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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 = (vtype)0x1.65a9fap+6f;
const vtype small_threshold = (vtype)0x1.0a2b24p+3f;
utype ux = as_utype(x);
utype aux = ux & (utype)EXSIGNBIT_SP32;
utype xs = ux ^ aux;
vtype y = as_vtype(aux);
// 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 tabulated above.
vtype indv = trunc(y);
utype indi = convert_utype(indv);
indi = (indi > (utype)36) ? (utype)0 : indi;
vtype dy = y - indv;
vtype dy2 = dy * dy;
vtype sdy = pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
(vtype)0.7746188980094184251527126e-12f,
(vtype)0.160576793121939886190847e-9f),
(vtype)0.250521176994133472333666e-7f),
(vtype)0.275573191913636406057211e-5f),
(vtype)0.198412698413242405162014e-3f),
(vtype)0.833333333333329931873097e-2f),
(vtype)0.166666666666666667013899e0f);
sdy = pocl_fma(sdy, dy*dy2, dy);
vtype cdy = pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
pocl_fma(dy2,
(vtype)0.1163921388172173692062032e-10f,
(vtype)0.208744349831471353536305e-8f),
(vtype)0.275573350756016588011357e-6f),
(vtype)0.248015872460622433115785e-4f),
(vtype)0.138888888889814854814536e-2f),
(vtype)0.416666666666660876512776e-1f),
(vtype)0.500000000000000005911074e0f);
cdy = pocl_fma(cdy, dy2, (vtype)1.0f);
v2type tv = USE_VTABLE(sinhcosh_tbl, indi);
vtype z = pocl_fma(tv.hi, sdy, tv.lo * cdy);
z = as_vtype(xs | as_utype(z));
// When y is large enough so that the negative exponential is negligible,
// so sinh(y) is approximated by sign(x)*exp(y)/2.
vtype t = exp(y - (vtype)0x1.62e500p-1f);
vtype zsmall = pocl_fma((vtype)0x1.a0210ep-18f, t, t);
zsmall = as_vtype(xs | as_utype(zsmall));
z = (y >= small_threshold) ? zsmall : z;
// Corner cases
vtype zinf = as_vtype((utype)PINFBITPATT_SP32 | xs);
z = (y >= max_sinh_arg) ? zinf : z;
z = as_vtype(
as_utype(aux > (utype)PINFBITPATT_SP32)
| as_utype((aux < (utype)0x38800000U) ? x : z) );
return z;
}
|
