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/* Double-precision vector (SVE) exp10 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 SpecialBound 307.0 /* floor (log10 (2^1023)). */
static const struct data
{
double poly[5];
double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound;
} data = {
/* Coefficients generated using Remez algorithm.
rel error: 0x1.9fcb9b3p-60
abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
max ulp err 0.52 +0.5. */
.poly = { 0x1.26bb1bbb55516p1, 0x1.53524c73cd32ap1, 0x1.0470591daeafbp1,
0x1.2bd77b1361ef6p0, 0x1.142b5d54e9621p-1 },
/* 1.5*2^46+1023. This value is further explained below. */
.shift = 0x1.800000000ffc0p+46,
.log10_2 = 0x1.a934f0979a371p1, /* 1/log2(10). */
.log2_10_hi = 0x1.34413509f79ffp-2, /* log2(10). */
.log2_10_lo = -0x1.9dc1da994fd21p-59,
.scale_thres = 1280.0,
.special_bound = SpecialBound,
};
#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->scale_thres);
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 exp10 using FEXPA instruction.
Maximum measured error is 1.02 ulp.
SV_NAME_D1 (exp10)(-0x1.2862fec805e58p+2) got 0x1.885a89551d782p-16
want 0x1.885a89551d781p-16. */
svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svbool_t no_big_scale = svacle (pg, x, d->special_bound);
svbool_t special = svnot_z (pg, no_big_scale);
/* n = round(x/(log10(2)/N)). */
svfloat64_t shift = sv_f64 (d->shift);
svfloat64_t z = svmla_x (pg, shift, x, d->log10_2);
svfloat64_t n = svsub_x (pg, z, shift);
/* r = x - n*log10(2)/N. */
svfloat64_t log2_10 = svld1rq (svptrue_b64 (), &d->log2_10_hi);
svfloat64_t r = x;
r = svmls_lane (r, n, log2_10, 0);
r = svmls_lane (r, n, log2_10, 1);
/* scale = 2^(n/N), computed using FEXPA. FEXPA does not propagate NaNs, so
for consistent NaN handling we have to manually propagate them. This
comes at significant performance cost. */
svuint64_t u = svreinterpret_u64 (z);
svfloat64_t scale = svexpa (u);
/* Approximate exp10(r) using polynomial. */
svfloat64_t r2 = svmul_x (pg, r, r);
svfloat64_t y = svmla_x (pg, svmul_x (pg, r, d->poly[0]), r2,
sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly + 1));
/* Assemble result as exp10(x) = 2^n * exp10(r). If |x| > SpecialBound
multiplication may overflow, so use special case routine. */
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, u, 46), 0x8000000000000000);
/* Copy sign to scale. */
scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale)));
return special_case (pg, scale, y, n, d);
}
/* No special case. */
return svmla_x (pg, scale, scale, y);
}
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