/*
Copyright (C) 2012, Tórur Biskopstø Strøm (torur.strom@gmail.com)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package org.reprap;
public final class Math
{
/*
* Square root function from http://atoms.alife.co.uk/sqrt/index.html
*/
final static int[] sqrttable =
{
0, 16, 22, 27, 32, 35, 39, 42, 45, 48, 50, 53, 55, 57,
59, 61, 64, 65, 67, 69, 71, 73, 75, 76, 78, 80, 81, 83,
84, 86, 87, 89, 90, 91, 93, 94, 96, 97, 98, 99, 101, 102,
103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118,
119, 120, 121, 122, 123, 124, 125, 126, 128, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145,
146, 147, 148, 149, 150, 150, 151, 152, 153, 154, 155, 155, 156, 157,
158, 159, 160, 160, 161, 162, 163, 163, 164, 165, 166, 167, 167, 168,
169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 178,
179, 180, 181, 181, 182, 183, 183, 184, 185, 185, 186, 187, 187, 188,
189, 189, 190, 191, 192, 192, 193, 193, 194, 195, 195, 196, 197, 197,
198, 199, 199, 200, 201, 201, 202, 203, 203, 204, 204, 205, 206, 206,
207, 208, 208, 209, 209, 210, 211, 211, 212, 212, 213, 214, 214, 215,
215, 216, 217, 217, 218, 218, 219, 219, 220, 221, 221, 222, 222, 223,
224, 224, 225, 225, 226, 226, 227, 227, 228, 229, 229, 230, 230, 231,
231, 232, 232, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238,
239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246,
246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253,
253, 254, 254, 255
};
/**
* A faster replacement for (int)(java.lang.Math.sqrt(x)). Completely accurate for x < 2147483648 (i.e. 2^31)...
*/
public static int sqrt(int x) {
int xn;
if (x >= 0x10000) {
if (x >= 0x1000000) {
if (x >= 0x10000000) {
if (x >= 0x40000000) {
xn = sqrttable[x >> 24] << 8;
} else {
xn = sqrttable[x >> 22] << 7;
}
} else {
if (x >= 0x4000000) {
xn = sqrttable[x >> 20] << 6;
} else {
xn = sqrttable[x >> 18] << 5;
}
}
xn = (xn + 1 + (x / xn)) >> 1;
xn = (xn + 1 + (x / xn)) >> 1;
return ((xn * xn) > x) ? --xn : xn;
} else {
if (x >= 0x100000) {
if (x >= 0x400000) {
xn = sqrttable[x >> 16] << 4;
} else {
xn = sqrttable[x >> 14] << 3;
}
} else {
if (x >= 0x40000) {
xn = sqrttable[x >> 12] << 2;
} else {
xn = sqrttable[x >> 10] << 1;
}
}
xn = (xn + 1 + (x / xn)) >> 1;
return ((xn * xn) > x) ? --xn : xn;
}
} else {
if (x >= 0x100) {
if (x >= 0x1000) {
if (x >= 0x4000) {
xn = (sqrttable[x >> 8]) + 1;
} else {
xn = (sqrttable[x >> 6] >> 1) + 1;
}
} else {
if (x >= 0x400) {
xn = (sqrttable[x >> 4] >> 2) + 1;
} else {
xn = (sqrttable[x >> 2] >> 3) + 1;
}
}
return ((xn * xn) > x) ? --xn : xn;
} else {
if (x >= 0) {
return sqrttable[x] >> 4;
}
}
}
return -1;
}
//From http://www.hackersdelight.org/divcMore.pdf
public static int divs5(int n)
{
int q, r;
n = n + (n>>31 & 4);
q = (n >> 1) + (n >> 2);
q = q + (q >> 4);
q = q + (q >> 8);
q = q + (q >> 16);
q = q >> 2;
r = n - q*5;
return q + (7*r >> 5);
}
public static int divs10(int n)
{
int q, r;
n = n + (n>>31 & 9);
q = (n >> 1) + (n >> 2);
q = q + (q >> 4);
q = q + (q >> 8);
q = q + (q >> 16);
q = q >> 3;
r = n - q*10;
return q + ((r + 6) >> 4);
}
public static int divs100(int n)
{
int q, r;
n = n + (n>>31 & 99);
q = (n >> 1) + (n >> 3) + (n >> 6) - (n >> 10) +
(n >> 12) + (n >> 13) - (n >> 16);
q = q + (q >> 20);
q = q >> 6;
r = n - q*100;
return q + ((r + 28) >> 7);
}
public static int divs1000(int n)
{
int q, r, t;
n = n + (n>>31 & 999);
t = (n >> 7) + (n >> 8) + (n >> 12);
q = (n >> 1) + t + (n >> 15) + (t >> 11) + (t >> 14) +
(n >> 26) + (t >> 21);
q = q >> 9;
r = n - q*1000;
return q + ((r + 24) >> 10);
}
private static final int[] modulotable = {0, 1, 99, 2, 3, 99, 4, 5,
5, 6, 99, 7, 8, 99, 9, 99,
-6,-5, 99,-4,-3,-3,-2, 99,
-1, 0, 99,-9, 99,-8,-7, 99};
public static int modulo10(int n)
{
int r;
r = n;
r = (0x19999999*r + (r >>> 1) + (r >>> 3)) >>> 28;
return modulotable[r + ((n >>> 31) << 4)];
}
}