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/*
* 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.
*/
_CL_OVERLOADABLE vtype atan2(vtype y, vtype x)
{
const vtype pi = (vtype)0x1.921fb6p+1f;
const vtype piby2 = (vtype)0x1.921fb6p+0f;
const vtype piby4 = (vtype)0x1.921fb6p-1f;
const vtype threepiby4 = (vtype)0x1.2d97c8p+1f;
vtype ax = fabs(x);
vtype ay = fabs(y);
vtype v = fmin(ax, ay);
vtype u = fmax(ax, ay);
// Scale since u could be large, as in "regular" divide
vtype s = (u > (vtype)0x1.0p+96f) ? (vtype)0x1.0p-32f : (vtype)1.0f;
vtype vbyu = s * MATH_DIVIDE(v, s*u);
vtype vbyu2 = vbyu * vbyu;
#define USE_2_2_APPROXIMATION
#if defined USE_2_2_APPROXIMATION
vtype p = mad(vbyu2, mad(vbyu2, (vtype)-0x1.7e1f78p-9f, (vtype)-0x1.7d1b98p-3f), (vtype)-0x1.5554d0p-2f) * vbyu2 * vbyu;
vtype q = mad(vbyu2, mad(vbyu2, (vtype)0x1.1a714cp-2f, (vtype)0x1.287c56p+0f), 1.0f);
#else
vtype p = mad(vbyu2, mad(vbyu2, (vtype)-0x1.55cd22p-5f, (vtype)-0x1.26cf76p-2f), (vtype)-0x1.55554ep-2f) * vbyu2 * vbyu;
vtype q = mad(vbyu2, mad(vbyu2, mad(vbyu2, (vtype)0x1.9f1304p-5f, (vtype)0x1.2656fap-1f), (vtype)0x1.76b4b8p+0f), (vtype)1.0f);
#endif
// Octant 0 result
vtype a = mad(p, MATH_RECIP(q), vbyu);
// Fix up 3 other octants
vtype at = piby2 - a;
a = (ay > ax) ? at : a;
at = pi - a;
a = (x < (vtype)0.0f) ? at : a;
// y == 0 => 0 for x >= 0, pi for x < 0
at = as_itype(x) < (itype)0 ? pi : (vtype)0.0f;
a = (y == (vtype)0.0f) ? at : a;
// if (!FINITE_ONLY()) {
// x and y are +- Inf
at = (x > (vtype)0.0f) ? piby4 : threepiby4;
a = ((ax == (vtype)INFINITY) & (ay == (vtype)INFINITY)) ? at : a;
// x or y is NaN
a = (isnan(x) | isnan(y)) ? as_vtype((utype)QNANBITPATT_SP32) : a;
// }
// Fixup sign and return
return copysign(a, y);
}
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