1 /* e_hypotl.c -- long double version of e_hypot.c.
2 * Conversion to long double by Jakub Jelinek, jakub@redhat.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
13 * ====================================================
16 /* __ieee754_hypotl(x,y)
19 * If (assume round-to-nearest) z=x*x+y*y
20 * has error less than sqrtl(2)/2 ulp, than
21 * sqrtl(z) has error less than 1 ulp (exercise).
23 * So, compute sqrtl(x*x+y*y) with some care as
24 * follows to get the error below 1 ulp:
27 * (if possible, set rounding to round-to-nearest)
29 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
30 * where x1 = x with lower 64 bits cleared, x2 = x-x1; else
32 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
33 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1,
34 * y1= y with lower 64 bits chopped, y2 = y-y1.
36 * NOTE: scaling may be necessary if some argument is too
40 * hypotl(x,y) is INF if x or y is +INF or -INF; else
41 * hypotl(x,y) is NAN if x or y is NAN.
44 * hypotl(x,y) returns sqrtl(x^2+y^2) with error less
45 * than 1 ulps (units in the last place)
49 #include <math_private.h>
52 __ieee754_hypotl(_Float128 x
, _Float128 y
)
54 _Float128 a
,b
,t1
,t2
,y1
,y2
,w
;
57 GET_LDOUBLE_MSW64(ha
,x
);
58 ha
&= 0x7fffffffffffffffLL
;
59 GET_LDOUBLE_MSW64(hb
,y
);
60 hb
&= 0x7fffffffffffffffLL
;
61 if(hb
> ha
) {a
=y
;b
=x
;j
=ha
; ha
=hb
;hb
=j
;} else {a
=x
;b
=y
;}
62 SET_LDOUBLE_MSW64(a
,ha
); /* a <- |a| */
63 SET_LDOUBLE_MSW64(b
,hb
); /* b <- |b| */
64 if((ha
-hb
)>0x78000000000000LL
) {return a
+b
;} /* x/y > 2**120 */
66 if(ha
> 0x5f3f000000000000LL
) { /* a>2**8000 */
67 if(ha
>= 0x7fff000000000000LL
) { /* Inf or NaN */
69 w
= a
+b
; /* for sNaN */
70 if (issignaling (a
) || issignaling (b
))
72 GET_LDOUBLE_LSW64(low
,a
);
73 if(((ha
&0xffffffffffffLL
)|low
)==0) w
= a
;
74 GET_LDOUBLE_LSW64(low
,b
);
75 if(((hb
^0x7fff000000000000LL
)|low
)==0) w
= b
;
78 /* scale a and b by 2**-9600 */
79 ha
-= 0x2580000000000000LL
;
80 hb
-= 0x2580000000000000LL
; k
+= 9600;
81 SET_LDOUBLE_MSW64(a
,ha
);
82 SET_LDOUBLE_MSW64(b
,hb
);
84 if(hb
< 0x20bf000000000000LL
) { /* b < 2**-8000 */
85 if(hb
<= 0x0000ffffffffffffLL
) { /* subnormal b or 0 */
87 GET_LDOUBLE_LSW64(low
,b
);
88 if((hb
|low
)==0) return a
;
90 SET_LDOUBLE_MSW64(t1
,0x7ffd000000000000LL
); /* t1=2^16382 */
94 GET_LDOUBLE_MSW64 (ha
, a
);
95 GET_LDOUBLE_MSW64 (hb
, b
);
105 } else { /* scale a and b by 2^9600 */
106 ha
+= 0x2580000000000000LL
; /* a *= 2^9600 */
107 hb
+= 0x2580000000000000LL
; /* b *= 2^9600 */
109 SET_LDOUBLE_MSW64(a
,ha
);
110 SET_LDOUBLE_MSW64(b
,hb
);
113 /* medium size a and b */
117 SET_LDOUBLE_MSW64(t1
,ha
);
119 w
= __ieee754_sqrtl(t1
*t1
-(b
*(-b
)-t2
*(a
+t1
)));
123 SET_LDOUBLE_MSW64(y1
,hb
);
126 SET_LDOUBLE_MSW64(t1
,ha
+0x0001000000000000LL
);
128 w
= __ieee754_sqrtl(t1
*y1
-(w
*(-w
)-(t1
*y2
+t2
*b
)));
133 GET_LDOUBLE_MSW64(high
,t1
);
134 SET_LDOUBLE_MSW64(t1
,high
+(k
<<48));
136 math_check_force_underflow_nonneg (w
);
140 strong_alias (__ieee754_hypotl
, __hypotl_finite
)