[gnu.g++.bug] bug report 16: destructor problem with reference argument

baud@GATECH.EDU (Kurt Baudendistel) (10/14/88)

BUG REPORT 16

BEHAVIOR:

if the abs function takes its argument by value "abs(Fix x)" it works
correctly. if, however, it takes its argument by reference "abs(Fix& x)",
the program bombs in the Fix destructor.

the abs function is defined in Fix.h. the version of Fix.h given has
it defined to take its argument by reference.

program output with value argument:

Fix(35,.1)
len = 35
siz = 3
ref = 1
man =  cccccccc000
val = 0.1

abs(Fix(35,.1))
len = 35
siz = 3
ref = 1
man =  cccccccc000
val = 0.1

program output with reference argument:

Fix(35,.1)
len = 35
siz = 3
ref = 1
man =  cccccccc000
val = 0.1

abs(Fix(35,.1))
Memory fault - core dumped

COMPILER VERSION: GNU C++ compiler driver, version 1.25.0

INPUT FILES:

bug.cc
Fix.h
Fix.cc
type.h

COMMAND LINE: g++ -v -g bug.cc Fix.cc

FILE NAMES:

tm.h = tm-vax.h
md = vax.md

MACHINE: vax 11/780 with BRL UNIX (4.2 BSD)

SOURCE FILES:
----------------------------------------------------------------------------
// bug.cc
#define make(x) cout << #x << "\n"; show(x)

#include <Fix.h>
main() {
  make(Fix(35,.1));
  make(abs(Fix(35,.1)));
}
----------------------------------------------------------------------------
// Fix.h
#ifndef _Fix_h
#define _Fix_h 1

#include <stream.h>
#include <std.h>
#include <stddef.h>
#include <type.h>
#include <Integer.h>

#define _Fix_min_length 	1
#define _Fix_max_length		65535

#define _Fix_min_value		-1.0
#define _Fix_max_value		1.0

struct _Frep                    // internal Fix representation
{
  uint16 len;          		// length in bits
  uint16 siz;			// allocated storage
  int16 ref;          		// reference count
  uint16 s[1];			// start of ushort array represention
};

typedef struct _Frep* _Fix;

extern _Frep _Frep_0;
extern _Frep _Frep_m1;
extern _Frep _Frep_quotient_bump;

extern uint16 Fix_default_length;

class Fix
{
  _Fix            rep;

		  Fix(_Fix);

  void		  unique();
  void  	  copy(int, uint16*);

public:
		  Fix();
                  Fix(Fix&);
		  Fix(double&);
                  Fix(long);
                  Fix(long, Fix&);
                  Fix(long, double&);

                  ~Fix();

  Fix             operator =  (Fix&);

  friend int      operator == (Fix&, Fix& );
  friend int      operator != (Fix&, Fix&);

  friend int      operator <  (Fix&, Fix&);
  friend int      operator <= (Fix&, Fix&);
  friend int      operator >  (Fix&, Fix&);
  friend int      operator >= (Fix&, Fix&);

  Fix&            operator +  ();
  Fix             operator -  ();

  friend Fix      operator +  (Fix&, Fix&);
  friend Fix      operator -  (Fix&, Fix&);
  friend Fix      operator *  (Fix&, Fix&);
  friend Fix      operator /  (Fix&, Fix&);

  friend Fix      operator *  (Fix&, long);
  friend Fix      operator *  (long, Fix&);
  friend Fix      operator %  (Fix&, long);
  friend Fix      operator << (Fix&, long);
  friend Fix      operator >> (Fix&, long);

  friend Fix     operator <? (Fix&, Fix&); // min
  friend Fix     operator >? (Fix&, Fix&); // max

  Fix            operator += (Fix&);
  Fix            operator -= (Fix&);
  Fix            operator *= (Fix&);
  Fix            operator /= (Fix&);

  Fix            operator *= (long);
  Fix            operator %= (long);
  Fix            operator <<=(long);
  Fix            operator >>=(long);

  friend char*    Ftoa(Fix&, int width = 8);
  friend Fix      atoF(const char*, long len = 32);
  
  friend istream& operator >> (istream&, Fix&);
  friend ostream& operator << (ostream&, Fix&);

