1 /* Convert string representing a number to float value, using given locale.
2    Copyright (C) 1997-2022 Free Software Foundation, Inc.
3    This file is part of the GNU C Library.
4 
5    The GNU C Library is free software; you can redistribute it and/or
6    modify it under the terms of the GNU Lesser General Public
7    License as published by the Free Software Foundation; either
8    version 2.1 of the License, or (at your option) any later version.
9 
10    The GNU C Library is distributed in the hope that it will be useful,
11    but WITHOUT ANY WARRANTY; without even the implied warranty of
12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
13    Lesser General Public License for more details.
14 
15    You should have received a copy of the GNU Lesser General Public
16    License along with the GNU C Library; if not, see
17    <https://www.gnu.org/licenses/>.  */
18 
19 #include <bits/floatn.h>
20 
21 #ifdef FLOAT
22 # define BUILD_DOUBLE 0
23 #else
24 # define BUILD_DOUBLE 1
25 #endif
26 
27 #if BUILD_DOUBLE
28 # if __HAVE_FLOAT64 && !__HAVE_DISTINCT_FLOAT64
29 #  define strtof64_l __hide_strtof64_l
30 #  define wcstof64_l __hide_wcstof64_l
31 # endif
32 # if __HAVE_FLOAT32X && !__HAVE_DISTINCT_FLOAT32X
33 #  define strtof32x_l __hide_strtof32x_l
34 #  define wcstof32x_l __hide_wcstof32x_l
35 # endif
36 #endif
37 
38 #include <locale.h>
39 
40 extern double ____strtod_l_internal (const char *, char **, int, locale_t);
41 
42 /* Configuration part.  These macros are defined by `strtold.c',
43    `strtof.c', `wcstod.c', `wcstold.c', and `wcstof.c' to produce the
44    `long double' and `float' versions of the reader.  */
45 #ifndef FLOAT
46 # include <math_ldbl_opt.h>
47 # define FLOAT		double
48 # define FLT		DBL
49 # ifdef USE_WIDE_CHAR
50 #  define STRTOF	wcstod_l
51 #  define __STRTOF	__wcstod_l
52 #  define STRTOF_NAN	__wcstod_nan
53 # else
54 #  define STRTOF	strtod_l
55 #  define __STRTOF	__strtod_l
56 #  define STRTOF_NAN	__strtod_nan
57 # endif
58 # define MPN2FLOAT	__mpn_construct_double
59 # define FLOAT_HUGE_VAL	HUGE_VAL
60 #endif
61 /* End of configuration part.  */
62 
63 #include <ctype.h>
64 #include <errno.h>
65 #include <float.h>
66 #include "../locale/localeinfo.h"
67 #include <math.h>
68 #include <math-barriers.h>
69 #include <math-narrow-eval.h>
70 #include <stdlib.h>
71 #include <string.h>
72 #include <stdint.h>
73 #include <rounding-mode.h>
74 #include <tininess.h>
75 
76 /* The gmp headers need some configuration frobs.  */
77 #define HAVE_ALLOCA 1
78 
79 /* Include gmp-mparam.h first, such that definitions of _SHORT_LIMB
80    and _LONG_LONG_LIMB in it can take effect into gmp.h.  */
81 #include <gmp-mparam.h>
82 #include <gmp.h>
83 #include "gmp-impl.h"
84 #include "longlong.h"
85 #include "fpioconst.h"
86 
87 #include <assert.h>
88 
89 
90 /* We use this code for the extended locale handling where the
91    function gets as an additional argument the locale which has to be
92    used.  To access the values we have to redefine the _NL_CURRENT and
93    _NL_CURRENT_WORD macros.  */
94 #undef _NL_CURRENT
95 #define _NL_CURRENT(category, item) \
96   (current->values[_NL_ITEM_INDEX (item)].string)
97 #undef _NL_CURRENT_WORD
98 #define _NL_CURRENT_WORD(category, item) \
99   ((uint32_t) current->values[_NL_ITEM_INDEX (item)].word)
100 
101 #if defined _LIBC || defined HAVE_WCHAR_H
102 # include <wchar.h>
103 #endif
104 
105 #ifdef USE_WIDE_CHAR
106 # include <wctype.h>
107 # define STRING_TYPE wchar_t
108 # define CHAR_TYPE wint_t
109 # define L_(Ch) L##Ch
110 # define ISSPACE(Ch) __iswspace_l ((Ch), loc)
111 # define ISDIGIT(Ch) __iswdigit_l ((Ch), loc)
112 # define ISXDIGIT(Ch) __iswxdigit_l ((Ch), loc)
113 # define TOLOWER(Ch) __towlower_l ((Ch), loc)
114 # define TOLOWER_C(Ch) __towlower_l ((Ch), _nl_C_locobj_ptr)
115 # define STRNCASECMP(S1, S2, N) \
116   __wcsncasecmp_l ((S1), (S2), (N), _nl_C_locobj_ptr)
117 #else
118 # define STRING_TYPE char
119 # define CHAR_TYPE char
120 # define L_(Ch) Ch
121 # define ISSPACE(Ch) __isspace_l ((Ch), loc)
122 # define ISDIGIT(Ch) __isdigit_l ((Ch), loc)
123 # define ISXDIGIT(Ch) __isxdigit_l ((Ch), loc)
124 # define TOLOWER(Ch) __tolower_l ((Ch), loc)
125 # define TOLOWER_C(Ch) __tolower_l ((Ch), _nl_C_locobj_ptr)
126 # define STRNCASECMP(S1, S2, N) \
127   __strncasecmp_l ((S1), (S2), (N), _nl_C_locobj_ptr)
128 #endif
129 
130 
131 /* Constants we need from float.h; select the set for the FLOAT precision.  */
132 #define MANT_DIG	PASTE(FLT,_MANT_DIG)
133 #define	DIG		PASTE(FLT,_DIG)
134 #define	MAX_EXP		PASTE(FLT,_MAX_EXP)
135 #define	MIN_EXP		PASTE(FLT,_MIN_EXP)
136 #define MAX_10_EXP	PASTE(FLT,_MAX_10_EXP)
137 #define MIN_10_EXP	PASTE(FLT,_MIN_10_EXP)
138 #define MAX_VALUE	PASTE(FLT,_MAX)
139 #define MIN_VALUE	PASTE(FLT,_MIN)
140 
141 /* Extra macros required to get FLT expanded before the pasting.  */
142 #define PASTE(a,b)	PASTE1(a,b)
143 #define PASTE1(a,b)	a##b
144 
145 /* Function to construct a floating point number from an MP integer
146    containing the fraction bits, a base 2 exponent, and a sign flag.  */
147 extern FLOAT MPN2FLOAT (mp_srcptr mpn, int exponent, int negative);
148 
149 /* Definitions according to limb size used.  */
150 #if	BITS_PER_MP_LIMB == 32
151 # define MAX_DIG_PER_LIMB	9
152 # define MAX_FAC_PER_LIMB	1000000000UL
153 #elif	BITS_PER_MP_LIMB == 64
154 # define MAX_DIG_PER_LIMB	19
155 # define MAX_FAC_PER_LIMB	10000000000000000000ULL
156 #else
157 # error "mp_limb_t size " BITS_PER_MP_LIMB "not accounted for"
158 #endif
159 
160 extern const mp_limb_t _tens_in_limb[MAX_DIG_PER_LIMB + 1];
161 
162 #ifndef	howmany
163 #define	howmany(x,y)		(((x)+((y)-1))/(y))
164 #endif
165 #define SWAP(x, y)		({ typeof(x) _tmp = x; x = y; y = _tmp; })
166 
167 #define	RETURN_LIMB_SIZE		howmany (MANT_DIG, BITS_PER_MP_LIMB)
168 
169 #define RETURN(val,end)							      \
170     do { if (endptr != NULL) *endptr = (STRING_TYPE *) (end);		      \
171 	 return val; } while (0)
172 
173 /* Maximum size necessary for mpn integers to hold floating point
174    numbers.  The largest number we need to hold is 10^n where 2^-n is
175    1/4 ulp of the smallest representable value (that is, n = MANT_DIG
176    - MIN_EXP + 2).  Approximate using 10^3 < 2^10.  */
177 #define	MPNSIZE		(howmany (1 + ((MANT_DIG - MIN_EXP + 2) * 10) / 3, \
178 				  BITS_PER_MP_LIMB) + 2)
179 /* Declare an mpn integer variable that big.  */
180 #define	MPN_VAR(name)	mp_limb_t name[MPNSIZE]; mp_size_t name##size
181 /* Copy an mpn integer value.  */
182 #define MPN_ASSIGN(dst, src) \
183 	memcpy (dst, src, (dst##size = src##size) * sizeof (mp_limb_t))
184 
185 
186 /* Set errno and return an overflowing value with sign specified by
187    NEGATIVE.  */
188 static FLOAT
overflow_value(int negative)189 overflow_value (int negative)
190 {
191   __set_errno (ERANGE);
192   FLOAT result = math_narrow_eval ((negative ? -MAX_VALUE : MAX_VALUE)
193 				   * MAX_VALUE);
194   return result;
195 }
196 
197 
198 /* Set errno and return an underflowing value with sign specified by
199    NEGATIVE.  */
200 static FLOAT
underflow_value(int negative)201 underflow_value (int negative)
202 {
203   __set_errno (ERANGE);
204   FLOAT result = math_narrow_eval ((negative ? -MIN_VALUE : MIN_VALUE)
205 				   * MIN_VALUE);
206   return result;
207 }
208 
209 
210 /* Return a floating point number of the needed type according to the given
211    multi-precision number after possible rounding.  */
212 static FLOAT
round_and_return(mp_limb_t * retval,intmax_t exponent,int negative,mp_limb_t round_limb,mp_size_t round_bit,int more_bits)213 round_and_return (mp_limb_t *retval, intmax_t exponent, int negative,
214 		  mp_limb_t round_limb, mp_size_t round_bit, int more_bits)
215 {
216   int mode = get_rounding_mode ();
217 
218   if (exponent < MIN_EXP - 1)
219     {
220       if (exponent < MIN_EXP - 1 - MANT_DIG)
