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_sin_float(VecType const & arg)
{
typedef typename VecType::int_vec int_vec;
const typename VecType::float_type four_over_pi = 1.27323954473516268615107010698011489627567716592367;
VecType sign = arg & VecType::gen_sign_mask();
VecType abs_arg = arg & VecType::gen_abs_mask();
VecType y = abs_arg * four_over_pi;
int_vec j = y.truncate_to_int();
/* cephes: j=(j+1) & (~1) */
j = (j + int_vec(1)) & int_vec(~1);
y = j.convert_to_float();
/* sign based on quadrant */
VecType swap_sign_bit = slli(j & int_vec(4), 29);
sign = sign ^ swap_sign_bit;
/* polynomial mask */
VecType poly_mask = VecType (mask_eq(j & int_vec(2), int_vec(0)));
/* black magic */
static float DP1 = 0.78515625;
static float DP2 = 2.4187564849853515625e-4;
static float DP3 = 3.77489497744594108e-8;
VecType base = ((abs_arg - y * DP1) - y * DP2) - y * DP3;
/* [0..pi/4] */
VecType z = base * base;
VecType p1 = (( 2.443315711809948E-005 * z
- 1.388731625493765E-003) * z
+ 4.166664568298827E-002) * z * z
-0.5f * z + 1.0
;
/* [pi/4..pi/2] */
VecType p2 = ((-1.9515295891E-4 * z
+ 8.3321608736E-3) * z
- 1.6666654611E-1) * z * base + base;
VecType approximation = select(p1, p2, poly_mask);
return approximation ^ sign;
}
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;
}
always_inline VecType vec_tan_float(VecType const & arg)
{
typedef typename VecType::int_vec int_vec;
const typename VecType::float_type four_over_pi = 1.27323954473516268615107010698011489627567716592367;
VecType sign = arg & VecType::gen_sign_mask();
VecType abs_arg = arg & VecType::gen_abs_mask();
VecType y = abs_arg * four_over_pi;
int_vec j = y.truncate_to_int();
/* cephes: j=(j+1) & (~1) */
j = (j + int_vec(1)) & int_vec(~1);
y = j.convert_to_float();
/* approximation mask */
VecType poly_mask = VecType (mask_eq(j & int_vec(2), int_vec(0)));
/* black magic */
static float DP1 = 0.78515625;
static float DP2 = 2.4187564849853515625e-4;
static float DP3 = 3.77489497744594108e-8;
VecType base = ((abs_arg - y * DP1) - y * DP2) - y * DP3;
VecType x = base; VecType x2 = x*x;
// sollya: fpminimax(tan(x), [|3,5,7,9,11,13|], [|24...|], [-pi/4,pi/4], x);
VecType approx =
x + x * x2 * (0.3333315551280975341796875 + x2 * (0.1333882510662078857421875 + x2 * (5.3409568965435028076171875e-2 + x2 * (2.443529665470123291015625e-2 + x2 * (3.1127030961215496063232421875e-3 + x2 * 9.3892104923725128173828125e-3)))));
//VecType recip = -reciprocal(approx);
VecType recip = -1.0 / approx;
VecType approximation = select(recip, approx, poly_mask);
return approximation ^ sign;
}
