C语言中有效的位反转算法（从MSB-> LSB到LSB-> MSB）

C语言中有效的位反转算法（从MSB-> LSB到LSB-> MSB）

注意 ：以下所有算法均使用C语言，但应可移植到您选择的语言中（当它们不那么快时，请不要看着我：）

选件

低内存（32位

int

，32位计算机）（从此处开始）：

unsigned intreverse(register unsigned int x){    x = (((x & 0xaaaaaaaa) >> 1) | ((x & 0x55555555) << 1));    x = (((x & 0xcccccccc) >> 2) | ((x & 0x33333333) << 2));    x = (((x & 0xf0f0f0f0) >> 4) | ((x & 0x0f0f0f0f) << 4));    x = (((x & 0xff00ff00) >> 8) | ((x & 0x00ff00ff) << 8));    return((x >> 16) | (x << 16));}

从著名的Bit Twiddling
Hacks页面
：

最快（查找表） ：

static const unsigned char BitReverseTable256[] = {  0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0,   0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8,   0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4,   0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC,   0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2,   0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA,  0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6,   0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE,  0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1,  0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9,   0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5,  0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD,  0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3,   0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB,  0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7,   0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF};unsigned int v; // reverse 32-bit value, 8 bits at timeunsigned int c; // c will get v reversed// Option 1:c = (BitReverseTable256[v & 0xff] << 24) |     (BitReverseTable256[(v >> 8) & 0xff] << 16) |     (BitReverseTable256[(v >> 16) & 0xff] << 8) |    (BitReverseTable256[(v >> 24) & 0xff]);// Option 2:unsigned char * p = (unsigned char *) &v;unsigned char * q = (unsigned char *) &c;q[3] = BitReverseTable256[p[0]]; q[2] = BitReverseTable256[p[1]]; q[1] = BitReverseTable256[p[2]]; q[0] = BitReverseTable256[p[3]];

您可以将此想法扩展到64位

int

，或以内存为代价进行交换（假设您的L1数据高速缓存足够大），并使用64K条目查找表一次反转16位。

---

其他

简单

unsigned int v;     // input bits to be reversedunsigned int r = v & 1; // r will be reversed bits of v; first get LSB of vint s = sizeof(v) * CHAR_BIT - 1; // extra shift needed at endfor (v >>= 1; v; v >>= 1){     r <<= 1;  r |= v & 1;  s--;}r <<= s; // shift when v's highest bits are zero

更快（32位处理器）

unsigned char b = x;b = ((b * 0x0802LU & 0x22110LU) | (b * 0x8020LU & 0x88440LU)) * 0x10101LU >> 16;

更快（64位处理器）

unsigned char b; // reverse this (8-bit) byteb = (b * 0x0202020202ULL & 0x010884422010ULL) % 1023;

如果要在32位上执行此 *** 作

int

，只需反转每个字节中的位，然后反转字节的顺序即可。那是：

unsigned int toReverse;unsigned int reversed;unsigned char inByte0 = (toReverse & 0xFF);unsigned char inByte1 = (toReverse & 0xFF00) >> 8;unsigned char inByte2 = (toReverse & 0xFF0000) >> 16;unsigned char inByte3 = (toReverse & 0xFF000000) >> 24;reversed = (reverseBits(inByte0) << 24) | (reverseBits(inByte1) << 16) | (reverseBits(inByte2) << 8) | (reverseBits(inByte3);

---

结果

我对两个最有前途的解决方案进行了基准测试，即查找表和按位与（第一个）。测试机器是一台笔记本电脑，带有4GB DDR2-800和一个Core 2 Duo
T7500 @ 2.4GHz，4MB L2缓存；YMMV。我在64位Linux上使用了 gcc
4.3.2。OpenMP（和GCC绑定）用于高分辨率计时器。

