long double atan2l(long double y, long double x)
{
- union IEEEl2bits ux, uy;
+ union ldshape ux, uy;
long double z;
- int32_t k,m;
- int16_t exptx, expsignx, expty, expsigny;
+ int m, ex, ey;
- uy.e = y;
- expsigny = uy.xbits.expsign;
- expty = expsigny & 0x7fff;
- ux.e = x;
- expsignx = ux.xbits.expsign;
- exptx = expsignx & 0x7fff;
- if ((exptx==0x7fff &&
- ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
- (expty==0x7fff &&
- ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
+ if (isnan(x) || isnan(y))
return x+y;
- if (expsignx==0x3fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
+ if (x == 1)
return atanl(y);
- m = ((expsigny>>15)&1) | ((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
-
- /* when y = 0 */
- if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
+ ux.f = x;
+ uy.f = y;
+ ex = ux.i.se & 0x7fff;
+ ey = uy.i.se & 0x7fff;
+ m = 2*(ux.i.se>>15) | uy.i.se>>15;
+ if (y == 0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
- case 2: return 2*pio2_hi+0x1p-1000; /* atan(+0,-anything) = pi */
- case 3: return -2*pio2_hi-0x1p-1000; /* atan(-0,-anything) =-pi */
+ case 2: return 2*pio2_hi; /* atan(+0,-anything) = pi */
+ case 3: return -2*pio2_hi; /* atan(-0,-anything) =-pi */
}
}
- /* when x = 0 */
- if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
- return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
- /* when x is INF */
- if (exptx == 0x7fff) {
- if (expty == 0x7fff) {
+ if (x == 0)
+ return m&1 ? -pio2_hi : pio2_hi;
+ if (ex == 0x7fff) {
+ if (ey == 0x7fff) {
switch(m) {
- case 0: return pio2_hi*0.5+0x1p-1000; /* atan(+INF,+INF) */
- case 1: return -pio2_hi*0.5-0x1p-1000; /* atan(-INF,+INF) */
- case 2: return 1.5*pio2_hi+0x1p-1000; /* atan(+INF,-INF) */
- case 3: return -1.5*pio2_hi-0x1p-1000; /* atan(-INF,-INF) */
+ case 0: return pio2_hi/2; /* atan(+INF,+INF) */
+ case 1: return -pio2_hi/2; /* atan(-INF,+INF) */
+ case 2: return 1.5*pio2_hi; /* atan(+INF,-INF) */
+ case 3: return -1.5*pio2_hi; /* atan(-INF,-INF) */
}
} else {
switch(m) {
case 0: return 0.0; /* atan(+...,+INF) */
case 1: return -0.0; /* atan(-...,+INF) */
- case 2: return 2*pio2_hi+0x1p-1000; /* atan(+...,-INF) */
- case 3: return -2*pio2_hi-0x1p-1000; /* atan(-...,-INF) */
+ case 2: return 2*pio2_hi; /* atan(+...,-INF) */
+ case 3: return -2*pio2_hi; /* atan(-...,-INF) */
}
}
}
- /* when y is INF */
- if (expty == 0x7fff)
- return expsigny < 0 ? -pio2_hi-0x1p-1000 : pio2_hi+0x1p-1000;
-
- /* compute y/x */
- k = expty-exptx;
- if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
- z = pio2_hi+0x1p-1000;
- m &= 1;
- } else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
+ if (ex+120 < ey || ey == 0x7fff)
+ return m&1 ? -pio2_hi : pio2_hi;
+ /* z = atan(|y/x|) without spurious underflow */
+ if ((m&2) && ey+120 < ex) /* |y/x| < 0x1p-120, x<0 */
z = 0.0;
- else /* safe to do y/x */
+ else
z = atanl(fabsl(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */