about summary refs log tree commit diff
path: root/stdlib/strtod.c
blob: 989984e66dd3930a33c81a9a9293cc6a6800a920 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
/* Read decimal floating point numbers.
Copyright (C) 1995 Free Software Foundation, Inc.
Contributed by Ulrich Drepper.

This file is part of the GNU C Library.

The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.

The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
Library General Public License for more details.

You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB.	 If
not, write to the Free Software Foundation, Inc., 675 Mass Ave,
Cambridge, MA 02139, USA.  */

/* Configuration part.  These macros are defined by `strtold.c' and `strtof.c'
   to produce the `long double' and `float' versions of the reader.  */
#ifndef FLOAT
#define	FLOAT		double
#define	FLT		DBL
#define	STRTOF		strtod
#define	MPN2FLOAT	__mpn_construct_double
#define	FLOAT_HUGE_VAL	HUGE_VAL
#endif
/* End of configuration part.  */

#include <ctype.h>
#include <errno.h>
#include <float.h>
#include <localeinfo.h>
#include <math.h>
#include <stdlib.h>
#include "../stdio/gmp.h"
#include "../stdio/gmp-impl.h"
#include <gmp-mparam.h>
#include "../stdio/longlong.h"
#include "../stdio/fpioconst.h"

/* #define NDEBUG 1 */
#include <assert.h>


/* Constants we need from float.h; select the set for the FLOAT precision.  */
#define MANT_DIG	PASTE(FLT,_MANT_DIG)
#define	MAX_EXP		PASTE(FLT,_MAX_EXP)
#define	MIN_EXP		PASTE(FLT,_MIN_EXP)
#define MAX_10_EXP	PASTE(FLT,_MAX_10_EXP)
#define MIN_10_EXP	PASTE(FLT,_MIN_10_EXP)
#define	MAX_10_EXP_LOG	PASTE(FLT,_MAX_10_EXP_LOG)

/* Extra macros required to get FLT expanded before the pasting.  */
#define PASTE(a,b)	PASTE1(a,b)
#define PASTE1(a,b)	a##b

/* Function to construct a floating point number from an MP integer
   containing the fraction bits, a base 2 exponent, and a sign flag.  */
extern FLOAT MPN2FLOAT (mp_srcptr mpn, int exponent, int negative);

/* Definitions according to limb size used.  */
#if	BITS_PER_MP_LIMB == 32
#  define MAX_DIG_PER_LIMB	9
#  define MAX_FAC_PER_LIMB	1000000000L
#elif	BITS_PER_MP_LIMB == 64
#  define MAX_DIG_PER_LIMB	19
#  define MAX_FAC_PER_LIMB	10000000000000000000L
#else
#  error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"	
#endif


/* Local data structure.  */
static const mp_limb _tens_in_limb[MAX_DIG_PER_LIMB] =
{    0,                  10,                100,
     1000,               10000,             100000,
     1000000,            10000000,          100000000
#if BITS_PER_MP_LIMB > 32
   , 1000000000,         10000000000,       100000000000,
     1000000000000,      10000000000000,    100000000000000,
     1000000000000000,   10000000000000000, 100000000000000000,
     1000000000000000000
#endif
#if BITS_PER_MP_LIMB > 64
  #error "Need to expand tens_in_limb table to" MAX_DIG_PER_LIMB
#endif
};

#ifndef	howmany
#define	howmany(x,y)		(((x)+((y)-1))/(y))
#endif
#define SWAP(x, y)		({ typeof(x) _tmp = x; x = y; y = _tmp; })

#define NDIG			(MAX_10_EXP - MIN_10_EXP + 2 * MANT_DIG)
#define	RETURN_LIMB_SIZE		howmany (MANT_DIG, BITS_PER_MP_LIMB)

#define RETURN(val,end) \
	do { if (endptr != 0) *endptr = (char *) end; return val; } while (0)

/* Maximum size necessary for mpn integers to hold floating point numbers.  */ 
#define	MPNSIZE		(howmany (MAX_EXP + MANT_DIG, BITS_PER_MP_LIMB) + 1)
/* Declare an mpn integer variable that big.  */
#define	MPN_VAR(name)	mp_limb name[MPNSIZE]; mp_size_t name##size
/* Copy an mpn integer value.  */
#define MPN_ASSIGN(dst, src) \
	memcpy (dst, src, (dst##size = src##size) * sizeof (mp_limb))


