~drizzle-trunk/drizzle/development

/* Copyright (C) 2007 MySQL AB

   This program is free software; you can redistribute it and/or modify

   it under the terms of the GNU General Public License as published by

   the Free Software Foundation; either version 2 of the License, or

   (at your option) any later version.

   This program 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 General Public License for more details.

   You should have received a copy of the GNU General Public License

   along with this program; if not, write to the Free Software

   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA */

/****************************************************************

  This file incorporates work covered by the following copyright and

  permission notice:

  The author of this software is David M. Gay.

  Copyright (c) 1991, 2000, 2001 by Lucent Technologies.

  Permission to use, copy, modify, and distribute this software for any

  purpose without fee is hereby granted, provided that this entire notice

  is included in all copies of any software which is or includes a copy

  or modification of this software and in all copies of the supporting

  documentation for such software.

  THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED

  WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY

  REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY

  OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.

 ***************************************************************/

#include <my_base.h> /* for EOVERFLOW on Windows */

#include <my_global.h>

#include <m_string.h>  /* for memcpy and NOT_FIXED_DEC */

/**

   Appears to suffice to not call malloc() in most cases.

   @todo

     see if it is possible to get rid of malloc().

     this constant is sufficient to avoid malloc() on all inputs I have tried.

*/

#define DTOA_BUFF_SIZE (420 * sizeof(void *))

/* Magic value returned by dtoa() to indicate overflow */

#define DTOA_OVERFLOW 9999

static double my_strtod_int(const char *, char **, int *, char *, size_t);

static char *dtoa(double, int, int, int *, int *, char **, char *, size_t);

static void dtoa_free(char *, char *, size_t);

/**

   @brief

   Converts a given floating point number to a zero-terminated string

   representation using the 'f' format.

   @details

   This function is a wrapper around dtoa() to do the same as

   sprintf(to, "%-.*f", precision, x), though the conversion is usually more

   precise. The only difference is in handling [-,+]infinity and nan values,

   in which case we print '0\0' to the output string and indicate an overflow.

   @param x           the input floating point number.

   @param precision   the number of digits after the decimal point.

                      All properties of sprintf() apply:

                      - if the number of significant digits after the decimal

                        point is less than precision, the resulting string is

                        right-padded with zeros

                      - if the precision is 0, no decimal point appears

                      - if a decimal point appears, at least one digit appears

                        before it

   @param to          pointer to the output buffer. The longest string which

                      my_fcvt() can return is FLOATING_POINT_BUFFER bytes

                      (including the terminating '\0').

   @param error       if not NULL, points to a location where the status of

                      conversion is stored upon return.

                      false  successful conversion

                      true   the input number is [-,+]infinity or nan.

                             The output string in this case is always '0'.

   @return            number of written characters (excluding terminating '\0')

*/

size_t my_fcvt(double x, int precision, char *to, my_bool *error)

{

  int decpt, sign, len, i;

  char *res, *src, *end, *dst= to;

  char buf[DTOA_BUFF_SIZE];

  DBUG_ASSERT(precision >= 0 && precision < NOT_FIXED_DEC && to != NULL);

  res= dtoa(x, 5, precision, &decpt, &sign, &end, buf, sizeof(buf));

  if (decpt == DTOA_OVERFLOW)

  {

    dtoa_free(res, buf, sizeof(buf));

    *to++= '0';

    *to= '\0';

    if (error != NULL)

      *error= true;

    return 1;

  }

  src= res;

  len= end - src;

  if (sign)

    *dst++= '-';

  if (decpt <= 0)

  {

    *dst++= '0';

    *dst++= '.';

    for (i= decpt; i < 0; i++)

      *dst++= '0';

  }

  for (i= 1; i <= len; i++)

  {

    *dst++= *src++;

    if (i == decpt && i < len)

      *dst++= '.';

  }

  while (i++ <= decpt)

    *dst++= '0';

  if (precision > 0)

  {

    if (len <= decpt)

      *dst++= '.';

    for (i= precision - max(0, (len - decpt)); i > 0; i--)

      *dst++= '0';

  }

  *dst= '\0';

  if (error != NULL)

    *error= false;

  dtoa_free(res, buf, sizeof(buf));

  return dst - to;

}

/**

   @brief

   Converts a given floating point number to a zero-terminated string

   representation with a given field width using the 'e' format

   (aka scientific notation) or the 'f' one.

