ieee.c

128位长双精度型数字运算包

static void toe24( x, y )
unsigned short *x, *y;
{
unsigned short i;
unsigned short *p;

#ifdef NANS
if( eiisnan(x) )
	{
	enan( y, 24 );
	return;
	}
#endif
p = &x[0];
#ifdef IBMPC
y += 1;
#endif
#ifdef DEC
y += 1;
#endif
*y = 0;	/* output high order */
if( *p++ )
	*y = 0x8000;	/* output sign bit */

i = *p++;
if( i >= 255 )
	{	/* Saturate at largest number less than infinity. */
#ifdef INFINITIES
	*y |= (unsigned short )0x7f80;
#ifdef IBMPC
	*(--y) = 0;
#endif
#ifdef DEC
	*(--y) = 0;
#endif
#ifdef MIEEE
	++y;
	*y = 0;
#endif
#else
	*y |= (unsigned short )0x7f7f;
#ifdef IBMPC
	*(--y) = 0xffff;
#endif
#ifdef DEC
	*(--y) = 0xffff;
#endif
#ifdef MIEEE
	++y;
	*y = 0xffff;
#endif
#endif
	return;
	}
if( i == 0 )
	{
	(void )eshift( x, 7 );
	}
else
	{
	i <<= 7;
	(void )eshift( x, 8 );
	}
i |= *p++ & (unsigned short )0x7f;	/* *p = xi[M] */
*y |= i;	/* high order output already has sign bit set */
#ifdef IBMPC
*(--y) = *p;
#endif
#ifdef DEC
*(--y) = *p;
#endif
#ifdef MIEEE
++y;
*y = *p;
#endif
}


/* Compare two e type numbers.
 *
 * unsigned short a[NE], b[NE];
 * ecmp( a, b );
 *
 *  returns +1 if a > b
 *           0 if a == b
 *          -1 if a < b
 *          -2 if either a or b is a NaN.
 */
int ecmp( a, b )
unsigned short *a, *b;
{
unsigned short ai[NI], bi[NI];
register unsigned short *p, *q;
register int i;
int msign;

#ifdef NANS
if (eisnan (a)  || eisnan (b))
	return( -2 );
#endif
emovi( a, ai );
p = ai;
emovi( b, bi );
q = bi;

if( *p != *q )
	{ /* the signs are different */
/* -0 equals + 0 */
	for( i=1; i<NI-1; i++ )
		{
		if( ai[i] != 0 )
			goto nzro;
		if( bi[i] != 0 )
			goto nzro;
		}
	return(0);
nzro:
	if( *p == 0 )
		return( 1 );
	else
		return( -1 );
	}
/* both are the same sign */
if( *p == 0 )
	msign = 1;
else
	msign = -1;
i = NI-1;
do
	{
	if( *p++ != *q++ )
		{
		goto diff;
		}
	}
while( --i > 0 );

return(0);	/* equality */



diff:

if( *(--p) > *(--q) )
	return( msign );		/* p is bigger */
else
	return( -msign );	/* p is littler */
}




/* Find nearest integer to x = floor( x + 0.5 )
 *
 * unsigned short x[NE], y[NE]
 * eround( x, y );
 */
void eround( x, y )
unsigned short *x, *y;
{

eadd( ehalf, x, y );
efloor( y, y );
}




/*
; convert long (32-bit) integer to e type
;
;	long l;
;	unsigned short x[NE];
;	ltoe( &l, x );
; note &l is the memory address of l
*/
void ltoe( lp, y )
long *lp;	/* lp is the memory address of a long integer */
unsigned short *y;	/* y is the address of a short */
{
unsigned short yi[NI];
unsigned long ll;
int k;

ecleaz( yi );
if( *lp < 0 )
	{
	ll =  (unsigned long )( -(*lp) ); /* make it positive */
	yi[0] = 0xffff; /* put correct sign in the e type number */
	}
else
	{
	ll = (unsigned long )( *lp );
	}
/* move the long integer to yi significand area */
if( sizeof(long) == 8 )
	{
	yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
	yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
	yi[M + 2] = (unsigned short) (ll >> 16);
	yi[M + 3] = (unsigned short) ll;
	yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
	}
else
	{
	yi[M] = (unsigned short )(ll >> 16); 
	yi[M+1] = (unsigned short )ll;
	yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
	}
if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
	ecleaz( yi );	/* it was zero */
else
	yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
emovo( yi, y );	/* output the answer */
}