/* Return a floating point number of the needed type according to the given
   multi-precision number after possible rounding.  */
static inline FLOAT
round_and_return (mp_limb *retval, int exponent, int negative,
		  mp_limb round_limb, mp_size_t round_bit, int more_bits)
{
  if (exponent < MIN_EXP)
    {
      mp_size_t shift = MIN_EXP - 1 - exponent;

      if (shift >= MANT_DIG)
	{
	  errno = EDOM;
	  return 0.0;
	}

      more_bits |= (round_limb & ((1 << round_bit) - 1)) != 0;
      if (shift >= BITS_PER_MP_LIMB)
	{
	  round_limb = retval[(shift - 1) / BITS_PER_MP_LIMB];
	  round_bit = (shift - 1) % BITS_PER_MP_LIMB;
#if RETURN_LIMB_SIZE <= 2
	  assert (RETURN_LIMB_SIZE == 2);
	  more_bits |= retval[0] != 0;
	  retval[0] = retval[1];
	  retval[1] = 0;
#else
	  int disp = shift / BITS_PER_MP_LIMB;
	  int i = 0;
	  while (retval[i] == 0 && i < disp)
	    ++i;
	  more_bits |= i < disp;
	  for (i = disp; i < RETURN_LIMB_SIZE; ++i)
	    retval[i - disp] = retval[i];
	  MPN_ZERO (&retval[RETURN_LIMB_SIZE - disp], disp);
#endif
	  shift %= BITS_PER_MP_LIMB;
	}
      else
	{
          round_limb = retval[0];
          round_bit = shift - 1;
	}
      (void) __mpn_rshift (retval, retval, RETURN_LIMB_SIZE, shift);
      exponent = MIN_EXP - 2;
    }

  if ((round_limb & (1 << round_bit)) != 0 &&
      (more_bits || (retval[0] & 1) != 0 ||
       (round_limb & ((1 << round_bit) - 1)) != 0))
    {
      mp_limb cy = __mpn_add_1 (retval, retval, RETURN_LIMB_SIZE, 1);
      if (cy || (retval[RETURN_LIMB_SIZE - 1]
		 & (1 << (MANT_DIG % BITS_PER_MP_LIMB))) != 0)
	{
	  ++exponent;
	  (void) __mpn_rshift (retval, retval, RETURN_LIMB_SIZE, 1);
	  retval[RETURN_LIMB_SIZE - 1] |= 1 << (MANT_DIG % BITS_PER_MP_LIMB);
	}
    }

  if (exponent > MAX_EXP)
    return negative ? -FLOAT_HUGE_VAL : FLOAT_HUGE_VAL;

  return MPN2FLOAT (retval, exponent, negative);
}


/* Read a multi-precision integer starting at STR with exactly DIGCNT digits
   into N.  Return the size of the number limbs in NSIZE at the first
   character od the string that is not part of the integer as the function
   value.  If the EXPONENT is small enough to be taken as an additional
   factor for the resulting number (see code) multiply by it.  */
static inline const char *
str_to_mpn (const char *str, int digcnt, mp_limb *n, mp_size_t *nsize,
	    int *exponent)
{
  /* Number of digits for actual limb.  */
  int cnt = 0;
  mp_limb low = 0;
  mp_limb base;

  *nsize = 0;
  assert (digcnt > 0);
  do
    {
      if (cnt == MAX_DIG_PER_LIMB)
	{
	  if (*nsize == 0)
	    n[0] = low;
	  else
	    {
	      mp_limb cy;
	      cy = __mpn_mul_1 (n, n, *nsize, MAX_FAC_PER_LIMB);
	      cy += __mpn_add_1 (n, n, *nsize, low);
	      if (cy != 0)
		n[*nsize] = cy;
	    }
	  ++(*nsize);
	  cnt = 0;
	  low = 0;
	}

