/src/moddable/xs/tools/fdlibm/e_hypot.c
Line | Count | Source |
1 | | |
2 | | /* |
3 | | * ==================================================== |
4 | | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | | * |
6 | | * Developed at SunSoft, 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*y1+((x-y)*(x-y)+(t1*y2+t2*y)) |
30 | | * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, |
31 | | * y1= y with lower 32 bits chopped, y2 = y-y1. |
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 "math_private.h" |
46 | | |
47 | | double |
48 | | __ieee754_hypot(double x, double y) |
49 | 19 | { |
50 | 19 | double a,b,t1,t2,y1,y2,w; |
51 | 19 | int32_t j,k,ha,hb; |
52 | | |
53 | 19 | GET_HIGH_WORD(ha,x); |
54 | 19 | ha &= 0x7fffffff; |
55 | 19 | GET_HIGH_WORD(hb,y); |
56 | 19 | hb &= 0x7fffffff; |
57 | 19 | if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
58 | 19 | a = fabs(a); |
59 | 19 | b = fabs(b); |
60 | 19 | if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ |
61 | 16 | k=0; |
62 | 16 | if(ha > 0x5f300000) { /* a>2**500 */ |
63 | 1 | if(ha >= 0x7ff00000) { /* Inf or NaN */ |
64 | 1 | u_int32_t low; |
65 | | /* Use original arg order iff result is NaN; quieten sNaNs. */ |
66 | 1 | w = fabsl(x+0.0L)-fabs(y+0); |
67 | 1 | GET_LOW_WORD(low,a); |
68 | 1 | if(((ha&0xfffff)|low)==0) w = a; |
69 | 1 | GET_LOW_WORD(low,b); |
70 | 1 | if(((hb^0x7ff00000)|low)==0) w = b; |
71 | 1 | return w; |
72 | 1 | } |
73 | | /* scale a and b by 2**-600 */ |
74 | 0 | ha -= 0x25800000; hb -= 0x25800000; k += 600; |
75 | 0 | SET_HIGH_WORD(a,ha); |
76 | 0 | SET_HIGH_WORD(b,hb); |
77 | 0 | } |
78 | 15 | if(hb < 0x20b00000) { /* b < 2**-500 */ |
79 | 12 | if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
80 | 12 | u_int32_t low; |
81 | 12 | GET_LOW_WORD(low,b); |
82 | 12 | if((hb|low)==0) return a; |
83 | 0 | t1=0; |
84 | 0 | SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ |
85 | 0 | b *= t1; |
86 | 0 | a *= t1; |
87 | 0 | k -= 1022; |
88 | 0 | } else { /* scale a and b by 2^600 */ |
89 | 0 | ha += 0x25800000; /* a *= 2^600 */ |
90 | 0 | hb += 0x25800000; /* b *= 2^600 */ |
91 | 0 | k -= 600; |
92 | 0 | SET_HIGH_WORD(a,ha); |
93 | 0 | SET_HIGH_WORD(b,hb); |
94 | 0 | } |
95 | 12 | } |
96 | | /* medium size a and b */ |
97 | 3 | w = a-b; |
98 | 3 | if (w>b) { |
99 | 1 | t1 = 0; |
100 | 1 | SET_HIGH_WORD(t1,ha); |
101 | 1 | t2 = a-t1; |
102 | 1 | w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
103 | 2 | } else { |
104 | 2 | a = a+a; |
105 | 2 | y1 = 0; |
106 | 2 | SET_HIGH_WORD(y1,hb); |
107 | 2 | y2 = b - y1; |
108 | 2 | t1 = 0; |
109 | 2 | SET_HIGH_WORD(t1,ha+0x00100000); |
110 | 2 | t2 = a - t1; |
111 | 2 | w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); |
112 | 2 | } |
113 | 3 | if(k!=0) { |
114 | 0 | t1 = 0.0; |
115 | 0 | SET_HIGH_WORD(t1,(1023+k)<<20); |
116 | 0 | return t1*w; |
117 | 3 | } else return w; |
118 | 3 | } |