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105 lines
2.3 KiB
105 lines
2.3 KiB
4 months ago
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/*
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* Double-precision vector log(x) function.
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*
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* Copyright (c) 2019, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#include "mathlib.h"
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#include "v_math.h"
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#include "v_log.h"
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#if V_SUPPORTED
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/* Worst-case error: 1.17 + 0.5 ulp. */
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static const f64_t Poly[] = {
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/* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */
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-0x1.ffffffffffff7p-2,
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0x1.55555555170d4p-2,
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-0x1.0000000399c27p-2,
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0x1.999b2e90e94cap-3,
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-0x1.554e550bd501ep-3,
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};
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#define A0 v_f64 (Poly[0])
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#define A1 v_f64 (Poly[1])
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#define A2 v_f64 (Poly[2])
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#define A3 v_f64 (Poly[3])
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#define A4 v_f64 (Poly[4])
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#define Ln2 v_f64 (0x1.62e42fefa39efp-1)
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#define N (1 << V_LOG_TABLE_BITS)
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#define OFF v_u64 (0x3fe6900900000000)
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struct entry
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{
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v_f64_t invc;
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v_f64_t logc;
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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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e.invc = __v_log_data[i].invc;
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e.logc = __v_log_data[i].logc;
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#else
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e.invc[0] = __v_log_data[i[0]].invc;
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e.logc[0] = __v_log_data[i[0]].logc;
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e.invc[1] = __v_log_data[i[1]].invc;
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e.logc[1] = __v_log_data[i[1]].logc;
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#endif
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return e;
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}
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VPCS_ATTR
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__attribute__ ((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 (log, x, y, cmp);
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}
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VPCS_ATTR
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v_f64_t
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V_NAME(log) (v_f64_t x)
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{
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v_f64_t z, r, r2, p, y, kd, hi;
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v_u64_t ix, iz, tmp, top, i, cmp;
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v_s64_t k;
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struct entry e;
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ix = v_as_u64_f64 (x);
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top = ix >> 48;
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cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
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/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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tmp = ix - OFF;
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i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;
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k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */
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iz = ix - (tmp & v_u64 (0xfffULL << 52));
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z = v_as_f64_u64 (iz);
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e = lookup (i);
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/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
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r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
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kd = v_to_f64_s64 (k);
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/* hi = r + log(c) + k*Ln2. */
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hi = v_fma_f64 (kd, Ln2, e.logc + r);
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/* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
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r2 = r * r;
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y = v_fma_f64 (A3, r, A2);
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p = v_fma_f64 (A1, r, A0);
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y = v_fma_f64 (A4, r2, y);
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y = v_fma_f64 (y, r2, p);
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y = v_fma_f64 (y, r2, hi);
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if (unlikely (v_any_u64 (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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#endif
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