niceSOFT/mpfr | Gitverse

src/strtofr.c
855 строк28 KB
Vincent Lefèvre
03 янв 2018, 13:53
03 янв 2018, 13:532fce388
/* mpfr_strtofr -- set a floating-point number from a string

Copyright 2004-2018 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR 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 3 of the License, or (at your
option) any later version.

The GNU MPFR 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 MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

#include <ctype.h>  /* For isspace */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

#define MPFR_MAX_BASE 62

struct parsed_string {
  int            negative; /* non-zero iff the number is negative */
  int            base;     /* base of the string */
  unsigned char *mantissa; /* raw significand (without any point) */
  unsigned char *mant;     /* stripped significand (without starting and
                              ending zeroes). This points inside the area
                              allocated for the mantissa field. */
  size_t         prec;     /* length of mant (zero for +/-0) */
  size_t         alloc;    /* allocation size of mantissa */
  mpfr_exp_t     exp_base; /* number of digits before the point */
  mpfr_exp_t     exp_bin;  /* exponent in case base=2 or 16, and the pxxx
                              format is used (i.e., exponent is given in
                              base 10) */
};

/* This table has been generated by the following program.
   For 2 <= b <= MPFR_MAX_BASE,
   RedInvLog2Table[b-2][0] / RedInvLog2Table[b-2][1]
   is an upper approximation of log(2)/log(b).
*/
static const unsigned long RedInvLog2Table[MPFR_MAX_BASE-1][2] = {
  {1UL, 1UL},
  {53UL, 84UL},
  {1UL, 2UL},
  {4004UL, 9297UL},
  {53UL, 137UL},
  {2393UL, 6718UL},
  {1UL, 3UL},
  {665UL, 2108UL},
  {4004UL, 13301UL},
  {949UL, 3283UL},
  {53UL, 190UL},
  {5231UL, 19357UL},
  {2393UL, 9111UL},
  {247UL, 965UL},
  {1UL, 4UL},
  {4036UL, 16497UL},
  {665UL, 2773UL},
  {5187UL, 22034UL},
  {4004UL, 17305UL},
  {51UL, 224UL},
  {949UL, 4232UL},
  {3077UL, 13919UL},
  {53UL, 243UL},
  {73UL, 339UL},
  {5231UL, 24588UL},
  {665UL, 3162UL},
  {2393UL, 11504UL},
  {4943UL, 24013UL},
  {247UL, 1212UL},
  {3515UL, 17414UL},
  {1UL, 5UL},
  {4415UL, 22271UL},
  {4036UL, 20533UL},
  {263UL, 1349UL},
  {665UL, 3438UL},
  {1079UL, 5621UL},
  {5187UL, 27221UL},
  {2288UL, 12093UL},
  {4004UL, 21309UL},
  {179UL, 959UL},
  {51UL, 275UL},
  {495UL, 2686UL},
  {949UL, 5181UL},
  {3621UL, 19886UL},
  {3077UL, 16996UL},
  {229UL, 1272UL},
  {53UL, 296UL},
  {109UL, 612UL},
  {73UL, 412UL},
  {1505UL, 8537UL},
  {5231UL, 29819UL},
  {283UL, 1621UL},
  {665UL, 3827UL},
  {32UL, 185UL},
  {2393UL, 13897UL},
  {1879UL, 10960UL},
  {4943UL, 28956UL},
  {409UL, 2406UL},
  {247UL, 1459UL},
  {231UL, 1370UL},
  {3515UL, 20929UL} };
#if 0
#define N 8
int main ()
{
  unsigned long tab[N];
  int i, n, base;
  mpfr_t x, y;
  mpq_t q1, q2;
  int overflow = 0, base_overflow;

  mpfr_init2 (x, 200);
  mpfr_init2 (y, 200);
  mpq_init (q1);
  mpq_init (q2);

