1  /* Single-precision vector (Advanced SIMD) log function.
       2  
       3     Copyright (C) 2023 Free Software Foundation, Inc.
       4     This file is part of the GNU C Library.
       5  
       6     The GNU C Library is free software; you can redistribute it and/or
       7     modify it under the terms of the GNU Lesser General Public
       8     License as published by the Free Software Foundation; either
       9     version 2.1 of the License, or (at your option) any later version.
      10  
      11     The GNU C Library is distributed in the hope that it will be useful,
      12     but WITHOUT ANY WARRANTY; without even the implied warranty of
      13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      14     Lesser General Public License for more details.
      15  
      16     You should have received a copy of the GNU Lesser General Public
      17     License along with the GNU C Library; if not, see
      18     <https://www.gnu.org/licenses/>.  */
      19  
      20  #include "v_math.h"
      21  
      22  static const struct data
      23  {
      24    float32x4_t poly[7];
      25    float32x4_t ln2, tiny_bound;
      26    uint32x4_t min_norm, special_bound, off, mantissa_mask;
      27  } data = {
      28    /* 3.34 ulp error.  */
      29    .poly = { V4 (-0x1.3e737cp-3f), V4 (0x1.5a9aa2p-3f), V4 (-0x1.4f9934p-3f),
      30  	    V4 (0x1.961348p-3f), V4 (-0x1.00187cp-2f), V4 (0x1.555d7cp-2f),
      31  	    V4 (-0x1.ffffc8p-2f) },
      32    .ln2 = V4 (0x1.62e43p-1f),
      33    .tiny_bound = V4 (0x1p-126),
      34    .min_norm = V4 (0x00800000),
      35    .special_bound = V4 (0x7f000000), /* asuint32(inf) - min_norm.  */
      36    .off = V4 (0x3f2aaaab),	    /* 0.666667.  */
      37    .mantissa_mask = V4 (0x007fffff)
      38  };
      39  
      40  #define P(i) d->poly[7 - i]
      41  
      42  static float32x4_t VPCS_ATTR NOINLINE
      43  special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
      44  {
      45    /* Fall back to scalar code.  */
      46    return v_call_f32 (logf, x, y, cmp);
      47  }
      48  
      49  float32x4_t VPCS_ATTR V_NAME_F1 (log) (float32x4_t x)
      50  {
      51    const struct data *d = ptr_barrier (&data);
      52    float32x4_t n, p, q, r, r2, y;
      53    uint32x4_t u, cmp;
      54  
      55    u = vreinterpretq_u32_f32 (x);
      56    cmp = vcgeq_u32 (vsubq_u32 (u, d->min_norm), d->special_bound);
      57  
      58    /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3.  */
      59    u = vsubq_u32 (u, d->off);
      60    n = vcvtq_f32_s32 (
      61        vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend.  */
      62    u = vandq_u32 (u, d->mantissa_mask);
      63    u = vaddq_u32 (u, d->off);
      64    r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
      65  
      66    /* y = log(1+r) + n*ln2.  */
      67    r2 = vmulq_f32 (r, r);
      68    /* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))).  */
      69    p = vfmaq_f32 (P (5), P (6), r);
      70    q = vfmaq_f32 (P (3), P (4), r);
      71    y = vfmaq_f32 (P (1), P (2), r);
      72    p = vfmaq_f32 (p, P (7), r2);
      73    q = vfmaq_f32 (q, p, r2);
      74    y = vfmaq_f32 (y, q, r2);
      75    p = vfmaq_f32 (r, d->ln2, n);
      76    y = vfmaq_f32 (p, y, r2);
      77  
      78    if (__glibc_unlikely (v_any_u32 (cmp)))
      79      return special_case (x, y, cmp);
      80    return y;
      81  }