=='e') {
 122                 e10 = scanexp(f, pok);
 123                 if (e10 == LLONG_MIN) {
 124                         if (pok) {
 125                                 shunget(f);
 126                         } else {
 127                                 shlim(f, 0);
 128                                 return 0;
 129                         }
 130                         e10 = 0;
 131                 }
 132                 lrp += e10;
 133         } else if (c>=0) {
 134                 shunget(f);
 135         }
 136         if (!gotdig) {
 137                 errno = EINVAL;
 138                 shlim(f, 0);
 139                 return 0;
 140         }
 141
 142         /* Handle zero specially to avoid nasty special cases later */
 143         if (!x[0]) return sign * 0.0;
 144
 145         /* Optimize small integers (w/no exponent) and over/under-flow */
 146         if (lrp==dc && dc<10 && (bits>30 || x[0]>>bits==0))
 147                 return sign * (long double)x[0];
 148         if (lrp > -emin/2) {
 149                 errno = ERANGE;
 150                 return sign * LDBL_MAX * LDBL_MAX;
 151         }
 152         if (lrp < emin-2*LDBL_MANT_DIG) {
 153                 errno = ERANGE;
 154                 return sign * LDBL_MIN * LDBL_MIN;
 155         }
 156
 157         /* Align incomplete final B1B digit */
 158         if (j) {
 159                 for (; j<9; j++) x[k]*=10;
 160                 k++;
 161                 j=0;
 162         }
 163
 164         a = 0;
 165         z = k;
 166         e2 = 0;
 167         rp = lrp;
 168
 169         /* Optimize small to mid-size integers (even in exp. notation) */
 170         if (lnz<9 && lnz<=rp && rp < 18) {
 171                 if (rp == 9) return sign * (long double)x[0];
 172                 if (rp < 9) return sign * (long double)x[0] / p10s[8-rp];
 173                 int bitlim = bits-3*(int)(rp-9);
 174                 if (bitlim>30 || x[0]>>bitlim==0)
 175                         return sign * (long double)x[0] * p10s[rp-10];
 176         }
 177
 178         /* Drop trailing zeros */
 179         for (; !x[z-1]; z--);
 180
 181         /* Align radix point to B1B digit boundary */
 182         if (rp % 9) {
 183                 int rpm9 = rp>=0 ? rp%9 : rp%9+9;
 184                 int p10 = p10s[8-rpm9];
 185                 uint32_t carry = 0;
 186                 for (k=a; k!=z; k++) {
 187                         uint32_t tmp = x[k] % p10;
 188                         x[k] = x[k]/p10 + carry;
 189                         carry = 1000000000/p10 * tmp;
 190                         if (k==a && !x[k]) {
 191                                 a = (a+1 & MASK);
 192                                 rp -= 9;
 193                         }
 194                 }
 195                 if (carry) x[z++] = carry;
 196                 rp += 9-rpm9;
 197         }
 198
 199         /* Upscale until desired number of bits are left of radix point */
 200         while (rp < 9*LD_B1B_DIG || (rp == 9*LD_B1B_DIG && x[a]<th[0])) {
 201                 uint32_t carry = 0;
 202                 e2 -= 29;
 203                 for (k=(z-1 & MASK); ; k=(k-1 & MASK)) {
 204                         uint64_t tmp = ((uint64_t)x[k] << 29) + carry;
 205                         if (tmp > 1000000000) {
 206                                 carry = tmp / 1000000000;
 207                                 x[k] = tmp % 1000000000;
 208                         } else {
 209                                 carry = 0;
 210                                 x[k] = tmp;
 211                         }
 212                         if (k==(z-1 & MASK) && k!=a && !x[k]) z = k;
 213                         if (k==a) break;
 214                 }
 215                 if (carry) {
 216                         rp += 9;
 217                         a = (a-1 & MASK);
 218                         if (a == z) {
 219                                 z = (z-1 & MASK);
 220                                 x[z-1 & MASK] |= x[z];
 221                         }
 222                         x[a] = carry;
 223                 }
 224         }
 225
 226         /* Downscale until exactly number of bits are left of radix point */
 227         for (;;) {
 228                 uint32_t carry = 0;
 229                 int sh = 1;
 230                 for (i=0; i<LD_B1B_DIG; i++) {
 231                         k = (a+i & MASK);
 232                         if (k == z || x[k] < th[i]) {
 233                                 i=LD_B1B_DIG;
 234                                 break;
 235                         }
 236                         if (x[a+i & MASK] > th[i]) break;
 237                 }
 238                 if (i==LD_B1B_DIG && rp==9*LD_B1B_DIG) break;
 239                 /* FIXME: find a way to compute optimal sh */