  for (base = 2 ; base < 63 ; base ++)
    {
      mpfr_set_ui (x, base, MPFR_RNDN);
      mpfr_log2 (x, x, MPFR_RNDN);
      mpfr_ui_div (x, 1, x, MPFR_RNDN);
      printf ("Base: %d x=%e ", base, mpfr_get_d1 (x));
      for (i = 0 ; i < N ; i++)
        {
          mpfr_floor (y, x);
          tab[i] = mpfr_get_ui (y, MPFR_RNDN);
          mpfr_sub (x, x, y, MPFR_RNDN);
          mpfr_ui_div (x, 1, x, MPFR_RNDN);
        }
      for (i = N-1 ; i >= 0 ; i--)
        if (tab[i] != 0)
          break;
      mpq_set_ui (q1, tab[i], 1);
      for (i = i-1 ; i >= 0 ; i--)
          {
            mpq_inv (q1, q1);
            mpq_set_ui (q2, tab[i], 1);
            mpq_add (q1, q1, q2);
          }
      printf("Approx: ", base);
      mpq_out_str (stdout, 10, q1);
      printf (" = %e\n", mpq_get_d (q1) );
      fprintf (stderr, "{");
      mpz_out_str (stderr, 10, mpq_numref (q1));
      fprintf (stderr, "UL, ");
      mpz_out_str (stderr, 10, mpq_denref (q1));
      fprintf (stderr, "UL},\n");
      if (mpz_cmp_ui (mpq_numref (q1), 1<<16-1) >= 0
          || mpz_cmp_ui (mpq_denref (q1), 1<<16-1) >= 0)
        overflow = 1, base_overflow = base;
    }

  mpq_clear (q2);
  mpq_clear (q1);
  mpfr_clear (y);
  mpfr_clear (x);
  if (overflow )
    printf ("OVERFLOW for base =%d!\n", base_overflow);
}
#endif


/* Compatible with any locale, but one still assumes that 'a', 'b', 'c',
   ..., 'z', and 'A', 'B', 'C', ..., 'Z' are consecutive values (like
   in any ASCII-based character set). */
static int
digit_value_in_base (int c, int base)
{
  int digit;

  MPFR_ASSERTD (base > 0 && base <= MPFR_MAX_BASE);

  if (c >= '0' && c <= '9')
    digit = c - '0';
  else if (c >= 'a' && c <= 'z')
    digit = (base >= 37) ? c - 'a' + 36 : c - 'a' + 10;
  else if (c >= 'A' && c <= 'Z')
    digit = c - 'A' + 10;
  else
    return -1;

  return MPFR_LIKELY (digit < base) ? digit : -1;
}

/* Compatible with any locale, but one still assumes that 'a', 'b', 'c',
   ..., 'z', and 'A', 'B', 'C', ..., 'Z' are consecutive values (like
   in any ASCII-based character set). */
/* TODO: support EBCDIC. */
static int
fast_casecmp (const char *s1, const char *s2)
{
  unsigned char c1, c2;

  do
    {
      c2 = *(const unsigned char *) s2++;
      if (c2 == '\0')
        return 0;
      c1 = *(const unsigned char *) s1++;
      if (c1 >= 'A' && c1 <= 'Z')
        c1 = c1 - 'A' + 'a';
    }
  while (c1 == c2);
  return 1;
}

/* Parse a string and fill pstr.
   Return the advanced ptr too.
   It returns:
      -1 if invalid string,
      0 if special string (like nan),
      1 if the string is OK.
      2 if overflows
   So it doesn't return the ternary value
   BUT if it returns 0 (NAN or INF), the ternary value is also '0'
   (ie NAN and INF are exact) */
static int
parse_string (mpfr_t x, struct parsed_string *pstr,
              const char **string, int base)
{
  const char *str = *string;
  unsigned char *mant;
  int point;
  int res = -1;  /* Invalid input return value */
  const char *prefix_str;
  int decimal_point;

  decimal_point = (unsigned char) MPFR_DECIMAL_POINT;

  /* Init variable */
  pstr->mantissa = NULL;

  /* Optional leading whitespace */
  while (isspace((unsigned char) *str)) str++;

