1*12b1df16SDavid du Colombier #include <u.h>
2*12b1df16SDavid du Colombier #include <libc.h>
3*12b1df16SDavid du Colombier
4*12b1df16SDavid du Colombier static long sqtab[64] =
5*12b1df16SDavid du Colombier {
6*12b1df16SDavid du Colombier 0x6cdb2, 0x726d4, 0x77ea3, 0x7d52f, 0x82a85, 0x87eb1, 0x8d1c0, 0x923bd,
7*12b1df16SDavid du Colombier 0x974b2, 0x9c4a8, 0xa13a9, 0xa61be, 0xaaeee, 0xafb41, 0xb46bf, 0xb916e,
8*12b1df16SDavid du Colombier 0xbdb55, 0xc247a, 0xc6ce3, 0xcb495, 0xcfb95, 0xd41ea, 0xd8796, 0xdcca0,
9*12b1df16SDavid du Colombier 0xe110c, 0xe54dd, 0xe9818, 0xedac0, 0xf1cd9, 0xf5e67, 0xf9f6e, 0xfdfef,
10*12b1df16SDavid du Colombier 0x01fe0, 0x05ee6, 0x09cfd, 0x0da30, 0x11687, 0x1520c, 0x18cc8, 0x1c6c1,
11*12b1df16SDavid du Colombier 0x20000, 0x2388a, 0x27068, 0x2a79e, 0x2de32, 0x3142b, 0x3498c, 0x37e5b,
12*12b1df16SDavid du Colombier 0x3b29d, 0x3e655, 0x41989, 0x44c3b, 0x47e70, 0x4b02b, 0x4e16f, 0x51241,
13*12b1df16SDavid du Colombier 0x542a2, 0x57296, 0x5a220, 0x5d142, 0x60000, 0x62e5a, 0x65c55, 0x689f2,
14*12b1df16SDavid du Colombier };
15*12b1df16SDavid du Colombier
16*12b1df16SDavid du Colombier double
sqrt(double arg)17*12b1df16SDavid du Colombier sqrt(double arg)
18*12b1df16SDavid du Colombier {
19*12b1df16SDavid du Colombier int e, ms;
20*12b1df16SDavid du Colombier double a, t;
21*12b1df16SDavid du Colombier union
22*12b1df16SDavid du Colombier {
23*12b1df16SDavid du Colombier double d;
24*12b1df16SDavid du Colombier struct
25*12b1df16SDavid du Colombier {
26*12b1df16SDavid du Colombier long ls;
27*12b1df16SDavid du Colombier long ms;
28*12b1df16SDavid du Colombier };
29*12b1df16SDavid du Colombier } u;
30*12b1df16SDavid du Colombier
31*12b1df16SDavid du Colombier u.d = arg;
32*12b1df16SDavid du Colombier ms = u.ms;
33*12b1df16SDavid du Colombier
34*12b1df16SDavid du Colombier /*
35*12b1df16SDavid du Colombier * sign extend the mantissa with
36*12b1df16SDavid du Colombier * exponent. result should be > 0 for
37*12b1df16SDavid du Colombier * normal case.
38*12b1df16SDavid du Colombier */
39*12b1df16SDavid du Colombier e = ms >> 20;
40*12b1df16SDavid du Colombier if(e <= 0) {
41*12b1df16SDavid du Colombier if(e == 0)
42*12b1df16SDavid du Colombier return 0;
43*12b1df16SDavid du Colombier return NaN();
44*12b1df16SDavid du Colombier }
45*12b1df16SDavid du Colombier
46*12b1df16SDavid du Colombier /*
47*12b1df16SDavid du Colombier * pick up arg/4 by adjusting exponent
48*12b1df16SDavid du Colombier */
49*12b1df16SDavid du Colombier u.ms = ms - (2 << 20);
50*12b1df16SDavid du Colombier a = u.d;
51*12b1df16SDavid du Colombier
52*12b1df16SDavid du Colombier /*
53*12b1df16SDavid du Colombier * use 5 bits of mantissa and 1 bit
54*12b1df16SDavid du Colombier * of exponent to form table index.
55*12b1df16SDavid du Colombier * insert exponent/2 - 1.
56*12b1df16SDavid du Colombier */
57*12b1df16SDavid du Colombier e = (((e - 1023) >> 1) + 1022) << 20;
58*12b1df16SDavid du Colombier u.ms = *(long*)((char*)sqtab + ((ms >> 13) & 0xfc)) | e;
59*12b1df16SDavid du Colombier u.ls = 0;
60*12b1df16SDavid du Colombier
61*12b1df16SDavid du Colombier /*
62*12b1df16SDavid du Colombier * three laps of newton
63*12b1df16SDavid du Colombier */
64*12b1df16SDavid du Colombier e = 1 << 20;
65*12b1df16SDavid du Colombier t = u.d;
66*12b1df16SDavid du Colombier u.d = t + a/t;
67*12b1df16SDavid du Colombier u.ms -= e; /* u.d /= 2; */
68*12b1df16SDavid du Colombier t = u.d;
69*12b1df16SDavid du Colombier u.d = t + a/t;
70*12b1df16SDavid du Colombier u.ms -= e; /* u.d /= 2; */
71*12b1df16SDavid du Colombier t = u.d;
72*12b1df16SDavid du Colombier
73*12b1df16SDavid du Colombier return t + a/t;
74*12b1df16SDavid du Colombier }
75*12b1df16SDavid du Colombier
76*12b1df16SDavid du Colombier /*
77*12b1df16SDavid du Colombier * this is the program that generated the table.
78*12b1df16SDavid du Colombier * it calls sqrt by some other means.
79*12b1df16SDavid du Colombier *
80*12b1df16SDavid du Colombier * void
81*12b1df16SDavid du Colombier * main(void)
82*12b1df16SDavid du Colombier * {
83*12b1df16SDavid du Colombier * int i;
84*12b1df16SDavid du Colombier * union U
85*12b1df16SDavid du Colombier * {
86*12b1df16SDavid du Colombier * double d;
87*12b1df16SDavid du Colombier * struct
88*12b1df16SDavid du Colombier * {
89*12b1df16SDavid du Colombier * long ls;
90*12b1df16SDavid du Colombier * long ms;
91*12b1df16SDavid du Colombier * };
92*12b1df16SDavid du Colombier * } u;
93*12b1df16SDavid du Colombier *
94*12b1df16SDavid du Colombier * for(i=0; i<64; i++) {
95*12b1df16SDavid du Colombier * u.ms = (i<<15) | 0x3fe04000;
96*12b1df16SDavid du Colombier * u.ls = 0;
97*12b1df16SDavid du Colombier * u.d = sqrt(u.d);
98*12b1df16SDavid du Colombier * print(" 0x%.5lux,", u.ms & 0xfffff);
99*12b1df16SDavid du Colombier * }
100*12b1df16SDavid du Colombier * print("\n");
101*12b1df16SDavid du Colombier * exits(0);
102*12b1df16SDavid du Colombier * }
103*12b1df16SDavid du Colombier */
104