/* 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);
}
}
/* 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;
}
}
}
}