      /* There might be thousands separators or radix characters in the string.
	 But these all can be ignored because we know the format of the number
	 is correct and we have an exact number of characters to read.  */
      while (!isdigit (*str))
	++str;
      low = low * 10 + *str++ - '0';
      ++cnt;
    }
  while (--digcnt > 0);

  if (*exponent > 0 && cnt + *exponent <= MAX_DIG_PER_LIMB)
    {
      low *= _tens_in_limb[*exponent];
      base = _tens_in_limb[cnt + *exponent];
      *exponent = 0;
    }
  else
    base = _tens_in_limb[cnt];

  if (*nsize == 0)
    {
      n[0] = low;
      *nsize = 1;
    }
  else
    {
      mp_limb cy;
      cy = __mpn_mul_1 (n, n, *nsize, base);
      cy += __mpn_add_1 (n, n, *nsize, low);
      if (cy != 0)
	n[(*nsize)++] = cy;
    }
  return str;
}


/* Shift {PTR, SIZE} COUNT bits to the left, and fill the vacated bits
   with the COUNT most significant bits of LIMB.

   Tege doesn't like this function so I have to write it here myself. :)
   --drepper */
static inline void
__mpn_lshift_1 (mp_limb *ptr, mp_size_t size, unsigned int count, mp_limb limb)
{
  if (count == BITS_PER_MP_LIMB)
    {
      /* Optimize the case of shifting by exactly a word:
	 just copy words, with no actual bit-shifting.  */
      mp_size_t i;
      for (i = size - 1; i > 0; --i)
	ptr[i] = ptr[i - 1];
      ptr[0] = limb;
    }
  else
    {
      (void) __mpn_lshift (ptr, ptr, size, count);
      ptr[0] |= limb >> (BITS_PER_MP_LIMB - count);
    }
}


/* Return a floating point number with the value of the given string NPTR.
   Set *ENDPTR to the character after the last used one.  If the number is
   smaller than the smallest representable number, set `errno' to ERANGE and
   return 0.0.  If the number is too big to be represented, set `errno' to
   ERANGE and return HUGE_VAL with the approriate sign.  */
FLOAT
STRTOF (nptr, endptr)
    const char *nptr;
    char **endptr;
{
  int negative;			/* The sign of the number.  */
  MPN_VAR (num);		/* MP representation of the number.  */
  int exponent;			/* Exponent of the number.  */

  /* When we have to compute fractional digits we form a fraction with a
     second multi-precision number (and we sometimes need a second for
     temporary results).  */
  MPN_VAR (den);

  /* Representation for the return value.  */
  mp_limb retval[RETURN_LIMB_SIZE];
  /* Number of bits currently in result value.  */
  int bits;

  /* Running pointer after the last character processed in the string.  */
  const char *cp;
  /* Start of significant part of the number.  */
  const char *startp;
  /* Points at the character following the integer and fractional digits.  */
  const char *expp;
  /* Total number of digit and number of digits in integer part.  */
  int dig_no, int_no;
  /* Contains the last character read.  */
  char c;

  /* The radix character of the current locale.  */
  wchar_t decimal;
#ifdef	USE_GROUPING
  /* The thousands character of the current locale.  */
  wchar_t thousands;
  /* The numeric grouping specification of the current locale,
     in the format described in <locale.h>.  */
  const char *grouping;

  /* Check the grouping of the integer part at [BEGIN,END).
     Return zero iff a separator is found out of place.  */
  int grouping_ok (const char *begin, const char *end)
    {
      if (grouping)
	while (end > begin)
	  {
	    const char *p = end;
	    do
	      --p;
	    while (*p != thousands && p > begin);
	    if (end - 1 - p != *grouping++)
	      return 0;		/* Wrong number of digits in this group.  */
	    end = p;		/* Correct group; trim it off the end.  */

	    if (*grouping == 0)
	      --grouping;	/* Same grouping repeats in next iteration.  */
	    else if (*grouping == CHAR_MAX || *grouping < 0)
	      {
		/* No further grouping allowed.  */
		while (end > begin)
		  if (*--end == thousands)
		    return 0;
	      }
	  }
      return 1;
    }
  /* Return with no conversion if the grouping of [STARTP,CP) is bad.  */
#define	CHECK_GROUPING if (! grouping_ok (startp, cp)) RETURN (0.0, nptr); else

  grouping = _numeric_info->grouping; /* Cache the grouping info array.  */
  if (*grouping <= 0 || *grouping == CHAR_MAX)
    grouping = NULL;
  else
    {
      /* Figure out the thousands seperator character.  */
      if (mbtowc (&thousands_sep, _numeric_info->thousands_sep,
		  strlen (_numeric_info->thousands_sep)) <= 0)
	thousands = (wchar_t) *_numeric_info->thousands_sep;
      if (thousands == L'\0')
	grouping = NULL;
    }
#else
#define	grouping	NULL
#define	thousands	L'\0'
#define	CHECK_GROUPING	((void) 0)
#endif

