位操作技巧

检测一个无符号数是不为2^n-1(^为幂)： x&(x+1) <o:p></o:p>

将最右侧0位改为1位： x | (x+1) <o:p></o:p>

二进制补码运算公式：
-x = ~x + 1 = ~(x-1)
~x = -x-1
-(~x) = x+1
~(-x) = x-1
x+y = x - ~y - 1 = (x|y)+(x&y)
x-y = x + ~y + 1 = (x|~y)-(~x&y)
x^y = (x|y)-(x&y)
x|y = (x&~y)+y
x&y = (~x|y)-~x <o:p></o:p>

x==y:    ~(x-y|y-x)
x!=y:    x-y|y-x
x< y:    (x-y)^((x^y)&((x-y)^x))
x<=y:    (x|~y)&((x^y)|~(y-x))
x< y:    (~x&y)|((~x|y)&(x-y))//无符号x,y比较
x<=y:    (~x|y)&((x^y)|~(y-x))//无符号x,y比较 <o:p></o:p>

使用位运算的无分支代码： <o:p></o:p>

计算绝对值
int abs( int x )
{
    int y ;
    y = x >> 31 ;
    return (x^y)-y ;//or: (x+y)^y
} <o:p></o:p>

符号函数：sign(x) = -1, x<0; 0, x == 0 ; 1, x > 0
int sign(int x)
{
    return (x>>31) | (unsigned(-x))>>31 ;//x=-2^31时失败(^为幂)
} <o:p></o:p>

三值比较：cmp(x,y) = -1, x y
int cmp( int x, int y )
{
    return (x>y)-(x-y) ;
} <o:p></o:p>

doz=x-y, x>=y; 0, x<y></y> int doz(int x, int y )
{
    int d ;
    d = x-y ;
    return d & ((~(d^((x^y)&(d^x))))>>31) ;
} <o:p></o:p>

int max(int x, int y )
{
    int m ;
    m = (x-y)>>31 ;
    return y & m | x & ~m ;
} <o:p></o:p>

不使用第三方交换x,y:
1.x ^= y ; y ^= x ; x ^= y ;
2.x = x+y ; y = x-y ; x = x-y ;
3.x = x-y ; y = y+x ; x = y-x ;
4.x = y-x ; x = y-x ; x = x+y ; <o:p></o:p>

双值交换:x = a, x==b; b, x==a//常规编码为x = x==a ? b :a ;
1.x = a+b-x ;
2.x = a^b^x ; <o:p></o:p>

下舍入到2的k次方的倍数:
1.x & ((-1)< 2.(((unsigned)x)>>k)<<k></k> 上舍入：
1. t = (1< 2.t = (-1)<<k x="(x-t-1)&amp;amp;t"></k>

位计数,统计1位的数量：
1.
int pop(unsigned x)
{
    x = x-((x>>1)&0x55555555) ;
    x = (x&0x33333333) + ((x>>2) & 0x33333333 ) ;
    x = (x+(x>>4)) & 0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv> ;
    x = x + (x>>8) ;
    x = x + (x>>16) ;
    return x & 0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="3" numbertype="1" negative="False" hasspace="False">0000003f</st1:chmetcnv> ;
}
2.
int pop(unsigned x) {
    static char table[256] = { 0,1,1,2, 1,2,2,3, ...., 6,7,7,8 } ;
    return table[x&0xff]+table[(x>>8)&0xff]+table[(x>>16)&0xff]+table[(x>>24)] ;
} <o:p></o:p>

奇偶性计算:
x = x ^ ( x>>1 ) ;
x = x ^ ( x>>2 ) ;
x = x ^ ( x>>4 ) ;
x = x ^ ( x>>8 ) ;
x = x ^ ( x>>16 ) ;
结果中位于x最低位，对无符号x,结果的第i位是原数第i位到最左侧位的奇偶性 <o:p></o:p>

位反转：
unsigned rev(unsigned x)
{
    x = (x & 0x55555555) << 1 | (x>>1) & 0x55555555 ;
    x = (x & 0x33333333) << 2 | (x>>2) & 0x33333333 ;
    x = (x & 0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv>) << 4 | (x>>4) & 0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0f</st1:chmetcnv> ;
    x = (x<<24) | ((x&0xff00)<<8) | ((x>>8) & 0xff00) | (x>>24) ;
    return x ;
} <o:p></o:p>

