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/*
* Double-precision SVE log2 function.
*
* Copyright (c) 2022-2024, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "pl_sig.h"
#include "pl_test.h"
#include "poly_sve_f64.h"
#define N (1 << V_LOG2_TABLE_BITS)
#define Off 0x3fe6900900000000
#define Max (0x7ff0000000000000)
#define Min (0x0010000000000000)
#define Thresh (0x7fe0000000000000) /* Max - Min. */
static svfloat64_t NOINLINE
special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
{
return sv_call_f64 (log2, x, y, cmp);
}
/* Double-precision SVE log2 routine.
Implements the same algorithm as AdvSIMD log10, with coefficients and table
entries scaled in extended precision.
The maximum observed error is 2.58 ULP:
SV_NAME_D1 (log2)(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
want 0x1.fffb34198d9ddp-5. */
svfloat64_t SV_NAME_D1 (log2) (svfloat64_t x, const svbool_t pg)
{
svuint64_t ix = svreinterpret_u64 (x);
svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
/* x = 2^k z; where z is in range [Off,2*Off) and exact.
The range is split into N subintervals.
The ith subinterval contains z and c is near its center. */
svuint64_t tmp = svsub_x (pg, ix, Off);
svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG2_TABLE_BITS);
i = svand_x (pg, i, (N - 1) << 1);
svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
svfloat64_t z = svreinterpret_f64 (
svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)));
svfloat64_t invc = svld1_gather_index (pg, &__v_log2_data.table[0].invc, i);
svfloat64_t log2c
= svld1_gather_index (pg, &__v_log2_data.table[0].log2c, i);
/* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
svfloat64_t r = svmad_x (pg, invc, z, -1.0);
svfloat64_t w = svmla_x (pg, log2c, r, __v_log2_data.invln2);
svfloat64_t r2 = svmul_x (pg, r, r);
svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log2_data.poly);
w = svadd_x (pg, k, w);
if (unlikely (svptest_any (pg, special)))
return special_case (x, svmla_x (svnot_z (pg, special), w, r2, y),
special);
return svmla_x (pg, w, r2, y);
}
PL_SIG (SV, D, 1, log2, 0.01, 11.1)
PL_TEST_ULP (SV_NAME_D1 (log2), 2.09)
PL_TEST_INTERVAL (SV_NAME_D1 (log2), -0.0, -0x1p126, 1000)
PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0.0, 0x1p-126, 4000)
PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-126, 0x1p-23, 50000)
PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-23, 1.0, 50000)
PL_TEST_INTERVAL (SV_NAME_D1 (log2), 1.0, 100, 50000)
PL_TEST_INTERVAL (SV_NAME_D1 (log2), 100, inf, 50000)
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