mirror of
https://github.com/freebsd/freebsd-src
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072a4ba82a
Sponsored by: Arm Ltd
117 lines
3.2 KiB
C
117 lines
3.2 KiB
C
/*
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* Double-precision vector erf(x) function.
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*
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* Copyright (c) 2019-2023, Arm Limited.
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* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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*/
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#include "v_math.h"
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#include "include/mathlib.h"
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#include "math_config.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#if V_SUPPORTED
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#define AbsMask v_u64 (0x7fffffffffffffff)
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#define AbsXMax v_f64 (0x1.8p+2)
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#define Scale v_f64 (0x1p+3)
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/* Special cases (fall back to scalar calls). */
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VPCS_ATTR
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NOINLINE static v_f64_t
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specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
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{
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return v_call_f64 (erf, x, y, cmp);
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}
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/* A structure to perform look-up in coeffs and other parameter tables. */
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struct entry
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{
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v_f64_t P[V_ERF_NCOEFFS];
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v_f64_t shift;
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};
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static inline struct entry
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lookup (v_u64_t i)
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{
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struct entry e;
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#ifdef SCALAR
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for (int j = 0; j < V_ERF_NCOEFFS; ++j)
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e.P[j] = __v_erf_data.coeffs[j][i];
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e.shift = __v_erf_data.shifts[i];
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#else
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for (int j = 0; j < V_ERF_NCOEFFS; ++j)
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{
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e.P[j][0] = __v_erf_data.coeffs[j][i[0]];
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e.P[j][1] = __v_erf_data.coeffs[j][i[1]];
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}
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e.shift[0] = __v_erf_data.shifts[i[0]];
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e.shift[1] = __v_erf_data.shifts[i[1]];
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#endif
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return e;
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}
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/* Optimized double precision vector error function erf. Maximum
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observed error is 1.75 ULP, in [0.110, 0.111]:
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verf(0x1.c5e0c2d5d0543p-4) got 0x1.fe0ed62a54987p-4
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want 0x1.fe0ed62a54985p-4. */
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VPCS_ATTR
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v_f64_t V_NAME (erf) (v_f64_t x)
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{
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/* Handle both inf/nan as well as small values (|x|<2^-28)
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If any condition in the lane is true then a loop over
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scalar calls will be performed. */
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v_u64_t ix = v_as_u64_f64 (x);
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v_u64_t atop = (ix >> 48) & v_u64 (0x7fff);
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v_u64_t special_case
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= v_cond_u64 (atop - v_u64 (0x3e30) >= v_u64 (0x7ff0 - 0x3e30));
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/* Get sign and absolute value. */
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v_u64_t sign = v_as_u64_f64 (x) & ~AbsMask;
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v_f64_t a = v_min_f64 (v_abs_f64 (x), AbsXMax);
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/* Compute index by truncating 8 * a with a=|x| saturated to 6.0. */
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#ifdef SCALAR
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v_u64_t i = v_trunc_u64 (a * Scale);
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#else
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v_u64_t i = vcvtq_n_u64_f64 (a, 3);
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#endif
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/* Get polynomial coefficients and shift parameter using lookup. */
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struct entry dat = lookup (i);
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/* Evaluate polynomial on transformed argument. */
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v_f64_t z = v_fma_f64 (a, Scale, dat.shift);
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v_f64_t r1 = v_fma_f64 (z, dat.P[1], dat.P[0]);
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v_f64_t r2 = v_fma_f64 (z, dat.P[3], dat.P[2]);
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v_f64_t r3 = v_fma_f64 (z, dat.P[5], dat.P[4]);
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v_f64_t r4 = v_fma_f64 (z, dat.P[7], dat.P[6]);
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v_f64_t r5 = v_fma_f64 (z, dat.P[9], dat.P[8]);
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v_f64_t z2 = z * z;
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v_f64_t y = v_fma_f64 (z2, r5, r4);
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y = v_fma_f64 (z2, y, r3);
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y = v_fma_f64 (z2, y, r2);
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y = v_fma_f64 (z2, y, r1);
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/* y=erf(x) if x>0, -erf(-x) otherwise. */
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y = v_as_f64_u64 (v_as_u64_f64 (y) ^ sign);
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if (unlikely (v_any_u64 (special_case)))
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return specialcase (x, y, special_case);
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return y;
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}
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VPCS_ALIAS
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PL_SIG (V, D, 1, erf, -6.0, 6.0)
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PL_TEST_ULP (V_NAME (erf), 1.26)
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PL_TEST_INTERVAL (V_NAME (erf), 0, 0xffff0000, 10000)
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PL_TEST_INTERVAL (V_NAME (erf), 0x1p-127, 0x1p-26, 40000)
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PL_TEST_INTERVAL (V_NAME (erf), -0x1p-127, -0x1p-26, 40000)
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PL_TEST_INTERVAL (V_NAME (erf), 0x1p-26, 0x1p3, 40000)
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PL_TEST_INTERVAL (V_NAME (erf), -0x1p-26, -0x1p3, 40000)
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PL_TEST_INTERVAL (V_NAME (erf), 0, inf, 40000)
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#endif
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