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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 float log1p(float x)
{
float w = x;
uint ux = as_uint(x);
uint ax = ux & EXSIGNBIT_SP32;
// |x| < 2^-4
float u2 = MATH_DIVIDE(x, 2.0f + x);
float u = u2 + u2;
float v = u * u;
// 2/(5 * 2^5), 2/(3 * 2^3)
float zsmall = pocl_fma(-u2, x, pocl_fma(v, 0x1.99999ap-7f, 0x1.555556p-4f) * v * u) + x;
// |x| >= 2^-4
ux = as_uint(x + 1.0f);
int m = (int)((ux >> EXPSHIFTBITS_SP32) & 0xff) - EXPBIAS_SP32;
float mf = (float)m;
uint indx = (ux & 0x007f0000) + ((ux & 0x00008000) << 1);
float F = as_float(indx | 0x3f000000);
// x > 2^24
float fg24 = F - as_float(0x3f000000 | (ux & MANTBITS_SP32));
// x <= 2^24
uint xhi = ux & 0xffff8000;
float xh = as_float(xhi);
float xt = (1.0f - xh) + w;
uint xnm = ((~(xhi & 0x7f800000)) - 0x00800000) & 0x7f800000;
xt = xt * as_float(xnm) * 0.5f;
float fl24 = F - as_float(0x3f000000 | (xhi & MANTBITS_SP32)) - xt;
float f = mf > 24.0f ? fg24 : fl24;
indx = indx >> 16;
float r = f * USE_TABLE(log_inv_tbl, indx);
// 1/3, 1/2
float poly = pocl_fma(pocl_fma(r, 0x1.555556p-2f, 0x1.0p-1f), r*r, r);
const float LOG2_HEAD = 0x1.62e000p-1f; // 0.693115234
const float LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833
float2 tv = USE_TABLE(loge_tbl, indx);
float z1 = pocl_fma(mf, LOG2_HEAD, tv.s0);
float z2 = pocl_fma(mf, LOG2_TAIL, -poly) + tv.s1;
float z = z1 + z2;
z = ax < 0x3d800000U ? zsmall : z;
// Edge cases
z = ax >= PINFBITPATT_SP32 ? w : z;
z = w < -1.0f ? as_float(QNANBITPATT_SP32) : z;
z = w == -1.0f ? as_float(NINFBITPATT_SP32) : z;
//fix subnormals
z = ax < 0x33800000 ? x : z;
return z;
}
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