   @details

   The format is chosen automatically to provide the most number of significant

   digits (and thus, precision) with a given field width. In many cases, the

   result is similar to that of sprintf(to, "%g", x) with a few notable

   differences:

   - the conversion is usually more precise than C library functions.

   - there is no 'precision' argument. instead, we specify the number of

     characters available for conversion (i.e. a field width).

   - the result never exceeds the specified field width. If the field is too

     short to contain even a rounded decimal representation, my_gcvt()

     indicates overflow and truncates the output string to the specified width.

   - float-type arguments are handled differently than double ones. For a

     float input number (i.e. when the 'type' argument is MY_GCVT_ARG_FLOAT)

     we deliberately limit the precision of conversion by FLT_DIG digits to

     avoid garbage past the significant digits.

   - unlike sprintf(), in cases where the 'e' format is preferred,  we don't

     zero-pad the exponent to save space for significant digits. The '+' sign

     for a positive exponent does not appear for the same reason.

   @param x           the input floating point number.

   @param type        is either MY_GCVT_ARG_FLOAT or MY_GCVT_ARG_DOUBLE.

                      Specifies the type of the input number (see notes above).

   @param width       field width in characters. The minimal field width to

                      hold any number representation (albeit rounded) is 7

                      characters ("-Ne-NNN").

   @param to          pointer to the output buffer. The result is always

                      zero-terminated, and the longest returned string is thus

                      'width + 1' bytes.

   @param error       if not NULL, points to a location where the status of

                      conversion is stored upon return.

                      false  successful conversion

                      true   the input number is [-,+]infinity or nan.

                             The output string in this case is always '0'.

   @return            number of written characters (excluding terminating '\0')

   @todo

   Check if it is possible and  makes sense to do our own rounding on top of

   dtoa() instead of calling dtoa() twice in (rare) cases when the resulting

   string representation does not fit in the specified field width and we want

   to re-round the input number with fewer significant digits. Examples:

     my_gcvt(-9e-3, ..., 4, ...);

     my_gcvt(-9e-3, ..., 2, ...);

     my_gcvt(1.87e-3, ..., 4, ...);

     my_gcvt(55, ..., 1, ...);

   We do our best to minimize such cases by:

   - passing to dtoa() the field width as the number of significant digits

   - removing the sign of the number early (and decreasing the width before

     passing it to dtoa())

   - choosing the proper format to preserve the most number of significant

     digits.

*/

size_t my_gcvt(double x, my_gcvt_arg_type type, int width, char *to,

               my_bool *error)

{

  int decpt, sign, len, exp_len;

  char *res, *src, *end, *dst= to, *dend= dst + width;

  char buf[DTOA_BUFF_SIZE];

  my_bool have_space, force_e_format;

  DBUG_ASSERT(width > 0 && to != NULL);

  /* We want to remove '-' from equations early */

  if (x < 0.)

    width--;

  res= dtoa(x, 4, type == MY_GCVT_ARG_DOUBLE ? width : min(width, FLT_DIG),

            &decpt, &sign, &end, buf, sizeof(buf));

  if (decpt == DTOA_OVERFLOW)

  {

    dtoa_free(res, buf, sizeof(buf));

    *to++= '0';

    *to= '\0';

    if (error != NULL)

      *error= true;

    return 1;

  }

  if (error != NULL)

    *error= false;

  src= res;

  len= end - res;

  /*

    Number of digits in the exponent from the 'e' conversion.

     The sign of the exponent is taken into account separetely, we don't need

     to count it here.

   */

  exp_len= 1 + (decpt >= 101 || decpt <= -99) + (decpt >= 11 || decpt <= -9);

  /*

     Do we have enough space for all digits in the 'f' format?

     Let 'len' be the number of significant digits returned by dtoa,

     and F be the length of the resulting decimal representation.

