ref: d1cebf608b05e45b148108ac6c16ae94f6862097
dir: /sys/src/libc/power/sqrt.c/
#include <u.h>
#include <libc.h>
static long sqtab[64] =
{
0x6cdb2, 0x726d4, 0x77ea3, 0x7d52f, 0x82a85, 0x87eb1, 0x8d1c0, 0x923bd,
0x974b2, 0x9c4a8, 0xa13a9, 0xa61be, 0xaaeee, 0xafb41, 0xb46bf, 0xb916e,
0xbdb55, 0xc247a, 0xc6ce3, 0xcb495, 0xcfb95, 0xd41ea, 0xd8796, 0xdcca0,
0xe110c, 0xe54dd, 0xe9818, 0xedac0, 0xf1cd9, 0xf5e67, 0xf9f6e, 0xfdfef,
0x01fe0, 0x05ee6, 0x09cfd, 0x0da30, 0x11687, 0x1520c, 0x18cc8, 0x1c6c1,
0x20000, 0x2388a, 0x27068, 0x2a79e, 0x2de32, 0x3142b, 0x3498c, 0x37e5b,
0x3b29d, 0x3e655, 0x41989, 0x44c3b, 0x47e70, 0x4b02b, 0x4e16f, 0x51241,
0x542a2, 0x57296, 0x5a220, 0x5d142, 0x60000, 0x62e5a, 0x65c55, 0x689f2,
};
double
sqrt(double arg)
{
int e, ms;
double a, t;
union
{
double d;
struct
{
long ms;
long ls;
};
} u;
u.d = arg;
ms = u.ms;
/*
* sign extend the mantissa with
* exponent. result should be > 0 for
* normal case.
*/
e = ms >> 20;
if(e <= 0) {
if(e == 0)
return 0;
return NaN();
}
/*
* pick up arg/4 by adjusting exponent
*/
u.ms = ms - (2 << 20);
a = u.d;
/*
* use 5 bits of mantissa and 1 bit
* of exponent to form table index.
* insert exponent/2 - 1.
*/
e = (((e - 1023) >> 1) + 1022) << 20;
u.ms = *(long*)((char*)sqtab + ((ms >> 13) & 0xfc)) | e;
u.ls = 0;
/*
* three laps of newton
*/
e = 1 << 20;
t = u.d;
u.d = t + a/t;
u.ms -= e; /* u.d /= 2; */
t = u.d;
u.d = t + a/t;
u.ms -= e; /* u.d /= 2; */
t = u.d;
return t + a/t;
}
/*
* this is the program that generated the table.
* it calls sqrt by some other means.
*
* void
* main(void)
* {
* int i;
* union U
* {
* double d;
* struct
* {
* long ms;
* long ls;
* };
* } u;
*
* for(i=0; i<64; i++) {
* u.ms = (i<<15) | 0x3fe04000;
* u.ls = 0;
* u.d = sqrt(u.d);
* print(" 0x%.5lux,", u.ms & 0xfffff);
* }
* print("\n");
* exits(0);
* }
*/