sysdeps/ieee754/flt-32/e_exp2f.c

   1 /* Single-precision 2^x function.
   2    Copyright (C) 2017 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    <http://www.gnu.org/licenses/>.  */
  18
  19 #include <math.h>
  20 #include <stdint.h>
  21 #include <shlib-compat.h>
  22 #include <libm-alias-float.h>
  23 #include "math_config.h"
  24
  25 /*
  26 EXP2F_TABLE_BITS = 5
  27 EXP2F_POLY_ORDER = 3
  28
  29 ULP error: 0.502 (nearest rounding.)
  30 Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
  31 Wrong count: 168353 (all nearest rounding wrong results with fma.)
  32 Non-nearest ULP error: 1 (rounded ULP error)
  33 */
  34
  35 #define N (1 << EXP2F_TABLE_BITS)
  36 #define T __exp2f_data.tab
  37 #define C __exp2f_data.poly
  38 #define SHIFT __exp2f_data.shift_scaled
  39
  40 static inline uint32_t
  41 top12 (float x)
  42 {
  43   return asuint (x) >> 20;
  44 }
  45
  46 float
  47 __exp2f (float x)
  48 {
  49   uint32_t abstop;
  50   uint64_t ki, t;
  51   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  52   double_t kd, xd, z, r, r2, y, s;
  53
  54   xd = (double_t) x;
  55   abstop = top12 (x) & 0x7ff;
  56   if (__glibc_unlikely (abstop >= top12 (128.0f)))
  57     {
  58       /* |x| >= 128 or x is nan.  */
  59       if (asuint (x) == asuint (-INFINITY))
  60         return 0.0f;
  61       if (abstop >= top12 (INFINITY))
  62         return x + x;
  63       if (x > 0.0f)
  64         return __math_oflowf (0);
  65       if (x <= -150.0f)
  66         return __math_uflowf (0);
  67 #if WANT_ERRNO_UFLOW
  68       if (x < -149.0f)
  69         return __math_may_uflowf (0);
  70 #endif
  71     }
  72
  73   /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
  74   kd = math_narrow_eval ((double) (xd + SHIFT)); /* Needs to be double.  */
  75   ki = asuint64 (kd);
  76   kd -= SHIFT; /* k/N for int k.  */
  77   r = xd - kd;
  78
  79   /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
  80   t = T[ki % N];
  81   t += ki << (52 - EXP2F_TABLE_BITS);
  82   s = asdouble (t);
  83   z = C[0] * r + C[1];
  84   r2 = r * r;
  85   y = C[2] * r + 1;
  86   y = z * r2 + y;
  87   y = y * s;
  88   return (float) y;
  89 }
  90 #ifndef __exp2f
  91 strong_alias (__exp2f, __ieee754_exp2f)
  92 strong_alias (__exp2f, __exp2f_finite)
  93 versioned_symbol (libm, __exp2f, exp2f, GLIBC_2_27);
  94 libm_alias_float_other (__exp2, exp2)
  95 #endif