support.c

<B>Digital的Unix操作系统VAX 4.2源码</B>

double sqrt(x)
double x;
{
        double q,s,b,r;
        double logb(),scalb();
        double t,zero=0.0;
        int m,n,i,finite();
#ifdef VAX
        int k=54;
#else   /* IEEE */
        int k=51;
#endif

    /* sqrt(NaN) is NaN, sqrt(+-0) = +-0 */
#ifndef vax
        if(x!=x) return(x);
#endif
        if(x==zero) return(x);

    /* sqrt(negative) is invalid */
        if(x<zero) {errno = EDOM; return(zero);}

    /* sqrt(INF) is INF */
        if(!finite(x)) return(x);               

    /* scale x to [1,4) */
        n=logb(x);
        x=scalb(x,-n);
        if((m=logb(x))!=0) x=scalb(x,-m);       /* subnormal number */
        m += n; 
        n = m/2;
        if((n+n)!=m) {x *= 2; m -=1; n=m/2;}

    /* generate sqrt(x) bit by bit (accumulating in q) */
            q=1.0; s=4.0; x -= 1.0; r=1;
            for(i=1;i<=k;i++) {
                t=s+1; x *= 4; r /= 2;
                if(t<=x) {
                    s=t+t+2, x -= t; q += r;}
                else
                    s *= 2;
                }
            
    /* generate the last bit and determine the final rounding */
            r/=2; x *= 4; 
            if(x==zero) goto end; 100+r; /* trigger inexact flag */
            if(s<x) {
                q+=r; x -=s; s += 2; s *= 2; x *= 4;
                t = (x-s)-5; 
                b=1.0+3*r/4; if(b==1.0) goto end; /* b==1 : Round-to-zero */
                b=1.0+r/4;   if(b>1.0) t=1;	/* b>1 : Round-to-(+INF) */
                if(t>=0) q+=r; }	      /* else: Round-to-nearest */
            else { 
                s *= 2; x *= 4; 
                t = (x-s)-1; 
                b=1.0+3*r/4; if(b==1.0) goto end;
                b=1.0+r/4;   if(b>1.0) t=1;
                if(t>=0) q+=r; }
            
end:        return(scalb(q,n));
}

#if 0
/* DREM(X,Y)
 * RETURN X REM Y =X-N*Y, N=[X/Y] ROUNDED (ROUNDED TO EVEN IN THE HALF WAY CASE)
 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 * INTENDED FOR ASSEMBLY LANGUAGE
 * CODED IN C BY K.C. NG, 3/23/85, 4/8/85.
 *
 * Warning: this code should not get compiled in unless ALL of
 * the following machine-dependent routines are supplied.
 * 
 * Required machine dependent functions (not on a VAX):
 *     swapINX(i): save inexact flag and reset it to "i"
 *     swapENI(e): save inexact enable and reset it to "e"
 */

double drem(x,y)	
double x,y;
{

#ifdef NATIONAL		/* order of words in floating point number */
	static n0=3,n1=2,n2=1,n3=0;
#else /* VAX, SUN, ZILOG */
	static n0=0,n1=1,n2=2,n3=3;
#endif

    	static unsigned short mexp =0x7ff0, m25 =0x0190, m57 =0x0390;
	static double zero=0.0;
	double hy,y1,t,t1;
	short k;
	long n;
	int i,e; 
	unsigned short xexp,yexp, *px  =(unsigned short *) &x  , 
	      		nx,nf,	  *py  =(unsigned short *) &y  ,
	      		sign,	  *pt  =(unsigned short *) &t  ,
	      			  *pt1 =(unsigned short *) &t1 ;

	xexp = px[n0] & mexp ;	/* exponent of x */
	yexp = py[n0] & mexp ;	/* exponent of y */
	sign = px[n0] &0x8000;	/* sign of x     */

/* return NaN if x is NaN, or y is NaN, or x is INF, or y is zero */
	if(x!=x) return(x); if(y!=y) return(y);	     /* x or y is NaN */
	if( xexp == mexp )   return(zero/zero);      /* x is INF */
	if(y==zero) return(y/y);

/* save the inexact flag and inexact enable in i and e respectively
 * and reset them to zero
 */
	i=swapINX(0);	e=swapENI(0);	

/* subnormal number */
	nx=0;
	if(yexp==0) {t=1.0,pt[n0]+=m57; y*=t; nx=m57;}

/* if y is tiny (biased exponent <= 57), scale up y to y*2**57 */
	if( yexp <= m57 ) {py[n0]+=m57; nx+=m57; yexp+=m57;}

	nf=nx;
	py[n0] &= 0x7fff;	
	px[n0] &= 0x7fff;

/* mask off the least significant 27 bits of y */
	t=y; pt[n3]=0; pt[n2]&=0xf800; y1=t;

/* LOOP: argument reduction on x whenever x > y */
loop:
	while ( x > y )
	{
	    t=y;
	    t1=y1;
	    xexp=px[n0]&mexp;	  /* exponent of x */
	    k=xexp-yexp-m25;
	    if(k>0) 	/* if x/y >= 2**26, scale up y so that x/y < 2**26 */
		{pt[n0]+=k;pt1[n0]+=k;}
	    n=x/t; x=(x-n*t1)-n*(t-t1);
	}	
    /* end while (x > y) */

	if(nx!=0) {t=1.0; pt[n0]+=nx; x*=t; nx=0; goto loop;}

/* final adjustment */

	hy=y/2.0;
	if(x>hy||((x==hy)&&n%2==1)) x-=y; 
	px[n0] ^= sign;
	if(nf!=0) { t=1.0; pt[n0]-=nf; x*=t;}