  // built-in functions
  friend Fix      abs(Fix&);		// absolute value
  friend int      sgn(Fix&);		// -1, 0, +1
  friend Integer  mantissa(Fix&);	// integer representation
  friend double   value(Fix&);		// double value
  friend long	  length(Fix&);		// field length
  friend void	  show(Fix&);		// show contents

  // error handlers
  void            error(char* msg);		// error handler
  void            range_error(char* msg);	// range error handler

  // internal class functions
  friend void	  mask(_Fix);
  friend int      compare(_Fix, _Fix = &_Frep_0);

  friend _Fix	  new_Fix(uint16);
  friend _Fix	  new_Fix(uint16, _Fix);
  friend _Fix	  new_Fix(uint16, double);

  friend _Fix	  copy(_Fix, _Fix);
  friend _Fix	  negate(_Fix, _Fix = NULL);
  friend _Fix	  add(_Fix, _Fix, _Fix = NULL);
  friend _Fix	  subtract(_Fix, _Fix, _Fix = NULL);
  friend _Fix	  multiply(_Fix, _Fix, _Fix = NULL);
  friend _Fix	  multiply(_Fix, long, _Fix = NULL);
  friend _Fix	  divide(_Fix, _Fix, _Fix = NULL, _Fix = NULL);
  friend _Fix	  shift(_Fix, long, _Fix = NULL);

  // non-operator versions for user
  friend void	  negate(Fix& x, Fix& r);
  friend void	  add(Fix& x, Fix& y, Fix& r);
  friend void	  subtract(Fix& x, Fix& y, Fix& r);
  friend void	  multiply(Fix& x, Fix& y, Fix& r);
  friend void	  divide(Fix& x, Fix& y, Fix& q, Fix& r);
  friend void	  shift(Fix& x, long y, Fix& r);
};

// error handlers

extern void	
  default_Fix_error_handler(char*),
  default_Fix_range_error_handler(char*);

extern one_arg_error_handler_t 
  Fix_error_handler,
  Fix_range_error_handler;

extern one_arg_error_handler_t 
  set_Fix_error_handler(one_arg_error_handler_t f),
  set_Fix_range_error_handler(one_arg_error_handler_t f);

typedef void (*Fix_peh)(_Fix&);
extern Fix_peh Fix_overflow_handler;

extern void 
  Fix_overflow_saturate(_Fix&),
  Fix_overflow_wrap(_Fix&),
  Fix_overflow_warning_saturate(_Fix&),
  Fix_overflow_warning(_Fix&),
  Fix_overflow_error(_Fix&);

extern Fix_peh set_overflow_handler(Fix_peh);

extern long Fix_set_default_length(long);

//#ifdef __OPTIMIZE__

inline void Fix::unique()
{
  if ( rep->ref > 1 )
  {
    rep->ref--;
    rep = new_Fix(rep->len,rep);
  }
}

inline void Fix::copy(int l, uint16* t)
{
  uint16 *s = rep->s;
  while ( l-- )
    *s++ = *t++;
}

inline void mask (_Fix x)
{
  int n = x->len & 0x0f;
  if ( n )
    x->s[x->siz - 1] &= 0xffff0000 >> n; 
}

inline _Fix copy(_Fix from, _Fix to)
{
  uint16 *ts = to->s, *fs = from->s;
  int ilim = to->siz < from->siz ? to->siz : from->siz;
  for ( int i=0; i < ilim; i++ )
    *ts++ = *fs++;
  for ( ; i < to->siz; i++ )
    *ts++ = 0;
  mask(to);
  return to;
}

inline Fix::Fix(_Fix f)
{
  rep = f;
}

inline Fix::Fix()
{
  rep = new_Fix(Fix_default_length);
}

inline Fix::Fix(long len)
{
  if ( len < _Fix_min_length || len > _Fix_max_length )
    error("illegal length in declaration");
  rep = new_Fix((uint16 )len);
}

inline Fix::Fix(double& d)
{
  rep = new_Fix(Fix_default_length,d);
}

inline Fix::Fix(Fix&  y)
{
  rep = y.rep, rep->ref++;
}

inline Fix::Fix(long len, Fix&  y)
{
  if ( len < _Fix_min_length || len > _Fix_max_length )
    error("illegal length in declaration");
  rep = new_Fix((uint16 )len,y.rep);
}

