mpa.c

glibc 2.9,最新版的C语言库函数

  for (   ; i<=p2; i++)     Y[i] = ZERO;
  return;
}


/*  add_magnitudes() adds the magnitudes of *x & *y assuming that           */
/*  abs(*x) >= abs(*y) > 0.                                                 */
/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */
/* No guard digit is used. The result equals the exact sum, truncated.      */
/* *x & *y are left unchanged.                                              */

static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {

  long i,j,k;
  long p2 = p;

  EZ = EX;

  i=p2;    j=p2+ EY - EX;    k=p2+1;

  if (j<1)
     {__cpy(x,z,p);  return; }
  else   Z[k] = ZERO;

  for (; j>0; i--,j--) {
    Z[k] += X[i] + Y[j];
    if (Z[k] >= RADIX) {
      Z[k]  -= RADIX;
      Z[--k] = ONE; }
    else
      Z[--k] = ZERO;
  }

  for (; i>0; i--) {
    Z[k] += X[i];
    if (Z[k] >= RADIX) {
      Z[k]  -= RADIX;
      Z[--k] = ONE; }
    else
      Z[--k] = ZERO;
  }

  if (Z[1] == ZERO) {
    for (i=1; i<=p2; i++)    Z[i] = Z[i+1]; }
  else   EZ += ONE;
}


/*  sub_magnitudes() subtracts the magnitudes of *x & *y assuming that      */
/*  abs(*x) > abs(*y) > 0.                                                  */
/* The sign of the difference *z is undefined. x&y may overlap but not x&z  */
/* or y&z. One guard digit is used. The error is less than one ulp.         */
/* *x & *y are left unchanged.                                              */

static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {

  long i,j,k;
  long p2 = p;

  EZ = EX;

  if (EX == EY) {
    i=j=k=p2;
    Z[k] = Z[k+1] = ZERO; }
  else {
    j= EX - EY;
    if (j > p2)  {__cpy(x,z,p);  return; }
    else {
      i=p2;   j=p2+1-j;   k=p2;
      if (Y[j] > ZERO) {
        Z[k+1] = RADIX - Y[j--];
        Z[k]   = MONE; }
      else {
        Z[k+1] = ZERO;
        Z[k]   = ZERO;   j--;}
    }
  }

  for (; j>0; i--,j--) {
    Z[k] += (X[i] - Y[j]);
    if (Z[k] < ZERO) {
      Z[k]  += RADIX;
      Z[--k] = MONE; }
    else
      Z[--k] = ZERO;
  }

  for (; i>0; i--) {
    Z[k] += X[i];
    if (Z[k] < ZERO) {
      Z[k]  += RADIX;
      Z[--k] = MONE; }
    else
      Z[--k] = ZERO;
  }

  for (i=1; Z[i] == ZERO; i++) ;
  EZ = EZ - i + 1;
  for (k=1; i <= p2+1; )
    Z[k++] = Z[i++];
  for (; k <= p2; )
    Z[k++] = ZERO;

  return;
}


/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap  */
/* but not x&z or y&z. One guard digit is used. The error is less than    */
/* one ulp. *x & *y are left unchanged.                                   */

void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {

  int n;

  if      (X[0] == ZERO)     {__cpy(y,z,p);  return; }
  else if (Y[0] == ZERO)     {__cpy(x,z,p);  return; }

  if (X[0] == Y[0])   {
    if (__acr(x,y,p) > 0)      {add_magnitudes(x,y,z,p);  Z[0] = X[0]; }
    else                     {add_magnitudes(y,x,z,p);  Z[0] = Y[0]; }
  }
  else                       {
    if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p);  Z[0] = X[0]; }
    else if (n == -1)        {sub_magnitudes(y,x,z,p);  Z[0] = Y[0]; }
    else                      Z[0] = ZERO;
  }
  return;
}


/* Subtract two multiple precision numbers. *z is set to *x - *y. x&y may */
/* overlap but not x&z or y&z. One guard digit is used. The error is      */
/* less than one ulp. *x & *y are left unchanged.                         */

void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {

  int n;

  if      (X[0] == ZERO)     {__cpy(y,z,p);  Z[0] = -Z[0];  return; }
  else if (Y[0] == ZERO)     {__cpy(x,z,p);                 return; }

  if (X[0] != Y[0])    {
    if (__acr(x,y,p) > 0)      {add_magnitudes(x,y,z,p);  Z[0] =  X[0]; }
    else                     {add_magnitudes(y,x,z,p);  Z[0] = -Y[0]; }
  }
  else                       {
    if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p);  Z[0] =  X[0]; }
    else if (n == -1)        {sub_magnitudes(y,x,z,p);  Z[0] = -Y[0]; }
    else                      Z[0] = ZERO;
  }
  return;
}


/* Multiply two multiple precision numbers. *z is set to *x * *y. x&y      */
/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is     */
/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp.   */
/* *x & *y are left unchanged.                                             */

void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {

  long i, i1, i2, j, k, k2;
  long p2 = p;
  double u, zk, zk2;

                      /* Is z=0? */
  if (X[0]*Y[0]==ZERO)
     { Z[0]=ZERO;  return; }

                       /* Multiply, add and carry */
  k2 = (p2<3) ? p2+p2 : p2+3;
  zk = Z[k2]=ZERO;
  for (k=k2; k>1; ) {
    if (k > p2)  {i1=k-p2; i2=p2+1; }
    else        {i1=1;   i2=k;   }
#if 1
    /* rearange this inner loop to allow the fmadd instructions to be
       independent and execute in parallel on processors that have
       dual symetrical FP pipelines.  */
    if (i1 < (i2-1))
    {
	/* make sure we have at least 2 iterations */
	if (((i2 - i1) & 1L) == 1L)
	{
                /* Handle the odd iterations case.  */
		zk2 = x->d[i2-1]*y->d[i1];
	}
	else
		zk2 = zero.d;
	/* Do two multiply/adds per loop iteration, using independent
           accumulators; zk and zk2.  */
	for (i=i1,j=i2-1; i<i2-1; i+=2,j-=2) 
	{
		zk += x->d[i]*y->d[j];
		zk2 += x->d[i+1]*y->d[j-1];
	}
	zk += zk2; /* final sum.  */
    }
    else
    {
        /* Special case when iterations is 1.  */
	zk += x->d[i1]*y->d[i1];
    }
#else
    /* The orginal code.  */
    for (i=i1,j=i2-1; i<i2; i++,j--)  zk += X[i]*Y[j];
#endif

    u = (zk + CUTTER)-CUTTER;
    if  (u > zk)  u -= RADIX;
    Z[k]  = zk - u;
    zk = u*RADIXI;
    --k;
  }
  Z[k] = zk;

                 /* Is there a carry beyond the most significant digit? */
  if (Z[1] == ZERO) {
    for (i=1; i<=p2; i++)  Z[i]=Z[i+1];
    EZ = EX + EY - 1; }
  else
    EZ = EX + EY;

  Z[0] = X[0] * Y[0];
  return;
}


/* Invert a multiple precision number. Set *y = 1 / *x.                     */
/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3,   */
/* 2.001*r**(1-p) for p>3.                                                  */
/* *x=0 is not permissible. *x is left unchanged.                           */

void __inv(const mp_no *x, mp_no *y, int p) {
  long i;
#if 0
  int l;
#endif
  double t;
  mp_no z,w;
  static const int np1[] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,
                            4,4,4,4,4,4,4,4,4,4,4,4,4,4,4};
  const mp_no mptwo = {1,{1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
                         0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
                         0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
                         0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};

  __cpy(x,&z,p);  z.e=0;  __mp_dbl(&z,&t,p);
  t=ONE/t;   __dbl_mp(t,y,p);    EY -= EX;

  for (i=0; i<np1[p]; i++) {
    __cpy(y,&w,p);
    __mul(x,&w,y,p);
    __sub(&mptwo,y,&z,p);
    __mul(&w,&z,y,p);
  }
  return;
}


/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */
/* are left unchanged. x&y may overlap but not x&z or y&z.                   */
/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3     */
/* and 3.001*r**(1-p) for p>3. *y=0 is not permissible.                      */

void __dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {

  mp_no w;

  if (X[0] == ZERO)    Z[0] = ZERO;
  else                {__inv(y,&w,p);   __mul(x,&w,z,p);}
  return;
}