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.
4 */
5
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
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
13 * is preserved.
14 * ====================================================
15 */
16
17/* __ieee754_hypotl(x,y)
18 *
19 * Method :
20 * If (assume round-to-nearest) z=x*x+y*y
21 * has error less than sqrt(2)/2 ulp, than
22 * sqrt(z) has error less than 1 ulp (exercise).
23 *
24 * So, compute sqrt(x*x+y*y) with some care as
25 * follows to get the error below 1 ulp:
26 *
27 * Assume x>y>0;
28 * (if possible, set rounding to round-to-nearest)
29 * 1. if x > 2y use
30 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
31 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
32 * 2. if x <= 2y use
33 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
34 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
35 * y1= y with lower 32 bits chopped, y2 = y-y1.
36 *
37 * NOTE: scaling may be necessary if some argument is too
38 * large or too tiny
39 *
40 * Special cases:
41 * hypot(x,y) is INF if x or y is +INF or -INF; else
42 * hypot(x,y) is NAN if x or y is NAN.
43 *
44 * Accuracy:
45 * hypot(x,y) returns sqrt(x^2+y^2) with error less
46 * than 1 ulps (units in the last place)
47 */
48
49#include <math.h>
50#include <math_private.h>
51#include <math-underflow.h>
52#include <libm-alias-finite.h>
53
54long double __ieee754_hypotl(long double x, long double y)
55{
56 long double a,b,t1,t2,y1,y2,w;
57 uint32_t j,k,ea,eb;
58
59 GET_LDOUBLE_EXP(ea,x);
60 ea &= 0x7fff;
61 GET_LDOUBLE_EXP(eb,y);
62 eb &= 0x7fff;
63 if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
64 SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
65 SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
66 if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
67 k=0;
68 if(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */
69 if(ea == 0x7fff) { /* Inf or NaN */
70 uint32_t exp __attribute__ ((unused));
71 uint32_t high,low;
72 w = a+b; /* for sNaN */
73 if (issignaling (a) || issignaling (b))
74 return w;
75 GET_LDOUBLE_WORDS(exp,high,low,a);
76 if(((high&0x7fffffff)|low)==0) w = a;
77 GET_LDOUBLE_WORDS(exp,high,low,b);
78 if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
79 return w;
80 }
81 /* scale a and b by 2**-9600 */
82 ea -= 0x2580; eb -= 0x2580; k += 9600;
83 SET_LDOUBLE_EXP(a,ea);
84 SET_LDOUBLE_EXP(b,eb);
85 }
86 if(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */
87 if(eb == 0) { /* subnormal b or 0 */
88 uint32_t exp __attribute__ ((unused));
89 uint32_t high,low;
90 GET_LDOUBLE_WORDS(exp,high,low,b);
91 if((high|low)==0) return a;
92 SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */
93 b *= t1;
94 a *= t1;
95 k -= 16382;
96 GET_LDOUBLE_EXP (ea, a);
97 GET_LDOUBLE_EXP (eb, b);
98 if (eb > ea)
99 {
100 t1 = a;
101 a = b;
102 b = t1;
103 j = ea;
104 ea = eb;
105 eb = j;
106 }
107 } else { /* scale a and b by 2^9600 */
108 ea += 0x2580; /* a *= 2^9600 */
109 eb += 0x2580; /* b *= 2^9600 */
110 k -= 9600;
111 SET_LDOUBLE_EXP(a,ea);
112 SET_LDOUBLE_EXP(b,eb);
113 }
114 }
115 /* medium size a and b */
116 w = a-b;
117 if (w>b) {
118 uint32_t high;
119 GET_LDOUBLE_MSW(high,a);
120 SET_LDOUBLE_WORDS(t1,ea,high,0);
121 t2 = a-t1;
122 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
123 } else {
124 uint32_t high;
125 GET_LDOUBLE_MSW(high,b);
126 a = a+a;
127 SET_LDOUBLE_WORDS(y1,eb,high,0);
128 y2 = b - y1;
129 GET_LDOUBLE_MSW(high,a);
130 SET_LDOUBLE_WORDS(t1,ea+1,high,0);
131 t2 = a - t1;
132 w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
133 }
134 if(k!=0) {
135 uint32_t exp;
136 t1 = 1.0;
137 GET_LDOUBLE_EXP(exp,t1);
138 SET_LDOUBLE_EXP(t1,exp+k);
139 w *= t1;
140 math_check_force_underflow_nonneg (w);
141 return w;
142 } else return w;
143}
144libm_alias_finite (__ieee754_hypotl, __hypotl)
145