amd-builtins/math64/atan2D.cl

/*
 * Copyright (c) 2014 Advanced Micro Devices, Inc.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

#include "math64.h"

__attribute__((overloadable, always_inline, weak)) double
atan2(double y, double x)
{
    USE_TABLE(double2, atan_jby256_tbl, ATAN_JBY256_TBL);

    const double pi = 3.1415926535897932e+00;          /* 0x400921fb54442d18 */
    const double piby2 = 1.5707963267948966e+00;       /* 0x3ff921fb54442d18 */
    const double piby4 = 7.8539816339744831e-01;       /* 0x3fe921fb54442d18 */
    const double three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */
    const double pi_head = 3.1415926218032836e+00;     /* 0x400921fb50000000 */
    const double pi_tail = 3.1786509547056392e-08;     /* 0x3e6110b4611a6263 */
    const double piby2_head = 1.5707963267948965e+00;  /* 0x3ff921fb54442d18 */
    const double piby2_tail = 6.1232339957367660e-17;  /* 0x3c91a62633145c07 */

    double x2 = x;
    int xneg = as_int2(x).hi < 0;
    int xexp = (as_int2(x).hi >> 20) & 0x7ff;

    double y2 = y;
    int yneg = as_int2(y).hi < 0;
    int yexp = (as_int2(y).hi >> 20) & 0x7ff;

    int cond2 = (xexp < 1021) & (yexp < 1021);
    int diffexp = yexp - xexp;

    // Scale up both x and y if they are both below 1/4
    double x1 = ldexp(x, 1024);
    int xexp1 = (as_int2(x1).hi >> 20) & 0x7ff;
    double y1 = ldexp(y, 1024);
    int yexp1 = (as_int2(y1).hi >> 20) & 0x7ff;
    int diffexp1 = yexp1 - xexp1;

    diffexp = cond2 ? diffexp1 : diffexp;
    x = cond2 ? x1 : x;
    y = cond2 ? y1 : y;

    // General case: take absolute values of arguments
    double u = fabs(x);
    double v = fabs(y);

    // Swap u and v if necessary to obtain 0 < v < u. Compute v/u.
    int swap_vu = u < v;
    double uu = u;
    u = swap_vu ? v : u;
    v = swap_vu ? uu : v;

    double vbyu = v / u;
    double q1, q2;

    // General values of v/u. Use a look-up table and series expansion.

    {
        double val = vbyu > 0.0625 ? vbyu : 0.063;
        int index = convert_int(fma(256.0, val, 0.5));
	double2 tv = atan_jby256_tbl[index - 16];
	q1 = tv.s0;
	q2 = tv.s1;
        double c = (double)index * 0x1.0p-8;

        // We're going to scale u and v by 2^(-u_exponent) to bring them close to 1
        // u_exponent could be EMAX so we have to do it in 2 steps
        int m = -((int)(as_ulong(u) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64);
	//double um = __amdil_ldexp_f64(u, m);
	//double vm = __amdil_ldexp_f64(v, m);
	double um = ldexp(u, m);
	double vm = ldexp(v, m);

        // 26 leading bits of u
        double u1 = as_double(as_ulong(um) & 0xfffffffff8000000UL);
        double u2 = um - u1;

        double r = MATH_DIVIDE(fma(-c, u2, fma(-c, u1, vm)), fma(c, vm, um));

        // Polynomial approximation to atan(r)
        double s = r * r;
        q2 = q2 + fma((s * fma(-s, 0.19999918038989143496, 0.33333333333224095522)), -r, r);
    }


    double q3, q4;
    {
        q3 = 0.0;
        q4 = vbyu;
    }

    double q5, q6;
    {
        double u1 = as_double(as_ulong(u) & 0xffffffff00000000UL);
        double u2 = u - u1;
        double vu1 = as_double(as_ulong(vbyu) & 0xffffffff00000000UL);
        double vu2 = vbyu - vu1;

        q5 = 0.0;
        double s = vbyu * vbyu;
        q6 = vbyu + fma(-vbyu * s,
                        fma(-s,
                            fma(-s,
                                fma(-s,
                                    fma(-s, 0.90029810285449784439E-01,
                                        0.11110736283514525407),
                                    0.14285713561807169030),
                                0.19999999999393223405),
                            0.33333333333333170500),
			 MATH_DIVIDE(fma(-u, vu2, fma(-u2, vu1, fma(-u1, vu1, v))), u));
    }


    q3 = vbyu < 0x1.d12ed0af1a27fp-27 ? q3 : q5;
    q4 = vbyu < 0x1.d12ed0af1a27fp-27 ? q4 : q6;

    q1 = vbyu > 0.0625 ? q1 : q3;
    q2 = vbyu > 0.0625 ? q2 : q4;

    // Tidy-up according to which quadrant the arguments lie in
    double res1, res2, res3, res4;
    q1 = swap_vu ? piby2_head - q1 : q1;
    q2 = swap_vu ? piby2_tail - q2 : q2;
    q1 = xneg ? pi_head - q1 : q1;
    q2 = xneg ? pi_tail - q2 : q2;
    q1 = q1 + q2;
    res4 = yneg ? -q1 : q1;

    res1 = yneg ? -three_piby4 : three_piby4;
    res2 = yneg ? -piby4 : piby4;
    res3 = xneg ? res1 : res2;

    res3 = isinf(x2) & isinf(y2) ? res3 : res4;
    res1 = yneg ? -pi : pi;

    // abs(x)/abs(y) > 2^56 and x < 0
    res3 = (diffexp < -56 && xneg) ? res1 : res3;

    res4 = MATH_DIVIDE(y, x);
    // x positive and dominant over y by a factor of 2^28
    res3 = diffexp < -28 & xneg == 0 ? res4 : res3;

    // abs(y)/abs(x) > 2^56
    res4 = yneg ? -piby2 : piby2;       // atan(y/x) is insignificant compared to piby2
    res3 = diffexp > 56 ? res4 : res3;

    res3 = x2 == 0.0 ? res4 : res3;   // Zero x gives +- pi/2 depending on sign of y
    res4 = xneg ? res1 : y2;

    res3 = y2 == 0.0 ? res4 : res3;   // Zero y gives +-0 for positive x and +-pi for negative x
    res3 = isnan(y2) ? y2 : res3;
    res3 = isnan(x2) ? x2 : res3;

    return res3;
}