Пример #1
0
double tan(double x) {
#include "utan.h"
#include "utan.tbl"

    int ux,i,n;
    double a,da,a2,b,db,c,dc,c1,cc1,c2,cc2,c3,cc3,fi,ffi,gi,pz,s,sy,
           t,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2;
    int p;
    number num,v;
    mp_no mpa,mpt1,mpt2;
#if 0
    mp_no mpy;
#endif

    int __branred(double, double *, double *);
    int __mpranred(double, mp_no *, int);

    /* x=+-INF, x=NaN */
    num.d = x;
    ux = num.i[HIGH_HALF];
    if ((ux&0x7ff00000)==0x7ff00000) return x-x;

    w=(x<ZERO) ? -x : x;

    /* (I) The case abs(x) <= 1.259e-8 */
    if (w<=g1.d)  return x;

    /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
    if (w<=g2.d) {

        /* First stage */
        x2 = x*x;
        t2 = x*x2*(d3.d+x2*(d5.d+x2*(d7.d+x2*(d9.d+x2*d11.d))));
        if ((y=x+(t2-u1.d*t2)) == x+(t2+u1.d*t2))  return y;

        /* Second stage */
        c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
                                               x2*a27.d))))));
        EMULV(x,x,x2,xx2,t1,t2,t3,t4,t5)
        ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
        MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
        MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
        MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
        MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
        MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
        MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
        MUL2(x ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(x    ,zero.d,c2,cc2,c1,cc1,t1,t2)
        if ((y=c1+(cc1-u2.d*c1)) == c1+(cc1+u2.d*c1))  return y;
        return tanMp(x);
    }
Пример #2
0
double
SECTION
__ieee754_atan2 (double y, double x)
{
  int i, de, ux, dx, uy, dy;
  static const int pr[MM] = { 6, 8, 10, 20, 32 };
  double ax, ay, u, du, u9, ua, v, vv, dv, t1, t2, t3, t7, t8,
    z, zz, cor, s1, ss1, s2, ss2;
#ifndef DLA_FMS
  double t4, t5, t6;
#endif
  number num;

  static const int ep = 59768832,	/*  57*16**5   */
    em = -59768832;		/* -57*16**5   */

  /* x=NaN or y=NaN */
  num.d = x;
  ux = num.i[HIGH_HALF];
  dx = num.i[LOW_HALF];
  if ((ux & 0x7ff00000) == 0x7ff00000)
    {
      if (((ux & 0x000fffff) | dx) != 0x00000000)
	return x + x;
    }
  num.d = y;
  uy = num.i[HIGH_HALF];
  dy = num.i[LOW_HALF];
  if ((uy & 0x7ff00000) == 0x7ff00000)
    {
      if (((uy & 0x000fffff) | dy) != 0x00000000)
	return y + y;
    }

  /* y=+-0 */
  if (uy == 0x00000000)
    {
      if (dy == 0x00000000)
	{
	  if ((ux & 0x80000000) == 0x00000000)
	    return 0;
	  else
	    return opi.d;
	}
    }
  else if (uy == 0x80000000)
    {
      if (dy == 0x00000000)
	{
	  if ((ux & 0x80000000) == 0x00000000)
	    return -0.0;
	  else
	    return mopi.d;
	}
    }

  /* x=+-0 */
  if (x == 0)
    {
      if ((uy & 0x80000000) == 0x00000000)
	return hpi.d;
      else
	return mhpi.d;
    }

