File: | src/lib/libm/src/e_hypot.c |
Warning: | line 119, column 6 The result of the left shift is undefined because the left operand is negative |
Press '?' to see keyboard shortcuts
Keyboard shortcuts:
1 | /* @(#)e_hypot.c 5.1 93/09/24 */ | |||
2 | /* | |||
3 | * ==================================================== | |||
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |||
5 | * | |||
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 | |||
9 | * is preserved. | |||
10 | * ==================================================== | |||
11 | */ | |||
12 | ||||
13 | /* hypot(x,y) | |||
14 | * | |||
15 | * Method : | |||
16 | * If (assume round-to-nearest) z=x*x+y*y | |||
17 | * has error less than sqrt(2)/2 ulp, than | |||
18 | * sqrt(z) has error less than 1 ulp (exercise). | |||
19 | * | |||
20 | * So, compute sqrt(x*x+y*y) with some care as | |||
21 | * follows to get the error below 1 ulp: | |||
22 | * | |||
23 | * Assume x>y>0; | |||
24 | * (if possible, set rounding to round-to-nearest) | |||
25 | * 1. if x > 2y use | |||
26 | * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y | |||
27 | * where x1 = x with lower 32 bits cleared, x2 = x-x1; else | |||
28 | * 2. if x <= 2y use | |||
29 | * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y)) | |||
30 | * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, | |||
31 | * yy1= y with lower 32 bits chopped, y2 = y-yy1. | |||
32 | * | |||
33 | * NOTE: scaling may be necessary if some argument is too | |||
34 | * large or too tiny | |||
35 | * | |||
36 | * Special cases: | |||
37 | * hypot(x,y) is INF if x or y is +INF or -INF; else | |||
38 | * hypot(x,y) is NAN if x or y is NAN. | |||
39 | * | |||
40 | * Accuracy: | |||
41 | * hypot(x,y) returns sqrt(x^2+y^2) with error less | |||
42 | * than 1 ulps (units in the last place) | |||
43 | */ | |||
44 | ||||
45 | #include <float.h> | |||
46 | #include <math.h> | |||
47 | ||||
48 | #include "math_private.h" | |||
49 | ||||
50 | double | |||
51 | hypot(double x, double y) | |||
52 | { | |||
53 | double a=x,b=y,t1,t2,yy1,y2,w; | |||
54 | int32_t j,k,ha,hb; | |||
55 | ||||
56 | GET_HIGH_WORD(ha,x)do { ieee_double_shape_type gh_u; gh_u.value = (x); (ha) = gh_u .parts.msw; } while (0); | |||
| ||||
57 | ha &= 0x7fffffff; | |||
58 | GET_HIGH_WORD(hb,y)do { ieee_double_shape_type gh_u; gh_u.value = (y); (hb) = gh_u .parts.msw; } while (0); | |||
59 | hb &= 0x7fffffff; | |||
60 | if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} | |||
61 | SET_HIGH_WORD(a,ha)do { ieee_double_shape_type sh_u; sh_u.value = (a); sh_u.parts .msw = (ha); (a) = sh_u.value; } while (0); /* a <- |a| */ | |||
62 | SET_HIGH_WORD(b,hb)do { ieee_double_shape_type sh_u; sh_u.value = (b); sh_u.parts .msw = (hb); (b) = sh_u.value; } while (0); /* b <- |b| */ | |||
63 | if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ | |||
64 | k=0; | |||
65 | if(ha > 0x5f300000) { /* a>2**500 */ | |||
66 | if(ha >= 0x7ff00000) { /* Inf or NaN */ | |||
67 | u_int32_t low; | |||
68 | w = a+b; /* for sNaN */ | |||
69 | GET_LOW_WORD(low,a)do { ieee_double_shape_type gl_u; gl_u.value = (a); (low) = gl_u .parts.lsw; } while (0); | |||
