例如,
n = 3432, result 4
n = 45, result 2
n = 33215, result 5
n = -357, result 3
我想我可以把它变成一个字符串然后得到字符串的长度,但这看起来很复杂和黑客.
pax*_*blo 134
递归方法:-)
int numPlaces (int n) {
if (n < 0) return numPlaces ((n == INT_MIN) ? MAX_INT: -n);
if (n < 10) return 1;
return 1 + numPlaces (n / 10);
}
或者迭代:
int numPlaces (int n) {
int r = 1;
if (n < 0) n = (n == INT_MIN) ? INT_MAX: -n;
while (n > 9) {
n /= 10;
r++;
}
return r;
}
或原始速度:
int numPlaces (int n) {
if (n < 0) n = (n == INT_MIN) ? INT_MAX : -n;
if (n < 10) return 1;
if (n < 100) return 2;
if (n < 1000) return 3;
if (n < 10000) return 4;
if (n < 100000) return 5;
if (n < 1000000) return 6;
if (n < 10000000) return 7;
if (n < 100000000) return 8;
if (n < 1000000000) return 9;
/* 2147483647 is 2^31-1 - add more ifs as needed
and adjust this final return as well. */
return 10;
}
上述内容已经过修改,以便更好地处理MININT.在任何不遵循合理的2 n二进制补码规则的奇怪系统上,它们可能需要进一步调整.
原始速度版本实际上优于浮点版本,修改如下:
int numPlaces (int n) {
if (n == 0) return 1;
return floor (log10 (abs (n))) + 1;
}
通过一亿次迭代,我得到以下结果:
Raw speed with 0: 0 seconds
Raw speed with 2^31-1: 1 second
Iterative with 2^31-1: 5 seconds
Recursive with 2^31-1: 6 seconds
Floating point with 1: 6 seconds
Floating point with 2^31-1: 7 seconds
这实际上让我感到惊讶 - 我认为英特尔芯片有一个不错的FPU,但我猜一般的FP操作仍然无法与手工优化的整数代码竞争.
更新以下stormsoul的建议:
通过stormsoul测试乘法迭代解决方案得到4秒的结果,虽然它比除法迭代解决方案快得多,但它仍然与优化的if语句解决方案不匹配.
从1000个随机生成的数字池中选择参数会将原始速度时间推迟到2秒,因此看起来每次使用相同的参数可能有一些优势,它仍然是列出的最快方法.
使用-O2进行编译可以提高速度但不会提高相对位置(我将迭代次数增加了十倍来检查).
任何进一步的分析都必须认真对待CPU效率的内部工作(不同类型的优化,缓存的使用,分支预测,你实际拥有的CPU,房间里的环境温度等),这将是妨碍我的有偿工作:-).这是一个有趣的转移,但在某些时候,优化投资的回报变得太小而无关紧要.我认为我们有足够的解决方案来回答这个问题(毕竟,这不是关于速度).
进一步更新:
这将是我对此答案的最终更新,除非明显不依赖于体系结构的错误.受到stormsoul勇敢测量的启发,我发布了我的测试程序(根据stormsoul自己的测试程序修改)以及这里答案中显示的所有方法的一些示例数字.请记住,这是在特定的机器上,您的里程可能会因您运行它的位置而有所不同(这就是我发布测试代码的原因).
