ldcomplex
csinhl(ldcomplex z) {
long double t, x, y, S, C;
int hx, ix, hy, iy, n;
ldcomplex ans;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
ix = hx & 0x7fffffff;
hy = HI_XWORD(y);
iy = hy & 0x7fffffff;
x = fabsl(x);
y = fabsl(y);
(void) sincosl(y, &S, &C);
if (ix >= 0x4004e000) { /* |x| > 60 = prec/2 (14,28,34,60) */
if (ix >= 0x400C62E4) { /* |x| > 11356.52... ~ log(2**16384) */
if (ix >= 0x7fff0000) { /* |x| is inf or NaN */
if (y == zero) {
LD_RE(ans) = x;
LD_IM(ans) = y;
} else if (iy >= 0x7fff0000) {
LD_RE(ans) = x;
LD_IM(ans) = x - y;
} else {
LD_RE(ans) = C * x;
LD_IM(ans) = S * x;
}
} else {
/* return exp(x)=t*2**n */
t = __k_cexpl(x, &n);
LD_RE(ans) = scalbnl(C * t, n - 1);
LD_IM(ans) = scalbnl(S * t, n - 1);
}
} else {
t = expl(x) * half;
LD_RE(ans) = C * t;
LD_IM(ans) = S * t;
}
} else {
if (x == zero) { /* x = 0, return (0,S) */
LD_RE(ans) = zero;
LD_IM(ans) = S;
} else {
LD_RE(ans) = C * sinhl(x);
LD_IM(ans) = S * coshl(x);
}
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
ldcomplex
casinhl(ldcomplex z) {
ldcomplex w, r, ans;
LD_RE(w) = -LD_IM(z);
LD_IM(w) = LD_RE(z);
r = casinl(w);
LD_RE(ans) = LD_IM(r);
LD_IM(ans) = -LD_RE(r);
return (ans);
}
ldcomplex
catanhl(ldcomplex z) {
long double x, y;
ldcomplex ans, ct;
x = LD_RE(z);
y = LD_IM(z);
LD_RE(z) = -y;
LD_IM(z) = x;
ct = catanl(z);
LD_RE(ans) = LD_IM(ct);
LD_IM(ans) = -LD_RE(ct);
return (ans);
}
ldcomplex
casinl(ldcomplex z) {
long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
ldcomplex ans;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
x = fabsl(x);
y = fabsl(y);
/* special cases */
/* x is inf or NaN */
if (ix >= 0x7fff0000) { /* x is inf or NaN */
if (isinfl(x)) { /* x is INF */
LD_IM(ans) = x;
if (iy >= 0x7fff0000) {
if (isinfl(y))
/* casin(inf + i inf) = pi/4 + i inf */
LD_RE(ans) = pi_4 + pi_4_l;
else /* casin(inf + i NaN) = NaN + i inf */
LD_RE(ans) = y + y;
} else /* casin(inf + iy) = pi/2 + i inf */
LD_RE(ans) = pi_2 + pi_2_l;
} else { /* x is NaN */
if (iy >= 0x7fff0000) {
/* INDENT OFF */
/*
* casin(NaN + i inf) = NaN + i inf
* casin(NaN + i NaN) = NaN + i NaN
*/
/* INDENT ON */
LD_IM(ans) = y + y;
LD_RE(ans) = x + x;
} else {
/* INDENT OFF */
/* casin(NaN + i y ) = NaN + i NaN */
/* INDENT ON */
LD_IM(ans) = LD_RE(ans) = x + y;
}
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
/* casin(+0 + i 0) = 0 + i 0. */
if (x == zero && y == zero)
return (z);
if (iy >= 0x7fff0000) { /* y is inf or NaN */
if (isinfl(y)) { /* casin( x + i inf ) = 0 + i inf */
LD_IM(ans) = y;
LD_RE(ans) = zero;
} else { /* casin( x + i NaN ) = NaN + i NaN */
LD_IM(ans) = x + y;
if (x == zero)
LD_RE(ans) = x;
else
LD_RE(ans) = y;
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
if (y == zero) { /* region 1: y=0 */
if (ix < 0x3fff0000) { /* |x| < 1 */
LD_RE(ans) = asinl(x);
LD_IM(ans) = zero;
} else {
LD_RE(ans) = pi_2 + pi_2_l;
if (ix >= ip1) /* |x| >= i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