  /* x=+-INF */
  if (ux == 0x7ff00000)
    {
      if (dx == 0x00000000)
	{
	  if (uy == 0x7ff00000)
	    {
	      if (dy == 0x00000000)
		return qpi.d;
	    }
	  else if (uy == 0xfff00000)
	    {
	      if (dy == 0x00000000)
		return mqpi.d;
	    }
	  else
	    {
	      if ((uy & 0x80000000) == 0x00000000)
		return 0;
	      else
		return -0.0;
	    }
	}
    }
  else if (ux == 0xfff00000)
    {
      if (dx == 0x00000000)
	{
	  if (uy == 0x7ff00000)
	    {
	      if (dy == 0x00000000)
		return tqpi.d;
	    }
	  else if (uy == 0xfff00000)
	    {
	      if (dy == 0x00000000)
		return mtqpi.d;
	    }
	  else
	    {
	      if ((uy & 0x80000000) == 0x00000000)
		return opi.d;
	      else
		return mopi.d;
	    }
	}
    }

  /* y=+-INF */
  if (uy == 0x7ff00000)
    {
      if (dy == 0x00000000)
	return hpi.d;
    }
  else if (uy == 0xfff00000)
    {
      if (dy == 0x00000000)
	return mhpi.d;
    }

  /* either x/y or y/x is very close to zero */
  ax = (x < 0) ? -x : x;
  ay = (y < 0) ? -y : y;
  de = (uy & 0x7ff00000) - (ux & 0x7ff00000);
  if (de >= ep)
    {
      return ((y > 0) ? hpi.d : mhpi.d);
    }
  else if (de <= em)
    {
      if (x > 0)
	{
	  if ((z = ay / ax) < TWOM1022)
	    return normalized (ax, ay, y, z);
	  else
	    return signArctan2 (y, z);
	}
      else
	{
	  return ((y > 0) ? opi.d : mopi.d);
	}
    }

  /* if either x or y is extremely close to zero, scale abs(x), abs(y). */
  if (ax < twom500.d || ay < twom500.d)
    {
      ax *= two500.d;
      ay *= two500.d;
    }

  /* Likewise for large x and y.  */
  if (ax > two500.d || ay > two500.d)
    {
      ax *= twom500.d;
      ay *= twom500.d;
    }

  /* x,y which are neither special nor extreme */
  if (ay < ax)
    {
      u = ay / ax;
      EMULV (ax, u, v, vv, t1, t2, t3, t4, t5);
      du = ((ay - v) - vv) / ax;
    }
  else
    {
      u = ax / ay;
      EMULV (ay, u, v, vv, t1, t2, t3, t4, t5);
      du = ((ax - v) - vv) / ay;
    }

  if (x > 0)
    {
      /* (i)   x>0, abs(y)< abs(x):  atan(ay/ax) */
      if (ay < ax)
	{
	  if (u < inv16.d)
	    {
	      v = u * u;

	      zz = du + u * v * (d3.d
				 + v * (d5.d
					+ v * (d7.d
					       + v * (d9.d
						      + v * (d11.d
							     + v * d13.d)))));

	      if ((z = u + (zz - u1.d * u)) == u + (zz + u1.d * u))
		return signArctan2 (y, z);

	      MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
	      s1 = v * (f11.d + v * (f13.d
				     + v * (f15.d + v * (f17.d + v * f19.d))));
	      ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);

	      if ((z = s1 + (ss1 - u5.d * s1)) == s1 + (ss1 + u5.d * s1))
		return signArctan2 (y, z);

	      return atan2Mp (x, y, pr);
	    }

	  i = (TWO52 + TWO8 * u) - TWO52;
	  i -= 16;
	  t3 = u - cij[i][0].d;
	  EADD (t3, du, v, dv);
	  t1 = cij[i][1].d;
	  t2 = cij[i][2].d;
	  zz = v * t2 + (dv * t2
			 + v * v * (cij[i][3].d
				    + v * (cij[i][4].d
					   + v * (cij[i][5].d
						  + v * cij[i][6].d))));
	  if (i < 112)
	    {
	      if (i < 48)
		u9 = u91.d;	/* u < 1/4	*/
	      else
		u9 = u92.d;
	    }		/* 1/4 <= u < 1/2 */
	  else
	    {
	      if (i < 176)
		u9 = u93.d;	/* 1/2 <= u < 3/4 */
	      else
		u9 = u94.d;
	    }		/* 3/4 <= u <= 1  */
	  if ((z = t1 + (zz - u9 * t1)) == t1 + (zz + u9 * t1))
	    return signArctan2 (y, z);

