1  /* Single-precision e^x function.
       2     Copyright (C) 2017-2023 Free Software Foundation, Inc.
       3     This file is part of the GNU C Library.
       4  
       5     The GNU C Library is free software; you can redistribute it and/or
       6     modify it under the terms of the GNU Lesser General Public
       7     License as published by the Free Software Foundation; either
       8     version 2.1 of the License, or (at your option) any later version.
       9  
      10     The GNU C Library is distributed in the hope that it will be useful,
      11     but WITHOUT ANY WARRANTY; without even the implied warranty of
      12     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      13     Lesser General Public License for more details.
      14  
      15     You should have received a copy of the GNU Lesser General Public
      16     License along with the GNU C Library; if not, see
      17     <https://www.gnu.org/licenses/>.  */
      18  
      19  #ifdef __expf
      20  # undef libm_hidden_proto
      21  # define libm_hidden_proto(ignored)
      22  #endif
      23  
      24  #include <math.h>
      25  #include <math-narrow-eval.h>
      26  #include <stdint.h>
      27  #include <libm-alias-finite.h>
      28  #include <libm-alias-float.h>
      29  #include "math_config.h"
      30  
      31  /*
      32  EXP2F_TABLE_BITS = 5
      33  EXP2F_POLY_ORDER = 3
      34  
      35  ULP error: 0.502 (nearest rounding.)
      36  Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
      37  Wrong count: 170635 (all nearest rounding wrong results with fma.)
      38  Non-nearest ULP error: 1 (rounded ULP error)
      39  */
      40  
      41  #define N (1 << EXP2F_TABLE_BITS)
      42  #define InvLn2N __exp2f_data.invln2_scaled
      43  #define T __exp2f_data.tab
      44  #define C __exp2f_data.poly_scaled
      45  
      46  static inline uint32_t
      47  top12 (float x)
      48  {
      49    return asuint (x) >> 20;
      50  }
      51  
      52  float
      53  __expf (float x)
      54  {
      55    uint32_t abstop;
      56    uint64_t ki, t;
      57    /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
      58    double_t kd, xd, z, r, r2, y, s;
      59  
      60    xd = (double_t) x;
      61    abstop = top12 (x) & 0x7ff;
      62    if (__glibc_unlikely (abstop >= top12 (88.0f)))
      63      {
      64        /* |x| >= 88 or x is nan.  */
      65        if (asuint (x) == asuint (-INFINITY))
      66  	return 0.0f;
      67        if (abstop >= top12 (INFINITY))
      68  	return x + x;
      69        if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
      70  	return __math_oflowf (0);
      71        if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
      72  	return __math_uflowf (0);
      73  #if WANT_ERRNO_UFLOW
      74        if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
      75  	return __math_may_uflowf (0);
      76  #endif
      77      }
      78  
      79    /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
      80    z = InvLn2N * xd;
      81  
      82    /* Round and convert z to int, the result is in [-150*N, 128*N] and
      83       ideally ties-to-even rule is used, otherwise the magnitude of r
      84       can be bigger which gives larger approximation error.  */
      85  #if TOINT_INTRINSICS
      86    kd = roundtoint (z);
      87    ki = converttoint (z);
      88  #else
      89  # define SHIFT __exp2f_data.shift
      90    kd = math_narrow_eval ((double) (z + SHIFT)); /* Needs to be double.  */
      91    ki = asuint64 (kd);
      92    kd -= SHIFT;
      93  #endif
      94    r = z - kd;
      95  
      96    /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
      97    t = T[ki % N];
      98    t += ki << (52 - EXP2F_TABLE_BITS);
      99    s = asdouble (t);
     100    z = C[0] * r + C[1];
     101    r2 = r * r;
     102    y = C[2] * r + 1;
     103    y = z * r2 + y;
     104    y = y * s;
     105    return (float) y;
     106  }
     107  
     108  #ifndef __expf
     109  hidden_def (__expf)
     110  strong_alias (__expf, __ieee754_expf)
     111  libm_alias_finite (__ieee754_expf, __expf)
     112  versioned_symbol (libm, __expf, expf, GLIBC_2_27);
     113  libm_alias_float_other (__exp, exp)
     114  #endif