随心所欲:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>
#include <time.h>
#define numof(a) (sizeof(a) / sizeof(a[0]))
/* Random numbers and accuracy checks. */
static int rndnum[10000];
static int rt[numof(rndnum)];
/* All digit counting functions here. */
static int count_recur (int n) {
if (n < 0) return count_recur ((n == INT_MIN) ? INT_MAX : -n);
if (n < 10) return 1;
return 1 + count_recur (n / 10);
}
static int count_diviter (int n) {
int r = 1;
if (n < 0) n = (n == INT_MIN) ? INT_MAX : -n;
while (n > 9) {
n /= 10;
r++;
}
return r;
}
static int count_multiter (int n) {
unsigned int num = abs(n);
unsigned int x, i;
for (x=10, i=1; ; x*=10, i++) {
if (num < x)
return i;
if (x > INT_MAX/10)
return i+1;
}
}
static int count_ifs (int n) {
if (n < 0) n = (n == INT_MIN) ? INT_MAX : -n;
if (n < 10) return 1;
if (n < 100) return 2;
if (n < 1000) return 3;
if (n < 10000) return 4;
if (n < 100000) return 5;
if (n < 1000000) return 6;
if (n < 10000000) return 7;
if (n < 100000000) return 8;
if (n < 1000000000) return 9;
/* 2147483647 is 2^31-1 - add more ifs as needed
and adjust this final return as well. */
return 10;
}
static int count_revifs (int n) {
if (n < 0) n = (n == INT_MIN) ? INT_MAX : -n;
if (n > 999999999) return 10;
if (n > 99999999) return 9;
if (n > 9999999) return 8;
if (n > 999999) return 7;
if (n > 99999) return 6;
if (n > 9999) return 5;
if (n > 999) return 4;
if (n > 99) return 3;
if (n > 9) return 2;
return 1;
}
static int count_log10 (int n) {
if (n < 0) n = (n == INT_MIN) ? INT_MAX : -n;
if (n == 0) return 1;
return floor (log10 (n)) + 1;
}
static int count_bchop (int n) {
int r = 1;
if (n < 0) n = (n == INT_MIN) ? INT_MAX : -n;
if (n >= 100000000) {
r += 8;
n /= 100000000;
}
if (n >= 10000) {
r += 4;
n /= 10000;
}
if (n >= 100) {
r += 2;
n /= 100;
}
if (n >= 10)
r++;
return r;
}
/* Structure to control calling of functions. */
typedef struct {
int (*fnptr)(int);
char *desc;
} tFn;
static tFn fn[] = {
NULL, NULL,
count_recur, " recursive",
count_diviter, " divide-iterative",
count_multiter, " multiply-iterative",
count_ifs, " if-statements",
count_revifs, "reverse-if-statements",
count_log10, " log-10",
count_bchop, " binary chop",
};
static clock_t clk[numof (fn)];
int main (int c, char *v[]) {
int i, j, k, r;
int s = 1;
/* Test code:
printf ("%11d %d\n", INT_MIN, count_recur(INT_MIN));
for (i = -1000000000; i != 0; i /= 10)
printf ("%11d %d\n", i, count_recur(i));
printf ("%11d %d\n", 0, count_recur(0));
for (i = 1; i != 1000000000; i *= 10)
printf ("%11d %d\n", i, count_recur(i));
printf ("%11d %d\n", 1000000000, count_recur(1000000000));
printf ("%11d %d\n", INT_MAX, count_recur(INT_MAX));
/* */
/* Randomize and create random pool of numbers. */
srand (time (NULL));
for (j = 0; j < numof (rndnum); j++) {
rndnum[j] = s * rand();
s = -s;
}
rndnum[0] = INT_MAX;
rndnum[1] = INT_MIN;
/* For testing. */
for (k = 0; k < numof (rndnum); k++) {
rt[k] = (fn[1].fnptr)(rndnum[k]);
}
/* Test each of the functions in turn. */
clk[0] = clock();
for (i = 1; i < numof (fn); i++) {
for (j = 0; j < 10000; j++) {
for (k = 0; k < numof (rndnum); k++) {
r = (fn[i].fnptr)(rndnum[k]);
/* Test code:
if (r != rt[k]) {
printf ("Mismatch error [%s] %d %d %d %d\n",
fn[i].desc, k, rndnum[k], rt[k], r);
return 1;
}
/* */
}
}
clk[i] = clock();
}
/* Print out results. */
for (i = 1; i < numof (fn); i++) {
printf ("Time for %s: %10d\n", fn[i].desc, (int)(clk[i] - clk[i-1]));
}
return 0;
}
请记住,您需要确保使用正确的命令行来编译它.特别是,您可能需要明确列出数学库才能
log10()正常工作.我在Debian下使用的命令行是gcc -o testprog testprog.c -lm.