  /* Find the locale's decimal point character.  */
  if (mbtowc (&decimal, _numeric_info->decimal_point,
	      strlen (_numeric_info->decimal_point)) <= 0)
    decimal = (wchar_t) *_numeric_info->decimal_point;


  /* Prepare number representation.  */
  exponent = 0;
  negative = 0;
  bits = 0;

  /* Parse string to get maximal legal prefix.  We need the number of
     characters of the interger part, the fractional part and the exponent.  */
  cp = nptr - 1;
  /* Ignore leading white space.  */
  do
    c = *++cp;
  while (isspace (c));

  /* Get sign of the result.  */
  if (c == '-')
    {
      negative = 1;
      c = *++cp;
    }
  else if (c == '+')
    c = *++cp;

  /* Return 0.0 if no legal string is found.
     No character is used even if a sign was found.  */
  if (!isdigit (c) && (c != decimal || !isdigit (cp[1])))
    RETURN (0.0, nptr);

  /* Record the start of the digits, in case we will check their grouping.  */
  startp = cp;

  /* Ignore leading zeroes.  This helps us to avoid useless computations.  */
  while (c == '0' || (thousands != L'\0' && c == thousands))
    c = *++cp;

  CHECK_GROUPING;

  /* If no other digit but a '0' is found the result is 0.0.
     Return current read pointer.  */
  if (!isdigit (c) && c != decimal)
    RETURN (0.0, cp);

  /* Remember first significant digit and read following characters until the
     decimal point, exponent character or any non-FP number character.  */
  startp = cp;
  dig_no = 0;
  while (dig_no < NDIG ||
	 /* If parsing grouping info, keep going past useful digits
	    so we can check all the grouping separators.  */
	 grouping)
    {
      if (isdigit (c))
	++dig_no;
      else if (thousands == L'\0' || c != thousands)
	/* Not a digit or separator: end of the integer part.  */
	break;
      c = *++cp;
    }

  CHECK_GROUPING;

  if (dig_no >= NDIG)
    /* Too many digits to be representable.  Assigning this to EXPONENT
       allows us to read the full number but return HUGE_VAL after parsing.  */
    exponent = MAX_10_EXP;

  /* We have the number digits in the integer part.  Whether these are all or
     any is really a fractional digit will be decided later.  */
  int_no = dig_no;

  /* Read the fractional digits.  */
  if (c == decimal)
    {
      if (isdigit (cp[1]))
	{
	  ++cp;
	  do
	    {
	      ++dig_no;
	      c = *++cp;
	    }
	  while (isdigit (c));
	}
    }

  /* Remember start of exponent (if any).  */
  expp = cp;

  /* Read exponent.  */
  if (tolower (c) == 'e')
    {
      int exp_negative = 0;

      c = *++cp;
      if (c == '-')
	{
	  exp_negative = 1;
	  c = *++cp;
	}
      else if (c == '+')
	c = *++cp;

      if (isdigit (c))
	{
	  do
	    {
	      if ((!exp_negative && exponent * 10 + int_no > MAX_10_EXP)
		  || (exp_negative
		      && exponent * 10 + int_no > -MIN_10_EXP + MANT_DIG))
		/* The exponent is too large/small to represent a valid
		   number.  */
		{
	 	  FLOAT retval;

		  /* Overflow or underflow.  */
		  errno = ERANGE;
		  retval = (exp_negative ? 0.0 :
			    negative ? -FLOAT_HUGE_VAL : FLOAT_HUGE_VAL);

		  /* Accept all following digits as part of the exponent.  */
		  do
		    ++cp;
		  while (isdigit (*cp));