221 	return underflow_value (negative);
222 
223       mp_size_t shift = MIN_EXP - 1 - exponent;
224       bool is_tiny = true;
225 
226       more_bits |= (round_limb & ((((mp_limb_t) 1) << round_bit) - 1)) != 0;
227       if (shift == MANT_DIG)
228 	/* This is a special case to handle the very seldom case where
229 	   the mantissa will be empty after the shift.  */
230 	{
231 	  int i;
232 
233 	  round_limb = retval[RETURN_LIMB_SIZE - 1];
234 	  round_bit = (MANT_DIG - 1) % BITS_PER_MP_LIMB;
235 	  for (i = 0; i < RETURN_LIMB_SIZE - 1; ++i)
236 	    more_bits |= retval[i] != 0;
237 	  MPN_ZERO (retval, RETURN_LIMB_SIZE);
238 	}
239       else if (shift >= BITS_PER_MP_LIMB)
240 	{
241 	  int i;
242 
243 	  round_limb = retval[(shift - 1) / BITS_PER_MP_LIMB];
244 	  round_bit = (shift - 1) % BITS_PER_MP_LIMB;
245 	  for (i = 0; i < (shift - 1) / BITS_PER_MP_LIMB; ++i)
246 	    more_bits |= retval[i] != 0;
247 	  more_bits |= ((round_limb & ((((mp_limb_t) 1) << round_bit) - 1))
248 			!= 0);
249 
250 	  /* __mpn_rshift requires 0 < shift < BITS_PER_MP_LIMB.  */
251 	  if ((shift % BITS_PER_MP_LIMB) != 0)
252 	    (void) __mpn_rshift (retval, &retval[shift / BITS_PER_MP_LIMB],
253 			         RETURN_LIMB_SIZE - (shift / BITS_PER_MP_LIMB),
254 			         shift % BITS_PER_MP_LIMB);
255 	  else
256 	    for (i = 0; i < RETURN_LIMB_SIZE - (shift / BITS_PER_MP_LIMB); i++)
257 	      retval[i] = retval[i + (shift / BITS_PER_MP_LIMB)];
258 	  MPN_ZERO (&retval[RETURN_LIMB_SIZE - (shift / BITS_PER_MP_LIMB)],
259 		    shift / BITS_PER_MP_LIMB);
260 	}
261       else if (shift > 0)
262 	{
263 	  if (TININESS_AFTER_ROUNDING && shift == 1)
264 	    {
265 	      /* Whether the result counts as tiny depends on whether,
266 		 after rounding to the normal precision, it still has
267 		 a subnormal exponent.  */
268 	      mp_limb_t retval_normal[RETURN_LIMB_SIZE];
269 	      if (round_away (negative,
270 			      (retval[0] & 1) != 0,
271 			      (round_limb
272 			       & (((mp_limb_t) 1) << round_bit)) != 0,
273 			      (more_bits
274 			       || ((round_limb
275 				    & ((((mp_limb_t) 1) << round_bit) - 1))
276 				   != 0)),
277 			      mode))
278 		{
279 		  mp_limb_t cy = __mpn_add_1 (retval_normal, retval,
280 					      RETURN_LIMB_SIZE, 1);
281 
282 		  if (((MANT_DIG % BITS_PER_MP_LIMB) == 0 && cy)
283 		      || ((MANT_DIG % BITS_PER_MP_LIMB) != 0
284 			  && ((retval_normal[RETURN_LIMB_SIZE - 1]
285 			       & (((mp_limb_t) 1)
286 				  << (MANT_DIG % BITS_PER_MP_LIMB)))
287 			      != 0)))
288 		    is_tiny = false;
289 		}
290 	    }
291 	  round_limb = retval[0];
292 	  round_bit = shift - 1;
293 	  (void) __mpn_rshift (retval, retval, RETURN_LIMB_SIZE, shift);
294 	}
295       /* This is a hook for the m68k long double format, where the
296 	 exponent bias is the same for normalized and denormalized
297 	 numbers.  */
298 #ifndef DENORM_EXP
299 # define DENORM_EXP (MIN_EXP - 2)
300 #endif
301       exponent = DENORM_EXP;
302       if (is_tiny
303 	  && ((round_limb & (((mp_limb_t) 1) << round_bit)) != 0
304 	      || more_bits
305 	      || (round_limb & ((((mp_limb_t) 1) << round_bit) - 1)) != 0))
306 	{
307 	  __set_errno (ERANGE);
308 	  FLOAT force_underflow = MIN_VALUE * MIN_VALUE;
309 	  math_force_eval (force_underflow);
310 	}
311     }
312 
313   if (exponent >= MAX_EXP)
314     goto overflow;
315 
316   bool half_bit = (round_limb & (((mp_limb_t) 1) << round_bit)) != 0;
317   bool more_bits_nonzero
318     = (more_bits
319        || (round_limb & ((((mp_limb_t) 1) << round_bit) - 1)) != 0);
320   if (round_away (negative,
321 		  (retval[0] & 1) != 0,
322 		  half_bit,
323 		  more_bits_nonzero,
324 		  mode))
325     {
326       mp_limb_t cy = __mpn_add_1 (retval, retval, RETURN_LIMB_SIZE, 1);
327 
328       if (((MANT_DIG % BITS_PER_MP_LIMB) == 0 && cy)
329 	  || ((MANT_DIG % BITS_PER_MP_LIMB) != 0
330 	      && (retval[RETURN_LIMB_SIZE - 1]
331 		  & (((mp_limb_t) 1) << (MANT_DIG % BITS_PER_MP_LIMB))) != 0))
332 	{
333 	  ++exponent;
334 	  (void) __mpn_rshift (retval, retval, RETURN_LIMB_SIZE, 1);
335 	  retval[RETURN_LIMB_SIZE - 1]
336 	    |= ((mp_limb_t) 1) << ((MANT_DIG - 1) % BITS_PER_MP_LIMB);
337 	}
338       else if (exponent == DENORM_EXP
339 	       && (retval[RETURN_LIMB_SIZE - 1]
340 		   & (((mp_limb_t) 1) << ((MANT_DIG - 1) % BITS_PER_MP_LIMB)))
341 	       != 0)
342 	  /* The number was denormalized but now normalized.  */
343 	exponent = MIN_EXP - 1;
344     }
345 
346   if (exponent >= MAX_EXP)
347   overflow:
348     return overflow_value (negative);
349 
350   if (half_bit || more_bits_nonzero)
351     {
352       FLOAT force_inexact = (FLOAT) 1 + MIN_VALUE;
353       math_force_eval (force_inexact);
354     }
355   return MPN2FLOAT (retval, exponent, negative);
356 }
357 
358 
359 /* Read a multi-precision integer starting at STR with exactly DIGCNT digits
360    into N.  Return the size of the number limbs in NSIZE at the first
361    character od the string that is not part of the integer as the function
362    value.  If the EXPONENT is small enough to be taken as an additional
363    factor for the resulting number (see code) multiply by it.  */
364 static const STRING_TYPE *
str_to_mpn(const STRING_TYPE * str,int digcnt,mp_limb_t * n,mp_size_t * nsize,intmax_t * exponent,const char * decimal,size_t decimal_len,const char * thousands)365 str_to_mpn (const STRING_TYPE *str, int digcnt, mp_limb_t *n, mp_size_t *nsize,
366 	    intmax_t *exponent
367 #ifndef USE_WIDE_CHAR
368 	    , const char *decimal, size_t decimal_len, const char *thousands
369 #endif
370 
371 	    )
372 {
373   /* Number of digits for actual limb.  */
374   int cnt = 0;
375   mp_limb_t low = 0;
376   mp_limb_t start;
377 
378   *nsize = 0;
379   assert (digcnt > 0);
380   do
381     {
382       if (cnt == MAX_DIG_PER_LIMB)
383 	{
384 	  if (*nsize == 0)
385 	    {
386 	      n[0] = low;
387 	      *nsize = 1;
388 	    }
389 	  else
390 	    {
391 	      mp_limb_t cy;
392 	      cy = __mpn_mul_1 (n, n, *nsize, MAX_FAC_PER_LIMB);
393 	      cy += __mpn_add_1 (n, n, *nsize, low);
394 	      if (cy != 0)
395 		{
396 		  assert (*nsize < MPNSIZE);
397 		  n[*nsize] = cy;
398 		  ++(*nsize);
399 		}
400 	    }
401 	  cnt = 0;
402 	  low = 0;
403 	}
404 
405       /* There might be thousands separators or radix characters in
406 	 the string.  But these all can be ignored because we know the
407 	 format of the number is correct and we have an exact number
408 	 of characters to read.  */
409 #ifdef USE_WIDE_CHAR
410       if (*str < L'0' || *str > L'9')
411 	++str;
412 #else
413       if (*str < '0' || *str > '9')
414 	{
415 	  int inner = 0;
416 	  if (thousands != NULL && *str == *thousands
417 	      && ({ for (inner = 1; thousands[inner] != '\0'; ++inner)
418 		      if (thousands[inner] != str[inner])
419 			break;
420 		    thousands[inner] == '\0'; }))
421 	    str += inner;
422 	  else
423 	    str += decimal_len;
424 	}
425 #endif
426       low = low * 10 + *str++ - L_('0');
427       ++cnt;
428     }
429   while (--digcnt > 0);
430 
431   if (*exponent > 0 && *exponent <= MAX_DIG_PER_LIMB - cnt)
432     {
433       low *= _tens_in_limb[*exponent];
434       start = _tens_in_limb[cnt + *exponent];
435       *exponent = 0;
436     }
437   else
438     start = _tens_in_limb[cnt];
439 
440   if (*nsize == 0)
441     {
442       n[0] = low;
443       *nsize = 1;
444     }
445   else
446     {
447       mp_limb_t cy;
448       cy = __mpn_mul_1 (n, n, *nsize, start);
449       cy += __mpn_add_1 (n, n, *nsize, low);
450       if (cy != 0)
451 	{
452 	  assert (*nsize < MPNSIZE);
453 	  n[(*nsize)++] = cy;
454 	}
455     }
456 
457   return str;
458 }
459 
460 
461 /* Shift {PTR, SIZE} COUNT bits to the left, and fill the vacated bits
462    with the COUNT most significant bits of LIMB.