而且,就结果而言,这是我环境的领导者:
优化等级0:
Time for reverse-if-statements: 1704
Time for if-statements: 2296
Time for binary chop: 2515
Time for multiply-iterative: 5141
Time for divide-iterative: 7375
Time for recursive: 10469
Time for log-10: 26953
优化级别3:
Time for if-statements: 1047
Time for binary chop: 1156
Time for reverse-if-statements: 1500
Time for multiply-iterative: 2937
Time for divide-iterative: 5391
Time for recursive: 8875
Time for log-10: 25438
edu*_*ffy 98
floor (log10 (abs (x))) + 1
http://en.wikipedia.org/wiki/Logarithm
R..*_*R.. 27
最短的答案: snprintf(0,0,"%+d",n)-1
lak*_*raj 26
二进制搜索伪算法得到v中的r的数字.
if (v < 0 ) v=-v;
r=1;
if (v >= 100000000)
{
r+=8;
v/=100000000;
}
if (v >= 10000) {
r+=4;
v/=10000;
}
if (v >= 100) {
r+=2;
v/=100;
}
if( v>=10)
{
r+=1;
}
return r;
vit*_*aut 11
这是Kendall Willets计算小数位数的一种非常快速的方法：
int count_digits(uint32_t n) {
#ifndef __has_builtin
# define __has_builtin(x) 0
#endif
#if __has_builtin(__builtin_clz)
// This increments the upper 32 bits (log10(T) - 1) when >= T is added.
# define K(T) (((sizeof(#T) - 1ull) << 32) - T)
static const uint64_t table[] = {
K(0), K(0), K(0), // 8
K(10), K(10), K(10), // 64
K(100), K(100), K(100), // 512
K(1000), K(1000), K(1000), // 4096
K(10000), K(10000), K(10000), // 32k
K(100000), K(100000), K(100000), // 256k
K(1000000), K(1000000), K(1000000), // 2048k
K(10000000), K(10000000), K(10000000), // 16M
K(100000000), K(100000000), K(100000000), // 128M
K(1000000000), K(1000000000), K(1000000000), // 1024M
K(1000000000), K(1000000000) // 4B
};
return (n + table[__builtin_clz(n | 1) ^ 31]) >> 32u;
#else
int count = 1;
for (;;) {
if (n < 10) return count;
if (n < 100) return count + 1;
if (n < 1000) return count + 2;
if (n < 10000) return count + 3;
n /= 10000u;
count += 4;
}
return count;
#endif
}
快速路径依赖__builtin_clz于 GCC 和 clang 中可用的路径，但由于回退工作得相当好count_digits是完全可移植的。
这会生成非常高效的代码（Godbolt）：
count_digits(unsigned int):
mov edx, edi
mov eax, edi
or edx, 1
bsr edx, edx
movsx rdx, edx
add rax, QWORD PTR count_digits(unsigned int)::table[0+rdx*8]
shr rax, 32
ret
在循环中除以10直到结果达到零.迭代次数将对应于小数位数.
