1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /* __ieee754_hypot(x,y)
13 *
14 * Method :
15 * If (assume round-to-nearest) z=x*x+y*y
16 * has error less than sqrt(2)/2 ulp, than
17 * sqrt(z) has error less than 1 ulp (exercise).
18 *
19 * So, compute sqrt(x*x+y*y) with some care as
20 * follows to get the error below 1 ulp:
21 *
22 * Assume x>y>0;
23 * (if possible, set rounding to round-to-nearest)
24 * 1. if x > 2y use
25 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
26 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
27 * 2. if x <= 2y use
28 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
29 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
30 * y1= y with lower 32 bits chopped, y2 = y-y1.
31 *
32 * NOTE: scaling may be necessary if some argument is too
33 * large or too tiny
34 *
35 * Special cases:
36 * hypot(x,y) is INF if x or y is +INF or -INF; else
37 * hypot(x,y) is NAN if x or y is NAN.
38 *
39 * Accuracy:
40 * hypot(x,y) returns sqrt(x^2+y^2) with error less
41 * than 1 ulps (units in the last place)
42 */
43
44 #include "math.h"
45 #include "math_private.h"
46
__ieee754_hypot(double x,double y)47 double __ieee754_hypot(double x, double y)
48 {
49 double a=x,b=y,t1,t2,_y1,y2,w;
50 int32_t j,k,ha,hb;
51
52 GET_HIGH_WORD(ha,x);
53 ha &= 0x7fffffff;
54 GET_HIGH_WORD(hb,y);
55 hb &= 0x7fffffff;
56 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
57 SET_HIGH_WORD(a,ha); /* a <- |a| */
58 SET_HIGH_WORD(b,hb); /* b <- |b| */
59 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
60 k=0;
61 if(ha > 0x5f300000) { /* a>2**500 */
62 if(ha >= 0x7ff00000) { /* Inf or NaN */
63 u_int32_t low;
64 w = a+b; /* for sNaN */
65 GET_LOW_WORD(low,a);
66 if(((ha&0xfffff)|low)==0) w = a;
67 GET_LOW_WORD(low,b);
68 if(((hb^0x7ff00000)|low)==0) w = b;
69 return w;
70 }
71 /* scale a and b by 2**-600 */
72 ha -= 0x25800000; hb -= 0x25800000; k += 600;
73 SET_HIGH_WORD(a,ha);
74 SET_HIGH_WORD(b,hb);
75 }
76 if(hb < 0x20b00000) { /* b < 2**-500 */
77 if(hb <= 0x000fffff) { /* subnormal b or 0 */
78 u_int32_t low;
79 GET_LOW_WORD(low,b);
80 if((hb|low)==0) return a;
81 t1=0;
82 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
83 b *= t1;
84 a *= t1;
85 k -= 1022;
86 } else { /* scale a and b by 2^600 */
87 ha += 0x25800000; /* a *= 2^600 */
88 hb += 0x25800000; /* b *= 2^600 */
89 k -= 600;
90 SET_HIGH_WORD(a,ha);
91 SET_HIGH_WORD(b,hb);
92 }
93 }
94 /* medium size a and b */
95 w = a-b;
96 if (w>b) {
97 t1 = 0;
98 SET_HIGH_WORD(t1,ha);
99 t2 = a-t1;
100 w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
101 } else {
102 a = a+a;
103 _y1 = 0;
104 SET_HIGH_WORD(_y1,hb);
105 y2 = b - _y1;
106 t1 = 0;
107 SET_HIGH_WORD(t1,ha+0x00100000);
108 t2 = a - t1;
109 w = __ieee754_sqrt(t1*_y1-(w*(-w)-(t1*y2+t2*b)));
110 }
111 if(k!=0) {
112 u_int32_t high;
113 t1 = 1.0;
114 GET_HIGH_WORD(high,t1);
115 SET_HIGH_WORD(t1,high+(k<<20));
116 return t1*w;
117 } else return w;
118 }
119
120 /*
121 * wrapper hypot(x,y)
122 */
123 #ifndef _IEEE_LIBM
hypot(double x,double y)124 double hypot(double x, double y)
125 {
126 double z = __ieee754_hypot(x, y);
127 if (_LIB_VERSION == _IEEE_)
128 return z;
129 if ((!isfinite(z)) && isfinite(x) && isfinite(y))
130 return __kernel_standard(x, y, 4); /* hypot overflow */
131 return z;
132 }
133 #else
134 strong_alias(__ieee754_hypot, hypot)
135 #endif
136 libm_hidden_def(hypot)
137