70 | if(((ha&0xfffff)|low)==0) w = a; | |||
71 | GET_LOW_WORD(low,b)do { ieee_double_shape_type gl_u; gl_u.value = (b); (low) = gl_u .parts.lsw; } while (0); | |||
72 | if(((hb^0x7ff00000)|low)==0) w = b; | |||
73 | return w; | |||
74 | } | |||
75 | /* scale a and b by 2**-600 */ | |||
76 | ha -= 0x25800000; hb -= 0x25800000; k += 600; | |||
77 | SET_HIGH_WORD(a,ha)do { ieee_double_shape_type sh_u; sh_u.value = (a); sh_u.parts .msw = (ha); (a) = sh_u.value; } while (0); | |||
78 | SET_HIGH_WORD(b,hb)do { ieee_double_shape_type sh_u; sh_u.value = (b); sh_u.parts .msw = (hb); (b) = sh_u.value; } while (0); | |||
79 | } | |||
80 | if(hb < 0x20b00000) { /* b < 2**-500 */ | |||
81 | if(hb <= 0x000fffff) { /* subnormal b or 0 */ | |||
82 | u_int32_t low; | |||
83 | GET_LOW_WORD(low,b)do { ieee_double_shape_type gl_u; gl_u.value = (b); (low) = gl_u .parts.lsw; } while (0); | |||
84 | if((hb|low)==0) return a; | |||
85 | t1=0; | |||
86 | SET_HIGH_WORD(t1,0x7fd00000)do { ieee_double_shape_type sh_u; sh_u.value = (t1); sh_u.parts .msw = (0x7fd00000); (t1) = sh_u.value; } while (0); /* t1=2^1022 */ | |||
87 | b *= t1; | |||
88 | a *= t1; | |||
89 | k -= 1022; | |||
90 | } else { /* scale a and b by 2^600 */ | |||
91 | ha += 0x25800000; /* a *= 2^600 */ | |||
92 | hb += 0x25800000; /* b *= 2^600 */ | |||
93 | k -= 600; | |||
94 | SET_HIGH_WORD(a,ha)do { ieee_double_shape_type sh_u; sh_u.value = (a); sh_u.parts .msw = (ha); (a) = sh_u.value; } while (0); | |||
95 | SET_HIGH_WORD(b,hb)do { ieee_double_shape_type sh_u; sh_u.value = (b); sh_u.parts .msw = (hb); (b) = sh_u.value; } while (0); | |||
96 | } | |||
97 | } | |||
98 | /* medium size a and b */ | |||
99 | w = a-b; | |||
100 | if (w>b) { | |||
101 | t1 = 0; | |||
102 | SET_HIGH_WORD(t1,ha)do { ieee_double_shape_type sh_u; sh_u.value = (t1); sh_u.parts .msw = (ha); (t1) = sh_u.value; } while (0); | |||
103 | t2 = a-t1; | |||
104 | w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); | |||
105 | } else { | |||
106 | a = a+a; | |||
107 | yy1 = 0; | |||
108 | SET_HIGH_WORD(yy1,hb)do { ieee_double_shape_type sh_u; sh_u.value = (yy1); sh_u.parts .msw = (hb); (yy1) = sh_u.value; } while (0); | |||
109 | y2 = b - yy1; | |||
110 | t1 = 0; | |||
111 | SET_HIGH_WORD(t1,ha+0x00100000)do { ieee_double_shape_type sh_u; sh_u.value = (t1); sh_u.parts .msw = (ha+0x00100000); (t1) = sh_u.value; } while (0); | |||
112 | t2 = a - t1; | |||
113 | w = sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b))); | |||
114 | } | |||
115 | if(k
| |||
116 | u_int32_t high; | |||
117 | t1 = 1.0; | |||
118 | GET_HIGH_WORD(high,t1)do { ieee_double_shape_type gh_u; gh_u.value = (t1); (high) = gh_u.parts.msw; } while (0); | |||
119 | SET_HIGH_WORD(t1,high+(k<<20))do { ieee_double_shape_type sh_u; sh_u.value = (t1); sh_u.parts .msw = (high+(k<<20)); (t1) = sh_u.value; } while (0); | |||
| ||||
120 | return t1*w; | |||
121 | } else return w; | |||
122 | } | |||
123 | DEF_STD(hypot)__asm__(".global " "hypot" " ; " "hypot" " = " "_libm_hypot"); | |||
124 | LDBL_MAYBE_CLONE(hypot)__asm(""); |