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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 sinh(vtype x)
{
// After dealing with special cases the computation is split into
// regions as follows:
//
// abs(x) >= max_sinh_arg:
// sinh(x) = sign(x)*Inf
//
// abs(x) >= small_threshold:
// sinh(x) = sign(x)*exp(abs(x))/2 computed using the
// splitexp and scaleDouble functions as for exp_amd().
//
// abs(x) < small_threshold:
// compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
// sinh(x) is then sign(x)*z.
const vtype max_sinh_arg = 7.10475860073943977113e+02; // 0x408633ce8fb9f87e
// This is where exp(-x) is insignificant compared to exp(x) = ln(2^27)
const vtype small_threshold = 0x1.2b708872320e2p+4;
vtype y = fabs(x);
// In this range we find the integer part y0 of y
// and the increment dy = y - y0. We then compute
// z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
// where sinh(y0) and cosh(y0) are obtained from tables
vtype indv = trunc(y);
itype indi = convert_itype(indv);
indi = min((itype)indi, (itype)36U);
vtype dy = y - indv;
vtype dy2 = dy * dy;
vtype sdy = dy * dy2 *
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
(vtype)0.7746188980094184251527126e-12,
(vtype)0.160576793121939886190847e-9),
(vtype)0.250521176994133472333666e-7),
(vtype)0.275573191913636406057211e-5),
(vtype)0.198412698413242405162014e-3),
(vtype)0.833333333333329931873097e-2),
(vtype)0.166666666666666667013899e0);
vtype cdy = dy2 *
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
(vtype)0.1163921388172173692062032e-10,
(vtype)0.208744349831471353536305e-8),
(vtype)0.275573350756016588011357e-6),
(vtype)0.248015872460622433115785e-4),
(vtype)0.138888888889814854814536e-2),
(vtype)0.416666666666660876512776e-1),
(vtype)0.500000000000000005911074e0);
// At this point sinh(dy) is approximated by dy + sdy.
// Shift some significant bits from dy to sdy.
vtype sdy1 = as_vtype(as_utype(dy) & 0xfffffffff8000000UL);
vtype sdy2 = sdy + (dy - sdy1);
v2type tv = USE_VTABLE(cosh_tbl, convert_uinttype(indi));
vtype cl = tv.lo;
vtype ct = tv.hi;
tv = USE_VTABLE(sinh_tbl, convert_uinttype(indi));
vtype sl = tv.lo;
vtype st = tv.hi;
vtype z = pocl_fma(cl, sdy1,
pocl_fma(sl, cdy,
pocl_fma(cl, sdy2,
pocl_fma(ct, sdy1,
pocl_fma(st, cdy, ct*sdy2)) + st))) + sl;
// Other cases
z = (y < 0x1.0p-28) | isnan(x) | isinf(x) ? y : z;
vtype t = exp(y - 0x1.62e42fefa3800p-1);
t = pocl_fma(t, (vtype)-0x1.ef35793c76641p-45, t);
z = (y >= small_threshold) ? t : z;
z = (y >= max_sinh_arg) ? as_vtype((utype)PINFBITPATT_DP64) : z;
return copysign(z, x);
}
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