		  RETURN (retval, cp);
		  /* NOTREACHED */
		}

	      exponent *= 10;
	      exponent += c - '0';
	      c = *++cp;
	    }
	  while (isdigit (c));
	}
      else
	cp = expp;

      if (exp_negative)
	exponent = -exponent;
    }

  /* We don't want to have to work with trailing zeroes after the radix.  */
  if (dig_no > int_no)
    {
      while (expp[-1] == '0')
	{
	  --expp;
	  --dig_no;
	}
      assert (dig_no >= int_no);
    }

  /* The whole string is parsed.  Store the address of the next character.  */
  if (endptr)
    *endptr = (char *) cp;

  if (dig_no == 0)
    return 0.0;

  /* Now we have the number of digits in total and the integer digits as well
     as the exponent and its sign.  We can decide whether the read digits are
     really integer digits or belong to the fractional part; i.e. we normalize
     123e-2 to 1.23.  */
  {
    register int incr = exponent < 0 ? MAX (-int_no, exponent)
				     : MIN (dig_no - int_no, exponent);
    int_no += incr;
    exponent -= incr;
  }

  if (int_no + exponent > MAX_10_EXP)
    {
      errno = ERANGE;
      return negative ? -FLOAT_HUGE_VAL : FLOAT_HUGE_VAL;
    }

  if (int_no - dig_no + exponent < MIN_10_EXP - MANT_DIG)
    {
      errno = ERANGE;
      return 0.0;
    }	

  if (int_no > 0)
    {
      /* Read the integer part as a multi-precision number to NUM.  */
      startp = str_to_mpn (startp, int_no, num, &numsize, &exponent);

      if (exponent > 0)
	{
	  /* We now multiply the gained number by the given power of ten.  */
	  mp_limb *psrc = num;
	  mp_limb *pdest = den;
	  int expbit = 1;
	  const struct mp_power *ttab = &_fpioconst_pow10[0];

	  assert (exponent < (1 << (MAX_10_EXP_LOG + 1)));
	  do
	    {
	      if ((exponent & expbit) != 0)
		{
		  mp_limb cy;
		  exponent ^= expbit;

		  /* FIXME: not the whole multiplication has to be done.
		     If we have the needed number of bits we only need the
		     information whether more non-zero bits follow.  */
		  if (numsize >= ttab->arraysize - 2)
		    cy = __mpn_mul (pdest, psrc, numsize,
				    &ttab->array[2], ttab->arraysize - 2);
		  else
		    cy = __mpn_mul (pdest, &ttab->array[2],
				    ttab->arraysize - 2,
				    psrc, numsize);
		  numsize += ttab->arraysize - 2;
		  if (cy == 0)
		    --numsize;
		  SWAP (psrc, pdest);
		}
	      expbit <<= 1;
	      ++ttab;
	    }
	  while (exponent != 0);

	  if (psrc == den)
	    memcpy (num, den, numsize * sizeof (mp_limb));
	}

      /* Determine how many bits of the result we already have.  */
      count_leading_zeros (bits, num[numsize - 1]);
      bits = numsize * BITS_PER_MP_LIMB - bits;

      /* We have already the first BITS bits of the result.  Together with
	 the information whether more non-zero bits follow this is enough
	 to determine the result.  */
      if (bits > MANT_DIG)
	{
	  const mp_size_t least_idx = (bits - MANT_DIG) / BITS_PER_MP_LIMB;
	  const mp_size_t least_bit = (bits - MANT_DIG) % BITS_PER_MP_LIMB;
	  const mp_size_t round_idx = least_bit == 0 ? least_idx - 1
						     : least_idx;
	  const mp_size_t round_bit = least_bit == 0 ? BITS_PER_MP_LIMB - 1
						     : least_idx - 1;
	  int i;

	  if (least_bit == 0)
	    memcpy (retval, &num[least_idx],
		    RETURN_LIMB_SIZE * sizeof (mp_limb));
	  else
	    (void) __mpn_rshift (retval, &num[least_idx],
				 numsize - least_idx + 1, least_bit);