	  t1 = u - hij[i][0].d;
	  EADD (t1, du, v, vv);
	  s1 = v * (hij[i][11].d
		    + v * (hij[i][12].d
			   +  v * (hij[i][13].d
				   + v * (hij[i][14].d
					  + v * hij[i][15].d))));
	  ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);

	  if ((z = s2 + (ss2 - ub.d * s2)) == s2 + (ss2 + ub.d * s2))
	    return signArctan2 (y, z);
	  return atan2Mp (x, y, pr);
	}

      /* (ii)  x>0, abs(x)<=abs(y):  pi/2-atan(ax/ay) */
      if (u < inv16.d)
	{
	  v = u * u;
	  zz = u * v * (d3.d
			+ v * (d5.d
			       + v * (d7.d
				      + v * (d9.d
					     + v * (d11.d
						    + v * d13.d)))));
	  ESUB (hpi.d, u, t2, cor);
	  t3 = ((hpi1.d + cor) - du) - zz;
	  if ((z = t2 + (t3 - u2.d)) == t2 + (t3 + u2.d))
	    return signArctan2 (y, z);

	  MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
	  s1 = v * (f11.d
		    + v * (f13.d
			   + v * (f15.d + v * (f17.d + v * f19.d))));
	  ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
	  SUB2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);

	  if ((z = s2 + (ss2 - u6.d)) == s2 + (ss2 + u6.d))
	    return signArctan2 (y, z);
	  return atan2Mp (x, y, pr);
	}

      i = (TWO52 + TWO8 * u) - TWO52;
      i -= 16;
      v = (u - cij[i][0].d) + du;

      zz = hpi1.d - v * (cij[i][2].d
			 + v * (cij[i][3].d
				+ v * (cij[i][4].d
				       + v * (cij[i][5].d
					      + v * cij[i][6].d))));
      t1 = hpi.d - cij[i][1].d;
      if (i < 112)
	ua = ua1.d;	/* w <  1/2 */
      else
	ua = ua2.d;	/* w >= 1/2 */
      if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
	return signArctan2 (y, z);

      t1 = u - hij[i][0].d;
      EADD (t1, du, v, vv);

      s1 = v * (hij[i][11].d
		+ v * (hij[i][12].d
		       + v * (hij[i][13].d
			      + v * (hij[i][14].d
				     + v * hij[i][15].d))));

      ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
      SUB2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);

      if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
	return signArctan2 (y, z);
      return atan2Mp (x, y, pr);
    }

  /* (iii) x<0, abs(x)< abs(y):  pi/2+atan(ax/ay) */
  if (ax < ay)
    {
      if (u < inv16.d)
	{
	  v = u * u;
	  zz = u * v * (d3.d
			+ v * (d5.d
			       + v * (d7.d
				      + v * (d9.d
					     + v * (d11.d + v * d13.d)))));
	  EADD (hpi.d, u, t2, cor);
	  t3 = ((hpi1.d + cor) + du) + zz;
	  if ((z = t2 + (t3 - u3.d)) == t2 + (t3 + u3.d))
	    return signArctan2 (y, z);

