平方数数字和 - 第11页 - 编程擂台 - 数学研发论坛

无心人 发表于 2008-7-14 10:13:06

那我修改下，用icc给编译下

如果时间比你少
甚至时间是你的120％
都算icc编译器厉害，呵呵

mathe 发表于 2008-7-14 10:16:44

呵呵，最好采用profiling再编译一把，这样编译器产生的代码可能会更好:lol

无心人 发表于 2008-7-14 10:42:29

0.000112 X = 1 S = 1
0.000235 X = 4 S = 4
0.000248 X = 9 S = 9
0.000260 X = 7 S = 16
0.000271 X = 13 S = 49
0.000282 X = 10 S = 64

****** 0.000292: Searched all perfect squares less then 10^2 ******

0.000307 X = 16 S = 169
0.000319 X = 19 S = 289
0.000330 X = 18 S = 576
0.000341 X = 22 S = 1849
0.000352 X = 27 S = 3969
0.000363 X = 25 S = 4489
0.000374 X = 31 S = 6889

****** 0.000385: Searched all perfect squares less then 10^4 ******

0.000400 X = 28 S = 17956
0.000412 X = 34 S = 27889
0.000425 X = 36 S = 69696
0.000438 X = 40 S = 97969
0.000616 X = 37 S = 98596
0.000638 X = 43 S = 499849
0.000652 X = 46 S = 698896

****** 0.000666: Searched all perfect squares less then 10^6 ******

0.000689 X = 45 S = 1887876
0.000707 X = 49 S = 2778889
0.000729 X = 52 S = 4999696
0.000758 X = 54 S = 9696996
0.000797 X = 55 S = 19998784
0.000855 X = 58 S = 46689889
0.000894 X = 61 S = 66699889
0.000921 X = 63 S = 79869969

****** 0.000954: Searched all perfect squares less then 10^8 ******

0.001139 X = 64 S = 277788889
0.001282 X = 67 S = 478996996
0.001489 X = 70 S = 876988996
0.001809 X = 73 S = 1749999889
0.002297 X = 72 S = 3679999569
0.002669 X = 76 S = 5599977889
0.003054 X = 79 S = 7998976969
0.003204 X = 81 S = 8998988769

****** 0.003346: Searched all perfect squares less then 10^10 ******

0.004232 X = 82 S = 17999978896
0.005733 X = 85 S = 36799899889
0.013798 X = 88 S = 88998998929
0.019962 X = 90 S = 297889998849
0.020022 X = 91 S = 299879997769
0.070643 X = 94 S = 897977978689
0.073355 X = 97 S = 975979998889

****** 0.073682: Searched all perfect squares less then 10^12 ******

0.206107 X = 100 S = 2699997789889
0.295351 X = 99 S = 3957779999889
0.438211 X = 103 S = 9879498789889
0.439921 X = 106 S = 9998768898889
0.780301 X = 108 S = 29998985899689
1.278534 X = 109 S = 85986989688889
1.387117 X = 112 S = 97888999968769

****** 1.396139: Searched all perfect squares less then 10^14 ******

2.541476 X = 115 S = 386999898769969
2.713739 X = 117 S = 429998989997889
3.123124 X = 118 S = 578889999977689
3.854804 X = 121 S = 898999897988929
5.541493 X = 124 S = 1959999889996996
7.524612 X = 127 S = 3699998989898689
10.197799 X = 126 S = 6788999798879769
12.371455 X = 130 S = 9895699989899689

****** 12.431427: Searched all perfect squares less then 10^16 ******

24.814522 X = 133 S = 38896878989988889
24.862220 X = 136 S = 38999699989995889
32.795631 X = 135 S = 67699789959899889
53.410336 X = 139 S = 188997899869998769
64.464989 X = 142 S = 279869897899999969
85.710894 X = 144 S = 498999778899898896
119.855649 X = 148 S = 989879999979599689

****** 120.465921: Searched all perfect squares less then 10^18 ******

164.041346 X = 145 S = 1877896979979898969
289.218007 X = 153 S = 5899989587897999889
314.673115 X = 151 S = 6979497898999879969
354.978235 X = 154 S = 8899988895999696889