	  /* Check whether any limb beside the ones in RETVAL are non-zero.  */
	  for (i = 0; num[i] == 0; ++i)
	    ;

	  return round_and_return (retval, bits - 1, negative,
				   num[round_idx], round_bit,
				   int_no < dig_no || i < round_idx);
	  /* NOTREACHED */
	}
      else if (dig_no == int_no)
	{
	  const mp_size_t target_bit = (MANT_DIG - 1) % BITS_PER_MP_LIMB;
	  const mp_size_t is_bit = (bits - 1) % BITS_PER_MP_LIMB;

	  if (target_bit == is_bit)
	    {
	      memcpy (&retval[RETURN_LIMB_SIZE - numsize], num,
		      numsize * sizeof (mp_limb));
	      /* FIXME: the following loop can be avoided if we assume a
		 maximal MANT_DIG value.  */
	      MPN_ZERO (retval, RETURN_LIMB_SIZE - numsize);
	    }
	  else if (target_bit > is_bit)
	    {
	      (void) __mpn_lshift (&retval[RETURN_LIMB_SIZE - numsize],
				   num, numsize, target_bit - is_bit);
	      /* FIXME: the following loop can be avoided if we assume a
		 maximal MANT_DIG value.  */
	      MPN_ZERO (retval, RETURN_LIMB_SIZE - numsize);
	    }
	  else
	    {
	      mp_limb cy;
	      assert (numsize < RETURN_LIMB_SIZE);

	      cy = __mpn_rshift (&retval[RETURN_LIMB_SIZE - numsize],
				 num, numsize, is_bit - target_bit);
	      retval[RETURN_LIMB_SIZE - numsize - 1] = cy;
	      /* FIXME: the following loop can be avoided if we assume a
		 maximal MANT_DIG value.  */
	      MPN_ZERO (retval, RETURN_LIMB_SIZE - numsize - 1);
	    }

	  return round_and_return (retval, bits - 1, negative, 0, 0, 0);
	  /* NOTREACHED */
	}

      /* Store the bits we already have.  */
      memcpy (retval, num, numsize * sizeof (mp_limb));
#if RETURN_LIMB_SIZE > 1
      if (numsize < RETURN_LIMB_SIZE)
        retval[numsize] = 0;
#endif
    }

  /* We have to compute at least some of the fractional digits.  */
  {
    /* We construct a fraction and the result of the division gives us
       the needed digits.  The denominator is 1.0 multiplied by the
       exponent of the lowest digit; i.e. 0.123 gives 123 / 1000 and
       123e6 gives 123 / 1000000.  */

    int expbit;
    int cnt;
    mp_limb cy;
    mp_limb *psrc = den;
    mp_limb *pdest = num;
    int neg_exp = dig_no - int_no - exponent;
    const struct mp_power *ttab = &_fpioconst_pow10[0];

    assert (dig_no > int_no && exponent <= 0);

    /* Construct the denominator.  */
    densize = 0;
    expbit = 1;
    do
      {
	if ((neg_exp & expbit) != 0)
	  {
	    mp_limb cy;
	    neg_exp ^= expbit;

	    if (densize == 0)
	      memcpy (psrc, &ttab->array[2],
		      (densize = ttab->arraysize - 2) * sizeof (mp_limb));
	    else
	      {
		cy = __mpn_mul (pdest, &ttab->array[2], ttab->arraysize - 2,
				psrc, densize);
		densize += ttab->arraysize - 2;
		if (cy == 0)
		  --densize;
		SWAP (psrc, pdest);
	      }
	  }
	expbit <<= 1;
	++ttab;
      }
    while (neg_exp != 0);

    if (psrc == num)
      memcpy (den, num, densize * sizeof (mp_limb));

    /* Read the fractional digits from the string.  */ 
    (void) str_to_mpn (startp, dig_no - int_no, num, &numsize, &exponent);


    /* We now have to shift both numbers so that the highest bit in the
       denominator is set.  In the same process we copy the numerator to
       a high place in the array so that the division constructs the wanted
       digits.  This is done by a "quasi fix point" number representation.

       num:   ddddddddddd . 0000000000000000000000
              |--- m ---|
       den:                            ddddddddddd      n >= m
                                       |--- n ---|
     */

    count_leading_zeros (cnt, den[densize - 1]);

    (void) __mpn_lshift (den, den, densize, cnt);
    cy = __mpn_lshift (num, num, numsize, cnt);
    if (cy != 0)
      num[numsize++] = cy;

