|
/* ieee.c
*
* Extended precision IEEE binary floating point arithmetic routines
*
* Numbers are stored in C language as arrays of 16-bit unsigned
* short integers. The arguments of the routines are pointers to
* the arrays.
*
*
* External e type data structure, simulates Intel 8087 chip
* temporary real format but possibly with a larger significand:
*
* NE-1 significand words (least significant word first,
* most significant bit is normally set)
* exponent (value = EXONE for 1.0,
* top bit is the sign)
*
*
* Internal data structure of a number (a "word" is 16 bits):
*
* ei[0] sign word (0 for positive, 0xffff for negative)
* ei[1] biased exponent (value = EXONE for the number 1.0)
* ei[2] high guard word (always zero after normalization)
* ei[3]
* to ei[NI-2] significand (NI-4 significand words,
* most significant word first,
* most significant bit is set)
* ei[NI-1] low guard word (0x8000 bit is rounding place)
*
*
*
* Routines for external format numbers
*
* asctoe( string, e ) ASCII string to extended double e type
* asctoe64( string, &d ) ASCII string to long double
* asctoe53( string, &d ) ASCII string to double
* asctoe24( string, &f ) ASCII string to single
* asctoeg( string, e, prec ) ASCII string to specified precision
* e24toe( &f, e ) IEEE single precision to e type
* e53toe( &d, e ) IEEE double precision to e type
* e64toe( &d, e ) IEEE long double precision to e type
* eabs(e) absolute value
* eadd( a, b, c ) c = b + a
* eclear(e) e = 0
* 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.
* ediv( a, b, c ) c = b / a
* efloor( a, b ) truncate to integer, toward -infinity
* efrexp( a, exp, s ) extract exponent and significand
* eifrac( e, &l, frac ) e to long integer and e type fraction
* euifrac( e, &l, frac ) e to unsigned long integer and e type fraction
* einfin( e ) set e to infinity, leaving its sign alone
* eldexp( a, n, b ) multiply by 2**n
* emov( a, b ) b = a
* emul( a, b, c ) c = b * a
* eneg(e) e = -e
* eround( a, b ) b = nearest integer value to a
* esub( a, b, c ) c = b - a
* e24toasc( &f, str, n ) single to ASCII string, n digits after decimal
* e53toasc( &d, str, n ) double to ASCII string, n digits after decimal
* e64toasc( &d, str, n ) long double to ASCII string
* etoasc( e, str, n ) e to ASCII string, n digits after decimal
* etoe24( e, &f ) convert e type to IEEE single precision
* etoe53( e, &d ) convert e type to IEEE double precision
* etoe64( e, &d ) convert e type to IEEE long double precision
* ltoe( &l, e ) long (32 bit) integer to e type
* ultoe( &l, e ) unsigned long (32 bit) integer to e type
* eisneg( e ) 1 if sign bit of e != 0, else 0
* eisinf( e ) 1 if e has maximum exponent (non-IEEE)
* or is infinite (IEEE)
* eisnan( e ) 1 if e is a NaN
* esqrt( a, b ) b = square root of a
*
*
* Routines for internal format numbers
*
* eaddm( ai, bi ) add significands, bi = bi + ai
* ecleaz(ei) ei = 0
* ecleazs(ei) set ei = 0 but leave its sign alone
* ecmpm( ai, bi ) compare significands, return 1, 0, or -1
* edivm( ai, bi ) divide significands, bi = bi / ai
* emdnorm(ai,l,s,exp) normalize and round off
* emovi( a, ai ) convert external a to internal ai
* emovo( ai, a ) convert internal ai to external a
* emovz( ai, bi ) bi = ai, low guard word of bi = 0
* emulm( ai, bi ) multiply significands, bi = bi * ai
* enormlz(ei) left-justify the significand
* eshdn1( ai ) shift significand and guards down 1 bit
* eshdn8( ai ) shift down 8 bits
* eshdn6( ai ) shift down 16 bits
* eshift( ai, n ) shift ai n bits up (or down if n < 0)
* eshup1( ai ) shift significand and guards up 1 bit
* eshup8( ai ) shift up 8 bits
* eshup6( ai ) shift up 16 bits
* esubm( ai, bi ) subtract significands, bi = bi - ai
*
*
* The result is always normalized and rounded to NI-4 word precision
* after each arithmetic operation.
*
* Exception flags are NOT fully supported.
*
* Define INFINITY in mconf.h for support of infinity; otherwise a
* saturation arithmetic is implemented.
*
* Define NANS for support of Not-a-Number items; otherwise the
* arithmetic will never produce a NaN output, and might be confused
* by a NaN input.
* If NaN's are supported, the output of ecmp(a,b) is -2 if
* either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
* may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
* if in doubt.
* Signaling NaN's are NOT supported; they are treated the same
* as quiet NaN's.
*
* Denormals are always supported here where appropriate (e.g., not
* for conversion to DEC numbers).
*/
/*
* Revision history:
*
* 5 Jan 84 PDP-11 assembly language version
* 2 Mar 86 fixed bug in asctoq()
* 6 Dec 86 C language version
* 30 Aug 88 100 digit version, improved rounding
* 15 May 92 80-bit long double support
*
* Author: S. L. Moshier.
*/
#include <stdio.h>
#include "mconf.h"
#include "ehead.h"
/* Change UNK into something else. */
#ifdef UNK
#undef UNK
#if BIGENDIAN
#define MIEEE 1
#else
#define IBMPC 1
#endif
#endif
/* NaN's require infinity support. */
#ifdef NANS
#ifndef INFINITY
#define INFINITY
#endif
#endif
/* This handles 64-bit long ints. */
#define LONGBITS (8 * sizeof(long))
/* Control register for rounding precision.