无心人 发表于 2008-7-14 10:43:56

修改后代码
基本维持GxQ原意

#include <stdlib.h>
#include <stdio.h>
#include <sys/time.h>

#define TEN_POW2 100UL
#define TEN_POW4 10000UL
#define UINT32 unsigned long
#define LIMBS    5

UINT32 m, s;
UINT32 pool[ TEN_POW4 + LIMBS * 39 + 1 ];

#define table(x) pool
#define value(x) pool[(x) + TEN_POW4]
#define delta(x) pool[(x) + TEN_POW4 + LIMBS]
#define index(x) pool[(x) + TEN_POW4 + LIMBS * 2]
#define exist(x) pool[(x) + TEN_POW4 + LIMBS * 3 + 1]

void init( void )
{
UINT32 i1, i2, i3, i4;
UINT32 * p = &table(0) - 1;

memset( pool, 0, sizeof( pool ));

for ( i1 = 0; i1 < 10; ++i1 )
{
   for ( i2 = 0; i2 < 10; ++i2 )
   {
         for ( i3 = 0; i3 < 10; ++i3 )
         {
            for ( i4 = 0; i4 < 10; ++i4 )
            {
               *(++p) = i1 + i2 + i3 + i4;
            }
         }
   }
}
}

void sumOfDigits( void )
{
s = 0;
for ( UINT32 i = 0; i <= m; ++i )
{
   value(i) += delta(i);
   if ( value(i) >= TEN_POW4 )
   {/* 当 i==m 时不会进入，因此时平方根<100^(m+1) */
         value(i) -= TEN_POW4;
         ++value(i+1);
   }

   s += table( value(i) );
}
}

#define add_value(x)    value(x) += delta(x)
#define mod_value(x)    if ( value(x) >= TEN_POW4 ){ value(x) -= TEN_POW4; ++value(x+1); }
#define lookup(x)       table( value(x) )

void sumOfDigits_1( void )
{
add_value(0);

s = lookup(0);
}

void sumOfDigits_2( void )
{
add_value(0);
add_value(1);

mod_value(0);

s = lookup( 0 ) + lookup( 1 );
}

void sumOfDigits_3( void )
{
add_value(0);
add_value(1);
add_value(2);

mod_value(0);
mod_value(1);

s = lookup( 0 ) + lookup( 1 ) + lookup( 2 );
}

void sumOfDigits_4( void )
{
add_value(0);
add_value(1);
add_value(2);
add_value(3);

mod_value(0);
mod_value(1);
mod_value(2);

s = lookup( 0 ) + lookup( 1 ) + lookup( 2 ) + lookup( 3 );
}

void sumOfDigits_5( void )
{
add_value(0);
add_value(1);
add_value(2);
add_value(3);
add_value(4);

mod_value(0);
mod_value(1);
mod_value(2);
mod_value(3);

s = lookup( 0 ) + lookup( 1 ) + lookup( 2 ) + lookup( 3 ) + lookup(
4 );
}

void sumOfDigits_6( void )
{
add_value(0);
add_value(1);
add_value(2);
add_value(3);
add_value(4);
add_value(5);

mod_value(0);
mod_value(1);
mod_value(2);
mod_value(3);
mod_value(4);

s = lookup( 0 ) + lookup( 1 ) + lookup( 2 ) + lookup( 3 ) + lookup(
4 ) \
   + lookup( 5 );
}

void sumOfDigits_7( void )
{
add_value(0);
add_value(1);
add_value(2);
add_value(3);
add_value(4);
add_value(5);
add_value(6);

mod_value(0);
mod_value(1);
mod_value(2);
mod_value(3);
mod_value(4);
mod_value(5);

s = lookup( 0 ) + lookup( 1 ) + lookup( 2 ) + lookup( 3 ) \
   + lookup( 4 ) + lookup( 5 ) + lookup( 6 );
}

typedef void ( *lpfnSumOfDigits )( void );

