1  /* Single-precision log 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  LOGF_TABLE_BITS = 4
      27  LOGF_POLY_ORDER = 4
      28  
      29  ULP error: 0.818 (nearest rounding.)
      30  Relative error: 1.957 * 2^-26 (before rounding.)
      31  */
      32  
      33  #define T __logf_data.tab
      34  #define A __logf_data.poly
      35  #define Ln2 __logf_data.ln2
      36  #define N (1 << LOGF_TABLE_BITS)
      37  #define OFF 0x3f330000
      38  
      39  float
      40  __logf (float x)
      41  {
      42    /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
      43    double_t z, r, r2, y, y0, invc, logc;
      44    uint32_t ix, iz, tmp;
      45    int k, i;
      46  
      47    ix = asuint (x);
      48  #if WANT_ROUNDING
      49    /* Fix sign of zero with downward rounding when x==1.  */
      50    if (__glibc_unlikely (ix == 0x3f800000))
      51      return 0;
      52  #endif
      53    if (__glibc_unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
      54      {
      55        /* x < 0x1p-126 or inf or nan.  */
      56        if (ix * 2 == 0)
      57  	return __math_divzerof (1);
      58        if (ix == 0x7f800000) /* log(inf) == inf.  */
      59  	return x;
      60        if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
      61  	return __math_invalidf (x);
      62        /* x is subnormal, normalize it.  */
      63        ix = asuint (x * 0x1p23f);
      64        ix -= 23 << 23;
      65      }
      66  
      67    /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
      68       The range is split into N subintervals.
      69       The ith subinterval contains z and c is near its center.  */
      70    tmp = ix - OFF;
      71    i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
      72    k = (int32_t) tmp >> 23; /* arithmetic shift */
      73    iz = ix - (tmp & 0x1ff << 23);
      74    invc = T[i].invc;
      75    logc = T[i].logc;
      76    z = (double_t) asfloat (iz);
      77  
      78    /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
      79    r = z * invc - 1;
      80    y0 = logc + (double_t) k * Ln2;
      81  
      82    /* Pipelined polynomial evaluation to approximate log1p(r).  */
      83    r2 = r * r;
      84    y = A[1] * r + A[2];
      85    y = A[0] * r2 + y;
      86    y = y * r2 + (y0 + r);
      87    return (float) y;
      88  }
      89  #ifndef __logf
      90  strong_alias (__logf, __ieee754_logf)
      91  libm_alias_finite (__ieee754_logf, __logf)
      92  versioned_symbol (libm, __logf, logf, GLIBC_2_27);
      93  libm_alias_float_other (__log, log)
      94  #endif