	  MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
	  s1 = v * (f11.d
		    + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d))));
	  ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);

	  if ((z = s2 + (ss2 - u7.d)) == s2 + (ss2 + u7.d))
	    return signArctan2 (y, z);
	  return atan2Mp (x, y, pr);
	}

      i = (TWO52 + TWO8 * u) - TWO52;
      i -= 16;
      v = (u - cij[i][0].d) + du;
      zz = hpi1.d + v * (cij[i][2].d
			 + v * (cij[i][3].d
				+ v * (cij[i][4].d
				       + v * (cij[i][5].d
					      + v * cij[i][6].d))));
      t1 = hpi.d + cij[i][1].d;
      if (i < 112)
	ua = ua1.d;	/* w <  1/2 */
      else
	ua = ua2.d;	/* w >= 1/2 */
      if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
	return signArctan2 (y, z);

      t1 = u - hij[i][0].d;
      EADD (t1, du, v, vv);
      s1 = v * (hij[i][11].d
		+ v * (hij[i][12].d
		       + v * (hij[i][13].d
			      + v * (hij[i][14].d
				     + v * hij[i][15].d))));
      ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
      ADD2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);

      if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
	return signArctan2 (y, z);
      return atan2Mp (x, y, pr);
    }

  /* (iv)  x<0, abs(y)<=abs(x):  pi-atan(ax/ay) */
  if (u < inv16.d)
    {
      v = u * u;
      zz = u * v * (d3.d
		    + v * (d5.d
			   + v * (d7.d
				  + v * (d9.d + v * (d11.d + v * d13.d)))));
      ESUB (opi.d, u, t2, cor);
      t3 = ((opi1.d + cor) - du) - zz;
      if ((z = t2 + (t3 - u4.d)) == t2 + (t3 + u4.d))
	return signArctan2 (y, z);

      MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
      s1 = v * (f11.d + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d))));
      ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
      MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
      ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
      SUB2 (opi.d, opi1.d, s1, ss1, s2, ss2, t1, t2);

      if ((z = s2 + (ss2 - u8.d)) == s2 + (ss2 + u8.d))
	return signArctan2 (y, z);
      return atan2Mp (x, y, pr);
    }

  i = (TWO52 + TWO8 * u) - TWO52;
  i -= 16;
  v = (u - cij[i][0].d) + du;
  zz = opi1.d - v * (cij[i][2].d
		     + v * (cij[i][3].d
			    + v * (cij[i][4].d
				   + v * (cij[i][5].d + v * cij[i][6].d))));
  t1 = opi.d - cij[i][1].d;
  if (i < 112)
    ua = ua1.d;	/* w <  1/2 */
  else
    ua = ua2.d;	/* w >= 1/2 */
  if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
    return signArctan2 (y, z);

  t1 = u - hij[i][0].d;

  EADD (t1, du, v, vv);

  s1 = v * (hij[i][11].d
	    + v * (hij[i][12].d
		   + v * (hij[i][13].d
			  + v * (hij[i][14].d + v * hij[i][15].d))));

  ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
  MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
  SUB2 (opi.d, opi1.d, s2, ss2, s1, ss1, t1, t2);

  if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
    return signArctan2 (y, z);
  return atan2Mp (x, y, pr);
}
/* routine computes the correctly rounded (to nearest) value of atan(x). */
double atan(double x) {


  double cor,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,u,u2,u3,
         v,vv,w,ww,y,yy,z,zz;
#if 0
  double y1,y2;
#endif
  int i,ux,dx;
#if 0
  int p;
#endif
  static const int pr[M]={6,8,10,32};
  number num;
#if 0
  mp_no mpt1,mpx,mpy,mpy1,mpy2,mperr;
#endif

  num.d = x;  ux = num.i[HIGH_HALF];  dx = num.i[LOW_HALF];

  /* x=NaN */
  if (((ux&0x7ff00000)==0x7ff00000) && (((ux&0x000fffff)|dx)!=0x00000000))
    return x+x;

  /* Regular values of x, including denormals +-0 and +-INF */
  u = (x<ZERO) ? -x : x;
  if (u<C) {
    if (u<B) {
      if (u<A) {                                           /* u < A */
         return x; }
      else {                                               /* A <= u < B */
        v=x*x;  yy=x*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
        if ((y=x+(yy-U1*x)) == x+(yy+U1*x))  return y;

