summaryrefslogtreecommitdiff
path: root/stdio-common/printf_fp.c
blob: ed225e05a6c0b9e27ca66abdc4f1063b41536bfc (plain)
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
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
/* Floating point output for `printf'.
   Copyright (C) 1995-1999,2000,2001,2002,2003 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Written by Ulrich Drepper <drepper@gnu.ai.mit.edu>, 1995.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 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
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

/* The gmp headers need some configuration frobs.  */
#define HAVE_ALLOCA 1

#include <libioP.h>
#include <alloca.h>
#include <ctype.h>
#include <float.h>
#include <gmp-mparam.h>
#include <gmp.h>
#include <stdlib/gmp-impl.h>
#include <stdlib/longlong.h>
#include <stdlib/fpioconst.h>
#include <locale/localeinfo.h>
#include <limits.h>
#include <math.h>
#include <printf.h>
#include <string.h>
#include <unistd.h>
#include <stdlib.h>
#include <wchar.h>

#ifdef COMPILE_WPRINTF
# define CHAR_T        wchar_t
#else
# define CHAR_T        char
#endif

#include "_i18n_number.h"

#ifndef NDEBUG
# define NDEBUG			/* Undefine this for debugging assertions.  */
#endif
#include <assert.h>

/* This defines make it possible to use the same code for GNU C library and
   the GNU I/O library.	 */
#define PUT(f, s, n) _IO_sputn (f, s, n)
#define PAD(f, c, n) (wide ? _IO_wpadn (f, c, n) : INTUSE(_IO_padn) (f, c, n))
/* We use this file GNU C library and GNU I/O library.	So make
   names equal.	 */
#undef putc
#define putc(c, f) (wide \
		    ? (int)_IO_putwc_unlocked (c, f) : _IO_putc_unlocked (c, f))
#define size_t     _IO_size_t
#define FILE	     _IO_FILE

/* Macros for doing the actual output.  */

#define outchar(ch)							      \
  do									      \
    {									      \
      register const int outc = (ch);					      \
      if (putc (outc, fp) == EOF)					      \
	return -1;							      \
      ++done;								      \
    } while (0)

#define PRINT(ptr, wptr, len)						      \
  do									      \
    {									      \
      register size_t outlen = (len);					      \
      if (len > 20)							      \
	{								      \
	  if (PUT (fp, wide ? (const char *) wptr : ptr, outlen) != outlen)   \
	    return -1;							      \
	  ptr += outlen;						      \
	  done += outlen;						      \
	}								      \
      else								      \
	{								      \
	  if (wide)							      \
	    while (outlen-- > 0)					      \
	      outchar (*wptr++);					      \
	  else								      \
	    while (outlen-- > 0)					      \
	      outchar (*ptr++);						      \
	}								      \
    } while (0)

#define PADN(ch, len)							      \
  do									      \
    {									      \
      if (PAD (fp, ch, len) != len)					      \
	return -1;							      \
      done += len;							      \
    }									      \
  while (0)

/* We use the GNU MP library to handle large numbers.

   An MP variable occupies a varying number of entries in its array.  We keep
   track of this number for efficiency reasons.  Otherwise we would always
   have to process the whole array.  */
#define MPN_VAR(name) mp_limb_t *name; mp_size_t name##size

#define MPN_ASSIGN(dst,src)						      \
  memcpy (dst, src, (dst##size = src##size) * sizeof (mp_limb_t))
#define MPN_GE(u,v) \
  (u##size > v##size || (u##size == v##size && __mpn_cmp (u, v, u##size) >= 0))

extern int __isinfl_internal (long double) attribute_hidden;
extern int __isnanl_internal (long double) attribute_hidden;

extern mp_size_t __mpn_extract_double (mp_ptr res_ptr, mp_size_t size,
				       int *expt, int *is_neg,
				       double value);
extern mp_size_t __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size,
					    int *expt, int *is_neg,
					    long double value);
extern unsigned int __guess_grouping (unsigned int intdig_max,
				      const char *grouping);


static wchar_t *group_number (wchar_t *buf, wchar_t *bufend,
			      unsigned int intdig_no, const char *grouping,
			      wchar_t thousands_sep, int ngroups)
     internal_function;


int
__printf_fp (FILE *fp,
	     const struct printf_info *info,
	     const void *const *args)
{
  /* The floating-point value to output.  */
  union
    {
      double dbl;
      __long_double_t ldbl;
    }
  fpnum;

  /* Locale-dependent representation of decimal point.	*/
  const char *decimal;
  wchar_t decimalwc;

  /* Locale-dependent thousands separator and grouping specification.  */
  const char *thousands_sep = NULL;
  wchar_t thousands_sepwc = 0;
  const char *grouping;

  /* "NaN" or "Inf" for the special cases.  */
  const char *special = NULL;
  const wchar_t *wspecial = NULL;

  /* We need just a few limbs for the input before shifting to the right
     position.	*/
  mp_limb_t fp_input[(LDBL_MANT_DIG + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB];
  /* We need to shift the contents of fp_input by this amount of bits.	*/
  int to_shift = 0;