/* restore inexact flag and inexact enable */
	swapINX(i); swapENI(e);	

	return(x);	
}
#endif

#if 0
/* SQRT
 * RETURN CORRECTLY ROUNDED (ACCORDING TO THE ROUNDING MODE) SQRT
 * FOR IEEE DOUBLE PRECISION ONLY, INTENDED FOR ASSEMBLY LANGUAGE
 * CODED IN C BY K.C. NG, 3/22/85.
 *
 * Warning: this code should not get compiled in unless ALL of
 * the following machine-dependent routines are supplied.
 * 
 * Required machine dependent functions:
 *     swapINX(i)  ...return the status of INEXACT flag and reset it to "i"
 *     swapRM(r)   ...return the current Rounding Mode and reset it to "r"
 *     swapENI(e)  ...return the status of inexact enable and reset it to "e"
 *     addc(t)     ...perform t=t+1 regarding t as a 64 bit unsigned integer
 *     subc(t)     ...perform t=t-1 regarding t as a 64 bit unsigned integer
 */

static unsigned long table[] = {
0, 1204, 3062, 5746, 9193, 13348, 18162, 23592, 29598, 36145, 43202, 50740,
58733, 67158, 75992, 85215, 83599, 71378, 60428, 50647, 41945, 34246, 27478,
21581, 16499, 12183, 8588, 5674, 3403, 1742, 661, 130, };

double newsqrt(x)
double x;
{
        double y,z,t,addc(),subc(),b54=134217728.*134217728.; /* b54=2**54 */
        long mx,scalx,mexp=0x7ff00000;
        int i,j,r,e,swapINX(),swapRM(),swapENI();       
        unsigned long *py=(unsigned long *) &y   ,
                      *pt=(unsigned long *) &t   ,
                      *px=(unsigned long *) &x   ;
#ifdef NATIONAL         /* ordering of word in a floating point number */
        int n0=1, n1=0; 
#else
        int n0=0, n1=1; 
#endif
/* Rounding Mode:  RN ...round-to-nearest 
 *                 RZ ...round-towards 0
 *                 RP ...round-towards +INF
 *		   RM ...round-towards -INF
 */
        int RN=0,RZ=1,RP=2,RM=3;/* machine dependent: work on a Zilog Z8070
                                 * and a National 32081 & 16081
                                 */

/* exceptions */
	if(x!=x||x==0.0) return(x);  /* sqrt(NaN) is NaN, sqrt(+-0) = +-0 */
	if(x<0) return((x-x)/(x-x)); /* sqrt(negative) is invalid */
        if((mx=px[n0]&mexp)==mexp) return(x);  /* sqrt(+INF) is +INF */

/* save, reset, initialize */
        e=swapENI(0);   /* ...save and reset the inexact enable */
        i=swapINX(0);   /* ...save INEXACT flag */
        r=swapRM(RN);   /* ...save and reset the Rounding Mode to RN */
        scalx=0;

/* subnormal number, scale up x to x*2**54 */
        if(mx==0) {x *= b54 ; scalx-=0x01b00000;}

/* scale x to avoid intermediate over/underflow:
 * if (x > 2**512) x=x/2**512; if (x < 2**-512) x=x*2**512 */
        if(mx>0x5ff00000) {px[n0] -= 0x20000000; scalx+= 0x10000000;}
        if(mx<0x1ff00000) {px[n0] += 0x20000000; scalx-= 0x10000000;}

/* magic initial approximation to almost 8 sig. bits */
        py[n0]=(px[n0]>>1)+0x1ff80000;
        py[n0]=py[n0]-table[(py[n0]>>15)&31];

/* Heron's rule once with correction to improve y to almost 18 sig. bits */
        t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0;

/* triple to almost 56 sig. bits; now y approx. sqrt(x) to within 1 ulp */
        t=y*y; z=t;  pt[n0]+=0x00100000; t+=z; z=(x-z)*y; 
        t=z/(t+x) ;  pt[n0]+=0x00100000; y+=t;

/* twiddle last bit to force y correctly rounded */ 
        swapRM(RZ);     /* ...set Rounding Mode to round-toward-zero */
        swapINX(0);     /* ...clear INEXACT flag */
        swapENI(e);     /* ...restore inexact enable status */
        t=x/y;          /* ...chopped quotient, possibly inexact */
        j=swapINX(i);   /* ...read and restore inexact flag */
        if(j==0) { if(t==y) goto end; else t=subc(t); }  /* ...t=t-ulp */
        b54+0.1;        /* ..trigger inexact flag, sqrt(x) is inexact */
        if(r==RN) t=addc(t);            /* ...t=t+ulp */
        else if(r==RP) { t=addc(t);y=addc(y);}/* ...t=t+ulp;y=y+ulp; */
        y=y+t;                          /* ...chopped sum */
        py[n0]=py[n0]-0x00100000;       /* ...correctly rounded sqrt(x) */
end:    py[n0]=py[n0]+scalx;            /* ...scale back y */
        swapRM(r);                      /* ...restore Rounding Mode */
        return(y);
}
#endif