  /* An optional sign `+' or `-' */
  pstr->negative = (*str == '-');
  if (*str == '-' || *str == '+')
    str++;

  /* Can be case-insensitive NAN */
  if (fast_casecmp (str, "@nan@") == 0)
    {
      str += 5;
      goto set_nan;
    }
  if (base <= 16 && fast_casecmp (str, "nan") == 0)
    {
      str += 3;
    set_nan:
      /* Check for "(dummychars)" */
      if (*str == '(')
        {
          const char *s;
          for (s = str+1 ; *s != ')' ; s++)
            if (!(*s >= 'A' && *s <= 'Z')
                && !(*s >= 'a' && *s <= 'z')
                && !(*s >= '0' && *s <= '9')
                && *s != '_')
              break;
          if (*s == ')')
            str = s+1;
        }
      *string = str;
      MPFR_SET_NAN(x);
      /* MPFR_RET_NAN not used as the return value isn't a ternary value */
      __gmpfr_flags |= MPFR_FLAGS_NAN;
      return 0;
    }

  /* Can be case-insensitive INF */
  if (fast_casecmp (str, "@inf@") == 0)
    {
      str += 5;
      goto set_inf;
    }
  if (base <= 16 && fast_casecmp (str, "infinity") == 0)
    {
      str += 8;
      goto set_inf;
    }
  if (base <= 16 && fast_casecmp (str, "inf") == 0)
    {
      str += 3;
    set_inf:
      *string = str;
      MPFR_SET_INF (x);
      (pstr->negative) ? MPFR_SET_NEG (x) : MPFR_SET_POS (x);
      return 0;
    }

  /* If base=0 or 16, it may include '0x' prefix */
  prefix_str = NULL;
  if ((base == 0 || base == 16) && str[0]=='0'
      && (str[1]=='x' || str[1] == 'X'))
    {
      prefix_str = str;
      base = 16;
      str += 2;
    }
  /* If base=0 or 2, it may include '0b' prefix */
  if ((base == 0 || base == 2) && str[0]=='0'
      && (str[1]=='b' || str[1] == 'B'))
    {
      prefix_str = str;
      base = 2;
      str += 2;
    }
  /* Else if base=0, we assume decimal base */
  if (base == 0)
    base = 10;
  pstr->base = base;

  /* Alloc mantissa */
  pstr->alloc = (size_t) strlen (str) + 1;
  pstr->mantissa = (unsigned char*) mpfr_allocate_func (pstr->alloc);

  /* Read mantissa digits */
 parse_begin:
  mant = pstr->mantissa;
  point = 0;
  pstr->exp_base = 0;
  pstr->exp_bin  = 0;

  for (;;) /* Loop until an invalid character is read */
    {
      int c = (unsigned char) *str++;
      /* The cast to unsigned char is needed because of digit_value_in_base;
         decimal_point uses this convention too. */
      if (c == '.' || c == decimal_point)
        {
          if (MPFR_UNLIKELY(point)) /* Second '.': stop parsing */
            break;
          point = 1;
          continue;
        }
      c = digit_value_in_base (c, base);
      if (c == -1)
        break;
      MPFR_ASSERTN (c >= 0); /* c is representable in an unsigned char */
      *mant++ = (unsigned char) c;
      if (!point)
        pstr->exp_base ++;
    }
  str--; /* The last read character was invalid */

  /* Update the # of char in the mantissa */
  pstr->prec = mant - pstr->mantissa;
  /* Check if there are no characters in the mantissa (Invalid argument) */
  if (pstr->prec == 0)
    {
      /* Check if there was a prefix (in such a case, we have to read
         again the mantissa without skipping the prefix)
         The allocated mantissa is still big enough since we will
         read only 0, and we alloc one more char than needed.
         FIXME: Not really friendly. Maybe cleaner code? */
      if (prefix_str != NULL)
        {
          str = prefix_str;
          prefix_str = NULL;
          goto parse_begin;
        }
      goto end;
    }

