private static Complex asin()

in commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java [1834:1950]
95 lines of code
22 McCabe index (conditional complexity)

    private static Complex asin(final double real, final double imaginary,
                                final ComplexConstructor constructor) {
        // Compute with positive values and determine sign at the end
        final double x = Math.abs(real);
        final double y = Math.abs(imaginary);
        // The result (without sign correction)
        final double re;
        final double im;

        // Handle C99 special cases
        if (Double.isNaN(x)) {
            if (isPosInfinite(y)) {
                re = x;
                im = y;
            } else {
                // No-use of the input constructor
                return NAN;
            }
        } else if (Double.isNaN(y)) {
            if (x == 0) {
                re = 0;
                im = y;
            } else if (isPosInfinite(x)) {
                re = y;
                im = x;
            } else {
                // No-use of the input constructor
                return NAN;
            }
        } else if (isPosInfinite(x)) {
            re = isPosInfinite(y) ? PI_OVER_4 : PI_OVER_2;
            im = x;
        } else if (isPosInfinite(y)) {
            re = 0;
            im = y;
        } else {
            // Special case for real numbers:
            if (y == 0 && x <= 1) {
                return constructor.create(Math.asin(real), imaginary);
            }

            final double xp1 = x + 1;
            final double xm1 = x - 1;

            if (inRegion(x, y, SAFE_MIN, SAFE_MAX)) {
                final double yy = y * y;
                final double r = Math.sqrt(xp1 * xp1 + yy);
                final double s = Math.sqrt(xm1 * xm1 + yy);
                final double a = 0.5 * (r + s);
                final double b = x / a;

                if (b <= B_CROSSOVER) {
                    re = Math.asin(b);
                } else {
                    final double apx = a + x;
                    if (x <= 1) {
                        re = Math.atan(x / Math.sqrt(0.5 * apx * (yy / (r + xp1) + (s - xm1))));
                    } else {
                        re = Math.atan(x / (y * Math.sqrt(0.5 * (apx / (r + xp1) + apx / (s + xm1)))));
                    }
                }

                if (a <= A_CROSSOVER) {
                    final double am1;
                    if (x < 1) {
                        am1 = 0.5 * (yy / (r + xp1) + yy / (s - xm1));
                    } else {
                        am1 = 0.5 * (yy / (r + xp1) + (s + xm1));
                    }
                    im = Math.log1p(am1 + Math.sqrt(am1 * (a + 1)));
                } else {
                    im = Math.log(a + Math.sqrt(a * a - 1));
                }
            } else {
                // Hull et al: Exception handling code from figure 4
                if (y <= (EPSILON * Math.abs(xm1))) {
                    if (x < 1) {
                        re = Math.asin(x);
                        im = y / Math.sqrt(xp1 * (1 - x));
                    } else {
                        re = PI_OVER_2;
                        if ((Double.MAX_VALUE / xp1) > xm1) {
                            // xp1 * xm1 won't overflow:
                            im = Math.log1p(xm1 + Math.sqrt(xp1 * xm1));
                        } else {
                            im = LN_2 + Math.log(x);
                        }
                    }
                } else if (y <= SAFE_MIN) {
                    // Hull et al: Assume x == 1.
                    // True if:
                    // E^2 > 8*sqrt(u)
                    //
                    // E = Machine epsilon: (1 + epsilon) = 1
                    // u = Double.MIN_NORMAL
                    re = PI_OVER_2 - Math.sqrt(y);
                    im = Math.sqrt(y);
                } else if (EPSILON * y - 1 >= x) {
                    // Possible underflow:
                    re = x / y;
                    im = LN_2 + Math.log(y);
                } else if (x > 1) {
                    re = Math.atan(x / y);
                    final double xoy = x / y;
                    im = LN_2 + Math.log(y) + 0.5 * Math.log1p(xoy * xoy);
                } else {
                    final double a = Math.sqrt(1 + y * y);
                    // Possible underflow:
                    re = x / a;
                    im = 0.5 * Math.log1p(2 * y * (y + a));
                }
            }
        }

        return constructor.create(changeSign(re, real),
                                  changeSign(im, imaginary));
    }