always_inline VecType vec_exp_tanh_float(VecType const & arg)
{
typedef typename VecType::int_vec int_vec;
/* Express e**x = e**g 2**n
* = e**g e**( n loge(2) )
* = e**( g + n loge(2) )
*/
// black magic
VecType x = arg;
VecType z = round(VecType(1.44269504088896341f) * x);
int_vec n = z.truncate_to_int();
x -= z*VecType(0.693359375f);
x -= z*VecType(-2.12194440e-4f);
/* Theoretical peak relative error in [-0.5, +0.5] is 3.5e-8. */
VecType p = 1.f +
x * (1.00000035762786865234375f +
x * (0.4999996721744537353515625f +
x * (0.16665561497211456298828125f +
x * (4.167006909847259521484375e-2f +
x * (8.420792408287525177001953125e-3f +
x * 1.386119984090328216552734375e-3f)))));
/* multiply by power of 2 */
VecType approx = ldexp_float(p, n);
return approx;
}
always_inline VecType vec_exp_float(VecType const & arg)
{
typedef typename VecType::int_vec int_vec;
/* Express e**x = e**g 2**n
* = e**g e**( n loge(2) )
* = e**( g + n loge(2) )
*/
// black magic
VecType x = arg;
VecType z = round(VecType(1.44269504088896341f) * x);
int_vec n = z.truncate_to_int();
x -= z*VecType(0.693359375f);
x -= z*VecType(-2.12194440e-4f);
/* Theoretical peak relative error in [-0.5, +0.5] is 3.5e-8. */
VecType p = VecType(VecType::gen_one()) +
x * (1.00000035762786865234375f +
x * (0.4999996721744537353515625f +
x * (0.16665561497211456298828125f +
x * (4.167006909847259521484375e-2f +
x * (8.420792408287525177001953125e-3f +
x * 1.386119984090328216552734375e-3f)))));
/* multiply by power of 2 */
VecType approx = ldexp_float(p, n);
/* handle min/max boundaries */
const VecType maxlogf(88.72283905206835f);
// const VecType minlogf(-103.278929903431851103f);
const VecType minlogf = -maxlogf;
const VecType max_float(std::numeric_limits<float>::max());
const VecType zero = VecType::gen_zero();
VecType too_large = mask_gt(arg, maxlogf);
VecType too_small = mask_lt(arg, minlogf);
VecType ret = select(approx, max_float, too_large);
ret = select(ret, zero, too_small);
return ret;
}