else if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
else {
xm1 = x - one;
LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
one)));
}
}
} else if (y <= E * fabsl(x - one)) { /* region 2: y < tiny*|x-1| */
if (ix < 0x3fff0000) { /* x < 1 */
LD_RE(ans) = asinl(x);
LD_IM(ans) = y / sqrtl((one + x) * (one - x));
} else {
LD_RE(ans) = pi_2 + pi_2_l;
if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
else if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
else
LD_IM(ans) = log1pl((x - one) + sqrtl((x -
one) * (x + one)));
}
} else if (y < Foursqrtu) { /* region 3 */
t = sqrtl(y);
LD_RE(ans) = pi_2 - (t - pi_2_l);
LD_IM(ans) = t;
} else if (E * y - one >= x) { /* region 4 */
LD_RE(ans) = x / y; /* need to fix underflow cases */
LD_IM(ans) = ln2 + logl(y);
} else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
/* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
t = x / y;
LD_RE(ans) = atanl(t);
LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
} else if (x < Foursqrtu) {
/* region 6: x is very small, < 4sqrt(min) */
A = sqrtl(one + y * y);
LD_RE(ans) = x / A; /* may underflow */
if (iy >= 0x3fff8000) /* if y > Acrossover */
LD_IM(ans) = logl(y + A);
else
LD_IM(ans) = half * log1pl((y + y) * (y + A));
} else { /* safe region */
y2 = y * y;
xp1 = x + one;
xm1 = x - one;
R = sqrtl(xp1 * xp1 + y2);
S = sqrtl(xm1 * xm1 + y2);
A = half * (R + S);
B = x / A;
if (B <= Bcrossover)
LD_RE(ans) = asinl(B);
else { /* use atan and an accurate approx to a-x */
Apx = A + x;
if (x <= one)
LD_RE(ans) = atanl(x / sqrtl(half * Apx * (y2 /
(R + xp1) + (S - xm1))));
else
LD_RE(ans) = atanl(x / (y * sqrtl(half * (Apx /
(R + xp1) + Apx / (S + xm1)))));
}
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (x < one)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
} else {
LD_IM(ans) = logl(A + sqrtl(A * A - one));
}
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
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
catanl(ldcomplex z) {
ldcomplex ans;
long double x, y, t1, ax, ay, t;
int hx, hy, ix, iy;
x = LD_RE(z);
y = LD_IM(z);
ax = fabsl(x);
ay = fabsl(y);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* x is inf or NaN */
if (ix >= 0x7fff0000) {
if (isinfl(x)) {
LD_RE(ans) = pi_2;
LD_IM(ans) = zero;
} else {
LD_RE(ans) = x + x;
if (iszerol(y) || (isinfl(y)))
LD_IM(ans) = zero;
else
LD_IM(ans) = (fabsl(y) - ay) / (fabsl(y) - ay);
}
} else if (iy >= 0x7fff0000) {
/* y is inf or NaN */
if (isinfl(y)) {
LD_RE(ans) = pi_2;
LD_IM(ans) = zero;
} else {
LD_RE(ans) = (fabsl(x) - ax) / (fabsl(x) - ax);
LD_IM(ans) = y;
}
} else if (iszerol(x)) {
/* INDENT OFF */
/*
* x = 0
* 1 1
* A = --- * atan2(2x, 1-x*x-y*y) = --- atan2(0,1-|y|)
* 2 2
*
* 1 [ (y+1)*(y+1) ] 1 2 1 2y
* B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
* 4 [ (y-1)*(y-1) ] 2 y-1 2 1-y
*/
/* INDENT ON */
t = one - ay;
if (ay == one) {
/* y=1: catan(0,1)=(0,+inf) with 1/0 signal */