    /* Now we are ready for the division.  But it is not necessary to
       do a full multi-precision division because we only need a small
       number of bits for the result.  So we do not use __mpn_divmod
       here but instead do the division here by hand and stop whenever
       the needed number of bits is reached.  The code itself comes
       from the GNU MP Library by Torbj\"orn Granlund.  */

    exponent = bits;

    switch (densize)
      {
      case 1:
	{
	  mp_limb d, n, quot;
	  int used = 0;

	  n = num[0];
	  d = den[0];
	  assert (numsize == 1 && n < d);

	  do
	    {
	      udiv_qrnnd (quot, n, n, 0, d);

#define got_limb							      \
	      if (bits == 0)						      \
		{							      \
		  register int cnt;					      \
		  if (quot == 0)					      \
		    cnt = BITS_PER_MP_LIMB;				      \
		  else							      \
		    count_leading_zeros (cnt, quot);			      \
		  exponent -= cnt;					      \
		  if (BITS_PER_MP_LIMB - cnt > MANT_DIG)		      \
		    {							      \
		      used = cnt + MANT_DIG;				      \
		      retval[0] = quot >> (BITS_PER_MP_LIMB - used);	      \
		      bits -= BITS_PER_MP_LIMB - used;			      \
		    }							      \
		  else							      \
		    {							      \
		      /* Note that we only clear the second element.  */      \
		      retval[1] = 0;					      \
		      retval[0] = quot;					      \
		      bits -= cnt;					      \
		    }							      \
		}							      \
	      else if (bits + BITS_PER_MP_LIMB <= MANT_DIG)		      \
		__mpn_lshift_1 (retval, RETURN_LIMB_SIZE, BITS_PER_MP_LIMB,    \
				quot);					      \
	      else							      \
		{							      \
		  used = MANT_DIG - bits;				      \
		  if (used > 0)						      \
		    __mpn_lshift_1 (retval, RETURN_LIMB_SIZE, used, quot);     \
		}							      \
	      bits += BITS_PER_MP_LIMB

              got_limb;
	    }
	  while (bits <= MANT_DIG);

	  return round_and_return (retval, exponent - 1, negative,
				   quot, BITS_PER_MP_LIMB - 1 - used,
				   n != 0);
	}
      case 2:
	{
	  mp_limb d0, d1, n0, n1;
	  mp_limb quot = 0;
	  int used = 0;

	  d0 = den[0];
	  d1 = den[1];

	  if (numsize < densize)
	    {
	      if (bits <= 0)
		exponent -= BITS_PER_MP_LIMB;
	      else
		{
		  if (bits + BITS_PER_MP_LIMB <= MANT_DIG)
		    __mpn_lshift_1 (retval, RETURN_LIMB_SIZE,
				    BITS_PER_MP_LIMB, 0);
		  else
		    {
		      used = MANT_DIG - bits;
		      if (used > 0)
			__mpn_lshift_1 (retval, RETURN_LIMB_SIZE, used, 0);
		    }
		  bits += BITS_PER_MP_LIMB;
		}
	      n1 = num[0];
	      n0 = 0;
	    }
	  else
	    {
	      n1 = num[1];
	      n0 = num[0];
	    }

	  while (bits <= MANT_DIG)
	    {
	      mp_limb r;

	      if (n1 == d1)
		{
		  /* QUOT should be either 111..111 or 111..110.  We need
		     special treatment of this rare case as normal division
		     would give overflow.  */
		  quot = ~(mp_limb) 0;

		  r = n0 + d1;
		  if (r < d1)	/* Carry in the addition?  */
		    {
		      add_ssaaaa (n1, n0, r - d0, 0, 0, d0);
		      goto have_quot;
		    }
		  n1 = d0 - (d0 != 0);
		  n0 = -d0;
		}
	      else
		{
		  udiv_qrnnd (quot, r, n1, n0, d1);
		  umul_ppmm (n1, n0, d0, quot);
		}

	    q_test:
	      if (n1 > r || (n1 == r && n0 > 0))
		{
		  /* The estimated QUOT was too large.  */
		  --quot;

		  sub_ddmmss (n1, n0, n1, n0, 0, d0);
		  r += d1;
		  if (r >= d1)	/* If not carry, test QUOT again.  */
		    goto q_test;
		}
	      sub_ddmmss (n1, n0, r, 0, n1, n0);

	    have_quot:
	      got_limb;
	    }
	    
	  return round_and_return (retval, exponent - 1, negative,
				   quot, BITS_PER_MP_LIMB - 1 - used,
				   n1 != 0 || n0 != 0);
	}
      default:
	{
	  int i;
	  mp_limb cy, dX, d1, n0, n1;
	  mp_limb quot = 0;
	  int used = 0;

	  dX = den[densize - 1];
	  d1 = den[densize - 2];