  /* The fraction of the floting-point value in question  */
  MPN_VAR(frac);
  /* and the exponent.	*/
  int exponent;
  /* Sign of the exponent.  */
  int expsign = 0;
  /* Sign of float number.  */
  int is_neg = 0;

  /* Scaling factor.  */
  MPN_VAR(scale);

  /* Temporary bignum value.  */
  MPN_VAR(tmp);

  /* Digit which is result of last hack_digit() call.  */
  wchar_t digit;

  /* The type of output format that will be used: 'e'/'E' or 'f'.  */
  int type;

  /* Counter for number of written characters.	*/
  int done = 0;

  /* General helper (carry limb).  */
  mp_limb_t cy;

  /* Nonzero if this is output on a wide character stream.  */
  int wide = info->wide;

  auto wchar_t hack_digit (void);

  wchar_t hack_digit (void)
    {
      mp_limb_t hi;

      if (expsign != 0 && type == 'f' && exponent-- > 0)
	hi = 0;
      else if (scalesize == 0)
	{
	  hi = frac[fracsize - 1];
	  frac[fracsize - 1] = __mpn_mul_1 (frac, frac, fracsize - 1, 10);
	}
      else
	{
	  if (fracsize < scalesize)
	    hi = 0;
	  else
	    {
	      hi = mpn_divmod (tmp, frac, fracsize, scale, scalesize);
	      tmp[fracsize - scalesize] = hi;
	      hi = tmp[0];

	      fracsize = scalesize;
	      while (fracsize != 0 && frac[fracsize - 1] == 0)
		--fracsize;
	      if (fracsize == 0)
		{
		  /* We're not prepared for an mpn variable with zero
		     limbs.  */
		  fracsize = 1;
		  return L'0' + hi;
		}
	    }

	  mp_limb_t _cy = __mpn_mul_1 (frac, frac, fracsize, 10);
	  if (_cy != 0)
	    frac[fracsize++] = _cy;
	}

      return L'0' + hi;
    }


  /* Figure out the decimal point character.  */
  if (info->extra == 0)
    {
      decimal = _NL_CURRENT (LC_NUMERIC, DECIMAL_POINT);
      decimalwc = _NL_CURRENT_WORD (LC_NUMERIC, _NL_NUMERIC_DECIMAL_POINT_WC);
    }
  else
    {
      decimal = _NL_CURRENT (LC_MONETARY, MON_DECIMAL_POINT);
      if (*decimal == '\0')
	decimal = _NL_CURRENT (LC_NUMERIC, DECIMAL_POINT);
      decimalwc = _NL_CURRENT_WORD (LC_MONETARY,
				    _NL_MONETARY_DECIMAL_POINT_WC);
      if (decimalwc == L'\0')
	decimalwc = _NL_CURRENT_WORD (LC_NUMERIC,
				      _NL_NUMERIC_DECIMAL_POINT_WC);
    }
  /* The decimal point character must not be zero.  */
  assert (*decimal != '\0');
  assert (decimalwc != L'\0');

  if (info->group)
    {
      if (info->extra == 0)
	grouping = _NL_CURRENT (LC_NUMERIC, GROUPING);
      else
	grouping = _NL_CURRENT (LC_MONETARY, MON_GROUPING);

      if (*grouping <= 0 || *grouping == CHAR_MAX)
	grouping = NULL;
      else
	{
	  /* Figure out the thousands separator character.  */
	  if (wide)
	    {
	      if (info->extra == 0)
		thousands_sepwc =
		  _NL_CURRENT_WORD (LC_NUMERIC, _NL_NUMERIC_THOUSANDS_SEP_WC);
	      else
		thousands_sepwc =
		  _NL_CURRENT_WORD (LC_MONETARY,
				    _NL_MONETARY_THOUSANDS_SEP_WC);
	    }
	  else
	    {
	      if (info->extra == 0)
		thousands_sep = _NL_CURRENT (LC_NUMERIC, THOUSANDS_SEP);
	      else
		thousands_sep = _NL_CURRENT (LC_MONETARY, MON_THOUSANDS_SEP);
	    }

	  if ((wide && thousands_sepwc == L'\0')
	      || (! wide && *thousands_sep == '\0'))
	    grouping = NULL;
	  else if (thousands_sepwc == L'\0')
	    /* If we are printing multibyte characters and there is a
	       multibyte representation for the thousands separator,
	       we must ensure the wide character thousands separator
	       is available, even if it is fake.  */
	    thousands_sepwc = 0xfffffffe;
	}
    }
  else
    grouping = NULL;

  /* Fetch the argument value.	*/
#ifndef __NO_LONG_DOUBLE_MATH
  if (info->is_long_double && sizeof (long double) > sizeof (double))
    {
      fpnum.ldbl = *(const long double *) args[0];

