ieee.c

128位长双精度型数字运算包

		eshup1(equot);
		equot[NI-2] |= j;
		eshup1(num);
		}
	goto divdon;
	}

/* The number of quotient bits to calculate is
 * NBITS + 1 scaling guard bit + 1 roundoff bit.
 */
fulldiv:

p = &equot[NI-2];
for( i=0; i<NBITS+2; i++ )
	{
	if( ecmpm(den,num) <= 0 )
		{
		esubm(den, num);
		j = 1;	/* quotient bit = 1 */
		}
	else
		j = 0;
	eshup1(equot);
	*p |= j;
	eshup1(num);
	}

divdon:

eshdn1( equot );
eshdn1( equot );

/* test for nonzero remainder after roundoff bit */
p = &num[M];
j = 0;
for( i=M; i<NI; i++ )
	{
	j |= *p++;
	}
if( j )
	j = 1;


for( i=0; i<NI; i++ )
	num[i] = equot[i];
return( (int )j );
}

/* Multiply significands */
int emulm( a, b )
unsigned short a[], b[];
{
unsigned short *p, *q;
int i, j, k;

equot[0] = b[0];
equot[1] = b[1];
for( i=M; i<NI; i++ )
	equot[i] = 0;

p = &a[NI-2];
k = NBITS;
while( *p == 0 ) /* significand is not supposed to be all zero */
	{
	eshdn6(a);
	k -= 16;
	}
if( (*p & 0xff) == 0 )
	{
	eshdn8(a);
	k -= 8;
	}

q = &equot[NI-1];
j = 0;
for( i=0; i<k; i++ )
	{
	if( *p & 1 )
		eaddm(b, equot);
/* remember if there were any nonzero bits shifted out */
	if( *q & 1 )
		j |= 1;
	eshdn1(a);
	eshdn1(equot);
	}

for( i=0; i<NI; i++ )
	b[i] = equot[i];

/* return flag for lost nonzero bits */
return(j);
}

#else

/* Multiply significand of e-type number b
by 16-bit quantity a, e-type result to c. */

void m16m( a, b, c )
unsigned short a;
unsigned short b[], c[];
{
register unsigned short *pp;
register unsigned long carry;
unsigned short *ps;
unsigned short p[NI];
unsigned long aa, m;
int i;

aa = a;
pp = &p[NI-2];
*pp++ = 0;
*pp = 0;
ps = &b[NI-1];

for( i=M+1; i<NI; i++ )
	{
	if( *ps == 0 )
		{
		--ps;
		--pp;
		*(pp-1) = 0;
		}
	else
		{
		m = (unsigned long) aa * *ps--;
		carry = (m & 0xffff) + *pp;
		*pp-- = (unsigned short )carry;
		carry = (carry >> 16) + (m >> 16) + *pp;
		*pp = (unsigned short )carry;
		*(pp-1) = carry >> 16;
		}
	}
for( i=M; i<NI; i++ )
	c[i] = p[i];
}


/* Divide significands. Neither the numerator nor the denominator
is permitted to have its high guard word nonzero.  */


int edivm( den, num )
unsigned short den[], num[];
{
int i;
register unsigned short *p;
unsigned long tnum;
unsigned short j, tdenm, tquot;
unsigned short tprod[NI+1];

p = &equot[0];
*p++ = num[0];
*p++ = num[1];

for( i=M; i<NI; i++ )
	{
	*p++ = 0;
	}
eshdn1( num );
tdenm = den[M+1];
for( i=M; i<NI; i++ )
	{
	/* Find trial quotient digit (the radix is 65536). */
	tnum = (((unsigned long) num[M]) << 16) + num[M+1];

	/* Do not execute the divide instruction if it will overflow. */
        if( (tdenm * 0xffffL) < tnum )
		tquot = 0xffff;
	else
		tquot = tnum / tdenm;

