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/*
* Double-precision vector erf(x) function.
*
* Copyright (c) 2019-2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "include/mathlib.h"
#include "math_config.h"
#include "pl_sig.h"
#if V_SUPPORTED
#define AbsMask v_u64 (0x7fffffffffffffff)
#define AbsXMax v_f64 (0x1.8p+2)
#define Scale v_f64 (0x1p+3)
/* Special cases (fall back to scalar calls). */
VPCS_ATTR
NOINLINE static v_f64_t
specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
{
return v_call_f64 (erf, x, y, cmp);
}
/* A structure to perform look-up in coeffs and other parameter tables. */
struct entry
{
v_f64_t P[V_ERF_NCOEFFS];
v_f64_t shift;
};
static inline struct entry
lookup (v_u64_t i)
{
struct entry e;
#ifdef SCALAR
for (int j = 0; j < V_ERF_NCOEFFS; ++j)
e.P[j] = __v_erf_data.coeffs[j][i];
e.shift = __v_erf_data.shifts[i];
#else
for (int j = 0; j < V_ERF_NCOEFFS; ++j)
{
e.P[j][0] = __v_erf_data.coeffs[j][i[0]];
e.P[j][1] = __v_erf_data.coeffs[j][i[1]];
}
e.shift[0] = __v_erf_data.shifts[i[0]];
e.shift[1] = __v_erf_data.shifts[i[1]];
#endif
return e;
}
/* Optimized double precision vector error function erf. Maximum
observed error is 1.75 ULP, in [0.110, 0.111]:
verf(0x1.c5e0c2d5d0543p-4) got 0x1.fe0ed62a54987p-4
want 0x1.fe0ed62a54985p-4. */
VPCS_ATTR
v_f64_t V_NAME (erf) (v_f64_t x)
{
/* Handle both inf/nan as well as small values (|x|<2^-28)
If any condition in the lane is true then a loop over
scalar calls will be performed. */
v_u64_t ix = v_as_u64_f64 (x);
v_u64_t atop = (ix >> 48) & v_u64 (0x7fff);
v_u64_t special_case
= v_cond_u64 (atop - v_u64 (0x3e30) >= v_u64 (0x7ff0 - 0x3e30));
/* Get sign and absolute value. */
v_u64_t sign = v_as_u64_f64 (x) & ~AbsMask;
v_f64_t a = v_min_f64 (v_abs_f64 (x), AbsXMax);
/* Compute index by truncating 8 * a with a=|x| saturated to 6.0. */
#ifdef SCALAR
v_u64_t i = v_trunc_u64 (a * Scale);
#else
v_u64_t i = vcvtq_n_u64_f64 (a, 3);
#endif
/* Get polynomial coefficients and shift parameter using lookup. */
struct entry dat = lookup (i);
/* Evaluate polynomial on transformed argument. */
v_f64_t z = v_fma_f64 (a, Scale, dat.shift);
v_f64_t r1 = v_fma_f64 (z, dat.P[1], dat.P[0]);
v_f64_t r2 = v_fma_f64 (z, dat.P[3], dat.P[2]);
v_f64_t r3 = v_fma_f64 (z, dat.P[5], dat.P[4]);
v_f64_t r4 = v_fma_f64 (z, dat.P[7], dat.P[6]);
v_f64_t r5 = v_fma_f64 (z, dat.P[9], dat.P[8]);
v_f64_t z2 = z * z;
v_f64_t y = v_fma_f64 (z2, r5, r4);
y = v_fma_f64 (z2, y, r3);
y = v_fma_f64 (z2, y, r2);
y = v_fma_f64 (z2, y, r1);
/* y=erf(x) if x>0, -erf(-x) otherwise. */
y = v_as_f64_u64 (v_as_u64_f64 (y) ^ sign);
if (unlikely (v_any_u64 (special_case)))
return specialcase (x, y, special_case);
return y;
}
VPCS_ALIAS
PL_SIG (V, D, 1, erf, -6.0, 6.0)
#endif
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