      /* Check for special values: not a number or infinity.  */
      if (__isnanl (fpnum.ldbl))
	{
	  if (isupper (info->spec))
	    {
	      special = "NAN";
	      wspecial = L"NAN";
	    }
	    else
	      {
		special = "nan";
		wspecial = L"nan";
	      }
	  is_neg = 0;
	}
      else if (__isinfl (fpnum.ldbl))
	{
	  if (isupper (info->spec))
	    {
	      special = "INF";
	      wspecial = L"INF";
	    }
	  else
	    {
	      special = "inf";
	      wspecial = L"inf";
	    }
	  is_neg = fpnum.ldbl < 0;
	}
      else
	{
	  fracsize = __mpn_extract_long_double (fp_input,
						(sizeof (fp_input) /
						 sizeof (fp_input[0])),
						&exponent, &is_neg,
						fpnum.ldbl);
	  to_shift = 1 + fracsize * BITS_PER_MP_LIMB - LDBL_MANT_DIG;
	}
    }
  else
#endif	/* no long double */
    {
      fpnum.dbl = *(const double *) args[0];

      /* Check for special values: not a number or infinity.  */
      if (__isnan (fpnum.dbl))
	{
	  is_neg = 0;
	  if (isupper (info->spec))
	    {
	      special = "NAN";
	      wspecial = L"NAN";
	    }
	  else
	    {
	      special = "nan";
	      wspecial = L"nan";
	    }
	}
      else if (__isinf (fpnum.dbl))
	{
	  is_neg = fpnum.dbl < 0;
	  if (isupper (info->spec))
	    {
	      special = "INF";
	      wspecial = L"INF";
	    }
	  else
	    {
	      special = "inf";
	      wspecial = L"inf";
	    }
	}
      else
	{
	  fracsize = __mpn_extract_double (fp_input,
					   (sizeof (fp_input)
					    / sizeof (fp_input[0])),
					   &exponent, &is_neg, fpnum.dbl);
	  to_shift = 1 + fracsize * BITS_PER_MP_LIMB - DBL_MANT_DIG;
	}
    }

  if (special)
    {
      int width = info->width;

      if (is_neg || info->showsign || info->space)
	--width;
      width -= 3;

      if (!info->left && width > 0)
	PADN (' ', width);

      if (is_neg)
	outchar ('-');
      else if (info->showsign)
	outchar ('+');
      else if (info->space)
	outchar (' ');

      PRINT (special, wspecial, 3);

      if (info->left && width > 0)
	PADN (' ', width);

      return done;
    }


  /* We need three multiprecision variables.  Now that we have the exponent
     of the number we can allocate the needed memory.  It would be more
     efficient to use variables of the fixed maximum size but because this
     would be really big it could lead to memory problems.  */
  {
    mp_size_t bignum_size = ((ABS (exponent) + BITS_PER_MP_LIMB - 1)
			     / BITS_PER_MP_LIMB
			     + (LDBL_MANT_DIG / BITS_PER_MP_LIMB > 2 ? 8 : 4))
			    * sizeof (mp_limb_t);
    frac = (mp_limb_t *) alloca (bignum_size);
    tmp = (mp_limb_t *) alloca (bignum_size);
    scale = (mp_limb_t *) alloca (bignum_size);
  }

  /* We now have to distinguish between numbers with positive and negative
     exponents because the method used for the one is not applicable/efficient
     for the other.  */
  scalesize = 0;
  if (exponent > 2)
    {
      /* |FP| >= 8.0.  */
      int scaleexpo = 0;
      int explog = LDBL_MAX_10_EXP_LOG;
      int exp10 = 0;
      const struct mp_power *powers = &_fpioconst_pow10[explog + 1];
      int cnt_h, cnt_l, i;

      if ((exponent + to_shift) % BITS_PER_MP_LIMB == 0)
	{
	  MPN_COPY_DECR (frac + (exponent + to_shift) / BITS_PER_MP_LIMB,
			 fp_input, fracsize);
	  fracsize += (exponent + to_shift) / BITS_PER_MP_LIMB;
	}
      else
	{
	  cy = __mpn_lshift (frac + (exponent + to_shift) / BITS_PER_MP_LIMB,
			     fp_input, fracsize,
			     (exponent + to_shift) % BITS_PER_MP_LIMB);
	  fracsize += (exponent + to_shift) / BITS_PER_MP_LIMB;
	  if (cy)
	    frac[fracsize++] = cy;
	}
      MPN_ZERO (frac, (exponent + to_shift) / BITS_PER_MP_LIMB);

      assert (powers > &_fpioconst_pow10[0]);
      do
	{
	  --powers;

