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/* Double-precision vector (SVE) exp2 function
Copyright (C) 2023 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"
#include "poly_sve_f64.h"
#define N (1 << V_EXP_TABLE_BITS)
#define BigBound 1022
#define UOFlowBound 1280
static const struct data
{
double poly[4];
double shift, big_bound, uoflow_bound;
} data = {
/* Coefficients are computed using Remez algorithm with
minimisation of the absolute error. */
.poly = { 0x1.62e42fefa3686p-1, 0x1.ebfbdff82c241p-3, 0x1.c6b09b16de99ap-5,
0x1.3b2abf5571ad8p-7 },
.shift = 0x1.8p52 / N,
.uoflow_bound = UOFlowBound,
.big_bound = BigBound,
};
#define SpecialOffset 0x6000000000000000 /* 0x1p513. */
/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
#define SpecialBias1 0x7000000000000000 /* 0x1p769. */
#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
/* Update of both special and non-special cases, if any special case is
detected. */
static inline svfloat64_t
special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
const struct data *d)
{
/* s=2^n may overflow, break it up into s=s1*s2,
such that exp = s + s*y can be computed as s1*(s2+s2*y)
and s1*s1 overflows only if n>0. */
/* If n<=0 then set b to 0x6, 0 otherwise. */
svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */
svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
/* Set s1 to generate overflow depending on sign of exponent n. */
svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
/* Offset s to avoid overflow in final result if n is below threshold. */
svfloat64_t s2 = svreinterpret_f64 (
svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
/* |n| > 1280 => 2^(n) overflows. */
svbool_t p_cmp = svacgt (pg, n, d->uoflow_bound);
svfloat64_t r1 = svmul_x (pg, s1, s1);
svfloat64_t r2 = svmla_x (pg, s2, s2, y);
svfloat64_t r0 = svmul_x (pg, r2, s1);
return svsel (p_cmp, r1, r0);
}
/* Fast vector implementation of exp2.
Maximum measured error is 1.65 ulp.
_ZGVsMxv_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
want 0x1.f8db0d4df721dp-1. */
svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svbool_t no_big_scale = svacle (pg, x, d->big_bound);
svbool_t special = svnot_z (pg, no_big_scale);
/* Reduce x to k/N + r, where k is integer and r in [-1/2N, 1/2N]. */
svfloat64_t shift = sv_f64 (d->shift);
svfloat64_t kd = svadd_x (pg, x, shift);
svuint64_t ki = svreinterpret_u64 (kd);
/* kd = k/N. */
kd = svsub_x (pg, kd, shift);
svfloat64_t r = svsub_x (pg, x, kd);
/* scale ~= 2^(k/N). */
svuint64_t idx = svand_x (pg, ki, N - 1);
svuint64_t sbits = svld1_gather_index (pg, __v_exp_data, idx);
/* This is only a valid scale when -1023*N < k < 1024*N. */
svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS);
svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top));
/* Approximate exp2(r) using polynomial. */
svfloat64_t r2 = svmul_x (pg, r, r);
svfloat64_t p = sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly);
svfloat64_t y = svmul_x (pg, r, p);
/* Assemble exp2(x) = exp2(r) * scale. */
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (pg, scale, y, kd, d);
return svmla_x (pg, scale, scale, y);
}
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