463 
464    Implemented as a macro, so that __builtin_constant_p works even at -O0.
465 
466    Tege doesn't like this macro so I have to write it here myself. :)
467    --drepper */
468 #define __mpn_lshift_1(ptr, size, count, limb) \
469   do									\
470     {									\
471       mp_limb_t *__ptr = (ptr);						\
472       if (__builtin_constant_p (count) && count == BITS_PER_MP_LIMB)	\
473 	{								\
474 	  mp_size_t i;							\
475 	  for (i = (size) - 1; i > 0; --i)				\
476 	    __ptr[i] = __ptr[i - 1];					\
477 	  __ptr[0] = (limb);						\
478 	}								\
479       else								\
480 	{								\
481 	  /* We assume count > 0 && count < BITS_PER_MP_LIMB here.  */	\
482 	  unsigned int __count = (count);				\
483 	  (void) __mpn_lshift (__ptr, __ptr, size, __count);		\
484 	  __ptr[0] |= (limb) >> (BITS_PER_MP_LIMB - __count);		\
485 	}								\
486     }									\
487   while (0)
488 
489 
490 #define INTERNAL(x) INTERNAL1(x)
491 #define INTERNAL1(x) __##x##_internal
492 #ifndef ____STRTOF_INTERNAL
493 # define ____STRTOF_INTERNAL INTERNAL (__STRTOF)
494 #endif
495 
496 /* This file defines a function to check for correct grouping.  */
497 #include "grouping.h"
498 
499 
500 /* Return a floating point number with the value of the given string NPTR.
501    Set *ENDPTR to the character after the last used one.  If the number is
502    smaller than the smallest representable number, set `errno' to ERANGE and
503    return 0.0.  If the number is too big to be represented, set `errno' to
504    ERANGE and return HUGE_VAL with the appropriate sign.  */
505 FLOAT
____STRTOF_INTERNAL(const STRING_TYPE * nptr,STRING_TYPE ** endptr,int group,locale_t loc)506 ____STRTOF_INTERNAL (const STRING_TYPE *nptr, STRING_TYPE **endptr, int group,
507 		     locale_t loc)
508 {
509   int negative;			/* The sign of the number.  */
510   MPN_VAR (num);		/* MP representation of the number.  */
511   intmax_t exponent;		/* Exponent of the number.  */
512 
513   /* Numbers starting `0X' or `0x' have to be processed with base 16.  */
514   int base = 10;
515 
516   /* When we have to compute fractional digits we form a fraction with a
517      second multi-precision number (and we sometimes need a second for
518      temporary results).  */
519   MPN_VAR (den);
520 
521   /* Representation for the return value.  */
522   mp_limb_t retval[RETURN_LIMB_SIZE];
523   /* Number of bits currently in result value.  */
524   int bits;
525 
526   /* Running pointer after the last character processed in the string.  */
527   const STRING_TYPE *cp, *tp;
528   /* Start of significant part of the number.  */
529   const STRING_TYPE *startp, *start_of_digits;
530   /* Points at the character following the integer and fractional digits.  */
531   const STRING_TYPE *expp;
532   /* Total number of digit and number of digits in integer part.  */
533   size_t dig_no, int_no, lead_zero;
534   /* Contains the last character read.  */
535   CHAR_TYPE c;
536 
537 /* We should get wint_t from <stddef.h>, but not all GCC versions define it
538    there.  So define it ourselves if it remains undefined.  */
539 #ifndef _WINT_T
540   typedef unsigned int wint_t;
541 #endif
542   /* The radix character of the current locale.  */
543 #ifdef USE_WIDE_CHAR
544   wchar_t decimal;
545 #else
546   const char *decimal;
547   size_t decimal_len;
548 #endif
549   /* The thousands character of the current locale.  */
550 #ifdef USE_WIDE_CHAR
551   wchar_t thousands = L'\0';
552 #else
553   const char *thousands = NULL;
554 #endif
555   /* The numeric grouping specification of the current locale,
556      in the format described in <locale.h>.  */
557   const char *grouping;
558   /* Used in several places.  */
559   int cnt;
560 
561   struct __locale_data *current = loc->__locales[LC_NUMERIC];
562 
563   if (__glibc_unlikely (group))
564     {
565       grouping = _NL_CURRENT (LC_NUMERIC, GROUPING);
566       if (*grouping <= 0 || *grouping == CHAR_MAX)
567 	grouping = NULL;
568       else
569 	{
570 	  /* Figure out the thousands separator character.  */
571 #ifdef USE_WIDE_CHAR
572 	  thousands = _NL_CURRENT_WORD (LC_NUMERIC,
573 					_NL_NUMERIC_THOUSANDS_SEP_WC);
574 	  if (thousands == L'\0')
575 	    grouping = NULL;
576 #else
577 	  thousands = _NL_CURRENT (LC_NUMERIC, THOUSANDS_SEP);
578 	  if (*thousands == '\0')
579 	    {
580 	      thousands = NULL;
581 	      grouping = NULL;
582 	    }
583 #endif
584 	}
585     }
586   else
587     grouping = NULL;
588 
589   /* Find the locale's decimal point character.  */
590 #ifdef USE_WIDE_CHAR
591   decimal = _NL_CURRENT_WORD (LC_NUMERIC, _NL_NUMERIC_DECIMAL_POINT_WC);
592   assert (decimal != L'\0');
593 # define decimal_len 1
594 #else
595   decimal = _NL_CURRENT (LC_NUMERIC, DECIMAL_POINT);
596   decimal_len = strlen (decimal);
597   assert (decimal_len > 0);
598 #endif
599 
600   /* Prepare number representation.  */
601   exponent = 0;
602   negative = 0;
603   bits = 0;
604 
605   /* Parse string to get maximal legal prefix.  We need the number of
606      characters of the integer part, the fractional part and the exponent.  */
607   cp = nptr - 1;
608   /* Ignore leading white space.  */
609   do
610     c = *++cp;
611   while (ISSPACE (c));
612 
613   /* Get sign of the result.  */
614   if (c == L_('-'))
615     {
616       negative = 1;
617       c = *++cp;
618     }
619   else if (c == L_('+'))
620     c = *++cp;
621 
622   /* Return 0.0 if no legal string is found.
