1  /* Single-precision vector (SVE) exp 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 "sv_math.h"
      21  
      22  static const struct data
      23  {
      24    float poly[5];
      25    float inv_ln2, ln2_hi, ln2_lo, shift, thres;
      26  } data = {
      27    /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
      28       compatibility with polynomial helpers.  */
      29    .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
      30  	    0x1.0e4020p-7f },
      31    .inv_ln2 = 0x1.715476p+0f,
      32    .ln2_hi = 0x1.62e4p-1f,
      33    .ln2_lo = 0x1.7f7d1cp-20f,
      34    /* 1.5*2^17 + 127.  */
      35    .shift = 0x1.903f8p17f,
      36    /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
      37       correctly by FEXPA.  */
      38    .thres = 0x1.5d5e2ap+6f,
      39  };
      40  
      41  #define C(i) sv_f32 (d->poly[i])
      42  #define ExponentBias 0x3f800000
      43  
      44  static svfloat32_t NOINLINE
      45  special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
      46  {
      47    return sv_call_f32 (expf, x, y, special);
      48  }
      49  
      50  /* Optimised single-precision SVE exp function.
      51     Worst-case error is 1.04 ulp:
      52     SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
      53  				  want 0x1.ba74bap+4.  */
      54  svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
      55  {
      56    const struct data *d = ptr_barrier (&data);
      57  
      58    /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
      59       x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
      60  
      61    /* Load some constants in quad-word chunks to minimise memory access (last
      62       lane is wasted).  */
      63    svfloat32_t invln2_and_ln2 = svld1rq_f32 (svptrue_b32 (), &d->inv_ln2);
      64  
      65    /* n = round(x/(ln2/N)).  */
      66    svfloat32_t z = svmla_lane_f32 (sv_f32 (d->shift), x, invln2_and_ln2, 0);
      67    svfloat32_t n = svsub_n_f32_x (pg, z, d->shift);
      68  
      69    /* r = x - n*ln2/N.  */
      70    svfloat32_t r = svmls_lane_f32 (x, n, invln2_and_ln2, 1);
      71    r = svmls_lane_f32 (r, n, invln2_and_ln2, 2);
      72  
      73  /* scale = 2^(n/N).  */
      74    svbool_t is_special_case = svacgt_n_f32 (pg, x, d->thres);
      75    svfloat32_t scale = svexpa_f32 (svreinterpret_u32_f32 (z));
      76  
      77    /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6.  */
      78    svfloat32_t p12 = svmla_f32_x (pg, C (1), C (2), r);
      79    svfloat32_t p34 = svmla_f32_x (pg, C (3), C (4), r);
      80    svfloat32_t r2 = svmul_f32_x (pg, r, r);
      81    svfloat32_t p14 = svmla_f32_x (pg, p12, p34, r2);
      82    svfloat32_t p0 = svmul_f32_x (pg, r, C (0));
      83    svfloat32_t poly = svmla_f32_x (pg, p0, r2, p14);
      84  
      85    if (__glibc_unlikely (svptest_any (pg, is_special_case)))
      86      return special_case (x, svmla_f32_x (pg, scale, scale, poly),
      87  			 is_special_case);
      88  
      89    return svmla_f32_x (pg, scale, scale, poly);
      90  }