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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 atanpi(vtype x) {
const vtype pi = (vtype)M_PI;
vtype v = fabs(x);
// 2^56 > v > 39/16
vtype a = (vtype)-1.0;
vtype b = v;
// (chi + clo) = arctan(infinity)
vtype chi = (vtype)1.57079632679489655800e+00;
vtype clo = (vtype)6.12323399573676480327e-17;
vtype ta = v - (vtype)1.5;
vtype tb = (vtype)1.0 + (vtype)1.5 * v;
itype l = (v <= (vtype)0x1.38p+1); // 39/16 > v > 19/16
a = l ? ta : a;
b = l ? tb : b;
// (chi + clo) = arctan(1.5)
chi = l ? (vtype)9.82793723247329054082e-01 : chi;
clo = l ? (vtype)1.39033110312309953701e-17 : clo;
ta = v - (vtype)1.0;
tb = (vtype)1.0 + v;
l = (v <= (vtype)0x1.3p+0); // 19/16 > v > 11/16
a = l ? ta : a;
b = l ? tb : b;
// (chi + clo) = arctan(1.)
chi = l ? (vtype)7.85398163397448278999e-01 : chi;
clo = l ? (vtype)3.06161699786838240164e-17 : clo;
ta = (vtype)2.0 * v - (vtype)1.0;
tb = (vtype)2.0 + v;
l = (v <= (vtype)0x1.6p-1); // 11/16 > v > 7/16
a = l ? ta : a;
b = l ? tb : b;
// (chi + clo) = arctan(0.5)
chi = l ? (vtype)4.63647609000806093515e-01 : chi;
clo = l ? (vtype)2.26987774529616809294e-17 : clo;
l = (v <= (vtype)0x1.cp-2); // v < 7/16
a = l ? v : a;
b = l ? (vtype)1.0 : b;;
chi = l ? (vtype)0.0 : chi;
clo = l ? (vtype)0.0 : clo;
// Core approximation: Remez(4,4) on [-7/16,7/16]
vtype r = a / b;
vtype s = r * r;
vtype qn = pocl_fma(s,
pocl_fma(s,
pocl_fma(s,
pocl_fma(s,
(vtype)0.142316903342317766e-3,
(vtype)0.304455919504853031e-1),
(vtype)0.220638780716667420e0),
(vtype)0.447677206805497472e0),
(vtype)0.268297920532545909e0);
vtype qd = pocl_fma(s,
pocl_fma(s,
pocl_fma(s,
pocl_fma(s,
(vtype)0.389525873944742195e-1,
(vtype)0.424602594203847109e0),
(vtype)0.141254259931958921e1),
(vtype)0.182596787737507063e1),
(vtype)0.804893761597637733e0);
vtype q = r * s * qn / qd;
r = (chi - ((q - clo) - r)) / pi;
vtype vp = v / pi;
vtype z = isnan(x) ? x : (vtype)0.5;
z = (v <= (vtype)0x1.0p+56) ? r : z;
z = (v < (vtype)0x1.0p-26) ? vp : z;
return x == v ? z : -z;
}
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