623      No character is used even if a sign was found.  */
624 #ifdef USE_WIDE_CHAR
625   if (c == (wint_t) decimal
626       && (wint_t) cp[1] >= L'0' && (wint_t) cp[1] <= L'9')
627     {
628       /* We accept it.  This funny construct is here only to indent
629 	 the code correctly.  */
630     }
631 #else
632   for (cnt = 0; decimal[cnt] != '\0'; ++cnt)
633     if (cp[cnt] != decimal[cnt])
634       break;
635   if (decimal[cnt] == '\0' && cp[cnt] >= '0' && cp[cnt] <= '9')
636     {
637       /* We accept it.  This funny construct is here only to indent
638 	 the code correctly.  */
639     }
640 #endif
641   else if (c < L_('0') || c > L_('9'))
642     {
643       /* Check for `INF' or `INFINITY'.  */
644       CHAR_TYPE lowc = TOLOWER_C (c);
645 
646       if (lowc == L_('i') && STRNCASECMP (cp, L_("inf"), 3) == 0)
647 	{
648 	  /* Return +/- infinity.  */
649 	  if (endptr != NULL)
650 	    *endptr = (STRING_TYPE *)
651 		      (cp + (STRNCASECMP (cp + 3, L_("inity"), 5) == 0
652 			     ? 8 : 3));
653 
654 	  return negative ? -FLOAT_HUGE_VAL : FLOAT_HUGE_VAL;
655 	}
656 
657       if (lowc == L_('n') && STRNCASECMP (cp, L_("nan"), 3) == 0)
658 	{
659 	  /* Return NaN.  */
660 	  FLOAT retval = NAN;
661 
662 	  cp += 3;
663 
664 	  /* Match `(n-char-sequence-digit)'.  */
665 	  if (*cp == L_('('))
666 	    {
667 	      const STRING_TYPE *startp = cp;
668 	      STRING_TYPE *endp;
669 	      retval = STRTOF_NAN (cp + 1, &endp, L_(')'));
670 	      if (*endp == L_(')'))
671 		/* Consume the closing parenthesis.  */
672 		cp = endp + 1;
673 	      else
674 		/* Only match the NAN part.  */
675 		cp = startp;
676 	    }
677 
678 	  if (endptr != NULL)
679 	    *endptr = (STRING_TYPE *) cp;
680 
681 	  return negative ? -retval : retval;
682 	}
683 
684       /* It is really a text we do not recognize.  */
685       RETURN (0.0, nptr);
686     }
687 
688   /* First look whether we are faced with a hexadecimal number.  */
689   if (c == L_('0') && TOLOWER (cp[1]) == L_('x'))
690     {
691       /* Okay, it is a hexa-decimal number.  Remember this and skip
692 	 the characters.  BTW: hexadecimal numbers must not be
693 	 grouped.  */
694       base = 16;
695       cp += 2;
696       c = *cp;
697       grouping = NULL;
698     }
699 
700   /* Record the start of the digits, in case we will check their grouping.  */
701   start_of_digits = startp = cp;
702 
703   /* Ignore leading zeroes.  This helps us to avoid useless computations.  */
704 #ifdef USE_WIDE_CHAR
705   while (c == L'0' || ((wint_t) thousands != L'\0' && c == (wint_t) thousands))
706     c = *++cp;
707 #else
708   if (__glibc_likely (thousands == NULL))
709     while (c == '0')
710       c = *++cp;
711   else
712     {
713       /* We also have the multibyte thousands string.  */
714       while (1)
715 	{
716 	  if (c != '0')
717 	    {
718 	      for (cnt = 0; thousands[cnt] != '\0'; ++cnt)
719 		if (thousands[cnt] != cp[cnt])
720 		  break;
721 	      if (thousands[cnt] != '\0')
722 		break;
723 	      cp += cnt - 1;
724 	    }
725 	  c = *++cp;
726 	}
727     }
728 #endif
729 
730   /* If no other digit but a '0' is found the result is 0.0.
731      Return current read pointer.  */
732   CHAR_TYPE lowc = TOLOWER (c);
733   if (!((c >= L_('0') && c <= L_('9'))
734 	|| (base == 16 && lowc >= L_('a') && lowc <= L_('f'))
735 	|| (
736 #ifdef USE_WIDE_CHAR
737 	    c == (wint_t) decimal
738 #else
739 	    ({ for (cnt = 0; decimal[cnt] != '\0'; ++cnt)
740 		 if (decimal[cnt] != cp[cnt])
741 		   break;
742 	       decimal[cnt] == '\0'; })
743 #endif
744 	    /* '0x.' alone is not a valid hexadecimal number.
745 	       '.' alone is not valid either, but that has been checked
746 	       already earlier.  */
747 	    && (base != 16
748 		|| cp != start_of_digits
749 		|| (cp[decimal_len] >= L_('0') && cp[decimal_len] <= L_('9'))
750 		|| ({ CHAR_TYPE lo = TOLOWER (cp[decimal_len]);
751 		      lo >= L_('a') && lo <= L_('f'); })))
752 	|| (base == 16 && (cp != start_of_digits
753 			   && lowc == L_('p')))
754 	|| (base != 16 && lowc == L_('e'))))
755     {
756 #ifdef USE_WIDE_CHAR
757       tp = __correctly_grouped_prefixwc (start_of_digits, cp, thousands,
758 					 grouping);
759 #else
760       tp = __correctly_grouped_prefixmb (start_of_digits, cp, thousands,
761 					 grouping);
762 #endif
763       /* If TP is at the start of the digits, there was no correctly
764 	 grouped prefix of the string; so no number found.  */
765       RETURN (negative ? -0.0 : 0.0,
766 	      tp == start_of_digits ? (base == 16 ? cp - 1 : nptr) : tp);
767     }
768 
769   /* Remember first significant digit and read following characters until the
770      decimal point, exponent character or any non-FP number character.  */
771   startp = cp;
772   dig_no = 0;
773   while (1)
774     {
775       if ((c >= L_('0') && c <= L_('9'))
776 	  || (base == 16
777 	      && ({ CHAR_TYPE lo = TOLOWER (c);
778 		    lo >= L_('a') && lo <= L_('f'); })))
779 	++dig_no;
780       else
781 	{
782 #ifdef USE_WIDE_CHAR
783 	  if (__builtin_expect ((wint_t) thousands == L'\0', 1)
784 	      || c != (wint_t) thousands)
785 	    /* Not a digit or separator: end of the integer part.  */
786 	    break;
787 #else
788 	  if (__glibc_likely (thousands == NULL))
789 	    break;
790 	  else
791 	    {
792 	      for (cnt = 0; thousands[cnt] != '\0'; ++cnt)
793 		if (thousands[cnt] != cp[cnt])
794 		  break;
795 	      if (thousands[cnt] != '\0')
796 		break;
797 	      cp += cnt - 1;
798 	    }
799 #endif
800 	}
801       c = *++cp;
802     }
803 
804   if (__builtin_expect (grouping != NULL, 0) && cp > start_of_digits)
805     {
806       /* Check the grouping of the digits.  */
807 #ifdef USE_WIDE_CHAR
808       tp = __correctly_grouped_prefixwc (start_of_digits, cp, thousands,
809 					 grouping);
810 #else
811       tp = __correctly_grouped_prefixmb (start_of_digits, cp, thousands,
812 					 grouping);
813 #endif
814       if (cp != tp)
815 	{
816 	  /* Less than the entire string was correctly grouped.  */
817 
818 	  if (tp == start_of_digits)
819 	    /* No valid group of numbers at all: no valid number.  */
820 	    RETURN (0.0, nptr);
821 
822 	  if (tp < startp)
823 	    /* The number is validly grouped, but consists
824 	       only of zeroes.  The whole value is zero.  */
825 	    RETURN (negative ? -0.0 : 0.0, tp);
826 
827 	  /* Recompute DIG_NO so we won't read more digits than
828 	     are properly grouped.  */
829 	  cp = tp;
830 	  dig_no = 0;
831 	  for (tp = startp; tp < cp; ++tp)
832 	    if (*tp >= L_('0') && *tp <= L_('9'))
833 	      ++dig_no;
834 
835 	  int_no = dig_no;
836 	  lead_zero = 0;
837 
838 	  goto number_parsed;
839 	}
840     }
841 
842   /* We have the number of digits in the integer part.  Whether these
843      are all or any is really a fractional digit will be decided
844      later.  */
845   int_no = dig_no;
846   lead_zero = int_no == 0 ? (size_t) -1 : 0;
847 
848   /* Read the fractional digits.  A special case are the 'american
849      style' numbers like `16.' i.e. with decimal point but without
850      trailing digits.  */
851   if (
852 #ifdef USE_WIDE_CHAR
853       c == (wint_t) decimal
854 #else
855       ({ for (cnt = 0; decimal[cnt] != '\0'; ++cnt)
856 	   if (decimal[cnt] != cp[cnt])
857 	     break;
858 	 decimal[cnt] == '\0'; })
859 #endif
860       )
861     {
862       cp += decimal_len;
863       c = *cp;
864       while ((c >= L_('0') && c <= L_('9'))
865 	     || (base == 16 && ({ CHAR_TYPE lo = TOLOWER (c);
866 				  lo >= L_('a') && lo <= L_('f'); })))
867 	{
868 	  if (c != L_('0') && lead_zero == (size_t) -1)
869 	    lead_zero = dig_no - int_no;
870 	  ++dig_no;
871 	  c = *++cp;
872 	}
873     }
874   assert (dig_no <= (uintmax_t) INTMAX_MAX);