假设您期望在零值中获得0位数:
int countDigits( int value )
{
int result = 0;
while( value != 0 ) {
value /= 10;
result++;
}
return result;
}
这是一个展开的二进制搜索，没有任何除法或乘法。根据给出的数字分布，它可能会也可能不会击败其他使用展开的 if 语句完成的数字，但应该始终击败使用循环和乘法/除法/log10 的数字。
由于随机数均匀分布在整个范围内，在我的机器上，它平均占 paxdiablo 的 count_bchop() 执行时间的 79%、count_ifs() 的时间的 88% 和 count_revifs() 的时间的 97%。
使用指数分布（一个数字有n位的概率等于它有m位的概率，其中m ? n）count_ifs() 和 count_revifs() 都击败了我的函数。我不知道为什么在这一点上。
int count_bsearch(int i)
{
if (i < 0)
{
if (i == INT_MIN)
return 10; // special case for -2^31 because 2^31 can't fit in a two's complement 32-bit integer
i = -i;
}
if (i < 100000) {
if (i < 1000) {
if (i < 10) return 1;
else if (i < 100) return 2;
else return 3;
} else {
if (i < 10000) return 4;
else return 5;
}
} else {
if (i < 10000000) {
if (i < 1000000) return 6;
else return 7;
} else {
if (i < 100000000) return 8;
else if (i < 1000000000) return 9;
else return 10;
}
}
}
你可以这样做:
floor (log10 (abs (x))) + 1
或者如果你想节省周期,你可以做比较
if(x<10)
return 1;
if(x<100)
return 2;
if(x<1000)
return 3;
etc etc
这避免了任何计算上昂贵的功能,例如日志甚至乘法或除法.虽然它不够优雅,但可以通过将其封装到一个函数中来隐藏它.它不复杂或难以维护,因此我不会因编码不良而忽略这种方法; 我觉得这样做会把洗澡水扔掉.
使用x86程序集和查找表的恒定成本版本:
int count_bsr(int i) {
struct {
int max;
int count;
} static digits[32] = {
{ 9, 1 }, { 9, 1 }, { 9, 1 }, { 9, 1 },
{ 99, 2 }, { 99, 2 }, { 99, 2 },
{ 999, 3 }, { 999, 3 }, { 999, 3 },
{ 9999, 4 }, { 9999, 4 }, { 9999, 4 }, { 9999, 4 },
{ 99999, 5 }, { 99999, 5 }, { 99999, 5 },
{ 999999, 6 }, { 999999, 6 }, { 999999, 6 },
{ 9999999, 7 }, { 9999999, 7 }, { 9999999, 7 }, { 9999999, 7 },
{ 99999999, 8 }, { 99999999, 8 }, { 99999999, 8 },
{ 999999999, 9 }, { 999999999, 9 }, { 999999999, 9 },
{ INT_MAX, 10 }, { INT_MAX, 10 }
};
register const int z = 0;
register unsigned log2;
if (i < 0) i = -i;
__asm__ __volatile__ (
"bsr %1, %0;" \
"cmovz %2, %0;"\
: "=r" (log2) \
: "rm" (i), "r"(z));
return digits[log2].count + ( i > digits[log2].max );
}
另一个,具有较小的查找表和从此处获取的log10近似值.
int count_bsr2( int i ) {
static const unsigned limits[] =
{0, 10, 100, 1000, 10000, 100000,
1000000, 10000000, 100000000, 1000000000};
register const int z = 0;
register int l, log2;
if (i < 0) i = -i;
__asm__ __volatile__ (
"bsr %1, %0;" \
"cmovz %2, %0;"\
: "=r" (log2) \
: "rm" (i), "r"(z));
l = (log2 + 1) * 1233 >> 12;
return (l + ((unsigned)i >= limits[l]));
}
这两个都利用了x86 -INT_MIN等于INT_MIN的事实.
更新:
根据建议,这里有count_bsr和一个稍微快一点的64位count_bsr_mod例程的时间,与二进制搜索和二进制斩波算法相比,使用非常好的paxdiablo测试程序进行修改以生成具有随机符号分布的集合.测试是使用gcc 4.9.2使用"-O3 -falign-functions = 16 -falign-jumps = 16 -march = corei7-avx"选项构建的,并在一个静止的Sandy Bridge系统上执行,并且关闭了turbo和sleep状态.
