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/* Double-precision vector (SVE) log function.
Copyright (C) 2023-2025 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
#define N (1 << V_LOG_TABLE_BITS)
#define Max (0x7ff0000000000000)
#define Min (0x0010000000000000)
#define Thresh (0x7fe0000000000000) /* Max - Min. */
static const struct data
{
double c0, c2;
double c1, c3;
double ln2, c4;
uint64_t off;
} data = {
.c0 = -0x1.ffffffffffff7p-2,
.c1 = 0x1.55555555170d4p-2,
.c2 = -0x1.0000000399c27p-2,
.c3 = 0x1.999b2e90e94cap-3,
.c4 = -0x1.554e550bd501ep-3,
.ln2 = 0x1.62e42fefa39efp-1,
.off = 0x3fe6900900000000,
};
static svfloat64_t NOINLINE
special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
svbool_t special, const struct data *d)
{
svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
return sv_call_f64 (log, x, svmla_x (svptrue_b64 (), hi, r2, y), special);
}
/* Double-precision SVE log routine.
Maximum measured error is 2.64 ulp:
SV_NAME_D1 (log)(0x1.95e54bc91a5e2p+184) got 0x1.fffffffe88cacp+6
want 0x1.fffffffe88cafp+6. */
svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
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, d->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);
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 kd = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
/* hi = r + log(c) + k*Ln2. */
svfloat64_t ln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->ln2);
svfloat64_t r = svmad_x (pg, invc, z, -1);
svfloat64_t hi = svmla_lane_f64 (logc, kd, ln2_and_c4, 0);
hi = svadd_x (pg, r, hi);
/* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);
svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);
y = svmla_lane_f64 (y, r2, ln2_and_c4, 1);
y = svmla_x (pg, p, r2, y);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (hi, tmp, y, r2, special, d);
return svmla_x (pg, hi, r2, y);
}
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