875 
876   /* Remember start of exponent (if any).  */
877   expp = cp;
878 
879   /* Read exponent.  */
880   lowc = TOLOWER (c);
881   if ((base == 16 && lowc == L_('p'))
882       || (base != 16 && lowc == L_('e')))
883     {
884       int exp_negative = 0;
885 
886       c = *++cp;
887       if (c == L_('-'))
888 	{
889 	  exp_negative = 1;
890 	  c = *++cp;
891 	}
892       else if (c == L_('+'))
893 	c = *++cp;
894 
895       if (c >= L_('0') && c <= L_('9'))
896 	{
897 	  intmax_t exp_limit;
898 
899 	  /* Get the exponent limit. */
900 	  if (base == 16)
901 	    {
902 	      if (exp_negative)
903 		{
904 		  assert (int_no <= (uintmax_t) (INTMAX_MAX
905 						 + MIN_EXP - MANT_DIG) / 4);
906 		  exp_limit = -MIN_EXP + MANT_DIG + 4 * (intmax_t) int_no;
907 		}
908 	      else
909 		{
910 		  if (int_no)
911 		    {
912 		      assert (lead_zero == 0
913 			      && int_no <= (uintmax_t) INTMAX_MAX / 4);
914 		      exp_limit = MAX_EXP - 4 * (intmax_t) int_no + 3;
915 		    }
916 		  else if (lead_zero == (size_t) -1)
917 		    {
918 		      /* The number is zero and this limit is
919 			 arbitrary.  */
920 		      exp_limit = MAX_EXP + 3;
921 		    }
922 		  else
923 		    {
924 		      assert (lead_zero
925 			      <= (uintmax_t) (INTMAX_MAX - MAX_EXP - 3) / 4);
926 		      exp_limit = (MAX_EXP
927 				   + 4 * (intmax_t) lead_zero
928 				   + 3);
929 		    }
930 		}
931 	    }
932 	  else
933 	    {
934 	      if (exp_negative)
935 		{
936 		  assert (int_no
937 			  <= (uintmax_t) (INTMAX_MAX + MIN_10_EXP - MANT_DIG));
938 		  exp_limit = -MIN_10_EXP + MANT_DIG + (intmax_t) int_no;
939 		}
940 	      else
941 		{
942 		  if (int_no)
943 		    {
944 		      assert (lead_zero == 0
945 			      && int_no <= (uintmax_t) INTMAX_MAX);
946 		      exp_limit = MAX_10_EXP - (intmax_t) int_no + 1;
947 		    }
948 		  else if (lead_zero == (size_t) -1)
949 		    {
950 		      /* The number is zero and this limit is
951 			 arbitrary.  */
952 		      exp_limit = MAX_10_EXP + 1;
953 		    }
954 		  else
955 		    {
956 		      assert (lead_zero
957 			      <= (uintmax_t) (INTMAX_MAX - MAX_10_EXP - 1));
958 		      exp_limit = MAX_10_EXP + (intmax_t) lead_zero + 1;
959 		    }
960 		}
961 	    }
962 
963 	  if (exp_limit < 0)
964 	    exp_limit = 0;
965 
966 	  do
967 	    {
968 	      if (__builtin_expect ((exponent > exp_limit / 10
969 				     || (exponent == exp_limit / 10
970 					 && c - L_('0') > exp_limit % 10)), 0))
971 		/* The exponent is too large/small to represent a valid
972 		   number.  */
973 		{
974 		  FLOAT result;
975 
976 		  /* We have to take care for special situation: a joker
977 		     might have written "0.0e100000" which is in fact
978 		     zero.  */
979 		  if (lead_zero == (size_t) -1)
980 		    result = negative ? -0.0 : 0.0;
981 		  else
982 		    {
983 		      /* Overflow or underflow.  */
984 		      result = (exp_negative
985 				? underflow_value (negative)
986 				: overflow_value (negative));
987 		    }
988 
989 		  /* Accept all following digits as part of the exponent.  */
990 		  do
991 		    ++cp;
992 		  while (*cp >= L_('0') && *cp <= L_('9'));
993 
994 		  RETURN (result, cp);
995 		  /* NOTREACHED */
996 		}
997 
998 	      exponent *= 10;
999 	      exponent += c - L_('0');
1000 
1001 	      c = *++cp;
1002 	    }
1003 	  while (c >= L_('0') && c <= L_('9'));
1004 
1005 	  if (exp_negative)
1006 	    exponent = -exponent;
1007 	}
1008       else
1009 	cp = expp;
1010     }
1011 
1012   /* We don't want to have to work with trailing zeroes after the radix.  */
1013   if (dig_no > int_no)
1014     {
1015       while (expp[-1] == L_('0'))
1016 	{
1017 	  --expp;
1018 	  --dig_no;
1019 	}
1020       assert (dig_no >= int_no);
1021     }
1022 
1023   if (dig_no == int_no && dig_no > 0 && exponent < 0)
1024     do
1025       {
1026 	while (! (base == 16 ? ISXDIGIT (expp[-1]) : ISDIGIT (expp[-1])))
1027 	  --expp;
1028 
1029 	if (expp[-1] != L_('0'))
1030 	  break;
1031 
1032 	--expp;
1033 	--dig_no;
1034 	--int_no;
1035 	exponent += base == 16 ? 4 : 1;
1036       }
1037     while (dig_no > 0 && exponent < 0);
1038 
1039  number_parsed:
1040 
1041   /* The whole string is parsed.  Store the address of the next character.  */
1042   if (endptr)
1043     *endptr = (STRING_TYPE *) cp;
1044 
1045   if (dig_no == 0)
1046     return negative ? -0.0 : 0.0;
1047 
1048   if (lead_zero)
1049     {
1050       /* Find the decimal point */
1051 #ifdef USE_WIDE_CHAR
1052       while (*startp != decimal)
1053 	++startp;
1054 #else
1055       while (1)
1056 	{
1057 	  if (*startp == decimal[0])
1058 	    {
1059 	      for (cnt = 1; decimal[cnt] != '\0'; ++cnt)
1060 		if (decimal[cnt] != startp[cnt])
1061 		  break;
1062 	      if (decimal[cnt] == '\0')
1063 		break;
1064 	    }
1065 	  ++startp;
1066 	}
1067 #endif
1068       startp += lead_zero + decimal_len;
1069       assert (lead_zero <= (base == 16
1070 			    ? (uintmax_t) INTMAX_MAX / 4
1071 			    : (uintmax_t) INTMAX_MAX));
1072       assert (lead_zero <= (base == 16
1073 			    ? ((uintmax_t) exponent
1074 			       - (uintmax_t) INTMAX_MIN) / 4
1075 			    : ((uintmax_t) exponent - (uintmax_t) INTMAX_MIN)));
1076       exponent -= base == 16 ? 4 * (intmax_t) lead_zero : (intmax_t) lead_zero;
1077       dig_no -= lead_zero;
1078     }
1079 
1080   /* If the BASE is 16 we can use a simpler algorithm.  */
1081   if (base == 16)
1082     {
1083       static const int nbits[16] = { 0, 1, 2, 2, 3, 3, 3, 3,
1084 				     4, 4, 4, 4, 4, 4, 4, 4 };
1085       int idx = (MANT_DIG - 1) / BITS_PER_MP_LIMB;
1086       int pos = (MANT_DIG - 1) % BITS_PER_MP_LIMB;
1087       mp_limb_t val;
1088 
1089       while (!ISXDIGIT (*startp))
1090 	++startp;
1091       while (*startp == L_('0'))
1092 	++startp;
1093       if (ISDIGIT (*startp))
1094 	val = *startp++ - L_('0');
1095       else
1096 	val = 10 + TOLOWER (*startp++) - L_('a');
1097       bits = nbits[val];
1098       /* We cannot have a leading zero.  */
1099       assert (bits != 0);
1100 
1101       if (pos + 1 >= 4 || pos + 1 >= bits)
1102 	{
1103 	  /* We don't have to care for wrapping.  This is the normal
1104 	     case so we add the first clause in the `if' expression as
1105 	     an optimization.  It is a compile-time constant and so does
1106 	     not cost anything.  */
1107 	  retval[idx] = val << (pos - bits + 1);
1108 	  pos -= bits;
1109 	}
1110       else
1111 	{
1112 	  retval[idx--] = val >> (bits - pos - 1);
1113 	  retval[idx] = val << (BITS_PER_MP_LIMB - (bits - pos - 1));
1114 	  pos = BITS_PER_MP_LIMB - 1 - (bits - pos - 1);
1115 	}
1116 
1117       /* Adjust the exponent for the bits we are shifting in.  */
1118       assert (int_no <= (uintmax_t) (exponent < 0
1119 				     ? (INTMAX_MAX - bits + 1) / 4
1120 				     : (INTMAX_MAX - exponent - bits + 1) / 4));
1121       exponent += bits - 1 + ((intmax_t) int_no - 1) * 4;
1122 
1123       while (--dig_no > 0 && idx >= 0)
1124 	{
1125 	  if (!ISXDIGIT (*startp))
1126 	    startp += decimal_len;
1127 	  if (ISDIGIT (*startp))
1128 	    val = *startp++ - L_('0');
1129 	  else
1130 	    val = 10 + TOLOWER (*startp++) - L_('a');
1131 
1132 	  if (pos + 1 >= 4)
1133 	    {
1134 	      retval[idx] |= val << (pos - 4 + 1);
1135 	      pos -= 4;
1136 	    }
1137 	  else
1138 	    {
1139 	      retval[idx--] |= val >> (4 - pos - 1);
1140 	      val <<= BITS_PER_MP_LIMB - (4 - pos - 1);
1141 	      if (idx < 0)
1142 		{
1143 		  int rest_nonzero = 0;
1144 		  while (--dig_no > 0)
1145 		    {
1146 		      if (*startp != L_('0'))
1147 			{
1148 			  rest_nonzero = 1;
1149 			  break;
1150 			}
1151 		      startp++;
1152 		    }
1153 		  return round_and_return (retval, exponent, negative, val,
1154 					   BITS_PER_MP_LIMB - 1, rest_nonzero);
