glibc/sysdeps/aarch64/fpu/log2f_advsimd.c

/* Single-precision vector (AdvSIMD) exp2 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
{
  uint32x4_t off, offset_lower_bound;
  uint16x8_t special_bound;
  uint32x4_t mantissa_mask;
  float32x4_t poly[9];
} data = {
  /* Coefficients generated using Remez algorithm approximate
     log2(1+r)/r for r in [ -1/3, 1/3 ].
     rel error: 0x1.c4c4b0cp-26.  */
  .poly = { V4 (0x1.715476p0f), /* (float)(1 / ln(2)).  */
	    V4 (-0x1.715458p-1f), V4 (0x1.ec701cp-2f), V4 (-0x1.7171a4p-2f),
	    V4 (0x1.27a0b8p-2f), V4 (-0x1.e5143ep-3f), V4 (0x1.9d8ecap-3f),
	    V4 (-0x1.c675bp-3f), V4 (0x1.9e495p-3f) },
  /* Lower bound is the smallest positive normal float 0x00800000. For
     optimised register use subnormals are detected after offset has been
     subtracted, so lower bound is 0x0080000 - offset (which wraps around).  */
  .offset_lower_bound = V4 (0x00800000 - 0x3f2aaaab),
  .special_bound = V8 (0x7f00), /* top16(asuint32(inf) - 0x00800000).  */
  .off = V4 (0x3f2aaaab),	/* 0.666667.  */
  .mantissa_mask = V4 (0x007fffff),
};

static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t n, uint32x4_t u_off, float32x4_t p, float32x4_t r,
	      uint16x4_t cmp, const struct data *d)
{
  /* Fall back to scalar code.  */
  return v_call_f32 (log2f, vreinterpretq_f32_u32 (vaddq_u32 (u_off, d->off)),
		     vfmaq_f32 (n, p, r), vmovl_u16 (cmp));
}

/* Fast implementation for single precision AdvSIMD log2,
   relies on same argument reduction as AdvSIMD logf.
   Maximum error: 2.48 ULPs
   _ZGVnN4v_log2f(0x1.558174p+0) got 0x1.a9be84p-2
				want 0x1.a9be8p-2.  */
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log2) (float32x4_t x)
{
  const struct data *d = ptr_barrier (&data);

  /* To avoid having to mov x out of the way, keep u after offset has been
     applied, and recover x by adding the offset back in the special-case
     handler.  */
  uint32x4_t u_off = vreinterpretq_u32_f32 (x);

  /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3.  */
  u_off = vsubq_u32 (u_off, d->off);
  float32x4_t n = vcvtq_f32_s32 (
      vshrq_n_s32 (vreinterpretq_s32_u32 (u_off), 23)); /* signextend.  */

  uint16x4_t special = vcge_u16 (vsubhn_u32 (u_off, d->offset_lower_bound),
				 vget_low_u16 (d->special_bound));

  uint32x4_t u = vaddq_u32 (vandq_u32 (u_off, d->mantissa_mask), d->off);
  float32x4_t r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));

  /* y = log2(1+r) + n.  */
  float32x4_t r2 = vmulq_f32 (r, r);
  float32x4_t p = v_pw_horner_8_f32 (r, r2, d->poly);

  if (__glibc_unlikely (v_any_u16h (special)))
    return special_case (n, u_off, p, r, special, d);
  return vfmaq_f32 (n, p, r);
}
libmvec_hidden_def (V_NAME_F1 (log2))
HALF_WIDTH_ALIAS_F1 (log2)