dcomplex
csinh(dcomplex z) {
double t, x, y, S, C;
int hx, ix, lx, hy, iy, ly, n;
dcomplex ans;
x = D_RE(z);
y = D_IM(z);
hx = HI_WORD(x);
lx = LO_WORD(x);
ix = hx & 0x7fffffff;
hy = HI_WORD(y);
ly = LO_WORD(y);
iy = hy & 0x7fffffff;
x = fabs(x);
y = fabs(y);
(void) sincos(y, &S, &C);
if (ix >= 0x403c0000) { /* |x| > 28 = prec/2 (14,28,34,60) */
if (ix >= 0x40862E42) { /* |x| > 709.78... ~ log(2**1024) */
if (ix >= 0x7ff00000) { /* |x| is inf or NaN */
if ((iy | ly) == 0) {
D_RE(ans) = x;
D_IM(ans) = y;
} else if (iy >= 0x7ff00000) {
D_RE(ans) = x;
D_IM(ans) = x - y;
} else {
D_RE(ans) = C * x;
D_IM(ans) = S * x;
}
} else {
/* return exp(x)=t*2**n */
t = __k_cexp(x, &n);
D_RE(ans) = scalbn(C * t, n - 1);
D_IM(ans) = scalbn(S * t, n - 1);
}
} else {
t = exp(x) * 0.5;
D_RE(ans) = C * t;
D_IM(ans) = S * t;
}
} else {
if ((ix | lx) == 0) { /* x = 0, return (0,S) */
D_RE(ans) = 0.0;
D_IM(ans) = S;
} else {
D_RE(ans) = C * sinh(x);
D_IM(ans) = S * cosh(x);
}
}
if (hx < 0)
D_RE(ans) = -D_RE(ans);
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}
dcomplex
ccos(dcomplex z) {
double x, y;
x = D_RE(z);
y = D_IM(z);
D_RE(z) = y;
D_IM(z) = -x;
return (ccosh(z));
}
dcomplex
csqrt(dcomplex z) {
dcomplex ans;
double x, y, t, ax, ay;
int n, ix, iy, hx, hy, lx, ly;
x = D_RE(z);
y = D_IM(z);
hx = HI_WORD(x);
lx = LO_WORD(x);
hy = HI_WORD(y);
ly = LO_WORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
ay = fabs(y);
ax = fabs(x);
if (ix >= 0x7ff00000 || iy >= 0x7ff00000) {
/* x or y is Inf or NaN */
if (ISINF(iy, ly))
D_IM(ans) = D_RE(ans) = ay;
else if (ISINF(ix, lx)) {
if (hx > 0) {
D_RE(ans) = ax;
D_IM(ans) = ay * zero;
} else {
D_RE(ans) = ay * zero;
D_IM(ans) = ax;
}
} else
D_IM(ans) = D_RE(ans) = ax + ay;
} else if ((iy | ly) == 0) { /* y = 0 */
if (hx >= 0) {
D_RE(ans) = sqrt(ax);
D_IM(ans) = zero;
} else {
D_IM(ans) = sqrt(ax);
D_RE(ans) = zero;
}
} else if (ix >= iy) {
n = (ix - iy) >> 20;
if (n >= 30) { /* x >> y or y=0 */
t = sqrt(ax);
} else if (ix >= 0x5f300000) { /* x > 2**500 */
ax *= twom601;
y *= twom601;
t = two300 * sqrt(ax + sqrt(ax * ax + y * y));
} else if (iy < 0x20b00000) { /* y < 2**-500 */
ax *= two599;
y *= two599;
t = twom300 * sqrt(ax + sqrt(ax * ax + y * y));
} else
t = sqrt(half * (ax + sqrt(ax * ax + ay * ay)));
if (hx >= 0) {
D_RE(ans) = t;
D_IM(ans) = ay / (t + t);
} else {
D_IM(ans) = t;
D_RE(ans) = ay / (t + t);
}
} else {
dcomplex
casinh(dcomplex z) {
dcomplex w, r, ans;
D_RE(w) = -D_IM(z);
D_IM(w) = D_RE(z);
r = casin(w);
D_RE(ans) = D_IM(r);
D_IM(ans) = -D_RE(r);
return (ans);
}
dcomplex
ctan(dcomplex z) {
double x, y;
dcomplex ans, ct;
x = D_RE(z);
y = D_IM(z);
D_RE(z) = y;
D_IM(z) = -x;
ct = ctanh(z);
D_RE(ans) = -D_IM(ct);
D_IM(ans) = D_RE(ct);
return (ans);
}
double
cimag(dcomplex z) {
return (D_IM(z));
}