LD_IM(ans) = ay / ax;
LD_RE(ans) = zero;
} else if (ay > one) { /* y>1 */
LD_IM(ans) = half * log1pl(two / (-t));
LD_RE(ans) = pi_2;
} else { /* y<1 */
LD_IM(ans) = half * log1pl((ay + ay) / t);
LD_RE(ans) = zero;
}
} else if (ay < E * (one + ax)) {
/* INDENT OFF */
/*
* Tiny y (relative to 1+|x|)
* |y| < E*(1+|x|)
* where E=2**-29, -35, -60 for double, extended, quad precision
*
* 1 [x<=1: atan(x)
* A = - * atan2(2x,1-x*x-y*y) ~ [ 1 1+x
* 2 [x>=1: - atan2(2,(1-x)*(-----))
* 2 x
*
* y/x
* B ~ t*(1-2t), where t = ----------------- is tiny
* x + (y-1)*(y-1)/x
*
* y
* (when x < 2**-60, t = ----------- )
* (y-1)*(y-1)
*/
/* INDENT ON */
if (ay == zero)
LD_IM(ans) = ay;
else {
t1 = ay - one;
if (ix < 0x3fc30000)
t = ay / (t1 * t1);
else if (ix > 0x403b0000)
t = (ay / ax) / ax;
else
t = ay / (ax * ax + t1 * t1);
LD_IM(ans) = t * (one - two * t);
}
if (ix < 0x3fff0000)
LD_RE(ans) = atanl(ax);
else
LD_RE(ans) = half * atan2l(two, (one - ax) * (one +
one / ax));
} else if (ay > Einv * (one + ax)) {
/* INDENT OFF */
/*
* Huge y relative to 1+|x|
* |y| > Einv*(1+|x|), where Einv~2**(prec/2+3),
* 1
* A ~ --- * atan2(2x, -y*y) ~ pi/2
* 2
* y
* B ~ t*(1-2t), where t = --------------- is tiny
* (y-1)*(y-1)
*/
/* INDENT ON */
LD_RE(ans) = pi_2;
t = (ay / (ay - one)) / (ay - one);
LD_IM(ans) = t * (one - (t + t));
} else if (ay == one) {
/* INDENT OFF */
/*
* y=1
* 1 1
* A = - * atan2(2x, -x*x) = --- atan2(2,-x)
* 2 2
*
* 1 [ x*x+4] 1 4 [ 0.5(log2-logx) if
* B = - log [ -----] = - log (1+ ---) = [ |x|<E, else 0.25*
* 4 [ x*x ] 4 x*x [ log1p((2/x)*(2/x))
*/
/* INDENT ON */
LD_RE(ans) = half * atan2l(two, -ax);
if (ax < E)
LD_IM(ans) = half * (ln2 - logl(ax));
else {
t = two / ax;
LD_IM(ans) = 0.25L * log1pl(t * t);
}
} else if (ax > Einv * Einv) {
/* INDENT OFF */
/*
* Huge x:
* when |x| > 1/E^2,
* 1 pi
* A ~ --- * atan2(2x, -x*x-y*y) ~ ---
* 2 2
* y y/x
* B ~ t*(1-2t), where t = --------------- = (-------------- )/x
* x*x+(y-1)*(y-1) 1+((y-1)/x)^2
*/
/* INDENT ON */
LD_RE(ans) = pi_2;
t = ((ay / ax) / (one + ((ay - one) / ax) * ((ay - one) /
ax))) / ax;
LD_IM(ans) = t * (one - (t + t));
} else if (ax < E * E * E * E) {
/* INDENT OFF */
/*
* Tiny x:
* when |x| < E^4, (note that y != 1)
* 1 1
* A = --- * atan2(2x, 1-x*x-y*y) ~ --- * atan2(2x,1-y*y)
* 2 2
*
* 1 [ (y+1)*(y+1) ] 1 2 1 2y
* B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
* 4 [ (y-1)*(y-1) ] 2 y-1 2 1-y
*/
/* INDENT ON */
LD_RE(ans) = half * atan2l(ax + ax, (one - ay) * (one + ay));
if (ay > one) /* y>1 */
LD_IM(ans) = half * log1pl(two / (ay - one));
else /* y<1 */
LD_IM(ans) = half * log1pl((ay + ay) / (one - ay));
} else {
/* INDENT OFF */
/*
* normal x,y
* 1
* A = --- * atan2(2x, 1-x*x-y*y)
* 2
*
* 1 [ x*x+(y+1)*(y+1) ] 1 4y
* B = - log [ --------------- ] = - log (1+ -----------------)
* 4 [ x*x+(y-1)*(y-1) ] 4 x*x + (y-1)*(y-1)
*/
/* INDENT ON */
t = one - ay;
if (iy >= 0x3ffe0000 && iy < 0x40000000) {