  /* Valid entry */
  res = 1;
  MPFR_ASSERTD (pstr->exp_base >= 0);

  /* an optional exponent (e or E, p or P, @) */
  if ( (*str == '@' || (base <= 10 && (*str == 'e' || *str == 'E')))
       && (!isspace((unsigned char) str[1])) )
    {
      char *endptr;
      /* the exponent digits are kept in ASCII */
      mpfr_exp_t sum;
      long read_exp = strtol (str + 1, &endptr, 10);
      if (endptr != str+1)
        str = endptr;
      sum =
        read_exp < MPFR_EXP_MIN ? (str = endptr, MPFR_EXP_MIN) :
        read_exp > MPFR_EXP_MAX ? (str = endptr, MPFR_EXP_MAX) :
        (mpfr_exp_t) read_exp;
      MPFR_SADD_OVERFLOW (sum, sum, pstr->exp_base,
                          mpfr_exp_t, mpfr_uexp_t,
                          MPFR_EXP_MIN, MPFR_EXP_MAX,
                          res = 2, res = 3);
      /* Since exp_base was positive, read_exp + exp_base can't
         do a negative overflow. */
      MPFR_ASSERTD (res != 3);
      pstr->exp_base = sum;
    }
  else if ((base == 2 || base == 16)
           && (*str == 'p' || *str == 'P')
           && (!isspace((unsigned char) str[1])))
    {
      char *endptr;
      long read_exp = strtol (str + 1, &endptr, 10);
      if (endptr != str+1)
        str = endptr;
      pstr->exp_bin =
        read_exp < MPFR_EXP_MIN ? (str = endptr, MPFR_EXP_MIN) :
        read_exp > MPFR_EXP_MAX ? (str = endptr, MPFR_EXP_MAX) :
        (mpfr_exp_t) read_exp;
    }

  /* Remove 0's at the beginning and end of mantissa[0..prec-1] */
  mant = pstr->mantissa;
  for ( ; (pstr->prec > 0) && (*mant == 0) ; mant++, pstr->prec--)
    pstr->exp_base--;
  for ( ; (pstr->prec > 0) && (mant[pstr->prec - 1] == 0); pstr->prec--);
  pstr->mant = mant;

  /* Check if x = 0 */
  if (pstr->prec == 0)
    {
      MPFR_SET_ZERO (x);
      if (pstr->negative)
        MPFR_SET_NEG(x);
      else
        MPFR_SET_POS(x);
      res = 0;
    }

  *string = str;
 end:
  if (pstr->mantissa != NULL && res != 1)
    mpfr_free_func (pstr->mantissa, pstr->alloc);
  return res;
}

/* Transform a parsed string to a mpfr_t according to the rounding mode
   and the precision of x.
   Returns the ternary value. */
static int
parsed_string_to_mpfr (mpfr_t x, struct parsed_string *pstr, mpfr_rnd_t rnd)
{
  mpfr_prec_t prec;
  mpfr_exp_t exp;
  mpfr_exp_t ysize_bits;
  mp_limb_t *y, *result;
  int count, exact;
  size_t pstr_size;
  mp_size_t ysize, real_ysize;
  int res, err;
  MPFR_ZIV_DECL (loop);
  MPFR_TMP_DECL (marker);

  /* initialize the working precision */
  prec = MPFR_PREC (x) + MPFR_INT_CEIL_LOG2 (MPFR_PREC (x));

  /* compute the value y of the leading characters as long as rounding is not
     possible */
  MPFR_TMP_MARK(marker);
  MPFR_ZIV_INIT (loop, prec);
  for (;;)
    {
      /* Set y to the value of the ~prec most significant bits of pstr->mant
         (as long as we guarantee correct rounding, we don't need to get
         exactly prec bits). */
      ysize = MPFR_PREC2LIMBS (prec);
      /* prec bits corresponds to ysize limbs */
      ysize_bits = ysize * GMP_NUMB_BITS;
      /* and to ysize_bits >= prec > MPFR_PREC (x) bits */
      /* we need to allocate one more limb to work around bug
         https://gmplib.org/list-archives/gmp-bugs/2013-December/003267.html */
      y = MPFR_TMP_LIMBS_ALLOC (2 * ysize + 2);
      y += ysize; /* y has (ysize+2) allocated limbs */

