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/*
* Single-precision vector erf(x) function.
*
* Copyright (c) 2020-2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "include/mathlib.h"
#include "math_config.h"
#include "v_math.h"
#if V_SUPPORTED
VPCS_ATTR v_f32_t V_NAME (expf) (v_f32_t);
#define AbsMask v_u32 (0x7fffffff)
/* Special cases (fall back to scalar calls). */
VPCS_ATTR
NOINLINE static v_f32_t
specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
{
return v_call_f32 (erff, x, y, cmp);
}
/* A structure to perform look-up in coeffs and other parameter tables. */
struct entry
{
v_f32_t P[V_ERFF_NCOEFFS];
};
static inline struct entry
lookup (v_u32_t i)
{
struct entry e;
#ifdef SCALAR
for (int j = 0; j < V_ERFF_NCOEFFS; ++j)
e.P[j] = __v_erff_data.coeffs[j][i];
#else
for (int j = 0; j < V_ERFF_NCOEFFS; ++j)
{
e.P[j][0] = __v_erff_data.coeffs[j][i[0]];
e.P[j][1] = __v_erff_data.coeffs[j][i[1]];
e.P[j][2] = __v_erff_data.coeffs[j][i[2]];
e.P[j][3] = __v_erff_data.coeffs[j][i[3]];
}
#endif
return e;
}
/* Optimized single precision vector error function erf.
Maximum measured at +/- 0.931, 1.25ULP:
v_erff(-0x1.dc59fap-1) got -0x1.9f9c88p-1
want -0x1.9f9c8ap-1. */
VPCS_ATTR
v_f32_t V_NAME (erff) (v_f32_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_u32_t ix = v_as_u32_f32 (x);
v_u32_t atop = (ix >> 16) & v_u32 (0x7fff);
v_u32_t cmp = v_cond_u32 (atop - v_u32 (0x3180) >= v_u32 (0x7ff0 - 0x3180));
/* Get sign and absolute value. */
v_u32_t sign = ix & ~AbsMask;
/* |x| < 0.921875. */
v_u32_t red = v_calt_f32 (x, v_f32 (0.921875f));
/* |x| > 4.0. */
v_u32_t bor = v_cagt_f32 (x, v_f32 (4.0f));
/* Avoid dependency in abs(x) in division (and comparison). */
v_u32_t i = v_sel_u32 (red, v_u32 (0), v_u32 (1));
/* Get polynomial coefficients. */
struct entry dat = lookup (i);
v_f32_t a = v_abs_f32 (x);
v_f32_t z = v_sel_f32 (red, x * x, a);
/* Evaluate Polynomial of |x| or x^2. */
v_f32_t r = dat.P[6];
r = v_fma_f32 (z, r, dat.P[5]);
r = v_fma_f32 (z, r, dat.P[4]);
r = v_fma_f32 (z, r, dat.P[3]);
r = v_fma_f32 (z, r, dat.P[2]);
r = v_fma_f32 (z, r, dat.P[1]);
r = v_sel_f32 (red, r, v_fma_f32 (z, r, dat.P[0]));
r = v_fma_f32 (a, r, a);
/* y = |x| + |x|*P(|x|) if |x| < 0.921875
1 - exp (-(|x|+|x|*P(x^2))) otherwise. */
v_f32_t y = v_sel_f32 (red, r, v_f32 (1.0f) - V_NAME (expf) (-r));
/* Boring domain (absolute value is required to get the sign of erf(-nan)
right). */
y = v_sel_f32 (bor, v_f32 (1.0f), v_abs_f32 (y));
/* y=erf(x) if x>0, -erf(-x) otherwise. */
y = v_as_f32_u32 (v_as_u32_f32 (y) ^ sign);
if (unlikely (v_any_u32 (cmp)))
return specialcase (x, y, cmp);
return y;
}
VPCS_ALIAS
#endif
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