	  /* The number of the product of two binary numbers with n and m
	     bits respectively has m+n or m+n-1 bits.	*/
	  if (exponent >= scaleexpo + powers->p_expo - 1)
	    {
	      if (scalesize == 0)
		{
#ifndef __NO_LONG_DOUBLE_MATH
		  if (LDBL_MANT_DIG > _FPIO_CONST_OFFSET * BITS_PER_MP_LIMB
		      && info->is_long_double)
		    {
#define _FPIO_CONST_SHIFT \
  (((LDBL_MANT_DIG + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB) \
   - _FPIO_CONST_OFFSET)
		      /* 64bit const offset is not enough for
			 IEEE quad long double.  */
		      tmpsize = powers->arraysize + _FPIO_CONST_SHIFT;
		      memcpy (tmp + _FPIO_CONST_SHIFT,
			      &__tens[powers->arrayoff],
			      tmpsize * sizeof (mp_limb_t));
		      MPN_ZERO (tmp, _FPIO_CONST_SHIFT);
		      /* Adjust exponent, as scaleexpo will be this much
			 bigger too.  */
		      exponent += _FPIO_CONST_SHIFT * BITS_PER_MP_LIMB;
		    }
		  else
#endif
		    {
		      tmpsize = powers->arraysize;
		      memcpy (tmp, &__tens[powers->arrayoff],
			      tmpsize * sizeof (mp_limb_t));
		    }
		}
	      else
		{
		  cy = __mpn_mul (tmp, scale, scalesize,
				  &__tens[powers->arrayoff
					 + _FPIO_CONST_OFFSET],
				  powers->arraysize - _FPIO_CONST_OFFSET);
		  tmpsize = scalesize + powers->arraysize - _FPIO_CONST_OFFSET;
		  if (cy == 0)
		    --tmpsize;
		}

	      if (MPN_GE (frac, tmp))
		{
		  int cnt;
		  MPN_ASSIGN (scale, tmp);
		  count_leading_zeros (cnt, scale[scalesize - 1]);
		  scaleexpo = (scalesize - 2) * BITS_PER_MP_LIMB - cnt - 1;
		  exp10 |= 1 << explog;
		}
	    }
	  --explog;
	}
      while (powers > &_fpioconst_pow10[0]);
      exponent = exp10;

      /* Optimize number representations.  We want to represent the numbers
	 with the lowest number of bytes possible without losing any
	 bytes. Also the highest bit in the scaling factor has to be set
	 (this is a requirement of the MPN division routines).  */
      if (scalesize > 0)
	{
	  /* Determine minimum number of zero bits at the end of
	     both numbers.  */
	  for (i = 0; scale[i] == 0 && frac[i] == 0; i++)
	    ;

	  /* Determine number of bits the scaling factor is misplaced.	*/
	  count_leading_zeros (cnt_h, scale[scalesize - 1]);

	  if (cnt_h == 0)
	    {
	      /* The highest bit of the scaling factor is already set.	So
		 we only have to remove the trailing empty limbs.  */
	      if (i > 0)
		{
		  MPN_COPY_INCR (scale, scale + i, scalesize - i);
		  scalesize -= i;
		  MPN_COPY_INCR (frac, frac + i, fracsize - i);
		  fracsize -= i;
		}
	    }
	  else
	    {
	      if (scale[i] != 0)
		{
		  count_trailing_zeros (cnt_l, scale[i]);
		  if (frac[i] != 0)
		    {
		      int cnt_l2;
		      count_trailing_zeros (cnt_l2, frac[i]);
		      if (cnt_l2 < cnt_l)
			cnt_l = cnt_l2;
		    }
		}
	      else
		count_trailing_zeros (cnt_l, frac[i]);

	      /* Now shift the numbers to their optimal position.  */
	      if (i == 0 && BITS_PER_MP_LIMB - cnt_h > cnt_l)
		{
		  /* We cannot save any memory.	 So just roll both numbers
		     so that the scaling factor has its highest bit set.  */

		  (void) __mpn_lshift (scale, scale, scalesize, cnt_h);
		  cy = __mpn_lshift (frac, frac, fracsize, cnt_h);
		  if (cy != 0)
		    frac[fracsize++] = cy;
		}
	      else if (BITS_PER_MP_LIMB - cnt_h <= cnt_l)
		{
		  /* We can save memory by removing the trailing zero limbs
		     and by packing the non-zero limbs which gain another
		     free one. */

		  (void) __mpn_rshift (scale, scale + i, scalesize - i,
				       BITS_PER_MP_LIMB - cnt_h);
		  scalesize -= i + 1;
		  (void) __mpn_rshift (frac, frac + i, fracsize - i,
				       BITS_PER_MP_LIMB - cnt_h);
		  fracsize -= frac[fracsize - i - 1] == 0 ? i + 1 : i;
		}
	      else
		{
		  /* We can only save the memory of the limbs which are zero.
		     The non-zero parts occupy the same number of limbs.  */

		  (void) __mpn_rshift (scale, scale + (i - 1),
				       scalesize - (i - 1),
				       BITS_PER_MP_LIMB - cnt_h);
		  scalesize -= i;
		  (void) __mpn_rshift (frac, frac + (i - 1),
				       fracsize - (i - 1),
				       BITS_PER_MP_LIMB - cnt_h);
		  fracsize -= frac[fracsize - (i - 1) - 1] == 0 ? i : i - 1;
		}
	    }
	}
    }
  else if (exponent < 0)
    {
      /* |FP| < 1.0.  */
      int exp10 = 0;
      int explog = LDBL_MAX_10_EXP_LOG;
      const struct mp_power *powers = &_fpioconst_pow10[explog + 1];
      mp_size_t used_limbs = fracsize - 1;

