* asan.c (handle_builtin_alloca): Deal with all alloca variants.

[official-gcc.git] / libquadmath / strtod / strtod_l.c

/* Convert string representing a number to float value, using given locale.
   Copyright (C) 1997-2012 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.

   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 <stdarg.h>
#include <string.h>
#include <stdint.h>
#include <stdbool.h>
#include <float.h>
#include <math.h>
#define NDEBUG 1
#include <assert.h>
#ifdef HAVE_ERRNO_H
#include <errno.h>
#endif

#ifdef HAVE_FENV_H
#include <fenv.h>
#endif

#ifdef HAVE_FENV_H
#include "quadmath-rounding-mode.h"
#endif
#include "../printf/quadmath-printf.h"
#include "../printf/fpioconst.h"

#undef L_
#ifdef USE_WIDE_CHAR
# define STRING_TYPE wchar_t
# define CHAR_TYPE wint_t
# define L_(Ch) L##Ch
# define ISSPACE(Ch) __iswspace_l ((Ch), loc)
# define ISDIGIT(Ch) __iswdigit_l ((Ch), loc)
# define ISXDIGIT(Ch) __iswxdigit_l ((Ch), loc)
# define TOLOWER(Ch) __towlower_l ((Ch), loc)
# define TOLOWER_C(Ch) __towlower_l ((Ch), _nl_C_locobj_ptr)
# define STRNCASECMP(S1, S2, N) \
  __wcsncasecmp_l ((S1), (S2), (N), _nl_C_locobj_ptr)
# define STRTOULL(S, E, B) ____wcstoull_l_internal ((S), (E), (B), 0, loc)
#else
# define STRING_TYPE char
# define CHAR_TYPE char
# define L_(Ch) Ch
# define ISSPACE(Ch) isspace (Ch)
# define ISDIGIT(Ch) isdigit (Ch)
# define ISXDIGIT(Ch) isxdigit (Ch)
# define TOLOWER(Ch) tolower (Ch)
# define TOLOWER_C(Ch) \
  ({__typeof(Ch) __tlc = (Ch); \
    (__tlc >= 'A' && __tlc <= 'Z') ? __tlc - 'A' + 'a' : __tlc; })
# define STRNCASECMP(S1, S2, N) \
  __quadmath_strncasecmp_c (S1, S2, N)
# ifdef HAVE_STRTOULL
#  define STRTOULL(S, E, B) strtoull (S, E, B)
# else
#  define STRTOULL(S, E, B) strtoul (S, E, B)
# endif

static inline int
__quadmath_strncasecmp_c (const char *s1, const char *s2, size_t n)
{
  const unsigned char *p1 = (const unsigned char *) s1;
  const unsigned char *p2 = (const unsigned char *) s2;
  int result;
  if (p1 == p2 || n == 0)
    return 0;
  while ((result = TOLOWER_C (*p1) - TOLOWER_C (*p2++)) == 0)
    if (*p1++ == '\0' || --n == 0)
      break;

  return result;
}
#endif


/* Constants we need from float.h; select the set for the FLOAT precision.  */
#define MANT_DIG        PASTE(FLT,_MANT_DIG)
#define DIG             PASTE(FLT,_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_VALUE       PASTE(FLT,_MAX)
#define MIN_VALUE       PASTE(FLT,_MIN)

/* 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);
\f
/* Definitions according to limb size used.  */
#if     BITS_PER_MP_LIMB == 32
# define MAX_DIG_PER_LIMB       9
# define MAX_FAC_PER_LIMB       1000000000UL
#elif   BITS_PER_MP_LIMB == 64
# define MAX_DIG_PER_LIMB       19
# define MAX_FAC_PER_LIMB       10000000000000000000ULL
#else
# error "mp_limb_t size " BITS_PER_MP_LIMB "not accounted for"
#endif

#define _tens_in_limb __quadmath_tens_in_limb
extern const mp_limb_t _tens_in_limb[MAX_DIG_PER_LIMB + 1] attribute_hidden;
\f
#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 HEXNDIG                 ((MAX_EXP - MIN_EXP + 7) / 8 + 2 * MANT_DIG)
#define RETURN_LIMB_SIZE                howmany (MANT_DIG, BITS_PER_MP_LIMB)

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

/* Maximum size necessary for mpn integers to hold floating point
   numbers.  The largest number we need to hold is 10^n where 2^-n is
   1/4 ulp of the smallest representable value (that is, n = MANT_DIG
   - MIN_EXP + 2).  Approximate using 10^3 < 2^10.  */
#define MPNSIZE         (howmany (1 + ((MANT_DIG - MIN_EXP + 2) * 10) / 3, \
                                  BITS_PER_MP_LIMB) + 2)
/* Declare an mpn integer variable that big.  */
#define MPN_VAR(name)   mp_limb_t 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_t))

/* Set errno and return an overflowing value with sign specified by
   NEGATIVE.  */
static FLOAT
overflow_value (int negative)
{
#if defined HAVE_ERRNO_H && defined ERANGE
  errno = ERANGE;
#endif
  FLOAT result = (negative ? -MAX_VALUE : MAX_VALUE) * MAX_VALUE;
  return result;
}

/* Set errno and return an underflowing value with sign specified by
   NEGATIVE.  */
static FLOAT
underflow_value (int negative)
{
#if defined HAVE_ERRNO_H && defined ERANGE
  errno = ERANGE;
#endif
  FLOAT result = (negative ? -MIN_VALUE : MIN_VALUE) * MIN_VALUE;
  return result;
}