* This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
*/
int rndprc = NBITS;
extern int rndprc;
#ifdef ANSIPROT
extern void eaddm ( unsigned short *, unsigned short * );
extern void esubm ( unsigned short *, unsigned short * );
extern void emdnorm ( unsigned short *, int, int, long, int );
extern void asctoeg ( char *, unsigned short *, int );
extern void enan ( unsigned short *, int );
extern void asctoe24 ( char *, unsigned short * );
extern void asctoe53 ( char *, unsigned short * );
extern void asctoe64 ( char *, unsigned short * );
extern void asctoe113 ( char *, unsigned short * );
extern void eremain ( unsigned short *, unsigned short *, unsigned short * );
extern void einit ( void );
extern void eiremain ( unsigned short *, unsigned short * );
extern int ecmp ( unsigned short *, unsigned short * );
extern int edivm ( unsigned short *, unsigned short * );
extern int emulm ( unsigned short *, unsigned short * );
extern int eisneg ( unsigned short * );
extern int eisinf ( unsigned short * );
extern void emovi ( unsigned short *, unsigned short * );
extern void emovo ( unsigned short *, unsigned short * );
extern void emovz ( unsigned short *, unsigned short * );
extern void ecleaz ( unsigned short * );
extern void eadd1 ( unsigned short *, unsigned short *, unsigned short * );
extern int eisnan ( unsigned short * );
extern int eiisnan ( unsigned short * );
static void toe24( unsigned short *, unsigned short * );
static void toe53( unsigned short *, unsigned short * );
static void toe64( unsigned short *, unsigned short * );
static void toe113( unsigned short *, unsigned short * );
void einfin ( unsigned short * );
void eshdn1 ( unsigned short * );
void eshup1 ( unsigned short * );
void eshup6 ( unsigned short * );
void eshdn6 ( unsigned short * );
void eshup8 ( unsigned short * );
void eshdn8 ( unsigned short * );
void m16m ( unsigned short, unsigned short *, unsigned short * );
int ecmpm ( unsigned short *, unsigned short * );
int enormlz ( unsigned short * );
void ecleazs ( unsigned short * );
int eshift ( unsigned short *, int );
void emov ( unsigned short *, unsigned short * );
void eneg ( unsigned short * );
void eclear ( unsigned short * );
void efloor ( unsigned short *, unsigned short * );
void eadd ( unsigned short *, unsigned short *, unsigned short * );
void esub ( unsigned short *, unsigned short *, unsigned short * );
void ediv ( unsigned short *, unsigned short *, unsigned short * );
void emul ( unsigned short *, unsigned short *, unsigned short * );
void e24toe ( unsigned short *, unsigned short * );
void e53toe ( unsigned short *, unsigned short * );
void e64toe ( unsigned short *, unsigned short * );
void e113toe ( unsigned short *, unsigned short * );
void etoasc ( unsigned short *, char *, int );
static int eiisinf ( unsigned short * );
#else
void eaddm(), esubm(), emdnorm(), asctoeg(), enan();
static void toe24(), toe53(), toe64(), toe113();
void eremain(), einit(), eiremain();
int ecmpm(), edivm(), emulm(), eisneg(), eisinf();
void emovi(), emovo(), emovz(), ecleaz(), eadd1();
/* void etodec(), todec(), dectoe(); */
int eisnan(), eiisnan(), ecmpm(), enormlz(), eshift();
void einfin(), eshdn1(), eshup1(), eshup6(), eshdn6();
void eshup8(), eshdn8(), m16m();
void eadd(), esub(), ediv(), emul();
void ecleazs(), emov(), eneg(), eclear(), efloor();
void e24toe(), e53toe(), e64toe(), e113toe(), etoasc();
static int eiisinf();
#endif
void einit()
{
}
/*
; Clear out entire external format number.
;
; unsigned short x[];
; eclear( x );
*/
void eclear( x )
register unsigned short *x;
{
register int i;
for( i=0; i<NE; i++ )
*x++ = 0;
}
/* Move external format number from a to b.
*
* emov( a, b );
*/
void emov( a, b )
register unsigned short *a, *b;
{
register int i;
for( i=0; i<NE; i++ )
*b++ = *a++;
}
/*
; Absolute value of external format number
;
; short x[NE];
; eabs( x );
*/
void eabs(x)
unsigned short x[]; /* x is the memory address of a short */
{
x[NE-1] &= 0x7fff; /* sign is top bit of last word of external format */
}
/*
; Negate external format number
;
; unsigned short x[NE];
; eneg( x );
*/
void eneg(x)
unsigned short x[];
{
#ifdef NANS
if( eisnan(x) )
return;
#endif
x[NE-1] ^= 0x8000; /* Toggle the sign bit */
}
/* Return 1 if external format number is negative,
* else return zero.
*/
int eisneg(x)
unsigned short x[];
{
#ifdef NANS
if( eisnan(x) )
return( 0 );
#endif
if( x[NE-1] & 0x8000 )
return( 1 );
else
return( 0 );
}
/* Return 1 if external format number has maximum possible exponent,
* else return zero.
*/
int eisinf(x)
unsigned short x[];
{
if( (x[NE-1] & 0x7fff) == 0x7fff )
{
#ifdef NANS
if( eisnan(x) )
return( 0 );
#endif
return( 1 );
}
else
return( 0 );
}
/* Check if e-type number is not a number.
*/
int eisnan(x)
unsigned short x[];
{
#ifdef NANS
int i;
/* NaN has maximum exponent */
if( (x[NE-1] & 0x7fff) != 0x7fff )
return (0);
/* ... and non-zero significand field. */
for( i=0; i<NE-1; i++ )
{
if( *x++ != 0 )
return (1);
}
#endif
return (0);
}
/*
; Fill entire number, including exponent and significand, with
; largest possible number. These programs implement a saturation
; value that is an ordinary, legal number. A special value
; "infinity" may also be implemented; this would require tests
; for that value and implementation of special rules for arithmetic
; operations involving inifinity.
