📄 ieee.c
字号:
}
}
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 );
for( j=0; j<NE-1; j++ )
{
if( t[j] != w[j] )
goto noint;
}
emov( t, u );
expon += (int )m;
noint:
p += NE;
m >>= 1;
}
while( m != 0 );
/* Rescale from integer significand */
u[NE-1] += y[NE-1] - (unsigned int )(EXONE + NBITS - 1);
emov( u, y );
/* Find power of 10 */
emov( eone, t );
m = MAXP;
p = &etens[0][0];
while( ecmp( ten, u ) <= 0 )
{
if( ecmp( p, u ) <= 0 )
{
ediv( p, u, u );
emul( p, t, t );
expon += (int )m;
}
m >>= 1;
if( m == 0 )
break;
p += NE;
}
}
else
{ /* Number is less than 1.0 */
/* Pad significand with trailing decimal zeros. */
if( y[NE-1] == 0 )
{
while( (y[NE-2] & 0x8000) == 0 )
{
emul( ten, y, y );
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