      /* Now shift the input value to its right place.	*/
      cy = __mpn_lshift (frac, fp_input, fracsize, to_shift);
      frac[fracsize++] = cy;
      assert (cy == 1 || (frac[fracsize - 2] == 0 && frac[0] == 0));

      expsign = 1;
      exponent = -exponent;

      assert (powers != &_fpioconst_pow10[0]);
      do
	{
	  --powers;

	  if (exponent >= powers->m_expo)
	    {
	      int i, incr, cnt_h, cnt_l;
	      mp_limb_t topval[2];

	      /* The __mpn_mul function expects the first argument to be
		 bigger than the second.  */
	      if (fracsize < powers->arraysize - _FPIO_CONST_OFFSET)
		cy = __mpn_mul (tmp, &__tens[powers->arrayoff
					    + _FPIO_CONST_OFFSET],
				powers->arraysize - _FPIO_CONST_OFFSET,
				frac, fracsize);
	      else
		cy = __mpn_mul (tmp, frac, fracsize,
				&__tens[powers->arrayoff + _FPIO_CONST_OFFSET],
				powers->arraysize - _FPIO_CONST_OFFSET);
	      tmpsize = fracsize + powers->arraysize - _FPIO_CONST_OFFSET;
	      if (cy == 0)
		--tmpsize;

	      count_leading_zeros (cnt_h, tmp[tmpsize - 1]);
	      incr = (tmpsize - fracsize) * BITS_PER_MP_LIMB
		     + BITS_PER_MP_LIMB - 1 - cnt_h;

	      assert (incr <= powers->p_expo);

	      /* If we increased the exponent by exactly 3 we have to test
		 for overflow.	This is done by comparing with 10 shifted
		 to the right position.	 */
	      if (incr == exponent + 3)
		{
		  if (cnt_h <= BITS_PER_MP_LIMB - 4)
		    {
		      topval[0] = 0;
		      topval[1]
			= ((mp_limb_t) 10) << (BITS_PER_MP_LIMB - 4 - cnt_h);
		    }
		  else
		    {
		      topval[0] = ((mp_limb_t) 10) << (BITS_PER_MP_LIMB - 4);
		      topval[1] = 0;
		      (void) __mpn_lshift (topval, topval, 2,
					   BITS_PER_MP_LIMB - cnt_h);
		    }
		}

	      /* We have to be careful when multiplying the last factor.
		 If the result is greater than 1.0 be have to test it
		 against 10.0.  If it is greater or equal to 10.0 the
		 multiplication was not valid.  This is because we cannot
		 determine the number of bits in the result in advance.  */
	      if (incr < exponent + 3
		  || (incr == exponent + 3 &&
		      (tmp[tmpsize - 1] < topval[1]
		       || (tmp[tmpsize - 1] == topval[1]
			   && tmp[tmpsize - 2] < topval[0]))))
		{
		  /* The factor is right.  Adapt binary and decimal
		     exponents.	 */
		  exponent -= incr;
		  exp10 |= 1 << explog;

		  /* If this factor yields a number greater or equal to
		     1.0, we must not shift the non-fractional digits down. */
		  if (exponent < 0)
		    cnt_h += -exponent;

		  /* Now we optimize the number representation.	 */
		  for (i = 0; tmp[i] == 0; ++i);
		  if (cnt_h == BITS_PER_MP_LIMB - 1)
		    {
		      MPN_COPY (frac, tmp + i, tmpsize - i);
		      fracsize = tmpsize - i;
		    }
		  else
		    {
		      count_trailing_zeros (cnt_l, tmp[i]);

		      /* Now shift the numbers to their optimal position.  */
		      if (i == 0 && BITS_PER_MP_LIMB - 1 - cnt_h > cnt_l)
			{
			  /* We cannot save any memory.	 Just roll the
			     number so that the leading digit is in a
			     separate limb.  */

			  cy = __mpn_lshift (frac, tmp, tmpsize, cnt_h + 1);
			  fracsize = tmpsize + 1;
			  frac[fracsize - 1] = cy;
			}
		      else if (BITS_PER_MP_LIMB - 1 - cnt_h <= cnt_l)
			{
			  (void) __mpn_rshift (frac, tmp + i, tmpsize - i,
					       BITS_PER_MP_LIMB - 1 - cnt_h);
			  fracsize = tmpsize - i;
			}
		      else
			{
			  /* We can only save the memory of the limbs which
			     are zero.	The non-zero parts occupy the same
			     number of limbs.  */