      /* pstr_size is the number of characters we read in pstr->mant
         to have at least ysize full limbs.
         We must have base^(pstr_size-1) >= (2^(GMP_NUMB_BITS))^ysize
         (in the worst case, the first digit is one and all others are zero).
         i.e., pstr_size >= 1 + ysize*GMP_NUMB_BITS/log2(base)
          Since ysize ~ prec/GMP_NUMB_BITS and prec < Umax/2 =>
          ysize*GMP_NUMB_BITS can not overflow.
         We compute pstr_size = 1 + ceil(ysize_bits * Num / Den)
          where Num/Den >= 1/log2(base)
         It is not exactly ceil(1/log2(base)) but could be one more (base 2)
         Quite ugly since it tries to avoid overflow:
         let Num = RedInvLog2Table[pstr->base-2][0]
         and Den = RedInvLog2Table[pstr->base-2][1],
         and ysize_bits = a*Den+b,
         then ysize_bits * Num/Den = a*Num + (b * Num)/Den,
         thus ceil(ysize_bits * Num/Den) = a*Num + floor(b * Num + Den - 1)/Den
      */
      {
        unsigned long Num = RedInvLog2Table[pstr->base-2][0];
        unsigned long Den = RedInvLog2Table[pstr->base-2][1];
        pstr_size = ((ysize_bits / Den) * Num)
          + (((ysize_bits % Den) * Num + Den - 1) / Den)
          + 1;
      }

      /* since pstr_size corresponds to at least ysize_bits full bits,
         and ysize_bits > prec, the weight of the neglected part of
         pstr->mant (if any) is < ulp(y) < ulp(x) */

      /* if the number of wanted characters is more than what we have in
         pstr->mant, round it down */
      if (pstr_size >= pstr->prec)
        pstr_size = pstr->prec;
      MPFR_ASSERTD (pstr_size == (mpfr_exp_t) pstr_size);

      /* convert str into binary: note that pstr->mant is big endian,
         thus no offset is needed */
      real_ysize = mpn_set_str (y, pstr->mant, pstr_size, pstr->base);
      MPFR_ASSERTD (real_ysize <= ysize+1);

      /* normalize y: warning we can even get ysize+1 limbs! */
      MPFR_ASSERTD (y[real_ysize - 1] != 0); /* mpn_set_str guarantees this */
      count_leading_zeros (count, y[real_ysize - 1]);
      /* exact means that the number of limbs of the output of mpn_set_str
         is less or equal to ysize */
      exact = real_ysize <= ysize;
      if (exact) /* shift y to the left in that case y should be exact */
        {
          /* we have enough limbs to store {y, real_ysize} */
          /* shift {y, num_limb} for count bits to the left */
          if (count != 0)
            mpn_lshift (y + ysize - real_ysize, y, real_ysize, count);
          if (real_ysize != ysize)
            {
              if (count == 0)
                mpn_copyd (y + ysize - real_ysize, y, real_ysize);
              MPN_ZERO (y, ysize - real_ysize);
            }
          /* for each bit shift decrease exponent of y */
          /* (This should not overflow) */
          exp = - ((ysize - real_ysize) * GMP_NUMB_BITS + count);
        }
      else  /* shift y to the right, by doing this we might lose some
               bits from the result of mpn_set_str (in addition to the
               characters neglected from pstr->mant) */
        {
          /* shift {y, num_limb} for (GMP_NUMB_BITS - count) bits
             to the right. FIXME: can we prove that count cannot be zero here,
             since mpn_rshift does not accept a shift of GMP_NUMB_BITS? */
          MPFR_ASSERTD (count != 0);
          exact = mpn_rshift (y, y, real_ysize, GMP_NUMB_BITS - count) ==
            MPFR_LIMB_ZERO;
          /* for each bit shift increase exponent of y */
          exp = GMP_NUMB_BITS - count;
        }