     Consider the following cases:

     1. decpt <= 0, i.e. we have "0.NNN" => F = len - decpt + 2

     2. 0 < decpt < len, i.e. we have "NNN.NNN" => F = len + 1

     3. len <= decpt, i.e. we have "NNN00" => F = decpt

  */

  have_space= (decpt <= 0 ? len - decpt + 2 :

               decpt > 0 && decpt < len ? len + 1 :

               decpt) <= width;

  /*

    The following is true when no significant digits can be placed with the

    specified field width using the 'f' format, and the 'e' format

    will not be truncated.

  */

  force_e_format= (decpt <= 0 && width <= 2 - decpt && width >= 3 + exp_len);

  /*

    Assume that we don't have enough space to place all significant digits in

    the 'f' format. We have to choose between the 'e' format and the 'f' one

    to keep as many significant digits as possible.

    Let E and F be the lengths of decimal representaion in the 'e' and 'f'

    formats, respectively. We want to use the 'f' format if, and only if F <= E.

    Consider the following cases:

    1. decpt <= 0.

       F = len - decpt + 2 (see above)

       E = len + (len > 1) + 1 + 1 (decpt <= -99) + (decpt <= -9) + 1

       ("N.NNe-MMM")

       (F <= E) <=> (len == 1 && decpt >= -1) || (len > 1 && decpt >= -2)

       We also need to ensure that if the 'f' format is chosen,

       the field width allows us to place at least one significant digit

       (i.e. width > 2 - decpt). If not, we prefer the 'e' format.

    2. 0 < decpt < len

       F = len + 1 (see above)

       E = len + 1 + 1 + ... ("N.NNeMMM")

       F is always less than E.

    3. len <= decpt <= width

       In this case we have enough space to represent the number in the 'f'

       format, so we prefer it with some exceptions.

    4. width < decpt

       The number cannot be represented in the 'f' format at all, always use

       the 'e' 'one.

  */

  if ((have_space ||

      /*

        Not enough space, let's see if the 'f' format provides the most number

        of significant digits.

      */

       ((decpt <= width && (decpt >= -1 || (decpt == -2 &&

                                            (len > 1 || !force_e_format)))) &&

         !force_e_format)) &&

       /*

         Use the 'e' format in some cases even if we have enough space for the

         'f' one. See comment for MAX_DECPT_FOR_F_FORMAT.

       */

      (!have_space || (decpt >= -MAX_DECPT_FOR_F_FORMAT + 1 &&

                       (decpt <= MAX_DECPT_FOR_F_FORMAT || len > decpt))))

  {

    /* 'f' format */

    int i;

    width-= (decpt < len) + (decpt <= 0 ? 1 - decpt : 0);

    /* Do we have to truncate any digits? */

    if (width < len)

    {

      if (width < decpt)

      {

        if (error != NULL)

          *error= true;

        width= decpt;

      }

      /*

        We want to truncate (len - width) least significant digits after the

        decimal point. For this we are calling dtoa with mode=5, passing the

        number of significant digits = (len-decpt) - (len-width) = width-decpt

      */

      dtoa_free(res, buf, sizeof(buf));

      res= dtoa(x, 5, width - decpt, &decpt, &sign, &end, buf, sizeof(buf));

      src= res;

      len= end - res;

    }

    if (len == 0)

    {

      /* Underflow. Just print '0' and exit */

      *dst++= '0';

      goto end;

    }

    /*

      At this point we are sure we have enough space to put all digits

      returned by dtoa

    */

    if (sign && dst < dend)

      *dst++= '-';

    if (decpt <= 0)

    {

      if (dst < dend)

        *dst++= '0';

      if (len > 0 && dst < dend)

        *dst++= '.';

      for (; decpt < 0 && dst < dend; decpt++)

        *dst++= '0';

    }

    for (i= 1; i <= len && dst < dend; i++)

    {

      *dst++= *src++;

      if (i == decpt && i < len && dst < dend)

        *dst++= '.';

    }

    while (i++ <= decpt && dst < dend)

      *dst++= '0';

  }

  else

  {

    /* 'e' format */

    int decpt_sign= 0;

    if (--decpt < 0)

    {

      decpt= -decpt;

      width--;

      decpt_sign= 1;

    }

    width-= 1 + exp_len; /* eNNN */

    if (len > 1)

      width--;

    if (width <= 0)

    {

      /* Overflow */

      if (error != NULL)

