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/*
* Copyright (c) 2014,2015 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 atanh(vtype x) {
vtype absx = fabs(x);
vtype ret = (absx == (vtype)1.0) ? as_vtype((utype)PINFBITPATT_DP64) : as_vtype((utype)QNANBITPATT_DP64);
// |x| >= 0.5
// Note that atanh(x) = 0.5 * ln((1+x)/(1-x))
// For greater accuracy we use
// ln((1+x)/(1-x)) = ln(1 + 2x/(1-x)) = log1p(2x/(1-x)).
vtype r = 0.5 * log1p((2.0 * absx) / ((vtype)1.0 - absx));
ret = (absx < (vtype)1.0) ? r : ret;
r = -ret;
ret = (x < (vtype)0.0) ? r : ret;
// Arguments up to 0.5 in magnitude are
// approximated by a [5,5] minimax polynomial
vtype t = x * x;
vtype pn = pocl_fma(t,
pocl_fma(t,
pocl_fma(t,
pocl_fma(t,
pocl_fma(t,
(vtype)-0.10468158892753136958e-3,
(vtype)0.28728638600548514553e-1),
(vtype)-0.28180210961780814148e0),
(vtype)0.88468142536501647470e0),
(vtype)-0.11028356797846341457e1),
(vtype)0.47482573589747356373e0);
vtype pd = pocl_fma(t,
pocl_fma(t,
pocl_fma(t,
pocl_fma(t,
pocl_fma(t,
(vtype)-0.35861554370169537512e-1,
(vtype)0.49561196555503101989e0),
(vtype)-0.22608883748988489342e1),
(vtype)0.45414700626084508355e1),
(vtype)-0.41631933639693546274e1),
(vtype)0.14244772076924206909e1);
r = pocl_fma(x*t, pn/pd, x);
ret = (absx < (vtype)0.5) ? r : ret;
return ret;
}
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