/*
; convert unsigned long (32-bit) integer to e type
;
;	unsigned long l;
;	unsigned short x[NE];
;	ltox( &l, x );
; note &l is the memory address of l
*/
void ultoe( lp, y )
unsigned long *lp; /* lp is the memory address of a long integer */
unsigned short *y;	/* y is the address of a short */
{
unsigned short yi[NI];
unsigned long ll;
int k;

ecleaz( yi );
ll = *lp;

/* move the long integer to ayi significand area */
if( sizeof(long) == 8 )
	{
	yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
	yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
	yi[M + 2] = (unsigned short) (ll >> 16);
	yi[M + 3] = (unsigned short) ll;
	yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
	}
else
	{
	yi[M] = (unsigned short )(ll >> 16); 
	yi[M+1] = (unsigned short )ll;
	yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
	}
if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
	ecleaz( yi );	/* it was zero */
else
	yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
emovo( yi, y );	/* output the answer */
}


/*
;	Find long integer and fractional parts

;	long i;
;	unsigned short x[NE], frac[NE];
;	xifrac( x, &i, frac );
 
  The integer output has the sign of the input.  The fraction is
  the positive fractional part of abs(x).
*/
void eifrac( x, i, frac )
unsigned short *x;
long *i;
unsigned short *frac;
{
unsigned short xi[NI];
int j, k;
unsigned long ll;

emovi( x, xi );
k = (int )xi[E] - (EXONE - 1);
if( k <= 0 )
	{
/* if exponent <= 0, integer = 0 and real output is fraction */
	*i = 0L;
	emovo( xi, frac );
	return;
	}
if( k > (8 * sizeof(long) - 1) )
	{
/*
;	long integer overflow: output large integer
;	and correct fraction
*/
	j = 8 * sizeof(long) - 1;
	if( xi[0] )
		*i = (long) ((unsigned long) 1) << j;
	else
		*i = (long) (((unsigned long) (~(0L))) >> 1);
	(void )eshift( xi, k );
	}
if( k > 16 )
	{
/*
  Shift more than 16 bits: shift up k-16 mod 16
  then shift by 16's.
*/
	j = k - ((k >> 4) << 4);
	eshift (xi, j);
	ll = xi[M];
	k -= j;
	do
		{
		eshup6 (xi);
		ll = (ll << 16) | xi[M];
		}
	while ((k -= 16) > 0);
	*i = ll;
	if (xi[0])
		*i = -(*i);
	}
else
	{
/* shift not more than 16 bits */
	eshift( xi, k );
	*i = (long )xi[M] & 0xffff;
	if( xi[0] )
		*i = -(*i);
	}
xi[0] = 0;
xi[E] = EXONE - 1;
xi[M] = 0;
if( (k = enormlz( xi )) > NBITS )
	ecleaz( xi );
else
	xi[E] -= (unsigned short )k;

emovo( xi, frac );
}


/*
;	Find unsigned long integer and fractional parts

;	unsigned long i;
;	unsigned short x[NE], frac[NE];
;	xifrac( x, &i, frac );

  A negative e type input yields integer output = 0
  but correct fraction.
*/
void euifrac( x, i, frac )
unsigned short *x;
unsigned long *i;
unsigned short *frac;
{
unsigned short xi[NI];
int j, k;
unsigned long ll;

emovi( x, xi );
k = (int )xi[E] - (EXONE - 1);
if( k <= 0 )
	{
/* if exponent <= 0, integer = 0 and argument is fraction */
	*i = 0L;
	emovo( xi, frac );
	return;
	}
if( k > (8 * sizeof(long)) )
	{
/*
;	long integer overflow: output large integer
;	and correct fraction
*/
	*i = ~(0L);
	(void )eshift( xi, k );
	}
else if( k > 16 )
	{
/*
  Shift more than 16 bits: shift up k-16 mod 16
  then shift up by 16's.
*/
	j = k - ((k >> 4) << 4);
	eshift (xi, j);
	ll = xi[M];
	k -= j;
	do
		{
		eshup6 (xi);
		ll = (ll << 16) | xi[M];
		}
	while ((k -= 16) > 0);
	*i = ll;
	}
else
	{
/* shift not more than 16 bits */
	eshift( xi, k );
	*i = (long )xi[M] & 0xffff;
	}

