mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-03 02:11:08 +00:00
123 lines
4.5 KiB
C
123 lines
4.5 KiB
C
/* Double-precision AdvSIMD expm1
|
|
|
|
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 "v_math.h"
|
|
#include "poly_advsimd_f64.h"
|
|
|
|
static const struct data
|
|
{
|
|
float64x2_t poly[11];
|
|
float64x2_t invln2, ln2_lo, ln2_hi, shift;
|
|
int64x2_t exponent_bias;
|
|
#if WANT_SIMD_EXCEPT
|
|
uint64x2_t thresh, tiny_bound;
|
|
#else
|
|
float64x2_t oflow_bound;
|
|
#endif
|
|
} data = {
|
|
/* Generated using fpminimax, with degree=12 in [log(2)/2, log(2)/2]. */
|
|
.poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5),
|
|
V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10),
|
|
V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16),
|
|
V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22),
|
|
V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29) },
|
|
.invln2 = V2 (0x1.71547652b82fep0),
|
|
.ln2_hi = V2 (0x1.62e42fefa39efp-1),
|
|
.ln2_lo = V2 (0x1.abc9e3b39803fp-56),
|
|
.shift = V2 (0x1.8p52),
|
|
.exponent_bias = V2 (0x3ff0000000000000),
|
|
#if WANT_SIMD_EXCEPT
|
|
/* asuint64(oflow_bound) - asuint64(0x1p-51), shifted left by 1 for abs
|
|
compare. */
|
|
.thresh = V2 (0x78c56fa6d34b552),
|
|
/* asuint64(0x1p-51) << 1. */
|
|
.tiny_bound = V2 (0x3cc0000000000000 << 1),
|
|
#else
|
|
/* Value above which expm1(x) should overflow. Absolute value of the
|
|
underflow bound is greater than this, so it catches both cases - there is
|
|
a small window where fallbacks are triggered unnecessarily. */
|
|
.oflow_bound = V2 (0x1.62b7d369a5aa9p+9),
|
|
#endif
|
|
};
|
|
|
|
static float64x2_t VPCS_ATTR NOINLINE
|
|
special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
|
|
{
|
|
return v_call_f64 (expm1, x, y, special);
|
|
}
|
|
|
|
/* Double-precision vector exp(x) - 1 function.
|
|
The maximum error observed error is 2.18 ULP:
|
|
_ZGVnN2v_expm1 (0x1.634ba0c237d7bp-2) got 0x1.a8b9ea8d66e22p-2
|
|
want 0x1.a8b9ea8d66e2p-2. */
|
|
float64x2_t VPCS_ATTR V_NAME_D1 (expm1) (float64x2_t x)
|
|
{
|
|
const struct data *d = ptr_barrier (&data);
|
|
|
|
uint64x2_t ix = vreinterpretq_u64_f64 (x);
|
|
|
|
#if WANT_SIMD_EXCEPT
|
|
/* If fp exceptions are to be triggered correctly, fall back to scalar for
|
|
|x| < 2^-51, |x| > oflow_bound, Inf & NaN. Add ix to itself for
|
|
shift-left by 1, and compare with thresh which was left-shifted offline -
|
|
this is effectively an absolute compare. */
|
|
uint64x2_t special
|
|
= vcgeq_u64 (vsubq_u64 (vaddq_u64 (ix, ix), d->tiny_bound), d->thresh);
|
|
if (__glibc_unlikely (v_any_u64 (special)))
|
|
x = v_zerofy_f64 (x, special);
|
|
#else
|
|
/* Large input, NaNs and Infs. */
|
|
uint64x2_t special = vceqzq_u64 (vcaltq_f64 (x, d->oflow_bound));
|
|
#endif
|
|
|
|
/* Reduce argument to smaller range:
|
|
Let i = round(x / ln2)
|
|
and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
|
|
exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
|
|
where 2^i is exact because i is an integer. */
|
|
float64x2_t n = vsubq_f64 (vfmaq_f64 (d->shift, d->invln2, x), d->shift);
|
|
int64x2_t i = vcvtq_s64_f64 (n);
|
|
float64x2_t f = vfmsq_f64 (x, n, d->ln2_hi);
|
|
f = vfmsq_f64 (f, n, d->ln2_lo);
|
|
|
|
/* Approximate expm1(f) using polynomial.
|
|
Taylor expansion for expm1(x) has the form:
|
|
x + ax^2 + bx^3 + cx^4 ....
|
|
So we calculate the polynomial P(f) = a + bf + cf^2 + ...
|
|
and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
|
|
float64x2_t f2 = vmulq_f64 (f, f);
|
|
float64x2_t f4 = vmulq_f64 (f2, f2);
|
|
float64x2_t f8 = vmulq_f64 (f4, f4);
|
|
float64x2_t p = vfmaq_f64 (f, f2, v_estrin_10_f64 (f, f2, f4, f8, d->poly));
|
|
|
|
/* Assemble the result.
|
|
expm1(x) ~= 2^i * (p + 1) - 1
|
|
Let t = 2^i. */
|
|
int64x2_t u = vaddq_s64 (vshlq_n_s64 (i, 52), d->exponent_bias);
|
|
float64x2_t t = vreinterpretq_f64_s64 (u);
|
|
|
|
if (__glibc_unlikely (v_any_u64 (special)))
|
|
return special_case (vreinterpretq_f64_u64 (ix),
|
|
vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t),
|
|
special);
|
|
|
|
/* expm1(x) ~= p * t + (t - 1). */
|
|
return vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t);
|
|
}
|