*/
void einfin(x)
register unsigned short *x;
{
register int i;
#ifdef INFINITY
for( i=0; i<NE-1; i++ )
*x++ = 0;
*x |= 32767;
#else
for( i=0; i<NE-1; i++ )
*x++ = 0xffff;
*x |= 32766;
if( rndprc < NBITS )
{
if (rndprc == 113)
{
*(x - 9) = 0;
*(x - 8) = 0;
}
if( rndprc == 64 )
{
*(x-5) = 0;
}
if( rndprc == 53 )
{
*(x-4) = 0xf800;
}
else
{
*(x-4) = 0;
*(x-3) = 0;
*(x-2) = 0xff00;
}
}
#endif
}
/* Move in external format number,
* converting it to internal format.
*/
void emovi( a, b )
unsigned short *a, *b;
{
register unsigned short *p, *q;
int i;
q = b;
p = a + (NE-1); /* point to last word of external number */
/* get the sign bit */
if( *p & 0x8000 )
*q++ = 0xffff;
else
*q++ = 0;
/* get the exponent */
*q = *p--;
*q++ &= 0x7fff; /* delete the sign bit */
#ifdef INFINITY
if( (*(q-1) & 0x7fff) == 0x7fff )
{
#ifdef NANS
if( eisnan(a) )
{
*q++ = 0;
for( i=3; i<NI; i++ )
*q++ = *p--;
return;
}
#endif
for( i=2; i<NI; i++ )
*q++ = 0;
return;
}
#endif
/* clear high guard word */
*q++ = 0;
/* move in the significand */
for( i=0; i<NE-1; i++ )
*q++ = *p--;
/* clear low guard word */
*q = 0;
}
/* Move internal format number out,
* converting it to external format.
*/
void emovo( a, b )
unsigned short *a, *b;
{
register unsigned short *p, *q;
unsigned short i;
p = a;
q = b + (NE-1); /* point to output exponent */
/* combine sign and exponent */
i = *p++;
if( i )
*q-- = *p++ | 0x8000;
else
*q-- = *p++;
#ifdef INFINITY
if( *(p-1) == 0x7fff )
{
#ifdef NANS
if( eiisnan(a) )
{
enan( b, NBITS );
return;
}
#endif
einfin(b);
return;
}
#endif
/* skip over guard word */
++p;
/* move the significand */
for( i=0; i<NE-1; i++ )
*q-- = *p++;
}
/* Clear out internal format number.
*/
void ecleaz( xi )
register unsigned short *xi;
{
register int i;
for( i=0; i<NI; i++ )
*xi++ = 0;
}
/* same, but don't touch the sign. */
void ecleazs( xi )
register unsigned short *xi;
{
register int i;
++xi;
for(i=0; i<NI-1; i++)
*xi++ = 0;
}
/* Move internal format number from a to b.
*/
void emovz( a, b )
register unsigned short *a, *b;
{
register int i;
for( i=0; i<NI-1; i++ )
*b++ = *a++;
/* clear low guard word */
*b = 0;
}
/* Return nonzero if internal format number is a NaN.
*/
int eiisnan (x)
unsigned short x[];
{
int i;
if( (x[E] & 0x7fff) == 0x7fff )
{
for( i=M+1; i<NI; i++ )
{
if( x[i] != 0 )
return(1);
}
}
return(0);
}
#ifdef INFINITY
/* Return nonzero if internal format number is infinite. */
static int
eiisinf (x)
unsigned short x[];
{
#ifdef NANS
if (eiisnan (x))
return (0);
#endif
if ((x[E] & 0x7fff) == 0x7fff)
return (1);
return (0);
}
#endif
/*
; Compare significands of numbers in internal format.
; Guard words are included in the comparison.
;
; unsigned short a[NI], b[NI];
; cmpm( a, b );
;
; for the significands:
; returns +1 if a > b
; 0 if a == b
; -1 if a < b
*/
int ecmpm( a, b )
register unsigned short *a, *b;
{
int i;
a += M; /* skip up to significand area */
b += M;
for( i=M; i<NI; i++ )
{
if( *a++ != *b++ )
goto difrnt;
}
return(0);
difrnt:
if( *(--a) > *(--b) )
return(1);
else
return(-1);
}
/*
; Shift significand down by 1 bit
*/
void eshdn1(x)
register unsigned short *x;
{
register unsigned short bits;
int i;
x += M; /* point to significand area */
bits = 0;
for( i=M; i<NI; i++ )
{
if( *x & 1 )
bits |= 1;
*x >>= 1;
if( bits & 2 )
*x |= 0x8000;
bits <<= 1;
++x;
}
}
/*
; Shift significand up by 1 bit
*/
void eshup1(x)
register unsigned short *x;
{
register unsigned short bits;
int i;
x += NI-1;
bits = 0;
for( i=M; i<NI; i++ )
{
if( *x & 0x8000 )
bits |= 1;
*x <<= 1;
if( bits & 2 )
*x |= 1;
bits <<= 1;
--x;
}
}
/*
; Shift significand down by 8 bits
*/
void eshdn8(x)
register unsigned short *x;
{
register unsigned short newbyt, oldbyt;
int i;
x += M;
oldbyt = 0;
for( i=M; i<NI; i++ )
{
newbyt = *x << 8;
*x >>= 8;
*x |= oldbyt;
oldbyt = newbyt;
++x;
}
}
/*
; Shift significand up by 8 bits
*/
void eshup8(x)
register unsigned short *x;
{
int i;
register unsigned short newbyt, oldbyt;
x += NI-1;
oldbyt = 0;
for( i=M; i<NI; i++ )
{
newbyt = *x >> 8;
*x <<= 8;
*x |= oldbyt;
oldbyt = newbyt;
--x;
}
}
/*
; Shift significand up by 16 bits
*/
void eshup6(x)
register unsigned short *x;
{
int i;
register unsigned short *p;
p = x + M;
x += M + 1;
for( i=M; i<NI-1; i++ )
*p++ = *x++;
*p = 0;
}
/*
; Shift significand down by 16 bits
*/
void eshdn6(x)
register unsigned short *x;
{
int i;
register unsigned short *p;
x += NI-1;
p = x + 1;
for( i=M; i<NI-1; i++ )
*(--p) = *(--x);
*(--p) = 0;
}
/*
; Add significands
; x + y replaces y
*/
void eaddm( x, y )
unsigned short *x, *y;
{
register unsigned long a;
int i;
unsigned int carry;
x += NI-1;
y += NI-1;
carry = 0;
for( i=M; i<NI; i++ )
{
a = (unsigned long )(*x) + (unsigned long )(*y) + carry;
if( a & 0x10000 )
carry = 1;
else
carry = 0;
*y = (unsigned short )a;
--x;
--y;
}
}
/*
; Subtract significands
; y - x replaces y
*/
void esubm( x, y )
unsigned short *x, *y;
{
unsigned long a;
int i;
unsigned int carry;
x += NI-1;
y += NI-1;
carry = 0;
for( i=M; i<NI; i++ )
{
a = (unsigned long )(*y) - (unsigned long )(*x) - carry;
if( a & 0x10000 )
carry = 1;
else
carry = 0;
*y = (unsigned short )a;
--x;
--y;
}
}
/* Divide significands */
static unsigned short equot[NI] = {0}; /* was static */
#if 0
int edivm( den, num )
unsigned short den[], num[];
{
int i;
register unsigned short *p, *q;
unsigned short j;
p = &equot[0];
*p++ = num[0];
*p++ = num[1];
for( i=M; i<NI; i++ )
{
*p++ = 0;
}
/* Use faster compare and subtraction if denominator
* has only 15 bits of significane.
