void
gsl_complex_arccos (complex_t const *a, complex_t *res)
{ /* z = arccos(a) */
gnm_float R = GSL_REAL (a), I = GSL_IMAG (a);
if (I == 0) {
gsl_complex_arccos_real (R, res);
} else {
gnm_float x = gnm_abs (R);
gnm_float y = gnm_abs (I);
gnm_float r = gnm_hypot (x + 1, y);
gnm_float s = gnm_hypot (x - 1, y);
gnm_float A = 0.5 * (r + s);
gnm_float B = x / A;
gnm_float y2 = y * y;
gnm_float real, imag;
const gnm_float A_crossover = 1.5;
const gnm_float B_crossover = 0.6417;
if (B <= B_crossover) {
real = gnm_acos (B);
} else {
if (x <= 1) {
gnm_float D = 0.5 * (A + x) *
(y2 / (r + x + 1) + (s + (1 - x)));
real = gnm_atan (gnm_sqrt (D) / x);
} else {
gnm_float Apx = A + x;
gnm_float D = 0.5 * (Apx / (r + x + 1) + Apx /
(s + (x - 1)));
real = gnm_atan ((y * gnm_sqrt (D)) / x);
}
}
if (A <= A_crossover) {
gnm_float Am1;
if (x < 1) {
Am1 = 0.5 * (y2 / (r + (x + 1)) + y2 /
(s + (1 - x)));
} else {
Am1 = 0.5 * (y2 / (r + (x + 1)) +
(s + (x - 1)));
}
imag = gnm_log1p (Am1 + gnm_sqrt (Am1 * (A + 1)));
} else {
imag = gnm_log (A + gnm_sqrt (A * A - 1));
}
complex_init (res, (R >= 0) ? real : M_PIgnum - real, (I >= 0) ?
-imag : imag);
}
}
gsl_complex gsl_complex_arccos(gsl_complex a)
{ /* z = arccos(a) */
double R = GSL_REAL(a), I = GSL_IMAG(a);
gsl_complex z;
if (I == 0) {
z = gsl_complex_arccos_real(R);
} else {
double x = fabs(R), y = fabs(I);
double r = hypot(x + 1, y), s = hypot(x - 1, y);
double A = 0.5 * (r + s);
double B = x / A;
double y2 = y * y;
double real, imag;
const double A_crossover = 1.5, B_crossover = 0.6417;
if (B <= B_crossover) {
real = acos(B);
} else {
if (x <= 1) {
double D =
0.5 * (A + x) * (y2 / (r + x + 1) + (s + (1 - x)));
real = atan(sqrt(D) / x);
} else {
double Apx = A + x;
double D = 0.5 * (Apx / (r + x + 1) + Apx / (s + (x - 1)));
real = atan((y * sqrt(D)) / x);
}
}
if (A <= A_crossover) {
double Am1;
if (x < 1) {
Am1 = 0.5 * (y2 / (r + (x + 1)) + y2 / (s + (1 - x)));
} else {
Am1 = 0.5 * (y2 / (r + (x + 1)) + (s + (x - 1)));
}
imag = log1p(Am1 + sqrt(Am1 * (A + 1)));
} else {
imag = log(A + sqrt(A * A - 1));
}
GSL_SET_COMPLEX(&z, (R >= 0) ? real : M_PI - real,
(I >= 0) ? -imag : imag);
}
return z;
}