Time for bsr mod: 270000 Time for bsr: 340000 Time for binary chop: 800000 Time for binary search: 770000 Time for binary search mod: 470000
测试来源,
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>
#include <time.h>
#define numof(a) (sizeof(a) / sizeof(a[0]))
/* Random numbers and accuracy checks. */
static int rndnum[10000];
static int rt[numof(rndnum)];
/* All digit counting functions here. */
static int count_bchop (int n) {
int r = 1;
if (n < 0) n = (n == INT_MIN) ? INT_MAX : -n;
if (n >= 100000000) {
r += 8;
n /= 100000000;
}
if (n >= 10000) {
r += 4;
n /= 10000;
}
if (n >= 100) {
r += 2;
n /= 100;
}
if (n >= 10)
r++;
return r;
}
static int count_bsearch(int i)
{
if (i < 0)
{
if (i == INT_MIN)
return 11; // special case for -2^31 because 2^31 can't fit in a two's complement 32-bit integer
i = -i;
}
if (i < 100000) {
if (i < 1000) {
if (i < 10) return 1;
else if (i < 100) return 2;
else return 3;
} else {
if (i < 10000) return 4;
else return 5;
}
} else {
if (i < 10000000) {
if (i < 1000000) return 6;
else return 7;
} else {
if (i < 100000000) return 8;
else if (i < 1000000000) return 9;
else return 10;
}
}
}
// Integer log base 10, modified binary search.
static int count_bsearch_mod(int i) {
unsigned x = (i >= 0) ? i : -i;
if (x > 99)
if (x > 999999)
if (x > 99999999)
return 9 + (x > 999999999);
else
return 7 + (x > 9999999);
else
if (x > 9999)
return 5 + (x > 99999);
else
return 3 + (x > 999);
else
return 1 + (x > 9);
}
static int count_bsr_mod(int i) {
struct {
int m_count;
int m_threshold;
} static digits[32] =
{
{ 1, 9 }, { 1, 9 }, { 1, 9 }, { 1, 9 },
{ 2, 99 }, { 2, 99 }, { 2, 99 },
{ 3, 999 }, { 3, 999 }, { 3, 999 },
{ 4, 9999 }, { 4, 9999 }, { 4, 9999 }, { 4, 9999 },
{ 5, 99999 }, { 5, 99999 }, { 5, 99999 },
{ 6, 999999 }, { 6, 999999 }, { 6, 999999 },
{ 7, 9999999 }, { 7, 9999999 }, { 7, 9999999 }, { 7, 9999999 },
{ 8, 99999999 }, { 8, 99999999 }, { 8, 99999999 },
{ 9, 999999999 }, { 9, 999999999 }, { 9, 999999999 },
{ 10, INT_MAX }, { 10, INT_MAX }
};
__asm__ __volatile__ (
"cdq \n\t"
"xorl %%edx, %0 \n\t"
"subl %%edx, %0 \n\t"
"movl %0, %%edx \n\t"
"bsrl %0, %0 \n\t"
"shlq $32, %%rdx \n\t"
"movq %P1(,%q0,8), %q0 \n\t"
"cmpq %q0, %%rdx \n\t"
"setg %%dl \n\t"
"addl %%edx, %0 \n\t"
: "+a"(i)
: "i"(digits)
: "rdx", "cc"
);
return i;
}
static int count_bsr(int i) {
struct {
int max;
int count;
} static digits[32] = {
{ 9, 1 }, { 9, 1 }, { 9, 1 }, { 9, 1 },
{ 99, 2 }, { 99, 2 }, { 99, 2 },
{ 999, 3 }, { 999, 3 }, { 999, 3 },
{ 9999, 4 }, { 9999, 4 }, { 9999, 4 }, { 9999, 4 },
{ 99999, 5 }, { 99999, 5 }, { 99999, 5 },
{ 999999, 6 }, { 999999, 6 }, { 999999, 6 },
{ 9999999, 7 }, { 9999999, 7 }, { 9999999, 7 }, { 9999999, 7 },
{ 99999999, 8 }, { 99999999, 8 }, { 99999999, 8 },
{ 999999999, 9 }, { 999999999, 9 }, { 999999999, 9 },
{ INT_MAX, 10 }, { INT_MAX, 10 }
};
register const int z = 0;