*/
p = &den[M+2];
if( *p++ == 0 )
{
for( i=M+3; i<NI; i++ )
{
if( *p++ != 0 )
goto fulldiv;
}
if( (den[M+1] & 1) != 0 )
goto fulldiv;
eshdn1(num);
eshdn1(den);
p = &den[M+1];
q = &num[M+1];
for( i=0; i<NBITS+2; i++ )
{
if( *p <= *q )
{
*q -= *p;
j = 1;
}
else
{
j = 0;
}
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 * ((unsigned long)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 INFINITY
if( j > NBITS )
{
ecleazs( s );
return;
}
#endif
exp -= j;
#ifndef INFINITY
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 INFINITY
overf:
#endif
#ifdef INFINITY
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 INFINITY
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 )
{
/* This could overflow, but let emovo take care of that. */
ltb += 1;
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 INFINITY
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 );
divsign:
if( sign )
*(c+(NE-1)) |= 0x8000;
else
*(c+(NE-1)) &= ~0x8000;
}
/*
; Multiply.
;
; unsigned short a[NE], b[NE], c[NE];
; emul( a, b, c ); c = b * a
*/
void emul( a, b, c )
unsigned short *a, *b, *c;
{
unsigned short ai[NI], bi[NI];
int i, j, 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
/* NaN times anything is the same NaN. */
if( eisnan(a) )
{
emov(a,c);
return;
}
if( eisnan(b) )
{
emov(b,c);
return;
}
/* Zero times infinity is a NaN. */
if( (eisinf(a) && (ecmp(b,ezero) == 0))
|| (eisinf(b) && (ecmp(a,ezero) == 0)) )
{
mtherr( "emul", DOMAIN );
enan( c, NBITS );
return;
}
#endif
/* Infinity times anything else is infinity. */
#ifdef INFINITY
if( eisinf(a) || eisinf(b) )
{
einfin(c);
goto mulsign;
}
#endif
emovi( a, ai );
emovi( b, bi );
lta = ai[E];
ltb = bi[E];
if( ai[E] == 0 )
{
for( i=1; i<NI-1; i++ )
{
if( ai[i] != 0 )
{
lta -= enormlz( ai );
goto mnzer1;
}
}
eclear(c);
goto mulsign;
}
mnzer1:
if( bi[E] == 0 )
{
for( i=1; i<NI-1; i++ )
{
if( bi[i] != 0 )
{
ltb -= enormlz( bi );
goto mnzer2;
}
}
eclear(c);
goto mulsign;
}
mnzer2:
/* Multiply significands */
j = emulm( ai, bi );
/* calculate exponent */
lt = lta + ltb - (EXONE - 1);
emdnorm( bi, j, 0, lt, 64 );
emovo( bi, c );
/* IEEE says sign is "-" if and only if operands have opposite signs. */
mulsign:
if( sign )
*(c+(NE-1)) |= 0x8000;
else
*(c+(NE-1)) &= ~0x8000;
}
/*
; Convert IEEE double precision to e type
; double d;
; unsigned short x[N+2];
; e53toe( &d, x );
*/
void e53toe( pe, y )
unsigned short *pe, *y;
{
#ifdef DEC
dectoe( pe, y ); /* see etodec.c */
#else
register unsigned short r;
register unsigned short *p, *e;
unsigned short yy[NI];
int denorm, k;
e = pe;
denorm = 0; /* flag if denormalized number */
ecleaz(yy);
#ifdef IBMPC
e += 3;
#endif
r = *e;
yy[0] = 0;
if( r & 0x8000 )
yy[0] = 0xffff;
yy[M] = (r & 0x0f) | 0x10;
r &= ~0x800f; /* strip sign and 4 significand bits */
#ifdef INFINITY
if( r == 0x7ff0 )
{
#ifdef NANS
#ifdef IBMPC
if( ((pe[3] & 0xf) != 0) || (pe[2] != 0)
|| (pe[1] != 0) || (pe[0] != 0) )
{
enan( y, NBITS );
return;
}
#else
if( ((pe[0] & 0xf) != 0) || (pe[1] != 0)
|| (pe[2] != 0) || (pe[3] != 0) )
{
enan( y, NBITS );
return;
}
#endif
#endif /* NANS */
eclear( y );
einfin( y );
if( yy[0] )
eneg(y);
return;
}
#endif
r >>= 4;
/* If zero exponent, then the significand is denormalized.