递增位反转后的数：
unsigned inc_r(unsigned x)
{
    unsigned m = 0x80000000 ;
    x ^= m ;
    if( (int)x >= 0 )
        do { m >>= 1 ; x ^= m ; } while( x < m ) ;
    return x ;
} <o:p></o:p>

混选位：
abcd efgh ijkl mnop ABCD EFGH IJKL MNOP->aAbB cCdD eEfF gGhH iIjJ kKlL mMnN oOpP
unsigned ps(unsigned x)
{
    unsigned t ;
    t = (x ^ (x>>8)) & 0x0000ff00; x = x ^ t ^ (t<<8) ;
    t = (x ^ (x>>4)) & 0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">00f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="0" numbertype="1" negative="False" hasspace="False">000f</st1:chmetcnv>0; x = x ^ t ^ (t<<4) ;
    t = (x ^ (x>>2)) & 0x<st1:chmetcnv w:st="on" tcsc="0" unitname="C" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0c</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="C" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0c</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="C" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0c</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="C" sourcevalue="0" numbertype="1" negative="False" hasspace="False">0c</st1:chmetcnv>; x = x ^ t ^ (t<<2) ;
    t = (x ^ (x>>1)) & 0x22222222; x = x ^ t ^ (t<<1) ;
    return x ;
} <o:p></o:p>

位压缩：
选择并右移字x中对应于掩码m的1位的位,如：compress(abcdefgh,01010101)=0000bdfh
compress_left(x,m)操作与此类似，但结果位在左边: bdfh0000.
unsigned compress(unsigned x, unsigned m)
{
    unsigned mk, mp, mv, t ;
    int i ; <o:p></o:p>

    x &= m ;
    mk = ~m << 1 ;
    for( i = 0 ; i < 5 ; ++i ) {
        mp = mk ^ ( mk << 1) ;
        mp ^= ( mp << 2 ) ;
        mp ^= ( mp << 4 ) ;
        mp ^= ( mp << 8 ) ;
        mp ^= ( mp << 16 ) ;
        mv = mp & m ;
        m = m ^ mv | (mv >> (1<         t = x & mv ;
        x  = x ^ t | ( t >> ( 1<         mk = mk & ~mp ;
    }
    return x ;
} <o:p></o:p>

位置换：
用32个5位数表示从最低位开始的位的目标位置，结果是一个32*5的位矩阵，
将该矩阵沿次对角线转置后用5个32位字p[5]存放。
SAG(x,m) = compress_left(x,m) | compress(x,~m) ;
准备工作：
void init( unsigned *p ) {
    p[1] = SAG( p[1], p[0] ) ;
    p[2] = SAG( SAG( p[2], p[0]), p[1] ) ;
    p[3] = SAG( SAG( SAG( p[3], p[0] ), p[1]), p[2] ) ;
    p[4] = SAG( SAG( SAG( SAG( p[4], p[0] ), p[1]) ,p[2]), p[3] ) ;
}
实际置换：
int rep( unsigned x ) {
    x = SAG(x,p[0]);
    x = SAG(x,p[1]);
    x = SAG(x,p[2]);
    x = SAG(x,p[3]);
    x = SAG(x,p[4]);
    return x ;
} <o:p></o:p>

二进制码到GRAY码的转换:
unsigned B<st1:chmetcnv w:st="on" tcsc="0" unitname="g" sourcevalue="2" numbertype="1" negative="False" hasspace="False">2G</st1:chmetcnv>(unsigned B )
{
    return B ^ (B>>1) ;
}
GRAY码到二进制码:
unsigned G2B(unsigned G)
{
    unsigned B ;
    B = G ^ (G>>1) ;
    B = G ^ (G>>2) ;
    B = G ^ (G>>4) ;
    B = G ^ (G>>8) ;
    B = G ^ (G>>16) ;
    return B ;
} <o:p></o:p>

找出最左0字节的位置:
int zbytel( unsigned x )
{
    static cahr table[16] = { 4,3,2,2, 1,1,1,1, 0,0,0,0, 0,0,0,0 } ;
    unsigned y ;
    y = (x&0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv>) + 0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv> ;
    y = ~(y|x|0x<st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv><st1:chmetcnv w:st="on" tcsc="0" unitname="F" sourcevalue="7" numbertype="1" negative="False" hasspace="False">7f</st1:chmetcnv>) ;
    return table[y*0x00204081 >> 28] ;//乘法可用移位和加完成
}

评论

1 楼 xo_tobacoo 2009-02-12  

很想看看，可是干扰的字符太多，请清理下哦！