sysdeps/ieee754/flt-32/e_expf.c

   1 /* Single-precision e^x function.
   2    Copyright (C) 2017-2024 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