      /* compute base^(exp_base - pstr_size) on n limbs */
      if (IS_POW2 (pstr->base))
        {
          /* Base: 2, 4, 8, 16, 32 */
          int pow2;
          mpfr_exp_t tmp;

          count_leading_zeros (pow2, (mp_limb_t) pstr->base);
          pow2 = GMP_NUMB_BITS - pow2 - 1; /* base = 2^pow2 */
          MPFR_ASSERTD (0 < pow2 && pow2 <= 5);
          /* exp += pow2 * (pstr->exp_base - pstr_size) + pstr->exp_bin
             with overflow checking
             and check that we can add/subtract 2 to exp without overflow */
          MPFR_SADD_OVERFLOW (tmp, pstr->exp_base, -(mpfr_exp_t) pstr_size,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN, MPFR_EXP_MAX,
                              goto overflow, goto underflow);
          /* On some FreeBsd/Alpha, LONG_MIN/1 produced an exception
             so we used to check for this before doing the division.
             Since this bug is closed now (Nov 26, 2009), we remove
             that check (http://www.freebsd.org/cgi/query-pr.cgi?pr=72024) */
          if (tmp > 0 && MPFR_EXP_MAX / pow2 <= tmp)
            goto overflow;
          else if (tmp < 0 && MPFR_EXP_MIN / pow2 >= tmp)
            goto underflow;
          tmp *= pow2;
          MPFR_SADD_OVERFLOW (tmp, tmp, pstr->exp_bin,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN, MPFR_EXP_MAX,
                              goto overflow, goto underflow);
          MPFR_SADD_OVERFLOW (exp, exp, tmp,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN+2, MPFR_EXP_MAX-2,
                              goto overflow, goto underflow);
          result = y;
          err = 0;
        }
      /* case non-power-of-two-base, and pstr->exp_base > pstr_size */
      else if (pstr->exp_base > (mpfr_exp_t) pstr_size)
        {
          mp_limb_t *z;
          mpfr_exp_t exp_z;

          result = MPFR_TMP_LIMBS_ALLOC (2 * ysize + 1);

          /* z = base^(exp_base-sptr_size) using space allocated at y-ysize */
          z = y - ysize;
          /* NOTE: exp_base-pstr_size can't overflow since pstr_size > 0 */
          err = mpfr_mpn_exp (z, &exp_z, pstr->base,
                              pstr->exp_base - pstr_size, ysize);
          if (err == -2)
            goto overflow;
          exact = exact && (err == -1);

          /* If exact is non zero, then z equals exactly the value of the
             pstr_size most significant digits from pstr->mant, i.e., the
             only difference can come from the neglected pstr->prec-pstr_size
             least significant digits of pstr->mant.
             If exact is zero, then z is rounded toward zero with respect
             to that value. */

          /* multiply(y = 0.mant[0]...mant[pr-1])_base by base^(exp-g):
             since both y and z are rounded toward zero, so is "result" */
          mpn_mul_n (result, y, z, ysize);

          /* compute the error on the product */
          if (err == -1)
            err = 0;
          err ++;

          /* compute the exponent of y */
          /* exp += exp_z + ysize_bits with overflow checking
             and check that we can add/subtract 2 to exp without overflow */
          MPFR_SADD_OVERFLOW (exp_z, exp_z, ysize_bits,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN, MPFR_EXP_MAX,
                              goto overflow, goto underflow);
          MPFR_SADD_OVERFLOW (exp, exp, exp_z,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN+2, MPFR_EXP_MAX-2,
                              goto overflow, goto underflow);

          /* normalize result */
          if (MPFR_LIMB_MSB (result[2 * ysize - 1]) == 0)
            {
              mp_limb_t *r = result + ysize - 1;
              mpn_lshift (r, r, ysize + 1, 1);
              /* Overflow checking not needed */
              exp --;
            }

