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/*
* Double-precision SVE erf(x) function.
*
* Copyright (c) 2020-2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#if SV_SUPPORTED
#define Scale (8.0)
#define AbsMask (0x7fffffffffffffff)
static NOINLINE sv_f64_t
__sv_erf_specialcase (sv_f64_t x, sv_f64_t y, svbool_t cmp)
{
return sv_call_f64 (erf, x, y, cmp);
}
/* Optimized double precision SVE error function erf. Maximum
observed error is 2.46 ULP:
__sv_erf(0x1.5644782ddd668p+2) got 0x1.ffffffffffeap-1
want 0x1.ffffffffffe9ep-1. */
sv_f64_t
__sv_erf_x (sv_f64_t x, const svbool_t pg)
{
/* Use top 16 bits to test for special cases and small values. */
sv_u64_t ix = sv_as_u64_f64 (x);
sv_u64_t atop = svand_n_u64_x (pg, svlsr_n_u64_x (pg, ix, 48), 0x7fff);
/* Handle both inf/nan as well as small values (|x|<2^-28). */
svbool_t cmp
= svcmpge_n_u64 (pg, svsub_n_u64_x (pg, atop, 0x3e30), 0x7ff0 - 0x3e30);
/* Get sign and absolute value. */
sv_f64_t a = sv_as_f64_u64 (svand_n_u64_x (pg, ix, AbsMask));
sv_u64_t sign = svand_n_u64_x (pg, ix, ~AbsMask);
/* i = trunc(Scale*x). */
sv_f64_t a_scale = svmul_n_f64_x (pg, a, Scale);
/* Saturate index of intervals. */
svbool_t a_lt_6 = svcmplt_n_u64 (pg, atop, 0x4018);
sv_u64_t i = svcvt_u64_f64_m (sv_u64 (V_ERF_NINTS - 1), a_lt_6, a_scale);
/* Load polynomial coefficients. */
sv_f64_t P_0 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[0], i);
sv_f64_t P_1 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[1], i);
sv_f64_t P_2 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[2], i);
sv_f64_t P_3 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[3], i);
sv_f64_t P_4 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[4], i);
sv_f64_t P_5 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[5], i);
sv_f64_t P_6 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[6], i);
sv_f64_t P_7 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[7], i);
sv_f64_t P_8 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[8], i);
sv_f64_t P_9 = sv_lookup_f64_x (pg, __v_erf_data.coeffs[9], i);
/* Get shift and scale. */
sv_f64_t shift = sv_lookup_f64_x (pg, __v_erf_data.shifts, i);
/* Transform polynomial variable.
Set z = 0 in the boring domain to avoid overflow. */
sv_f64_t z = svmla_f64_m (a_lt_6, shift, sv_f64 (Scale), a);
/* Evaluate polynomial P(z) using level-2 Estrin. */
sv_f64_t r1 = sv_fma_f64_x (pg, z, P_1, P_0);
sv_f64_t r2 = sv_fma_f64_x (pg, z, P_3, P_2);
sv_f64_t r3 = sv_fma_f64_x (pg, z, P_5, P_4);
sv_f64_t r4 = sv_fma_f64_x (pg, z, P_7, P_6);
sv_f64_t r5 = sv_fma_f64_x (pg, z, P_9, P_8);
sv_f64_t z2 = svmul_f64_x (pg, z, z);
sv_f64_t z4 = svmul_f64_x (pg, z2, z2);
sv_f64_t q2 = sv_fma_f64_x (pg, r4, z2, r3);
sv_f64_t q1 = sv_fma_f64_x (pg, r2, z2, r1);
sv_f64_t y = sv_fma_f64_x (pg, z4, r5, q2);
y = sv_fma_f64_x (pg, z4, y, q1);
/* y = erf(x) if x > 0, -erf(-x) otherwise. */
y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign));
if (unlikely (svptest_any (pg, cmp)))
return __sv_erf_specialcase (x, y, cmp);
return y;
}
strong_alias (__sv_erf_x, _ZGVsMxv_erf)
#endif
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