1 /* e_hypotl.c -- long double version of e_hypot.c.
2 * Conversion to long double by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com.
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
14 * ====================================================
17 #if defined(LIBM_SCCS) && !defined(lint)
18 static char rcsid
[] = "$NetBSD: $";
21 /* __ieee754_hypotl(x,y)
24 * If (assume round-to-nearest) z=x*x+y*y
25 * has error less than sqrt(2)/2 ulp, than
26 * sqrt(z) has error less than 1 ulp (exercise).
28 * So, compute sqrt(x*x+y*y) with some care as
29 * follows to get the error below 1 ulp:
32 * (if possible, set rounding to round-to-nearest)
34 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
35 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
37 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
38 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
39 * y1= y with lower 32 bits chopped, y2 = y-y1.
41 * NOTE: scaling may be necessary if some argument is too
45 * hypot(x,y) is INF if x or y is +INF or -INF; else
46 * hypot(x,y) is NAN if x or y is NAN.
49 * hypot(x,y) returns sqrt(x^2+y^2) with error less
50 * than 1 ulps (units in the last place)
54 #include "math_private.h"
57 long double __ieee754_hypotl(long double x
, long double y
)
59 long double __ieee754_hypotl(x
,y
)
63 long double a
,b
,t1
,t2
,y1
,y2
,w
;
66 GET_LDOUBLE_EXP(ea
,x
);
68 GET_LDOUBLE_EXP(eb
,y
);
70 if(eb
> ea
) {a
=y
;b
=x
;j
=ea
; ea
=eb
;eb
=j
;} else {a
=x
;b
=y
;}
71 SET_LDOUBLE_EXP(a
,ea
); /* a <- |a| */
72 SET_LDOUBLE_EXP(b
,eb
); /* b <- |b| */
73 if((ea
-eb
)>0x46) {return a
+b
;} /* x/y > 2**70 */
75 if(ea
> 0x5f3f) { /* a>2**8000 */
76 if(ea
== 0x7fff) { /* Inf or NaN */
77 u_int32_t exp
,high
,low
;
78 w
= a
+b
; /* for sNaN */
79 GET_LDOUBLE_WORDS(exp
,high
,low
,a
);
80 if(((high
&0x7fffffff)|low
)==0) w
= a
;
81 GET_LDOUBLE_WORDS(exp
,high
,low
,b
);
82 if(((eb
^0x7fff)|(high
&0x7fffffff)|low
)==0) w
= b
;
85 /* scale a and b by 2**-9600 */
86 ea
-= 0x2580; eb
-= 0x2580; k
+= 9600;
87 SET_LDOUBLE_EXP(a
,ea
);
88 SET_LDOUBLE_EXP(b
,eb
);
90 if(eb
< 0x20bf) { /* b < 2**-8000 */
91 if(eb
== 0) { /* subnormal b or 0 */
92 u_int32_t exp
,high
,low
;
93 GET_LDOUBLE_WORDS(exp
,high
,low
,b
);
94 if((high
|low
)==0) return a
;
95 SET_LDOUBLE_WORDS(t1
, 0x7ffd, 0, 0); /* t1=2^16382 */
99 } else { /* scale a and b by 2^9600 */
100 ea
+= 0x2580; /* a *= 2^9600 */
101 eb
+= 0x2580; /* b *= 2^9600 */
103 SET_LDOUBLE_EXP(a
,ea
);
104 SET_LDOUBLE_EXP(b
,eb
);
107 /* medium size a and b */
111 GET_LDOUBLE_MSW(high
,a
);
112 SET_LDOUBLE_WORDS(t1
,ea
,high
,0);
114 w
= __ieee754_sqrtl(t1
*t1
-(b
*(-b
)-t2
*(a
+t1
)));
117 GET_LDOUBLE_MSW(high
,b
);
119 SET_LDOUBLE_WORDS(y1
,eb
,high
,0);
121 GET_LDOUBLE_MSW(high
,a
);
122 SET_LDOUBLE_WORDS(t1
,ea
+1,high
,0);
124 w
= __ieee754_sqrtl(t1
*y1
-(w
*(-w
)-(t1
*y2
+t2
*b
)));
129 GET_LDOUBLE_EXP(exp
,t1
);
130 SET_LDOUBLE_EXP(t1
,exp
+k
);