if( xi[0] )  /* A negative value yields unsigned integer 0. */
	*i = 0L;

xi[0] = 0;
xi[E] = EXONE - 1;
xi[M] = 0;
if( (k = enormlz( xi )) > NBITS )
	ecleaz( xi );
else
	xi[E] -= (unsigned short )k;

emovo( xi, frac );
}



/*
;	Shift significand
;
;	Shifts significand area up or down by the number of bits
;	given by the variable sc.
*/
int eshift( x, sc )
unsigned short *x;
int sc;
{
unsigned short lost;
unsigned short *p;

if( sc == 0 )
	return( 0 );

lost = 0;
p = x + NI-1;

if( sc < 0 )
	{
	sc = -sc;
	while( sc >= 16 )
		{
		lost |= *p;	/* remember lost bits */
		eshdn6(x);
		sc -= 16;
		}

	while( sc >= 8 )
		{
		lost |= *p & 0xff;
		eshdn8(x);
		sc -= 8;
		}

	while( sc > 0 )
		{
		lost |= *p & 1;
		eshdn1(x);
		sc -= 1;
		}
	}
else
	{
	while( sc >= 16 )
		{
		eshup6(x);
		sc -= 16;
		}

	while( sc >= 8 )
		{
		eshup8(x);
		sc -= 8;
		}

	while( sc > 0 )
		{
		eshup1(x);
		sc -= 1;
		}
	}
if( lost )
	lost = 1;
return( (int )lost );
}



/*
;	normalize
;
; Shift normalizes the significand area pointed to by argument
; shift count (up = positive) is returned.
*/
int enormlz(x)
unsigned short x[];
{
register unsigned short *p;
int sc;

sc = 0;
p = &x[M];
if( *p != 0 )
	goto normdn;
++p;
if( *p & 0x8000 )
	return( 0 );	/* already normalized */
while( *p == 0 )
	{
	eshup6(x);
	sc += 16;
/* With guard word, there are NBITS+16 bits available.
 * return true if all are zero.
 */
	if( sc > NBITS )
		return( sc );
	}
/* see if high byte is zero */
while( (*p & 0xff00) == 0 )
	{
	eshup8(x);
	sc += 8;
	}
/* now shift 1 bit at a time */
while( (*p  & 0x8000) == 0)
	{
	eshup1(x);
	sc += 1;
	if( sc > (NBITS+16) )
		{
		mtherr( "enormlz", UNDERFLOW );
		return( sc );
		}
	}
return( sc );

/* Normalize by shifting down out of the high guard word
   of the significand */
normdn:

if( *p & 0xff00 )
	{
	eshdn8(x);
	sc -= 8;
	}
while( *p != 0 )
	{
	eshdn1(x);
	sc -= 1;

	if( sc < -NBITS )
		{
		mtherr( "enormlz", OVERFLOW );
		return( sc );
		}
	}
return( sc );
}




/* Convert e type number to decimal format ASCII string.
 * The constants are for 64 bit precision.
 */

#define NTEN 12
#define MAXP 4096

#if NE == 10
static unsigned short etens[NTEN + 1][NE] =
{
  {0x6576, 0x4a92, 0x804a, 0x153f,
   0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,},	/* 10**4096 */
  {0x6a32, 0xce52, 0x329a, 0x28ce,
   0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,},	/* 10**2048 */
  {0x526c, 0x50ce, 0xf18b, 0x3d28,
   0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
  {0x9c66, 0x58f8, 0xbc50, 0x5c54,
   0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
  {0x851e, 0xeab7, 0x98fe, 0x901b,
   0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
  {0x0235, 0x0137, 0x36b1, 0x336c,
   0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
  {0x50f8, 0x25fb, 0xc76b, 0x6b71,
   0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
  {0x0000, 0x0000, 0x0000, 0x0000,
   0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
  {0x0000, 0x0000, 0x0000, 0x0000,
   0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
  {0x0000, 0x0000, 0x0000, 0x0000,
   0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
  {0x0000, 0x0000, 0x0000, 0x0000,
   0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
  {0x0000, 0x0000, 0x0000, 0x0000,
   0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
  {0x0000, 0x0000, 0x0000, 0x0000,
   0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,},	/* 10**1 */
};