lpfnSumOfDigits lpfn[ ] = { sumOfDigits, sumOfDigits_1, sumOfDigits_2,
sumOfDigits_3, \
sumOfDigits_4, sumOfDigits_5, sumOfDigits_6, sumOfDigits_7 };

int main( void )
{
UINT32 i;
struct timeval start, end;
double timeuse;
lpfnSumOfDigits SumOfDigits = lpfn[ 1 ];

gettimeofday(&start, NULL);

init();

index(0) = 1;
delta(0) = -1;
m = 0;
for ( ; ; )
{
   delta(0) += 2;
   if ( delta(0) > TEN_POW4 )
   {
         delta(0) = 1;

         i = 0;
         while ( TEN_POW4 == ++delta(++i) )
         {
            delta(i) = 0;
         }
   }

   SumOfDigits();

   if ( 0 == exist(s) )
   {
         exist(s) = 1;

         gettimeofday(&end, NULL);
         timeuse = 1000000 * ( end.tv_sec - start.tv_sec ) + end.tv_usec - start.tv_usec;
         timeuse /= 1000000;

         printf( "%6.6f", timeuse );
         printf( "\tX = %u\t\tS = %u", s, value( i = m ) );
         while ( 0 != i )
         {
            printf( "%04u", value(--i) );
         }
         printf( "\n" );
   }

   i = -1;
   while ( TEN_POW2 == ++index(++i) )
   {
         index(i) = 0;
   }

   if ( m < i )
   {
         m = i;

         gettimeofday(&end, NULL);
         timeuse = 1000000 * ( end.tv_sec - start.tv_sec ) + end.tv_usec - start.tv_usec;
         timeuse /= 1000000;

         printf( "\n****** %6.6f: Searched all perfect squares less then 10^%u ******\n\n", timeuse, 4*m );

         if ( LIMBS == i )
         {
            break;
         }

#if ( LIMBS > 7)
         if ( m + 1 >= sizeof( lpfn ) / sizeof( lpfn ))
         {
            SumOfDigits = lpfn[ 0 ];
         }
         else
#endif
         {

            SumOfDigits = lpfn[ m + 1 ];
         }
   }
   else if ( i == m && 10 == index(m) )
   {
         gettimeofday(&end, NULL);
         timeuse = 1000000 * ( end.tv_sec - start.tv_sec ) + end.tv_usec - start.tv_usec;
         timeuse /= 1000000;

         printf( "\n****** %6.6f: Searched all perfect squares less then 10^%u ******\n\n", timeuse, 4*m + 2 );
   }
}

gettimeofday(&end, NULL);
timeuse = 1000000 * ( end.tv_sec - start.tv_sec ) + end.tv_usec - start.tv_usec;
timeuse /= 1000000;

printf( "\nComputation took %6.6f\n\n", timeuse );

system( "pause" );

return 0;
}

／／／／／／／／／／／／／／／／／／／／
可以看出，所用时间远大于我原来贴的时间
下面我贴我修改的他原始程序的代码

无心人 发表于 2008-7-14 10:45:09

#include <stdlib.h>
#include <stdio.h>
#include <sys/time.h>

#define TEN_POW2 100UL
#define TEN_POW4 10000UL

int main( void )
{
struct timeval start, end;
double timeuse;
unsigned long table[ TEN_POW4 ];
unsigned long mark[ 9*32 + 1 ];
unsigned long value[ 8 ], delta[ 8 ];
unsigned long * p = table;

unsigned long i, j, k, m, s;
long t;
unsigned long i2, i3, i4, s2, s3;

for ( i4 = 0; i4 < 10; ++i4 )
{
   for ( i3 = 0; i3 < 10; ++i3 )
   {
         s3 = i4 + i3;
         for ( i2 = 0; i2 < 10; ++i2 )
         {
            s2 = s3 + i2;
            for ( i = 0; i < 10; ++i )
            {
               *p++ = s2 + i;
            }
         }
   }
}

for (i=0; i < 8; i ++)
{
   value = 0;
   delta = 0;
}

for (i = 0; i < 9*32 + 1; i ++)
   mark = 0;

value[ 0 ] = 0;
delta[ 0 ] = 1;
m = 1;
k = 0;