			  (void) __mpn_rshift (frac, tmp + (i - 1),
					       tmpsize - (i - 1),
					       BITS_PER_MP_LIMB - 1 - cnt_h);
			  fracsize = tmpsize - (i - 1);
			}
		    }
		  used_limbs = fracsize - 1;
		}
	    }
	  --explog;
	}
      while (powers != &_fpioconst_pow10[1] && exponent > 0);
      /* All factors but 10^-1 are tested now.	*/
      if (exponent > 0)
	{
	  int cnt_l;

	  cy = __mpn_mul_1 (tmp, frac, fracsize, 10);
	  tmpsize = fracsize;
	  assert (cy == 0 || tmp[tmpsize - 1] < 20);

	  count_trailing_zeros (cnt_l, tmp[0]);
	  if (cnt_l < MIN (4, exponent))
	    {
	      cy = __mpn_lshift (frac, tmp, tmpsize,
				 BITS_PER_MP_LIMB - MIN (4, exponent));
	      if (cy != 0)
		frac[tmpsize++] = cy;
	    }
	  else
	    (void) __mpn_rshift (frac, tmp, tmpsize, MIN (4, exponent));
	  fracsize = tmpsize;
	  exp10 |= 1;
	  assert (frac[fracsize - 1] < 10);
	}
      exponent = exp10;
    }
  else
    {
      /* This is a special case.  We don't need a factor because the
	 numbers are in the range of 0.0 <= fp < 8.0.  We simply
	 shift it to the right place and divide it by 1.0 to get the
	 leading digit.	 (Of course this division is not really made.)	*/
      assert (0 <= exponent && exponent < 3 &&
	      exponent + to_shift < BITS_PER_MP_LIMB);

      /* Now shift the input value to its right place.	*/
      cy = __mpn_lshift (frac, fp_input, fracsize, (exponent + to_shift));
      frac[fracsize++] = cy;
      exponent = 0;
    }

  {
    int width = info->width;
    wchar_t *wbuffer, *wstartp, *wcp;
    int buffer_malloced;
    int chars_needed;
    int expscale;
    int intdig_max, intdig_no = 0;
    int fracdig_min, fracdig_max, fracdig_no = 0;
    int dig_max;
    int significant;
    int ngroups = 0;

    if (_tolower (info->spec) == 'e')
      {
	type = info->spec;
	intdig_max = 1;
	fracdig_min = fracdig_max = info->prec < 0 ? 6 : info->prec;
	chars_needed = 1 + 1 + fracdig_max + 1 + 1 + 4;
	/*	       d   .	 ddd	     e	 +-  ddd  */
	dig_max = INT_MAX;		/* Unlimited.  */
	significant = 1;		/* Does not matter here.  */
      }
    else if (_tolower (info->spec) == 'f')
      {
	type = 'f';
	fracdig_min = fracdig_max = info->prec < 0 ? 6 : info->prec;
	dig_max = INT_MAX;		/* Unlimited.  */
	significant = 1;		/* Does not matter here.  */
	if (expsign == 0)
	  {
	    intdig_max = exponent + 1;
	    /* This can be really big!	*/  /* XXX Maybe malloc if too big? */
	    chars_needed = exponent + 1 + 1 + fracdig_max;
	  }
	else
	  {
	    intdig_max = 1;
	    chars_needed = 1 + 1 + fracdig_max;
	  }
      }
    else
      {
	dig_max = info->prec < 0 ? 6 : (info->prec == 0 ? 1 : info->prec);
	if ((expsign == 0 && exponent >= dig_max)
	    || (expsign != 0 && exponent > 4))
	  {
	    if ('g' - 'G' == 'e' - 'E')
	      type = 'E' + (info->spec - 'G');
	    else
	      type = isupper (info->spec) ? 'E' : 'e';
	    fracdig_max = dig_max - 1;
	    intdig_max = 1;
	    chars_needed = 1 + 1 + fracdig_max + 1 + 1 + 4;
	  }
	else
	  {
	    type = 'f';
	    intdig_max = expsign == 0 ? exponent + 1 : 0;
	    fracdig_max = dig_max - intdig_max;
	    /* We need space for the significant digits and perhaps
	       for leading zeros when < 1.0.  The number of leading
	       zeros can be as many as would be required for
	       exponential notation with a negative two-digit
	       exponent, which is 4.  */
	    chars_needed = dig_max + 1 + 4;
	  }
	fracdig_min = info->alt ? fracdig_max : 0;
	significant = 0;		/* We count significant digits.	 */
      }

    if (grouping)
      {
	/* Guess the number of groups we will make, and thus how
	   many spaces we need for separator characters.  */
	ngroups = __guess_grouping (intdig_max, grouping);
	chars_needed += ngroups;
      }

    /* Allocate buffer for output.  We need two more because while rounding
       it is possible that we need two more characters in front of all the
       other output.  If the amount of memory we have to allocate is too
       large use `malloc' instead of `alloca'.  */
    buffer_malloced = ! __libc_use_alloca (chars_needed * 2 * sizeof (wchar_t));
    if (buffer_malloced)
      {
	wbuffer = (wchar_t *) malloc ((2 + chars_needed) * sizeof (wchar_t));
	if (wbuffer == NULL)
	  /* Signal an error to the caller.  */
	  return -1;
      }
    else
      wbuffer = (wchar_t *) alloca ((2 + chars_needed) * sizeof (wchar_t));
    wcp = wstartp = wbuffer + 2;	/* Let room for rounding.  */

