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/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* 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 log1p(vtype x)
{
vtype w = x;
utype ux = as_utype(x);
utype ax = ux & (utype)EXSIGNBIT_SP32;
// |x| < 2^-4
vtype u2 = MATH_DIVIDE(x, (vtype)2.0f + x);
vtype u = u2 + u2;
vtype v = u * u;
// 2/(5 * 2^5), 2/(3 * 2^3)
vtype zsmall = pocl_fma(-u2, x, pocl_fma(v, (vtype)0x1.99999ap-7f, (vtype)0x1.555556p-4f) * v * u) + x;
// |x| >= 2^-4
ux = as_utype(x + 1.0f);
itype m = as_itype((ux >> EXPSHIFTBITS_SP32) & (utype)0xff) - (itype)EXPBIAS_SP32;
vtype mf = convert_vtype(m);
utype indx = (ux & (utype)0x007f0000) + ((ux & (utype)0x00008000) << 1);
vtype F = as_vtype(indx | (utype)0x3f000000);
// x > 2^24
vtype fg24 = F - as_vtype((utype)0x3f000000 | (ux & (utype)MANTBITS_SP32));
// x <= 2^24
utype xhi = ux & (utype)0xffff8000;
vtype xh = as_vtype(xhi);
vtype xt = ((vtype)1.0f - xh) + w;
utype xnm = ((~(xhi & (utype)0x7f800000)) - (utype)0x00800000) & (utype)0x7f800000;
xt = xt * as_vtype(xnm) * 0.5f;
vtype fl24 = F - as_vtype((utype)0x3f000000 | (xhi & (utype)MANTBITS_SP32)) - xt;
vtype f = (mf > (vtype)24.0f) ? fg24 : fl24;
indx = indx >> 16;
vtype r = f * USE_VTABLE(log_inv_tbl, indx);
// 1/3, 1/2
vtype poly = pocl_fma(pocl_fma(r, (vtype)0x1.555556p-2f, (vtype)0x1.0p-1f), r*r, r);
const vtype LOG2_HEAD = (vtype)0x1.62e000p-1f; // 0.693115234
const vtype LOG2_TAIL = (vtype)0x1.0bfbe8p-15f; // 0.0000319461833
v2type tv = USE_VTABLE(loge_tbl, indx);
vtype s0 = tv.lo;
vtype s1 = tv.hi;
vtype z1 = pocl_fma(mf, LOG2_HEAD, s0);
vtype z2 = pocl_fma(mf, LOG2_TAIL, -poly) + s1;
vtype z = z1 + z2;
z = (ax < (utype)0x3d800000U) ? zsmall : z;
// Edge cases
z = (ax >= (utype)PINFBITPATT_SP32) ? w : z;
z = (w < (vtype)-1.0f) ? as_vtype((utype)QNANBITPATT_SP32) : z;
z = (w == (vtype)-1.0f) ? as_vtype((utype)NINFBITPATT_SP32) : z;
//fix subnormals
z = (ax < (utype)0x33800000) ? x : z;
return z;
}
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