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git.ipfire.org Git - thirdparty/glibc.git/blob - sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
1 /* @(#)e_hypotl.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
13 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid
[] = "$NetBSD: e_hypotl.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
17 /* __ieee754_hypotl(x,y)
20 * If (assume round-to-nearest) z=x*x+y*y
21 * has error less than sqrtl(2)/2 ulp, than
22 * sqrtl(z) has error less than 1 ulp (exercise).
24 * So, compute sqrtl(x*x+y*y) with some care as
25 * follows to get the error below 1 ulp:
28 * (if possible, set rounding to round-to-nearest)
30 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
31 * where x1 = x with lower 53 bits cleared, x2 = x-x1; else
33 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
34 * where t1 = 2x with lower 53 bits cleared, t2 = 2x-t1,
35 * y1= y with lower 53 bits chopped, y2 = y-y1.
37 * NOTE: scaling may be necessary if some argument is too
41 * hypotl(x,y) is INF if x or y is +INF or -INF; else
42 * hypotl(x,y) is NAN if x or y is NAN.
45 * hypotl(x,y) returns sqrtl(x^2+y^2) with error less
46 * than 1 ulps (units in the last place)
50 #include "math_private.h"
52 static const long double two600
= 0x1.0p
+600L;
53 static const long double two1022
= 0x1.0p
+1022L;
56 long double __ieee754_hypotl(long double x
, long double y
)
58 long double __ieee754_hypotl(x
,y
)
62 long double a
,b
,t1
,t2
,y1
,y2
,w
,kld
;
65 GET_LDOUBLE_MSW64(ha
,x
);
66 ha
&= 0x7fffffffffffffffLL
;
67 GET_LDOUBLE_MSW64(hb
,y
);
68 hb
&= 0x7fffffffffffffffLL
;
69 if(hb
> ha
) {a
=y
;b
=x
;j
=ha
; ha
=hb
;hb
=j
;} else {a
=x
;b
=y
;}
70 a
= fabsl(a
); /* a <- |a| */
71 b
= fabsl(b
); /* b <- |b| */
72 if((ha
-hb
)>0x3c0000000000000LL
) {return a
+b
;} /* x/y > 2**60 */
75 if(ha
> 0x5f30000000000000LL
) { /* a>2**500 */
76 if(ha
>= 0x7ff0000000000000LL
) { /* Inf or NaN */
78 w
= a
+b
; /* for sNaN */
79 GET_LDOUBLE_LSW64(low
,a
);
80 if(((ha
&0xfffffffffffffLL
)|(low
&0x7fffffffffffffffLL
))==0)
82 GET_LDOUBLE_LSW64(low
,b
);
83 if(((hb
^0x7ff0000000000000LL
)|(low
&0x7fffffffffffffffLL
))==0)
87 /* scale a and b by 2**-600 */
88 ha
-= 0x2580000000000000LL
; hb
-= 0x2580000000000000LL
; k
+= 600;
94 if(hb
< 0x20b0000000000000LL
) { /* b < 2**-500 */
95 if(hb
<= 0x000fffffffffffffLL
) { /* subnormal b or 0 */
97 GET_LDOUBLE_LSW64(low
,b
);
98 if((hb
|(low
&0x7fffffffffffffffLL
))==0) return a
;
99 t1
=two1022
; /* t1=2^1022 */
104 } else { /* scale a and b by 2^600 */
105 ha
+= 0x2580000000000000LL
; /* a *= 2^600 */
106 hb
+= 0x2580000000000000LL
; /* b *= 2^600 */
113 /* medium size a and b */
116 SET_LDOUBLE_WORDS64(t1
,ha
,0);
118 w
= __ieee754_sqrtl(t1
*t1
-(b
*(-b
)-t2
*(a
+t1
)));
121 SET_LDOUBLE_WORDS64(y1
,hb
,0);
123 SET_LDOUBLE_WORDS64(t1
,ha
+0x0010000000000000LL
,0);
125 w
= __ieee754_sqrtl(t1
*y1
-(w
*(-w
)-(t1
*y2
+t2
*b
)));