圆周率的计算
/* Part 1: 概念
圆周率是在一个圆上作『内接正N边形』和『外切正N边形』
当N越大时，所作出来的这两个正N边形的『周长』也就会越接近
当然啦！这个『周长』也就会越接近这个圆的圆周了
然後再以基本定义求出圆周率
定义：
圆的周长
π（圆周率）＝ ─────
直径
资料来源：牛顿杂志 */
/* Part 2: 运行结果
下列是算到小数点以下一千位的圆周率(要算更多也可以)：
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944
5923078164 0628620899 8628034825 3421170679 8214808651 3282306647
0938446095 5058223172 5359408128 4811174502 8410270193 8521105559
6446229489 5493038196 4428810975 6659334461 2847564823 3786783165
2712019091 4564856692 3460348610 4543266482 1339360726 0249141273
7245870066 0631558817 4881520920 9628292540 9171536436 7892590360
0113305305 4882046652 1384146951 9415116094 3305727036 5759591953
0921861173 8193261179 3105118548 0744623799 6274956735 1885752724
8912279381 8301194912 9833673362 4406566430 8602139494 6395224737
1907021798 6094370277 0539217176 2931767523 8467481846 7669405132
0005681271 4526356082 7785771342 7577896091 7363717872 1468440901
2249534301 4654958537 1050792279 6892589235 4201995611 2129021960
8640344181 5981362977 4771309960 5187072113 4999999837 2978049951
0597317328 1609631859 5024459455 3469083026 4252230825 3344685035
2619311881 7101000313 7838752886 5875332083 8142061717 7669147303
5982534904 2875546873 1159562863 8823537875 9375195778 1857780532
1712268066 1300192787 6611195909 2164201989
*/
/* 源程序如下：
** PI.C - Computes Pi to an arbitrary number of digits
**
** Uses far arrays so may be compiled in any memory model
*/
#include<stdio.h>
#include<stdlib.h>
#if defined(__ZTC__)
#include <dos.h>
#define FAR _far
#define Fcalloc farcalloc
#define Ffree farfree
#define Size_T unsigned long
#elif defined(__TURBOC__)
#include <alloc.h>
#define FAR far
#define Fcalloc farcalloc
#define Ffree farfree
#define Size_T unsigned long
#else /* assume MSC/QC */
#include <malloc.h>
#define FAR _far
#define Fcalloc _fcalloc
#define Ffree _ffree
#define Size_T size_t
#endif
long kf, ks;
long FAR *mf, FAR *ms;
long cnt, n, temp, nd;
long i;
long col, col1;
long loc, stor[21];
void shift(long FAR *l1, long FAR *l2, long lp, long lmod)
{
long k;
k = ((*l2) > 0 ? (*l2) / lmod: -(-(*l2) / lmod) - 1);
*l2 -= k * lmod;
*l1 += k * lp;
}
void yprint(long m)
{
if (cnt<n)
{
if (++col == 11)
{
col = 1;
if (++col1 == 6)
{
col1 = 0;
printf("\n");
printf("%4ld",m%10);
}
else printf("%3ld",m%10);
}
else printf("%ld",m);
cnt++;
}
}
void xprint(long m)
{
long ii, wk, wk1;
if (m < 8)
{
for (ii = 1; ii <= loc; )
yprint(stor[(int)(ii++)]);
loc = 0;
}
else
{
if (m > 9)
{
wk = m / 10;
m %= 10;
for (wk1 = loc; wk1 >= 1; wk1--)
{
wk += stor[(int)wk1];
stor[(int)wk1] = wk % 10;
wk /= 10;
}
}
}
stor[(int)(++loc)] = m;
}
void memerr(int errno)
{
printf("\a\nOut of memory error #%d\n", errno);
if (2 == errno)
Ffree(mf);
_exit(2);
}
int main(int argc, char *argv[])
{
int i=0;
char *endp;
stor[i++] = 0;
if (argc < 2)
{
puts("\aUsage: PI <number_of_digits>");
return(1);
}
n = strtol(argv[1], &endp, 10);
if (NULL == (mf = Fcalloc((Size_T)(n + 3L), (Size_T)sizeof(long))))
memerr(1);
if (NULL == (ms = Fcalloc((Size_T)(n + 3L), (Size_T)sizeof(long))))
memerr(2);
printf("\nApproximation of PI to %ld digits\n", (long)n);
cnt = 0;
kf = 25;
ks = 57121L;
mf[1] = 1L;
for (i = 2; i <= (int)n; i += 2)
{
mf[i] = -16L;
mf[i+1] = 16L;
}
for (i = 1; i <= (int)n; i += 2)
{
ms[i] = -4L;
ms[i+1] = 4L;
}
printf("\n 3.");
while (cnt < n)
{
for (i = 0; ++i <= (int)n - (int)cnt; )
{
mf[i] *= 10L;
ms[i] *= 10L;
}
for (i =(int)(n - cnt + 1); --i >= 2; )
{
temp = 2 * i - 1;
shift(&mf[i - 1], &mf[i], temp - 2, temp * kf);
shift(&ms[i - 1], &ms[i], temp - 2, temp * ks);
}
nd = 0;
shift((long FAR *)&nd, &mf[1], 1L, 5L);
shift((long FAR *)&nd, &ms[1], 1L, 239L);
xprint(nd);
}
printf("\n\nCalculations Completed!\n");
Ffree(ms);
Ffree(mf);
return(0);
}