sysdeps/ieee754/flt-32/e_logf.c

   1 /* Single-precision log function.
   2    Copyright (C) 2017-2022 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