/* y close to 1 */
LD_RE(ans) = half * (atan2l((ax + ax), (t * (one +
ay) - ax * ax)));
} else if (ix >= 0x3ffe0000 && ix < 0x40000000) {
/* x close to 1 */
LD_RE(ans) = half * atan2l((ax + ax), ((one - ax) *
(one + ax) - ay * ay));
} else
LD_RE(ans) = half * atan2l((ax + ax), ((one - ax *
ax) - ay * ay));
LD_IM(ans) = 0.25L * log1pl((4.0L * ay) / (ax * ax + t * t));
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
ldcomplex
cacosl(ldcomplex z) {
long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
ldcomplex ans;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* x is 0 */
if (x == zero) {
if (y == zero || (iy >= 0x7fff0000)) {
LD_RE(ans) = pi_2 + pi_2_l;
LD_IM(ans) = -y;
return (ans);
}
}
/* |y| is inf or NaN */
if (iy >= 0x7fff0000) {
if (isinfl(y)) { /* cacos(x + i inf) = pi/2 - i inf */
LD_IM(ans) = -y;
if (ix < 0x7fff0000) {
LD_RE(ans) = pi_2 + pi_2_l;
} else if (isinfl(x)) {
if (hx >= 0)
LD_RE(ans) = pi_4 + pi_4_l;
else
LD_RE(ans) = pi3_4 + pi3_4_l;
} else {
LD_RE(ans) = x;
}
} else { /* cacos(x + i NaN) = NaN + i NaN */
LD_RE(ans) = y + x;
if (isinfl(x))
LD_IM(ans) = -fabsl(x);
else
LD_IM(ans) = y;
}
return (ans);
}
y = fabsl(y);
if (ix >= 0x7fff0000) { /* x is inf or NaN */
if (isinfl(x)) { /* x is INF */
LD_IM(ans) = -fabsl(x);
if (iy >= 0x7fff0000) {
if (isinfl(y)) {
/* INDENT OFF */
/* cacos(inf + i inf) = pi/4 - i inf */
/* cacos(-inf+ i inf) =3pi/4 - i inf */
/* INDENT ON */
if (hx >= 0)
LD_RE(ans) = pi_4 + pi_4_l;
else
LD_RE(ans) = pi3_4 + pi3_4_l;
} else
/* INDENT OFF */
/* cacos(inf + i NaN) = NaN - i inf */
/* INDENT ON */
LD_RE(ans) = y + y;
} else {
/* INDENT OFF */
/* cacos(inf + iy ) = 0 - i inf */
/* cacos(-inf+ iy ) = pi - i inf */
/* INDENT ON */
if (hx >= 0)
LD_RE(ans) = zero;
else
LD_RE(ans) = pi + pi_l;
}
} else { /* x is NaN */
/* INDENT OFF */
/*
* cacos(NaN + i inf) = NaN - i inf
* cacos(NaN + i y ) = NaN + i NaN
* cacos(NaN + i NaN) = NaN + i NaN
*/
/* INDENT ON */
LD_RE(ans) = x + y;
if (iy >= 0x7fff0000) {
LD_IM(ans) = -y;
} else {
LD_IM(ans) = x;
}
}
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
if (y == zero) { /* region 1: y=0 */
if (ix < 0x3fff0000) { /* |x| < 1 */
LD_RE(ans) = acosl(x);
LD_IM(ans) = zero;
} else {
LD_RE(ans) = zero;
x = fabsl(x);
if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
else if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
else {
xm1 = x - one;
LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
one)));
}
}
} else if (y <= E * fabsl(fabsl(x) - one)) {
/* region 2: y < tiny*||x|-1| */
if (ix < 0x3fff0000) { /* x < 1 */
LD_RE(ans) = acosl(x);
x = fabsl(x);
LD_IM(ans) = y / sqrtl((one + x) * (one - x));
} else if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
if (hx >= 0)
LD_RE(ans) = y / x;
else {
if (ix >= ip1 + 0x00040000)
LD_RE(ans) = pi + pi_l;
else {
t = pi_l + y / x;
LD_RE(ans) = pi + t;
}
}
LD_IM(ans) = ln2 + logl(fabsl(x));
} else {
x = fabsl(x);
t = sqrtl((x - one) * (x + one));