* So, take back the understood high significand bit. */
if( r == 0 )
{
denorm = 1;
yy[M] &= ~0x10;
}
r += EXONE - 01777;
yy[E] = r;
p = &yy[M+1];
#ifdef IBMPC
*p++ = *(--e);
*p++ = *(--e);
*p++ = *(--e);
#endif
#ifdef MIEEE
++e;
*p++ = *e++;
*p++ = *e++;
*p++ = *e++;
#endif
(void )eshift( yy, -5 );
if( denorm )
{ /* if zero exponent, then normalize the significand */
if( (k = enormlz(yy)) > NBITS )
ecleazs(yy);
else
yy[E] -= (unsigned short )(k-1);
}
emovo( yy, y );
#endif /* not DEC */
}
void e64toe( pe, y )
unsigned short *pe, *y;
{
unsigned short yy[NI];
unsigned short *p, *q, *e;
int i;
e = pe;
p = yy;
for( i=0; i<NE-5; i++ )
*p++ = 0;
#ifdef IBMPC
for( i=0; i<5; i++ )
*p++ = *e++;
#endif
#ifdef DEC
for( i=0; i<5; i++ )
*p++ = *e++;
#endif
#ifdef MIEEE
p = &yy[0] + (NE-1);
*p-- = *e++;
++e;
for( i=0; i<4; i++ )
*p-- = *e++;
#endif
#ifdef IBMPC
/* For Intel long double, shift denormal significand up 1
-- but only if the top significand bit is zero. */
if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0)
{
unsigned short temp[NI+1];
emovi(yy, temp);
eshup1(temp);
emovo(temp,y);
return;
}
#endif
#ifdef INFINITY
/* Point to the exponent field. */
p = &yy[NE-1];
if( *p == 0x7fff )
{
#ifdef NANS
#ifdef IBMPC
for( i=0; i<4; i++ )
{
if((i != 3 && pe[i] != 0)
/* Check for Intel long double infinity pattern. */
|| (i == 3 && pe[i] != 0x8000))
{
enan( y, NBITS );
return;
}
}
#else
for( i=1; i<=4; i++ )
{
if( pe[i] != 0 )
{
enan( y, NBITS );
return;
}
}
#endif
#endif /* NANS */
eclear( y );
einfin( y );
if( *p & 0x8000 )
eneg(y);
return;
}
#endif
p = yy;
q = y;
for( i=0; i<NE; i++ )
*q++ = *p++;
}
void e113toe(pe,y)
unsigned short *pe, *y;
{
register unsigned short r;
unsigned short *e, *p;
unsigned short yy[NI];
int i;
e = pe;
ecleaz(yy);
#ifdef IBMPC
e += 7;
#endif
r = *e;
yy[0] = 0;
if( r & 0x8000 )
yy[0] = 0xffff;
r &= 0x7fff;
#ifdef INFINITY
if( r == 0x7fff )
{
#ifdef NANS
#ifdef IBMPC
for( i=0; i<7; i++ )
{
if( pe[i] != 0 )
{
enan( y, NBITS );
return;
}
}
#else
for( i=1; i<8; i++ )
{
if( pe[i] != 0 )
{
enan( y, NBITS );
return;
}
}
#endif
#endif /* NANS */
eclear( y );
einfin( y );
if( *e & 0x8000 )
eneg(y);
return;
}
#endif /* INFINITY */
yy[E] = r;
p = &yy[M + 1];
#ifdef IBMPC
for( i=0; i<7; i++ )
*p++ = *(--e);
#endif
#ifdef MIEEE
++e;
for( i=0; i<7; i++ )
*p++ = *e++;
#endif
/* If denormal, remove the implied bit; else shift down 1. */
if( r == 0 )
{
yy[M] = 0;
}
else
{
yy[M] = 1;
eshift( yy, -1 );
}
emovo(yy,y);
}
/*
; Convert IEEE single precision to e type
; float d;
; unsigned short x[N+2];
; dtox( &d, x );
*/
void e24toe( pe, y )
unsigned short *pe, *y;
{
register unsigned short r;
register unsigned short *p, *e;
unsigned short yy[NI];
int denorm, k;
e = pe;
denorm = 0; /* flag if denormalized number */
ecleaz(yy);
#ifdef IBMPC
e += 1;
#endif
#ifdef DEC
e += 1;
#endif
r = *e;
yy[0] = 0;
if( r & 0x8000 )
yy[0] = 0xffff;
yy[M] = (r & 0x7f) | 0200;
r &= ~0x807f; /* strip sign and 7 significand bits */
#ifdef INFINITY
if( r == 0x7f80 )
{
#ifdef NANS
#ifdef MIEEE
if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) )
{
enan( y, NBITS );
return;
}
#else
if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) )
{
enan( y, NBITS );
return;
}
#endif
#endif /* NANS */
eclear( y );
einfin( y );
if( yy[0] )
eneg(y);
return;
}
#endif
r >>= 7;
/* If zero exponent, then the significand is denormalized.