        EMULV(x,x,v,vv,t1,t2,t3,t4,t5)                       /* v+vv=x^2 */
        s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
        ADD2(f9.d,ff9.d,s1,ZERO,s2,ss2,t1,t2)
        MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(f7.d,ff7.d,s1,ss1,s2,ss2,t1,t2)
        MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(f5.d,ff5.d,s1,ss1,s2,ss2,t1,t2)
        MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(f3.d,ff3.d,s1,ss1,s2,ss2,t1,t2)
        MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
        MUL2(x,ZERO,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
        ADD2(x,ZERO,s2,ss2,s1,ss1,t1,t2)
        if ((y=s1+(ss1-U5*s1)) == s1+(ss1+U5*s1))  return y;

        return atanMp(x,pr);
      } }
    else {  /* B <= u < C */
      i=(TWO52+TWO8*u)-TWO52;  i-=16;
      z=u-cij[i][0].d;
      yy=z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+
                        z*(cij[i][5].d+z* cij[i][6].d))));
      t1=cij[i][1].d;
      if (i<112) {
        if (i<48)  u2=U21;    /* u < 1/4        */
        else       u2=U22; }  /* 1/4 <= u < 1/2 */
      else {
        if (i<176) u2=U23;    /* 1/2 <= u < 3/4 */
        else       u2=U24; }  /* 3/4 <= u <= 1  */
      if ((y=t1+(yy-u2*t1)) == t1+(yy+u2*t1))  return __signArctan(x,y);

      z=u-hij[i][0].d;
      s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
         z*(hij[i][14].d+z* hij[i][15].d))));
      ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
      MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2)
      MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2)
      MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2)
      MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2)
      if ((y=s2+(ss2-U6*s2)) == s2+(ss2+U6*s2))  return __signArctan(x,y);

      return atanMp(x,pr);
    }
  }
Пример #4
0
double
SECTION
__ieee754_log(double x) {
#define M 4
  static const int pr[M]={8,10,18,32};
  int i,j,n,ux,dx,p;
#if 0
  int k;
#endif
  double dbl_n,u,p0,q,r0,w,nln2a,luai,lubi,lvaj,lvbj,
	 sij,ssij,ttij,A,B,B0,y,y1,y2,polI,polII,sa,sb,
	 t1,t2,t7,t8,t,ra,rb,ww,
	 a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c;
#ifndef DLA_FMS
  double t3,t4,t5,t6;
#endif
  number num;
  mp_no mpx,mpy,mpy1,mpy2,mperr;

#include "ulog.tbl"
#include "ulog.h"

  /* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */

  num.d = x;  ux = num.i[HIGH_HALF];  dx = num.i[LOW_HALF];
  n=0;
  if (__builtin_expect(ux < 0x00100000, 0)) {
    if (__builtin_expect(((ux & 0x7fffffff) | dx) == 0, 0))
      return MHALF/ZERO; /* return -INF */
    if (__builtin_expect(ux < 0, 0))
      return (x-x)/ZERO;                         /* return NaN  */
    n -= 54;    x *= two54.d;                              /* scale x     */
    num.d = x;
  }
  if (__builtin_expect(ux >= 0x7ff00000, 0))
    return x+x;                        /* INF or NaN  */

  /* Regular values of x */

  w = x-ONE;
  if (__builtin_expect(ABS(w) > U03, 1)) { goto case_03; }


  /*--- Stage I, the case abs(x-1) < 0.03 */

  t8 = MHALF*w;
  EMULV(t8,w,a,aa,t1,t2,t3,t4,t5)
  EADD(w,a,b,bb)

  /* Evaluate polynomial II */
  polII = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+
	  w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*w*w*w;
  c = (aa+bb)+polII;

  /* End stage I, case abs(x-1) < 0.03 */
  if ((y=b+(c+b*E2)) == b+(c-b*E2))  return y;

