圓周率的計算 (轉)

圓周率的計算 (轉)[@more@]/* Part 1: 概念

  圓周率是在一個圓上作『內接正N邊形』和『外切正N邊形』
  當N越大時，所作出來的這兩個正N邊形的『周長』也就會越接近
  當然啦！這個『周長』也就會越接近這個圓的圓周了

  然後再以基本定義求出圓周率

  定義：
  圓的周長
  π（圓周率）＝ ─────
  直徑


資料來源：牛頓雜誌 */


/*  Part 2: 執行結果

下列是算到小數點以下一千位的圓周率(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

*/

/*  源如下：??
**  PI.C - Computes Pi to an arbitrary number of digits
**
**  Uses far arrays so may be compiled in any memory model
*/

#include
#include

#if defined(__ZTC__)
 #include
 #define FAR _far
 #define Fcalloc farcalloc
 #define Ffree farfree
 #define Size_T unsigned long
#elif defined(__TURBOC__)
 #include
 #define FAR far
 #define Fcalloc farcalloc
 #define Ffree farfree
 #define Size_T unsigned long
#else /* assume MSC/QC */
 #include
 #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  {
  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("anOut of memory error #%dn", 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 ");
  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 digitsn", (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("nnCalculations Completed!n");
  Ffree(ms);
  Ffree(mf);
  return(0);
}