1  /* Single-precision log2 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  #include <math.h>
      20  #include <stdint.h>
      21  #include <libm-alias-finite.h>
      22  #include <libm-alias-float.h>
      23  #include "math_config.h"
      24  
      25  /*
      26  LOG2F_TABLE_BITS = 4
      27  LOG2F_POLY_ORDER = 4
      28  
      29  ULP error: 0.752 (nearest rounding.)
      30  Relative error: 1.9 * 2^-26 (before rounding.)
      31  */
      32  
      33  #define N (1 << LOG2F_TABLE_BITS)
      34  #define T __log2f_data.tab
      35  #define A __log2f_data.poly
      36  #define OFF 0x3f330000
      37  
      38  float
      39  __log2f (float x)
      40  {
      41    /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
      42    double_t z, r, r2, p, y, y0, invc, logc;
      43    uint32_t ix, iz, top, tmp;
      44    int k, i;
      45  
      46    ix = asuint (x);
      47  #if WANT_ROUNDING
      48    /* Fix sign of zero with downward rounding when x==1.  */
      49    if (__glibc_unlikely (ix == 0x3f800000))
      50      return 0;
      51  #endif
      52    if (__glibc_unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
      53      {
      54        /* x < 0x1p-126 or inf or nan.  */
      55        if (ix * 2 == 0)
      56  	return __math_divzerof (1);
      57        if (ix == 0x7f800000) /* log2(inf) == inf.  */
      58  	return x;
      59        if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
      60  	return __math_invalidf (x);
      61        /* x is subnormal, normalize it.  */
      62        ix = asuint (x * 0x1p23f);
      63        ix -= 23 << 23;
      64      }
      65  
      66    /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
      67       The range is split into N subintervals.
      68       The ith subinterval contains z and c is near its center.  */
      69    tmp = ix - OFF;
      70    i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
      71    top = tmp & 0xff800000;
      72    iz = ix - top;
      73    k = (int32_t) tmp >> 23; /* arithmetic shift */
      74    invc = T[i].invc;
      75    logc = T[i].logc;
      76    z = (double_t) asfloat (iz);
      77  
      78    /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
      79    r = z * invc - 1;
      80    y0 = logc + (double_t) k;
      81  
      82    /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
      83    r2 = r * r;
      84    y = A[1] * r + A[2];
      85    y = A[0] * r2 + y;
      86    p = A[3] * r + y0;
      87    y = y * r2 + p;
      88    return (float) y;
      89  }
      90  #ifndef __log2f
      91  strong_alias (__log2f, __ieee754_log2f)
      92  libm_alias_finite (__ieee754_log2f, __log2f)
      93  versioned_symbol (libm, __log2f, log2f, GLIBC_2_27);
      94  libm_alias_float_other (__log2, log2)
      95  #endif