 240                 if (rp > 9+9*LD_B1B_DIG) sh = 9;
 241                 e2 += sh;
 242                 for (k=a; k!=z; k=(k+1 & MASK)) {
 243                         uint32_t tmp = x[k] & (1<<sh)-1;
 244                         x[k] = (x[k]>>sh) + carry;
 245                         carry = (1000000000>>sh) * tmp;
 246                         if (k==a && !x[k]) {
 247                                 a = (a+1 & MASK);
 248                                 i--;
 249                                 rp -= 9;
 250                         }
 251                 }
 252                 if (carry) {
 253                         if ((z+1 & MASK) != a) {
 254                                 x[z] = carry;
 255                                 z = (z+1 & MASK);
 256                         } else x[z-1 & MASK] |= 1;
 257                 }
 258         }
 259
 260         /* Assemble desired bits into floating point variable */
 261         for (y=i=0; i<LD_B1B_DIG; i++) {
 262                 if ((a+i & MASK)==z) x[(z=(z+1 & MASK))-1] = 0;
 263                 y = 1000000000.0L * y + x[a+i & MASK];
 264         }
 265
 266         y *= sign;
 267
 268         /* Limit precision for denormal results */
 269         if (bits > LDBL_MANT_DIG+e2-emin) {
 270                 bits = LDBL_MANT_DIG+e2-emin;
 271                 if (bits<0) bits=0;
 272                 denormal = 1;
 273         }
 274
 275         /* Calculate bias term to force rounding, move out lower bits */
 276         if (bits < LDBL_MANT_DIG) {
 277                 bias = copysignl(scalbn(1, 2*LDBL_MANT_DIG-bits-1), y);
 278                 frac = fmodl(y, scalbn(1, LDBL_MANT_DIG-bits));
 279                 y -= frac;
 280                 y += bias;
 281         }
 282
 283         /* Process tail of decimal input so it can affect rounding */
 284         if ((a+i & MASK) != z) {
 285                 uint32_t t = x[a+i & MASK];
 286                 if (t < 500000000 && (t || (a+i+1 & MASK) != z))
 287                         frac += 0.25*sign;
 288                 else if (t > 500000000)
 289                         frac += 0.75*sign;
 290                 else if (t == 500000000) {
 291                         if ((a+i+1 & MASK) == z)
 292                                 frac += 0.5*sign;
 293                         else
 294                                 frac += 0.75*sign;
 295                 }
 296                 if (LDBL_MANT_DIG-bits >= 2 && !fmodl(frac, 1))
 297                         frac++;
 298         }
 299
 300         y += frac;
 301         y -= bias;
 302
 303         if ((e2+LDBL_MANT_DIG & INT_MAX) > emax-5) {
 304                 if (fabs(y) >= CONCAT(0x1p, LDBL_MANT_DIG)) {
 305                         if (denormal && bits==LDBL_MANT_DIG+e2-emin)
 306                                 denormal = 0;
 307                         y *= 0.5;
 308                         e2++;
 309                 }
 310                 if (e2+LDBL_MANT_DIG>emax || (denormal && frac))
 311                         errno = ERANGE;
 312         }
 313
 314         return scalbnl(y, e2);
 315 }
 316
 317 static long double hexfloat(FILE *f, int bits, int emin, int sign, int pok)
 318 {
 319         uint32_t x = 0;
 320         long double y = 0;
 321         long double scale = 1;
 322         long double bias = 0;
 323         int gottail = 0, gotrad = 0, gotdig = 0;
 324         long long rp = 0;
 325         long long dc = 0;
 326         long long e2 = 0;
 327         int d;
 328         int c;
 329
 330         c = shgetc(f);
 331
 332         /* Skip leading zeros */
 333         for (; c=='0'; c = shgetc(f)) gotdig = 1;
 334
 335         if (c=='.') {
 336                 gotrad = 1;
 337                 c = shgetc(f);
 338                 /* Count zeros after the radix point before significand */
 339                 for (rp=0; c=='0'; c = shgetc(f), rp--) gotdig = 1;
 340         }
 341
 342         for (; c-'0'<10U || (c|32)-'a'<6U || c=='.'; c = shgetc(f)) {
 343                 if (c=='.') {
 344                         if (gotrad) break;
 345                         rp = dc;
 346                         gotrad = 1;
 347                 } else {
 348                         gotdig = 1;
 349                         if (c > '9') d = (c|32)+10-'a';
 350                         else d = c-'0';
 351                         if (dc<8) {
 352                                 x = x*16 + d;
 353                         } else if (dc < LDBL_MANT_DIG/4+1) {
 354                                 y += d*(scale/=16);
 355                         } else if (d && !gottail) {
 356                                 y += 0.5*scale;
 357                                 gottail = 1;
 358                         }
 359                         dc++;
 360                 }
 361         }
 362         if (!gotdig) {
