/*===--------------------------------------------------------------------------
 *                   ROCm Device Libraries
 *
 * This file is distributed under the University of Illinois Open Source
 * License. See LICENSE.TXT for details.
 *===------------------------------------------------------------------------*/

#include "mathD.h"

#define DOUBLE_SPECIALIZATION
#include "ep.h"

CONSTATTR double
MATH_MANGLE(asin)(double x)
{
    // Computes arcsin(x).
    // The argument is first reduced by noting that arcsin(x)
    // is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
    // For denormal and small arguments arcsin(x) = x to machine
    // accuracy. Remaining argument ranges are handled as follows.
    // For abs(x) <= 0.5 use
    // arcsin(x) = x + x^3*R(x^2)
    // where R(x^2) is a rational minimax approximation to
    // (arcsin(x) - x)/x^3.
    // For abs(x) > 0.5 exploit the identity:
    // arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
    // together with the above rational approximation, and
    // reconstruct the terms carefully.


    double y = BUILTIN_ABS_F64(x);
    bool transform = y >= 0.5;

    double rt = MATH_MAD(y, -0.5, 0.5);
    double y2 = y * y;
    double r = transform ? rt : y2;

    double u = r * MATH_MAD(r, MATH_MAD(r, MATH_MAD(r, MATH_MAD(r, 
                   MATH_MAD(r, MATH_MAD(r, MATH_MAD(r, MATH_MAD(r, 
                   MATH_MAD(r, MATH_MAD(r, MATH_MAD(r, 
                       0x1.059859fea6a70p-5, -0x1.0a5a378a05eafp-6), 0x1.4052137024d6ap-6), 0x1.ab3a098a70509p-8),
                       0x1.8ed60a300c8d2p-7), 0x1.c6fa84b77012bp-7), 0x1.1c6c111dccb70p-6), 0x1.6e89f0a0adacfp-6),
                       0x1.f1c72c668963fp-6), 0x1.6db6db41ce4bdp-5), 0x1.333333336fd5bp-4), 0x1.5555555555380p-3);

    double v = MATH_MAD(y, u, y);
    if (transform) {
        double2 s = root2(r);
        double2 ve = fsub(con(0x1.921fb54442d18p-1, 0x1.1a62633145c07p-55), fadd(s, mul(s, u)));
        v = ve.hi + ve.hi;
        v = y == 1.0 ? 0x1.921fb54442d18p+0 : v;
    }

    return BUILTIN_COPYSIGN_F64(v, x);
}