        *error= true;

      width= 0;

    }

    /* Do we have to truncate any digits? */

    if (width < len)

    {

      /* Yes, re-convert with a smaller width */

      dtoa_free(res, buf, sizeof(buf));

      res= dtoa(x, 4, width, &decpt, &sign, &end, buf, sizeof(buf));

      src= res;

      len= end - res;

      if (--decpt < 0)

        decpt= -decpt;

    }

    /*

      At this point we are sure we have enough space to put all digits

      returned by dtoa

    */

    if (sign && dst < dend)

      *dst++= '-';

    if (dst < dend)

      *dst++= *src++;

    if (len > 1 && dst < dend)

    {

      *dst++= '.';

      while (src < end && dst < dend)

        *dst++= *src++;

    }

    if (dst < dend)

      *dst++= 'e';

    if (decpt_sign && dst < dend)

      *dst++= '-';

    if (decpt >= 100 && dst < dend)

    {

      *dst++= decpt / 100 + '0';

      decpt%= 100;

      if (dst < dend)

        *dst++= decpt / 10 + '0';

    }

    else if (decpt >= 10 && dst < dend)

      *dst++= decpt / 10 + '0';

    if (dst < dend)

      *dst++= decpt % 10 + '0';

  }

end:

  dtoa_free(res, buf, sizeof(buf));

  *dst= '\0';

  return dst - to;

}

/**

   @brief

   Converts string to double (string does not have to be zero-terminated)

   @details

   This is a wrapper around dtoa's version of strtod().

   @param str     input string

   @param end     address of a pointer to the first character after the input

                  string. Upon return the pointer is set to point to the first

                  rejected character.

   @param error   Upon return is set to EOVERFLOW in case of underflow or

                  overflow.

   @return        The resulting double value. In case of underflow, 0.0 is

                  returned. In case overflow, signed DBL_MAX is returned.

*/

double my_strtod(const char *str, char **end, int *error)

{

  char buf[DTOA_BUFF_SIZE];

  double res;

  DBUG_ASSERT(str != NULL && end != NULL && *end != NULL && error != NULL);

  res= my_strtod_int(str, end, error, buf, sizeof(buf));

  return (*error == 0) ? res : (res < 0 ? -DBL_MAX : DBL_MAX);

}

double my_atof(const char *nptr)

{

  int error;

  const char *end= nptr+65535;                  /* Should be enough */

  return (my_strtod(nptr, (char**) &end, &error));

}

/****************************************************************

 *

 * The author of this software is David M. Gay.

 *

 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.

 *

 * Permission to use, copy, modify, and distribute this software for any

 * purpose without fee is hereby granted, provided that this entire notice

 * is included in all copies of any software which is or includes a copy

 * or modification of this software and in all copies of the supporting

 * documentation for such software.

 *

 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED

 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY

 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY

 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.

 *

 ***************************************************************/

/* Please send bug reports to David M. Gay (dmg at acm dot org,

 * with " at " changed at "@" and " dot " changed to ".").      */

/*

  Original copy of the software is located at http://www.netlib.org/fp/dtoa.c

  It was adjusted to serve MySQL server needs:

  * strtod() was modified to not expect a zero-terminated string.

    It now honors 'se' (end of string) argument as the input parameter,

    not just as the output one.

  * in dtoa(), in case of overflow/underflow/NaN result string now contains "0";

    decpt is set to DTOA_OVERFLOW to indicate overflow.

  * support for VAX, IBM mainframe and 16-bit hardware removed

  * we always assume that 64-bit integer type is available

  * support for Kernigan-Ritchie style headers (pre-ANSI compilers)

    removed

  * all gcc warnings ironed out

  * we always assume multithreaded environment, so we had to change

    memory allocation procedures to use stack in most cases;

    malloc is used as the last resort.

  * pow5mult rewritten to use pre-calculated pow5 list instead of

    the one generated on the fly.

*/

/*

  On a machine with IEEE extended-precision registers, it is

  necessary to specify double-precision (53-bit) rounding precision

  before invoking strtod or dtoa.  If the machine uses (the equivalent

  of) Intel 80x87 arithmetic, the call

       _control87(PC_53, MCW_PC);

  does this with many compilers.  Whether this or another call is

  appropriate depends on the compiler; for this to work, it may be

  necessary to #include "float.h" or another system-dependent header

  file.