    /* Do the real work: put digits in allocated buffer.  */
    if (expsign == 0 || type != 'f')
      {
	assert (expsign == 0 || intdig_max == 1);
	while (intdig_no < intdig_max)
	  {
	    ++intdig_no;
	    *wcp++ = hack_digit ();
	  }
	significant = 1;
	if (info->alt
	    || fracdig_min > 0
	    || (fracdig_max > 0 && (fracsize > 1 || frac[0] != 0)))
	  *wcp++ = decimalwc;
      }
    else
      {
	/* |fp| < 1.0 and the selected type is 'f', so put "0."
	   in the buffer.  */
	*wcp++ = L'0';
	--exponent;
	*wcp++ = decimalwc;
      }

    /* Generate the needed number of fractional digits.	 */
    while (fracdig_no < fracdig_min
	   || (fracdig_no < fracdig_max && (fracsize > 1 || frac[0] != 0)))
      {
	++fracdig_no;
	*wcp = hack_digit ();
	if (*wcp++ != L'0')
	  significant = 1;
	else if (significant == 0)
	  {
	    ++fracdig_max;
	    if (fracdig_min > 0)
	      ++fracdig_min;
	  }
      }

    /* Do rounding.  */
    digit = hack_digit ();
    if (digit > L'4')
      {
	wchar_t *wtp = wcp;

	if (digit == L'5'
	    && ((*(wcp - 1) != decimalwc && (*(wcp - 1) & 1) == 0)
		|| ((*(wcp - 1) == decimalwc && (*(wcp - 2) & 1) == 0))))
	  {
	    /* This is the critical case.	 */
	    if (fracsize == 1 && frac[0] == 0)
	      /* Rest of the number is zero -> round to even.
		 (IEEE 754-1985 4.1 says this is the default rounding.)  */
	      goto do_expo;
	    else if (scalesize == 0)
	      {
		/* Here we have to see whether all limbs are zero since no
		   normalization happened.  */
		size_t lcnt = fracsize;
		while (lcnt >= 1 && frac[lcnt - 1] == 0)
		  --lcnt;
		if (lcnt == 0)
		  /* Rest of the number is zero -> round to even.
		     (IEEE 754-1985 4.1 says this is the default rounding.)  */
		  goto do_expo;
	      }
	  }

	if (fracdig_no > 0)
	  {
	    /* Process fractional digits.  Terminate if not rounded or
	       radix character is reached.  */
	    while (*--wtp != decimalwc && *wtp == L'9')
	      *wtp = '0';
	    if (*wtp != decimalwc)
	      /* Round up.  */
	      (*wtp)++;
	  }

	if (fracdig_no == 0 || *wtp == decimalwc)
	  {
	    /* Round the integer digits.  */
	    if (*(wtp - 1) == decimalwc)
	      --wtp;

	    while (--wtp >= wstartp && *wtp == L'9')
	      *wtp = L'0';

	    if (wtp >= wstartp)
	      /* Round up.  */
	      (*wtp)++;
	    else
	      /* It is more critical.  All digits were 9's.  */
	      {
		if (type != 'f')
		  {
		    *wstartp = '1';
		    exponent += expsign == 0 ? 1 : -1;
		  }
		else if (intdig_no == dig_max)
		  {
		    /* This is the case where for type %g the number fits
		       really in the range for %f output but after rounding
		       the number of digits is too big.	 */
		    *--wstartp = decimalwc;
		    *--wstartp = L'1';

		    if (info->alt || fracdig_no > 0)
		      {
			/* Overwrite the old radix character.  */
			wstartp[intdig_no + 2] = L'0';
			++fracdig_no;
		      }

		    fracdig_no += intdig_no;
		    intdig_no = 1;
		    fracdig_max = intdig_max - intdig_no;
		    ++exponent;
		    /* Now we must print the exponent.	*/
		    type = isupper (info->spec) ? 'E' : 'e';
		  }
		else
		  {
		    /* We can simply add another another digit before the
		       radix.  */
		    *--wstartp = L'1';
		    ++intdig_no;
		  }

		/* While rounding the number of digits can change.
		   If the number now exceeds the limits remove some
		   fractional digits.  */
		if (intdig_no + fracdig_no > dig_max)
		  {
		    wcp -= intdig_no + fracdig_no - dig_max;
		    fracdig_no -= intdig_no + fracdig_no - dig_max;
		  }
	      }
	  }
      }

  do_expo:
    /* Now remove unnecessary '0' at the end of the string.  */
    while (fracdig_no > fracdig_min && *(wcp - 1) == L'0')
      {
	--wcp;
	--fracdig_no;
      }
    /* If we eliminate all fractional digits we perhaps also can remove
       the radix character.  */
    if (fracdig_no == 0 && !info->alt && *(wcp - 1) == decimalwc)
      --wcp;

    if (grouping)
      /* Add in separator characters, overwriting the same buffer.  */
      wcp = group_number (wstartp, wcp, intdig_no, grouping, thousands_sepwc,
			  ngroups);

    /* Write the exponent if it is needed.  */
    if (type != 'f')
      {
	*wcp++ = (wchar_t) type;
	*wcp++ = expsign ? L'-' : L'+';