/* Return a floating point number of the needed type according to the given
   multi-precision number after possible rounding.  */
static FLOAT
round_and_return (mp_limb_t *retval, intmax_t exponent, int negative,
                  mp_limb_t round_limb, mp_size_t round_bit, int more_bits)
{
#ifdef HAVE_FENV_H
  int mode = get_rounding_mode ();
#endif

  if (exponent < MIN_EXP - 1)
    {
      mp_size_t shift;
      bool is_tiny;

      if (exponent < MIN_EXP - 1 - MANT_DIG)
        return underflow_value (negative);

      shift = MIN_EXP - 1 - exponent;
      is_tiny = true;

      more_bits |= (round_limb & ((((mp_limb_t) 1) << round_bit) - 1)) != 0;
      if (shift == MANT_DIG)
        /* This is a special case to handle the very seldom case where
           the mantissa will be empty after the shift.  */
        {
          int i;

          round_limb = retval[RETURN_LIMB_SIZE - 1];
          round_bit = (MANT_DIG - 1) % BITS_PER_MP_LIMB;
          for (i = 0; i < RETURN_LIMB_SIZE; ++i)
            more_bits |= retval[i] != 0;
          MPN_ZERO (retval, RETURN_LIMB_SIZE);
        }
      else if (shift >= BITS_PER_MP_LIMB)
        {
          int i;

          round_limb = retval[(shift - 1) / BITS_PER_MP_LIMB];
          round_bit = (shift - 1) % BITS_PER_MP_LIMB;
          for (i = 0; i < (shift - 1) / BITS_PER_MP_LIMB; ++i)
            more_bits |= retval[i] != 0;
          more_bits |= ((round_limb & ((((mp_limb_t) 1) << round_bit) - 1))
                        != 0);

          (void) mpn_rshift (retval, &retval[shift / BITS_PER_MP_LIMB],
                             RETURN_LIMB_SIZE - (shift / BITS_PER_MP_LIMB),
                             shift % BITS_PER_MP_LIMB);
          MPN_ZERO (&retval[RETURN_LIMB_SIZE - (shift / BITS_PER_MP_LIMB)],
                    shift / BITS_PER_MP_LIMB);
        }
      else if (shift > 0)
        {
#ifdef HAVE_FENV_H
          if (TININESS_AFTER_ROUNDING && shift == 1)
            {
              /* Whether the result counts as tiny depends on whether,
                 after rounding to the normal precision, it still has
                 a subnormal exponent.  */
              mp_limb_t retval_normal[RETURN_LIMB_SIZE];
              if (round_away (negative,
                              (retval[0] & 1) != 0,
                              (round_limb
                               & (((mp_limb_t) 1) << round_bit)) != 0,
                              (more_bits
                               || ((round_limb
                                    & ((((mp_limb_t) 1) << round_bit) - 1))
                                   != 0)),
                              mode))
                {
                  mp_limb_t cy = mpn_add_1 (retval_normal, retval,
                                              RETURN_LIMB_SIZE, 1);

                  if (((MANT_DIG % BITS_PER_MP_LIMB) == 0 && cy) ||
                      ((MANT_DIG % BITS_PER_MP_LIMB) != 0 &&
                       ((retval_normal[RETURN_LIMB_SIZE - 1]
                        & (((mp_limb_t) 1) << (MANT_DIG % BITS_PER_MP_LIMB)))
                        != 0)))
                    is_tiny = false;
                }
            }
#endif
          round_limb = retval[0];
          round_bit = shift - 1;
          (void) mpn_rshift (retval, retval, RETURN_LIMB_SIZE, shift);
        }
      /* This is a hook for the m68k long double format, where the
         exponent bias is the same for normalized and denormalized
         numbers.  */
#ifndef DENORM_EXP
# define DENORM_EXP (MIN_EXP - 2)
#endif
      exponent = DENORM_EXP;
      if (is_tiny
          && ((round_limb & (((mp_limb_t) 1) << round_bit)) != 0
              || more_bits
              || (round_limb & ((((mp_limb_t) 1) << round_bit) - 1)) != 0))
        {
#if defined HAVE_ERRNO_H && defined ERANGE
          errno = ERANGE;
#endif
          volatile FLOAT force_underflow_exception = MIN_VALUE * MIN_VALUE;
          (void) force_underflow_exception;
        }
    }

  if (exponent > MAX_EXP)
    goto overflow;

#ifdef HAVE_FENV_H
  if (round_away (negative,
                  (retval[0] & 1) != 0,
                  (round_limb & (((mp_limb_t) 1) << round_bit)) != 0,
                  (more_bits
                   || (round_limb & ((((mp_limb_t) 1) << round_bit) - 1)) != 0),
                  mode))
    {
      mp_limb_t cy = mpn_add_1 (retval, retval, RETURN_LIMB_SIZE, 1);

      if (((MANT_DIG % BITS_PER_MP_LIMB) == 0 && cy) ||
          ((MANT_DIG % BITS_PER_MP_LIMB) != 0 &&
           (retval[RETURN_LIMB_SIZE - 1]
            & (((mp_limb_t) 1) << (MANT_DIG % BITS_PER_MP_LIMB))) != 0))
        {
          ++exponent;
          (void) mpn_rshift (retval, retval, RETURN_LIMB_SIZE, 1);
          retval[RETURN_LIMB_SIZE - 1]
            |= ((mp_limb_t) 1) << ((MANT_DIG - 1) % BITS_PER_MP_LIMB);
        }
      else if (exponent == DENORM_EXP
               && (retval[RETURN_LIMB_SIZE - 1]
                   & (((mp_limb_t) 1) << ((MANT_DIG - 1) % BITS_PER_MP_LIMB)))
               != 0)
          /* The number was denormalized but now normalized.  */
        exponent = MIN_EXP - 1;
    }
#endif

  if (exponent > MAX_EXP)
  overflow:
    return overflow_value (negative);

