2017-02-16 Paul Thomas <pault@gcc.gnu.org>

[official-gcc.git] / libquadmath / printf / printf_fp.c

/* Floating point output for `printf'.
   Copyright (C) 1995-2012 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, see
   <http://www.gnu.org/licenses/>.  */

#include <config.h>
#include <float.h>
#include <limits.h>
#include <math.h>
#include <string.h>
#include <unistd.h>
#include <stdlib.h>
#include <stdbool.h>
#define NDEBUG
#include <assert.h>
#ifdef HAVE_ERRNO_H
#include <errno.h>
#endif
#include <stdio.h>
#include <stdarg.h>
#ifdef HAVE_FENV_H
#include "quadmath-rounding-mode.h"
#endif
#include "quadmath-printf.h"
#include "fpioconst.h"

#ifdef USE_I18N_NUMBER_H
#include "_i18n_number.h"
#endif

\f
/* Macros for doing the actual output.  */

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

\f
/* 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 mp_size_t mpn_extract_flt128 (mp_ptr res_ptr, mp_size_t size,
                                     int *expt, int *is_neg,
                                     __float128 value) attribute_hidden;
static 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);


int
__quadmath_printf_fp (struct __quadmath_printf_file *fp,
                      const struct printf_info *info,
                      const void *const *args)
{
  /* The floating-point value to output.  */
  __float128 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 = L_('\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[(FLT128_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 last_digit, next_digit;
  bool more_bits;

  /* 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;

  /* Buffer in which we produce the output.  */
  wchar_t *wbuffer = NULL;
  /* Flag whether wbuffer is malloc'ed or not.  */
  int buffer_malloced = 0;

  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.  */
#ifdef USE_NL_LANGINFO
  if (info->extra == 0)
    decimal = nl_langinfo (DECIMAL_POINT);
  else
    {
      decimal = nl_langinfo (MON_DECIMAL_POINT);
      if (*decimal == '\0')
        decimal = nl_langinfo (DECIMAL_POINT);
    }
  /* The decimal point character must never be zero.  */
  assert (*decimal != '\0');
#elif defined USE_LOCALECONV
  const struct lconv *lc = localeconv ();
  if (info->extra == 0)
    decimal = lc->decimal_point;
  else
    {
      decimal = lc->mon_decimal_point;
      if (decimal == NULL || *decimal == '\0')
        decimal = lc->decimal_point;
    }
  if (decimal == NULL || *decimal == '\0')
    decimal = ".";
#else
  decimal = ".";
#endif
#ifdef USE_NL_LANGINFO_WC
  if (info->extra == 0)
    decimalwc = nl_langinfo_wc (_NL_NUMERIC_DECIMAL_POINT_WC);
  else
    {
      decimalwc = nl_langinfo_wc (_NL_MONETARY_DECIMAL_POINT_WC);
      if (decimalwc == L_('\0'))
        decimalwc = nl_langinfo_wc (_NL_NUMERIC_DECIMAL_POINT_WC);
    }
  /* The decimal point character must never be zero.  */
  assert (decimalwc != L_('\0'));
#else
  decimalwc = L_('.');
#endif

#if defined USE_NL_LANGINFO && defined USE_NL_LANGINFO_WC
  if (info->group)
    {
      if (info->extra == 0)
        grouping = nl_langinfo (GROUPING);
      else
        grouping = nl_langinfo (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_langinfo_wc (_NL_NUMERIC_THOUSANDS_SEP_WC);
              else
                thousands_sepwc = nl_langinfo_wc (_NL_MONETARY_THOUSANDS_SEP_WC);

              if (thousands_sepwc == L_('\0'))
                grouping = NULL;
            }
          else
            {
              if (info->extra == 0)
                thousands_sep = nl_langinfo (THOUSANDS_SEP);
              else
                thousands_sep = nl_langinfo (MON_THOUSANDS_SEP);
              if (*thousands_sep == '\0')
                grouping = NULL;
            }
        }
    }
  else
#elif defined USE_NL_LANGINFO
  if (info->group && !wide)
    {
      if (info->extra == 0)
        grouping = nl_langinfo (GROUPING);
      else
        grouping = nl_langinfo (MON_GROUPING);

      if (*grouping <= 0 || *grouping == CHAR_MAX)
        grouping = NULL;
      else
        {
          /* Figure out the thousands separator character.  */
          if (info->extra == 0)
            thousands_sep = nl_langinfo (THOUSANDS_SEP);
          else
            thousands_sep = nl_langinfo (MON_THOUSANDS_SEP);