inline Fix::Fix(long len, double& d)
{
  if ( len < _Fix_min_length || len > _Fix_max_length )
    error("illegal length in declaration");
  rep = new_Fix((uint16 )len,d);
}

inline Fix::~Fix()
{
  if ( --rep->ref <= 0 ) delete rep;
}

inline Fix  Fix::operator = (Fix&  y)
{
  if ( --rep->ref <= 0 ) delete rep;
  if ( rep->len == y.rep->len )
    rep = y.rep, rep->ref++;
  else
    copy(rep->len,y.rep->s);
  return *this;
}

inline int operator == (Fix&  x, Fix&  y)
{
  return compare(x.rep, y.rep) == 0; 
}

inline int operator != (Fix&  x, Fix&  y)
{
  return compare(x.rep, y.rep) != 0; 
}

inline int operator <  (Fix&  x, Fix&  y)
{
  return compare(x.rep, y.rep) <  0; 
}

inline int operator <= (Fix&  x, Fix&  y)
{
  return compare(x.rep, y.rep) <= 0; 
}

inline int operator >  (Fix&  x, Fix&  y)
{
  return compare(x.rep, y.rep) >  0; 
}

inline int operator >= (Fix&  x, Fix&  y)
{
  return compare(x.rep, y.rep) >= 0; 
}

inline Fix& Fix::operator +  ()
{
  return *this;
}

inline Fix Fix::operator -  ()
{
  _Fix r = negate(rep); return r;
}

inline Fix      operator +  (Fix&  x, Fix& y)
{
  _Fix r = add(x.rep, y.rep); return r;
}

inline Fix      operator -  (Fix&  x, Fix& y)
{
  _Fix r = subtract(x.rep, y.rep); return r;
}

inline Fix      operator *  (Fix&  x, Fix& y)
{
  _Fix r = multiply(x.rep, y.rep); return r;
}

inline Fix      operator *  (Fix&  x, long y)
{
  _Fix r = multiply(x.rep, y); return r;
}

inline Fix      operator *  (long  y, Fix& x)
{
  _Fix r = multiply(x.rep, y); return r;
}

inline Fix operator / (Fix& x, Fix& y)
{
  _Fix r = divide(x.rep, y.rep); return r;
}

inline Fix  Fix::operator += (Fix& y)
{
  unique(); add(rep, y.rep, rep); return *this;
}

inline Fix  Fix::operator -= (Fix& y)
{
  unique(); subtract(rep, y.rep, rep); return *this;
}

inline Fix  Fix::operator *= (Fix& y)
{
  unique(); multiply(rep, y.rep, rep); return *this;
}

inline Fix  Fix::operator *= (long y)
{
  unique(); multiply(rep, y, rep); return *this;
}

inline Fix Fix::operator /= (Fix& y)
{
  unique(); divide(rep, y.rep, rep); return *this;
}

inline Fix operator % (Fix& x, long y)
{
  Fix r((long )x.rep->len + y, x); return r;
}

inline Fix Fix::operator %= (long y)
{
  Fix r((long )rep->len + y, *this); return *this = r;
}

inline Fix      operator << (Fix&  x, long y)
{
  _Fix rep = shift(x.rep, y); return rep;
}

inline Fix      operator >> (Fix&  x, long y)
{  
  _Fix rep = shift(x.rep, -y); return rep;
}

inline Fix Fix::operator <<= (long y)
{
  unique(); shift(rep, y, rep); return *this;
}

inline Fix  Fix::operator >>= (long y)
{
  unique(); shift(rep, -y, rep); return *this;
}

inline Fix operator <? (Fix& x, Fix& y)
{
  if ( compare(x.rep, y.rep) <= 0 ) return x; else return y;
}

inline Fix operator >? (Fix& x, Fix& y)
{
  if ( compare(x.rep, y.rep) >= 0 ) return x; else return y;
}

inline Fix abs(Fix&  x)
{
  return compare(x.rep) >= 0 ? x : -x;
}

inline int sgn(Fix& x)
{
  int a = compare(x.rep);
  return a == 0 ? 0 : (a > 0 ? 1 : -1);
}