反向

#include <stdlib.h>#include <stdio.h>#include <omp.h>unsigned intreverse(register unsigned int x){    x = (((x & 0xaaaaaaaa) >> 1) | ((x & 0x55555555) << 1));    x = (((x & 0xcccccccc) >> 2) | ((x & 0x33333333) << 2));    x = (((x & 0xf0f0f0f0) >> 4) | ((x & 0x0f0f0f0f) << 4));    x = (((x & 0xff00ff00) >> 8) | ((x & 0x00ff00ff) << 8));    return((x >> 16) | (x << 16));}int main(){    unsigned int *ints = malloc(100000000*sizeof(unsigned int));    unsigned int *ints2 = malloc(100000000*sizeof(unsigned int));    for(unsigned int i = 0; i < 100000000; i++)      ints[i] = rand();    unsigned int *inptr = ints;    unsigned int *outptr = ints2;    unsigned int *endptr = ints + 100000000;    // Starting the time measurement    double start = omp_get_wtime();    // Computations to be measured    while(inptr != endptr)    {      (*outptr) = reverse(*inptr);      inptr++;      outptr++;    }    // Measuring the elapsed time    double end = omp_get_wtime();    // Time calculation (in seconds)    printf("Time: %f secondsn", end-start);    free(ints);    free(ints2);    return 0;}

reverse_lookup.c

#include <stdlib.h>#include <stdio.h>#include <omp.h>static const unsigned char BitReverseTable256[] = {  0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0,   0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8,   0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4,   0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC,   0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2,   0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA,  0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6,   0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE,  0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1,  0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9,   0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5,  0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD,  0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3,   0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB,  0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7,   0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF};int main(){    unsigned int *ints = malloc(100000000*sizeof(unsigned int));    unsigned int *ints2 = malloc(100000000*sizeof(unsigned int));    for(unsigned int i = 0; i < 100000000; i++)      ints[i] = rand();    unsigned int *inptr = ints;    unsigned int *outptr = ints2;    unsigned int *endptr = ints + 100000000;    // Starting the time measurement    double start = omp_get_wtime();    // Computations to be measured    while(inptr != endptr)    {    unsigned int in = *inptr;    // Option 1:    //*outptr = (BitReverseTable256[in & 0xff] << 24) |     //    (BitReverseTable256[(in >> 8) & 0xff] << 16) |     //    (BitReverseTable256[(in >> 16) & 0xff] << 8) |    //    (BitReverseTable256[(in >> 24) & 0xff]);    // Option 2:    unsigned char * p = (unsigned char *) &(*inptr);    unsigned char * q = (unsigned char *) &(*outptr);    q[3] = BitReverseTable256[p[0]];     q[2] = BitReverseTable256[p[1]];     q[1] = BitReverseTable256[p[2]];     q[0] = BitReverseTable256[p[3]];      inptr++;      outptr++;    }    // Measuring the elapsed time    double end = omp_get_wtime();    // Time calculation (in seconds)    printf("Time: %f secondsn", end-start);    free(ints);    free(ints2);    return 0;}

我在几种不同的优化条件下尝试了这两种方法，在每个级别上进行了3次试验，每个试验都随机抽取了1亿个样本

unsignedints

。对于查找表选项，我尝试了按位hacks页面上给出的两种方案（选项1和2）。结果如下所示。

按位与

mrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -o reverse reverse.cmrj10@mjlap:~/pre$ ./reverseTime: 2.000593 secondsmrj10@mjlap:~/pre$ ./reverseTime: 1.938893 secondsmrj10@mjlap:~/pre$ ./reverseTime: 1.936365 secondsmrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -O2 -o reverse reverse.cmrj10@mjlap:~/pre$ ./reverseTime: 0.942709 secondsmrj10@mjlap:~/pre$ ./reverseTime: 0.991104 secondsmrj10@mjlap:~/pre$ ./reverseTime: 0.947203 secondsmrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -O3 -o reverse reverse.cmrj10@mjlap:~/pre$ ./reverseTime: 0.922639 secondsmrj10@mjlap:~/pre$ ./reverseTime: 0.892372 secondsmrj10@mjlap:~/pre$ ./reverseTime: 0.891688 seconds

查找表（选项1）

mrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -o reverse_lookup reverse_lookup.cmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.201127 seconds   mrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.196129 seconds   mrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.235972 seconds   mrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -O2 -o reverse_lookup reverse_lookup.cmrj10@mjlap:~/pre$ ./reverse_lookupTime: 0.633042 seconds   mrj10@mjlap:~/pre$ ./reverse_lookupTime: 0.655880 seconds   mrj10@mjlap:~/pre$ ./reverse_lookupTime: 0.633390 seconds   mrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -O3 -o reverse_lookup reverse_lookup.cmrj10@mjlap:~/pre$ ./reverse_lookupTime: 0.652322 seconds   mrj10@mjlap:~/pre$ ./reverse_lookupTime: 0.631739 seconds   mrj10@mjlap:~/pre$ ./reverse_lookupTime: 0.652431 seconds