          if (*thousands_sep == '\0')
            grouping = NULL;
        }
    }
  else
#elif defined USE_LOCALECONV
  if (info->group && !wide)
    {
      if (info->extra == 0)
        grouping = lc->grouping;
      else
        grouping = lc->mon_grouping;

      if (grouping == NULL || *grouping <= 0 || *grouping == CHAR_MAX)
        grouping = NULL;
      else
        {
          /* Figure out the thousands separator character.  */
          if (info->extra == 0)
            thousands_sep = lc->thousands_sep;
          else
            thousands_sep = lc->mon_thousands_sep;

          if (thousands_sep == NULL || *thousands_sep == '\0')
            grouping = NULL;
        }
    }
  else
#endif
    grouping = NULL;
  if (grouping != NULL && !wide)
    /* 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 = (wchar_t) 0xfffffffe;

  /* Fetch the argument value.  */
    {
      fpnum = **(const __float128 **) args[0];

      /* Check for special values: not a number or infinity.  */
      if (isnanq (fpnum))
        {
          ieee854_float128 u = { .value = fpnum };
          is_neg = u.ieee.negative != 0;
          if (isupper (info->spec))
            {
              special = "NAN";
              wspecial = L_("NAN");
            }
          else
            {
              special = "nan";
                wspecial = L_("nan");
            }
        }
      else if (isinfq (fpnum))
        {
          is_neg = fpnum < 0;
          if (isupper (info->spec))
            {
              special = "INF";
              wspecial = L_("INF");
            }
          else
            {
              special = "inf";
              wspecial = L_("inf");
            }
        }
      else
        {
          fracsize = mpn_extract_flt128 (fp_input,
                                         (sizeof (fp_input) /
                                          sizeof (fp_input[0])),
                                         &exponent, &is_neg, fpnum);
          to_shift = 1 + fracsize * BITS_PER_MP_LIMB - FLT128_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
                             + (FLT128_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 = FLT128_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)
                {
                  if (FLT128_MANT_DIG > _FPIO_CONST_OFFSET * BITS_PER_MP_LIMB)
                    {
#define _FPIO_CONST_SHIFT \
  (((FLT128_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
                    {
                      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 = FLT128_MAX_10_EXP_LOG;
      const struct mp_power *powers = &_fpioconst_pow10[explog + 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);
                        }
                    }
                }
            }
          --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 1.0 <= |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 *wstartp, *wcp;
    size_t chars_needed;
    int expscale;
    int intdig_max, intdig_no = 0;
    int fracdig_min;
    int fracdig_max;
    int dig_max;
    int significant;
    int ngroups = 0;
    char spec = tolower (info->spec);

    if (spec == 'e')
      {
        type = info->spec;
        intdig_max = 1;
        fracdig_min = fracdig_max = info->prec < 0 ? 6 : info->prec;
        chars_needed = 1 + 1 + (size_t) fracdig_max + 1 + 1 + 4;
        /*             d   .     ddd         e   +-  ddd  */
        dig_max = __INT_MAX__;          /* Unlimited.  */
        significant = 1;                /* Does not matter here.  */
      }
    else if (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 = (size_t) exponent + 1 + 1 + (size_t) fracdig_max;
          }
        else
          {
            intdig_max = 1;
            chars_needed = 1 + 1 + (size_t) 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 + (size_t) 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 = (size_t) 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);
        /* Allocate one more character in case rounding increases the
           number of groups.  */
        chars_needed += ngroups + 1;
      }

    /* 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'.  */
    if (__builtin_expect (chars_needed >= (size_t) -1 / sizeof (wchar_t) - 2
                          || chars_needed < fracdig_max, 0))
      {
        /* Some overflow occurred.  */
#if defined HAVE_ERRNO_H && defined ERANGE
        errno = ERANGE;
#endif
        return -1;
      }
    size_t wbuffer_to_alloc = (2 + chars_needed) * sizeof (wchar_t);
    buffer_malloced = wbuffer_to_alloc >= 4096;
    if (__builtin_expect (buffer_malloced, 0))
      {
        wbuffer = (wchar_t *) malloc (wbuffer_to_alloc);
        if (wbuffer == NULL)
          /* Signal an error to the caller.  */
          return -1;
      }
    else
      wbuffer = (wchar_t *) alloca (wbuffer_to_alloc);
    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.  */
    int fracdig_no = 0;
    int added_zeros = 0;
    while (fracdig_no < fracdig_min + added_zeros
           || (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)
              ++added_zeros;
          }
      }

    /* Do rounding.  */
    last_digit = wcp[-1] != decimalwc ? wcp[-1] : wcp[-2];
    next_digit =hack_digit ();

    if (next_digit != L_('0') && next_digit != L_('5'))
      more_bits = true;
    else if (fracsize == 1 && frac[0] == 0)
      /* Rest of the number is zero.  */
      more_bits = false;
    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;
        more_bits = lcnt > 0;
      }
    else
      more_bits = true;