inline long length(Fix& x)
{
  return x.rep->len;
}

inline ostream& operator << (ostream& s, Fix& y)
{
  return s << Ftoa(y);
}

inline void	negate (Fix& x, Fix& r)
{
  negate(x.rep, r.rep);
}

inline void	add (Fix& x, Fix& y, Fix& r)
{
  add(x.rep, y.rep, r.rep);
}

inline void	subtract (Fix& x, Fix& y, Fix& r)
{
  subtract(x.rep, y.rep, r.rep);
}

inline void	multiply (Fix& x, Fix& y, Fix& r)
{
  multiply(x.rep, y.rep, r.rep);
}

inline void	divide (Fix& x, Fix& y, Fix& q, Fix& r)
{
  divide(x.rep, y.rep, q.rep, r.rep);
}

inline void	shift (Fix& x, long y, Fix& r)
{
  shift(x.rep, y, r.rep);
}

//#endif

#endif
----------------------------------------------------------------------------
// Fix.cc
#include <Fix.h>
#include <Obstack.h>
#include <std.h>

// default parameters

uint16 Fix_default_length = 16;
Fix_peh Fix_overflow_handler = Fix_overflow_saturate;

_Frep _Frep_0	= { 16, 1, 1, { 0 } };
_Frep _Frep_m1	= { 16, 1, 1, { 0x8000 } };
_Frep _Frep_quotient_bump = { 16, 1, 1, { 0x4000 } };

// error handling

void default_Fix_error_handler(char* msg)
{
  cerr << "Fix: " << msg << "\n";
  abort();
}

void default_Fix_range_error_handler(char* msg)
{
  cerr << "Fix: range error in " << msg << "\n";
  //abort();
}

one_arg_error_handler_t Fix_error_handler = default_Fix_error_handler;
one_arg_error_handler_t Fix_range_error_handler 
  = default_Fix_range_error_handler;

one_arg_error_handler_t set_Fix_error_handler(one_arg_error_handler_t f)
{
  one_arg_error_handler_t old = Fix_error_handler;
  Fix_error_handler = f;
  return old;
}

one_arg_error_handler_t set_Fix_range_error_handler(one_arg_error_handler_t f)
{
  one_arg_error_handler_t old = Fix_range_error_handler;
  Fix_range_error_handler = f;
  return old;
}

void Fix::error(char* msg)
{
  (*Fix_error_handler)(msg);
}

void Fix::range_error(char* msg)
{
  (*Fix_range_error_handler)(msg);
}

// allocate a new _Frep

inline _Fix _new_Fix(uint16 len)
{
  int siz = (len + 15) >> 4;

  _Fix z = malloc(sizeof(_Frep) + (siz - 1) * sizeof(uint16));
  if (z == 0)
    (*Fix_error_handler)("out of memory");

  z->len = len;
  z->siz = siz;
  z->ref = 1;
  return z;
}

_Fix new_Fix(uint16 len)
{
  return _new_Fix(len);
}

_Fix new_Fix(uint16 len, _Fix x)
{
  _Fix z = _new_Fix(len);
  return copy(x,z);
}

_Fix new_Fix(uint16 len, double d)
{
  _Fix z = _new_Fix(len);

  if ( d == _Fix_max_value )
  {
    z->s[0] = 0x7fff;
    for ( int i=1; i < z->siz; i++ )
      z->s[i] = 0xffff;
  }
  else if ( d < _Fix_min_value || d > _Fix_max_value )
    (*Fix_range_error_handler)("declaration");
  else
  {
    d *= 32768;
    for ( int i=0; i < z->siz; i++ )
    {
      z->s[i] = (int16 )d;
      d -= z->s[i];
      d *= 65536;
    }
    if ( d >= 32768 )
      z->s[z->siz-1]++;
  }
  mask(z);
  return z;
}

// convert to a double 

double value(Fix& x)
{ 
  double d = 0.0;
  for ( int i=x.rep->siz-1; i >= 0; i-- )
  {
    d += x.rep->s[i];
    d *= 1./65536.;
  }
  d *= 2.;
  return d < 1. ? d : d - 2.;
}

