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/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* Copyright (c) 2017 Michal Babej / Tampere University of Technology
*
* 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 acosh(vtype x) {
utype ux = as_utype(x);
// Arguments greater than 1/sqrt(epsilon) in magnitude are
// approximated by acosh(x) = ln(2) + ln(x)
// For 2.0 <= x <= 1/sqrt(epsilon) the approximation is
// acosh(x) = ln(x + sqrt(x*x-1)) */
itype high = (ux > (utype)0x46000000);
itype med = (ux > (utype)0x40000000);
vtype w = x - (vtype)1.0f;
vtype s = w*w + 2.0f*w;
vtype t = x*x - (vtype)1.0f;
vtype r = sqrt(select(s, t, med)) + select(w, x, med);
vtype v = select(r, x, high) - select((vtype)0.0f, (vtype)1.0f, med);
vtype z = log1p(v) + select((vtype)0.0f, (vtype)0x1.62e430p-1f, high);
z = select(z, x, (ux >= (utype)PINFBITPATT_SP32));
z = select(z, as_vtype((utype)QNANBITPATT_SP32), (x < (vtype)1.0f));
return z;
}
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