  /*--- Stage II, the case abs(x-1) < 0.03 */

  a = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+
	    w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d))))))));
  EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5)
  ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d9.d,dd9.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d8.d,dd8.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d7.d,dd7.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d6.d,dd6.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d5.d,dd5.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d4.d,dd4.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d3.d,dd3.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(d2.d,dd2.d,s2,ss2,s3,ss3,t1,t2)
  MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(w,ZERO,    s3,ss3, b, bb,t1,t2)

  /* End stage II, case abs(x-1) < 0.03 */
  if ((y=b+(bb+b*E4)) == b+(bb-b*E4))  return y;
  goto stage_n;

  /*--- Stage I, the case abs(x-1) > 0.03 */
  case_03:

  /* Find n,u such that x = u*2**n,   1/sqrt(2) < u < sqrt(2)  */
  n += (num.i[HIGH_HALF] >> 20) - 1023;
  num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
  if (num.d > SQRT_2) { num.d *= HALF;  n++; }
  u = num.d;  dbl_n = (double) n;

  /* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
  num.d += h1.d;
  i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;

  /* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
  num.d = u*Iu[i].d + h2.d;
  j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;

  /* Compute w=(u-ui*vj)/(ui*vj) */
  p0=(ONE+(i-75)*DEL_U)*(ONE+(j-180)*DEL_V);
  q=u-p0;   r0=Iu[i].d*Iv[j].d;   w=q*r0;

  /* Evaluate polynomial I */
  polI = w+(a2.d+a3.d*w)*w*w;

  /* Add up everything */
  nln2a = dbl_n*LN2A;
  luai  = Lu[i][0].d;   lubi  = Lu[i][1].d;
  lvaj  = Lv[j][0].d;   lvbj  = Lv[j][1].d;
  EADD(luai,lvaj,sij,ssij)
  EADD(nln2a,sij,A  ,ttij)
  B0 = (((lubi+lvbj)+ssij)+ttij)+dbl_n*LN2B;
  B  = polI+B0;

  /* End stage I, case abs(x-1) >= 0.03 */
  if ((y=A+(B+E1)) == A+(B-E1))  return y;


  /*--- Stage II, the case abs(x-1) > 0.03 */

  /* Improve the accuracy of r0 */
  EMULV(p0,r0,sa,sb,t1,t2,t3,t4,t5)
  t=r0*((ONE-sa)-sb);
  EADD(r0,t,ra,rb)

  /* Compute w */
  MUL2(q,ZERO,ra,rb,w,ww,t1,t2,t3,t4,t5,t6,t7,t8)

  EADD(A,B0,a0,aa0)

  /* Evaluate polynomial III */
  s1 = (c3.d+(c4.d+c5.d*w)*w)*w;
  EADD(c2.d,s1,s2,ss2)
  MUL2(s2,ss2,w,ww,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
  MUL2(s3,ss3,w,ww,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(s2,ss2,w,ww,s3,ss3,t1,t2)
  ADD2(s3,ss3,a0,aa0,a1,aa1,t1,t2)

  /* End stage II, case abs(x-1) >= 0.03 */
  if ((y=a1+(aa1+E3)) == a1+(aa1-E3)) return y;


  /* Final stages. Use multi-precision arithmetic. */
  stage_n:

  for (i=0; i<M; i++) {
    p = pr[i];
    __dbl_mp(x,&mpx,p);  __dbl_mp(y,&mpy,p);
    __mplog(&mpx,&mpy,p);
    __dbl_mp(e[i].d,&mperr,p);
    __add(&mpy,&mperr,&mpy1,p);  __sub(&mpy,&mperr,&mpy2,p);
    __mp_dbl(&mpy1,&y1,p);       __mp_dbl(&mpy2,&y2,p);
    if (y1==y2)   return y1;
  }
  return y1;
}
Пример #5
0
double
__ieee754_sqrt (double x)
{
#include "uroot.h"
    static const double
    rt0 = 9.99999999859990725855365213134618E-01,
    rt1 = 4.99999999495955425917856814202739E-01,
    rt2 = 3.75017500867345182581453026130850E-01,
    rt3 = 3.12523626554518656309172508769531E-01;
    static const double big = 134217728.0;
    double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;
    mynumber a, c = { { 0, 0 } };
    int4 k;