// extract mantissa to Integer

Integer mantissa(Fix& x)
{
  Integer a = 0;
  for ( int i=0; i < x.rep->siz; i++ )
    a = (a << 16) + x.rep->s[i];
  int n = x.rep->len & 0x0f;
  if ( n )
    a >>= 16 - n;
  return a;
}

// comparison functions
  
inline static int docmp(uint16* x, uint16* y, int siz)
{
  int diff = (int16 )*x - (int16 )*y;
  while ( --siz && !diff )
    diff = (int32 )(uint32 )*++x - (int32 )(uint32 )*++y;
  return diff;
}

inline static int docmpz(uint16* x, int siz)
{
  while ( siz-- )
    if ( *x++ ) return 1;
  return 0;
}

int compare(_Fix x, _Fix y = &_Frep_0)
{
  if ( x->siz == y->siz )
    return docmp(x->s, y->s, x->siz);
  else
  {
    int r;
    _Fix longer, shorter;
    if ( x->siz > y->siz )
    {
      longer = x;
      shorter = y;
      r = 1;
    }
    else
    {
      longer = y;
      shorter = x;
      r = -1;
    }
    int diff = docmp(x->s, y->s, shorter->siz);
    if ( diff )
      return diff;
    else if ( docmpz(&longer->s[shorter->siz], longer->siz-shorter->siz) )
      return r;
    else
      return 0;
  }
}

// arithmetic functions

_Fix add(_Fix x, _Fix y, _Fix r = NULL)
{
  uint16 xsign = x->s[0], ysign = y->s[0];
  _Fix longer, shorter;
  if ( x->len >= y->len )
    longer = x, shorter = y;
  else
    longer = y, shorter = x;
  if ( r == NULL )
    r = new_Fix(longer->len);
  for ( int i=r->siz-1; i >= longer->siz; i-- )
    r->s[i] = 0;
  for ( ; i >= shorter->siz; i-- )
    r->s[i] = longer->s[i];
  uint16 carry = 0;
  uint32 sum;
  for ( ; i >= 0; i-- )
  {
    sum = (uint32 )carry + (uint32 )x->s[i] + (uint32 )y->s[i];
    carry = sum >> 16;
    r->s[i] = sum;
  }
  if ( (xsign ^ sum) & (ysign ^ sum) & 0x8000 )
    (*Fix_overflow_handler)(r);
  return r;
}

_Fix subtract(_Fix x, _Fix y, _Fix r = NULL)
{
  uint16 xsign = x->s[0], ysign = y->s[0];
  _Fix longer, shorter;
  if ( x->len >= y->len )
    longer = x, shorter = y;
  else
    longer = y, shorter = x;
  if ( r == NULL )
    r = new_Fix(longer->len);
  for ( int i=r->siz-1; i >= longer->siz; i-- )
    r->s[i] = 0;
  for ( ; i >= shorter->siz; i-- )
    r->s[i] = (longer == x ? x->s[i] : -y->s[i]);
  int16 carry = 0;
  uint32 sum;
  for ( ; i >= 0; i-- )
  {
    sum = (int32 )carry + (uint32 )x->s[i] - (uint32 )y->s[i];
    carry = sum >> 16;
    r->s[i] = sum;
  }
  if ( (xsign ^ sum) & (~ysign ^ sum) & 0x8000 )
    (*Fix_overflow_handler)(r);
  return r;
}

_Fix multiply(_Fix x, _Fix y, _Fix r = NULL)
{
  if ( r == NULL )
    r = new_Fix(x->len + y->len - 1);
  int xsign = x->s[0] & 0x8000,
    ysign = y->s[0] & 0x8000;
  Fix X(x->len), Y(y->len);
  if ( xsign )
    x = negate(x,X.rep);
  if ( ysign )
    y = negate(y,Y.rep);
  for ( int i=0; i < r->siz; i++ )
    r->s[i] = 0;
  for ( i=x->siz-1; i >= 0; i-- )
  {
    uint32 carry = 0;
    for ( int j=y->siz-1; j >= 0; j-- ) 
    {
      int k = i + j + 1;
      uint32 a = (uint32 )x->s[i] * (uint32 )y->s[j];
      uint32 b = ((a << 1) & 0xffff) + carry;
      if ( k < r->siz )
      {
	b += r->s[k];
        r->s[k] = b;
      }
      if ( k < r->siz + 1 )
        carry = ((a >> 15) & 0x0001ffff) + (b >> 16);
    }
    r->s[i] = carry;
  }
  if ( xsign != ysign )
    negate(r,r);
  return r;
}

