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
52long double __ieee754_hypotl(long double x, long double y)
53{
54 long double a,b,t1,t2,y1,y2,w;
55 uint32_t j,k,ea,eb;
56
57 GET_LDOUBLE_EXP(ea,x);
58 ea &= 0x7fff;
59 GET_LDOUBLE_EXP(eb,y);
60 eb &= 0x7fff;
61 if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
62 SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
63 SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
64 if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
65 k=0;
66 if(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */
67 if(ea == 0x7fff) { /* Inf or NaN */
68 uint32_t exp __attribute__ ((unused));
69 uint32_t high,low;
70 w = a+b; /* for sNaN */
71 if (issignaling (a) || issignaling (b))
72 return w;
73 GET_LDOUBLE_WORDS(exp,high,low,a);
74 if(((high&0x7fffffff)|low)==0) w = a;
75 GET_LDOUBLE_WORDS(exp,high,low,b);
76 if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
77 return w;
78 }
79 /* scale a and b by 2**-9600 */
80 ea -= 0x2580; eb -= 0x2580; k += 9600;
81 SET_LDOUBLE_EXP(a,ea);
82 SET_LDOUBLE_EXP(b,eb);
83 }
84 if(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */
85 if(eb == 0) { /* subnormal b or 0 */
86 uint32_t exp __attribute__ ((unused));
87 uint32_t high,low;
88 GET_LDOUBLE_WORDS(exp,high,low,b);
89 if((high|low)==0) return a;
90 SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */
91 b *= t1;
92 a *= t1;
93 k -= 16382;
94 GET_LDOUBLE_EXP (ea, a);
95 GET_LDOUBLE_EXP (eb, b);
96 if (eb > ea)
97 {
98 t1 = a;
99 a = b;
100 b = t1;
101 j = ea;
102 ea = eb;
103 eb = j;
104 }
105 } else { /* scale a and b by 2^9600 */
106 ea += 0x2580; /* a *= 2^9600 */
107 eb += 0x2580; /* b *= 2^9600 */
108 k -= 9600;
109 SET_LDOUBLE_EXP(a,ea);
110 SET_LDOUBLE_EXP(b,eb);
111 }
112 }
113 /* medium size a and b */
114 w = a-b;
115 if (w>b) {
116 uint32_t high;
117 GET_LDOUBLE_MSW(high,a);
118 SET_LDOUBLE_WORDS(t1,ea,high,0);
119 t2 = a-t1;
120 w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
121 } else {
122 uint32_t high;
123 GET_LDOUBLE_MSW(high,b);
124 a = a+a;
125 SET_LDOUBLE_WORDS(y1,eb,high,0);
126 y2 = b - y1;
127 GET_LDOUBLE_MSW(high,a);
128 SET_LDOUBLE_WORDS(t1,ea+1,high,0);
129 t2 = a - t1;
130 w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
131 }
132 if(k!=0) {
133 uint32_t exp;
134 t1 = 1.0;
135 GET_LDOUBLE_EXP(exp,t1);
136 SET_LDOUBLE_EXP(t1,exp+k);
137 w *= t1;
138 math_check_force_underflow_nonneg (w);
139 return w;
140 } else return w;
141}
142strong_alias (__ieee754_hypotl, __hypotl_finite)
143