  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 const STRING_TYPE *
str_to_mpn (const STRING_TYPE *str, int digcnt, mp_limb_t *n, mp_size_t *nsize,
            intmax_t *exponent
#ifndef USE_WIDE_CHAR
            , const char *decimal, size_t decimal_len, const char *thousands
#endif

            )
{
  /* Number of digits for actual limb.  */
  int cnt = 0;
  mp_limb_t low = 0;
  mp_limb_t start;

  *nsize = 0;
  assert (digcnt > 0);
  do
    {
      if (cnt == MAX_DIG_PER_LIMB)
        {
          if (*nsize == 0)
            {
              n[0] = low;
              *nsize = 1;
            }
          else
            {
              mp_limb_t cy;
              cy = mpn_mul_1 (n, n, *nsize, MAX_FAC_PER_LIMB);
              cy += mpn_add_1 (n, n, *nsize, low);
              if (cy != 0)
                {
                  assert (*nsize < MPNSIZE);
                  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.  */
#ifdef USE_WIDE_CHAR
      if (*str < L'0' || *str > L'9')
        ++str;
#else
      if (*str < '0' || *str > '9')
        {
          int inner = 0;
          if (thousands != NULL && *str == *thousands
              && ({ for (inner = 1; thousands[inner] != '\0'; ++inner)
                      if (thousands[inner] != str[inner])
                        break;
                    thousands[inner] == '\0'; }))
            str += inner;
          else
            str += decimal_len;
        }
#endif
      low = low * 10 + *str++ - L_('0');
      ++cnt;
    }
  while (--digcnt > 0);

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

  if (*nsize == 0)
    {
      n[0] = low;
      *nsize = 1;
    }
  else
    {
      mp_limb_t cy;
      cy = mpn_mul_1 (n, n, *nsize, start);
      cy += mpn_add_1 (n, n, *nsize, low);
      if (cy != 0)
        {
          assert (*nsize < MPNSIZE);
          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.

   Implemented as a macro, so that __builtin_constant_p works even at -O0.

   Tege doesn't like this macro so I have to write it here myself. :)
   --drepper */
#define mpn_lshift_1(ptr, size, count, limb) \
  do                                                                    \
    {                                                                   \
      mp_limb_t *__ptr = (ptr);                                         \
      if (__builtin_constant_p (count) && count == BITS_PER_MP_LIMB)    \
        {                                                               \
          mp_size_t i;                                                  \
          for (i = (size) - 1; i > 0; --i)                              \
            __ptr[i] = __ptr[i - 1];                                    \
          __ptr[0] = (limb);                                            \
        }                                                               \
      else                                                              \
        {                                                               \
          /* We assume count > 0 && count < BITS_PER_MP_LIMB here.  */  \
          unsigned int __count = (count);                               \
          (void) mpn_lshift (__ptr, __ptr, size, __count);              \
          __ptr[0] |= (limb) >> (BITS_PER_MP_LIMB - __count);           \
        }                                                               \
    }                                                                   \
  while (0)


#define INTERNAL(x) INTERNAL1(x)
#define INTERNAL1(x) __##x##_internal
#ifndef ____STRTOF_INTERNAL
# define ____STRTOF_INTERNAL INTERNAL (__STRTOF)
#endif

/* This file defines a function to check for correct grouping.  */
#include "grouping.h"


/* 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 appropriate sign.  */
FLOAT
____STRTOF_INTERNAL (nptr, endptr, group)
     const STRING_TYPE *nptr;
     STRING_TYPE **endptr;
     int group;
{
  int negative;                 /* The sign of the number.  */
  MPN_VAR (num);                /* MP representation of the number.  */
  intmax_t exponent;            /* Exponent of the number.  */

  /* Numbers starting `0X' or `0x' have to be processed with base 16.  */
  int base = 10;

  /* 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_t retval[RETURN_LIMB_SIZE];
  /* Number of bits currently in result value.  */
  int bits;

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

/* We should get wint_t from <stddef.h>, but not all GCC versions define it
   there.  So define it ourselves if it remains undefined.  */
#ifndef _WINT_T
  typedef unsigned int wint_t;
#endif
  /* The radix character of the current locale.  */
#ifdef USE_WIDE_CHAR
  wchar_t decimal;
#else
  const char *decimal;
  size_t decimal_len;
#endif
  /* The thousands character of the current locale.  */
#ifdef USE_WIDE_CHAR
  wchar_t thousands = L'\0';
#else
  const char *thousands = NULL;
#endif
  /* The numeric grouping specification of the current locale,
     in the format described in <locale.h>.  */
  const char *grouping;
  /* Used in several places.  */
  int cnt;

