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整數的 over- flow 背後的數學
(高顯忠, sjgau4311@gmail.com, 2011-02-08 11:51)
1樓
#if 0
// double 算出來的正確值，和 整數算出來的
因為 整數的 over- flow 的錯誤值之間的關係，如下：
no= 10
sum= 55,
xs= 55
js= 55
no= 20
sum= 210,
xs= 210
js= 210
no= 40
sum= 820,
xs= 820
js= 820
no= 80
sum= 3240,
xs= 3240
js= 3240
no= 160
sum= 12880,
xs= 12880
js= 12880
no= 320
sum= 51360,
xs= 51360
js= 51360
no= 640
sum= 205120,
xs= 205120
js= 205120
no= 1280
sum= 819840,
xs= 819840
js= 819840
no= 2560
sum= 3278080,
xs= 3278080
js= 3278080
no= 5120
sum= 13109760,
xs= 13109760
js= 13109760
no= 10240
sum= 52433920,
xs= 52433920
js= 52433920
no= 20480
sum= 209725440,
xs= 209725440
js= 209725440
no= 40960
sum= 838881280,
xs= 838881280
js= 838881280
no= 81920
sum= -939483136,
xs= 3355484160
js= -939483136
no= 163840
sum= 536952832,
xs= 13421854720
js= 536952832
no= 327680
sum= -2147319808,
xs= 53687255040
js= -2147319808
no= 655360
sum= 327680,
xs= 214748692480
js= 327680
no= 1310720
sum= 655360,
xs= 858994114560
js= 655360
no= 2621440
sum= 1310720,
xs= 3435975147520
js= 1310720
no= 5242880
sum= 2621440,
xs= 13743897968640
js= 2621440
no= 10485760
sum= 5242880,
xs= 54975586631680
js= 5242880
no= 20971520
sum= 10485760,
xs= 219902336040960
js= 10485760
no= 41943040
sum= 20971520,
xs= 879609323192320
js= 20971520
no= 83886080
sum= 41943040,
xs= 3518437250826240
js= 41943040
no= 167772160
sum= 83886080,
xs= 14073748919418880
js= 83886080
no= 335544320
sum= 167772160,
xs= 56294995509903360
js= 167772160
no= 671088640
sum= 335544320,
xs= 225179981704069120
js= 335544320
no= 1342177280
sum= 671088640,
xs= 900719926145187840
js= 671088640
Press any key to continue
#endif
// ----------------------------------------------
#include <stdio.h>
#include <math.h>
#include <process.h>
#include <conio.h>
#include "sj-01.h"
// ----------------------------------------------
// for time1(), time2()
int main()
{
int no, sum, i, js;
double xs;
no= 10;
while (no > 0) {
sum= 0;
for (i=1;i<=no;i++) {
sum+= i;
}
xs= (1.0 + no)*(no - 1.0 + 1.0)/2.0;
skip(1);
printf("no= %d \n", no);
printf("sum= %d, \n xs= %.0lf \n", sum, xs);
xs= fmod(xs, pow(2, 32));
if (xs > ((pow(2, 31)) - 1)) {
xs-= pow(2, 32);
}
js= (int) xs;
if (js != sum) {
skip(3);
printf("*** error of js <> sum, \n");
pause();
}
// ------------------------------------------------
printf("\n js= %d \n", js);
// pause();
no*= 2;
}
return(0);
}// end of main()