117 lines
3.3 KiB
C
117 lines
3.3 KiB
C
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/*
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* Single-precision vector erf(x) function.
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*
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* Copyright (c) 2020-2023, 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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VPCS_ATTR v_f32_t V_NAME (expf) (v_f32_t);
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#define AbsMask v_u32 (0x7fffffff)
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/* Special cases (fall back to scalar calls). */
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VPCS_ATTR
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NOINLINE static v_f32_t
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specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
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{
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return v_call_f32 (erff, 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_f32_t P[V_ERFF_NCOEFFS];
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};
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static inline struct entry
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lookup (v_u32_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_ERFF_NCOEFFS; ++j)
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e.P[j] = __v_erff_data.coeffs[j][i];
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#else
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for (int j = 0; j < V_ERFF_NCOEFFS; ++j)
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{
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e.P[j][0] = __v_erff_data.coeffs[j][i[0]];
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e.P[j][1] = __v_erff_data.coeffs[j][i[1]];
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e.P[j][2] = __v_erff_data.coeffs[j][i[2]];
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e.P[j][3] = __v_erff_data.coeffs[j][i[3]];
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}
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#endif
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return e;
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}
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/* Optimized single precision vector error function erf.
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Maximum measured at +/- 0.931, 1.25ULP:
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v_erff(-0x1.dc59fap-1) got -0x1.9f9c88p-1
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want -0x1.9f9c8ap-1. */
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VPCS_ATTR
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v_f32_t V_NAME (erff) (v_f32_t x)
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{
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/* Handle both inf/nan as well as small values (|x|<2^-28). If any condition
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in the lane is true then a loop over scalar calls will be performed. */
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v_u32_t ix = v_as_u32_f32 (x);
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v_u32_t atop = (ix >> 16) & v_u32 (0x7fff);
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v_u32_t cmp = v_cond_u32 (atop - v_u32 (0x3180) >= v_u32 (0x7ff0 - 0x3180));
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/* Get sign and absolute value. */
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v_u32_t sign = ix & ~AbsMask;
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/* |x| < 0.921875. */
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v_u32_t red = v_calt_f32 (x, v_f32 (0.921875f));
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/* |x| > 4.0. */
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v_u32_t bor = v_cagt_f32 (x, v_f32 (4.0f));
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/* Avoid dependency in abs(x) in division (and comparison). */
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v_u32_t i = v_sel_u32 (red, v_u32 (0), v_u32 (1));
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/* Get polynomial coefficients. */
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struct entry dat = lookup (i);
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v_f32_t a = v_abs_f32 (x);
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v_f32_t z = v_sel_f32 (red, x * x, a);
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/* Evaluate Polynomial of |x| or x^2. */
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v_f32_t r = dat.P[6];
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r = v_fma_f32 (z, r, dat.P[5]);
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r = v_fma_f32 (z, r, dat.P[4]);
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r = v_fma_f32 (z, r, dat.P[3]);
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r = v_fma_f32 (z, r, dat.P[2]);
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r = v_fma_f32 (z, r, dat.P[1]);
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r = v_sel_f32 (red, r, v_fma_f32 (z, r, dat.P[0]));
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r = v_fma_f32 (a, r, a);
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/* y = |x| + |x|*P(|x|) if |x| < 0.921875
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1 - exp (-(|x|+|x|*P(x^2))) otherwise. */
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v_f32_t y = v_sel_f32 (red, r, v_f32 (1.0f) - V_NAME (expf) (-r));
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/* Boring domain (absolute value is required to get the sign of erf(-nan)
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right). */
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y = v_sel_f32 (bor, v_f32 (1.0f), v_abs_f32 (y));
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/* y=erf(x) if x>0, -erf(-x) otherwise. */
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y = v_as_f32_u32 (v_as_u32_f32 (y) ^ sign);
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if (unlikely (v_any_u32 (cmp)))
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return specialcase (x, y, cmp);
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return y;
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}
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VPCS_ALIAS
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PL_SIG (V, F, 1, erf, -4.0, 4.0)
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PL_TEST_ULP (V_NAME (erff), 0.76)
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PL_TEST_INTERVAL (V_NAME (erff), 0, 0xffff0000, 10000)
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PL_TEST_INTERVAL (V_NAME (erff), 0x1p-127, 0x1p-26, 40000)
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PL_TEST_INTERVAL (V_NAME (erff), -0x1p-127, -0x1p-26, 40000)
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PL_TEST_INTERVAL (V_NAME (erff), 0x1p-26, 0x1p3, 40000)
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PL_TEST_INTERVAL (V_NAME (erff), -0x1p-26, -0x1p3, 40000)
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PL_TEST_INTERVAL (V_NAME (erff), 0, inf, 40000)
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#endif
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