#if defined USE_LOCALECONV && !defined USE_NL_LANGINFO
  const struct lconv *lc = localeconv ();
#endif

  if (__builtin_expect (group, 0))
    {
#ifdef USE_NL_LANGINFO
      grouping = nl_langinfo (GROUPING);
      if (*grouping <= 0 || *grouping == CHAR_MAX)
        grouping = NULL;
      else
        {
          /* Figure out the thousands separator character.  */
#ifdef USE_WIDE_CHAR
          thousands = nl_langinfo_wc (_NL_NUMERIC_THOUSANDS_SEP_WC);
          if (thousands == L'\0')
            grouping = NULL;
#else
          thousands = nl_langinfo (THOUSANDS_SEP);
          if (*thousands == '\0')
            {
              thousands = NULL;
              grouping = NULL;
            }
#endif
        }
#elif defined USE_LOCALECONV
      grouping = lc->grouping;
      if (grouping == NULL || *grouping <= 0 || *grouping == CHAR_MAX)
        grouping = NULL;
      else
        {
          /* Figure out the thousands separator character.  */
          thousands = lc->thousands_sep;
          if (thousands == NULL || *thousands == '\0')
            {
              thousands = NULL;
              grouping = NULL;
            }
        }
#else
      grouping = NULL;
#endif
    }
  else
    grouping = NULL;

  /* Find the locale's decimal point character.  */
#ifdef USE_WIDE_CHAR
  decimal = nl_langinfo_wc (_NL_NUMERIC_DECIMAL_POINT_WC);
  assert (decimal != L'\0');
# define decimal_len 1
#else
#ifdef USE_NL_LANGINFO
  decimal = nl_langinfo (DECIMAL_POINT);
  decimal_len = strlen (decimal);
  assert (decimal_len > 0);
#elif defined USE_LOCALECONV
  decimal = lc->decimal_point;
  if (decimal == NULL || *decimal == '\0')
    decimal = ".";
  decimal_len = strlen (decimal);
#else
  decimal = ".";
  decimal_len = 1;
#endif
#endif

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

  /* Parse string to get maximal legal prefix.  We need the number of
     characters of the integer 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 == L_('-'))
    {
      negative = 1;
      c = *++cp;
    }
  else if (c == L_('+'))
    c = *++cp;

  /* Return 0.0 if no legal string is found.
     No character is used even if a sign was found.  */
#ifdef USE_WIDE_CHAR
  if (c == (wint_t) decimal
      && (wint_t) cp[1] >= L'0' && (wint_t) cp[1] <= L'9')
    {
      /* We accept it.  This funny construct is here only to indent
         the code correctly.  */
    }
#else
  for (cnt = 0; decimal[cnt] != '\0'; ++cnt)
    if (cp[cnt] != decimal[cnt])
      break;
  if (decimal[cnt] == '\0' && cp[cnt] >= '0' && cp[cnt] <= '9')
    {
      /* We accept it.  This funny construct is here only to indent
         the code correctly.  */
    }
#endif
  else if (c < L_('0') || c > L_('9'))
    {
      /* Check for `INF' or `INFINITY'.  */
      CHAR_TYPE lowc = TOLOWER_C (c);

      if (lowc == L_('i') && STRNCASECMP (cp, L_("inf"), 3) == 0)
        {
          /* Return +/- infinity.  */
          if (endptr != NULL)
            *endptr = (STRING_TYPE *)
                      (cp + (STRNCASECMP (cp + 3, L_("inity"), 5) == 0
                             ? 8 : 3));

          return negative ? -FLOAT_HUGE_VAL : FLOAT_HUGE_VAL;
        }

      if (lowc == L_('n') && STRNCASECMP (cp, L_("nan"), 3) == 0)
        {
          /* Return NaN.  */
          FLOAT retval = NAN;

          cp += 3;

          /* Match `(n-char-sequence-digit)'.  */
          if (*cp == L_('('))
            {
              const STRING_TYPE *startp = cp;
              do
                ++cp;
              while ((*cp >= L_('0') && *cp <= L_('9'))
                     || ({ CHAR_TYPE lo = TOLOWER (*cp);
                           lo >= L_('a') && lo <= L_('z'); })
                     || *cp == L_('_'));

              if (*cp != L_(')'))
                /* The closing brace is missing.  Only match the NAN
                   part.  */
                cp = startp;
              else
                {
                  /* This is a system-dependent way to specify the
                     bitmask used for the NaN.  We expect it to be
                     a number which is put in the mantissa of the
                     number.  */
                  STRING_TYPE *endp;
                  unsigned long long int mant;

                  mant = STRTOULL (startp + 1, &endp, 0);
                  if (endp == cp)
                    SET_MANTISSA (retval, mant);

                  /* Consume the closing brace.  */
                  ++cp;
                }
            }

          if (endptr != NULL)
            *endptr = (STRING_TYPE *) cp;

          return retval;
        }

      /* It is really a text we do not recognize.  */
      RETURN (0.0, nptr);
    }

  /* First look whether we are faced with a hexadecimal number.  */
  if (c == L_('0') && TOLOWER (cp[1]) == L_('x'))
    {
      /* Okay, it is a hexa-decimal number.  Remember this and skip
         the characters.  BTW: hexadecimal numbers must not be
         grouped.  */
      base = 16;
      cp += 2;
      c = *cp;
      grouping = NULL;
    }

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

  /* Ignore leading zeroes.  This helps us to avoid useless computations.  */
#ifdef USE_WIDE_CHAR
  while (c == L'0' || ((wint_t) thousands != L'\0' && c == (wint_t) thousands))
    c = *++cp;
#else
  if (__builtin_expect (thousands == NULL, 1))
    while (c == '0')
      c = *++cp;
  else
    {
      /* We also have the multibyte thousands string.  */
      while (1)
        {
          if (c != '0')
            {
              for (cnt = 0; thousands[cnt] != '\0'; ++cnt)
                if (thousands[cnt] != cp[cnt])
                  break;
              if (thousands[cnt] != '\0')
                break;
              cp += cnt - 1;
            }
          c = *++cp;
        }
    }
#endif