          /* if the low ysize limbs of {result, 2*ysize} are all zero,
             then the result is still "exact" (if it was before) */
          exact = exact && (mpn_scan1 (result, 0)
                            >= (unsigned long) ysize_bits);
          result += ysize;
        }
      /* case exp_base < pstr_size */
      else if (pstr->exp_base < (mpfr_exp_t) pstr_size)
        {
          mp_limb_t *z;
          mpfr_exp_t exp_z;

          result = MPFR_TMP_LIMBS_ALLOC (3 * ysize + 1);

          /* set y to y * K^ysize */
          y = y - ysize;  /* we have allocated ysize limbs at y - ysize */
          MPN_ZERO (y, ysize);

          /* pstr_size - pstr->exp_base can overflow */
          MPFR_SADD_OVERFLOW (exp_z, (mpfr_exp_t) pstr_size, -pstr->exp_base,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN, MPFR_EXP_MAX,
                              goto underflow, goto overflow);

          /* (z, exp_z) = base^(exp_base-pstr_size) */
          z = result + 2*ysize + 1;
          err = mpfr_mpn_exp (z, &exp_z, pstr->base, exp_z, ysize);
          /* Since we want y/z rounded toward zero, we must get an upper
             bound of z. If err >= 0, the error on z is bounded by 2^err. */
          if (err >= 0)
            {
              mp_limb_t cy;
              unsigned long h = err / GMP_NUMB_BITS;
              unsigned long l = err - h * GMP_NUMB_BITS;

              if (h >= ysize) /* not enough precision in z */
                goto next_loop;
              cy = mpn_add_1 (z, z, ysize - h, MPFR_LIMB_ONE << l);
              if (cy != 0) /* the code below requires z on ysize limbs */
                goto next_loop;
            }
          exact = exact && (err == -1);
          if (err == -2)
            goto underflow; /* FIXME: Sure? */
          if (err == -1)
            err = 0;

          /* compute y / z */
          /* result will be put into result + n, and remainder into result */
          mpn_tdiv_qr (result + ysize, result, (mp_size_t) 0, y,
                       2 * ysize, z, ysize);

          /* exp -= exp_z + ysize_bits with overflow checking
             and check that we can add/subtract 2 to exp without overflow */
          MPFR_SADD_OVERFLOW (exp_z, exp_z, ysize_bits,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN, MPFR_EXP_MAX,
                              goto underflow, goto overflow);
          MPFR_SADD_OVERFLOW (exp, exp, -exp_z,
                              mpfr_exp_t, mpfr_uexp_t,
                              MPFR_EXP_MIN+2, MPFR_EXP_MAX-2,
                              goto overflow, goto underflow);
          err += 2;
          /* if the remainder of the division is zero, then the result is
             still "exact" if it was before */
          exact = exact && (mpn_popcount (result, ysize) == 0);

          /* normalize result */
          if (result[2 * ysize] == MPFR_LIMB_ONE)
            {
              mp_limb_t *r = result + ysize;

              exact = exact && ((*r & MPFR_LIMB_ONE) == 0);
              mpn_rshift (r, r, ysize + 1, 1);
              /* Overflow Checking not needed */
              exp ++;
            }
          result += ysize;
        }
      /* case exp_base = pstr_size: no multiplication or division needed */
      else
        {
          /* base^(exp-pr) = 1             nothing to compute */
          result = y;
          err = 0;
        }

      /* If result is exact, we still have to consider the neglected part
         of the input string. For a directed rounding, in that case we could
         still correctly round, since the neglected part is less than
         one ulp, but that would make the code more complex, and give a
         speedup for rare cases only. */
      exact = exact && (pstr_size == pstr->prec);

      /* at this point, result is an approximation rounded toward zero
         of the pstr_size most significant digits of pstr->mant, with
         equality in case exact is non-zero. */