*/

/*

  #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3

       and dtoa should round accordingly.

  #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3

       and Honor_FLT_ROUNDS is not #defined.

  TODO: check if we can get rid of the above two

*/

typedef int32_t Long;

typedef uint32_t ULong;

typedef int64_t LLong;

typedef uint64_t ULLong;

typedef union { double d; ULong L[2]; } U;

#if defined(WORDS_BIGENDIAN) || (defined(__FLOAT_WORD_ORDER) &&        \

                                 (__FLOAT_WORD_ORDER == __BIG_ENDIAN))

#define word0(x) ((U*)&x)->L[0]

#define word1(x) ((U*)&x)->L[1]

#else

#define word0(x) ((U*)&x)->L[1]

#define word1(x) ((U*)&x)->L[0]

#endif

#define dval(x) ((U*)&x)->d

/* #define P DBL_MANT_DIG */

/* Ten_pmax= floor(P*log(2)/log(5)) */

/* Bletch= (highest power of 2 < DBL_MAX_10_EXP) / 16 */

/* Quick_max= floor((P-1)*log(FLT_RADIX)/log(10) - 1) */

/* Int_max= floor(P*log(FLT_RADIX)/log(10) - 1) */

#define Exp_shift  20

#define Exp_shift1 20

#define Exp_msk1    0x100000

#define Exp_mask  0x7ff00000

#define P 53

#define Bias 1023

#define Emin (-1022)

#define Exp_1  0x3ff00000

#define Exp_11 0x3ff00000

#define Ebits 11

#define Frac_mask  0xfffff

#define Frac_mask1 0xfffff

#define Ten_pmax 22

#define Bletch 0x10

#define Bndry_mask  0xfffff

#define Bndry_mask1 0xfffff

#define LSB 1

#define Sign_bit 0x80000000

#define Log2P 1

#define Tiny1 1

#define Quick_max 14

#define Int_max 14

#ifndef Flt_Rounds

#ifdef FLT_ROUNDS

#define Flt_Rounds FLT_ROUNDS

#else

#define Flt_Rounds 1

#endif

#endif /*Flt_Rounds*/

#ifdef Honor_FLT_ROUNDS

#define Rounding rounding

#undef Check_FLT_ROUNDS

#define Check_FLT_ROUNDS

#else

#define Rounding Flt_Rounds

#endif

#define rounded_product(a,b) a*= b

#define rounded_quotient(a,b) a/= b

#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))

#define Big1 0xffffffff

#define FFFFFFFF 0xffffffffUL

/* This is tested to be enough for dtoa */

#define Kmax 15

#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign,   \

                          2*sizeof(int) + y->wds*sizeof(ULong))

/* Arbitrary-length integer */

typedef struct Bigint

{

  union {

    ULong *x;              /* points right after this Bigint object */

    struct Bigint *next;   /* to maintain free lists */

  } p;

  int k;                   /* 2^k = maxwds */

  int maxwds;              /* maximum length in 32-bit words */

  int sign;                /* not zero if number is negative */

  int wds;                 /* current length in 32-bit words */

} Bigint;

/* A simple stack-memory based allocator for Bigints */

typedef struct Stack_alloc

{

  char *begin;

  char *free;

  char *end;

  /*

    Having list of free blocks lets us reduce maximum required amount

    of memory from ~4000 bytes to < 1680 (tested on x86).

  */

  Bigint *freelist[Kmax+1];

} Stack_alloc;

/*

  Try to allocate object on stack, and resort to malloc if all

  stack memory is used.

*/

static Bigint *Balloc(int k, Stack_alloc *alloc)

{

  Bigint *rv;

  if (k <= Kmax &&  alloc->freelist[k])

  {

    rv= alloc->freelist[k];

    alloc->freelist[k]= rv->p.next;

  }

  else

  {

    int x, len;

    x= 1 << k;

    len= sizeof(Bigint) + x * sizeof(ULong);

    if (alloc->free + len <= alloc->end)

    {

      rv= (Bigint*) alloc->free;

      alloc->free+= len;

    }

    else

      rv= (Bigint*) malloc(len);

    rv->k= k;

    rv->maxwds= x;

  }

  rv->sign= rv->wds= 0;

  rv->p.x= (ULong*) (rv + 1);

  return rv;

}

/*

  If object was allocated on stack, try putting it to the free

  list. Otherwise call free().