  /* If no other digit but a '0' is found the result is 0.0.
     Return current read pointer.  */
  CHAR_TYPE lowc = TOLOWER (c);
  if (!((c >= L_('0') && c <= L_('9'))
        || (base == 16 && lowc >= L_('a') && lowc <= L_('f'))
        || (
#ifdef USE_WIDE_CHAR
            c == (wint_t) decimal
#else
            ({ for (cnt = 0; decimal[cnt] != '\0'; ++cnt)
                 if (decimal[cnt] != cp[cnt])
                   break;
               decimal[cnt] == '\0'; })
#endif
            /* '0x.' alone is not a valid hexadecimal number.
               '.' alone is not valid either, but that has been checked
               already earlier.  */
            && (base != 16
                || cp != start_of_digits
                || (cp[decimal_len] >= L_('0') && cp[decimal_len] <= L_('9'))
                || ({ CHAR_TYPE lo = TOLOWER (cp[decimal_len]);
                      lo >= L_('a') && lo <= L_('f'); })))
        || (base == 16 && (cp != start_of_digits
                           && lowc == L_('p')))
        || (base != 16 && lowc == L_('e'))))
    {
#ifdef USE_WIDE_CHAR
      tp = __correctly_grouped_prefixwc (start_of_digits, cp, thousands,
                                         grouping);
#else
      tp = __correctly_grouped_prefixmb (start_of_digits, cp, thousands,
                                         grouping);
#endif
      /* If TP is at the start of the digits, there was no correctly
         grouped prefix of the string; so no number found.  */
      RETURN (negative ? -0.0 : 0.0,
              tp == start_of_digits ? (base == 16 ? cp - 1 : nptr) : tp);
    }

  /* 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 (1)
    {
      if ((c >= L_('0') && c <= L_('9'))
          || (base == 16
              && ({ CHAR_TYPE lo = TOLOWER (c);
                    lo >= L_('a') && lo <= L_('f'); })))
        ++dig_no;
      else
        {
#ifdef USE_WIDE_CHAR
          if (__builtin_expect ((wint_t) thousands == L'\0', 1)
              || c != (wint_t) thousands)
            /* Not a digit or separator: end of the integer part.  */
            break;
#else
          if (__builtin_expect (thousands == NULL, 1))
            break;
          else
            {
              for (cnt = 0; thousands[cnt] != '\0'; ++cnt)
                if (thousands[cnt] != cp[cnt])
                  break;
              if (thousands[cnt] != '\0')
                break;
              cp += cnt - 1;
            }
#endif
        }
      c = *++cp;
    }

  if (__builtin_expect (grouping != NULL, 0) && cp > start_of_digits)
    {
      /* Check the grouping of the digits.  */
#ifdef USE_WIDE_CHAR
      tp = __correctly_grouped_prefixwc (start_of_digits, cp, thousands,
                                         grouping);
#else
      tp = __correctly_grouped_prefixmb (start_of_digits, cp, thousands,
                                         grouping);
#endif
      if (cp != tp)
        {
          /* Less than the entire string was correctly grouped.  */

          if (tp == start_of_digits)
            /* No valid group of numbers at all: no valid number.  */
            RETURN (0.0, nptr);

          if (tp < startp)
            /* The number is validly grouped, but consists
               only of zeroes.  The whole value is zero.  */
            RETURN (negative ? -0.0 : 0.0, tp);

          /* Recompute DIG_NO so we won't read more digits than
             are properly grouped.  */
          cp = tp;
          dig_no = 0;
          for (tp = startp; tp < cp; ++tp)
            if (*tp >= L_('0') && *tp <= L_('9'))
              ++dig_no;

          int_no = dig_no;
          lead_zero = 0;

          goto number_parsed;
        }
    }

  /* We have the number of digits in the integer part.  Whether these
     are all or any is really a fractional digit will be decided
     later.  */
  int_no = dig_no;
  lead_zero = int_no == 0 ? (size_t) -1 : 0;

  /* Read the fractional digits.  A special case are the 'american
     style' numbers like `16.' i.e. with decimal point but without
     trailing digits.  */
  if (
#ifdef USE_WIDE_CHAR
      c == (wint_t) decimal
#else
      ({ for (cnt = 0; decimal[cnt] != '\0'; ++cnt)
           if (decimal[cnt] != cp[cnt])
             break;
         decimal[cnt] == '\0'; })
#endif
      )
    {
      cp += decimal_len;
      c = *cp;
      while ((c >= L_('0') && c <= L_('9')) ||
             (base == 16 && ({ CHAR_TYPE lo = TOLOWER (c);
                               lo >= L_('a') && lo <= L_('f'); })))
        {
          if (c != L_('0') && lead_zero == (size_t) -1)
            lead_zero = dig_no - int_no;
          ++dig_no;
          c = *++cp;
        }
    }
  assert (dig_no <= (uintmax_t) INTMAX_MAX);

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

  /* Read exponent.  */
  lowc = TOLOWER (c);
  if ((base == 16 && lowc == L_('p'))
      || (base != 16 && lowc == L_('e')))
    {
      int exp_negative = 0;

