实现以下目的的最有效算法是：
0010 0000 => 0000 0100
转换是从MSB-> LSB到LSB-> MSB。所有位都必须反转；也就是说，这 不是 字节序交换。
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：）
低内存（32位int，32位计算机）（从此处开始）：
int
unsigned int reverse(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 time unsigned 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。
简单
unsigned int v; // input bits to be reversed unsigned int r = v & 1; // r will be reversed bits of v; first get LSB of v int s = sizeof(v) * CHAR_BIT - 1; // extra shift needed at end for (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) byte b = (b * 0x0202020202ULL & 0x010884422010ULL) % 1023;
如果要在32位上执行此操作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);
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 int reverse(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 seconds\n", 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 seconds\n", 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unsigned ints。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。
unsigned ints
按位与
mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -o reverse reverse.c mrj10@mjlap:~/code$ ./reverse Time: 2.000593 seconds mrj10@mjlap:~/code$ ./reverse Time: 1.938893 seconds mrj10@mjlap:~/code$ ./reverse Time: 1.936365 seconds mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -O2 -o reverse reverse.c mrj10@mjlap:~/code$ ./reverse Time: 0.942709 seconds mrj10@mjlap:~/code$ ./reverse Time: 0.991104 seconds mrj10@mjlap:~/code$ ./reverse Time: 0.947203 seconds mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -O3 -o reverse reverse.c mrj10@mjlap:~/code$ ./reverse Time: 0.922639 seconds mrj10@mjlap:~/code$ ./reverse Time: 0.892372 seconds mrj10@mjlap:~/code$ ./reverse Time: 0.891688 seconds
查找表（选项1）
mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -o reverse_lookup reverse_lookup.c mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.201127 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.196129 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.235972 seconds mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -O2 -o reverse_lookup reverse_lookup.c mrj10@mjlap:~/code$ ./reverse_lookup Time: 0.633042 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 0.655880 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 0.633390 seconds mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -O3 -o reverse_lookup reverse_lookup.c mrj10@mjlap:~/code$ ./reverse_lookup Time: 0.652322 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 0.631739 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 0.652431 seconds
查找表（选项2）
mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -o reverse_lookup reverse_lookup.c mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.671537 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.688173 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.664662 seconds mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -O2 -o reverse_lookup reverse_lookup.c mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.049851 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.048403 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.085086 seconds mrj10@mjlap:~/code$ gcc -fopenmp -std=c99 -O3 -o reverse_lookup reverse_lookup.c mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.082223 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.053431 seconds mrj10@mjlap:~/code$ ./reverse_lookup Time: 1.081224 seconds
*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。
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：
ld
32位
.L3: movl (%r12,%rsi), %ecx movzbl %cl, %eax movzbl BitReverseTable256(%rax), %edx movl %ecx, %eax shrl $24, %eax mov %eax, %eax movzbl BitReverseTable256(%rax), %eax sall $24, %edx orl %eax, %edx movzbl %ch, %eax shrl $16, %ecx movzbl BitReverseTable256(%rax), %eax movzbl %cl, %ecx sall $16, %eax orl %eax, %edx movzbl BitReverseTable256(%rcx), %eax sall $8, %eax orl %eax, %edx movl %edx, (%r13,%rsi) addq $4, %rsi cmpq $400000000, %rsi jne .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）：
uint64_t
.L3: movq (%r12,%rsi), %rdx movq %rdx, %rax shrq $24, %rax andl $255, %eax movzbl BitReverseTable256(%rax), %ecx movzbq %dl,%rax movzbl BitReverseTable256(%rax), %eax salq $24, %rax orq %rax, %rcx movq %rdx, %rax shrq $56, %rax movzbl BitReverseTable256(%rax), %eax salq $32, %rax orq %rax, %rcx movzbl %dh, %eax shrq $16, %rdx movzbl BitReverseTable256(%rax), %eax salq $16, %rax orq %rax, %rcx movzbq %dl,%rax shrq $16, %rdx movzbl BitReverseTable256(%rax), %eax salq $8, %rax orq %rax, %rcx movzbq %dl,%rax shrq $8, %rdx movzbl BitReverseTable256(%rax), %eax salq $56, %rax orq %rax, %rcx movzbq %dl,%rax shrq $8, %rdx movzbl BitReverseTable256(%rax), %eax andl $255, %edx salq $48, %rax orq %rax, %rcx movzbl BitReverseTable256(%rdx), %eax salq $40, %rax orq %rax, %rcx movq %rcx, (%r13,%rsi) addq $8, %rsi cmpq $400000000, %rsi jne .L3