		/* Prove that the divide worked. */
/*
	tcheck = (unsigned long )tquot * tdenm;
	if( tnum - tcheck > tdenm )
		tquot = 0xffff;
*/
	/* Multiply denominator by trial quotient digit. */
	m16m( tquot, den, tprod );
	/* The quotient digit may have been overestimated. */
	if( ecmpm( tprod, num ) > 0 )
		{
		tquot -= 1;
		esubm( den, tprod );
		if( ecmpm( tprod, num ) > 0 )
			{
			tquot -= 1;
			esubm( den, tprod );
			}
		}
/*
	if( ecmpm( tprod, num ) > 0 )
		{
		eshow( "tprod", tprod );
		eshow( "num  ", num );
		printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
			 tnum, den[M+1], tquot );
		}
*/
	esubm( tprod, num );
/*
	if( ecmpm( num, den ) >= 0 )
		{
		eshow( "num  ", num );
		eshow( "den  ", den );
		printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
			 tnum, den[M+1], tquot );
		}
*/
	equot[i] = tquot;
	eshup6(num);
	}
/* test for nonzero remainder after roundoff bit */
p = &num[M];
j = 0;
for( i=M; i<NI; i++ )
	{
	j |= *p++;
	}
if( j )
	j = 1;

for( i=0; i<NI; i++ )
	num[i] = equot[i];

return( (int )j );
}



/* Multiply significands */
int emulm( a, b )
unsigned short a[], b[];
{
unsigned short *p, *q;
unsigned short pprod[NI];
unsigned short j;
int i;

equot[0] = b[0];
equot[1] = b[1];
for( i=M; i<NI; i++ )
	equot[i] = 0;

j = 0;
p = &a[NI-1];
q = &equot[NI-1];
for( i=M+1; i<NI; i++ )
	{
	if( *p == 0 )
		{
		--p;
		}
	else
		{
		m16m( *p--, b, pprod );
		eaddm(pprod, equot);
		}
	j |= *q;
	eshdn6(equot);
	}

for( i=0; i<NI; i++ )
	b[i] = equot[i];

/* return flag for lost nonzero bits */
return( (int)j );
}


/*
eshow(str, x)
char *str;
unsigned short *x;
{
int i;

printf( "%s ", str );
for( i=0; i<NI; i++ )
	printf( "%04x ", *x++ );
printf( "\n" );
}
*/
#endif



/*
 * Normalize and round off.
 *
 * The internal format number to be rounded is "s".
 * Input "lost" indicates whether the number is exact.
 * This is the so-called sticky bit.
 *
 * Input "subflg" indicates whether the number was obtained
 * by a subtraction operation.  In that case if lost is nonzero
 * then the number is slightly smaller than indicated.
 *
 * Input "exp" is the biased exponent, which may be negative.
 * the exponent field of "s" is ignored but is replaced by
 * "exp" as adjusted by normalization and rounding.
 *
 * Input "rcntrl" is the rounding control.
 */

static int rlast = -1;
static int rw = 0;
static unsigned short rmsk = 0;
static unsigned short rmbit = 0;
static unsigned short rebit = 0;
static int re = 0;
static unsigned short rbit[NI] = {0,0,0,0,0,0,0,0};

void emdnorm( s, lost, subflg, exp, rcntrl )
unsigned short s[];
int lost;
int subflg;
long exp;
int rcntrl;
{
int i, j;
unsigned short r;

/* Normalize */
j = enormlz( s );

/* a blank significand could mean either zero or infinity. */
#ifndef INFINITIES
if( j > NBITS )
	{
	ecleazs( s );
	return;
	}
#endif
exp -= j;
#ifndef INFINITIES
if( exp >= 32767L )
	goto overf;
#else
if( (j > NBITS) && (exp < 32767L) )
	{
	ecleazs( s );
	return;
	}
#endif
if( exp < 0L )
	{
	if( exp > (long )(-NBITS-1) )
		{
		j = (int )exp;
		i = eshift( s, j );
		if( i )
			lost = 1;
		}
	else
		{
		ecleazs( s );
		return;
		}
	}
/* Round off, unless told not to by rcntrl. */
if( rcntrl == 0 )
	goto mdfin;
/* Set up rounding parameters if the control register changed. */
if( rndprc != rlast )
	{
	ecleaz( rbit );
	switch( rndprc )
		{
		default:
		case NBITS:
			rw = NI-1; /* low guard word */
			rmsk = 0xffff;
			rmbit = 0x8000;
			rebit = 1;
			re = rw - 1;
			break;
		case 113:
			rw = 10;
			rmsk = 0x7fff;
			rmbit = 0x4000;
			rebit = 0x8000;
			re = rw;
			break;
		case 64:
			rw = 7;
			rmsk = 0xffff;
			rmbit = 0x8000;
			rebit = 1;
			re = rw-1;
			break;
/* For DEC arithmetic */
		case 56:
			rw = 6;
			rmsk = 0xff;
			rmbit = 0x80;
			rebit = 0x100;
			re = rw;
			break;
		case 53:
			rw = 6;
			rmsk = 0x7ff;
			rmbit = 0x0400;
			rebit = 0x800;
			re = rw;
			break;
		case 24:
			rw = 4;
			rmsk = 0xff;
			rmbit = 0x80;
			rebit = 0x100;
			re = rw;
			break;
		}
	rbit[re] = rebit;
	rlast = rndprc;
	}