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

      if (c >= L_('0') && c <= L_('9'))
        {
          intmax_t exp_limit;

          /* Get the exponent limit. */
          if (base == 16)
            {
              if (exp_negative)
                {
                  assert (int_no <= (uintmax_t) (INTMAX_MAX
                                                 + MIN_EXP - MANT_DIG) / 4);
                  exp_limit = -MIN_EXP + MANT_DIG + 4 * (intmax_t) int_no;
                }
              else
                {
                  if (int_no)
                    {
                      assert (lead_zero == 0
                              && int_no <= (uintmax_t) INTMAX_MAX / 4);
                      exp_limit = MAX_EXP - 4 * (intmax_t) int_no + 3;
                    }
                  else if (lead_zero == (size_t) -1)
                    {
                      /* The number is zero and this limit is
                         arbitrary.  */
                      exp_limit = MAX_EXP + 3;
                    }
                  else
                    {
                      assert (lead_zero
                              <= (uintmax_t) (INTMAX_MAX - MAX_EXP - 3) / 4);
                      exp_limit = (MAX_EXP
                                   + 4 * (intmax_t) lead_zero
                                   + 3);
                    }
                }
            }
          else
            {
              if (exp_negative)
                {
                  assert (int_no
                          <= (uintmax_t) (INTMAX_MAX + MIN_10_EXP - MANT_DIG));
                  exp_limit = -MIN_10_EXP + MANT_DIG + (intmax_t) int_no;
                }
              else
                {
                  if (int_no)
                    {
                      assert (lead_zero == 0
                              && int_no <= (uintmax_t) INTMAX_MAX);
                      exp_limit = MAX_10_EXP - (intmax_t) int_no + 1;
                    }
                  else if (lead_zero == (size_t) -1)
                    {
                      /* The number is zero and this limit is
                         arbitrary.  */
                      exp_limit = MAX_10_EXP + 1;
                    }
                  else
                    {
                      assert (lead_zero
                              <= (uintmax_t) (INTMAX_MAX - MAX_10_EXP - 1));
                      exp_limit = MAX_10_EXP + (intmax_t) lead_zero + 1;
                    }
                }
            }

          if (exp_limit < 0)
            exp_limit = 0;

          do
            {
              if (__builtin_expect ((exponent > exp_limit / 10
                                     || (exponent == exp_limit / 10
                                         && c - L_('0') > exp_limit % 10)), 0))
                /* The exponent is too large/small to represent a valid
                   number.  */
                {
                  FLOAT result;

                  /* We have to take care for special situation: a joker
                     might have written "0.0e100000" which is in fact
                     zero.  */
                  if (lead_zero == (size_t) -1)
                    result = negative ? -0.0 : 0.0;
                  else
                    {
                      /* Overflow or underflow.  */
#if defined HAVE_ERRNO_H && defined ERANGE
                      errno = ERANGE;
#endif
                      result = (exp_negative ? (negative ? -0.0 : 0.0) :
                                negative ? -FLOAT_HUGE_VAL : FLOAT_HUGE_VAL);
                    }

                  /* Accept all following digits as part of the exponent.  */
                  do
                    ++cp;
                  while (*cp >= L_('0') && *cp <= L_('9'));

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

              exponent *= 10;
              exponent += c - L_('0');

              c = *++cp;
            }
          while (c >= L_('0') && c <= L_('9'));

          if (exp_negative)
            exponent = -exponent;
        }
      else
        cp = expp;
    }

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

  if (dig_no == int_no && dig_no > 0 && exponent < 0)
    do
      {
        while (! (base == 16 ? ISXDIGIT (expp[-1]) : ISDIGIT (expp[-1])))
          --expp;

        if (expp[-1] != L_('0'))
          break;

        --expp;
        --dig_no;
        --int_no;
        exponent += base == 16 ? 4 : 1;
      }
    while (dig_no > 0 && exponent < 0);

 number_parsed:

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

  if (dig_no == 0)
    return negative ? -0.0 : 0.0;

  if (lead_zero)
    {
      /* Find the decimal point */
#ifdef USE_WIDE_CHAR
      while (*startp != decimal)
        ++startp;
#else
      while (1)
        {
          if (*startp == decimal[0])
            {
              for (cnt = 1; decimal[cnt] != '\0'; ++cnt)
                if (decimal[cnt] != startp[cnt])
                  break;
              if (decimal[cnt] == '\0')
                break;
            }
          ++startp;
        }
#endif
      startp += lead_zero + decimal_len;
      assert (lead_zero <= (base == 16
                            ? (uintmax_t) INTMAX_MAX / 4
                            : (uintmax_t) INTMAX_MAX));
      assert (lead_zero <= (base == 16
                            ? ((uintmax_t) exponent
                               - (uintmax_t) INTMAX_MIN) / 4
                            : ((uintmax_t) exponent - (uintmax_t) INTMAX_MIN)));
      exponent -= base == 16 ? 4 * (intmax_t) lead_zero : (intmax_t) lead_zero;
      dig_no -= lead_zero;
    }

