mirror of
git://sourceware.org/git/glibc.git
synced 2024-11-21 01:12:26 +08:00
e302e10213
This includes a fix for big-endian in AdvSIMD log, some cosmetic changes, and numerous small optimisations mainly around inlining and using indexed variants of MLA intrinsics. Reviewed-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
133 lines
4.9 KiB
C
133 lines
4.9 KiB
C
/* Single-precision vector (Advanced SIMD) tan function
|
|
|
|
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 "v_math.h"
|
|
#include "poly_advsimd_f32.h"
|
|
|
|
static const struct data
|
|
{
|
|
float32x4_t poly[6];
|
|
float32x4_t pi_consts;
|
|
float32x4_t shift;
|
|
#if !WANT_SIMD_EXCEPT
|
|
float32x4_t range_val;
|
|
#endif
|
|
} data = {
|
|
/* Coefficients generated using FPMinimax. */
|
|
.poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f),
|
|
V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) },
|
|
/* Stores constants: (-pi/2)_high, (-pi/2)_mid, (-pi/2)_low, and 2/pi. */
|
|
.pi_consts
|
|
= { -0x1.921fb6p+0f, 0x1.777a5cp-25f, 0x1.ee59dap-50f, 0x1.45f306p-1f },
|
|
.shift = V4 (0x1.8p+23f),
|
|
#if !WANT_SIMD_EXCEPT
|
|
.range_val = V4 (0x1p15f),
|
|
#endif
|
|
};
|
|
|
|
#define RangeVal v_u32 (0x47000000) /* asuint32(0x1p15f). */
|
|
#define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f). */
|
|
#define Thresh v_u32 (0x16000000) /* asuint32(RangeVal) - TinyBound. */
|
|
|
|
/* Special cases (fall back to scalar calls). */
|
|
static float32x4_t VPCS_ATTR NOINLINE
|
|
special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
|
|
{
|
|
return v_call_f32 (tanf, x, y, cmp);
|
|
}
|
|
|
|
/* Use a full Estrin scheme to evaluate polynomial. */
|
|
static inline float32x4_t
|
|
eval_poly (float32x4_t z, const struct data *d)
|
|
{
|
|
float32x4_t z2 = vmulq_f32 (z, z);
|
|
#if WANT_SIMD_EXCEPT
|
|
/* Tiny z (<= 0x1p-31) will underflow when calculating z^4.
|
|
If fp exceptions are to be triggered correctly,
|
|
sidestep this by fixing such lanes to 0. */
|
|
uint32x4_t will_uflow
|
|
= vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound);
|
|
if (__glibc_unlikely (v_any_u32 (will_uflow)))
|
|
z2 = vbslq_f32 (will_uflow, v_f32 (0), z2);
|
|
#endif
|
|
float32x4_t z4 = vmulq_f32 (z2, z2);
|
|
return v_estrin_5_f32 (z, z2, z4, d->poly);
|
|
}
|
|
|
|
/* Fast implementation of AdvSIMD tanf.
|
|
Maximum error is 3.45 ULP:
|
|
__v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
|
|
want 0x1.ff9850p-1. */
|
|
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tan) (float32x4_t x)
|
|
{
|
|
const struct data *d = ptr_barrier (&data);
|
|
float32x4_t special_arg = x;
|
|
|
|
/* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
|
|
regression. */
|
|
#if WANT_SIMD_EXCEPT
|
|
uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
|
|
/* If fp exceptions are to be triggered correctly, also special-case tiny
|
|
input, as this will load to overflow later. Fix any special lanes to 1 to
|
|
prevent any exceptions being triggered. */
|
|
uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh);
|
|
if (__glibc_unlikely (v_any_u32 (special)))
|
|
x = vbslq_f32 (special, v_f32 (1.0f), x);
|
|
#else
|
|
/* Otherwise, special-case large and special values. */
|
|
uint32x4_t special = vcageq_f32 (x, d->range_val);
|
|
#endif
|
|
|
|
/* n = rint(x/(pi/2)). */
|
|
float32x4_t q = vfmaq_laneq_f32 (d->shift, x, d->pi_consts, 3);
|
|
float32x4_t n = vsubq_f32 (q, d->shift);
|
|
/* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
|
|
uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1));
|
|
|
|
/* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */
|
|
float32x4_t r;
|
|
r = vfmaq_laneq_f32 (x, n, d->pi_consts, 0);
|
|
r = vfmaq_laneq_f32 (r, n, d->pi_consts, 1);
|
|
r = vfmaq_laneq_f32 (r, n, d->pi_consts, 2);
|
|
|
|
/* If x lives in an interval, where |tan(x)|
|
|
- is finite, then use a polynomial approximation of the form
|
|
tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
|
|
- grows to infinity then use symmetries of tangent and the identity
|
|
tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
|
|
the same polynomial approximation of tan as above. */
|
|
|
|
/* Invert sign of r if odd quadrant. */
|
|
float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1)));
|
|
|
|
/* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
|
|
float32x4_t z2 = vmulq_f32 (r, r);
|
|
float32x4_t p = eval_poly (z2, d);
|
|
float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
|
|
|
|
/* Compute reciprocal and apply if required. */
|
|
float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y);
|
|
|
|
if (__glibc_unlikely (v_any_u32 (special)))
|
|
return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special);
|
|
return vbslq_f32 (pred_alt, inv_y, y);
|
|
}
|
|
libmvec_hidden_def (V_NAME_F1 (tan))
|
|
HALF_WIDTH_ALIAS_F1 (tan)
|