register unsigned log2;
if (i < 0) i = -i;
__asm__ __volatile__ (
"bsr %1, %0;" \
"cmovz %2, %0;"\
: "=r" (log2) \
: "rm" (i), "r"(z));
return digits[log2].count + ( i > digits[log2].max );
}
/* Structure to control calling of functions. */
typedef struct {
int (*fnptr)(int);
const char *desc;
} tFn;
static tFn fn[] = {
{ NULL, NULL },
{ count_bsr_mod, " bsr mod" },
{ count_bsr, " bsr" },
{ count_bchop, " binary chop" },
{ count_bsearch, " binary search" },
{ count_bsearch_mod," binary search mod"}
};
static clock_t clk[numof (fn)];
int main (int c, char *v[]) {
int i, j, k, r;
int s = 1;
/* Test code:
printf ("%11d %d\n", INT_MIN, count_bsearch(INT_MIN));
//for (i = -1000000000; i != 0; i /= 10)
for (i = -999999999; i != 0; i /= 10)
printf ("%11d %d\n", i, count_bsearch(i));
printf ("%11d %d\n", 0, count_bsearch(0));
for (i = 1; i != 1000000000; i *= 10)
printf ("%11d %d\n", i, count_bsearch(i));
printf ("%11d %d\n", 1000000000, count_bsearch(1000000000));
printf ("%11d %d\n", INT_MAX, count_bsearch(INT_MAX));
return 0;
/* */
/* Randomize and create random pool of numbers. */
int p, n;
p = n = 0;
srand (time (NULL));
for (j = 0; j < numof (rndnum); j++) {
rndnum[j] = ((rand() & 2) - 1) * rand();
}
rndnum[0] = INT_MAX;
rndnum[1] = INT_MIN;
/* For testing. */
for (k = 0; k < numof (rndnum); k++) {
rt[k] = (fn[1].fnptr)(rndnum[k]);
}
/* Test each of the functions in turn. */
clk[0] = clock();
for (i = 1; i < numof (fn); i++) {
for (j = 0; j < 10000; j++) {
for (k = 0; k < numof (rndnum); k++) {
r = (fn[i].fnptr)(rndnum[k]);
/* Test code:
if (r != rt[k]) {
printf ("Mismatch error [%s] %d %d %d %d\n",
fn[i].desc, k, rndnum[k], rt[k], r);
return 1;
}
/* */
}
}
clk[i] = clock();
}
/* Print out results. */
for (i = 1; i < numof (fn); i++) {
printf ("Time for %s: %10d\n", fn[i].desc, (int)(clk[i] - clk[i-1]));
}
return 0;
}
我在谷歌搜索中偶然发现了这个：http ://web.archive.org/web/20190108211528/http: //www.hackersdelight.org/hdcodetxt/ilog.c.txt
快速基准测试清楚地表明二分搜索方法获胜。lakshmanaraj 的代码非常好，Alexander Korobka 的代码快了约 30%，Deadcode 的代码仍然要快一点（约 10%），但我发现上面链接中的以下技巧进一步提高了 10%。
// Integer log base 10, modified binary search.
int ilog10c(unsigned x) {
if (x > 99)
if (x < 1000000)
if (x < 10000)
return 3 + ((int)(x - 1000) >> 31);
// return 3 - ((x - 1000) >> 31); // Alternative.
// return 2 + ((999 - x) >> 31); // Alternative.
// return 2 + ((x + 2147482648) >> 31); // Alternative.
else
return 5 + ((int)(x - 100000) >> 31);
else
if (x < 100000000)
return 7 + ((int)(x - 10000000) >> 31);
else
return 9 + ((int)((x-1000000000)&~x) >> 31);
// return 8 + (((x + 1147483648) | x) >> 31); // Alternative.
else
if (x > 9)
return 1;
else
return ((int)(x - 1) >> 31);
// return ((int)(x - 1) >> 31) | ((unsigned)(9 - x) >> 31); // Alt.
// return (x > 9) + (x > 0) - 1; // Alt.
}
请注意，这是日志 10，而不是位数，因此digits = ilog10c(x)+1.
不支持底片，但这很容易用-.