  /* If the BASE is 16 we can use a simpler algorithm.  */
  if (base == 16)
    {
      static const int nbits[16] = { 0, 1, 2, 2, 3, 3, 3, 3,
                                     4, 4, 4, 4, 4, 4, 4, 4 };
      int idx = (MANT_DIG - 1) / BITS_PER_MP_LIMB;
      int pos = (MANT_DIG - 1) % BITS_PER_MP_LIMB;
      mp_limb_t val;

      while (!ISXDIGIT (*startp))
        ++startp;
      while (*startp == L_('0'))
        ++startp;
      if (ISDIGIT (*startp))
        val = *startp++ - L_('0');
      else
        val = 10 + TOLOWER (*startp++) - L_('a');
      bits = nbits[val];
      /* We cannot have a leading zero.  */
      assert (bits != 0);

      if (pos + 1 >= 4 || pos + 1 >= bits)
        {
          /* We don't have to care for wrapping.  This is the normal
             case so we add the first clause in the `if' expression as
             an optimization.  It is a compile-time constant and so does
             not cost anything.  */
          retval[idx] = val << (pos - bits + 1);
          pos -= bits;
        }
      else
        {
          retval[idx--] = val >> (bits - pos - 1);
          retval[idx] = val << (BITS_PER_MP_LIMB - (bits - pos - 1));
          pos = BITS_PER_MP_LIMB - 1 - (bits - pos - 1);
        }

      /* Adjust the exponent for the bits we are shifting in.  */
      assert (int_no <= (uintmax_t) (exponent < 0
                                     ? (INTMAX_MAX - bits + 1) / 4
                                     : (INTMAX_MAX - exponent - bits + 1) / 4));
      exponent += bits - 1 + ((intmax_t) int_no - 1) * 4;

      while (--dig_no > 0 && idx >= 0)
        {
          if (!ISXDIGIT (*startp))
            startp += decimal_len;
          if (ISDIGIT (*startp))
            val = *startp++ - L_('0');
          else
            val = 10 + TOLOWER (*startp++) - L_('a');

          if (pos + 1 >= 4)
            {
              retval[idx] |= val << (pos - 4 + 1);
              pos -= 4;
            }
          else
            {
              retval[idx--] |= val >> (4 - pos - 1);
              val <<= BITS_PER_MP_LIMB - (4 - pos - 1);
              if (idx < 0)
                {
                  int rest_nonzero = 0;
                  while (--dig_no > 0)
                    {
                      if (*startp != L_('0'))
                        {
                          rest_nonzero = 1;
                          break;
                        }
                      startp++;
                    }
                  return round_and_return (retval, exponent, negative, val,
                                           BITS_PER_MP_LIMB - 1, rest_nonzero);
                }

              retval[idx] = val;
              pos = BITS_PER_MP_LIMB - 1 - (4 - pos - 1);
            }
        }

      /* We ran out of digits.  */
      MPN_ZERO (retval, idx);

      return round_and_return (retval, exponent, negative, 0, 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 intmax_t incr = (exponent < 0
                              ? MAX (-(intmax_t) int_no, exponent)
                              : MIN ((intmax_t) dig_no - (intmax_t) int_no,
                                     exponent));
    int_no += incr;
    exponent -= incr;
  }

  if (__builtin_expect (exponent > MAX_10_EXP + 1 - (intmax_t) int_no, 0))
    return overflow_value (negative);

  if (__builtin_expect (exponent < MIN_10_EXP - (DIG + 1), 0))
    return underflow_value (negative);

  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
#ifndef USE_WIDE_CHAR
                           , decimal, decimal_len, thousands
#endif
                           );

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

          do
            {
              if ((exponent & expbit) != 0)
                {
                  size_t size = ttab->arraysize - _FPIO_CONST_OFFSET;
                  mp_limb_t 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 - _FPIO_CONST_OFFSET)
                    cy = mpn_mul (pdest, psrc, numsize,
                                  &__tens[ttab->arrayoff
                                          + _FPIO_CONST_OFFSET],
                                  size);
                  else
                    cy = mpn_mul (pdest, &__tens[ttab->arrayoff
                                                 + _FPIO_CONST_OFFSET],
                                  size, psrc, numsize);
                  numsize += size;
                  if (cy == 0)
                    --numsize;
                  (void) SWAP (psrc, pdest);
                }
              expbit <<= 1;
              ++ttab;
            }
          while (exponent != 0);

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

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

      /* Now we know the exponent of the number in base two.
         Check it against the maximum possible exponent.  */
      if (__builtin_expect (bits > MAX_EXP, 0))
        return overflow_value (negative);

      /* 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)
        {
          int i;
          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_bit - 1;

          if (least_bit == 0)
            memcpy (retval, &num[least_idx],
                    RETURN_LIMB_SIZE * sizeof (mp_limb_t));
          else
            {
              for (i = least_idx; i < numsize - 1; ++i)
                retval[i - least_idx] = (num[i] >> least_bit)
                                        | (num[i + 1]
                                           << (BITS_PER_MP_LIMB - least_bit));
              if (i - least_idx < RETURN_LIMB_SIZE)
                retval[RETURN_LIMB_SIZE - 1] = num[i] >> 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_t));
              /* 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_t 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_t));
#if RETURN_LIMB_SIZE > 1
      if (numsize < RETURN_LIMB_SIZE)
# if RETURN_LIMB_SIZE == 2
        retval[numsize] = 0;
# else
        MPN_ZERO (retval + numsize, RETURN_LIMB_SIZE - numsize);
# endif
#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
       123e-6 gives 123 / 1000000.  */

    int expbit;
    int neg_exp;
    int more_bits;
    int need_frac_digits;
    mp_limb_t cy;
    mp_limb_t *psrc = den;
    mp_limb_t *pdest = num;
    const struct mp_power *ttab = &_fpioconst_pow10[0];

    assert (dig_no > int_no
            && exponent <= 0
            && exponent >= MIN_10_EXP - (DIG + 1));

