35 /* HYPOT(X,Y)
36  * RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
42  *	copysign(x,y)
48  *	1. replace x by |x| and y by |y|, and swap x and
49  *	   y if y > x (hence x is never smaller than y).
50  *	2. Hypot(x,y) is computed by:
51  *	   Case I, x/y > 2
53  *				       y
54  *		hypot = x + -----------------------------
56  *			    sqrt ( 1 + [x/y]  )  +  x/y
58  *	   Case II, x/y <= 2
59  *				                   y
60  *		hypot = x + --------------------------------------------------
62  *				     			[x/y]   -  2
63  *			   (sqrt(2)+1) + (x-y)/y + -----------------------------
65  *			    			  sqrt ( 1 + [x/y]  )  + sqrt(2)
70  *	hypot(x,y) is INF if x or y is +INF or -INF; else
71  *	hypot(x,y) is NAN if x or y is NAN.
74  * 	hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
77  *      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
91 vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
95 ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
105 hypot(double x, double y)  in hypot()  argument
108 		      small=1.0E-18;	/* fl(1+small)==1 */  in hypot()
114 	    if(finite(y))  in hypot()
117 		y=copysign(y,one);  in hypot()
118 		if(y > x)  in hypot()
119 		    { t=x; x=y; y=t; }  in hypot()
121 		if(y == zero) return(x);  in hypot()
123 		if(exp-(int)logb(y) > ibig )  in hypot()
127 	    /* start computing sqrt(x^2 + y^2) */  in hypot()
128 		r=x-y;  in hypot()
129 		if(r>y) { 	/* x/y > 2 */  in hypot()
130 		    r=x/y;  in hypot()
132 		else {		/* 1 <= x/y <= 2 */  in hypot()
133 		    r/=y; t=r*(r+2.0);  in hypot()
137 		r=y/r;  in hypot()
142 	    else if(y==y)   	   /* y is +-INF */  in hypot()
143 		     return(copysign(y,one));  in hypot()
145 		     return(y);	   /* y is NaN and x is finite */  in hypot()
147 	else if(x==x) 		   /* x is +-INF */  in hypot()
149 	else if(finite(y))  in hypot()
150 	         return(x);		   /* x is NaN, y is finite */  in hypot()
152 	else if(y!=y) return(y);  /* x and y is NaN */  in hypot()
154 	else return(copysign(y,one));   /* y is INF */  in hypot()
164  *	hypot(x,y)
167  *	cabs(z) = hypot(x,y) .
170 struct complex { double x, y; };  member
176 	return hypot(z.x,z.y);
183 	return hypot(z->x,z->y);
186 /* A faster but less accurate version of cabs(x,y) */
188 double hypot(x,y)
189 double x, y;
192 		      small=1.0E-18;	/* fl(1+small)==1 */
198 	    if(finite(y))
201 		y=copysign(y,one);
202 		if(y > x)
203 		    { temp=x; x=y; y=temp; }
205 		if(y == zero) return(x);
207 		x=scalb(x,-exp);
208 		if(exp-(int)logb(y) > ibig )
211 		else y=scalb(y,-exp);
212 		return(scalb(sqrt(x*x+y*y),exp));
215 	    else if(y==y)   	   /* y is +-INF */
216 		     return(copysign(y,one));
218 		     return(y);	   /* y is NaN and x is finite */
220 	else if(x==x) 		   /* x is +-INF */
222 	else if(finite(y))
223 	         return(x);		   /* x is NaN, y is finite */
224 	else if(y!=y) return(y);  	/* x and y is NaN */
225 	else return(copysign(y,one));   /* y is INF */