    a.x = x;
    k = a.i[HIGH_HALF];
    a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000;
    t = inroot[(k & 0x001fffff) >> 14];
    s = a.x;
    /*----------------- 2^-1022  <= | x |< 2^1024  -----------------*/
    if (k > 0x000fffff && k < 0x7ff00000)
    {
        int rm = __fegetround ();
        fenv_t env;
        libc_feholdexcept_setround (&env, FE_TONEAREST);
        double ret;
        y = 1.0 - t * (t * s);
        t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3)));
        c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1);
        y = t * s;
        hy = (y + big) - big;
        del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy));
        res = y + del;
        if (res == (res + 1.002 * ((y - res) + del)))
            ret = res * c.x;
        else
        {
            res1 = res + 1.5 * ((y - res) + del);
            EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */
            res = ((((z - s) + zz) < 0) ? max (res, res1) :
                   min (res, res1));
            ret = res * c.x;
        }
        math_force_eval (ret);
        libc_fesetenv (&env);
        double dret = x / ret;
        if (dret != ret)
        {
            double force_inexact = 1.0 / 3.0;
            math_force_eval (force_inexact);
            /* The square root is inexact, ret is the round-to-nearest
               value which may need adjusting for other rounding
               modes.  */
            switch (rm)
            {
#ifdef FE_UPWARD
            case FE_UPWARD:
                if (dret > ret)
                    ret = (res + 0x1p-1022) * c.x;
                break;
#endif

#ifdef FE_DOWNWARD
            case FE_DOWNWARD:
#endif
#ifdef FE_TOWARDZERO
            case FE_TOWARDZERO:
#endif
#if defined FE_DOWNWARD || defined FE_TOWARDZERO
                if (dret < ret)
                    ret = (res - 0x1p-1022) * c.x;
                break;
#endif

            default:
                break;
            }
        }
        /* Otherwise (x / ret == ret), either the square root was exact or
           the division was inexact.  */
        return ret;
    }
Пример #6
0
/* routine computes the correctly rounded (to nearest) value of atan(x). */
double
atan (double x)
{
  double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3,
	 v, vv, w, ww, y, yy, z, zz;
#ifndef DLA_FMS
  double t4, t5, t6;
#endif
  int i, ux, dx;
  static const int pr[M] = { 6, 8, 10, 32 };
  number num;

  num.d = x;
  ux = num.i[HIGH_HALF];
  dx = num.i[LOW_HALF];

  /* x=NaN */
  if (((ux & 0x7ff00000) == 0x7ff00000)
      && (((ux & 0x000fffff) | dx) != 0x00000000))
    return x + x;

  /* Regular values of x, including denormals +-0 and +-INF */
  SET_RESTORE_ROUND (FE_TONEAREST);
  u = (x < 0) ? -x : x;
  if (u < C)
    {
      if (u < B)
	{
	  if (u < A)
	    {
	      math_check_force_underflow_nonneg (u);
	      return x;
	    }
	  else
	    {			/* A <= u < B */
	      v = x * x;
	      yy = d11.d + v * d13.d;
	      yy = d9.d + v * yy;
	      yy = d7.d + v * yy;
	      yy = d5.d + v * yy;
	      yy = d3.d + v * yy;
	      yy *= x * v;

	      if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
		return y;

	      EMULV (x, x, v, vv, t1, t2, t3, t4, t5);	/* v+vv=x^2 */

	      s1 = f17.d + v * f19.d;
	      s1 = f15.d + v * s1;
	      s1 = f13.d + v * s1;
	      s1 = f11.d + v * s1;
	      s1 *= v;