_Fix multiply(_Fix x, long y, _Fix r = NULL )
{
  uint32 ay = abs(y);
  int16 x0 = x->s[0];
  Fix X(x->len);
  if ( x0 < 0 )
    x = negate(x,X.rep);
  if ( r == NULL )
    r = new_Fix(x->len);
  uint16 carry = 0;
  for ( int i=r->siz-1; i >= x->siz; i-- )
    r->s[i] = 0;
  uint32 a;
  for ( ; i >= 0; i-- )
  {
    a = x->s[i] * ay + carry;
    r->s[i] = a;
    carry = a >> 16;
  }
  if ( a & 0xffff8000 )
    (*Fix_range_error_handler)("multiply by long");
  if ( (x0 < 0) ^ (y < 0) )
    negate(r,r);
  return r;
}

_Fix divide(_Fix x, _Fix y, _Fix q = NULL, _Fix r = NULL)
{
  int xsign = x->s[0] & 0x8000, 
    ysign = y->s[0] & 0x8000;
  if ( q == NULL )
    q = new_Fix(x->len);
  copy(&_Frep_0,q);
  if ( r == NULL )
    r = new_Fix(x->len + y->len - 1);
  if ( xsign )
    negate(x,r);
  else
    copy(x,r);
  Fix Y(y->len);
  y = ( ysign ? negate(y,Y.rep) : copy(y,Y.rep) );
  if ( !compare(y) )
    (*Fix_range_error_handler)("division -- division by zero");
  else if ( compare(x,y) >= 0 )
    if ( compare(x,y) == 0 && xsign ^ ysign != 0 )
    {
      copy(&_Frep_m1,q);
      copy(&_Frep_0,r);
    }
    else
      (*Fix_range_error_handler)("division");
  else
  {
    _Fix t;
    Fix S(r->len),
      W(q->len,&_Frep_quotient_bump);
    for ( int i=1; i < q->len; i++ )
    {
      shift(y,-1,y);
      subtract(r,y,S.rep);
      int s_status = compare(S.rep);
      if ( s_status == 0 ) 
      {
	t = r, r = S.rep, S.rep = t;
	break;
      }
      else if ( s_status > 0 )
      {
	t = r, r = S.rep, S.rep = t;
	add(q,W.rep,q);
      }
      shift(W.rep,-1,W.rep);
    }
    if ( xsign ^ ysign )
      negate(q,q);
  }
  return q;
}

_Fix shift(_Fix x, long y, _Fix r = NULL )
{
  if ( y == 0 )
    return x;
  else if ( r == NULL )
    r = new_Fix(x->len);

  long ay = abs(y),
    ayh = ay >> 4,
    ayl = ay & 0x0f;
  int xl, u, ilow, ihigh;
  uint16 *rs, *xsl, *xsr;

  if ( y > 0 )
  {
    rs = r->s;
    xsl = x->s + ayh;
    xsr = xsl + 1;
    xl = ayl;
    u = 1;
    ihigh = x->siz - ayh - 1;
    ilow = 0;
  }
  else
  {
    rs = &r->s[r->siz - 1];
    xsr = &x->s[r->siz - 1] - ayh;
    xsl = xsr - 1;
    xl = 16 - ayl;
    u = -1;
    ihigh = r->siz - ayh - 1;
    ilow = ihigh - x->siz;
  }

  int xr = 16 - xl;
  uint16 xrmask = 0xffffL >> xr;
  for ( int i=0; i < ilow; i++, rs+=u, xsl+=u, xsr+=u )
    *rs = 0;
  for ( ; i < ihigh; i++, rs+=u, xsl+=u, xsr+=u )
    *rs = (*xsl << xl) + ((*xsr >> xr) & xrmask);
  *rs = (y > 0 ? (*xsl << xl) : ((*xsr >> xr) & xrmask));
  rs += u;
  for ( ; i < r->siz; i++, rs+=u )
    *rs = 0;
  return r;
}