1155 		}
1156 
1157 	      retval[idx] = val;
1158 	      pos = BITS_PER_MP_LIMB - 1 - (4 - pos - 1);
1159 	    }
1160 	}
1161 
1162       /* We ran out of digits.  */
1163       MPN_ZERO (retval, idx);
1164 
1165       return round_and_return (retval, exponent, negative, 0, 0, 0);
1166     }
1167 
1168   /* Now we have the number of digits in total and the integer digits as well
1169      as the exponent and its sign.  We can decide whether the read digits are
1170      really integer digits or belong to the fractional part; i.e. we normalize
1171      123e-2 to 1.23.  */
1172   {
1173     intmax_t incr = (exponent < 0
1174 		     ? MAX (-(intmax_t) int_no, exponent)
1175 		     : MIN ((intmax_t) dig_no - (intmax_t) int_no, exponent));
1176     int_no += incr;
1177     exponent -= incr;
1178   }
1179 
1180   if (__glibc_unlikely (exponent > MAX_10_EXP + 1 - (intmax_t) int_no))
1181     return overflow_value (negative);
1182 
1183   /* 10^(MIN_10_EXP-1) is not normal.  Thus, 10^(MIN_10_EXP-1) /
1184      2^MANT_DIG is below half the least subnormal, so anything with a
1185      base-10 exponent less than the base-10 exponent (which is
1186      MIN_10_EXP - 1 - ceil(MANT_DIG*log10(2))) of that value
1187      underflows.  DIG is floor((MANT_DIG-1)log10(2)), so an exponent
1188      below MIN_10_EXP - (DIG + 3) underflows.  But EXPONENT is
1189      actually an exponent multiplied only by a fractional part, not an
1190      integer part, so an exponent below MIN_10_EXP - (DIG + 2)
1191      underflows.  */
1192   if (__glibc_unlikely (exponent < MIN_10_EXP - (DIG + 2)))
1193     return underflow_value (negative);
1194 
1195   if (int_no > 0)
1196     {
1197       /* Read the integer part as a multi-precision number to NUM.  */
1198       startp = str_to_mpn (startp, int_no, num, &numsize, &exponent
1199 #ifndef USE_WIDE_CHAR
1200 			   , decimal, decimal_len, thousands
1201 #endif
1202 			   );
1203 
1204       if (exponent > 0)
1205 	{
1206 	  /* We now multiply the gained number by the given power of ten.  */
1207 	  mp_limb_t *psrc = num;
1208 	  mp_limb_t *pdest = den;
1209 	  int expbit = 1;
1210 	  const struct mp_power *ttab = &_fpioconst_pow10[0];
1211 
1212 	  do
1213 	    {
1214 	      if ((exponent & expbit) != 0)
1215 		{
1216 		  size_t size = ttab->arraysize - _FPIO_CONST_OFFSET;
1217 		  mp_limb_t cy;
1218 		  exponent ^= expbit;
1219 
1220 		  /* FIXME: not the whole multiplication has to be
1221 		     done.  If we have the needed number of bits we
1222 		     only need the information whether more non-zero
1223 		     bits follow.  */
1224 		  if (numsize >= ttab->arraysize - _FPIO_CONST_OFFSET)
1225 		    cy = __mpn_mul (pdest, psrc, numsize,
1226 				    &__tens[ttab->arrayoff
1227 					   + _FPIO_CONST_OFFSET],
1228 				    size);
1229 		  else
1230 		    cy = __mpn_mul (pdest, &__tens[ttab->arrayoff
1231 						  + _FPIO_CONST_OFFSET],
1232 				    size, psrc, numsize);
1233 		  numsize += size;
1234 		  if (cy == 0)
1235 		    --numsize;
1236 		  (void) SWAP (psrc, pdest);
1237 		}
1238 	      expbit <<= 1;
1239 	      ++ttab;
1240 	    }
1241 	  while (exponent != 0);
1242 
1243 	  if (psrc == den)
1244 	    memcpy (num, den, numsize * sizeof (mp_limb_t));
1245 	}
1246 
1247       /* Determine how many bits of the result we already have.  */
1248       count_leading_zeros (bits, num[numsize - 1]);
1249       bits = numsize * BITS_PER_MP_LIMB - bits;
1250 
1251       /* Now we know the exponent of the number in base two.
1252 	 Check it against the maximum possible exponent.  */
1253       if (__glibc_unlikely (bits > MAX_EXP))
1254 	return overflow_value (negative);
1255 
1256       /* We have already the first BITS bits of the result.  Together with
1257 	 the information whether more non-zero bits follow this is enough
1258 	 to determine the result.  */
1259       if (bits > MANT_DIG)
1260 	{
1261 	  int i;
1262 	  const mp_size_t least_idx = (bits - MANT_DIG) / BITS_PER_MP_LIMB;
1263 	  const mp_size_t least_bit = (bits - MANT_DIG) % BITS_PER_MP_LIMB;
1264 	  const mp_size_t round_idx = least_bit == 0 ? least_idx - 1
1265 						     : least_idx;
1266 	  const mp_size_t round_bit = least_bit == 0 ? BITS_PER_MP_LIMB - 1
1267 						     : least_bit - 1;
1268 
1269 	  if (least_bit == 0)
1270 	    memcpy (retval, &num[least_idx],
1271 		    RETURN_LIMB_SIZE * sizeof (mp_limb_t));
1272 	  else
1273 	    {
1274 	      for (i = least_idx; i < numsize - 1; ++i)
1275 		retval[i - least_idx] = (num[i] >> least_bit)
1276 					| (num[i + 1]
1277 					   << (BITS_PER_MP_LIMB - least_bit));
1278 	      if (i - least_idx < RETURN_LIMB_SIZE)
1279 		retval[RETURN_LIMB_SIZE - 1] = num[i] >> least_bit;
1280 	    }
1281 
1282 	  /* Check whether any limb beside the ones in RETVAL are non-zero.  */
1283 	  for (i = 0; num[i] == 0; ++i)
1284 	    ;
1285 
1286 	  return round_and_return (retval, bits - 1, negative,
1287 				   num[round_idx], round_bit,
1288 				   int_no < dig_no || i < round_idx);
1289 	  /* NOTREACHED */
1290 	}
1291       else if (dig_no == int_no)
1292 	{
1293 	  const mp_size_t target_bit = (MANT_DIG - 1) % BITS_PER_MP_LIMB;
1294 	  const mp_size_t is_bit = (bits - 1) % BITS_PER_MP_LIMB;
1295 
1296 	  if (target_bit == is_bit)
1297 	    {
1298 	      memcpy (&retval[RETURN_LIMB_SIZE - numsize], num,
1299 		      numsize * sizeof (mp_limb_t));
1300 	      /* FIXME: the following loop can be avoided if we assume a
1301 		 maximal MANT_DIG value.  */
1302 	      MPN_ZERO (retval, RETURN_LIMB_SIZE - numsize);
1303 	    }
1304 	  else if (target_bit > is_bit)
1305 	    {
1306 	      (void) __mpn_lshift (&retval[RETURN_LIMB_SIZE - numsize],
1307 				   num, numsize, target_bit - is_bit);
1308 	      /* FIXME: the following loop can be avoided if we assume a
1309 		 maximal MANT_DIG value.  */
1310 	      MPN_ZERO (retval, RETURN_LIMB_SIZE - numsize);
1311 	    }
1312 	  else
1313 	    {
1314 	      mp_limb_t cy;
1315 	      assert (numsize < RETURN_LIMB_SIZE);
1316 
1317 	      cy = __mpn_rshift (&retval[RETURN_LIMB_SIZE - numsize],
1318 				 num, numsize, is_bit - target_bit);
1319 	      retval[RETURN_LIMB_SIZE - numsize - 1] = cy;
1320 	      /* FIXME: the following loop can be avoided if we assume a
1321 		 maximal MANT_DIG value.  */
1322 	      MPN_ZERO (retval, RETURN_LIMB_SIZE - numsize - 1);
1323 	    }
1324 
1325 	  return round_and_return (retval, bits - 1, negative, 0, 0, 0);
1326 	  /* NOTREACHED */
1327 	}
1328 
1329       /* Store the bits we already have.  */
1330       memcpy (retval, num, numsize * sizeof (mp_limb_t));
1331 #if RETURN_LIMB_SIZE > 1
1332       if (numsize < RETURN_LIMB_SIZE)
1333 # if RETURN_LIMB_SIZE == 2
1334 	retval[numsize] = 0;
1335 # else
1336 	MPN_ZERO (retval + numsize, RETURN_LIMB_SIZE - numsize);
1337 # endif
1338 #endif
1339     }
1340 
1341   /* We have to compute at least some of the fractional digits.  */
1342   {
1343     /* We construct a fraction and the result of the division gives us
1344        the needed digits.  The denominator is 1.0 multiplied by the
1345        exponent of the lowest digit; i.e. 0.123 gives 123 / 1000 and
1346        123e-6 gives 123 / 1000000.  */
1347 
1348     int expbit;
1349     int neg_exp;
1350     int more_bits;
1351     int need_frac_digits;
1352     mp_limb_t cy;
1353     mp_limb_t *psrc = den;
1354     mp_limb_t *pdest = num;
1355     const struct mp_power *ttab = &_fpioconst_pow10[0];
1356 
1357     assert (dig_no > int_no
1358 	    && exponent <= 0
1359 	    && exponent >= MIN_10_EXP - (DIG + 2));
1360 
1361     /* We need to compute MANT_DIG - BITS fractional bits that lie
1362        within the mantissa of the result, the following bit for
1363        rounding, and to know whether any subsequent bit is 0.