*/

static void Bfree(Bigint *v, Stack_alloc *alloc)

{

  char *gptr= (char*) v;                       /* generic pointer */

  if (gptr < alloc->begin || gptr >= alloc->end)

    free(gptr);

  else if (v->k <= Kmax)

  {

    /*

      Maintain free lists only for stack objects: this way we don't

      have to bother with freeing lists in the end of dtoa;

      heap should not be used normally anyway.

    */

    v->p.next= alloc->freelist[v->k];

    alloc->freelist[v->k]= v;

  }

}

/*

  This is to place return value of dtoa in: tries to use stack

  as well, but passes by free lists management and just aligns len by

  sizeof(ULong).

*/

static char *dtoa_alloc(int i, Stack_alloc *alloc)

{

  char *rv;

  int aligned_size= (i + sizeof(ULong) - 1) / sizeof(ULong) * sizeof(ULong);

  if (alloc->free + aligned_size <= alloc->end)

  {

    rv= alloc->free;

    alloc->free+= aligned_size;

  }

  else

    rv= malloc(i);

  return rv;

}

/*

  dtoa_free() must be used to free values s returned by dtoa()

  This is the counterpart of dtoa_alloc()

*/

static void dtoa_free(char *gptr, char *buf, size_t buf_size)

{

  if (gptr < buf || gptr >= buf + buf_size)

    free(gptr);

}

/* Bigint arithmetic functions */

/* Multiply by m and add a */

static Bigint *multadd(Bigint *b, int m, int a, Stack_alloc *alloc)

{

  int i, wds;

  ULong *x;

  ULLong carry, y;

  Bigint *b1;

  wds= b->wds;

  x= b->p.x;

  i= 0;

  carry= a;

  do

  {

    y= *x * (ULLong)m + carry;

    carry= y >> 32;

    *x++= (ULong)(y & FFFFFFFF);

  }

  while (++i < wds);

  if (carry)

  {

    if (wds >= b->maxwds)

    {

      b1= Balloc(b->k+1, alloc);

      Bcopy(b1, b);

      Bfree(b, alloc);

      b= b1;

    }

    b->p.x[wds++]= (ULong) carry;

    b->wds= wds;

  }

  return b;

}

static Bigint *s2b(const char *s, int nd0, int nd, ULong y9, Stack_alloc *alloc)

{

  Bigint *b;

  int i, k;

  Long x, y;

  x= (nd + 8) / 9;

  for (k= 0, y= 1; x > y; y <<= 1, k++) ;

  b= Balloc(k, alloc);

  b->p.x[0]= y9;

  b->wds= 1;

  i= 9;

  if (9 < nd0)

  {

    s+= 9;

    do

      b= multadd(b, 10, *s++ - '0', alloc);

    while (++i < nd0);

    s++;

  }

  else

    s+= 10;

  for(; i < nd; i++)

    b= multadd(b, 10, *s++ - '0', alloc);

  return b;

}

static int hi0bits(register ULong x)

{

  register int k= 0;

  if (!(x & 0xffff0000))

  {

    k= 16;

    x<<= 16;

  }

  if (!(x & 0xff000000))

  {

    k+= 8;

    x<<= 8;

  }

  if (!(x & 0xf0000000))

  {

    k+= 4;

    x<<= 4;

  }

  if (!(x & 0xc0000000))

  {

    k+= 2;

    x<<= 2;

  }

  if (!(x & 0x80000000))

  {

    k++;

    if (!(x & 0x40000000))

      return 32;

  }

  return k;

}

static int lo0bits(ULong *y)

{

  register int k;

  register ULong x= *y;

  if (x & 7)

  {

    if (x & 1)

      return 0;

    if (x & 2)

    {

      *y= x >> 1;

      return 1;

    }

    *y= x >> 2;

    return 2;

  }

  k= 0;

  if (!(x & 0xffff))

  {

    k= 16;