_Fix negate(_Fix x, _Fix r = NULL)
{
  if ( r == NULL )
    r = new_Fix(x->len);
  uint32 carry = 1;
  for ( int i=r->siz-1; i >= x->siz; i-- )
    r->s[i] = 0;
  for ( ; i >= 0; i-- )
  {
    uint32 a = (uint16 )~x->s[i] + carry;	// bug work-around
    r->s[i] = a;
    carry = a >> 16;
  }
  return r;
}

// io functions

Fix atoF(const char* a, long len = 32)
{
  return Fix(len,atof(a));
}

char* Ftoa(Fix& x, int width = 8)
{
  int a, b;
  char *s = ecvt(value(x), width-2, &a, &b);
  char *t = new char[strlen(s) + 3];
  strcpy(t,"0.");
  strcat(t,s);
  return t;
}

extern Obstack _libgxx_io_ob;
extern char* _libgxx_io_oblast;

istream& operator >> (istream& s, Fix& y)
{
  int got_one = 0;
  if (!s.readable())
  {
    s.error();
    return s;
  }

  if (_libgxx_io_oblast) _libgxx_io_ob.free(_libgxx_io_oblast);

  char sign = 0, point = 0;
  char ch;
  s >> WS;
  while (s.good())
  {
    s.get(ch);
    if (ch == '-')
    {
      if (sign == 0)
      {
        sign = 1;
        _libgxx_io_ob.grow(ch);
      }
      else
        break;
    }
    if (ch == '.')
    {
      if (point == 0)
      {
        point = 1;
        _libgxx_io_ob.grow(ch);
      }
      else
        break;
    }
    else if (ch >= '0' && ch <= '9')
    {
      got_one = 1;
      _libgxx_io_ob.grow(ch);
    }
    else
      break;
  }
  char * p = (char*)(_libgxx_io_ob.finish(0));
  _libgxx_io_oblast = p;
  if (s.good())
    s.unget(ch);
  if (!got_one)
    s.error();
  else
    y = atoF(p);
  return s;
}

void show(Fix& x)
{
  cout << "len = " << x.rep->len << "\n";
  cout << "siz = " << x.rep->siz << "\n";
  cout << "ref = " << x.rep->ref << "\n";
  cout << "man = " 
    << Itoa(mantissa(x)<<16-(x.rep->len & 0x0f ?: 16),16,4*x.rep->siz)
    << "\n";
  cout << "val = " << value(x) << "\n";
  cout << "\n";
}

// parameter setting operations

Fix_peh set_overflow_handler(Fix_peh new_handler) {
  Fix_peh old_handler = Fix_overflow_handler;
  Fix_overflow_handler = new_handler;
  return old_handler;
}

long Fix_set_default_length(long newlen)
{
  uint16 oldlen = Fix_default_length;
  if ( newlen < _Fix_min_length || newlen > _Fix_max_length )
    (*Fix_error_handler)("illegal length in Fix_set_default_length");
  Fix_default_length = newlen;
  return oldlen;
}

// overflow handlers

void Fix_overflow_saturate(_Fix& r) {
  if ( (int16 )r->s[0] > 0 ) 
  {
    r->s[0] = 0x8000;
    for ( int i=1; i < r->siz; i++ )
      r->s[i] = 0;
  }
  else
  {
    r->s[0] = 0x7fff;
    for ( int i=1; i < r->siz; i++ )
      r->s[i] = 0xffff;
    mask(r);
  }
}

void Fix_overflow_wrap(_Fix& r) {}

void Fix_overflow_warning_saturate(_Fix& r) {
  Fix_overflow_warning(r);
  Fix_overflow_saturate(r);
}

void Fix_overflow_warning(_Fix& r) {
  cerr << "Fix: overflow warning\n"; 
}

void Fix_overflow_error(_Fix& r) {
  cerr << "Fix: overflow error\n"; 
  abort();
}
----------------------------------------------------------------------------
//
// type.h : machine type definitions
//

#ifndef TYPEH
#define TYPEH

typedef short int int16;
typedef long int int32;
typedef unsigned short int uint16;
typedef unsigned long int uint32;

typedef unsigned int uint;

typedef unsigned char byte;

#endif
----------------------------------------------------------------------------