gettimeofday(&start, NULL);

for ( ; ; )
{
   s = 0;
   for ( i = 0; i < m; ++i )
   {
         value[ i ] += delta[ i ];
         if ( value[ i ] >= TEN_POW4 )
         {
            value[ i ] -= TEN_POW4;
            ++value[ i + 1 ];
         }

         s += table[ value[ i ] ];
   }


   if (value)
      {
         m++;
         s++;
      }

   if ( 0 == mark[ s ])
   {
   mark = 1;

   gettimeofday(&end, NULL);
   timeuse = 1000000 * ( end.tv_sec - start.tv_sec ) + end.tv_usec - start.tv_usec;
   timeuse /= 1000000;

   printf("%8.6f:%", timeuse);
   printf("%4d", s);
   for (t=m-1;t>=0;t--)
      printf("%4d", value);
   printf("\n");
   }

   if (m >= 9)
      break;

   delta[ 0 ] += 2;

   i = 0;
   while ( delta[ i ] >= TEN_POW4 )
   {
         delta[ i ] -= TEN_POW4;
         ++delta[ ++i ];
   }
   k ++;
   if (k == 0)
   {
   printf("\n");
   printf("Current: ");
   for (t=m-1;t>=0; t--)
      printf("%04d", value);
   printf("\n\n");
   }
}

s = 0;
i = 0;
printf( "\n" );

return 0;
}

／／／／／／／／／／／／／／／／／／／／／／／／／／／
我估计原因在于他分离了加和下面的调整进位造成的

无心人 发表于 2008-7-14 10:49:56

TO: mathe
如何进行二次优化？？
用intel C++?
我对105#原始程序进行下优化

mathe 发表于 2008-7-14 11:05:30

查看了一下,第一次编译用
-prof-gen
选项
第二次编译在同一个目录下用
-prof-use

gxqcn 发表于 2008-7-14 11:11:43

我曾对比过，用 ICC 编译该代码，效率不升反降。:L 不知问题出在哪里？:Q:
各位不妨测试一下，尤其是无心人对比测试一下看看。。。

无心人 发表于 2008-7-14 11:16:30

:lol

可能是你优化的不如icc彻底
反而让icc给优化倒了

你不用优化选项
光产生sse2代码试下

无心人 发表于 2008-7-14 11:37:26

0.000004: 1 1
0.000119: 4 4
0.000130: 9 9
0.000138: 7 16
0.000146: 13 49
0.000154: 10 64
0.000162: 16 169
0.000170: 19 289
0.000179: 18 576
0.000187: 221849
0.000195: 273969
0.000203: 254489
0.000212: 316889
0.000221: 28 17956
0.000230: 34 27889
0.000240: 36 69696
0.000249: 40 97969
0.000258: 37 98596
0.000273: 43 499849
0.000284: 46 698896
0.000301: 45 1887876
0.000314: 49 2778889
0.000330: 52 4999696
0.000350: 54 9696996
0.000379: 5519998784
0.000419: 5846689889
0.000446: 6166699889
0.000466: 6379869969
0.000600: 64 277788889
0.000697: 67 478996996
0.000837: 70 876988996
0.001050: 73 1749999889
0.001375: 72 3679999569
0.001624: 76 5599977889
0.001891: 79 7998976969
0.001994: 81 8998988769
0.002726: 82 17999978896
0.003747: 85 36799899889
0.005625: 88 88998998929
0.011515: 90297889998849
0.011592: 91299879997769
0.052307: 94897977978689
0.054137: 97975979998889
0.096983: 100 2699997789889
0.105409: 99 3957779999889
0.163203: 103 9879498789889
0.163819: 106 9998768898889
0.255277: 108 29998985899689
0.399672: 109 85986989688889
0.422920: 112 97888999968769
0.765848: 115 386999898769969
0.832703: 117 429998989997889
1.053660: 118 578889999977689
1.342495: 121 898999897988929
1.908987: 1241959999889996996
2.504875: 1273699998989898689
3.311136: 1266788999798879769
3.927256: 1309895699989899689
二次优化后的结果

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