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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
#if defined(COMPILING_LOG2)
log2(vtype x)
#elif defined(COMPILING_LOGB)
logb(vtype x)
#elif defined(COMPILING_LOG10)
log10(vtype x)
#else
log(vtype x)
#endif
{
#ifdef COMPILING_LOGB
#define COMPILING_LOG2
#endif
#if defined(COMPILING_LOG10)
// log10e_lead and log10e_tail sum to an extra-precision version of log10(e) (19 bits in lead)
const vtype log10e_lead = (vtype)4.34293746948242187500e-01; /* 0x3fdbcb7800000000 */
const vtype log10e_tail = (vtype)7.3495500964015109100644e-7; /* 0x3ea8a93728719535 */
#elif defined(COMPILING_LOG2)
// log2e_lead and log2e_tail sum to an extra-precision version of log2(e) (19 bits in lead)
const vtype log2e_lead = (vtype)1.44269180297851562500E+00; /* 0x3FF7154400000000 */
const vtype log2e_tail = (vtype)3.23791044778235969970E-06; /* 0x3ECB295C17F0BBBE */
#endif
// log_thresh1 = 9.39412117004394531250e-1 = 0x3fee0faa00000000
// log_thresh2 = 1.06449508666992187500 = 0x3ff1082c00000000
const vtype log_thresh1 = (vtype)0x1.e0faap-1;
const vtype log_thresh2 = (vtype)0x1.1082cp+0;
itype is_near = (x >= log_thresh1) & (x <= log_thresh2);
// Near 1 code
vtype r = x - (vtype)1.0;
vtype u = r / ((vtype)2.0 + r);
vtype correction = r * u;
u = u + u;
vtype v = u * u;
vtype r1 = r;
const vtype ca_1 = (vtype)8.33333333333317923934e-02; /* 0x3fb55555555554e6 */
const vtype ca_2 = (vtype)1.25000000037717509602e-02; /* 0x3f89999999bac6d4 */
const vtype ca_3 = (vtype)2.23213998791944806202e-03; /* 0x3f62492307f1519f */
const vtype ca_4 = (vtype)4.34887777707614552256e-04; /* 0x3f3c8034c85dfff0 */
vtype r2 = pocl_fma(u*v,
pocl_fma(v,
pocl_fma(v,
pocl_fma(v, ca_4, ca_3),
ca_2),
ca_1),
-correction);
#if defined(COMPILING_LOG10)
r = r1;
r1 = as_vtype(as_utype(r1) & (utype)0xffffffff00000000);
r2 = r2 + (r - r1);
vtype ret_near = pocl_fma(log10e_lead, r1,
pocl_fma(log10e_lead, r2,
pocl_fma(log10e_tail, r1, log10e_tail * r2)));
#elif defined(COMPILING_LOG2)
r = r1;
r1 = as_vtype(as_utype(r1) & (utype)0xffffffff00000000);
r2 = r2 + (r - r1);
vtype ret_near = pocl_fma(log2e_lead, r1,
pocl_fma(log2e_lead, r2,
pocl_fma(log2e_tail, r1, log2e_tail * r2)));
#else
vtype ret_near = r1 + r2;
#endif
// This is the far from 1 code
// Deal with subnormal
utype ux = as_utype(x);
utype uxs = as_utype(
as_vtype((utype)0x03d0000000000000UL | ux)
- (vtype)0x1.0p-962);
itype c = (ux < IMPBIT_DP64);
ux = c ? uxs : ux;
itype expadjust = c ? (itype)60 : (itype)0;
itype xexp = ((as_itype(ux) >> 52) & 0x7ff) - (itype)EXPBIAS_DP64 - expadjust;
vtype f = as_vtype((utype)HALFEXPBITS_DP64 | (ux & (utype)MANTBITS_DP64));
uinttype index = convert_uinttype(ux >> 45);
index = (((uinttype)0x80 | (index & (uinttype)0x7e)) >> 1)
+ (index & (uinttype)0x1);
v2type tv = USE_VTABLE(ln_tbl, index - (uinttype)64);
vtype z1 = tv.lo;
vtype q = tv.hi;
vtype f1 = convert_vtype(index) * 0x1.0p-7;
vtype f2 = f - f1;
u = f2 / pocl_fma(f2, (vtype)0.5, f1);
v = u * u;
const vtype cb_1 = (vtype)8.33333333333333593622e-02; /* 0x3fb5555555555557 */
const vtype cb_2 = (vtype)1.24999999978138668903e-02; /* 0x3f89999999865ede */
const vtype cb_3 = (vtype)2.23219810758559851206e-03; /* 0x3f6249423bd94741 */
vtype poly = v * pocl_fma(v, pocl_fma(v, cb_3, cb_2), cb_1);
vtype z2 = q + pocl_fma(u, poly, u);
vtype dxexp = convert_vtype(xexp);
#if defined (COMPILING_LOG10)
// Add xexp * log(2) to z1,z2 to get log(x)
r1 = pocl_fma(dxexp, log2_lead, z1);
r2 = pocl_fma(dxexp, log2_tail, z2);
vtype ret_far = pocl_fma(log10e_lead, r1,
pocl_fma(log10e_lead, r2,
pocl_fma(log10e_tail, r1, log10e_tail*r2)));
#elif defined(COMPILING_LOG2)
r1 = pocl_fma(log2e_lead, z1, dxexp);
r2 = pocl_fma(log2e_lead, z2, pocl_fma(log2e_tail, z1, log2e_tail*z2));
vtype ret_far = r1 + r2;
#else
r1 = pocl_fma(dxexp, log2_lead, z1);
r2 = pocl_fma(dxexp, log2_tail, z2);
vtype ret_far = r1 + r2;
#endif
vtype ret = is_near ? ret_near : ret_far;
ret = isinf(x) ? as_vtype((utype)PINFBITPATT_DP64) : ret;
ret = (isnan(x) | (x < (vtype)0.0))
? as_vtype((utype)QNANBITPATT_DP64) : ret;
ret = (x == (vtype)0.0) ? as_vtype((utype)NINFBITPATT_DP64) : ret;
return ret;
}
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