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/* Double-precision SVE log1p
Copyright (C) 2023-2024 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"
static const struct data
{
double poly[19];
double ln2_hi, ln2_lo;
uint64_t hfrt2_top, onemhfrt2_top, inf, mone;
} data = {
/* Generated using Remez in [ sqrt(2)/2 - 1, sqrt(2) - 1]. Order 20
polynomial, however first 2 coefficients are 0 and 1 so are not stored. */
.poly = { -0x1.ffffffffffffbp-2, 0x1.55555555551a9p-2, -0x1.00000000008e3p-2,
0x1.9999999a32797p-3, -0x1.555555552fecfp-3, 0x1.249248e071e5ap-3,
-0x1.ffffff8bf8482p-4, 0x1.c71c8f07da57ap-4, -0x1.9999ca4ccb617p-4,
0x1.7459ad2e1dfa3p-4, -0x1.554d2680a3ff2p-4, 0x1.3b4c54d487455p-4,
-0x1.2548a9ffe80e6p-4, 0x1.0f389a24b2e07p-4, -0x1.eee4db15db335p-5,
0x1.e95b494d4a5ddp-5, -0x1.15fdf07cb7c73p-4, 0x1.0310b70800fcfp-4,
-0x1.cfa7385bdb37ep-6, },
.ln2_hi = 0x1.62e42fefa3800p-1,
.ln2_lo = 0x1.ef35793c76730p-45,
/* top32(asuint64(sqrt(2)/2)) << 32. */
.hfrt2_top = 0x3fe6a09e00000000,
/* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */
.onemhfrt2_top = 0x00095f6200000000,
.inf = 0x7ff0000000000000,
.mone = 0xbff0000000000000,
};
#define AbsMask 0x7fffffffffffffff
#define BottomMask 0xffffffff
static svfloat64_t NOINLINE
special_case (svbool_t special, svfloat64_t x, svfloat64_t y)
{
return sv_call_f64 (log1p, x, y, special);
}
/* Vector approximation for log1p using polynomial on reduced interval. Maximum
observed error is 2.46 ULP:
_ZGVsMxv_log1p(0x1.654a1307242a4p+11) got 0x1.fd5565fb590f4p+2
want 0x1.fd5565fb590f6p+2. */
svfloat64_t SV_NAME_D1 (log1p) (svfloat64_t x, svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svuint64_t ix = svreinterpret_u64 (x);
svuint64_t ax = svand_x (pg, ix, AbsMask);
svbool_t special
= svorr_z (pg, svcmpge (pg, ax, d->inf), svcmpge (pg, ix, d->mone));
/* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f
is in [sqrt(2)/2, sqrt(2)]):
log1p(x) = k*log(2) + log1p(f).
f may not be representable exactly, so we need a correction term:
let m = round(1 + x), c = (1 + x) - m.
c << m: at very small x, log1p(x) ~ x, hence:
log(1+x) - log(m) ~ c/m.
We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */
/* Obtain correctly scaled k by manipulation in the exponent.
The scalar algorithm casts down to 32-bit at this point to calculate k and
u_red. We stay in double-width to obtain f and k, using the same constants
as the scalar algorithm but shifted left by 32. */
svfloat64_t m = svadd_x (pg, x, 1);
svuint64_t mi = svreinterpret_u64 (m);
svuint64_t u = svadd_x (pg, mi, d->onemhfrt2_top);
svint64_t ki = svsub_x (pg, svreinterpret_s64 (svlsr_x (pg, u, 52)), 0x3ff);
svfloat64_t k = svcvt_f64_x (pg, ki);
/* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */
svuint64_t utop
= svadd_x (pg, svand_x (pg, u, 0x000fffff00000000), d->hfrt2_top);
svuint64_t u_red = svorr_x (pg, utop, svand_x (pg, mi, BottomMask));
svfloat64_t f = svsub_x (pg, svreinterpret_f64 (u_red), 1);
/* Correction term c/m. */
svfloat64_t cm = svdiv_x (pg, svsub_x (pg, x, svsub_x (pg, m, 1)), m);
/* Approximate log1p(x) on the reduced input using a polynomial. Because
log1p(0)=0 we choose an approximation of the form:
x + C0*x^2 + C1*x^3 + C2x^4 + ...
Hence approximation has the form f + f^2 * P(f)
where P(x) = C0 + C1*x + C2x^2 + ...
Assembling this all correctly is dealt with at the final step. */
svfloat64_t f2 = svmul_x (pg, f, f), f4 = svmul_x (pg, f2, f2),
f8 = svmul_x (pg, f4, f4), f16 = svmul_x (pg, f8, f8);
svfloat64_t p = sv_estrin_18_f64_x (pg, f, f2, f4, f8, f16, d->poly);
svfloat64_t ylo = svmla_x (pg, cm, k, d->ln2_lo);
svfloat64_t yhi = svmla_x (pg, f, k, d->ln2_hi);
svfloat64_t y = svmla_x (pg, svadd_x (pg, ylo, yhi), f2, p);
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (special, x, y);
return y;
}
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