* So, take back the understood high significand bit. */
if( r == 0 )
{
denorm = 1;
yy[M] &= ~0200;
}
r += EXONE - 0177;
yy[E] = r;
p = &yy[M+1];
#ifdef IBMPC
*p++ = *(--e);
#endif
#ifdef DEC
*p++ = *(--e);
#endif
#ifdef MIEEE
++e;
*p++ = *e++;
#endif
(void )eshift( yy, -8 );
if( denorm )
{ /* if zero exponent, then normalize the significand */
if( (k = enormlz(yy)) > NBITS )
ecleazs(yy);
else
yy[E] -= (unsigned short )(k-1);
}
emovo( yy, y );
}
void etoe113(x,e)
unsigned short *x, *e;
{
unsigned short xi[NI];
long exp;
int rndsav;
#ifdef NANS
if( eisnan(x) )
{
enan( e, 113 );
return;
}
#endif
emovi( x, xi );
exp = (long )xi[E];
#ifdef INFINITY
if( eisinf(x) )
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 113;
emdnorm( xi, 0, 0, exp, 64 );
rndprc = rndsav;
nonorm:
toe113 (xi, e);
}
/* move out internal format to ieee long double */
static void toe113(a,b)
unsigned short *a, *b;
{
register unsigned short *p, *q;
unsigned short i;
#ifdef NANS
if( eiisnan(a) )
{
enan( b, 113 );
return;
}
#endif
p = a;
#ifdef MIEEE
q = b;
#else
q = b + 7; /* point to output exponent */
#endif
/* If not denormal, delete the implied bit. */
if( a[E] != 0 )
{
eshup1 (a);
}
/* combine sign and exponent */
i = *p++;
#ifdef MIEEE
if( i )
*q++ = *p++ | 0x8000;
else
*q++ = *p++;
#else
if( i )
*q-- = *p++ | 0x8000;
else
*q-- = *p++;
#endif
/* skip over guard word */
++p;
/* move the significand */
#ifdef MIEEE
for (i = 0; i < 7; i++)
*q++ = *p++;
#else
for (i = 0; i < 7; i++)
*q-- = *p++;
#endif
}
void etoe64( x, e )
unsigned short *x, *e;
{
unsigned short xi[NI];
long exp;
int rndsav;
#ifdef NANS
if( eisnan(x) )
{
enan( e, 64 );
return;
}
#endif
emovi( x, xi );
exp = (long )xi[E]; /* adjust exponent for offset */
#ifdef INFINITY
if( eisinf(x) )
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 64;
emdnorm( xi, 0, 0, exp, 64 );
rndprc = rndsav;
nonorm:
toe64( xi, e );
}
/* move out internal format to ieee long double */
static void toe64( a, b )
unsigned short *a, *b;
{
register unsigned short *p, *q;
unsigned short i;
#ifdef NANS
if( eiisnan(a) )
{
enan( b, 64 );
return;
}
#endif
#ifdef IBMPC
/* Shift Intel denormal significand down 1. */
if( a[E] == 0 )
eshdn1(a);
#endif
p = a;
#ifdef MIEEE
q = b;
#else
q = b + 4; /* point to output exponent */
#if 1
/* NOTE: if data type is 96 bits wide, clear the last word here. */
*(q+1)= 0;
#endif
#endif
/* combine sign and exponent */
i = *p++;
#ifdef MIEEE
if( i )
*q++ = *p++ | 0x8000;
else
*q++ = *p++;
*q++ = 0;
#else
if( i )
*q-- = *p++ | 0x8000;
else
*q-- = *p++;
#endif
/* skip over guard word */
++p;
/* move the significand */
#ifdef MIEEE
for( i=0; i<4; i++ )
*q++ = *p++;
#else
#ifdef INFINITY
if (eiisinf (a))
{
/* Intel long double infinity. */
*q-- = 0x8000;
*q-- = 0;
*q-- = 0;
*q = 0;
return;
}
#endif
for( i=0; i<4; i++ )
*q-- = *p++;
#endif
}
/*
; e type to IEEE double precision
; double d;
; unsigned short x[NE];
; etoe53( x, &d );
*/
#ifdef DEC
void etoe53( x, e )
unsigned short *x, *e;
{
etodec( x, e ); /* see etodec.c */
}
static void toe53( x, y )
unsigned short *x, *y;
{
todec( x, y );
}
#else
void etoe53( x, e )
unsigned short *x, *e;
{
unsigned short xi[NI];
long exp;
int rndsav;
#ifdef NANS
if( eisnan(x) )
{
enan( e, 53 );
return;
}
#endif
emovi( x, xi );
exp = (long )xi[E] - (EXONE - 0x3ff); /* adjust exponent for offsets */
#ifdef INFINITY
if( eisinf(x) )
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 53;
emdnorm( xi, 0, 0, exp, 64 );
rndprc = rndsav;
nonorm:
toe53( xi, e );
}
static void toe53( x, y )
unsigned short *x, *y;
{
unsigned short i;
unsigned short *p;
#ifdef NANS
if( eiisnan(x) )
{
enan( y, 53 );
return;
}
#endif
p = &x[0];
#ifdef IBMPC
y += 3;
#endif
*y = 0; /* output high order */
if( *p++ )
*y = 0x8000; /* output sign bit */
i = *p++;
if( i >= (unsigned int )2047 )
{ /* Saturate at largest number less than infinity. */
#ifdef INFINITY
*y |= 0x7ff0;
#ifdef IBMPC
*(--y) = 0;
*(--y) = 0;
*(--y) = 0;
#endif
#ifdef MIEEE
++y;
*y++ = 0;
*y++ = 0;
*y++ = 0;
#endif
#else
*y |= (unsigned short )0x7fef;
#ifdef IBMPC
*(--y) = 0xffff;
*(--y) = 0xffff;
*(--y) = 0xffff;
#endif
#ifdef MIEEE
++y;
*y++ = 0xffff;
*y++ = 0xffff;
*y++ = 0xffff;
#endif
#endif
return;
}
if( i == 0 )
{
(void )eshift( x, 4 );
}
else
{
i <<= 4;
(void )eshift( x, 5 );
}
i |= *p++ & (unsigned short )0x0f; /* *p = xi[M] */
*y |= (unsigned short )i; /* high order output already has sign bit set */
#ifdef IBMPC
*(--y) = *p++;
*(--y) = *p++;
*(--y) = *p;
#endif
#ifdef MIEEE
++y;
*y++ = *p++;
*y++ = *p++;
*y++ = *p++;
#endif
}
#endif /* not DEC */
/*
; e type to IEEE single precision
; float d;
; unsigned short x[N+2];
; xtod( x, &d );
*/
void etoe24( x, e )
unsigned short *x, *e;
{
long exp;
unsigned short xi[NI];
int rndsav;
#ifdef NANS
if( eisnan(x) )
{
enan( e, 24 );
return;
}
#endif
emovi( x, xi );
exp = (long )xi[E] - (EXONE - 0177); /* adjust exponent for offsets */
#ifdef INFINITY
if( eisinf(x) )
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 24;
emdnorm( xi, 0, 0, exp, 64 );