1364        Computing a bit with value 2^-n means looking at n digits after
1365        the decimal point.  */
1366     if (bits > 0)
1367       {
1368 	/* The bits required are those immediately after the point.  */
1369 	assert (int_no > 0 && exponent == 0);
1370 	need_frac_digits = 1 + MANT_DIG - bits;
1371       }
1372     else
1373       {
1374 	/* The number is in the form .123eEXPONENT.  */
1375 	assert (int_no == 0 && *startp != L_('0'));
1376 	/* The number is at least 10^(EXPONENT-1), and 10^3 <
1377 	   2^10.  */
1378 	int neg_exp_2 = ((1 - exponent) * 10) / 3 + 1;
1379 	/* The number is at least 2^-NEG_EXP_2.  We need up to
1380 	   MANT_DIG bits following that bit.  */
1381 	need_frac_digits = neg_exp_2 + MANT_DIG;
1382 	/* However, we never need bits beyond 1/4 ulp of the smallest
1383 	   representable value.  (That 1/4 ulp bit is only needed to
1384 	   determine tinyness on machines where tinyness is determined
1385 	   after rounding.)  */
1386 	if (need_frac_digits > MANT_DIG - MIN_EXP + 2)
1387 	  need_frac_digits = MANT_DIG - MIN_EXP + 2;
1388 	/* At this point, NEED_FRAC_DIGITS is the total number of
1389 	   digits needed after the point, but some of those may be
1390 	   leading 0s.  */
1391 	need_frac_digits += exponent;
1392 	/* Any cases underflowing enough that none of the fractional
1393 	   digits are needed should have been caught earlier (such
1394 	   cases are on the order of 10^-n or smaller where 2^-n is
1395 	   the least subnormal).  */
1396 	assert (need_frac_digits > 0);
1397       }
1398 
1399     if (need_frac_digits > (intmax_t) dig_no - (intmax_t) int_no)
1400       need_frac_digits = (intmax_t) dig_no - (intmax_t) int_no;
1401 
1402     if ((intmax_t) dig_no > (intmax_t) int_no + need_frac_digits)
1403       {
1404 	dig_no = int_no + need_frac_digits;
1405 	more_bits = 1;
1406       }
1407     else
1408       more_bits = 0;
1409 
1410     neg_exp = (intmax_t) dig_no - (intmax_t) int_no - exponent;
1411 
1412     /* Construct the denominator.  */
1413     densize = 0;
1414     expbit = 1;
1415     do
1416       {
1417 	if ((neg_exp & expbit) != 0)
1418 	  {
1419 	    mp_limb_t cy;
1420 	    neg_exp ^= expbit;
1421 
1422 	    if (densize == 0)
1423 	      {
1424 		densize = ttab->arraysize - _FPIO_CONST_OFFSET;
1425 		memcpy (psrc, &__tens[ttab->arrayoff + _FPIO_CONST_OFFSET],
1426 			densize * sizeof (mp_limb_t));
1427 	      }
1428 	    else
1429 	      {
1430 		cy = __mpn_mul (pdest, &__tens[ttab->arrayoff
1431 					      + _FPIO_CONST_OFFSET],
1432 				ttab->arraysize - _FPIO_CONST_OFFSET,
1433 				psrc, densize);
1434 		densize += ttab->arraysize - _FPIO_CONST_OFFSET;
1435 		if (cy == 0)
1436 		  --densize;
1437 		(void) SWAP (psrc, pdest);
1438 	      }
1439 	  }
1440 	expbit <<= 1;
1441 	++ttab;
1442       }
1443     while (neg_exp != 0);
1444 
1445     if (psrc == num)
1446       memcpy (den, num, densize * sizeof (mp_limb_t));
1447 
1448     /* Read the fractional digits from the string.  */
1449     (void) str_to_mpn (startp, dig_no - int_no, num, &numsize, &exponent
1450 #ifndef USE_WIDE_CHAR
1451 		       , decimal, decimal_len, thousands
1452 #endif
1453 		       );
1454 
1455     /* We now have to shift both numbers so that the highest bit in the
1456        denominator is set.  In the same process we copy the numerator to
1457        a high place in the array so that the division constructs the wanted
1458        digits.  This is done by a "quasi fix point" number representation.
1459 
1460        num:   ddddddddddd . 0000000000000000000000
1461 	      |--- m ---|
1462        den:                            ddddddddddd      n >= m
1463 				       |--- n ---|
1464      */
1465 
1466     count_leading_zeros (cnt, den[densize - 1]);
1467 
1468     if (cnt > 0)
1469       {
1470 	/* Don't call `mpn_shift' with a count of zero since the specification
1471 	   does not allow this.  */
1472 	(void) __mpn_lshift (den, den, densize, cnt);
1473 	cy = __mpn_lshift (num, num, numsize, cnt);
1474 	if (cy != 0)
1475 	  num[numsize++] = cy;
1476       }
1477 
1478     /* Now we are ready for the division.  But it is not necessary to
1479        do a full multi-precision division because we only need a small
1480        number of bits for the result.  So we do not use __mpn_divmod
1481        here but instead do the division here by hand and stop whenever
1482        the needed number of bits is reached.  The code itself comes
1483        from the GNU MP Library by Torbj\"orn Granlund.  */
1484 
1485     exponent = bits;
1486 
1487     switch (densize)
1488       {
1489       case 1:
1490 	{
1491 	  mp_limb_t d, n, quot;
1492 	  int used = 0;
1493 
1494 	  n = num[0];
1495 	  d = den[0];
1496 	  assert (numsize == 1 && n < d);
1497 
1498 	  do
1499 	    {
1500 	      udiv_qrnnd (quot, n, n, 0, d);
1501 
1502 #define got_limb							      \
1503 	      if (bits == 0)						      \
1504 		{							      \
1505 		  int cnt;						      \
1506 		  if (quot == 0)					      \
1507 		    cnt = BITS_PER_MP_LIMB;				      \
1508 		  else							      \
1509 		    count_leading_zeros (cnt, quot);			      \
1510 		  exponent -= cnt;					      \
1511 		  if (BITS_PER_MP_LIMB - cnt > MANT_DIG)		      \
1512 		    {							      \
1513 		      used = MANT_DIG + cnt;				      \
1514 		      retval[0] = quot >> (BITS_PER_MP_LIMB - used);	      \
1515 		      bits = MANT_DIG + 1;				      \
1516 		    }							      \
1517 		  else							      \
1518 		    {							      \
1519 		      /* Note that we only clear the second element.  */      \
1520 		      /* The conditional is determined at compile time.  */   \
1521 		      if (RETURN_LIMB_SIZE > 1)				      \
1522 			retval[1] = 0;					      \
1523 		      retval[0] = quot;					      \
1524 		      bits = -cnt;					      \
1525 		    }							      \
1526 		}							      \
1527 	      else if (bits + BITS_PER_MP_LIMB <= MANT_DIG)		      \
1528 		__mpn_lshift_1 (retval, RETURN_LIMB_SIZE, BITS_PER_MP_LIMB,   \
1529 				quot);					      \
1530 	      else							      \
1531 		{							      \
1532 		  used = MANT_DIG - bits;				      \
1533 		  if (used > 0)						      \
1534 		    __mpn_lshift_1 (retval, RETURN_LIMB_SIZE, used, quot);    \
1535 		}							      \
1536 	      bits += BITS_PER_MP_LIMB
1537 
1538 	      got_limb;
1539 	    }
1540 	  while (bits <= MANT_DIG);
1541 
1542 	  return round_and_return (retval, exponent - 1, negative,
1543 				   quot, BITS_PER_MP_LIMB - 1 - used,
1544 				   more_bits || n != 0);
1545 	}
1546       case 2:
1547 	{
1548 	  mp_limb_t d0, d1, n0, n1;
1549 	  mp_limb_t quot = 0;
1550 	  int used = 0;
1551 
1552 	  d0 = den[0];
1553 	  d1 = den[1];
1554 
1555 	  if (numsize < densize)
1556 	    {
1557 	      if (num[0] >= d1)
1558 		{
1559 		  /* The numerator of the number occupies fewer bits than
1560 		     the denominator but the one limb is bigger than the
1561 		     high limb of the numerator.  */
1562 		  n1 = 0;
1563 		  n0 = num[0];
1564 		}
1565 	      else
1566 		{
1567 		  if (bits <= 0)
1568 		    exponent -= BITS_PER_MP_LIMB;
1569 		  else
1570 		    {
1571 		      if (bits + BITS_PER_MP_LIMB <= MANT_DIG)