/* Shift down 1 temporarily if the data structure has an implied
 * most significant bit and the number is denormal.
 * For rndprc = 64 or NBITS, there is no implied bit.
 * But Intel long double denormals lose one bit of significance even so.
 */
#ifdef IBMPC
if( (exp <= 0) && (rndprc != NBITS) )
#else
if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
#endif
	{
	lost |= s[NI-1] & 1;
	eshdn1(s);
	}
/* Clear out all bits below the rounding bit,
 * remembering in r if any were nonzero.
 */
r = s[rw] & rmsk;
if( rndprc < NBITS )
	{
	i = rw + 1;
	while( i < NI )
		{
		if( s[i] )
			r |= 1;
		s[i] = 0;
		++i;
		}
	}
s[rw] &= ~rmsk;
if( (r & rmbit) != 0 )
	{
	if( r == rmbit )
		{
		if( lost == 0 )
			{ /* round to even */
			if( (s[re] & rebit) == 0 )
				goto mddone;
			}
		else
			{
			if( subflg != 0 )
				goto mddone;
			}
		}
	eaddm( rbit, s );
	}
mddone:
#ifdef IBMPC
if( (exp <= 0) && (rndprc != NBITS) )
#else
if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
#endif
	{
	eshup1(s);
	}
if( s[2] != 0 )
	{ /* overflow on roundoff */
	eshdn1(s);
	exp += 1;
	}
mdfin:
s[NI-1] = 0;
if( exp >= 32767L )
	{
#ifndef INFINITIES
overf:
#endif
#ifdef INFINITIES
	s[1] = 32767;
	for( i=2; i<NI-1; i++ )
		s[i] = 0;
#else
	s[1] = 32766;
	s[2] = 0;
	for( i=M+1; i<NI-1; i++ )
		s[i] = 0xffff;
	s[NI-1] = 0;
	if( (rndprc < 64) || (rndprc == 113) )
		{
		s[rw] &= ~rmsk;
		if( rndprc == 24 )
			{
			s[5] = 0;
			s[6] = 0;
			}
		}
#endif
	return;
	}
if( exp < 0 )
	s[1] = 0;
else
	s[1] = (unsigned short )exp;
}



/*
;	Subtract external format numbers.
;
;	unsigned short a[NE], b[NE], c[NE];
;	esub( a, b, c );	 c = b - a
*/

static int subflg = 0;

void esub( a, b, c )
unsigned short *a, *b, *c;
{

#ifdef NANS
if( eisnan(a) )
	{
	emov (a, c);
	return;
	}
if( eisnan(b) )
	{
	emov(b,c);
	return;
	}
/* Infinity minus infinity is a NaN.
 * Test for subtracting infinities of the same sign.
 */
if( eisinf(a) && eisinf(b) && ((eisneg (a) ^ eisneg (b)) == 0))
	{
	mtherr( "esub", DOMAIN );
	enan( c, NBITS );
	return;
	}
#endif
subflg = 1;
eadd1( a, b, c );
}


/*
;	Add.
;
;	unsigned short a[NE], b[NE], c[NE];
;	eadd( a, b, c );	 c = b + a
*/
void eadd( a, b, c )
unsigned short *a, *b, *c;
{

#ifdef NANS
/* NaN plus anything is a NaN. */
if( eisnan(a) )
	{
	emov(a,c);
	return;
	}
if( eisnan(b) )
	{
	emov(b,c);
	return;
	}
/* Infinity minus infinity is a NaN.
 * Test for adding infinities of opposite signs.
 */
if( eisinf(a) && eisinf(b)
	&& ((eisneg(a) ^ eisneg(b)) != 0) )
	{
	mtherr( "eadd", DOMAIN );
	enan( c, NBITS );
	return;
	}
#endif
subflg = 0;
eadd1( a, b, c );
}

void eadd1( a, b, c )
unsigned short *a, *b, *c;
{
unsigned short ai[NI], bi[NI], ci[NI];
int i, lost, j, k;
long lt, lta, ltb;