rndprc = rndsav;
nonorm:
toe24( xi, e );
}
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 INFINITY
*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 );
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 );
expon -= 1;
}
}
else
{
emovi( y, w );
for( i=0; i<NDEC+1; i++ )
{
if( (w[NI-1] & 0x7) != 0 )
break;
/* multiply by 10 */
emovz( w, u );
eshdn1( u );
eshdn1( u );
eaddm( w, u );
u[1] += 3;
while( u[2] != 0 )
{
eshdn1(u);
u[1] += 1;
}
if( u[NI-1] != 0 )
break;
if( eone[NE-1] <= u[1] )
break;
emovz( u, w );
expon -= 1;
}
emovo( w, y );
}
k = -MAXP;
p = &emtens[0][0];
r = &etens[0][0];
emov( y, w );
emov( eone, t );
while( ecmp( eone, w ) > 0 )
{
if( ecmp( p, w ) >= 0 )
{
emul( r, w, w );
emul( r, t, t );
expon += k;
}
k /= 2;
if( k == 0 )
break;
p += NE;
r += NE;
}
ediv( t, eone, t );
}
isone:
/* Find the first (leading) digit. */
emovi( t, w );
emovz( w, t );
emovi( y, w );
emovz( w, y );
eiremain( t, y );
digit = equot[NI-1];
while( (digit == 0) && (ecmp(y,ezero) != 0) )
{
eshup1( y );
emovz( y, u );
eshup1( u );
eshup1( u );
eaddm( u, y );
eiremain( t, y );
digit = equot[NI-1];
expon -= 1;
}
s = string;
if( sign )
*s++ = '-';
else
*s++ = ' ';
/* Examine number of digits requested by caller. */
if( ndigs < 0 )
ndigs = 0;
if( ndigs > NDEC )
ndigs = NDEC;
if( digit == 10 )
{
*s++ = '1';
*s++ = '.';
if( ndigs > 0 )
{
*s++ = '0';
ndigs -= 1;
}
expon += 1;
}
else
{
*s++ = (char )digit + '0';
*s++ = '.';
}
/* Generate digits after the decimal point. */
for( k=0; k<=ndigs; k++ )
{
/* multiply current number by 10, without normalizing */
eshup1( y );
emovz( y, u );
eshup1( u );
eshup1( u );
eaddm( u, y );
eiremain( t, y );
*s++ = (char )equot[NI-1] + '0';
}
digit = equot[NI-1];
--s;
ss = s;
/* round off the ASCII string */
if( digit > 4 )
{
/* Test for critical rounding case in ASCII output. */
if( digit == 5 )
{
emovo( y, t );
if( ecmp(t,ezero) != 0 )
goto roun; /* round to nearest */
if( (*(s-1) & 1) == 0 )
goto doexp; /* round to even */
}
/* Round up and propagate carry-outs */
roun:
--s;
k = *s & 0x7f;
/* Carry out to most significant digit? */
if( k == '.' )
{
--s;
k = *s;
k += 1;
*s = (char )k;
/* Most significant digit carries to 10? */
if( k > '9' )
{
expon += 1;
*s = '1';
}
goto doexp;
}
/* Round up and carry out from less significant digits */
k += 1;
*s = (char )k;
if( k > '9' )
{
*s = '0';
goto roun;
}
}
doexp:
/*
if( expon >= 0 )
sprintf( ss, "e+%d", expon );
else
sprintf( ss, "e%d", expon );
*/
sprintf( ss, "E%d", expon );
bxit:
rndprc = rndsav;
}
/*
; ASCTOQ
; ASCTOQ.MAC LATEST REV: 11 JAN 84
; SLM, 3 JAN 78
;
; Convert ASCII string to quadruple precision floating point
;
; Numeric input is free field decimal number
; with max of 15 digits with or without
; decimal point entered as ASCII from teletype.
; Entering E after the number followed by a second
; number causes the second number to be interpreted
; as a power of 10 to be multiplied by the first number
; (i.e., "scientific" notation).
;
; Usage:
; asctoq( string, q );
*/
/* ASCII to single */
void asctoe24( s, y )
char *s;
unsigned short *y;
{
asctoeg( s, y, 24 );
}
/* ASCII to double */
void asctoe53( s, y )
char *s;
unsigned short *y;
{
#ifdef DEC
asctoeg( s, y, 56 );
#else
asctoeg( s, y, 53 );
#endif
}
/* ASCII to long double */
void asctoe64( s, y )
char *s;
unsigned short *y;
{
asctoeg( s, y, 64 );
}
/* ASCII to 128-bit long double */
void asctoe113 (s, y)
char *s;
unsigned short *y;
{
asctoeg( s, y, 113 );
}
/* ASCII to super double */
void asctoe( s, y )
char *s;
unsigned short *y;
{
asctoeg( s, y, NBITS );
}
/* Space to make a copy of the input string: */
static char lstr[82] = {0};
void asctoeg( ss, y, oprec )
char *ss;
unsigned short *y;
int oprec;
{
unsigned short yy[NI], xt[NI], tt[NI];
int esign, decflg, sgnflg, nexp, exp, prec, lost;
int k, trail, c, rndsav;
long lexp;
unsigned short nsign, *p;
char *sp, *s;
/* Copy the input string. */
s = ss;
while( *s == ' ' ) /* skip leading spaces */
++s;
sp = lstr;
for( k=0; k<79; k++ )
{
if( (*sp++ = *s++) == '\0' )
break;
}
*sp = '\0';
s = lstr;
rndsav = rndprc;
rndprc = NBITS; /* Set to full precision */
lost = 0;
nsign = 0;
decflg = 0;
sgnflg = 0;
nexp = 0;
exp = 0;
prec = 0;
ecleaz( yy );
trail = 0;
nxtcom:
k = *s - '0';
if( (k >= 0) && (k <= 9) )
{
/* Ignore leading zeros */
if( (prec == 0) && (decflg == 0) && (k == 0) )
goto donchr;
/* Identify and strip trailing zeros after the decimal point. */
if( (trail == 0) && (decflg != 0) )
{
sp = s;
while( (*sp >= '0') && (*sp <= '9') )
++sp;
/* Check for syntax error */
c = *sp & 0x7f;
if( (c != 'e') && (c != 'E') && (c != '\0')
&& (c != '\n') && (c != '\r') && (c != ' ')
&& (c != ',') )
goto error;
--sp;
while( *sp == '0' )
*sp-- = 'z';
trail = 1;
if( *s == 'z' )
goto donchr;
}
/* If enough digits were given to more than fill up the yy register,
* continuing until overflow into the high guard word yy[2]
* guarantees that there will be a roundoff bit at the top
* of the low guard word after normalization.
