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/*
* Double-precision SVE log(x) function.
*
* Copyright (c) 2020-2023, 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"
#define P(i) sv_f64 (__v_log_data.poly[i])
#define N (1 << V_LOG_TABLE_BITS)
#define Off (0x3fe6900900000000)
#define MaxTop (0x7ff)
#define MinTop (0x001)
#define ThreshTop (0x7fe) /* MaxTop - MinTop. */
static svfloat64_t NOINLINE
special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
{
return sv_call_f64 (log, x, y, cmp);
}
/* SVE port of AdvSIMD log algorithm.
Maximum measured error is 2.17 ulp:
SV_NAME_D1 (log)(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2
want 0x1.ffffff1cca045p-2. */
svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
{
svuint64_t ix = svreinterpret_u64 (x);
svuint64_t top = svlsr_x (pg, ix, 52);
svbool_t cmp = svcmpge (pg, svsub_x (pg, top, MinTop), sv_u64 (ThreshTop));
/* 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);
/* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N.
The actual value of i is double this due to table layout. */
svuint64_t i
= svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1);
svint64_t k
= svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift. */
svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
svfloat64_t z = svreinterpret_f64 (iz);
/* Lookup in 2 global lists (length N). */
svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
svfloat64_t r = svmad_x (pg, invc, z, -1);
svfloat64_t kd = svcvt_f64_x (pg, k);
/* hi = r + log(c) + k*Ln2. */
svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2);
/* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
svfloat64_t r2 = svmul_x (pg, r, r);
svfloat64_t y = svmla_x (pg, P (2), r, P (3));
svfloat64_t p = svmla_x (pg, P (0), r, P (1));
y = svmla_x (pg, y, r2, P (4));
y = svmla_x (pg, p, r2, y);
if (unlikely (svptest_any (pg, cmp)))
return special_case (x, svmla_x (svnot_z (pg, cmp), hi, r2, y), cmp);
return svmla_x (pg, hi, r2, y);
}
PL_SIG (SV, D, 1, log, 0.01, 11.1)
PL_TEST_ULP (SV_NAME_D1 (log), 1.68)
PL_TEST_INTERVAL (SV_NAME_D1 (log), -0.0, -inf, 1000)
PL_TEST_INTERVAL (SV_NAME_D1 (log), 0, 0x1p-149, 1000)
PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-149, 0x1p-126, 4000)
PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-126, 0x1p-23, 50000)
PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-23, 1.0, 50000)
PL_TEST_INTERVAL (SV_NAME_D1 (log), 1.0, 100, 50000)
PL_TEST_INTERVAL (SV_NAME_D1 (log), 100, inf, 50000)
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