1572 			__mpn_lshift_1 (retval, RETURN_LIMB_SIZE,
1573 					BITS_PER_MP_LIMB, 0);
1574 		      else
1575 			{
1576 			  used = MANT_DIG - bits;
1577 			  if (used > 0)
1578 			    __mpn_lshift_1 (retval, RETURN_LIMB_SIZE, used, 0);
1579 			}
1580 		      bits += BITS_PER_MP_LIMB;
1581 		    }
1582 		  n1 = num[0];
1583 		  n0 = 0;
1584 		}
1585 	    }
1586 	  else
1587 	    {
1588 	      n1 = num[1];
1589 	      n0 = num[0];
1590 	    }
1591 
1592 	  while (bits <= MANT_DIG)
1593 	    {
1594 	      mp_limb_t r;
1595 
1596 	      if (n1 == d1)
1597 		{
1598 		  /* QUOT should be either 111..111 or 111..110.  We need
1599 		     special treatment of this rare case as normal division
1600 		     would give overflow.  */
1601 		  quot = ~(mp_limb_t) 0;
1602 
1603 		  r = n0 + d1;
1604 		  if (r < d1)	/* Carry in the addition?  */
1605 		    {
1606 		      add_ssaaaa (n1, n0, r - d0, 0, 0, d0);
1607 		      goto have_quot;
1608 		    }
1609 		  n1 = d0 - (d0 != 0);
1610 		  n0 = -d0;
1611 		}
1612 	      else
1613 		{
1614 		  udiv_qrnnd (quot, r, n1, n0, d1);
1615 		  umul_ppmm (n1, n0, d0, quot);
1616 		}
1617 
1618 	    q_test:
1619 	      if (n1 > r || (n1 == r && n0 > 0))
1620 		{
1621 		  /* The estimated QUOT was too large.  */
1622 		  --quot;
1623 
1624 		  sub_ddmmss (n1, n0, n1, n0, 0, d0);
1625 		  r += d1;
1626 		  if (r >= d1)	/* If not carry, test QUOT again.  */
1627 		    goto q_test;
1628 		}
1629 	      sub_ddmmss (n1, n0, r, 0, n1, n0);
1630 
1631 	    have_quot:
1632 	      got_limb;
1633 	    }
1634 
1635 	  return round_and_return (retval, exponent - 1, negative,
1636 				   quot, BITS_PER_MP_LIMB - 1 - used,
1637 				   more_bits || n1 != 0 || n0 != 0);
1638 	}
1639       default:
1640 	{
1641 	  int i;
1642 	  mp_limb_t cy, dX, d1, n0, n1;
1643 	  mp_limb_t quot = 0;
1644 	  int used = 0;
1645 
1646 	  dX = den[densize - 1];
1647 	  d1 = den[densize - 2];
1648 
1649 	  /* The division does not work if the upper limb of the two-limb
1650 	     numerator is greater than or equal to the denominator.  */
1651 	  if (__mpn_cmp (num, &den[densize - numsize], numsize) >= 0)
1652 	    num[numsize++] = 0;
1653 
1654 	  if (numsize < densize)
1655 	    {
1656 	      mp_size_t empty = densize - numsize;
1657 	      int i;
1658 
1659 	      if (bits <= 0)
1660 		exponent -= empty * BITS_PER_MP_LIMB;
1661 	      else
1662 		{
1663 		  if (bits + empty * BITS_PER_MP_LIMB <= MANT_DIG)
1664 		    {
1665 		      /* We make a difference here because the compiler
1666 			 cannot optimize the `else' case that good and
1667 			 this reflects all currently used FLOAT types
1668 			 and GMP implementations.  */
1669 #if RETURN_LIMB_SIZE <= 2
1670 		      assert (empty == 1);
1671 		      __mpn_lshift_1 (retval, RETURN_LIMB_SIZE,
1672 				      BITS_PER_MP_LIMB, 0);
1673 #else
1674 		      for (i = RETURN_LIMB_SIZE - 1; i >= empty; --i)
1675 			retval[i] = retval[i - empty];
1676 		      while (i >= 0)
1677 			retval[i--] = 0;
1678 #endif
1679 		    }
1680 		  else
1681 		    {
1682 		      used = MANT_DIG - bits;
1683 		      if (used >= BITS_PER_MP_LIMB)
1684 			{
1685 			  int i;
1686 			  (void) __mpn_lshift (&retval[used
1687 						       / BITS_PER_MP_LIMB],
1688 					       retval,
1689 					       (RETURN_LIMB_SIZE
1690 						- used / BITS_PER_MP_LIMB),
1691 					       used % BITS_PER_MP_LIMB);
1692 			  for (i = used / BITS_PER_MP_LIMB - 1; i >= 0; --i)
1693 			    retval[i] = 0;
1694 			}
1695 		      else if (used > 0)
1696 			__mpn_lshift_1 (retval, RETURN_LIMB_SIZE, used, 0);
1697 		    }
1698 		  bits += empty * BITS_PER_MP_LIMB;
1699 		}
1700 	      for (i = numsize; i > 0; --i)
1701 		num[i + empty] = num[i - 1];
1702 	      MPN_ZERO (num, empty + 1);
1703 	    }
1704 	  else
1705 	    {
1706 	      int i;
1707 	      assert (numsize == densize);
1708 	      for (i = numsize; i > 0; --i)
1709 		num[i] = num[i - 1];
1710 	      num[0] = 0;
1711 	    }
1712 
1713 	  den[densize] = 0;
1714 	  n0 = num[densize];
1715 
1716 	  while (bits <= MANT_DIG)
1717 	    {
1718 	      if (n0 == dX)
1719 		/* This might over-estimate QUOT, but it's probably not
1720 		   worth the extra code here to find out.  */
1721 		quot = ~(mp_limb_t) 0;
1722 	      else
1723 		{
1724 		  mp_limb_t r;
1725 
1726 		  udiv_qrnnd (quot, r, n0, num[densize - 1], dX);
1727 		  umul_ppmm (n1, n0, d1, quot);
1728 
1729 		  while (n1 > r || (n1 == r && n0 > num[densize - 2]))
1730 		    {
1731 		      --quot;
1732 		      r += dX;
1733 		      if (r < dX) /* I.e. "carry in previous addition?" */
1734 			break;
1735 		      n1 -= n0 < d1;
1736 		      n0 -= d1;
1737 		    }
1738 		}
1739 
1740 	      /* Possible optimization: We already have (q * n0) and (1 * n1)
1741 		 after the calculation of QUOT.  Taking advantage of this, we
1742 		 could make this loop make two iterations less.  */
1743 
1744 	      cy = __mpn_submul_1 (num, den, densize + 1, quot);
1745 
1746 	      if (num[densize] != cy)
1747 		{
1748 		  cy = __mpn_add_n (num, num, den, densize);
1749 		  assert (cy != 0);
1750 		  --quot;
1751 		}
1752 	      n0 = num[densize] = num[densize - 1];
1753 	      for (i = densize - 1; i > 0; --i)
1754 		num[i] = num[i - 1];
1755 	      num[0] = 0;
1756 
1757 	      got_limb;
1758 	    }
1759 
1760 	  for (i = densize; i >= 0 && num[i] == 0; --i)
1761 	    ;
1762 	  return round_and_return (retval, exponent - 1, negative,
1763 				   quot, BITS_PER_MP_LIMB - 1 - used,
1764 				   more_bits || i >= 0);
1765 	}
1766       }
1767   }
1768 
1769   /* NOTREACHED */
1770 }
1771 #if defined _LIBC && !defined USE_WIDE_CHAR
libc_hidden_def(____STRTOF_INTERNAL)1772 libc_hidden_def (____STRTOF_INTERNAL)
1773 #endif
1774 
1775 /* External user entry point.  */
1776 
1777 FLOAT
1778 #ifdef weak_function
1779 weak_function
1780 #endif
1781 __STRTOF (const STRING_TYPE *nptr, STRING_TYPE **endptr, locale_t loc)
1782 {
1783   return ____STRTOF_INTERNAL (nptr, endptr, 0, loc);
1784 }
1785 #if defined _LIBC
1786 libc_hidden_def (__STRTOF)
1787 libc_hidden_ver (__STRTOF, STRTOF)
1788 #endif
1789 weak_alias (__STRTOF, STRTOF)
1790 
1791 #ifdef LONG_DOUBLE_COMPAT
1792 # if LONG_DOUBLE_COMPAT(libc, GLIBC_2_1)
1793 #  ifdef USE_WIDE_CHAR
1794 compat_symbol (libc, __wcstod_l, __wcstold_l, GLIBC_2_1);
1795 #  else
1796 compat_symbol (libc, __strtod_l, __strtold_l, GLIBC_2_1);
1797 #  endif
1798 # endif
1799 # if LONG_DOUBLE_COMPAT(libc, GLIBC_2_3)
1800 #  ifdef USE_WIDE_CHAR
1801 compat_symbol (libc, wcstod_l, wcstold_l, GLIBC_2_3);
1802 #  else
1803 compat_symbol (libc, strtod_l, strtold_l, GLIBC_2_3);
1804 #  endif
1805 # endif
1806 #endif
1807 
1808 #if BUILD_DOUBLE
1809 # if __HAVE_FLOAT64 && !__HAVE_DISTINCT_FLOAT64
1810 #  undef strtof64_l
1811 #  undef wcstof64_l
1812 #  ifdef USE_WIDE_CHAR
1813 weak_alias (wcstod_l, wcstof64_l)
1814 #  else
1815 weak_alias (strtod_l, strtof64_l)
1816 #  endif
1817 # endif
1818 # if __HAVE_FLOAT32X && !__HAVE_DISTINCT_FLOAT32X
1819 #  undef strtof32x_l
1820 #  undef wcstof32x_l
1821 #  ifdef USE_WIDE_CHAR
1822 weak_alias (wcstod_l, wcstof32x_l)
1823 #  else
1824 weak_alias (strtod_l, strtof32x_l)
1825 #  endif
1826 # endif
1827 #endif
1828