*/
if( yy[2] == 0 )
{
if( decflg )
nexp += 1; /* count digits after decimal point */
eshup1( yy ); /* multiply current number by 10 */
emovz( yy, xt );
eshup1( xt );
eshup1( xt );
eaddm( xt, yy );
ecleaz( xt );
xt[NI-2] = (unsigned short )k;
eaddm( xt, yy );
}
else
{
/* Mark any lost non-zero digit. */
lost |= k;
/* Count lost digits before the decimal point. */
if (decflg == 0)
nexp -= 1;
}
prec += 1;
goto donchr;
}
switch( *s )
{
case 'z':
break;
case 'E':
case 'e':
goto expnt;
case '.': /* decimal point */
if( decflg )
goto error;
++decflg;
break;
case '-':
nsign = 0xffff;
if( sgnflg )
goto error;
++sgnflg;
break;
case '+':
if( sgnflg )
goto error;
++sgnflg;
break;
case ',':
case ' ':
case '\0':
case '\n':
case '\r':
goto daldone;
case 'i':
case 'I':
goto infinite;
default:
error:
#ifdef NANS
enan( yy, NI*16 );
#else
mtherr( "asctoe", DOMAIN );
ecleaz(yy);
#endif
goto aexit;
}
donchr:
++s;
goto nxtcom;
/* Exponent interpretation */
expnt:
esign = 1;
exp = 0;
++s;
/* check for + or - */
if( *s == '-' )
{
esign = -1;
++s;
}
if( *s == '+' )
++s;
while( (*s >= '0') && (*s <= '9') )
{
exp *= 10;
exp += *s++ - '0';
if (exp > 4977)
{
if (esign < 0)
goto zero;
else
goto infinite;
}
}
if( esign < 0 )
exp = -exp;
if( exp > 4932 )
{
infinite:
ecleaz(yy);
yy[E] = 0x7fff; /* infinity */
goto aexit;
}
if( exp < -4977 )
{
zero:
ecleaz(yy);
goto aexit;
}
daldone:
nexp = exp - nexp;
/* Pad trailing zeros to minimize power of 10, per IEEE spec. */
while( (nexp > 0) && (yy[2] == 0) )
{
emovz( yy, xt );
eshup1( xt );
eshup1( xt );
eaddm( yy, xt );
eshup1( xt );
if( xt[2] != 0 )
break;
nexp -= 1;
emovz( xt, yy );
}
if( (k = enormlz(yy)) > NBITS )
{
ecleaz(yy);
goto aexit;
}
lexp = (EXONE - 1 + NBITS) - k;
emdnorm( yy, lost, 0, lexp, 64 );
/* convert to external format */
/* Multiply by 10**nexp. If precision is 64 bits,
* the maximum relative error incurred in forming 10**n
* for 0 <= n <= 324 is 8.2e-20, at 10**180.
* For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947.
* For 0 >= n >= -999, it is -1.55e-19 at 10**-435.
*/
lexp = yy[E];
if( nexp == 0 )
{
k = 0;
goto expdon;
}
esign = 1;
if( nexp < 0 )
{
nexp = -nexp;
esign = -1;
if( nexp > 4096 )
{ /* Punt. Can't handle this without 2 divides. */
emovi( etens[0], tt );
lexp -= tt[E];
k = edivm( tt, yy );
lexp += EXONE;
nexp -= 4096;
}
}
p = &etens[NTEN][0];
emov( eone, xt );
exp = 1;
do
{
if( exp & nexp )
emul( p, xt, xt );
p -= NE;
exp = exp + exp;
}
while( exp <= MAXP );
emovi( xt, tt );
if( esign < 0 )
{
lexp -= tt[E];
k = edivm( tt, yy );
lexp += EXONE;
}
else
{
lexp += tt[E];
k = emulm( tt, yy );
lexp -= EXONE - 1;
}
expdon:
/* Round and convert directly to the destination type */
if( oprec == 53 )
lexp -= EXONE - 0x3ff;
else if( oprec == 24 )
lexp -= EXONE - 0177;
#ifdef DEC
else if( oprec == 56 )
lexp -= EXONE - 0201;
#endif
rndprc = oprec;
emdnorm( yy, k, 0, lexp, 64 );
aexit:
rndprc = rndsav;
yy[0] = nsign;
switch( oprec )
{
#ifdef DEC
case 56:
todec( yy, y ); /* see etodec.c */
break;
#endif
case 53:
toe53( yy, y );
break;
case 24:
toe24( yy, y );
break;
case 64:
toe64( yy, y );
break;
case 113:
toe113( yy, y );
break;
case NBITS:
emovo( yy, y );
break;
}
}
/* y = largest integer not greater than x
* (truncated toward minus infinity)
*
* unsigned short x[NE], y[NE]
*
* efloor( x, y );
*/
static unsigned short bmask[] = {
0xffff,
0xfffe,
0xfffc,
0xfff8,
0xfff0,
0xffe0,
0xffc0,
0xff80,
0xff00,
0xfe00,
0xfc00,
0xf800,
0xf000,
0xe000,
0xc000,
0x8000,
0x0000,
};
void efloor( x, y )
unsigned short x[], y[];
{
register unsigned short *p;
int e, expon, i;
unsigned short f[NE];
emov( x, f ); /* leave in external format */
expon = (int )f[NE-1];
e = (expon & 0x7fff) - (EXONE - 1);
if( e <= 0 )
{
eclear(y);
goto isitneg;
}
/* number of bits to clear out */
e = NBITS - e;
emov( f, y );
if( e <= 0 )
return;
p = &y[0];
while( e >= 16 )
{
*p++ = 0;
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.186 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|