 363                 shunget(f);
 364                 if (pok) {
 365                         shunget(f);
 366                         if (gotrad) shunget(f);
 367                 } else {
 368                         shlim(f, 0);
 369                 }
 370                 return sign * 0.0;
 371         }
 372         if (!gotrad) rp = dc;
 373         while (dc<8) x *= 16, dc++;
 374         if ((c|32)=='p') {
 375                 e2 = scanexp(f, pok);
 376                 if (e2 == LLONG_MIN) {
 377                         if (pok) {
 378                                 shunget(f);
 379                         } else {
 380                                 shlim(f, 0);
 381                                 return 0;
 382                         }
 383                         e2 = 0;
 384                 }
 385         } else {
 386                 shunget(f);
 387         }
 388         e2 += 4*rp - 32;
 389
 390         if (!x) return sign * 0.0;
 391         if (e2 > -emin) {
 392                 errno = ERANGE;
 393                 return sign * LDBL_MAX * LDBL_MAX;
 394         }
 395         if (e2 < emin-2*LDBL_MANT_DIG) {
 396                 errno = ERANGE;
 397                 return sign * LDBL_MIN * LDBL_MIN;
 398         }
 399
 400         while (x < 0x80000000) {
 401                 if (y>=0.5) {
 402                         x += x + 1;
 403                         y += y - 1;
 404                 } else {
 405                         x += x;
 406                         y += y;
 407                 }
 408                 e2--;
 409         }
 410
 411         if (bits > 32+e2-emin) {
 412                 bits = 32+e2-emin;
 413                 if (bits<0) bits=0;
 414         }
 415
 416         if (bits < LDBL_MANT_DIG)
 417                 bias = copysignl(scalbn(1, 32+LDBL_MANT_DIG-bits-1), sign);
 418
 419         if (bits<32 && y && !(x&1)) x++, y=0;
 420
 421         y = bias + sign*(long double)x + sign*y;
 422         y -= bias;
 423
 424         if (!y) errno = ERANGE;
 425
 426         return scalbnl(y, e2);
 427 }
 428
 429 long double __floatscan(FILE *f, int prec, int pok)
 430 {
 431         int sign = 1;
 432         size_t i;
 433         int bits;
 434         int emin;
 435         int c;
 436
 437         switch (prec) {
 438         case 0:
 439                 bits = FLT_MANT_DIG;
 440                 emin = FLT_MIN_EXP-bits;
 441                 break;
 442         case 1:
 443                 bits = DBL_MANT_DIG;
 444                 emin = DBL_MIN_EXP-bits;
 445                 break;
 446         case 2:
 447                 bits = LDBL_MANT_DIG;
 448                 emin = LDBL_MIN_EXP-bits;
 449                 break;
 450         default:
 451                 return 0;
 452         }
 453
 454         while (isspace((c=shgetc(f))));
 455
 456         if (c=='+' || c=='-') {
 457                 sign -= 2*(c=='-');
 458                 c = shgetc(f);
 459         }
 460
 461         for (i=0; i<8 && (c|32)=="infinity"[i]; i++)
 462                 if (i<7) c = shgetc(f);
 463         if (i==3 || i==8 || (i>3 && pok)) {
 464                 if (i!=8) {
 465                         shunget(f);
 466                         if (pok) for (; i>3; i--) shunget(f);
 467                 }
 468                 return sign * INFINITY;
 469         }
 470         if (!i) for (i=0; i<3 && (c|32)=="nan"[i]; i++)
 471                 if (i<2) c = shgetc(f);
 472         if (i==3) {
 473                 if (shgetc(f) != '(') {
 474                         shunget(f);
 475                         return NAN;
 476                 }
 477                 for (i=1; ; i++) {
 478                         c = shgetc(f);
 479                         if (c-'0'<10U || c-'A'<26U || c-'a'<26U || c=='_')
 480                                 continue;
 481                         if (c==')') return NAN;
 482                         shunget(f);
 483                         if (!pok) {
 484                                 errno = EINVAL;
 485                                 shlim(f, 0);
 486                                 return 0;
 487                         }
 488                         while (i--) shunget(f);
 489                         return NAN;
 490                 }
 491                 return NAN;
 492         }
 493
 494         if (i) {
 495                 shunget(f);
 496                 errno = EINVAL;
 497                 shlim(f, 0);
 498                 return 0;
 499         }
 500
 501         if (c=='0') {
 502                 c = shgetc(f);
 503                 if ((c|32) == 'x')
 504                         return hexfloat(f, bits, emin, sign, pok);
 505                 shunget(f);
 506                 c = '0';
 507         }
 508
 509         return decfloat(f, c, bits, emin, sign, pok);
 510 }