#ifdef INFINITIES
if( eisinf(a) )
	{
	emov(a,c);
	if( subflg )
		eneg(c);
	return;
	}
if( eisinf(b) )
	{
	emov(b,c);
	return;
	}
#endif
emovi( a, ai );
emovi( b, bi );
if( subflg )
	ai[0] = ~ai[0];

/* compare exponents */
lta = ai[E];
ltb = bi[E];
lt = lta - ltb;
if( lt > 0L )
	{	/* put the larger number in bi */
	emovz( bi, ci );
	emovz( ai, bi );
	emovz( ci, ai );
	ltb = bi[E];
	lt = -lt;
	}
lost = 0;
if( lt != 0L )
	{
	if( lt < (long )(-NBITS-1) )
		goto done;	/* answer same as larger addend */
	k = (int )lt;
	lost = eshift( ai, k ); /* shift the smaller number down */
	}
else
	{
/* exponents were the same, so must compare significands */
	i = ecmpm( ai, bi );
	if( i == 0 )
		{ /* the numbers are identical in magnitude */
		/* if different signs, result is zero */
		if( ai[0] != bi[0] )
			{
			eclear(c);
			return;
			}
		/* if same sign, result is double */
		/* double denomalized tiny number */
		if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) )
			{
			eshup1( bi );
			goto done;
			}
		/* add 1 to exponent unless both are zero! */
		for( j=1; j<NI-1; j++ )
			{
			if( bi[j] != 0 )
				{
				ltb += 1;
				if( ltb >= 0x7fff )
					{
					eclear(c);
					einfin(c);
					if( ai[0] != 0 )
						eneg(c);
					return;
					}
				break;
				}
			}
		bi[E] = (unsigned short )ltb;
		goto done;
		}
	if( i > 0 )
		{	/* put the larger number in bi */
		emovz( bi, ci );
		emovz( ai, bi );
		emovz( ci, ai );
		}
	}
if( ai[0] == bi[0] )
	{
	eaddm( ai, bi );
	subflg = 0;
	}
else
	{
	esubm( ai, bi );
	subflg = 1;
	}
emdnorm( bi, lost, subflg, ltb, 64 );

done:
emovo( bi, c );
}



/*
;	Divide.
;
;	unsigned short a[NE], b[NE], c[NE];
;	ediv( a, b, c );	c = b / a
*/
void ediv( a, b, c )
unsigned short *a, *b, *c;
{
unsigned short ai[NI], bi[NI];
int i, sign;
long lt, lta, ltb;

/* IEEE says if result is not a NaN, the sign is "-" if and only if
   operands have opposite signs -- but flush -0 to 0 later if not IEEE.  */
sign = eisneg(a) ^ eisneg(b);

#ifdef NANS
/* Return any NaN input. */
if( eisnan(a) )
	{
	emov(a,c);
	return;
	}
if( eisnan(b) )
	{
	emov(b,c);
	return;
	}
/* Zero over zero, or infinity over infinity, is a NaN. */
if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0))
	|| (eisinf (a) && eisinf (b)) )
	{
	mtherr( "ediv", DOMAIN );
	enan( c, NBITS );
	return;
	}
#endif
/* Infinity over anything else is infinity. */
#ifdef INFINITIES
if( eisinf(b) )
	{
	einfin(c);
	goto divsign;
	}
if( eisinf(a) )
	{
	eclear(c);
	goto divsign;
	}
#endif
emovi( a, ai );
emovi( b, bi );
lta = ai[E];
ltb = bi[E];
if( bi[E] == 0 )
	{ /* See if numerator is zero. */
	for( i=1; i<NI-1; i++ )
		{
		if( bi[i] != 0 )
			{
			ltb -= enormlz( bi );
			goto dnzro1;
			}
		}
	eclear(c);
	goto divsign;
	}
dnzro1:

if( ai[E] == 0 )
	{	/* possible divide by zero */
	for( i=1; i<NI-1; i++ )
		{
		if( ai[i] != 0 )
			{
			lta -= enormlz( ai );
			goto dnzro2;
			}
		}
	einfin(c);
	mtherr( "ediv", SING );
	goto divsign;
	}
dnzro2:

i = edivm( ai, bi );
/* calculate exponent */
lt = ltb - lta + EXONE;
emdnorm( bi, i, 0, lt, 64 );
emovo( bi, c );