always_inline VecType vec_log_float(VecType x)
{
typedef typename VecType::int_vec int_vec;
int_vec e;
x = frexp_float( x, e );
const VecType sqrt_05 = 0.707106781186547524f;
const VecType x_smaller_sqrt_05 = mask_lt(x, sqrt_05);
e = e + int_vec(x_smaller_sqrt_05);
VecType x_add = x;
x_add = x_add & x_smaller_sqrt_05;
x += x_add - VecType(VecType::gen_one());
VecType y =
(((((((( 7.0376836292E-2 * x
- 1.1514610310E-1) * x
+ 1.1676998740E-1) * x
- 1.2420140846E-1) * x
+ 1.4249322787E-1) * x
- 1.6668057665E-1) * x
+ 2.0000714765E-1) * x
- 2.4999993993E-1) * x
+ 3.3333331174E-1) * x * x*x;
VecType fe = e.convert_to_float();
y += fe * -2.12194440e-4;
y -= 0.5 * x*x; /* y - 0.5 x^2 */
VecType z = x + y; /* ... + x */
return z + 0.693359375 * fe;
}
always_inline VecType vec_ceil_float(VecType const & arg)
{
typedef VecType vec;
const vec rounded = vec_round_float(arg);
const vec rounded_smaller = mask_lt(rounded, arg);
const vec add = rounded_smaller & vec::gen_one();
return rounded + add;
}
always_inline VecType vec_undenormalize(VecType arg)
{
typedef typename VecType::float_type float_type;
const float_type min_positive_value = std::numeric_limits<float_type>::min();
const VecType abs_arg = abs(arg);
const VecType abs_arg_lt_min = mask_lt(abs_arg, min_positive_value);
const VecType zero = VecType::gen_zero();
const VecType result = select(arg, zero, abs_arg_lt_min);
return result;
}
always_inline VecType vec_tanh_float(VecType const & arg)
{
/* this order of computation (large->small->medium) seems to be the most efficient on sse*/
const VecType sign_arg = arg & VecType::gen_sign_mask();
const VecType abs_arg = arg ^ sign_arg;
const VecType one = VecType::gen_one();
const VecType two (2.f);
const VecType maxlogf_2 (22.f);
const VecType limit_small (0.625f);
/* large values */
const VecType abs_big = mask_gt(abs_arg, maxlogf_2);
const VecType result_limit_abs = one;
/* small values */
const VecType f1((float)-5.70498872745e-3);
const VecType f2((float) 2.06390887954e-2);
const VecType f3((float)-5.37397155531e-2);
const VecType f4((float) 1.33314422036e-1);
const VecType f5((float)-3.33332819422e-1);
const VecType arg_sqr = abs_arg * abs_arg;
const VecType result_small = ((((f1 * arg_sqr
+ f2) * arg_sqr
+ f3) * arg_sqr
+ f4) * arg_sqr
+ f5) * arg_sqr * arg
+ arg;
const VecType abs_small = mask_lt(abs_arg, limit_small);
/* medium values */
const VecType result_medium_abs = one - two / (vec_exp_tanh_float(abs_arg + abs_arg) + one);
/* select from large and medium branches and set sign */
const VecType result_lm_abs = select(result_medium_abs, result_limit_abs, abs_big);
const VecType result_lm = result_lm_abs | sign_arg;
const VecType result = select(result_lm, result_small, abs_small);
return result;
}
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;
}