LD_RE(ans) = (hx >= 0)? y / t : pi - (y / t - pi_l);
if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + t);
else
LD_IM(ans) = log1pl(t - (one - x));
}
} else if (y < Foursqrtu) { /* region 3 */
t = sqrtl(y);
LD_RE(ans) = (hx >= 0)? t : pi + pi_l;
LD_IM(ans) = t;
} else if (E * y - one >= fabsl(x)) { /* region 4 */
LD_RE(ans) = pi_2 + pi_2_l;
LD_IM(ans) = ln2 + logl(y);
} else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
/* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
t = x / y;
LD_RE(ans) = atan2l(y, x);
LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
} else if (fabsl(x) < Foursqrtu) {
/* region 6: x is very small, < 4sqrt(min) */
LD_RE(ans) = pi_2 + pi_2_l;
A = sqrtl(one + y * y);
if (iy >= 0x3fff8000) /* if y > Acrossover */
LD_IM(ans) = logl(y + A);
else
LD_IM(ans) = half * log1pl((y + y) * (y + A));
} else { /* safe region */
t = fabsl(x);
y2 = y * y;
xp1 = t + one;
xm1 = t - one;
R = sqrtl(xp1 * xp1 + y2);
S = sqrtl(xm1 * xm1 + y2);
A = half * (R + S);
B = t / A;
if (B <= Bcrossover)
LD_RE(ans) = (hx >= 0)? acosl(B) : acosl(-B);
else { /* use atan and an accurate approx to a-x */
Apx = A + t;
if (t <= one)
LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
(R + xp1) + (S - xm1))), x);
else
LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
(R + xp1) + Apx / (S + xm1)))), x);
}
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (ix < 0x3fff0000)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
} else {
LD_IM(ans) = logl(A + sqrtl(A * A - one));
}
}
if (hy >= 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
ldcomplex
csqrtl(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);
if (ix >= 0x7fff0000 || iy >= 0x7fff0000) {
/* x or y is Inf or NaN */
if (isinfl(y))
LD_IM(ans) = LD_RE(ans) = ay;
else if (isinfl(x)) {
if (hx > 0) {
LD_RE(ans) = ax;
LD_IM(ans) = ay * zero;
} else {
LD_RE(ans) = ay * zero;
LD_IM(ans) = ax;
}
} else
LD_IM(ans) = LD_RE(ans) = ax + ay;
} else if (y == zero) {
if (hx >= 0) {
LD_RE(ans) = sqrtl(ax);
LD_IM(ans) = zero;
} else {
LD_IM(ans) = sqrtl(ax);
LD_RE(ans) = zero;
}
} else if (ix >= iy) {
n = (ix - iy) >> 16;
#if defined(__x86) /* 64 significant bits */
if (n >= 35)
#else /* 113 significant bits */
if (n >= 60)
#endif
t = sqrtl(ax);
else if (ix >= 0x5f3f0000) { /* x > 2**8000 */
ax *= twom9001;
y *= twom9001;
t = two4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
} else if (iy <= 0x20bf0000) { /* y < 2**-8000 */
ax *= two8999;
y *= two8999;
t = twom4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
} else
t = sqrtl(half * (ax + sqrtl(ax * ax + y * y)));
if (hx >= 0) {
LD_RE(ans) = t;
LD_IM(ans) = ay / (t + t);
} else {
LD_IM(ans) = t;
LD_RE(ans) = ay / (t + t);
}
} else {
long double
cabsl(ldcomplex z) {
return (hypotl(LD_RE(z), LD_IM(z)));
}
long double
cargl(ldcomplex z) {
return (atan2l(LD_IM(z), LD_RE(z)));
}
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);
}