	  /* The division does not work if the upper limb of the two-limb
	     numerator is greater than the denominator.  */
	  if (num[numsize - 1] > dX)
	    num[numsize++] = 0;

	  if (numsize < densize)
	    {
	      mp_size_t empty = densize - numsize;

	      if (bits <= 0)
		{
		  register int i;
		  for (i = numsize; i > 0; --i)
		    num[i + empty] = num[i - 1];
		  MPN_ZERO (num, empty + 1);
		  exponent -= empty * BITS_PER_MP_LIMB;
		}
	      else
		{
		  if (bits + empty * BITS_PER_MP_LIMB <= MANT_DIG)
		    {
		      /* We make a difference here because the compiler
			 cannot optimize the `else' case that good and
			 this reflects all currently used FLOAT types
			 and GMP implementations.  */
		      register int i;
#if RETURN_LIMB_SIZE <= 2
		      assert (empty == 1);
		      __mpn_lshift_1 (retval, RETURN_LIMB_SIZE,
				      BITS_PER_MP_LIMB, 0);
#else
		      for (i = RETURN_LIMB_SIZE; i > empty; --i)
			retval[i] = retval[i - empty];
#endif
		      retval[1] = 0;
		      for (i = numsize; i > 0; --i)
			num[i + empty] = num[i - 1];
		      MPN_ZERO (num, empty + 1);
		    }
		  else
		    {
		      used = MANT_DIG - bits;
		      if (used >= BITS_PER_MP_LIMB)
			{
			  register int i;
			  (void) __mpn_lshift (&retval[used
						       / BITS_PER_MP_LIMB],
					       retval, RETURN_LIMB_SIZE,
					       used % BITS_PER_MP_LIMB);
			  for (i = used / BITS_PER_MP_LIMB; i >= 0; --i)
			    retval[i] = 0;
			}
		      else if (used > 0)
			__mpn_lshift_1 (retval, RETURN_LIMB_SIZE, used, 0);
		    }
		  bits += empty * BITS_PER_MP_LIMB;
		}
	    }
	  else
	    {
	      int i;
	      assert (numsize == densize);
	      for (i = numsize; i > 0; --i)
		num[i] = num[i - 1];
	    }

	  den[densize] = 0;
	  n0 = num[densize];

	  while (bits <= MANT_DIG)
	    {
	      if (n0 == dX)
		/* This might over-estimate QUOT, but it's probably not
		   worth the extra code here to find out.  */
		quot = ~(mp_limb) 0;
	      else
		{
		  mp_limb r;

		  udiv_qrnnd (quot, r, n0, num[densize - 1], dX);
		  umul_ppmm (n1, n0, d1, quot);

		  while (n1 > r || (n1 == r && n0 > num[densize - 2]))
		    {
		      --quot;
		      r += dX;
		      if (r < dX) /* I.e. "carry in previous addition?" */
			break;
		      n1 -= n0 < d1;
		      n0 -= d1;
		    }
		}

	      /* Possible optimization: We already have (q * n0) and (1 * n1)
		 after the calculation of QUOT.  Taking advantage of this, we
		 could make this loop make two iterations less.  */

	      cy = __mpn_submul_1 (num, den, densize + 1, quot);

	      if (num[densize] != cy)
		{
		  cy = __mpn_add_n (num, num, den, densize);
		  assert (cy != 0);
		  --quot;
		}
	      n0 = num[densize] = num[densize - 1];
	      for (i = densize - 1; i > 0; --i)
		num[i] = num[i - 1];

	      got_limb;
	    }

	  for (i = densize - 1; num[i] != 0 && i >= 0; --i)
	    ;
	  return round_and_return (retval, exponent - 1, negative,
				   quot, BITS_PER_MP_LIMB - 1 - used,
				   i >= 0);
	}
      }
  }

  /* NOTREACHED */
}