    /* We need to compute MANT_DIG - BITS fractional bits that lie
       within the mantissa of the result, the following bit for
       rounding, and to know whether any subsequent bit is 0.
       Computing a bit with value 2^-n means looking at n digits after
       the decimal point.  */
    if (bits > 0)
      {
        /* The bits required are those immediately after the point.  */
        assert (int_no > 0 && exponent == 0);
        need_frac_digits = 1 + MANT_DIG - bits;
      }
    else
      {
        /* The number is in the form .123eEXPONENT.  */
        assert (int_no == 0 && *startp != L_('0'));
        /* The number is at least 10^(EXPONENT-1), and 10^3 <
           2^10.  */
        int neg_exp_2 = ((1 - exponent) * 10) / 3 + 1;
        /* The number is at least 2^-NEG_EXP_2.  We need up to
           MANT_DIG bits following that bit.  */
        need_frac_digits = neg_exp_2 + MANT_DIG;
        /* However, we never need bits beyond 1/4 ulp of the smallest
           representable value.  (That 1/4 ulp bit is only needed to
           determine tinyness on machines where tinyness is determined
           after rounding.)  */
        if (need_frac_digits > MANT_DIG - MIN_EXP + 2)
          need_frac_digits = MANT_DIG - MIN_EXP + 2;
        /* At this point, NEED_FRAC_DIGITS is the total number of
           digits needed after the point, but some of those may be
           leading 0s.  */
        need_frac_digits += exponent;
        /* Any cases underflowing enough that none of the fractional
           digits are needed should have been caught earlier (such
           cases are on the order of 10^-n or smaller where 2^-n is
           the least subnormal).  */
        assert (need_frac_digits > 0);
      }

    if (need_frac_digits > (intmax_t) dig_no - (intmax_t) int_no)
      need_frac_digits = (intmax_t) dig_no - (intmax_t) int_no;

    if ((intmax_t) dig_no > (intmax_t) int_no + need_frac_digits)
      {
        dig_no = int_no + need_frac_digits;
        more_bits = 1;
      }
    else
      more_bits = 0;

    neg_exp = (intmax_t) dig_no - (intmax_t) int_no - exponent;

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

            if (densize == 0)
              {
                densize = ttab->arraysize - _FPIO_CONST_OFFSET;
                memcpy (psrc, &__tens[ttab->arrayoff + _FPIO_CONST_OFFSET],
                        densize * sizeof (mp_limb_t));
              }
            else
              {
                cy = mpn_mul (pdest, &__tens[ttab->arrayoff
                                             + _FPIO_CONST_OFFSET],
                              ttab->arraysize - _FPIO_CONST_OFFSET,
                              psrc, densize);
                densize += ttab->arraysize - _FPIO_CONST_OFFSET;
                if (cy == 0)
                  --densize;
                (void) SWAP (psrc, pdest);
              }
          }
        expbit <<= 1;
        ++ttab;
      }
    while (neg_exp != 0);

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

    /* Read the fractional digits from the string.  */
    (void) str_to_mpn (startp, dig_no - int_no, num, &numsize, &exponent
#ifndef USE_WIDE_CHAR
                       , decimal, decimal_len, thousands
#endif
                       );

    /* 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]);

    if (cnt > 0)
      {
        /* Don't call `mpn_shift' with a count of zero since the specification
           does not allow this.  */
        (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_t 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 = MANT_DIG + cnt;                                  \
                      retval[0] = quot >> (BITS_PER_MP_LIMB - used);          \
                      bits = MANT_DIG + 1;                                    \
                    }                                                         \
                  else                                                        \
                    {                                                         \
                      /* Note that we only clear the second element.  */      \
                      /* The conditional is determined at compile time.  */   \
                      if (RETURN_LIMB_SIZE > 1)                               \
                        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,
                                   more_bits || n != 0);
        }
      case 2:
        {
          mp_limb_t d0, d1, n0, n1;
          mp_limb_t quot = 0;
          int used = 0;

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

          if (numsize < densize)
            {
              if (num[0] >= d1)
                {
                  /* The numerator of the number occupies fewer bits than
                     the denominator but the one limb is bigger than the
                     high limb of the numerator.  */
                  n1 = 0;
                  n0 = num[0];
                }
              else
                {
                  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_t 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_t) 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,
                                   more_bits || n1 != 0 || n0 != 0);
        }
      default:
        {
          int i;
          mp_limb_t cy, dX, d1, n0, n1;
          mp_limb_t 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 (mpn_cmp (num, &den[densize - numsize], numsize) > 0)
            num[numsize++] = 0;

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

              if (bits <= 0)
                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.  */
#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 - 1; i >= empty; --i)
                        retval[i] = retval[i - empty];
                      while (i >= 0)
                        retval[i--] = 0;
#endif
                    }
                  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),
                                             used % BITS_PER_MP_LIMB);
                          for (i = used / BITS_PER_MP_LIMB - 1; 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;
                }
              for (i = numsize; i > 0; --i)
                num[i + empty] = num[i - 1];
              MPN_ZERO (num, empty + 1);
            }
          else
            {
              int i;
              assert (numsize == densize);
              for (i = numsize; i > 0; --i)
                num[i] = num[i - 1];
              num[0] = 0;
            }

          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_t) 0;
              else
                {
                  mp_limb_t 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];
              num[0] = 0;

              got_limb;
            }

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

  /* NOTREACHED */
}