查找表（选项2）

mrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -o reverse_lookup reverse_lookup.cmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.671537 secondsmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.688173 secondsmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.664662 secondsmrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -O2 -o reverse_lookup reverse_lookup.cmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.049851 secondsmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.048403 secondsmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.085086 secondsmrj10@mjlap:~/pre$ gcc -fopenmp -std=c99 -O3 -o reverse_lookup reverse_lookup.cmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.082223 secondsmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.053431 secondsmrj10@mjlap:~/pre$ ./reverse_lookupTime: 1.081224 seconds

结论

*如果您担心性能 *，请使用带有选项1的查找表
（字节寻址很慢）。如果您需要从系统中挤出内存的最后一个字节（并且您可能会关心位反转的性能），那么按位“与”方法的优化版本也不会太差劲。

警告

是的，我知道基准代码是一个完整的技巧。我们非常欢迎有关如何改进它的建议。我了解的事情：

• 我无权使用ICC。这可能会更快（如果可以测试，请在评论中回复）。
• 在一些具有较大L1D的现代微体系结构上，使用64K查找表可能效果很好。
• -mtune = native不适用于-O2 / -O3（

  ld

  炸毁了一些疯狂的符号重新定义错误），因此我不相信为我的微体系结构调整生成的代码。
• 使用SSE可能有一种更快的方法。我不知道该怎么做，但是有了快速复制，按位与和打包以及令人费解的指令，这里肯定会有一些东西。
• 我知道只有足够多的x86组件很危险；这是在-O3上为选项1生成的代码GCC，因此比我本人更了解的人可以查看一下：

32位

.L3:movl    (%r12,%rsi), %ecxmovzbl  %cl, %eaxmovzbl  BitReverseTable256(%rax), %edxmovl    %ecx, %eaxshrl    , %eaxmov     %eax, %eaxmovzbl  BitReverseTable256(%rax), %eaxsall    , %edxorl     %eax, %edxmovzbl  %ch, %eaxshrl    , %ecxmovzbl  BitReverseTable256(%rax), %eaxmovzbl  %cl, %ecxsall    , %eaxorl     %eax, %edxmovzbl  BitReverseTable256(%rcx), %eaxsall    , %eaxorl     %eax, %edxmovl    %edx, (%r13,%rsi)addq    , %rsicmpq    0000000, %rsijne     .L3

编辑：我也尝试

uint64_t

在计算机上使用类型，以查看是否有任何性能提升。性能比32位快大约10％，无论您是一次使用64位类型同时反转两个32位

int

类型上的位，还是实际上反转了64
位类型的一半，性能几乎相同位值。汇编代码如下所示（对于前一种情况，一次反转两种32位

int

类型的位）：

.L3:movq    (%r12,%rsi), %rdxmovq    %rdx, %raxshrq    , %raxandl    5, %eaxmovzbl  BitReverseTable256(%rax), %ecxmovzbq  %dl,%raxmovzbl  BitReverseTable256(%rax), %eaxsalq    , %raxorq     %rax, %rcxmovq    %rdx, %raxshrq    , %raxmovzbl  BitReverseTable256(%rax), %eaxsalq    , %raxorq     %rax, %rcxmovzbl  %dh, %eaxshrq    , %rdxmovzbl  BitReverseTable256(%rax), %eaxsalq    , %raxorq     %rax, %rcxmovzbq  %dl,%raxshrq    , %rdxmovzbl  BitReverseTable256(%rax), %eaxsalq    , %raxorq     %rax, %rcxmovzbq  %dl,%raxshrq    , %rdxmovzbl  BitReverseTable256(%rax), %eaxsalq    , %raxorq     %rax, %rcxmovzbq  %dl,%raxshrq    , %rdxmovzbl  BitReverseTable256(%rax), %eaxandl    5, %edxsalq    , %raxorq     %rax, %rcxmovzbl  BitReverseTable256(%rdx), %eaxsalq    , %raxorq     %rax, %rcxmovq    %rcx, (%r13,%rsi)addq    , %rsicmpq    0000000, %rsijne     .L3