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/* Double-precision vector (SVE) exp2 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 BigBound 1022
#define UOFlowBound 1280
static const struct data
{
double c2, c4;
double c0, c1, c3;
double shift, big_bound, uoflow_bound;
} data = {
/* Coefficients are computed using Remez algorithm with
minimisation of the absolute error. */
.c0 = 0x1.62e42fefa39efp-1, .c1 = 0x1.ebfbdff82a31bp-3,
.c2 = 0x1.c6b08d706c8a5p-5, .c3 = 0x1.3b2ad2ff7d2f3p-7,
.c4 = 0x1.5d8761184beb3p-10, .shift = 0x1.800000000ffc0p+46,
.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 = svacle (pg, n, d->uoflow_bound);
svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1);
svfloat64_t r2 = svmla_x (pg, s2, s2, y);
svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1);
return svsel (p_cmp, r0, r1);
}
/* Fast vector implementation of exp2.
Maximum measured error is 0.52 + 0.5 ulp.
_ZGVsMxv_exp2 (0x1.3b72ad5b701bfp-1) got 0x1.8861641b49e08p+0
want 0x1.8861641b49e07p+0. */
svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svbool_t special = svacge (pg, x, d->big_bound);
svfloat64_t z = svadd_x (svptrue_b64 (), x, d->shift);
svfloat64_t n = svsub_x (svptrue_b64 (), z, d->shift);
svfloat64_t r = svsub_x (svptrue_b64 (), x, n);
svfloat64_t scale = svexpa (svreinterpret_u64 (z));
svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
svfloat64_t c24 = svld1rq (svptrue_b64 (), &d->c2);
/* Approximate exp2(r) using polynomial. */
/* y = exp2(r) - 1 ~= r * (C0 + C1 r + C2 r^2 + C3 r^3 + C4 r^4). */
svfloat64_t p12 = svmla_lane (sv_f64 (d->c1), r, c24, 0);
svfloat64_t p34 = svmla_lane (sv_f64 (d->c3), r, c24, 1);
svfloat64_t p = svmla_x (pg, p12, p34, r2);
p = svmad_x (pg, p, r, d->c0);
svfloat64_t y = svmul_x (svptrue_b64 (), r, p);
/* Assemble exp2(x) = exp2(r) * scale. */
if (__glibc_unlikely (svptest_any (pg, special)))
{
/* FEXPA zeroes the sign bit, however the sign is meaningful to the
special case function so needs to be copied.
e = sign bit of u << 46. */
svuint64_t e = svand_x (pg, svlsl_x (pg, svreinterpret_u64 (z), 46),
0x8000000000000000);
scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale)));
return special_case (pg, scale, y, n, d);
}
return svmla_x (pg, scale, scale, y);
}
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