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/* Single-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_f32.h"
static const struct data
{
float32x4_t poly[5];
float32x4_t invln2, ln2_lo, ln2_hi, shift;
int32x4_t exponent_bias;
#if WANT_SIMD_EXCEPT
uint32x4_t thresh;
#else
float32x4_t oflow_bound;
#endif
} data = {
/* Generated using fpminimax with degree=5 in [-log(2)/2, log(2)/2]. */
.poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5),
V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) },
.invln2 = V4 (0x1.715476p+0f),
.ln2_hi = V4 (0x1.62e4p-1f),
.ln2_lo = V4 (0x1.7f7d1cp-20f),
.shift = V4 (0x1.8p23f),
.exponent_bias = V4 (0x3f800000),
#if !WANT_SIMD_EXCEPT
/* Value above which expm1f(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 = V4 (0x1.5ebc4p+6),
#else
/* asuint(oflow_bound) - asuint(0x1p-23), shifted left by 1 for absolute
compare. */
.thresh = V4 (0x1d5ebc40),
#endif
};
/* asuint(0x1p-23), shifted by 1 for abs compare. */
#define TinyBound v_u32 (0x34000000 << 1)
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
{
return v_call_f32 (expm1f, x, y, special);
}
/* Single-precision vector exp(x) - 1 function.
The maximum error is 1.51 ULP:
_ZGVnN4v_expm1f (0x1.8baa96p-2) got 0x1.e2fb9p-2
want 0x1.e2fb94p-2. */
float32x4_t VPCS_ATTR V_NAME_F1 (expm1) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
uint32x4_t ix = vreinterpretq_u32_f32 (x);
#if WANT_SIMD_EXCEPT
/* If fp exceptions are to be triggered correctly, fall back to scalar for
|x| < 2^-23, |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. */
uint32x4_t special
= vcgeq_u32 (vsubq_u32 (vaddq_u32 (ix, ix), TinyBound), d->thresh);
if (__glibc_unlikely (v_any_u32 (special)))
x = v_zerofy_f32 (x, special);
#else
/* Handles very large values (+ve and -ve), +/-NaN, +/-Inf. */
uint32x4_t special = vceqzq_u32 (vcaltq_f32 (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. */
float32x4_t j = vsubq_f32 (vfmaq_f32 (d->shift, d->invln2, x), d->shift);
int32x4_t i = vcvtq_s32_f32 (j);
float32x4_t f = vfmsq_f32 (x, j, d->ln2_hi);
f = vfmsq_f32 (f, j, 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). */
float32x4_t p = v_horner_4_f32 (f, d->poly);
p = vfmaq_f32 (f, vmulq_f32 (f, f), p);
/* Assemble the result.
expm1(x) ~= 2^i * (p + 1) - 1
Let t = 2^i. */
int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias);
float32x4_t t = vreinterpretq_f32_s32 (u);
if (__glibc_unlikely (v_any_u32 (special)))
return special_case (vreinterpretq_f32_u32 (ix),
vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t),
special);
/* expm1(x) ~= p * t + (t - 1). */
return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t);
}
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