static unsigned short emtens[NTEN + 1][NE] =
{
  {0x2030, 0xcffc, 0xa1c3, 0x8123,
   0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,},	/* 10**-4096 */
  {0x8264, 0xd2cb, 0xf2ea, 0x12d4,
   0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,},	/* 10**-2048 */
  {0xf53f, 0xf698, 0x6bd3, 0x0158,
   0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
  {0xe731, 0x04d4, 0xe3f2, 0xd332,
   0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
  {0xa23e, 0x5308, 0xfefb, 0x1155,
   0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
  {0xe26d, 0xdbde, 0xd05d, 0xb3f6,
   0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
  {0x2a20, 0x6224, 0x47b3, 0x98d7,
   0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
  {0x0b5b, 0x4af2, 0xa581, 0x18ed,
   0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
  {0xbf71, 0xa9b3, 0x7989, 0xbe68,
   0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
  {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b,
   0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
  {0xc155, 0xa4a8, 0x404e, 0x6113,
   0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
  {0xd70a, 0x70a3, 0x0a3d, 0xa3d7,
   0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
  {0xcccd, 0xcccc, 0xcccc, 0xcccc,
   0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,},	/* 10**-1 */
};
#else
static unsigned short etens[NTEN+1][NE] = {
{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */
{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */
{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,},
{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,},
{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,},
{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,},
{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,},
{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,},
{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,},
{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,},
{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,},
{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,},
{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */
};

static unsigned short emtens[NTEN+1][NE] = {
{0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */
{0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */
{0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,},
{0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,},
{0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,},
{0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,},
{0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,},
{0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,},
{0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,},
{0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,},
{0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,},
{0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,},
{0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */
};
#endif

void e24toasc( x, string, ndigs )
unsigned short x[];
char *string;
int ndigs;
{
unsigned short w[NI];

e24toe( x, w );
etoasc( w, string, ndigs );
}


void e53toasc( x, string, ndigs )
unsigned short x[];
char *string;
int ndigs;
{
unsigned short w[NI];

e53toe( x, w );
etoasc( w, string, ndigs );
}


void e64toasc( x, string, ndigs )
unsigned short x[];
char *string;
int ndigs;
{
unsigned short w[NI];

e64toe( x, w );
etoasc( w, string, ndigs );
}

void e113toasc (x, string, ndigs)
unsigned short x[];
char *string;
int ndigs;
{
unsigned short w[NI];

e113toe (x, w);
etoasc (w, string, ndigs);
}


void etoasc( x, string, ndigs )
unsigned short x[];
char *string;
int ndigs;
{
long digit;
unsigned short y[NI], t[NI], u[NI], w[NI];
unsigned short *p, *r, *ten;
unsigned short sign;
int i, j, k, expon, rndsav;
char *s, *ss;
unsigned short m;

rndsav = rndprc;
#ifdef NANS
if( eisnan(x) )
	{
	sprintf( string, " NaN " );
	goto bxit;
	}
#endif
rndprc = NBITS;		/* set to full precision */
emov( x, y ); /* retain external format */
if( y[NE-1] & 0x8000 )
	{
	sign = 0xffff;
	y[NE-1] &= 0x7fff;
	}
else
	{
	sign = 0;
	}
expon = 0;
ten = &etens[NTEN][0];
emov( eone, t );
/* Test for zero exponent */
if( y[NE-1] == 0 )
	{
	for( k=0; k<NE-1; k++ )
		{
		if( y[k] != 0 )
			goto tnzro; /* denormalized number */
		}
	goto isone; /* legal all zeros */
	}
tnzro:

/* Test for infinity.
 */
if( y[NE-1] == 0x7fff )
	{
	if( sign )
		sprintf( string, " -Infinity " );
	else
		sprintf( string, " Infinity " );
	goto bxit;
	}

/* Test for exponent nonzero but significand denormalized.
 * This is an error condition.
 */
if( (y[NE-1] != 0) && ((y[NE-2] & 0x8000) == 0) )
	{
	mtherr( "etoasc", DOMAIN );
	sprintf( string, "NaN" );
	goto bxit;
	}

/* Compare to 1.0 */
i = ecmp( eone, y );
if( i == 0 )
	goto isone;

if( i < 0 )
	{ /* Number is greater than 1 */
/* Convert significand to an integer and strip trailing decimal zeros. */
	emov( y, u );
	u[NE-1] = EXONE + NBITS - 1;

	p = &etens[NTEN-4][0];
	m = 16;
do
	{
	ediv( p, u, t );
	efloor( t, w );