1 #include <u.h>
2 #include <libc.h>
3
4 static long sqtab[64] =
5 {
6 0x6cdb2, 0x726d4, 0x77ea3, 0x7d52f, 0x82a85, 0x87eb1, 0x8d1c0, 0x923bd,
7 0x974b2, 0x9c4a8, 0xa13a9, 0xa61be, 0xaaeee, 0xafb41, 0xb46bf, 0xb916e,
8 0xbdb55, 0xc247a, 0xc6ce3, 0xcb495, 0xcfb95, 0xd41ea, 0xd8796, 0xdcca0,
9 0xe110c, 0xe54dd, 0xe9818, 0xedac0, 0xf1cd9, 0xf5e67, 0xf9f6e, 0xfdfef,
10 0x01fe0, 0x05ee6, 0x09cfd, 0x0da30, 0x11687, 0x1520c, 0x18cc8, 0x1c6c1,
11 0x20000, 0x2388a, 0x27068, 0x2a79e, 0x2de32, 0x3142b, 0x3498c, 0x37e5b,
12 0x3b29d, 0x3e655, 0x41989, 0x44c3b, 0x47e70, 0x4b02b, 0x4e16f, 0x51241,
13 0x542a2, 0x57296, 0x5a220, 0x5d142, 0x60000, 0x62e5a, 0x65c55, 0x689f2,
14 };
15
16 double
sqrt(double arg)17 sqrt(double arg)
18 {
19 int e, ms;
20 double a, t;
21 union
22 {
23 double d;
24 struct
25 {
26 long ms;
27 long ls;
28 };
29 } u;
30
31 u.d = arg;
32 ms = u.ms;
33
34 /*
35 * sign extend the mantissa with
36 * exponent. result should be > 0 for
37 * normal case.
38 */
39 e = ms >> 20;
40 if(e <= 0) {
41 if(e == 0)
42 return 0;
43 return NaN();
44 }
45
46 /*
47 * pick up arg/4 by adjusting exponent
48 */
49 u.ms = ms - (2 << 20);
50 a = u.d;
51
52 /*
53 * use 5 bits of mantissa and 1 bit
54 * of exponent to form table index.
55 * insert exponent/2 - 1.
56 */
57 e = (((e - 1023) >> 1) + 1022) << 20;
58 u.ms = *(long*)((char*)sqtab + ((ms >> 13) & 0xfc)) | e;
59 u.ls = 0;
60
61 /*
62 * three laps of newton
63 */
64 e = 1 << 20;
65 t = u.d;
66 u.d = t + a/t;
67 u.ms -= e; /* u.d /= 2; */
68 t = u.d;
69 u.d = t + a/t;
70 u.ms -= e; /* u.d /= 2; */
71 t = u.d;
72
73 return t + a/t;
74 }
75
76 /*
77 * this is the program that generated the table.
78 * it calls sqrt by some other means.
79 *
80 * void
81 * main(void)
82 * {
83 * int i;
84 * union U
85 * {
86 * double d;
87 * struct
88 * {
89 * long ms;
90 * long ls;
91 * };
92 * } u;
93 *
94 * for(i=0; i<64; i++) {
95 * u.ms = (i<<15) | 0x3fe04000;
96 * u.ls = 0;
97 * u.d = sqrt(u.d);
98 * print(" 0x%.5lux,", u.ms & 0xfffff);
99 * }
100 * print("\n");
101 * exits(0);
102 * }
103 */
104