	/* Find the magnitude of the exponent.	*/
	expscale = 10;
	while (expscale <= exponent)
	  expscale *= 10;

	if (exponent < 10)
	  /* Exponent always has at least two digits.  */
	  *wcp++ = L'0';
	else
	  do
	    {
	      expscale /= 10;
	      *wcp++ = L'0' + (exponent / expscale);
	      exponent %= expscale;
	    }
	  while (expscale > 10);
	*wcp++ = L'0' + exponent;
      }

    /* Compute number of characters which must be filled with the padding
       character.  */
    if (is_neg || info->showsign || info->space)
      --width;
    width -= wcp - wstartp;

    if (!info->left && info->pad != '0' && width > 0)
      PADN (info->pad, width);

    if (is_neg)
      outchar ('-');
    else if (info->showsign)
      outchar ('+');
    else if (info->space)
      outchar (' ');

    if (!info->left && info->pad == '0' && width > 0)
      PADN ('0', width);

    {
      char *buffer = NULL;
      char *cp = NULL;
      char *tmpptr;

      if (! wide)
	{
	  /* Create the single byte string.  */
	  size_t decimal_len;
	  size_t thousands_sep_len;
	  wchar_t *copywc;

	  decimal_len = strlen (decimal);

	  if (thousands_sep == NULL)
	    thousands_sep_len = 0;
	  else
	    thousands_sep_len = strlen (thousands_sep);

	  if (buffer_malloced)
	    {
	      buffer = (char *) malloc (2 + chars_needed + decimal_len
					+ ngroups * thousands_sep_len);
	      if (buffer == NULL)
		/* Signal an error to the caller.  */
		return -1;
	    }
	  else
	    buffer = (char *) alloca (2 + chars_needed + decimal_len
				      + ngroups * thousands_sep_len);

	  /* Now copy the wide character string.  Since the character
	     (except for the decimal point and thousands separator) must
	     be coming from the ASCII range we can esily convert the
	     string without mapping tables.  */
	  for (cp = buffer, copywc = wstartp; copywc < wcp; ++copywc)
	    if (*copywc == decimalwc)
	      cp = (char *) __mempcpy (cp, decimal, decimal_len);
	    else if (*copywc == thousands_sepwc)
	      cp = (char *) __mempcpy (cp, thousands_sep, thousands_sep_len);
	    else
	      *cp++ = (char) *copywc;
	}

      tmpptr = buffer;
      if (__builtin_expect (info->i18n, 0))
        {
#ifdef COMPILE_WPRINTF
	  wstartp = _i18n_number_rewrite (wstartp, wcp);
#else
	  tmpptr = _i18n_number_rewrite (tmpptr, cp);
#endif
        }

      PRINT (tmpptr, wstartp, wide ? wcp - wstartp : cp - tmpptr);

      /* Free the memory if necessary.  */
      if (buffer_malloced)
	{
	  free (buffer);
	  free (wbuffer);
	}
    }

    if (info->left && width > 0)
      PADN (info->pad, width);
  }
  return done;
}
libc_hidden_def (__printf_fp)

/* Return the number of extra grouping characters that will be inserted
   into a number with INTDIG_MAX integer digits.  */

unsigned int
__guess_grouping (unsigned int intdig_max, const char *grouping)
{
  unsigned int groups;

  /* We treat all negative values like CHAR_MAX.  */

  if (*grouping == CHAR_MAX || *grouping <= 0)
    /* No grouping should be done.  */
    return 0;

  groups = 0;
  while (intdig_max > (unsigned int) *grouping)
    {
      ++groups;
      intdig_max -= *grouping++;

      if (*grouping == CHAR_MAX
#if CHAR_MIN < 0
	  || *grouping < 0
#endif
	  )
	/* No more grouping should be done.  */
	break;
      else if (*grouping == 0)
	{
	  /* Same grouping repeats.  */
	  groups += (intdig_max - 1) / grouping[-1];
	  break;
	}
    }

  return groups;
}

/* Group the INTDIG_NO integer digits of the number in [BUF,BUFEND).
   There is guaranteed enough space past BUFEND to extend it.
   Return the new end of buffer.  */

static wchar_t *
internal_function
group_number (wchar_t *buf, wchar_t *bufend, unsigned int intdig_no,
	      const char *grouping, wchar_t thousands_sep, int ngroups)
{
  wchar_t *p;

  if (ngroups == 0)
    return bufend;

  /* Move the fractional part down.  */
  __wmemmove (buf + intdig_no + ngroups, buf + intdig_no,
	      bufend - (buf + intdig_no));

  p = buf + intdig_no + ngroups - 1;
  do
    {
      unsigned int len = *grouping++;
      do
	*p-- = buf[--intdig_no];
      while (--len > 0);
      *p-- = thousands_sep;

      if (*grouping == CHAR_MAX
#if CHAR_MIN < 0
	  || *grouping < 0
#endif
	  )
	/* No more grouping should be done.  */
	break;
      else if (*grouping == 0)
	/* Same grouping repeats.  */
	--grouping;
    } while (intdig_no > (unsigned int) *grouping);

  /* Copy the remaining ungrouped digits.  */
  do
    *p-- = buf[--intdig_no];
  while (p > buf);

  return bufend + ngroups;
}