      /* test if rounding is possible, and if so exit the loop.
         Note: we also need to be able to determine the correct ternary value,
         thus we use the MPFR_PREC(x) + (rnd == MPFR_RNDN) trick.
         For example if result = xxx...xxx111...111 and rnd = RNDN,
         then we know the correct rounding is xxx...xx(x+1), but we cannot know
         the correct ternary value. */
      if (exact || mpfr_round_p (result, ysize, ysize_bits - err - 1,
                                 MPFR_PREC(x) + (rnd == MPFR_RNDN)))
        break;

    next_loop:
      /* update the prec for next loop */
      MPFR_ZIV_NEXT (loop, prec);
    } /* loop */
  MPFR_ZIV_FREE (loop);

  /* round y */
  if (mpfr_round_raw (MPFR_MANT (x), result,
                      ysize_bits,
                      pstr->negative, MPFR_PREC(x), rnd, &res ))
    {
      /* overflow when rounding y */
      MPFR_MANT (x)[MPFR_LIMB_SIZE (x) - 1] = MPFR_LIMB_HIGHBIT;
      /* Overflow Checking not needed */
      exp ++;
    }

  if (res == 0) /* fix ternary value */
    {
      exact = exact && (pstr_size == pstr->prec);
      if (!exact)
        res = (pstr->negative) ? 1 : -1;
    }

  /* Set sign of x before exp since check_range needs a valid sign */
  (pstr->negative) ? MPFR_SET_NEG (x) : MPFR_SET_POS (x);

  /* DO NOT USE MPFR_SET_EXP. The exp may be out of range! */
  MPFR_SADD_OVERFLOW (exp, exp, ysize_bits,
                      mpfr_exp_t, mpfr_uexp_t,
                      MPFR_EXP_MIN, MPFR_EXP_MAX,
                      goto overflow, goto underflow);
  MPFR_EXP (x) = exp;
  res = mpfr_check_range (x, res, rnd);
  goto end;

 underflow:
  /* This is called when there is a huge overflow
     (Real expo < MPFR_EXP_MIN << __gmpfr_emin */
  if (rnd == MPFR_RNDN)
    rnd = MPFR_RNDZ;
  res = mpfr_underflow (x, rnd, (pstr->negative) ? -1 : 1);
  goto end;

 overflow:
  res = mpfr_overflow (x, rnd, (pstr->negative) ? -1 : 1);

 end:
  MPFR_TMP_FREE (marker);
  return res;
}

static void
free_parsed_string (struct parsed_string *pstr)
{
  mpfr_free_func (pstr->mantissa, pstr->alloc);
}

int
mpfr_strtofr (mpfr_t x, const char *string, char **end, int base,
              mpfr_rnd_t rnd)
{
  int res;
  struct parsed_string pstr;

  /* For base <= 36, parsing is case-insensitive. */
  MPFR_ASSERTN (base == 0 || (base >= 2 && base <= 62));

  /* If an error occurred, it must return 0. */
  MPFR_SET_ZERO (x);
  MPFR_SET_POS (x);

  MPFR_STAT_STATIC_ASSERT (MPFR_MAX_BASE >= 62);
  res = parse_string (x, &pstr, &string, base);
  /* If res == 0, then it was exact (NAN or INF),
     so it is also the ternary value */
  if (MPFR_UNLIKELY (res == -1))  /* invalid data */
    res = 0;  /* x is set to 0, which is exact, thus ternary value is 0 */
  else if (res == 1)
    {
      res = parsed_string_to_mpfr (x, &pstr, rnd);
      free_parsed_string (&pstr);
    }
  else if (res == 2)
    res = mpfr_overflow (x, rnd, (pstr.negative) ? -1 : 1);
  MPFR_ASSERTD (res != 3);
#if 0
  else if (res == 3)
    {
      /* This is called when there is a huge overflow
         (Real expo < MPFR_EXP_MIN << __gmpfr_emin */
      if (rnd == MPFR_RNDN)
        rnd = MPFR_RNDZ;
      res = mpfr_underflow (x, rnd, (pstr.negative) ? -1 : 1);
    }
#endif

  if (end != NULL)
    *end = (char *) string;
  return res;
}