#ifdef HAVE_FENV_H
    int rounding_mode = get_rounding_mode ();
    if (round_away (is_neg, (last_digit - L_('0')) & 1, next_digit >= L_('5'),
                    more_bits, rounding_mode))
      {
        wchar_t *wtp = wcp;

        if (fracdig_no > 0)
          {
            /* Process fractional digits.  Terminate if not rounded or
               radix character is reached.  */
            int removed = 0;
            while (*--wtp != decimalwc && *wtp == L_('9'))
              {
                *wtp = L_('0');
                ++removed;
              }
            if (removed == fracdig_min && added_zeros > 0)
              --added_zeros;
            if (*wtp != decimalwc)
              /* Round up.  */
              (*wtp)++;
            else if (__builtin_expect (spec == 'g' && type == 'f' && info->alt
                                       && wtp == wstartp + 1
                                       && wstartp[0] == L_('0'),
                                       0))
              /* This is a special case: the rounded number is 1.0,
                 the format is 'g' or 'G', and the alternative format
                 is selected.  This means the result must be "1.".  */
              --added_zeros;
          }

        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;

                    /* The above exponent adjustment could lead to 1.0e-00,
                       e.g. for 0.999999999.  Make sure exponent 0 always
                       uses + sign.  */
                    if (exponent == 0)
                      expsign = 0;
                  }
                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;
                  }
              }
          }
      }
#endif

    /* Now remove unnecessary '0' at the end of the string.  */
    while (fracdig_no > fracdig_min + added_zeros && *(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)
      {
        /* Rounding might have changed the number of groups.  We allocated
           enough memory but we need here the correct number of groups.  */
        if (intdig_no != intdig_max)
          ngroups = guess_grouping (intdig_no, 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')
      {
        if (__builtin_expect (expsign != 0 && exponent == 4 && spec == 'g', 0))
          {
            /* This is another special case.  The exponent of the number is
               really smaller than -4, which requires the 'e'/'E' format.
               But after rounding the number has an exponent of -4.  */
            assert (wcp >= wstartp + 1);
            assert (wstartp[0] == L_('1'));
            memcpy (wstartp, L_("0.0001"), 6 * sizeof (wchar_t));
            wstartp[1] = decimalwc;
            if (wcp >= wstartp + 2)
              {
                size_t cnt;
                for (cnt = 0; cnt < wcp - (wstartp + 2); cnt++)
                  wstartp[6 + cnt] = L_('0');
                wcp += 4;
              }
            else
              wcp += 5;
          }
        else
          {
            *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 *buffer_end __attribute__((__unused__)) = 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;
#ifdef USE_I18N_NUMBER_H
          size_t factor = (info->i18n
                           ? nl_langinfo_wc (_NL_CTYPE_MB_CUR_MAX)
                           : 1);
#else
          size_t factor = 1;
#endif

          decimal_len = strlen (decimal);

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

          size_t nbuffer = (2 + chars_needed * factor + decimal_len
                            + ngroups * thousands_sep_len);
          if (__builtin_expect (buffer_malloced, 0))
            {
              buffer = (char *) malloc (nbuffer);
              if (buffer == NULL)
                {
                  /* Signal an error to the caller.  */
                  free (wbuffer);
                  return -1;
                }
            }
          else
            buffer = (char *) alloca (nbuffer);
          buffer_end = buffer + nbuffer;

          /* 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)
              memcpy (cp, decimal, decimal_len), cp += decimal_len;
            else if (*copywc == thousands_sepwc)
              memcpy (cp, thousands_sep, thousands_sep_len), cp += thousands_sep_len;
            else
              *cp++ = (char) *copywc;
        }

      tmpptr = buffer;
#if USE_I18N_NUMBER_H
      if (__builtin_expect (info->i18n, 0))
        {
          tmpptr = _i18n_number_rewrite (tmpptr, cp, buffer_end);
          cp = buffer_end;
          assert ((uintptr_t) buffer <= (uintptr_t) tmpptr);
          assert ((uintptr_t) tmpptr < (uintptr_t) buffer_end);
        }
#endif

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

      /* Free the memory if necessary.  */
      if (__builtin_expect (buffer_malloced, 0))
        {
          free (buffer);
          free (wbuffer);
        }
    }

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

static 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 *
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.  */
  memmove (buf + intdig_no + ngroups, buf + intdig_no,
           (bufend - (buf + intdig_no)) * sizeof (wchar_t));

  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;
}