ldcomplex
clogl(ldcomplex z) {
ldcomplex ans;
long double x, y, t, ax, ay;
int n, ix, iy, hx, hy;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
ay = fabsl(y);
ax = fabsl(x);
LD_IM(ans) = atan2l(y, x);
if (ix < iy || (ix == iy && ix < 0x7fff0000 && ax < ay)) {
/* swap x and y to force ax>=ay */
t = ax;
ax = ay;
ay = t;
n = ix, ix = iy;
iy = n;
}
n = (ix - iy) >> 16;
if (ix >= 0x7fff0000) { /* x or y is Inf or NaN */
if (isinfl(ax))
LD_RE(ans) = ax;
else if (isinfl(ay))
LD_RE(ans) = ay;
else
LD_RE(ans) = ax + ay;
} else if (ay == zero)
LD_RE(ans) = logl(ax);
else if (((0x3fffffff - ix) ^ (ix - 0x3ffe0000)) >= 0) {
/* 0.5 <= x < 2 */
if (ix >= 0x3fff0000) {
if (ax == one)
LD_RE(ans) = half * log1pl(ay * ay);
else if (n >= SIGP7)
LD_RE(ans) = logl(ax);
else
LD_RE(ans) = half * (log1pl(ay * ay + (ax -
one) * (ax + one)));
} else if (n >= SIGP7)
LD_RE(ans) = logl(ax);
else
LD_RE(ans) = __k_clog_rl(x, y, &t);
} else if (n >= HSIGP7)
LD_RE(ans) = logl(ax);
else if (ix < 0x5f3f0000 && iy >= 0x20bf0000)
/* 2**-8000 < y < x < 2**8000 */
LD_RE(ans) = half * logl(ax * ax + ay * ay);
else {
t = ay / ax;
LD_RE(ans) = logl(ax) + half * log1pl(t * t);
}
return (ans);
}
ldcomplex
cpowl(ldcomplex z, ldcomplex w) {
ldcomplex ans;
long double x, y, u, v, t, c, s, r;
long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2;
int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k;
x = LD_RE(z);
y = LD_IM(z);
u = LD_RE(w);
v = LD_IM(w);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
hu = HI_XWORD(u);
hv = HI_XWORD(v);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
iu = hu & 0x7fffffff;
iv = hv & 0x7fffffff;
j = 0;
if (v == zero) { /* z**(real) */
if (u == one) { /* (anything) ** 1 is itself */
LD_RE(ans) = x;
LD_IM(ans) = y;
} else if (u == zero) { /* (anything) ** 0 is 1 */
LD_RE(ans) = one;
LD_IM(ans) = zero;
} else if (y == zero) { /* real ** real */
LD_IM(ans) = zero;
if (hx < 0 && ix < hiinf && iu < hiinf) {
/* -x ** u is exp(i*pi*u)*pow(x,u) */
r = powl(-x, u);
sincospil(u, &s, &c);
LD_RE(ans) = (c == zero)? c: c * r;
LD_IM(ans) = (s == zero)? s: s * r;
} else
LD_RE(ans) = powl(x, u);
} else if (x == zero || ix >= hiinf || iy >= hiinf) {
if (isnanl(x) || isnanl(y) || isnanl(u))
LD_RE(ans) = LD_IM(ans) = x + y + u;
else {
if (x == zero)
r = fabsl(y);
else
r = fabsl(x) + fabsl(y);
t = atan2pil(y, x);
sincospil(t * u, &s, &c);
LD_RE(ans) = (c == zero)? c: c * r;
LD_IM(ans) = (s == zero)? s: s * r;
}
} else if (fabsl(x) == fabsl(y)) { /* |x| = |y| */
if (hx >= 0) {
t = (hy >= 0)? 0.25L : -0.25L;
sincospil(t * u, &s, &c);
} else if ((LAST(u) & 3) == 0) {
t = (hy >= 0)? 0.75L : -0.75L;
sincospil(t * u, &s, &c);
} else {
r = (hy >= 0)? u : -u;
t = -0.25L * r;
w1 = r + t;
w2 = t - (w1 - r);
sincospil(w1, &t1, &t2);
sincospil(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
}
if (ix < 0x3ffe0000) /* |x| < 1/2 */
r = powl(fabsl(x + x), u) * exp2l(-0.5L * u);
else if (ix >= 0x3fff0000 || iu < 0x400cfff8)
/* |x| >= 1 or |u| < 16383 */
r = powl(fabsl(x), u) * exp2l(0.5L * u);
else /* special treatment */
j = 2;
if (j == 0) {
LD_RE(ans) = (c == zero)? c: c * r;
LD_IM(ans) = (s == zero)? s: s * r;
}
} else
j = 1;
if (j == 0)
return (ans);
}
if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
/*
* non-zero imag part(s) with inf component(s) yields NaN
*/
t = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v);
LD_RE(ans) = LD_IM(ans) = t - t;
} else {
k = 0; /* no scaling */
if (iu > 0x7ffe0000 || iv > 0x7ffe0000) {
u *= 1.52587890625000000000e-05L;
v *= 1.52587890625000000000e-05L;
k = 1; /* scale u and v by 2**-16 */
}
/*
* Use similated higher precision arithmetic to compute:
* r = u * log(hypot(x, y)) - v * atan2(y, x)
* q = u * atan2(y, x) + v * log(hypot(x, y))
*/
t1 = __k_clog_rl(x, y, &t2);
t3 = __k_atan2l(y, x, &t4);
x1 = t1; HALF(x1);
y1 = t3; HALF(y1);
u1 = u; HALF(u1);
v1 = v; HALF(v1);
x2 = t2 - (x1 - t1); /* log(hypot(x,y)) = x1 + x2 */
y2 = t4 - (y1 - t3); /* atan2(y,x) = y1 + y2 */
/* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */
if (j != 2) {
b[0] = u1 * y1;
b[1] = (u - u1) * y1 + u * y2;
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = v1 * x1;
b[3] = (v - v1) * x1 + v * x2;
w1 = sum4fpl(b, &w2);
}
sincosl(w1, &t1, &t2);
sincosl(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
if (k == 1) /* square j times */
for (i = 0; i < 10; i++) {
t1 = s * c;
c = (c + s) * (c - s);
s = t1 + t1;
}
}
/* compute r = u * (t1, t2) - v * (t3, t4) */
b[0] = u1 * x1;
b[1] = (u - u1) * x1 + u * x2;
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = -v1 * y1;
b[3] = (v1 - v) * y1 - v * y2;
w1 = sum4fpl(b, &w2);
}
/* scale back unless w1 is large enough to cause exception */
if (k != 0 && fabsl(w1) < 20000.0L) {
w1 *= 65536.0L; w2 *= 65536.0L;
}
hx = HI_XWORD(w1);
ix = hx & 0x7fffffff;
/* compute exp(w1 + w2) */
k = 0;
if (ix < 0x3f8c0000) /* exp(tiny < 2**-115) = 1 */
r = one;
else if (ix >= 0x400c6760) /* overflow/underflow */
r = (hx < 0)? tiny * tiny : huge * huge;
else { /* compute exp(w1 + w2) */
k = (int) (invln2 * w1 + ((hx >= 0)? 0.5L : -0.5L));
t1 = (long double) k;
t2 = w1 - t1 * ln2hil;
t3 = w2 - t1 * ln2lol;
r = expl(t2 + t3);
}
if (c != zero) c *= r;
if (s != zero) s *= r;
if (k != 0) {
c = scalbnl(c, k);
s = scalbnl(s, k);
}
LD_RE(ans) = c;
LD_IM(ans) = s;
}
return (ans);
}