	      ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7,
		    t8);
	      ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
	      if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
		return y;

	      return atanMp (x, pr);
	    }
	}
      else
	{			/* B <= u < C */
	  i = (TWO52 + TWO8 * u) - TWO52;
	  i -= 16;
	  z = u - cij[i][0].d;
	  yy = cij[i][5].d + z * cij[i][6].d;
	  yy = cij[i][4].d + z * yy;
	  yy = cij[i][3].d + z * yy;
	  yy = cij[i][2].d + z * yy;
	  yy *= z;

	  t1 = cij[i][1].d;
	  if (i < 112)
	    {
	      if (i < 48)
		u2 = U21;	/* u < 1/4        */
	      else
		u2 = U22;
	    }			/* 1/4 <= u < 1/2 */
	  else
	    {
	      if (i < 176)
		u2 = U23;	/* 1/2 <= u < 3/4 */
	      else
		u2 = U24;
	    }			/* 3/4 <= u <= 1  */
	  if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
	    return __signArctan (x, y);

	  z = u - hij[i][0].d;

	  s1 = hij[i][14].d + z * hij[i][15].d;
	  s1 = hij[i][13].d + z * s1;
	  s1 = hij[i][12].d + z * s1;
	  s1 = hij[i][11].d + z * s1;
	  s1 *= z;

	  ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
	  if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
	    return __signArctan (x, y);

	  return atanMp (x, pr);
	}
    }
  else
    {
      if (u < D)
	{			/* C <= u < D */
	  w = 1 / u;
	  EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
	  ww = w * ((1 - t1) - t2);
	  i = (TWO52 + TWO8 * w) - TWO52;
	  i -= 16;
	  z = (w - cij[i][0].d) + ww;

	  yy = cij[i][5].d + z * cij[i][6].d;
	  yy = cij[i][4].d + z * yy;
	  yy = cij[i][3].d + z * yy;
	  yy = cij[i][2].d + z * yy;
	  yy = HPI1 - z * yy;

	  t1 = HPI - cij[i][1].d;
	  if (i < 112)
	    u3 = U31;           /* w <  1/2 */
	  else
	    u3 = U32;           /* w >= 1/2 */
	  if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
	    return __signArctan (x, y);

	  DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9,
		t10);
	  t1 = w - hij[i][0].d;
	  EADD (t1, ww, z, zz);

	  s1 = hij[i][14].d + z * hij[i][15].d;
	  s1 = hij[i][13].d + z * s1;
	  s1 = hij[i][12].d + z * s1;
	  s1 = hij[i][11].d + z * s1;
	  s1 *= z;

	  ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	  ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
	  SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
	  if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
	    return __signArctan (x, y);

	  return atanMp (x, pr);
	}
      else
	{
	  if (u < E)
	    {                   /* D <= u < E */
	      w = 1 / u;
	      v = w * w;
	      EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);

	      yy = d11.d + v * d13.d;
	      yy = d9.d + v * yy;
	      yy = d7.d + v * yy;
	      yy = d5.d + v * yy;
	      yy = d3.d + v * yy;
	      yy *= w * v;

	      ww = w * ((1 - t1) - t2);
	      ESUB (HPI, w, t3, cor);
	      yy = ((HPI1 + cor) - ww) - yy;
	      if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
		return __signArctan (x, y);

	      DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8,
		    t9, t10);
	      MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);

	      s1 = f17.d + v * f19.d;
	      s1 = f15.d + v * s1;
	      s1 = f13.d + v * s1;
	      s1 = f11.d + v * s1;
	      s1 *= v;

	      ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
	      MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
	      ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
	      SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);

	      if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8))
		return __signArctan (x, y);

	      return atanMp (x, pr);
	    }
	  else
	    {
	      /* u >= E */
	      if (x > 0)
		return HPI;
	      else
		return MHPI;
	    }
	}
    }
}